Characteristics of the Atmospheric Boundary Layer

Berichte des Meteorologischen Institutes der Universität Freiburg Nr. 11

Dirk Schindler

Characteristics of the Atmospheric Boundary Layer over a Scots Pine Forest

Freiburg, Juni 2004

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ISSN 1435-618X Alle Rechte, insbesondere die Rechte der Vervielfältigung und Verbreitung sowie der Übersetzung vorbehalten. Eigenverlag des Meteorologischen Instituts der Albert-Ludwigs-Universität Freiburg Druck:

Druckerei der Albert-Ludwigs-Universität Freiburg

Herausgeber:

Prof. Dr. Helmut Mayer und PD Dr. Andreas Matzarakis Meteorologisches Institut der Universität Freiburg Werderring 10, D-79085 Freiburg Tel.: 0049/761/203-3590; Fax: 0049/761/203-3586 e-mail: [email protected]

Dokumentation:

Ber. Meteor. Inst. Univ. Freiburg Nr. 11, 2004, 139 S.

Dissertation, angenommen von der Fakultät für Forst- und Umweltwissenschaften der Albert-Ludwigs-Universität Freiburg

ACKNOWLEDGEMENT First of all I thank Prof. Dr. H. Mayer, head of the Meteorological Institute, for supervising this work, providing the scientific support and helpful suggestions during numerous discussions on the topic. Thanks go to Gerhard Fernbach and Dirk Redepenning, the technical staff of the Meteorological Institute, for technical support and endurance during the measurement campaigns. I’m grateful for all professional discussions and the computational support by my colleagues of the Meteorological Institute. Further thanks go to the crew of the MCR–Lab, University of Basel, in particular to Andreas Christen for providing the LabView–based sonic data acquisition software and IDL programs.

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TABLE OF CONTENTS page ACKNOWLEDGEMENT ......................................................................................

3

TABLE OF CONTENTS ........................................................................................

5

SUMMARY..............................................................................................................

9

ZUSAMMENFASSUNG.........................................................................................

13

1.

INTRODUCTION .................................................................................

17

2.

NECESSITY AND OBJECTIVES.......................................................

19

3.

THEORETICAL CONCEPTS.............................................................

21

3.1

Turbulence in the lower atmosphere .......................................................

21

3.2

Depth and structure of the atmospheric boundary layer..........................

22

3.3

Airflow over tall plant canopies ..............................................................

24

3.3.1

Airflow well above tall plant canopies ....................................................

24

3.3.2

Airflow just above and within tall plant canopies ...................................

25

3.3.3

Turbulence structure over tall plant canopies..........................................

27

3.3.3.1

Length scales ...........................................................................................

27

3.3.3.2

Spectra .....................................................................................................

27

3.3.4

Turbulence structure within tall plant canopies.......................................

29

3.3.5

Plane mixing layer analogy .....................................................................

30

3.4

Measurement principles...........................................................................

32

3.4.1

Sound detection and ranging ...................................................................

32

3.4.1.1

Sodar equation for monostatic sodar systems..........................................

33

3.4.1.2

Doppler shift ............................................................................................

35

3.4.2

Sonic anemometer and thermometer .......................................................

36

3.4.3

Eddy covariance method..........................................................................

37

3.4.3.1

Theoretical considerations.......................................................................

37

3.4.3.2

Applicability of the eddy covariance method..........................................

38

4.

METHODS.............................................................................................

41

4.1

Forest meteorological experimental site Hartheim..................................

41

4.1.1

Scots pine forest.......................................................................................

41

4.1.2

Instrumentation ........................................................................................

43

6

4.1.2.1

page Tower–based instrumentation.................................................................. 43

4.1.2.2

Remote sensing........................................................................................

45

4.2

Data processing and calculations.............................................................

46

4.2.1

General procedures ..................................................................................

46

4.2.2

Sonic anemometer ...................................................................................

46

4.2.2.1

Turbulence statistics ................................................................................

46

4.2.2.2

Spectral analysis ......................................................................................

47

4.2.2.3

Length scales ...........................................................................................

48

4.2.2.4

Quadrant analysis ....................................................................................

48

4.2.3

Sodar ........................................................................................................

50

5.

RESULTS ...............................................................................................

51

5.1

Mean meteorological conditions .............................................................

51

5.2

Mean airflow characteristics above and within the Hartheim Scots pine forest ................................................................................................

52

5.2.1

Mean wind speed profile .........................................................................

52

5.2.2

Normalised wind speed difference ..........................................................

56

5.2.3

Mean shear length scale...........................................................................

58

5.2.4

Wind direction .........................................................................................

59

5.3

Turbulence statistics ................................................................................

61

5.3.1

Family portrait of canopy turbulence ......................................................

61

5.3.2

General remarks.......................................................................................

63

5.3.3

Second order statistics .............................................................................

63

5.3.4

Higher order statistics..............................................................................

68

5.4

Spectral analysis ......................................................................................

70

5.4.1

General remarks.......................................................................................

70

5.4.2

Velocity spectra .......................................................................................

71

5.4.3

Cospectra .................................................................................................

75

5.5

Conditional sampling...............................................................................

78

5.5.1

Joint probability distribution ...................................................................

78

5.5.1.1

General remarks.......................................................................................

78

5.5.1.2

Turbulent momentum transfer .................................................................

79

5.5.1.3

Turbulent sensible heat transfer...............................................................

82

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5.5.2

page Quadrant analysis .................................................................................... 85

5.5.2.1

General remarks.......................................................................................

85

5.5.2.2

Turbulent momentum transfer .................................................................

85

5.5.2.3

Turbulent sensible heat transfer...............................................................

90

5.5.2.4

Cumulative momentum and heat flux fractions.......................................

95

6.

DISCUSSION.........................................................................................

99

6.1

Turbulence measurements over tall plant canopies.................................

99

6.2

Experimental setup ..................................................................................

99

6.2.1

In situ measurements ...............................................................................

99

6.2.2

Sodar measurements above the Hartheim Scots pine forest.................... 100

6.3

Family portrait of canopy turbulence ...................................................... 102

6.4

Turbulence characteristics ....................................................................... 103

6.4.1

Turbulence statistics ................................................................................ 103

6.4.2

Spectral analysis ...................................................................................... 105

6.4.3

Conditional sampling............................................................................... 108

6.5

Plane mixing layer analogy ..................................................................... 110

6.6

Plant canopy characteristics..................................................................... 110

7.

CONCLUSIONS .................................................................................... 113

REFERENCES ........................................................................................................ 115 LIST OF ABBREVIATIONS................................................................................. 125 LIST OF SYMBOLS............................................................................................... 127 LIST OF FIGURE CAPTIONS ............................................................................. 131 LIST OF TABLE CAPTIONS ............................................................................... 135

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SUMMARY Turbulence characteristics above (z/h = 1.94) and below (z/h = 0.32) the Scots pine (Pinus sylvestris L.) forest canopy at the forest meteorological experimental site Hartheim were studied in two rather extensive measurement periods MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) representing the seasons winter and summer. The forest meteorological experimental site Hartheim is located in the flat southern Upper Rhine Valley. The Hartheim Scots pine forest is even–aged and has a horizontally rather homogeneous canopy. To investigate turbulence characteristics above and within the Hartheim Scots pine forest, a combination of tower–based and remote sensing instrumentation was chosen. The tower–based instrumentation, consisting of a vertical cup anemometer profile (eight cup anemometers) and two sonic anemometers, was used to examine turbulence characteristics above and below the Scots pine forest canopy in the relative height range z/h = 0.14 to z/h = 2.08. The remote sensing device, a flat array sodar, was used to probe turbulence characteristics exceeding the measuring range of the tower–based instrumentation up to a relative height of z/h = 14.08 (200 m a.g.l.). Turbulence statistics above and below the Hartheim Scots pine forest canopy were determined for both measurement periods. Turbulence characteristics were studied in further detail by computing spectra of the streamwise and vertical wind velocity components (u and w) as well as cospectra of the velocity fluctuations (u´ and w´), the fluctuations of the vertical velocity component and the sonic temperature (w´ and tsv´). Coherent motions were investigated by applying conditional sampling techniques, (1) the determination of the joint probability distributions of (u´, w´) as well as of (w´, tsv´), and (2) the quadrant analysis. All results were compared to other tall plant canopies, in particular to the so–called ‘family portrait’ of canopy turbulence (RAUPACH et al., 1996). Although mean meteorological conditions between MP1 and MP2 differed considerably mean airflow characteristics in both measurement periods were similar. Atmospheric stability conditions determined by h/L were dominated by stable atmospheric conditions in MP1 and by unstable atmospheric conditions in MP2. In MP1 mean wind speeds alternated between comparatively long periods with very low wind speeds and short periods with rather high wind speeds. In MP2 the wind conditions showed a more regular

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pattern with higher wind speeds mostly during daytime and lower wind speeds during nighttime. The very low mean wind speeds in both measurement periods affected turbulence characteristics at the forest meteorological experimental site Hartheim. Results of sodar measurements are presented only for the horizontal wind speed in MP1. Most of the sodar data were discarded because they failed plausibility checks. Mean turbulence statistics computed from the sonic measurements above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy were mostly in the range of those reported for other forests. Below the Scots pine forest canopy the normalised mean momentum flux ( − u´w´ / u *2 ) was zero under all atmospheric stability conditions.

w was strongly positive kurtotic and negatively skewed each with highest values under neutral atmospheric stability conditions. u was positively kurtotic and showed little skewness. In consequence of the very low mean wind speeds within the subcanopy trunk space the streamwise and vertical turbulence intensities (Tiu and Tiw) were extraordinarily large compared to other tall plant canopies. Above the Hartheim Scots pine forest canopy the u * –normalised streamwise and vertical standard deviations of the velocity components (σu/ u * and σw/ u * ) were smaller than the expected surface layer values. In both measurement periods the streamwise and the vertical velocity skewnesses (Sku and Skw) were near zero. w was negatively and u positively kurtotic. Spectral analysis shows that below the Hartheim Scots pine forest canopy the normalised mean vertical spectral peak frequencies ( fˆmax (w)) were lower than above the Scots pine forest canopy. The normalised mean streamwise spectral peak frequencies ( fˆmax (u)) were shifted towards higher frequencies under all atmospheric stability conditions. In MP2 atmospheric stability conditions had a marked effect on mean above– canopy fˆmax (u) and fˆmax (w). Under unstable atmospheric conditions mean fˆmax (u) showed the lowest, under stable atmospheric conditions mean fˆmax (w) the highest frequency observed in both measurement periods. Within the subcanopy trunk space of the Hartheim Scots pine forest streamwise and vertical velocity spectra established no f–2/3 slope in the inertial subrange. Instead, the

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slopes of the inertial subranges of both wind velocity components were steeper at mid−frequencies indicating a relative deficit of spectral energy and showed excess at the highest frequencies. With one exception, cospectral peak frequencies of the momentum flux ( fˆmax (uw)) and the sensible heat ( fˆmax (wtsv)) showed an atmospheric stability– dependent shift towards lower frequencies pointing to larger eddy sizes as atmospheric stability decreased. Further details of the turbulence structure above and below the Hartheim Scots pine forest canopy were revealed by examining normalised joint probability distributions of (u´, w´) as well as of (w´, tsv´) and by applying quadrant analysis. Results of both conditional sampling techniques support the idea that the turbulent momentum and heat transfer above the Hartheim Scots pine forest canopy was dominated by intermittent events (ejection and sweep events), at least under unstable atmospheric conditions. With reservations this was also true within the subcanopy trunk space. Normalised joint probability distributions of (u´, w´) showed no distinct structure in turbulent momentum transfer because the importance of the outward and inward interaction events increased pointing to a rather Gaussian nature of below–canopy turbulence. However, cumulative momentum and heat flux fractions obtained by quadrant analysis exhibited intermittent turbulence, i.e. large portions of both momentum and heat were transferred in comparatively short time in both measurement periods. No unexpected differences of turbulence characteristics – based on mean values for three atmospheric stability classes – between MP1 and MP2 were observed. The main difference between both measurement periods was the change in the occurrence of the most pronounced turbulence variables from neutral atmospheric stability in MP1 to unstable atmospheric conditions in MP2.

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13

ZUSAMMENFASSUNG

In zwei relativ langen Meßperioden MP1 (1. November 2002 bis 31. Januar 2003) und MP2 (1. bis 31. Juli 2003) wurden Turbulenzeigenschaften über (z/h = 1.94) dem Kiefernwald (Pinus sylvestris L.) sowie im Stammraum (z/h = 0.32) des Kiefernwaldes an der Forstmeteorologischen Meßstelle Hartheim untersucht. Die beiden Meßperioden wurden so gewählt, daß sie die Turbulenzeigenschaften im Winter und im Sommer repräsentieren. Der gleichaltrige Kiefernwald an der Forstmeteorologischen Meßstelle Hartheim ist in alle Richtungen horizontal vergleichsweise homogenen und befindet sich in der ebenen Rheinaue im südlichen Oberrheingraben. Um die Turbulenzeigenschaften über und im Hartheimer Kiefernwald zu untersuchen, wurde eine Methodenkombination aus bodengebundenen und fernerkundlichen Meßsystemen angewendet. Das bodengebundene Meßsystem besteht aus einem vertikalen Schalenkreuzanemometerprofil (acht Schalenkreuzanemometer) und zwei Ultraschallanemometern. Es dient der Untersuchung der Turbulenzeigenschaften im Stammraum sowie direkt über dem Kiefernwald im Höhenbereich zwischen z/h = 0.14 und z/h = 2.08. Das fernerkundliche Meßsystem, ein Sodar, wurde dazu verwendet, die Turbulenzeigenschaften der Strömung in einem Höhenbereich, der den Höhenbereich des bodengebundenen Meßsystems übersteigt, bis in eine Höhe von 200 m über Grund zu untersuchen. Die turbulenten Strömungseigenschaften über und im Hartheimer Kiefernwald wurden in den beiden Untersuchungszeiträumen statistisch beschrieben. Weiterhin wurden die Turbulenzeigenschaften durch die Anwendung der Spektralanalyse auf die in Hauptwindrichtung rotierte horizontale und vertikale Windvektorkomponente (u und w) untersucht. Kospektren wurden für die Fluktuationen von u und w (u´ und w´) sowie für die Fluktuationen von w und der Schalltemperatur (tsv´) (w´ und tsv´) berechnet. Kohärente Strukturen wurden durch Methoden der bedingten Probenahme, (1) durch die Untersuchung der gemeinsamen Wahrscheinlichkeitsdichteverteilung von (u´, w´) sowie von (w´, tsv´), (2) durch die Quadrantenanalyse, untersucht. Alle Untersuchungsergebnisse, wurden mit Untersuchungsergebnissen, die für andere hohe Vegetationsformen vorliegen, insbesondere den Ergebnissen, die im sogenannten „Familienportrait“ der Bestandesturbulenz (RAUPACH et al., 1996) zusammengefaßt sind, verglichen.

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Obwohl sich die mittleren meteorologischen Bedingungen in MP1 und MP2 deutlich unterscheiden, sind die mittleren Strömungseigenschaften in beiden Meßperioden ähnlich. Die atmosphärischen Stabilitätszustände wurden durch h/L klassifiziert. Für MP1 zeigte sich eine Dominanz stabiler, für MP2 eine Dominanz labiler atmosphärischer Stabilitätszustände. In MP1 wechselten sich relativ lange Perioden mit sehr geringen mittleren Windgeschwindigkeiten mit kurzen Perioden mit hohen mittleren Windgeschwindigkeiten ab. In MP2 wies die mittlere Windgeschwindigkeit einen regelmäßigeren Verlauf mit höheren Windgeschwindigkeiten am Tag und geringeren Windgeschwindigkeiten in der Nacht auf. Die sehr geringen mittleren Windgeschwindigkeiten in beiden Meßperioden hatten einen Einfluß auf die Turbulenzeigenschaften an der Forstmeteorologischen Meßstelle Hartheim. Ergebnisse aus Sodarmessungen liegen nur für die horizontale Windgeschwindigkeit in MP1 vor, da der Großteil der Sodardaten durch Plausibilitätstests verworfen wurde. Die mittleren statistischen Turbulenzeigenschaften, die für die Ultraschallanemometermessungen über (z/h = 1.94) und im (z/h = 0.32) Hartheimer Kiefernwald bestimmt wurden, sind überwiegend in der Größenordung wie diejenigen, die für andere Wälder vorliegen. Im Stammraum des Kiefernwaldes war der normierte mittlere Impulsfluß ( − u´w´ / u *2 ) unter allen atmosphärischen Stabilitätsbedingungen null. w war deutlich leptokurtisch und wies eine negative Schiefe mit jeweils den höchsten Werten unter neutralen atmosphärischen Stabilitätsbedingungen auf. u war leptokurtisch und zeigte nur geringe Schiefe. Als Folge der sehr geringen mittleren Windgeschwindigkeiten im Bestandesraum waren die horizontalen und vertikalen Turbulenzintensitäten (Tiu and Tiw) im Vergleich zu anderen Wäldern außergewöhnlich hoch. Über dem Hartheimer Kiefernwald waren die mit der Schubspannungsgeschwindigkeit ( u * ) normierten horizontalen und vertikalen Standardabweichungen der Windvektorkomponenten (σu/ u * and σw/ u * ) kleiner als die für die bodennahe Atmosphäre erwarteten Werte. In beiden Meßperioden waren die Schiefen der horizontalen und vertikalen Windvektorkomponenten (Sku und Skw) nahe Null, w zeigte eine negative und u eine positive Kurtosis. Durch die Spektralanalyse wird gezeigt, daß im Bestandesraum des Hartheimer Kiefernwaldes die normierten mittleren vertikalen spektralen Peak–Frequenzen ( fˆmax (w))

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niedriger waren als über dem Kiefernbestand. Die normierten mittleren horizontalen spektralen Peak–Frequenzen ( fˆmax (u)) waren im Bestandesraum des Kiefernwaldes unter allen atmosphärischen Stabilitätszuständen gegenüber den horizontalen Peak– Frequenzen über dem Kiefernwald zu höheren Frequenzen hin verschoben. In MP2 hatten die atmosphärischen Stabilitätsbedingungen einen deutlichen Effekt auf fˆmax (u) und fˆmax (w) über dem Kiefernbestand. Unter labilen atmosphärischen Bedingungen wies fˆmax (u) die niedrigste, unter stabilen atmosphärischen Bedingungen fˆmax (w) die höchste

mittlere Frequenz der beiden Meßperioden auf. Im Bestandesraum des Kiefernwaldes bildete sich keine für die bodennahe Atmosphäre typische f–2/3 Steigung im Trägheitsbereich der Spektren der horizontalen und vertikalen Windvektorkomponente aus. Statt dessen wiesen die Steigungen der Trägheitsbereiche der Spektren beider Windvektorkomponenten im mittleren Frequenzbereich größere Steigungen auf, die auf ein relatives Defizit spektraler Energie in diesem Frequenzbereich hindeuteten. Die kospektralen Peak–Frequenzen des Impulsflusses ( fˆmax (uw)) und des fühlbaren Wärmeflusses ( fˆmax (wtsv)) wiesen mit einer Ausnahme ebenfalls eine stabilitätsabhängige Verschiebung zu niedrigeren Frequenzen auf. Die niedrigsten Peak–Frequenzen traten bei labilen atmosphärischen Bedingungen auf. Genauerer Aufschluß über die turbulenten Strukturen über dem Hartheimer Kiefernwald und in seinem Bestandesraum wurde durch die Untersuchung der normierten gemeinsamen Wahrscheinlichkeitsdichteverteilungen von (u´, w´) und (w´, tsv´) sowie durch die Anwendung der Quadrantenanalyse erzielt. Die Ergebnisse dieser beiden bedingten Probenahmemethoden stützen die Hinweise auf einen hohen Anteil intermittierenden Austausches von Impuls und fühlbarer Wärme über dem Kiefernwald, zumindest unter labilen Schichtungsbedingungen. Mit Einschränkungen gilt dies auch für den Bestandesraum des Hartheimer Kiefernwaldes (z/h = 0.32). Durch die normierten gemeinsamen Wahrscheinlichkeitsdichteverteilungen von (u´, w´) konnte keine eindeutige Struktur des turbulenten Impulsaustausches festgestellt werden, da die Bedeutung von unkorrelierten Turbulenzereignissen im Be-

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standesraum des Kieferwaldes zunahm. Die erzielten Ergebnisse lassen eher auf normalverteilte Turbulenzeigenschaften im Bestandesraums schließen. Durch Quadrantenanalyse bestimmte kumulierte Impuls– und Wärmeflußfraktionen zeigten jedoch, daß in beiden Meßperioden ein bedeutender Teil des Impuls– und fühlbaren Wärmeaustausches in verhältnismäßig kurzer Zeit geschah, was auf intermittierende Turbulenz hinweist. Zwischen MP1 und MP2 traten keine unerwarteten Änderungen der Turbulenzeigenschaften hinsichtlich der sich ändernden atmosphärischen Stabilitätsbedingungen – basierend auf Mittelwerten für drei Stabilitätsklassen – auf. Der Hauptunterschied zwischen beiden Meßperioden ergab sich als Folge der stärkeren Labilisierung der atmosphärischen Grenzschicht in MP2. Die am deutlichsten ausgeprägten Turbulenzgrößen traten in MP2 nicht mehr wie in MP1 unter neutralen, sondern unter labilen atmosphärischen Bedingungen auf.

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1.

INTRODUCTION

The turbulent velocity field drives the air mass exchange between the Earth’s surface and the atmosphere. Turbulent air mass exchange depends on surface properties as well as on atmospheric states and processes. Since forests cover about 30 % of the dry land area (FAO, 2001), great importance is attached to the turbulent air mass exchange between forests and the troposphere. Due to the vertical extent, biomass, and roughness of forests the physical and chemical properties of the overlying atmospheric boundary layer are markedly modified (PANOFSKY and DUTTON, 1984; OKE, 1987; STULL, 1988; GARRATT, 1992; KAIMAL and FINNIGAN, 1994; FINNIGAN, 2000; AUBINET et al., 2000). Turbulent air mass exchange processes between forests and the atmosphere are experimentally studied because of their importance for: -

climate change (RUNNING et al., 1999; CANADELL et al., 2000; BROWN, 2002),

-

global and regional mass and energy exchange (JAEGER and KESSLER, 1996),

-

global and regional biogeochemical cycles, e.g. the carbon dioxide cycle of forests (MAHLI et al., 1999; BALDOCCHI et al., 2001; LAW et al., 2002),

-

the dispersion of seeds, trace gases, and aerosols (ANDREAE and CRUTZEN, 1997; HORN et al., 2001; NATHAN et al., 2002),

-

storm damages in forests (MAYER and SCHINDLER, 2002; MARSHALL et al., 2002),

-

the regulation of the microclimate within forests (RAUPACH and THOM, 1981),

-

the initialisation and evaluation of analytical and numerical models (KAIMAL and FINNIGAN, 1994).

Since the 1960s the gradient–diffusion theory (K–Theory) has been used to study air mass exchange between the Earth’s surface and the atmosphere over tall plant canopies (THOM et al., 1975; KONDO and AKASHI, 1976). Beginning in the 1970s, high–order closure turbulence models and Lagrangian diffusion models (WILSON and SHAW, 1977; SHAW and PEREIRA, 1982; MEYERS and PAW U, 1986, 1987; RAUPACH, 1987; KATUL and ALBERTSON, 1998; MASSMAN and WEIL, 1999; LEUNING, 2000) have made it possible to study not only mean wind velocity speed within and above tall plant canopies but also the statistical characteristics of canopy turbulence. In the late 1970s, experi-

18

mental studies showed that there are distinct anomalies in flux–gradient relationships above tall plant canopies (GARRATT, 1978; RAUPACH, 1979; DENMEAD and BRADLEY, 1985; CELLIER and BRUNET, 1992) and that turbulent air mass exchange within the upper part and just above tall plant canopies is dominated by large organised turbulent motions (BALDOCCHI and MEYERS, 1988a; BERGSTRÖM and HÖGSTRÖM, 1989; GAO et al., 1989; MAITANI and SHAW, 1990; LEE and BLACK, 1993a, 1993b; KRUIJT et al., 2000; VILLANI et al., 2003). Besides experimental studies wind tunnel studies with artificial plant canopies (RAUPACH GAN

et al., 1986; BRUNET et al., 1994; STACEY et al., 1994; SHAW et al., 1995; FINNI-

and SHAW, 2000; NOVAK et al., 2000; MARSHALL et al., 2002) and large eddy

simulation (LES) (SHAW and SCHUMANN, 1992; KANDA and HINO, 1994; SU et al., 1998, 2000) extended and changed the view of plant canopy turbulence. It is now widely accepted that turbulent exchange between tall plant canopies on flat ground and the atmosphere is no random process and that the turbulent velocity field shows several universal features (FINNIGAN and BRUNET, 1995; RAUPACH et al., 1996; BRUNET and IRVINE, 2000; FINNIGAN, 2000): -

mean wind speed profiles show a point of inflexion,

-

vertical variability in second and higher order statistics,

-

major contributions to the turbulent air mass exchange between tall plant canopies and the atmosphere arise from large coherent structures,

-

wind velocity moments scale with integral time and length scales,

-

normalised turbulence spectra show a vertical invariance of the position of the spectral peak and departures from classical inertial subrange behaviour,

-

aerodynamic drag on the plant elements is the cause of the inflected wind speed profile and of the spectral short cut mechanism.

Despite considerable progress in the investigation of turbulent exchange processes between tall plant canopies and the atmosphere the detailed turbulent structures and dynamic controls on these structures just above and within tall plant canopies are still not completely understood (BRUNET and IRVINE, 2000; KRUIJT et al., 2000; LIU et al., 2001; MARSHALL et al., 2002; VILLANI et al., 2003).

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2.

NECESSITY AND OBJECTIVES

The atmospheric boundary layer is structured vertically into several conceptual sublayers because the main airflow characteristics, e.g. the velocity field, air temperature, and air moisture, show different height dependent features (PANOFSKY and DUTTON, 1984; STULL, 1988; GARRATT, 1992; KAIMAL and FINNIGAN, 1994; FOKEN, 2003). To investigate mean airflow characteristics over a Scots pine forest up to several stand heights, remote sensing and in situ measurements (profile and eddy covariance method) were conducted at the forest meteorological experimental site Hartheim in the Upper Rhine Valley. This methodological combination enables the continuous measurement of the main airflow characteristics exceeding the measuring range of tower–based measurements. Up to now airflow characteristics of the atmospheric boundary layer over forests exceeding the range of tower–based instrumentation are little experimentally studied because -

remote sensing devices for operational use are available only for a short time,

-

of the extensive infrastructure and the problematic experimental setup.

Therefore, airflow characteristics above and within forests were often studied based on selected time series and in a narrow range of atmospheric stability conditions when airflow characteristics were most pronounced (LU and FITZJARRALD, 1994; BRUNET and IRVINE, 2000). Furthermore, most of the knowledge of turbulent airflow characteristics and air mass exchange processes between tall plant canopies and the atmosphere has been gained of studies in relatively dense plant canopies (GREEN et al., 1995; POGGI et al., 2004). Few studies investigated turbulence characteristics in thinly stocked plant canopies such as the Hartheim Scots pine forest. Starting from these deficits the aim of this study is to examine airflow characteristics above and within the Hartheim Scots pine forest the under more general conditions as a function of -

atmospheric stability conditions,

-

seasonal dynamics,

up to a height of 200 m a.g.l.

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Target quantities are variables, which are suitable to describe the turbulent air mass exchange between the Scots pine forest and the atmosphere (e.g. normalised standard deviations of the wind vector components (σu/ u * , σw/ u * ), integral streamwise and vertical length scales (Lu, Lw), streamwise and vertical velocity skewnesses (Sku, Skw)).

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3.

THEORECTICAL CONCEPTS

3.1

Turbulence in the lower atmosphere

The energy budget of the atmosphere requires the conversion of large–scale motions into turbulence before dissipation into heat. The turbulence production is associated with instabilities of the velocity field. The turbulence producing mechanism may be either mechanical or convective. Mechanical turbulence production is mainly due to friction of the ground (shear production) whereas convective turbulence is mainly related to heating and cooling of the ground (buoyant production) (KAIMAL and FINNIGAN,

1994). Large–scale and small–scale motions are assumed to be uncorrelated. For

most purposes the state of the atmosphere – neglecting effects of stratospheric and tropospheric chemistry – can be described by the following variables: -

wind vector M (m s–1),

-

air density ρ (kg m–3),

-

absolute temperature T (K) or potential temperature θ (K),

-

specific moisture q (g kg–1),

-

air pressure p (hPa).

These parameters are functions of the directions in space x, y, z, and the time t (s) and can be described by the following equations: -

equation of state,

-

conservation equations of momentum,

-

conservation equation of mass,

-

conservation equation of heat,

-

conservation equation of moisture.

To be able to distinguish between mean and turbulent airflow in the atmospheric boundary layer, Reynolds decomposition is applied to the above variables and the above equations are simplified by assuming -

incompressibility,

-

horizontal fluctuations of ρ, θ, p are negligible,

22

-

molecular diffusivity is negligible,

-

hydrostatic equilibrium of the mean flow,

-

zero subsidence,

and by rotating the underlying coordinate system. Detailed discussions on the simplifications and further scaling arguments made in atmospheric dynamics are given in PANOFSKY and DUTTON (1984), STULL (1988), GARRATT (1992),

3.2

KAIMAL and FINNIGAN (1994), STULL (2000), and FOKEN (2003).

Depth and structure of the atmospheric boundary layer

All micrometeorological measurements are made within the atmospheric boundary layer (ABL) (Fig. 3.1). The ABL is the turbulent region adjacent to the Earth’s surface (WYNGAARD, 1986), which is directly influenced by the effects of the surface (GARRATT,

1992). The ABL depth is typically about 10 % of the depth of the troposphere.

Micrometeorological processes in the ABL have a typical time scale of one day or a spatial scale of 1 km or less (FOKEN, 2003). The ABL depth is a function of mechanical and buoyant mixing and is also modified by synoptic scale motions. Over land surfaces in high pressure regions the ABL structure is subject to a diurnal cycle with three major components: statically unstable mixed layer (ML), statically neutral residual layer (RL), and statically stable boundary layer (SBL). During daytime, the ABL is called ML or convective boundary layer (CBL) and is the result of convectively driven turbulence. The mean daytime ABL depth can be assumed to be 1–3 km. At the top of the ABL the stable entrainment zone (EZ) is a boundary between the turbulence in the ML and the streamlined flow of the free atmosphere (FA) above. At night, a SBL forms under a RL and the SBL depth can go down to only a few tens of metres. Turbulence in the SBL is mechanically driven. The ABL is bounded above by a capping inversion (CI) (STULL, 1988). Usually, the lowest 10 % of the daytime ABL are called surface layer (SL). In the SL the mean properties of the airflow – wind speed, air temperature, and humidity – show their greatest gradients. Over very rough surfaces (e.g. forests, urban areas) the SL can be further divided into an inertial sublayer (ISL) and a roughness sublayer (RSL).

23

km 10 free atmosphere

inertial sublayer

roughness sublayer

surface layer

0.1

troposphere

mixed layer

atmospheric boundary layer

1

0.01 canopy layer

Fig. 3.1:

Daytime structure of the troposphere over a forest with a meteorological measurement tower (after MONCRIEFF et al., 2000)

The RSL is the layer immediately above the roughness elements where individual roughness elements have a direct effect on the characteristics of the airflow (KAIMAL and FINNIGAN, 1994; MAHRT, 2000). Main characteristics of the RSL are horizontally and vertically varying flux densities. Furthermore, wake turbulence caused by the roughness elements and thermal effects enhance turbulence in the RSL over the turbulence in the ISL. Eddy diffusion coefficients are increased above their logarithmic values encountered in the ISL. The depth of the RSL is assumed to be two to three times the height of the vegetation. In the ISL the influence of surface properties on airflow properties decreases, e.g. the wind direction is increasingly modified by the Coriolis force, and vertical flux densities are considered to be constant with height (OKE, 1987; GARRATT, 1992; CELLIER and BRUNET, 1992; KAIMAL and FINNIGAN, 1994). Additionally, a canopy layer (CL) forms near the ground. The depth of the CL is roughly the mean depth of the roughness elements. In case of vegetation it is the mean vegetation height (OKE, 1987).

24

Since irregular patches of land uses cover the Earth’s surface near ground airflows are modified by changes in surface properties (e.g. roughness, thermal properties). The layer of air whose properties have been modified by the new surface is called an internal boundary layer (IBL) because it forms within an existing boundary layer. It is only close to the new surface that the atmospheric conditions within the IBL are fully adjusted to the properties of the new surface and an equilibrium layer (EL) is believed to form. The suggestions concerning the depth of the EL above the zero plane displacement (d) of the new surface lie between 1 to 10 % of the distance downwind the change in surface roughness (GASH, 1986; KAIMAL and FINNIGAN, 1994; FOKEN, 2003). For a detailed description of the influence of changing surface properties on the structure of the lower ABL see GARRATT (1990), IRVINE et al. (1997), and MAHRT (2000).

3.3

Airflow over tall plant canopies

3.3.1

Airflow well above tall plant canopies

A logarithmic law is usually used to describe the variation of the mean wind speed with height in the SL. Close to the ground frictional drag reduces the wind speed to zero whereas pressure gradient forces increase the wind speed with height. Above dense plant canopies the logarithmic wind profile is calculated as (STULL, 1988):   u    z − d  ( ) + ψ − U (z) =  *  ln z d / L  m  κ    z 0  

(3.1)

horizontal wind speed (m s–1), von Karman constant (0.35–0.43), height above ground (m), Obukhov length (m), zero plane displacement (m), aerodynamic roughness length (m), –1 u* : friction velocity (m s ), Ψm: nondimensional stability function. U: κ: z: L: d: z0 :

Since a dense plant canopy acts like an elevated surface the logarithmic wind profile has an elevated origin (U = 0 m s–1) at the height z = d + z0. The aerodynamic roughness length z0 is a measure of the surface roughness and represents the influence of the surface characteristics on the flux–gradient relationships in the SL. z0 is on the order of

25

10 % of the height of the vegetation elements. d represents the vertical displacement of the streamlines due to the presence of a tall surface cover (SHAW et al., 1988) and is the height of the mean momentum sink (THOM, 1971). d is in the range of 60 to 90 % of the height of the roughness elements. Compilations of z0 and d values for plant canopies can be found in JARVIS et al. (1975), OKE (1987), STULL (1988), WIERINGA (1993), KAIMAL and FINNIGAN (1994), and MAHRT et al. (2001). Detailed descriptions of Ψm(z–d/L) and nondimensional SL functions for momentum (φm), heat (φh), and water

vapour (φq) above plant canopies can be found in STULL (1988), CELLIER and BRUNET (1992), and KAIMAL and FINNIGAN (1994): φm ( z − d / L) =

κ (z − d ) ∂U u* ∂z

(3.2)

φ h ( z − d / L) =

κ (z − d ) ∂θ T* ∂z

(3.3)

φq ( z − d / L) =

κ (z − d ) ∂q q* ∂z

(3.4)

where q * and T* are defined as q* =

w´q´ w´θ´ and T* = . u* u*

The turbulent diffusion coefficients for momentum (Km), heat (Kh), and water vapour (Kq) are: Km =

κ u * (z − d ) φm

(3.5)

Kh =

κ u * (z − d ) φh

(3.6)

Kq =

κ u * (z − d ) φq

(3.7)

3.3.2

Airflow just above and within tall plant canopies

Turbulence just above and within a plant canopy results from the distribution of sources and sinks of momentum and scalars within the plant canopy. This source and sink distribution causes a variation in the time averaged moments of velocities and scalars.

26

Therefore, these measurements of the airflow are subject to serious uncertainties because of very high turbulence variability. Since measurements, which account for the horizontal variability of the airflow just above and within plant canopies are complex and expensive, airflow characteristics are mainly measured at a single point. The results of these single–point measurements can be summarised as (KAIMAL and FINNIGAN, 1994; FINNIGAN and BRUNET, 1995; RAUPACH et al., 1996; FINNIGAN, 2000): -

inflexion of the mean wind speed profile at the canopy top,

-

vertical inhomogeneity in second order moments,

-

velocity moments scale with single length and time scales,

-

coherent structures control canopy turbulence,

-

canopy turbulence is dominated by intermittent downward moving gusts.

The inflexion of the mean wind speed profile over plant canopies is caused by the canopy drag. The inflexion point corresponds to a hydrodynamic instability, which initiates coherent structures. As a result canopy airflow statistics are more similar to mixing than to SL airflow statistics (RAUPACH et al., 1996). The mean wind shear shows a maximum at the canopy top. U and ∂U/∂z are diminshed within the canopy at a rate determined by the density of the foliage. The plant area density a(z) is the area of plant surface per unit volume. The integral of a(z) through the whole canopy depth is called the plant area index (PAI): h

PAI = ∫ a (z) dz

(3.8)

0

where h is the mean plant canopy height. In general, RSL gradients of turbulent flux densities of momentum, heat, and water vapour are smaller than the corresponding ISL gradients. This leads to an enhancement of Km, Kh, and Kq in the RSL. The increase in Km, Kh, and Kq can be quantified by the nondimensional factor β (RAUPACH, 1979; CELLIER and BRUNET, 1992): βm , h , q

K *m , h , q = K m, h ,q

(3.9)

27

where K*m,h,q represents the eddy diffusion coefficients in the RSL and Km,h,q the eddy diffusion coefficients in the ISL.

3.3.3

Turbulence structure over tall plant canopies

3.3.3.1 Length scales

The usual method for obtaining information on length scales in the SL is to apply the Taylor frozen turbulence hypothesis to single–point turbulence measurements, although the applicableness of this approach is questionable within tall plant canopies because of high turbulence intensities (RAUPACH et al., 1996). Important measures of eddy scale in the SL are single–point Eulerian integral length scales for the streamwise (u), the lateral (v), and the vertical (w) wind vector component (Lu, Lv, and Lw). Lu, Lv, and Lw are defined as (KAIMAL and FINNIGAN, 1994): U Lu = 2 σu

Lv =

Lw =

U σ 2v U σ 2w

∞

∫ u´(t ) u´(t + τ) dτ

(3.10)

0

∞

∫ v´(t ) v´(t + τ) dτ

(3.11)

0

∞

∫ w´(t ) w´(t + τ) dτ

(3.12)

0

where τ is the time lag with respect to time t.

3.3.3.2 Spectra

Calculation of the spectral energy density of the wind vector components provides a measure of the relative importance of different scales of turbulence. Turbulence spectra information can be used to improve the knowledge of (BALDOCCHI and HUTCHISON, 1988): -

dispersion of pollutants, spores, pollen,

-

exchange of CO2, water vapour, heat,

-

plant canopy movement,

28

-

dissipation of turbulence as affected by plant parts,

and to improve the parameterisation of higher order turbulence closure models. An important indicator of eddy scale is the position of the peak of the u, v, and w energy spectra. The spectral energy densities Su(k), Sv(k), and Sw(k), where k represents the wavenumber, are the Fourier transforms of single–point, time–delayed autocovariance functions and represent the contributions of different eddy scales to turbulent kinetic energy (TKE). Energy spectra in the ABL can be partitioned into three main spectral regions (Fig. 3.2) (KAIMAL and FINNIGAN, 1994): -

A: Energy containing range, where energy is produced by buoyancy and shear.

-

B: Inertial subrange, where both energy production and energy loss to dissipation are insignificant but energy is handed down to smaller and smaller scales.

-

C: Dissipation range, where kinetic energy is converted into heat.

∼

∼

Fig. 3.2

Idealised energy spectrum in the atmospheric boundary layer showing the energy containing range (A), the inertial subrange (B), and the dissipation range (C). Si (i = u, v, w) is the spectral energy density, k the wavenumber, Λ the integral length scale of turbulence and η the Kolmogorov microscale (adopted from KAIMAL and FINNIGAN, 1994)

29

Shear and buoyancy produce eddies in the energy–containing range. The spectral energy reaches its maximum at a wavenumber corresponding approximately to the Eulerian integral length scale (k ~ 1/Λ). The length scale of eddies directly affected by viscous dissipation is the Kolmogorov microscale η, given by η = (υ3 ε) 1 / 4 , where ν is the kinematic viscosity of air and ε is the dissipation rate of TKE. Λ ranges typically from 10 to 500 m and η is of order of 0.001 m in the ABL. An inertial subrange will exist if there is a sufficient large gap between Λ and η and turbulent energy is neither produced nor destructed. In the inertial subrange S(k) is proportional to k–5/3 and if turbulence is isotropic, the u, v, and w spectra show the following relationship:

4 S v (k ) = S w (k ) = S u (k ) 3

(3.13)

At the high wavenumber end of the spectrum the spectral slope becomes steeper as the viscous dissipation begins to remove significant amounts of TKE and converts it into heat. Taylor’s hypothesis enables the conversion of wavenumber k = 2π/λ to frequency, where λ is the wavelength approximated by U/fc and fc is the cyclic frequency.

3.3.4

Turbulence structure within tall plant canopies

Spectra measured in the RSL depart from the shapes and scaling relationships developed for the SL. Within tall plant canopies two additional processes, which modify the turbulence spectra, must be considered (FINNIGAN and BRUNET, 1995; FINNIGAN, 2000): -

As the mean flow does work against the aerodynamic drag of the plants, kinetic energy of the mean flow (MKE) is converted into heat. Wake and waving production mechanisms cause the conversion of MKE to TKE. This fine–scale wake component of TKE is termed wake kinetic energy (WKE). WKE can represent a source of energy at higher wavenumbers than 1/Λ.

-

Wake and waving production mechanisms convert eddies generated by shear production to finer–scale eddies. This process is called ‘spectral short cut’ (BALDOCCHI

and MEYERS, 1988b) and represents the removal of energy from turbulent ed-

dies rather than from the mean flow.

30

These processes have consequences within the inertial subrange of the turbulence spectra because -

they alter the rate of decrease of Su(k), Sv(k) and Sw(k) with increasing k,

-

they disturb the isotropy observed in the inertial subrange of turbulence spectra above tall plant canopies.

3.3.5

Plane mixing layer analogy

The turbulence statistics in the RSL differ from those in the ISL. The differences can be explained by taking a plane mixing layer (PML) rather than a boundary layer as a model for RSL turbulence. The characteristics of the mean airflow and the turbulence near the top of a forest canopy are rather similar to the airflow characteristics on the low–speed side of a PML than to the airflow characteristics of a boundary layer (FINNIGAN and BRUNET, 1995; RAUPACH et al., 1996; FINNIGAN, 2000). The PML is a free shear layer which forms when two airstreams of different velocity, initially kept separate by a splitter plate, are allowed to mix downstream of the trailing edge of the plate. The width of the mixing layer can be characterised by the vorticity thickness (δω): δw =

∆U (dU / dz )max

(3.14)

where ∆U is the difference between the free stream velocities above and below the splitter plate. Under the assumptions that the inflexion point in the wind speed profile is at z = h (maximum shear) and that U0 0.3). L is the Obukhov length and was calculated as: L=−

4.2.2

u *3 t sv κ g w´t sv ´

(4.1)

Sonic anemometer

4.2.2.1 Turbulence statistics

For the calculation of turbulence statistics sonic anemometer data received additional data processing (KAIMAL and FINNIGAN, 1994; VICKERS and MAHRT, 1997; AUBINET et al., 2000; KRUIJT et al., 2000; RANNIK et al., 2003):

47

-

despiking (removal of ‘spikes’, i.e. unrealistically large or small values caused by rain, insects, etc.),

-

rotation of the coordinate system around the z–axis to force v = 0 ,

-

computation of second and higher order statistics from fluctuating terms,

-

block averaging into 10 minute intervals, afterwards computation as hourly values.

4.2.2.2 Spectral analysis

Using one hour data (MP1: USA–1, 215 samples at 10 Hz; R2, 216 samples at 20.8 Hz; MP2: USA–1, 216 samples at 20 Hz), fast Fourier transforms (FFT) were performed to calculate spectral energy densities of the wind vector components u and w as well as the cospectral energies densities of uw and wtsv. The spectra processing included the following procedures (STULL, 1988; KAIMAL and FINNIGAN, 1994; MAZZONI, 1996; FEIGENWINTER,

2000; VILLANI et al., 2003):

-

linear detrending of the sonic anemometer time series,

-

application of a tapering window (Hanning window), i.e. application of a modified data window with smoother edges,

-

calculation of FFT spectra,

-

normalisation of the frequency f by h/Uh,

-

normalisation of the spectral energy density S(f) by f/variance,

-

interpolation of single spectra by a cubic spline,

-

smoothing the FFT spectra by logarithmically averaging over 30 frequency bins and assigning the mean value of each frequency bin to the corresponding centre frequency of the bin.

Cospectra were computed in the same way as the spectra. To make cospectra comparable among each other f was normalised by h/Uh, S(f) by f/covariance.

48

4.2.2.3 Length scales

To investigate the average eddy size at the two sonic anemometer levels the single– point Eulerian integral length scales for u (Lu) (3.10) and w (Lw) (3.11) were determined by (KAIMAL and FINNIGAN, 1994): -

calculation of the autocorrelation functions for u and w,

-

calculation of the integral time scales for u (Tu) and w (Tw) from the autocorrelation functions by integrating over time lag until the first zero–crossing, multiplication of Tu and Tw by the local wind speed U.

-

4.2.2.4 Quadrant analysis

Quadrant analysis (LU and WILLMARTH, 1973; SHAW et al., 1983) was used to analyse

(

(

)

)

the structure of the turbulent momentum flux u´w´ and the turbulent heat flux w´t sv ´

within and above the Hartheim Scots pine forest canopy. Referring to u´w´ , quadrant analysis partitions the relative contributions of the instantaneous product of u´ and w´ to u´w´ , which will be sorted into four categories according to the sign of the two fluctuat-

ing components. On a u´–w´ plane, where u´ is the x–axis and w´ is the y–axis, four quadrants can be defined (SHAW et al., 1983) (Fig. 4.5): quadrant I:

u´ > 0, w´ > 0,

outward interaction: upward transfer by updrafts of fast air parcels

quadrant II:

u´ < 0, w´ > 0,

ejection or burst:

downward transfer by updrafts of slow air parcels

quadrant III:

u´ < 0, w´ < 0,

inward interaction:

upward transfer by downdrafts of slow air parcels

sweep or gust:

downward transfer by down– drafts of fast air parcels

quadrant IV: u´ > 0, w´ < 0,

Quadrants II and IV contribute to downward transfer of momentum, while quadrants I and III contribute to upward momentum transfer. Information about the importance of turbulent events with large values is obtained by defining a hole size (H): H=

u´w´ u´w´

(4.2)

49

where the point (u´, w´) lies on the hyperbola which bounds the hole region. By progressively increasing the magnitude of H, the importance of events exhibiting large values of |u´w´| can be determined within each quadrant (SHAW et al., 1983).

Fig. 4.5:

Quadrants (I, II, III, IV) and hyperbolic excluded regions (grey region) for the streamwise and vertical velocity fluctuations (u´ and w´) (adapted from SHAW et al., 1983)

Momentum flux fractions S(i,H) can be determined according to (RAUPACH, 1981): S(i, H) =

u´w´ (i, H) u´w´

(4.3)

where the angle brackets denote a conditional average: 1 u´w´ (i, H) = lim t sp → ∞ t sp

t sp

∫ u´(t )w´(t ) I(i, H)(t ) dt 0

with tsp as the sampling period. The conditioning function I(i,H) is expressed as:

(4.4)

50

1, if the po int (u´, w´) lies in the quadrant i   and u´w´ > H u´w´ I(i, H) =   0, otherwise 

(4.5)

The time fractions T(i,H) in connection with the S(i,H) are defined as: t sp

T(i, H) = lim

t sp →∞

4.2.3

∫ I(i, H)(t ) dt

(4.6)

0

Sodar

In MP1 and MP2 the FAS64 was driven by different versions of the Scintec sodar software FASrun (MP1: FASrun 1.11.1; MP2: FASrun 2.0.0 p40). The different FASrun versions were necessary due to the upgrade of the sodar electronic. Both versions of FASrun applied intrinsic data control and data correction procedures online to the sodar data (SCINTEC, 2002). Furthermore, in MP1 the signal–to–noise ratios (SNR) of the wind vector components were checked (ANTONIOU et al., 2003) and only data with SNR greater than 1.4 (Scintec, personal communication) were used for further data processing. This was not possible for MP2 because FASrun 2.0.0 p40 did not display SNR data. Additionally, in both measurement periods the horizontal wind speed of the second range gate (40–60 m above the forest canopy) of the sodar was compared to the wind speed measured with the cup anemometer just above (15.5 m) the Hartheim Scots pine forest canopy. All sodar wind speed data less than the wind speed at this level were excluded from further data analysis.

51

5.

RESULTS

5.1

Mean meteorological conditions

In comparison to the measurement period MP2 (2003–07–01 to 2003–07–31), the mean meteorological conditions above the Hartheim Scots pine forest canopy top in the measurement period MP1 (2002–11–01 to 2003–01–31) were characterised by (Table 5.1): -

lower mean global radiation (G),

-

lower mean net radiation (Rn),

-

lower mean air temperature at the canopy top (Th),

-

similar mean wind speed at the canopy top (Uh),

-

similar mean friction velocity ( u * ),

-

positive mean surface layer temperature scale ( T* ).

Table 5.1: Mean values of global radiation G, net radiation Rn, air temperature at z = h Th, wind speed at z = h Uh, friction velocity u * , and the surface layer temperature scale T* at the forest meteorological experimental site Hartheim in the measurement periods MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) measurement period mean MP1 mean maximum mean minimum mean MP2 mean maximum mean minimum

Rn G –2 (W m ) (W m–2) 33.0 174.1 0.0 253.3 790.4 0.0

1.1 105.4 –48.0 169.4 629.0 –59.5

Th (°C)

Uh (m s–1)

4.5 7.0 1.9 20.7 26.5 14.6

1.42 2.39 0.53 1.13 2.33 0.08

u* (m s–1) 0.40 0.71 0.15 0.41 0.83 0.12

T* (°C) 0.02 0.08 –0.09 –0.12 0.09 –0.46

Besides the differences in the absolute mean values, the differences in the course of the meteorological variables in MP1 and MP2 can be outlined as follows: -

The daily cycles of G, Rn, and Th had smaller mean amplitudes in MP1 than in MP2.

52

In MP1 Uh and u * showed a more irregular pattern with periods of rather high and

-

low values. -

In MP2 Uh and u * were subjected to a strong regular daily cycle.

-

In MP2 T* values showed greater daily mean amplitudes.

Furthermore, MP1 was characterised by long foggy periods. MP2 was exceptionally warm. The number of hourly mean values of the atmospheric stability conditions unstable (h/L < –0.3), neutral (–0.3 ≤ h/L ≤ 0.3), and stable (h/L > 0.3) in MP1 and MP2 are listed in Table 5.2.

Table 5.2: Number of hourly mean values of different atmospheric stability conditions (unstable, neutral, and stable) at the forest meteorological experimental site Hartheim in the measurement periods MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) measurement period

all

MP1 MP2

2208 744

atmospheric stability conditions neutral unstable (h/L < –0.3) (–0.3 ≤ h/L ≤ 0.3) 544 462

264 104

stable (h/L > 0.3) 1400 178

5.2

Mean airflow characteristics above and within the Hartheim Scots pine forest

5.2.1

Mean wind speed profile

To characterise the mean airflow structure above and below the Hartheim Scots pine forest canopy in December 2002 (exemplary for MP1) and in July 2003 (MP2), Figs. 5.1 and 5.2 show hourly mean cup anemometer wind speed classes (1.25 m s–1 increment) for the eight measurement levels. A common feature of the hourly mean wind speed values is that they were rather low throughout most of December 2002 and July 2003. The absolute hourly mean wind speed values measured at the highest measurement level (z/h = 2.08) did not exceed 10 m s–1 during both months. The low above– and below–canopy mean wind speeds are clearly reflected in the colour–coded wind speed classes displayed in Figs. 5.1 and 5.2.

53

Fig. 5.1:

Hourly mean horizontal wind speeds U(z) at different heights at the forest meteorological experimental site Hartheim in December 2002

Fig. 5.2:

Hourly mean horizontal wind speeds U(z) at different heights at the forest meteorological experimental site Hartheim in July 2003

54

Particularly below the Scots pine forest canopy mean wind speeds often fell below the threshold velocities of the cup anemometers, which are on the order of 0.2 to 0.3 m s–1. A further feature of the mean airflow was that in MP2 – expect for the first few days – a daily cycle in the wind speed was discernible. During December 2002 no clear daily wind velocity pattern was observable. Fig. 5.1 shows that during this month an irregular pattern with periods with very low hourly mean wind speeds alternated with periods with higher wind speeds. To display mean wind speed profiles up to z/h = 14.08 (200 m a.g.l.) data from cup anemometer measurements (z/h = 0.14 to z/h = 2.08) and sodar data were combined for three atmospheric stability classes (unstable, neutral, stable) in MP1 (Fig. 5.3).

100

z/h

10

1

unstable neutral stable

0 0

Fig. 5.3:

2

4

6

8 -1 U(z) (m s )

10

12

14

Combined mean wind speed profiles U(z) under different atmospheric stability conditions (number of profiles: unstable: 20; neutral: 7; stable: 78) at the forest meteorological experimental site Hartheim up to z/h = 14.08 (200 m a.g.l.) in MP1 (2002–11–01 to 2003–01–31)

Throughout the whole profile wind speeds under neutral atmospheric stability conditions were highest, especially within the Hartheim Scots pine forest. Under unstable and

55

stable stratification within–canopy wind speeds were very low. No combined mean wind speed profiles were available for MP2 since no sodar data passed the plausibility check (see section 4.2.3) and consequently were rejected from further analysis. To examine the effects of atmospheric stability conditions on the mean wind speed profiles in further detail, Fig. 5.4 displays the normalised mean wind speed profiles for the stability classes unstable (number of profiles in MP1: 506; MP2: 318), neutral (number of profiles in MP1: 251; MP2: 91), and stable (number of profiles in MP1: 1323; MP2: 153) in MP1 (Fig. 5.4a) and MP2 (Fig. 5.4b) up to z/h = 2.08. In both measurement periods the normalised mean wind speed profiles above the Hartheim Scots forest canopy were more or less logarithmic with strong wind shear at the forest canopy top and a rapid decrease in wind speeds within the forest canopy. 2.5

2.5

a

b 2.0

1.5

1.5 z/h

z/h

2.0

1.0

1.0

0.5

0.5 unstable neutral stable

unstable neutral stable

0.0

0.0

0

1

2

3

4

0

U(z)/Uh

Fig. 5.4

1

2

3

4

U(z)/Uh

Normalised mean wind speed profiles U(z)/Uh under different atmospheric stability conditions in (a) MP1 (2002–11–01 to 2003–01–31) and (b) MP2 (2003–07–01 to 2003–07–31) up to z/h = 2.08

In MP1 within–canopy wind speed profiles were nearly identical under all atmospheric stability conditions. Under neutral atmospheric stability conditions the mean wind speed profile above the Hartheim Scots forest canopy was steepest.

56

In MP2 within–canopy wind speed profiles showed different magnitudes with highest wind speeds under unstable atmospheric conditions. Under stable atmospheric conditions the within–canopy profiles show the lowest, under unstable atmospheric conditions the highest values. Under unstable conditions the above–canopy profile was steepest. This decrease in the wind speed gradient is expected in the surface layer (OKE, 1987; KRUIJT et al., 2000; VILLANI et al., 2003). In both measurement periods a weak secondary maximum in the normalised mean wind speed profiles can be observed in the subcanopy trunk space (z/h = 0.42). A secondary wind speed maximum was also observed in other plant canopies having a relatively porous subcanopy trunk space where the airflow is less restricted (MAYER, 1976; BALDOCCHI

and HUTCHISON, 1987; BALDOCCHI and MEYERS, 1988a; LEE and BLACK,

1993a).

5.2.2

Normalised wind speed difference

The relationship between wind speeds in the subcanopy trunk space of the Hartheim Scots pine forest (6.0 m, z/h = 0.42) and wind speeds above the Hartheim Scots pine forest (29.6 m, z/h = 2.08) under different atmospheric stability conditions was analysed by normalised mean wind speed differences ((U29.6–U6.0)/U29.6). In Figs. 5.5 and 5.6 (U29.6–U6.0)/U29.6 are plotted as grey scale coded circles as function of the friction velocity ( u * ) and the surface layer temperature scale ( T* ). u * and T* were determined at z/h = 1.94 and used as measures for dynamical and thermal atmospheric stability conditions (LOHOU et al., 2003). Negative T* values are related to unstable atmospheric conditions. T* values near 0 represent neutral, positive T* values stable atmospheric conditions. In MP1 (Fig. 5.5) stable and neutral atmospheric conditions dominate. T* values cluster around 0. Under stable atmospheric conditions the normalised wind speed differences were near 1 (mainly for small u * values). Under neutral atmospheric conditions the normalised wind speed differences decrease but stay constant with increasing u * , under unstable atmospheric conditions they were smallest.

57

Fig. 5.5:

Normalised mean wind speed differences (U29.6–U6.0)/U29.6 at the experimental site Hartheim as a function of friction velocity u * and surface layer temperature scale T* in MP1 (2002–11–01 to 2003–01–31)

In MP2 (Fig. 5.6) unstable atmospheric conditions prevailed. As seen in MP1 the normalised wind speed differences were mainly around 1 under neutral and stable atmospheric conditions. Under unstable atmospheric conditions they were clearly smaller than 1. The results shown in Figs. 5.5 and 5.6 complement the results presented in Fig. 5.4. Under unstable atmospheric conditions the wind speeds within the subcanopy trunk space of the Hartheim Scots pine forest were relatively higher compared to the wind speeds above the Scots pine forest than under neutral and unstable atmospheric conditions.

58

Fig. 5.6:

5.2.3

Normalised mean wind speed differences (U29.6–U6.0)/U29.6 at the experimental site Hartheim as a function of friction velocity u * and surface layer temperature scale T* in MP2 (2003–07–01 to 2003–07–31)

Mean shear length scale

RAUPACH et al. (1996) postulated that the airflow structure in the vicinity of a plant canopy is more similar to that of a plane mixing layer than to a boundary layer. Thus, it must be controlled by plane mixing layer parameters. They proposed that in the roughness sublayer above tall plant canopies the shear length scale (Ls), corresponding to half of the vorticity thickness in plane mixing layers, controls coherent motions (3.14). Mean Ls values were calculated from four levels of the mean wind speed profile between z/h = 0.70 and z/h = 1.35. Since no wind speed measurements directly at the Hartheim Scots pine forest canopy top were available Uh values were approximated using cubic splines and (dU/dz)z=h values using second order polynomials. As done by

59

BRUNET and IRVINE (2000), Ls values determined for situations when wind speed was too low to be correctly measured by the cup anemometers were discarded. Mean Ls values for MP1 and MP2 under various stability conditions are listed in Table 5.3. In MP1 Ls was greatest under neutral conditions (6.9 m) and roughly corresponded to the value of 0.5h proposed by RAUPACH et al. (1996) for moderately dense plant canopies. In MP2 under neutral atmospheric stability conditions mean Ls was lower than expected (5.8 m). Ls exhibited the highest value under unstable atmospheric conditions (7.7 m). The results obtained for unstable conditions in MP2 were as expected. The wind profile becomes steeper in unstable conditions, i.e. dU/dz becomes smaller than under neutral atmospheric stability conditions leading to an increase of Ls (BRUNET and IRVINE, 2000).

Table 5.3: Mean shear length scale Ls at the canopy top of the Hartheim Scots pine forest under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) atmospheric stability conditions unstable neutral stable

5.2.4

Ls (m) MP1 6.4 6.9 5.8

MP2 7.7 5.8 5.1

Wind direction

In MP1 the sonic anemometers enabled the comparison of wind directions (dd) above (dd27.5m) and below (dd4.5m) the Hartheim Scots pine forest (Fig. 5.7). Wind directions were deduced from the horizontal wind vector components u and v of the sonic anemometer measurements at these heights. To check the plausibility of the sonic anemometer wind direction at 27.5 m, it was compared to the permanent wind direction measurement at the top of TH. The comparison yielded a clockwise offset of 10° of the sonic anemometer wind direction (r2 = 0.99). Wind directions above and below the Scots pine forest canopy could not be compared for MP2 since only above–canopy wind direction data were available.

60

Above the Hartheim Scots pine forest canopy southern wind directions (53 %) dominated over northern wind directions (21 %) in MP1. Eastern (12 %) and western (14 %) wind directions played a minor role. Fig. 5.7a shows all wind direction data above the forest canopy plotted against the wind direction data determined below the forest canopy. It is obvious that the wind directions at these heights were closely coupled.

Fig. 5.7:

Comparison of wind directions above (dd27.5m) and below (dd4.5m) the Hartheim Scots pine forest canopy in MP1 (2002–11–01 to 2003–01–31). (a) comparison of all available wind direction data, (b–f) comparison of wind direction data for different classes of friction velocity u *

61

To further analyse the relationship between dd27.5m and dd4.5m and to reveal the influence of different atmospheric conditions, Figs. 5.7b to 5.7f show the comparison of the two wind directions for different classes of friction velocity u * . It turns out that the data in the lowest class of u * ( u * < 0.2 m s–1) show two main axes (Fig. 5.7b). For a broad range of dd27.5m, dd4.5m is found to be between 20°–50° and 210°–240°. With increasing u * (Fig. 5.7c) the two axes become blurred. Beginning u * = 0.4 m s–1 another axis be-

comes visible (Fig. 5.7d). It is rotated 90° against the two axes seen with lower u * . When u * > 0.8 m s–1 (Fig. 5.7f) one data cluster crystallises out. High u * values occurred mainly when the wind came from southerly directions during MP1. The data exhibit a clockwise rotation of dd4.5m about 20°–30°. Low u * –values were observed under unstable and stable atmospheric conditions (97 % of the data in the lowest class of u * (Fig. 5.7b)), whereas high u * –values occurred under neutral atmospheric conditions (83 % of the data in the highest class of u * (Fig. 5.7f)). A possible explanation of the rotation of the wind direction inside the forest could be the orientation of the tree rows at the experimental site. The tree rows are oriented in SSW–NNE direction, i.e. the main direction of the airflow below the Hartheim Scots pine forest canopy.

5.3

Turbulence statistics

5.3.1

Family portrait of canopy turbulence

To obtain an understanding of turbulence above and below the Hartheim Scots pine forest canopy, second and higher order statistical moments such as turbulence intensity and skewness of the wind velocity components were analysed. All turbulence statistics presented here are primarily compared to the so–called ‘family portrait’ of plant canopy turbulence (RAUPACH, 1988; RAUPACH et al., 1996). The ‘family portrait’ of plant canopy turbulence is a compilation of single–point turbulence statistics measured mainly in neutral and near–neutral atmospheric stability conditions in twelve horizontally homogeneous canopies, ranging from wind tunnel models through cereal crops to forests (FINNIGAN, 2000). Table 5.4 is a compilation of studies conducted in tall plant canopies to which the results of this study are compared. Not all cited studies are conducted over

62

forest canopies. FINNIGAN (1979a) presented results of turbulence measurements over wheat, BALDOCCHI and HUTCHISON (1987), and BALDOCCHI and HUTCHISON (1988) presented results of turbulence measurements of an almond orchard, CHEN (1990) reported results of turbulence measurements for mallee bushland.

Table 5.4: Compilation of cited turbulence studies, which were conducted in tall plant canopies and to which the results of this work are compared (several of the cited studies are part of the ‘family portrait’ of canopy turbulence (RAUPACH et al., 1996)) canopy height (m)

plant density (stems ha–1)

area index

1.25

714300

–

almond orchard

8

156

LAI: 1.3

almond orchard

8

156

LAI: 1.3

deciduous forest

23

–

LAI: 4.9

mixed forest

18

–

LAI: 1.6

Scots pine forest

16

350

–

mixed forest

18

–

–

Black spruce

12

7450

LAI: 10

AMIRO (1990a, 1990b)

Jack pine

15

675

LAI: 4

AMIRO (1990a, 1990b)

trembling aspen

10

–

LAI: 2

AMIRO (1990a, 1990b)

mallee bushland

2.3

–

–

CHEN (1990)

deciduous forest

18

–

–

MAITANI and SHAW (1990)

Douglas–fir

16.7

575

–

LEE and BLACK (1993a, 1993b)

Sitka spruce

12

3584

LAI: 10.2

GARDINER (1994)

Sitka spruce

8

625

LAI: 3.2

GREEN et al. (1995)

deciduous forest tropical rain forest tropical rain forest Sitka spruce

18

–

LAI: 2

SU et al. (1998)

30–35

–

LAI: 5–6

KRUIJT et al. (2000)

40

–

LAI: 4

KRUIJT et al. (2000)

8

625

LAI: 3.2

NOVAK et al. (2000)

mixed forest

26

–

LAI: 10

LIU et al. (2001)

mixed forest

22

–

VAI: 3.9

VILLANI et al. (2003)

plant canopy wheat

literature FINNIGAN (1979a, 1979b) BALDOCCHI and HUTCHISON (1987) BALDOCCHI and HUTCHISON (1988) BALDOCCHI and MEYERS (1988a, 1988b) SHAW et al. (1988) BERGSTRÖM and HÖGSTRÖM (1989) GAO et al. (1989)

63

5.3.2

General remarks

A part of the Hartheim Scots pine forest in the north as well as the forest meteorological experimental site itself was thinned in the period between MP1 and MP2. Turbulence statistics were nonetheless calculated for all available data because -

the thinned part of the forest covers only a small area and should contribute relatively little to the footprint of the turbulence measurements above the Scots pine forest canopy at z/h = 1.94,

-

northern wind directions (dd ≤ 45° and dd ≥ 315°) played a minor role in both measurement periods (MP1: 21 %; MP2: 15 %),

-

mean northern turbulence statistics were in the range of the variability of the turbulence statistics from all other wind directions.

Since in MP1 alone two sonic anemometers were available, only for MP1 above– and below–canopy turbulence statistics are presented. The number of hourly mean values of the various turbulence variables that were discarded (e.g. exceptional high or low values, erroneous data) before the calculation of the overall mean values was in the range of 5 % to 7 % of the number of hourly mean values presented in Table 5.2. No wind speed limit was applied to the data because of the general low wind speed level at the experimental site Hartheim. The dashed lines in Figs. 5.8 to 5.10 are used to clarify the diagrams and represent no linear relationship of the displayed variables.

5.3.3

Second order statistics

To characterise the variability of the airflow above and within the Hartheim Scots pine forest, streamwise and vertical turbulence intensities (Tiu = σu/u and Tiw = σw/u) (Fig. 5.8a) were computed (Table 5.5). In both measurement periods Tiu and Tiw above the Scots pine forest canopy (z/h = 1.94) were of similar magnitude with Tiu slightly greater than Tiw. Tiu was greatest under unstable, Tiu and Tiw were smallest under stable stratification. In MP1 below the Hartheim Scots pine forest canopy (z/h = 0.32) Tiu was greater than above the Scots pine forest canopy. Under stable atmospheric conditions Tiu and under unstable atmospheric conditions Tiw were greatest. Tiw was clearly smaller than Tiu.

64

2.0

1.6

1.6

1.2

1.2

z/h

z/h

2.0

0.8

0.8

0.4

0.4 unstable neutral stable

u w

a 0.0 0.0

0.5

1.0

1.5

2.0

Tiu, Tiw

Fig. 5.8:

u w

b 0.0 2.5

0.0

0.5

1.0

unstable neutral stable

1.5

2.0

σu/u*, σw/u*

(a) Mean streamwise and vertical turbulence intensities Tiu and Tiw, (b) normalised mean streamwise and vertical standard deviations σu/ u * and σw/ u * above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31)

Limitations of Tiw below plant canopies were also reported by FINNIGAN (1979a) and BALDOCCHI and HUTCHISON (1987). They are the result of the restriction of the vertical fluctuations by the ground surface (FINNIGAN, 1979a). Following AMIRO (1990a) and NOVAK et al. (2000) the observed limitations are rather attributed to the low mean wind speeds within the Hartheim Scots pine forest canopy than to high standard deviations. Similar high magnitudes of normalised standard deviations for a pine forest and an aspen forest were reported by AMIRO (1990a). On the other hand, the magnitudes of below–canopy Tiu and Tiw were considerably greater than those observed by MAYER (1978), AMIRO and DAVIS (1988), BALDOCCHI and MEYERS (1988a), SHAW et al. (1988), and LEE and BLACK (1993a).

65

Table 5.5: Mean turbulence statistics above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) MP

MP1

z/h stability conditions

MP2

0.32

1.94

1.94

unstable neutral stable unstable neutral stable unstable neutral stable

Tiu

2.14

1.69

2.23

0.34

0.31

0.27

0.39

0.30

0.23

Tiw

1.09

0.87

0.94

0.23

0.23

0.18

0.27

0.18

0.16

σu/ u *

1.10

0.83

0.91

1.83

1.82

1.89

1.50

1.40

2.23

σw/ u *

0.34

0.25

0.26

1.17

1.17

1.16

1.07

0.84

1.39

− u´w´ / u *2

0.00

0.02

0.00

0.77

0.72

0.78

0.87

0.95

0.91

Lu/h

0.18

0.23

0.22

2.11

3.08

2.11

2.65

2.91

2.05

Lw/h

0.08

0.13

0.08

0.76

1.03

0.67

0.90

0.58

0.49

–ruw

0.00

0.00

0.00

0.06

0.40

0.09

0.15

0.25

0.06

Sku

0.07

–0.26

–0.10

0.17

0.25

0.16

0.17

0.17

0.13

Skw

–0.36

–0.63

–0.41

0.04

–0.04

0.00

0.08

–0.07

–0.04

Kru

0.11

0.43

0.31

–0.23

–0.21

–0.18

–0.27

–0.19

–0.10

Krw

1.33

2.09

1.47

0.60

0.46

0.73

0.19

0.66

0.64

Fig. 5.8b shows the normalised ( u * obtained at z/h = 1.94) mean standard deviations of the streamwise and the vertical wind velocity components (σu/ u * and σw/ u * ) for three atmospheric stability conditions. In MP1 above the Hartheim Scots forest canopy under all atmospheric stability conditions σu/ u * was in the range 1.82 to 1.89. σw/ u * was nearly constant (1.16 to 1.17). In the subcanopy trunk space σu/ u * and σw/ u * were clearly lower than above the canopy (Table 5.5). Except under stable atmospheric conditions, in MP2 σu/ u * as well as σw/ u * were lower than in MP1. The reduced normalised mean standard deviations below the Hartheim Scots pine forest canopy suggest that turbulence energy was suppressed by the trees (GREEN et al., 1995). Above the Scots pine forest canopy σu/ u * as well as σw/ u * were lower than the expected surface layer values of 2.5 and 1.25 (GARRATT, 1992). Nonetheless, mean σu/ u * and mean σw/ u * values above and below the Scots pine forest canopy are in general

66

agreement with the values presented by RAUPACH et al. (1996), SHAW et al. (1988), SU et al. (1998), and GREEN et al. (1995). Mean values of − u´w´ / u *2 were used as further indicators of the airflow structure above and below the Hartheim Scots pine forest canopy under different stability conditions (Fig. 5.9a). In MP1 and MP2 above–canopy mean values of − u´w´ / u *2 were of the same magnitude, but with higher values in MP2. Atmospheric stability conditions had only a minor effect on − u´w´ / u *2 . Below the Scots pine forest canopy mean − u´w´ / u *2 values were 0 under unstable and stable atmospheric stability conditions (neutral: 0.02). Above the Scots pine forest canopy, mean − u´w´ / u *2 values were slightly lower than the values presented by RAUPACH et al. (1996) and NOVAK et al. (2000). Below–canopy values resemble the observations of GREEN et al. (1995), RAUPACH et al. (1996), SU et al. (1998), NOVAK et al. (2000), KRUIJT et al. (2000), and VILLANI et al. (2003).

2.0

1.6

1.6

1.2

1.2

z/h

z/h

2.0

0.8

0.8

0.4

0.4 unstable neutral stable

a

b

0.0

0.0 0.0

0.2

0.4

0.6

–u´w´/u*

Fig. 5.9:

2

0.8

1.0

u w

unstable neutral stable

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Lu/h, Lw/h

(a) Normalised mean momentum flux densities − u´w´ / u *2 , (b) normalised mean streamwise and vertical integral length scales Lu/h and Lw/h above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31)

67

In the description of turbulence, velocity length scales are equally important as velocity moments. The Eulerian length scales for u (Lu) and w (Lw) were obtained by applying Taylor’s frozen turbulence hypothesis to the respective integral time scales. Lu and Lw are good indicators of the size of the energy containing eddies (FINNIGAN, 2000). Normalised mean values of Lu (Lu/h) and Lw (Lw/h) are presented in Fig. 5.9b. The results of this study show that in both measurement periods mean Lu/h was greatest under neutral atmospheric stability conditions (MP1: 3.08; MP2: 2.91) at z/h = 1.94. In MP1 above–canopy Lw/h was greatest under neutral stratification (1.03), in MP2 under unstable stratification (0.90). Under stable atmospheric conditions Lw/h was generally smallest. Below the Scots pine forest canopy Lu/h was on the order of 0.2. Lw/h was in the range 0.08 to 0.13. Above– and below–canopy Lu/h and Lw/h were on the order of the values presented at z/h = 2.0 by RAUPACH et al. (1996). The correlation coefficient –ruw ( ruw = −u´w´ / σ u σ w ) is a measure of efficiency of turbulent momentum transfer (Fig. 5.10). Above the Hartheim Scots pine forest canopy under different atmospheric stability conditions –ruw was in the range 0.06 to 0.40. Within the subcanopy trunk space of the Hartheim Scots pine forest (z/h = 0.32) mean –ruw values were generally 0. The mean –ruw value under neutral atmospheric stability conditions in MP1 (0.40) corresponds to the results summarised in the ‘family portrait’ of canopy turbulence (RAUPACH

et al., 1996). Compared to the ‘family portrait’, the mean above–canopy –ruw

value (0.25) in MP2 was somewhat to low. All mean below–canopy –ruw values were lower than the reference values of the ‘family portrait’ of canopy turbulence.

68

2.0

1.6

z/h

1.2

0.8

0.4 unstable neutral stable

0.0 0.0

0.2

0.4

0.6

–ruw

Fig. 5.10: Mean correlation coefficient –ruw above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31)

5.3.4

Higher order statistics

The skewnesses of the streamwise and vertical wind velocity component (Sku and Skw) (Fig. 5.11a) provide a measure of the asymmetry of the probability density distributions of u and w. Velocity fluctuations exceeding the mean value lead to positive, velocity fluctuations smaller than the mean value lead to negative skewed distributions. Positive Sku values give the indication that fast moving air penetrates into a tall plant canopy from above. Since within the tall plant canopy there is no source for the creation of large updrafts, w should be negatively skewed (FINNIGAN, 1979b; SHAW and SEGINER, 1987; RAUPACH et al., 1986). Above the Hartheim Scots pine forest canopy (z/h = 1.94) Sku and Skw were mainly close to 0 in MP1 and MP2, i.e. the velocity fluctuations were more or less symmetrically distributed (Table 5.5). Mean Sku values were generally positive. Mean Skw values were both slightly negative and slightly positive. In MP1 within the subcanopy trunk space Sku was also close to 0. Mean below–canopy Skw values departed most clearly

69

from 0 under all atmospheric stability conditions. The observed mean Sku and Skw values for MP1 and MP2 are in accordance with the values presented by GREEN et al. (1995), RAUPACH et al. (1996), NOVAK et al. (2000), and KRUIJT et al. (2000). Above the Hartheim Scots pine forest canopy the kurtosis of the streamwise velocity component (Kru) (Fig. 5.11b) was negative but close to 0 (–0.10 to –0.27) for all atmospheric stability conditions. The kurtosis of the vertical velocity component (Krw) was generally positive and deviated more clearly from 0 (0.46 to 0.73). An exception was Krw under unstable atmospheric conditions in MP2 (0.19). Within the subcanopy trunk space Kru was quite variable (–0.08 to 0.43). Under neutral atmospheric stability conditions Krw reached 2.09 whereas under unstable atmospheric conditions Krw was 1.33.

2.0

1.6

1.6

1.2

1.2 z/h

z/h

2.0

0.8

0.8

0.4

0.4

a 0.0 -0.8

unstable neutral stable

u w -0.6

-0.4

-0.2

Sku, Skw

0.0

0.2

0.4

0.0 -0.5

0.0

unstable neutral stable

u w

b 0.5

1.0

1.5

2.0

2.5

Kru, Krw

Fig. 5.11: (a) Mean streamwise and vertical velocity skewnesses Sku and Skw, (b) mean streamwise and vertical velocity kurtoses Kru and Krw above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31)

70

Standard normal distributions have a kurtosis of 0. Positive kurtosis indicates a more peaked and negative kurtosis a flatter distribution of velocity components. High positive Krw values below the Hartheim Scots pine forest canopy point out that the vertical velocity fluctuations showed peaked distributions.

5.4

Spectral analysis

5.4.1

General remarks

Spectral analysis of the time series of u and w was carried out to examine the frequency contributions of different eddy scales to the corresponding time series. To be able to compare whether the dominant eddies can be associated with the same turbulent events at the two sonic anemometer measurement heights above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy, the streamwise and vertical spectral energy densities were normalised as already mentioned in section 4.2.2.2: f S(f ) Sˆ(f ) = σi2

(5.1)

h fˆ = f Uh

(5.2)

where S and Sˆ are the spectral energy density and the normalised spectral energy density, σi2 (i = u, w) is the variance of the corresponding time series, f and fˆ are the natural frequency and the normalised natural frequency, h is the canopy height, and Uh is the mean wind speed at the canopy top. Based on criteria found in literature (KAIMAL and FINNIGAN, 1994) single (co)spectra were inspected visually. Obviously erroneous (co)spectra were discarded. Table 5.6 contains the number of hourly (co)spectra used to calculate the mean (co)spectra in MP1 and MP2. The f–2/3 and f–4/3 slope lines in Figs. 5.12 to 5.15 indicate the expected inertial subrange drop–off of the presented spectral and cospectral energy densities for locally isotropic turbulence (KAIMAL and FINNIGAN, 1994).

71

Table 5.6: Number of hourly (co)spectra used to calculate mean (co)spectra above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) z/h

MP

cospectra

u

w

u´w´

w´tsv´

unstable neutral stable unstable neutral stable unstable neutral stable unstable neutral stable

273 206 890 – – – 298 185 929 247 69 133

542 264 1358 – – – 377 264 1371 299 87 172

412 256 924 – – – 280 195 886 225 63 122

344 185 1060 – – – 303 207 1082 254 64 172

1 0.32 2

1 1.94 2

5.4.2

spectra

atmospheric stability conditions

Velocity spectra

An important feature of wind velocity spectra is the location of the spectral peak frequency ( fˆmax ) because fˆmax is an indicator for the most frequent eddy scales. Normalised mean maximum streamwise and vertical frequencies fˆmax (u) and fˆmax (w) as well as normalised mean maximum streamwise and vertical spectral energy densities Sˆmax (u) and Sˆmax (w) were compared (1) above and below the Hartheim Scots pine forest canopy in MP1, and (2) above the Scots pine forest canopy between MP1 and MP2. In MP1 below–canopy mean fˆmax (u) values (Fig. 5.12) were higher than the corresponding above–canopy mean fˆmax (u) values under all atmospheric stability conditions (Table 5.7). Under stable atmospheric conditions mean above– and below–canopy fˆmax (u) values were highest and under neutral atmospheric stability conditions lowest.

72

Fig. 5.12: Normalised mean streamwise and vertical spectral energy densities f Si(f)/ σi2 (i = u, w) above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31). The f–2/3 lines indicate the expected inertial subrange drop–off

Mean fˆmax (w) values above and below the Hartheim Scots pine forest canopy were higher than the mean fˆmax (u) values. Under all atmospheric stability conditions above– canopy mean fˆmax (w) values were higher than the corresponding below–canopy values. In MP1 and MP2 above– as well as below–canopy mean fˆmax (w) values were shifted towards higher frequencies as atmospheric stability increased. The magnitudes of these frequency shifts were different. In MP2 they were much more pronounced than in MP1. Mean fˆmax (w) doubled from 0.39 under neutral to 0.80 under stable atmospheric conditions. The shift of fˆmax (u) with increasing atmospheric stability occurred not as distinct

73

as the shift of fˆmax (w). In MP1 mean fˆmax (u) values above and below the Scots pine forest canopy were lower under neutral than under unstable atmospheric conditions. Under stable atmospheric conditions the highest mean fˆmax (u) values were observed.

Table 5.7: Normalised spectral peak frequencies ( fˆmax ) and normalised spectral peak energy densities ( Sˆmax ) for the streamwise and vertical velocity component (u and w) above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) z/h

wind vector atmospheric component stability conditions u

0.32 w

u 1.94 w

unstable neutral stable unstable neutral stable unstable neutral stable unstable neutral stable

MP1 fˆmax 0.17 0.16 0.23 0.25 0.28 0.30 0.11 0.09 0.13 0.31 0.35 0.42

MP2 Sˆmax 0.12 0.14 0.13 0.11 0.14 0.12 0.09 0.11 0.10 0.09 0.10 0.08

fˆmax – – – – – – 0.03 0.12 0.14 0.25 0.39 0.80

Sˆmax – – – – – – 0.09 0.09 0.10 0.09 0.09 0.09

LIU et al. (2001) and VILLANI et al. (2003) reported that under unstable atmospheric conditions, larger eddies – the result of strong convection and mixing – caused a shift of fˆmax (u) towards a lower value as seen above the Scots pine forest canopy in MP2 (Fig.

5.13). Under stable conditions VILLANI et al. (2003) observed a shift of fˆmax (u) and fˆmax (w) towards higher frequencies and suggested that turbulence structures were

smaller under these conditions. fˆmax (u) values presented in the ‘family portrait’ of canopy turbulence accumulate at 0.15 (± 0.05) and fˆmax (w) values cluster around 0.45 (± 0.05) (RAUPACH et al., 1996).

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Fig. 5.13: Normalised mean streamwise and vertical spectral energy densities f Si(f)/ σi2 (i = u, w) above (z/h = 1.94) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31). The f–2/3 lines indicate the expected inertial subrange drop–off

Under all atmospheric stability conditions below–canopy mean spectra were more peaked and exhibited greater mean Sˆmax (u) and Sˆmax (w) values than the corresponding spectra above the Hartheim Scots pine forest canopy. Above and below the Scots pine forest canopy mean Sˆmax (u) and Sˆmax (w) values were very uniform with highest values under neutral atmospheric stability conditions in MP1 and MP2. Another feature to characterise turbulence is the slope of the inertial subrange in the wind velocity spectra. Above the Hartheim Scots pine forest canopy velocity spectra roughly showed the expected f–2/3 inertial subrange drop–off at mid–frequencies in MP1 and MP2. But the drop–off flattened at higher frequencies. Below the Scots pine forest

75

canopy streamwise and vertical spectra showed a steeper drop−off at mid–frequencies indicating a relative deficit of spectral power. At the high frequency end a flattening of the spectra was observed. Spectra similar to the below–canopy spectra determined within the subcanopy trunk space of the Hartheim Scots pine forest were observed within other forests (AMIRO and DAVIS, 1988; BALDOCCHI and HUTCHISON, 1988; BALDOCCHI DINER,

5.4.3

and MEYERS, 1988b; AMIRO, 1990b; FITZJARRALD and MOORE, 1990; GAR-

1994; KRUIJT et al., 2000; VILLANI et al., 2003).

Cospectra

Normalised cospectral energy densities for the streamwise and vertical velocity component (momentum flux cospectra) and for the vertical velocity component and the sonic temperature (sensible heat flux cospectra) (f Suw(f)/ u´w´ and f Swt sv (f)/ w´t sv ´ ) are presented in Figs. 5.14 and 5.15. In MP1 fˆmax (uw) and fˆmax (wtsv) showed slightly lower mean values under unstable than under neutral and stable atmospheric conditions above the Hartheim Scots pine forest canopy (Table 5.8). In MP2 the stability dependence of fˆmax (uw) and fˆmax (wtsv) was more pronounced and this confirms the stability–dependent results obtained for fˆmax (u) and fˆmax (w). Based on above–canopy mean fˆmax (uw) and fˆmax (wtsv) values airflow under unstable atmospheric conditions was dominated by larger eddy scales than under stable atmospheric conditions. In MP1 below–canopy fˆmax (uw) showed the same behaviour as above–canopy fˆmax (uw), i.e. below–canopy fˆmax (uw) increased with growing atmospheric stability.

Mean below–canopy fˆmax (uw) values were higher than the corresponding above canopy values. The shift of below–canopy fˆmax (uw) towards higher frequencies was also reported by BALDOCCHI and MEYERS (1988b).

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Fig. 5.14: Normalised mean streamwise and vertical cospectral energy densities f Suw(f)/ u´w´ and f Swt sv (f)/ w´t sv ´ above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31). The f–4/3 lines indicate the expected inertial subrange drop–off

Only below–canopy mean fˆmax (wtsv) values deviated from the stability–dependent pattern obtained for the other cospectral peak frequencies: fˆmax (wtsv) was highest under unstable atmospheric conditions. Above and below the Hartheim Scots pine forest canopy mean Sˆmax (uw) and Sˆmax (wtsv) values were of similar magnitude under all atmospheric stability conditions in MP1 and MP2. Below the Scots pine forest canopy Sˆmax (uw) and Sˆmax (wtsv) were slightly greater.

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Fig. 5.15: Normalised mean streamwise and vertical cospectral energy densities f Suw(f)/ u´w´ and f Swt sv (f)/ w´t sv ´ above (z/h = 1.94) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31). The f–4/3 lines indicate the expected inertial subrange drop–off

Above and below the Hartheim Scots pine forest canopy the inertial subrange drop–off of the u´w´– and w´tsv´–cospectra was steeper (≈ –1.5 to –1.9) than the expected f–4/3 inertial subrange drop–off. This suggests that in the inertial subrange of the cospectra the eddy cascade of momentum and heat transfer was faster than expected. BALDOCCHI and HUTCHISON (1988) as well as AMIRO (1990b) found cospectral slopes in the inertial subrange close to –1. AMIRO (1990b) attributed this discrepancy to the lack of local isotropy in the inertial subrange in the individual velocity spectra. A relative deficit of cospectral energy at mid–frequencies as reported by AMIRO (1990b) was not observed during MP1 and MP2.

78

Table 5.8: Normalised cospectral peak frequencies ( fˆmax ) and normalised cospectral peak energy densities ( Sˆmax ) for the u´w´– and w´tsv´–cospectra above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) z/h

cospectra

atmospheric stability conditions

u´w´ 0.32 w´tsv´

u´w´ 1.94 w´tsv´

unstable neutral stable unstable neutral stable unstable neutral stable unstable neutral stable

5.5

Conditional sampling

5.5.1

Joint probability distribution

MP1 fˆmax 0.09 0.28 0.34 0.17 0.11 0.14 0.04 0.04 0.06 0.04 0.04 0.06

MP2 Sˆmax 0.20 0.20 0.17 0.22 0.15 0.21 0.13 0.16 0.15 0.13 0.15 0.14

fˆmax – – – – – – 0.03 0.06 0.07 0.03 0.06 0.07

Sˆmax – – – – – – 0.13 0.16 0.17 0.13 0.15 0.15

5.5.1.1 General remarks

The presence of turbulence structure was further investigated through joint probability distributions of the fluctuations of the streamwise and the vertical wind velocity component (u´ and w´) as well as of w´ and the fluctuations of the sonic temperature (tsv´). There are four possible combinations of (u´, w´) and (w´, tsv´) (quadrant I: outward interaction; quadrant II: ejection; quadrant III: inward interaction; quadrant IV: sweep) on an u´–w´ plane revealing the structure of turbulent transport more explicitly than the turbulence statistics (see Fig. 4.5). Joint probability distributions were constructed by counting the number of occurrences of (u´, w´) and (w´, tsv´) in 20 times 20 equally spaced classes between ±2 standard deviations of the corresponding time series. The number of discarded hourly joint probability distributions was 5 % to 7 % of the maximal possible number of hourly joint probability distributions (Table 5.2).

79

5.5.1.2 Turbulent momentum transfer

Above the Hartheim Scots pine forest canopy (z/h = 1.94) elliptical contour plots of σi– normalised (i = u, w) joint probability distributions of (u´, w´) point at a downward momentum transfer. They show no marked differences for different atmospheric stability conditions in MP1 (Fig. 5.16a–c) and MP2 (Fig. 5.16d–f). The σi–normalised joint probability distributions are asymmetrical and exhibit a correlation between u´ and w´. Neither serious skewness nor serious kurtosis can be seen in the above–canopy the contour plots. In both measurement periods the proportions of σi–normalised joint probability distributions of (u´, w´) in quadrants II and IV were smaller than in quadrants I and III (Table 5.9). Nonetheless, quadrants II and IV seem to dominate the turbulent momentum transfer. This discrepancy between smaller proportions of σi–normalised joint probability distributions of (u´, w´) and higher intensities in quadrants II and IV leads to the conclusion that turbulent events in quadrants II and IV must be more intense than the turbulent events in quadrants I and III and is a first indication for intermittent turbulent momentum transfer. In addition, for all atmospheric stability conditions the proportions of σi– normalised joint probability distributions of (u´, w´) in quadrant II were somewhat greater than the σi–normalised joint probability distributions of (u´, w´) in quadrant IV. Therefore sweep events must be slightly more intermittent and transport more momentum than ejection events (GARDINER, 1994; GREEN et al., 1995; KRUIJT et al., 2000). Within the subcanopy trunk space (z/h = 0.32) of the Hartheim Scots pine forest the momentum transfer dies down and no obvious structure in turbulent momentum transport can be found in the corresponding contour plots (Fig. 5.17a–c). No sweep–ejection pattern as shown for the above–canopy momentum transfer can be observed. Under all atmospheric stability conditions the proportions of σi–normalised joint probability distributions of (u´, w´) were greater in quadrants III and IV than in quadrants I and II (Table 5.9). The lack of a distinct below–canopy pattern of momentum transfer is consistent with the observations of GARDINER (1994) and KRUIJT et al. (2000).

80

Fig. 5.16: Mean σi–normalised (i = u, w) joint probability distributions of the fluctuations of the streamwise and vertical velocity components (u´, w´) above (z/h = 1.94) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) (a–c) and MP2 (2003–07–01 to 2003–07–31) (d–f). Contour lines stand for 0.002 probability intervals

81

Fig. 5.17: (a–c) Mean σi–normalised (i = u, w, tsv) joint probability distributions of the fluctuations of the streamwise and the vertical velocity components (u´, w´), (d–f) w´ and the sonic temperature (w´, tsv´) below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31). Contour lines stand for 0.002 probability intervals

82

Table 5.9: Mean proportions (%) of σi −normalised (i = u, w) joint probability distributions of the fluctuations of the streamwise and the vertical velocity components (u´, w´) in the quadrants I to IV above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) MP z/h % I II III IV

MP1

MP2 0.32 1.94 1.94 unstable neutral stable unstable neutral stable unstable neutral stable 0.23 0.22 0.23 0.28 0.29 0.28 0.28 0.28 0.27 0.23 0.22 0.22 0.23 0.20 0.22 0.22 0.21 0.22 0.27 0.29 0.28 0.29 0.33 0.30 0.29 0.31 0.30 0.27 0.27 0.26 0.20 0.18 0.20 0.20 0.20 0.21

5.5.1.3 Turbulent sensible heat transfer

Under unstable atmospheric conditions σi–normalised (i = w´, tsv´) joint probability distributions of (w´, tsv´) below (Fig. 5.17d–f) and above (Fig. 5.18a–c) the Hartheim Scots pine forest canopy in MP1 and MP2 (Fig. 5.18d–f) exhibit an asymmetric pattern including the quadrants I and III. An upward sensible heat transfer can be observed above and below the Hartheim Scots pine forest canopy. Despite the visual impression, the proportions of σi–normalised joint probability distributions of (w´, tsv´) under these atmospheric stability conditions were greater in the quadrants II and IV (Table 5.10). A similar pattern was also observed by MAITANI and SHAW (1990). Under neutral and stable atmospheric conditions a different pattern emerges. In MP1 below the Scots pine forest canopy the proportions of σi–normalised joint probability distributions of (w´, tsv´) were greater in the quadrants I and IV than in the quadrants II and III. Above the Scots pine forest canopy the proportions of σi–normalised joint probability distributions of (w´, tsv´) were greater in the quadrants I and III than in the quadrants II and IV. In MP2 quadrants II and IV showed the greatest proportions of σi– normalised joint probability distributions of (w´, tsv´). Based on the number and the proportions of σi–normalised joint probability distributions of (w´, tsv´) presented in Figs. 5.17d–f and 5.18a–f, the intensities of turbulent events per quadrant should be different as already seen for the turbulent momentum

83

transfer. In MP1 above the Scots pine forest canopy an upward turbulent heat transfer took place under unstable conditions (Fig. 5.18a) although the proportions of σi– normalised joint probability distributions of (w´, tsv´) in the quadrants I and III were smaller than in the quadrants II and IV. Under neutral und stable atmospheric conditions the proportions of σi–normalised joint probability distributions of (w´, tsv´) were smaller in the quadrants II and IV and the contour plots (Fig. 5.18b, c) indicate a downward turbulent sensible heat transfer. In MP2 the proportions of σi–normalised joint probability distributions of (w´, tsv´) in the quadrants I and III were smaller than in the quadrants II and IV under all atmospheric stability conditions. The form of the contour plots indicates upward turbulent heat transfer, which is most pronounced under unstable atmospheric stability conditions (Fig. 5.18d). According to the turbulent momentum transfer the discrepancy between smaller proportions of σi–normalised joint probability distributions of (w´, tsv´) and higher intensities in quadrants I and III leads to the conclusion that turbulent events in quadrants I and III must be more intense than the turbulent events in quadrants II and IV and hints at intermittent turbulent sensible heat transfer.

Table 5.10: Mean proportions (%) of σi −normalised (i = w, tsv) joint probability distributions of the fluctuations of the vertical velocity component and the sonic temperature (w´, tsv´) in the quadrants I to IV above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) MP z/h % I II III IV

MP1

MP2 0.32 1.94 1.94 unstable neutral stable unstable neutral stable unstable neutral stable 0.24 0.28 0.26 0.23 0.27 0.27 0.20 0.23 0.24 0.28 0.22 0.25 0.28 0.23 0.23 0.33 0.28 0.26 0.19 0.23 0.21 0.23 0.27 0.28 0.18 0.21 0.23 0.29 0.27 0.28 0.26 0.24 0.22 0.30 0.28 0.26

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Fig. 5.18: Mean σi–normalised (i = w, tsv) joint probability distributions of the fluctuations of the vertical velocity component and the sonic temperature (w´, tsv´) above (z/h = 1.94) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) (a–c) and MP2 (2003–07–01 to 2003–07–31) (d–f). Contour lines stand for 0.002 probability intervals

85

5.5.2

Quadrant analysis

5.5.2.1 General remarks

The relative importance of dominant, short–lived turbulent events is revealed by performing the quadrant analysis with an excluded hole region (H) of varying size (SHAW et al., 1983). H is a measure of intermittency in which, with increasing values of H, the occurrence and importance of intermittent events is revealed. Quadrant analysis was performed for both the turbulent momentum (u´w´) and the turbulent sensible heat flux (w´tsv´) above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy. Turbulent events exceeding five times the mean momentum and sensible heat flux for hole size H = 0 (5 % to 12 %) were excluded from the analysis since these events can dominate the results (SHAW et al., 1983; FEIGENWINTER, 2000). Momentum flux fractions (S(i,H)) and time fractions (T(i,H)) for different hole sizes were calculated by replacing the integrals presented in (4.4) and (4.6) by sums over the corresponding measurement interval.

5.5.2.2 Turbulent momentum transfer

Mean turbulent momentum flux fractions S(i,H) (i = I, II, III, IV) at z/h = 1.94 for four quadrants on a x–y plane (quadrant I: outward interaction; quadrant II: ejection; quadrant III: inward interaction; quadrant IV: sweep) under different atmospheric stability conditions are shown in Fig. 5.19 (MP1) and Fig. 5.20 (MP2). In both measurement periods under all atmospheric stability conditions sweep events exceeded ejection events (Table 5.11). This is in agreement with results obtained for wheat by FINNIGAN (1979b) and for corn by SHAW et al. (1983), but is in contrast to the results obtained by BERGSTRÖM and HÖGSTRÖM (1989), GAO et al. (1989), MAITANI and SHAW (1990), LEE and BLACK (1993a), SU et al. (1998), and NOVAK et al. (2000) who report that well above the forest canopy top ejection events become increasingly more important or even dominate over sweep events.

86

2.0

momentum flux fraction S(i,H)

1.6

unstable neutral stable

II

I

III

IV

1.2 0.8 0.4 0.0 0.0 0.4 0.8 1.2 1.6

z/h = 1.94

2.0 30 25 20 15 10

5

0 0

5

10 15 20 25 30

hole size H

Fig. 5.19: Mean turbulent momentum flux fractions S(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions above (z/h = 1.94) the Hartheim Scots pine forest canopy in MP1 (2002–11–01 to 2003–01–31) 2.0

momentum flux fraction S(i,H)

1.6

unstable neutral stable

II

I

III

IV

1.2 0.8 0.4 0.0 0.0 0.4 0.8 1.2 1.6

z/h = 1.94

2.0 30 25 20 15 10

5

0 0

5

10 15 20 25 30

hole size H

Fig. 5.20: Mean turbulent momentum flux fractions S(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions above (z/h = 1.94) the Hartheim Scots pine forest canopy in MP2 (2003–07–01 to 2003–07–31)

87

Table 5.11: Mean momentum flux fractions S(i,H) (i = I, II, III, IV) for hole size H = 0 above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11– 01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) MP MP1 MP2 z/h 0.32 1.94 1.94 S(i,0) unstable neutral stable unstable neutral stable unstable neutral stable I 1.49 1.44 1.50 0.45 0.63 0.50 0.53 0.33 0.63 II 1.40 1.47 1.47 0.59 1.03 0.75 0.70 0.52 0.86 III 0.92 0.97 1.10 0.33 0.33 0.37 0.34 0.21 0.43 IV 1.04 1.14 1.22 0.74 1.24 0.87 0.88 0.62 1.02

Fig. 5.21 illustrates the mean momentum flux fractions S(i,H) under different atmospheric stability conditions below the Scots pine forest canopy in MP1. Mean momentum flux fractions are more uniformly distributed under the four quadrants.

2.0

momentum flux fraction S(i,H)

1.6

unstable neutral stable

II

I

III

IV

1.2 0.8 0.4 0.0 0.0 0.4 0.8 1.2 1.6

z/h = 0.32

2.0 30 25 20 15 10

5

0 0

5

10 15 20 25 30

hole size H

Fig. 5.21: Mean turbulent momentum flux fractions S(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions below (z/h = 0.32) the Hartheim Scots pine forest canopy in MP1 (2002–11–01 to 2003–01–31)

88

Ejection events exceed sweep events. Outward and inward interaction events exhibit equally large values as ejection and sweep events. In all four quadrants mean momentum flux fractions decrease only slowly towards H = 30 and are non–zero. FINNIGAN (1979b), BALDOCCHI and HUTCHISON (1987), BALDOCCHI and MEYERS (1988a), LEE and BLACK (1993a), GREEN et al. (1995), and SU et al. (1998) also observed a similar increase of the importance of interaction events in the subcanopy trunk space. SHAW et al. (1983), GAO et al. (1989), MAITANI and SHAW (1990), and for artificial plant canopies in the wind tunnel, RAUPACH et al. (1986) and NOVAK et al. (2000) observed identified sweep events as the major contributors to the total momentum flux within the respective plant canopy. Mean S(i,0) values were – with few exceptions – smaller than 1 above the Hartheim Scots pine forest. Below the Scots pine forest canopy mean S(i,0) values exceeded 1 in most cases. BALDOCCHI and MEYERS (1988a) report magnitudes of S(i,0) to be 1 to 3 for a deciduous forest. In other studies (SHAW et al., 1983; BERGSTRÖM and HÖGSTRÖM, 1989; LEE and BLACK, 1993a; NOVAK et al., 2000) S(i,0) values were found to be generally smaller than 1. The mean momentum flux fraction ratios S(IV,0)/S(I,0), S(IV,0)/S(II,0), and S(IV,0)/S(III,0) under different atmospheric stability conditions give an impression of the importance of sweep events (Table 5.12). In MP1 within–canopy sweep events exceeded only inward interaction events. The sweep–to–ejection ratio (S(IV,0)/S(II,0)) below the Scots pine forest canopy was smaller than 1 with the highest values for stable atmospheric conditions. Similar results concerning the below–canopy momentum flux fraction distribution (z/h = 0.14) under near–neutral atmospheric conditions were reported by BALDOCCHI and HUTCHISON (1987). For an almond orchard they determined S(IV,0)/S(I,0), S(IV,0)/S(II,0), and S(IV,0)/S(III,0) to be 0.77, 0.86, and 0.79, respectively. BALDOCCHI and MEYERS (1988a) reported sweep–to–ejection ratios in the range of 1.1 to 2.3 below the canopy of a deciduous forest. Above the Scots pine forest canopy sweep events dominate over all other kinds of turbulence with no marked differences between MP1 and MP2. The sweep–to–ejection ratios were in the range of 1.16 and 1.26 with the highest values under unstable atmos-

89

pheric conditions. This is in contrast to the results of LEE and BLACK (1993a). They determined S(IV,0)/S(II,0) to be 0.86 at z/h =1.38, i.e. ejection events dominate over sweep events.

Table 5.12: Mean momentum flux fraction ratios S(IV,H)/S(I,H), S(IV,H)/S(II,H), and S(IV,H)/S(III,H) for H = 0 above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) MP

MP1

z/h S(IV,0)/S(i,0)

MP2

0.32

1.94

1.94

unstable neutral stable unstable neutral stable unstable neutral stable

S(IV,0)/S(I,0)

0.70

0.79

0.81

1.64

1.96

1.74

1.65

1.87

1.61

S(IV,0)/S(II,0)

0.74

0.78

0.83

1.25

1.20

1.16

1.26

1.19

1.18

S(IV,0)/S(III,0)

1.13

1.17

1.11

2.23

3.09

2.34

2.55

2.92

2.37

The relative importance of uncorrelated (S(I,0) + S(III,0)) to organised contributions (S(II,0) + S(IV,0)) to the turbulent momentum transfer at hole size H = 0 can be examined by the ratio ES (SHAW et al., 1983): ES =

S(I,0) + S(III,0) S(II,0) + S(IV,0)

(5.3)

In MP1 and MP2 above–canopy mean ES values varied in the same range with the least negative values under neutral atmospheric conditions (Table 5.13). In MP1 within– canopy ES values ranged between –0.92 and –0.99. BALDOCCHI and MEYERS (1988a) presented ES values on the order of –0.3 to –0.8, LEE and BLACK (1993a) reported ES values between –0.26 and –0.39 in the layer z/h = 0.6 to z/h = 1.38, –2.44 at z/h = 0.12, and –3.45 at z/h = 0.42. ES values observed by BERGSTRÖM and HÖGSTRÖM (1989) above a Scots pine forest were roughly in the range of –0.2 to –0.4. Mean ES values close to –1 within the subcanopy trunk space of the Hartheim Scots pine forest indicate that uncorrelated and organised contributions to the turbulent momentum transfer were on the same order of magnitude and confirm the results found by the σi–normalised (i = u, w) joint probability distributions of (u´, w´).

90

Above the Hartheim Scots pine forest organised contributions to the turbulent momentum transfer were roughly twice as large as uncorrelated contributions.

Table 5.13: Mean ratios of uncorrelated to organised contributions (ES) to the turbulent momentum transfer above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) z/h 0.32

1.94

ES

atmospheric stability conditions

MP1 –0.99 –0.92 –0.97 –0.56 –0.45 –0.54

unstable neutral stable unstable neutral stable

MP2 – – – –0.56 –0.48 –0.56

5.5.2.3 Turbulent sensible heat transfer

For mean turbulent heat flux fraction values HF(i,H) (i = I, II, III, IV) for H = 0 under different atmospheric stability conditions a clear pattern as presented for S(i,0) cannot be observed in MP1 and MP2 (Table 5.14).

Table 5.14: Mean turbulent heat flux fractions HF(i,H) (i = I, II, III, IV) for H = 0 above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) MP

MP1

z/h

MP2

0.32

HF(i,0) unstable

1.94

1.94

neutral

stable

unstable

neutral

stable

unstable

neutral

stable

I

1.05

0.98

1.19

0.88

1.04

0.55

0.76

1.21

0.77

II

0.78

1.18

1.05

0.71

1.26

0.85

0.39

1.04

0.80

III

0.92

0.82

1.13

0.83

1.10

0.54

0.67

1.19

0.74

IV

0.68

0.99

0.99

0.69

1.28

0.82

0.36

0.96

0.72

91

In MP1 under unstable atmospheric conditions quadrants I and III dominated the turbulent sensible heat transfer (Fig. 5.22) above the Scots pine forest canopy. This is in accordance with the presented normalised joint probability distributions of (w´, tsv´) and is a further indication that organised motions causing an upward heat transfer were dominant these conditions. Under neutral stratification quadrant IV exhibited the largest value and under stable atmospheric conditions quadrants II and IV were dominant contributors to the turbulent sensible heat transfer. A slightly different picture evolved in MP2 (Fig. 5.23). Under unstable and neutral atmospheric conditions quadrants I and III were dominant whereas under stable atmospheric conditions the turbulent heat flux fractions were almost equally distributed under the four quadrants. Below the Hartheim Scots pine forest canopy quadrants I and III were dominant under unstable and stable atmospheric conditions in MP1 (Fig. 5.24). Quadrants II and IV dominated under neutral atmospheric stability conditions.

2.0 1.6

unstable neutral stable

II

I

III

IV

heat flux fraction HF(i,H)

1.2 0.8 0.4 0.0 0.0 0.4 0.8 1.2 1.6

z/h = 1.94

2.0 30 25 20 15 10

5

0 0

5

10 15 20 25 30

hole size H

Fig. 5.22: Mean turbulent heat flux fractions HF(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions above (z/h = 1.94) the Hartheim Scots pine forest canopy in MP1 (2002–11–01 to 2003–01–31)

92

2.0 1.6

unstable neutral stable

II

I

III

IV

heat flux fraction HF(i,H)

1.2 0.8 0.4 0.0 0.0 0.4 0.8 1.2 1.6

z/h = 1.94

2.0 30 25 20 15 10

5

0 0

5

10 15 20 25 30

hole size H

Fig. 5.23: Mean turbulent heat flux fractions HF(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions above (z/h = 1.94) the Hartheim Scots pine forest canopy in MP2 (2003–07–01 to 2003–07–31) 2.0 1.6

unstable neutral stable

II

I

III

IV

heat flux fraction HF(i,H)

1.2 0.8 0.4 0.0 0.0 0.4 0.8 1.2 1.6

z/h = 0.32

2.0 30 25 20 15 10

5

0 0

5

10 15 20 25 30

hole size H

Fig. 5.24: Mean turbulent heat flux fractions HF(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions below (z/h = 0.32) the Hartheim Scots pine forest canopy in MP1 (2002–11–01 to 2003–01–31)

93

The importance of the mean contributions of the four quadrants I, II, III, and IV to the turbulent transfer of sensible heat was analysed by the ratios HF(III,0)/HF(I,0), HF(III,0)/HF(II,0), and HF(III,0)/HF(IV,0) for different atmospheric stability conditions (Table 5.15). In both measurement periods above and below the Hartheim Scots pine forest canopy HF(III,0) dominated over HF(II,0) and HF(IV,0) under unstable atmospheric conditions. Mean values of HF(III,0)/HF(I,0) were smaller than 1 and indicate that warm updraft contributions to sensible heat flux densities exceeded cool downdraft contributions (LEE and BLACK, 1993b). LEE and BLACK (1993b) estimated HF(III,0)/HF(I,0) values smaller than 1 only above their forest canopy. Cool downdraft contributions exceeded warm updraft contribution in the middle and the base of their forest canopy (z/h = 0.6 and z/h = 0.42), but close to the ground, at z/h = 0.12, the warm updraft contributions again exceeded the cool downdraft contributions.

Table 5.15: Mean turbulent heat flux fraction ratios HF(III,H)/HF(I,H), HF(III,H)/ HF(II,H), and HF(III,H)/HF(IV,H) for H = 0 above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) MP

MP1

z/h HF(III,0)/HF(i,0)

MP2

0.32

1.94

1.94

unstable neutral stable unstable neutral stable unstable neutral stable

HF(III,0)/HF(I,0)

0.87

0.84

0.95

0.94

1.06

0.99

0.89

0.98

0.96

HF(III,0)/HF(II,0)

1.17

0.69

1.07

1.17

0.88

0.64

1.73

1.14

0.92

HF(III,0)/HF(IV,0)

1.35

0.82

1.13

1.21

0.86

0.66

1.86

1.24

1.03

The relative importance of interaction quadrants (contributions to an upward turbulent heat transfer) to ejection and sweep quadrants (contributions to a downward turbulent heat transfer) at H = 0 can be examined by the ratio EHF (BERGSTRÖM and HÖGSTRÖM, 1989): E HF =

S(II,0) + S(IV,0) S(I,0) + S(III,0)

(5.4)

In MP1 and MP2 above the Hartheim Scots pine forest canopy EHF mean values ranged between –0.53 and –1.54 (Table 5.16). The most negative values occurred under stable,

94

the least negative EHF values under unstable atmospheric conditions. Below–canopy EHF values showed a different pattern with the most negative value under neutral atmospheric conditions and were in the range of –0.74 to –1.21. The magnitudes of the EHF values determined in MP1 and MP2 clearly departed from the EHF values determined by LEE and BLACK (1993b) and BERGSTRÖM and HÖGSTRÖM (1989) who determined EHF values of order –0.1 to –0.3. According to LEE and BLACK (1993b) EHF values greater than –1 indicate that the turbulent transport of sensible heat is of large scale and not driven by the local temperature gradient. Above the Hartheim Scots pine forest canopy, at least under unstable atmospheric conditions, quadrants II and IV contributed just as much (MP2) or even more (MP1) to the turbulent sensible heat transfer as quadrants I and III producing EHF values smaller than –1. Bearing in mind the conclusion of LEE and BLACK (1993b) this means – under unstable atmospheric conditions – that the turbulent sensible heat transfer above the Hartheim Scots pine forest was driven by the local temperature gradient. Otherwise, the turbulent sensible heat transfer was driven by large scale motions. Below the Hartheim Scots pine forest canopy only under neutral stratification EHF value were smaller than –1.

Table 5.16: Mean ratios of uncorrelated to organised contributions (EHF) to the turbulent sensible heat transfer above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) z/h 0.32

1.94

atmospheric stability conditions unstable neutral stable unstable neutral stable

EHF MP1 –0.74 –1.21 –0.88 –0.82 –1.18 –1.54

MP2 – – – –0.53 –0.83 –1.01

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5.5.2.4 Cumulative momentum and heat flux fractions

Cumulative mean momentum flux fractions SH = ∑i =1 S(i, H) , heat flux fractions 4

HFH =

∑

4 i =1

HF(i, H ) , and time fractions TH =

∑

4 i =1

T (i, H ) are measures of intermittency

(SHAW et al., 1983). SH, HFH, and TH for hole sizes up to H = 30 are shown for MP1 in Figs. 5.25 and 5.26, and for MP2 in Fig. 5.27. In all figures it is obvious that SH, HFH, and TH are different functions of H. At all times above and below the Hartheim Scot pine forest canopy rather large amounts of momentum and sensible heat were transferred in relatively small fractions of time. For example, in MP1 below the Hartheim Scots pine forest canopy (z/h = 0.32) under unstable atmospheric conditions HFH determined at H = 5 made up for 77 % of the total momentum flux but was realised in only 29 % of TH (Table 5.17).

Table 5.17: Cumulative turbulent momentum flux fractions SH, heat flux fractions HFH, and time fractions TH for the hole sizes H = 5, 10, 20 above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) MP

MP1

z/h H

MP2

0.32 SH (%)

TH (%)

1.94

HFH (%)

TH (%)

SH (%)

TH (%)

1.94

HFH (%)

TH (%)

SH (%)

TH (%)

HFH (%)

TH (%)

unstable 5

77

29

69

18

54

15

67

20

59

13

53

11

10

55

14

49

8

34

8

44

10

36

5

31

3

20

28

4

28

3

17

5

24

4

17

1

16

1

neutral 5

77

32

73

24

67

26

77

32

42

8

77

23

10

55

16

49

10

42

14

57

19

18

2

58

12

20

30

6

25

3

19

7

34

10

5

0

37

5

stable 5

81

31

79

24

60

19

61

17

66

17

65

17

10

60

16

59

12

37

10

36

7

44

7

41

7

20

34

6

35

5

17

5

18

3

21

2

21

2

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Below–canopy SH and TH showed uniform behaviour with increasing hole size with no significant differences under the different atmospheric stability conditions (Fig. 5.25). Under stable atmospheric conditions below–canopy HFH showed a higher level than HFH under unstable and neutral atmospheric conditions (Fig. 5.26). The corresponding TH values nonetheless revealed that under unstable atmospheric conditions more momentum was transferred in shorter time than under stable conditions. In MP1 above the Hartheim Scots pine forest canopy the decrease in turbulent momentum transfer and cumulative time with increasing hole size was also similar with only minor differences under different atmospheric stability conditions. For example, under unstable atmospheric conditions 54 % of above–canopy SH at H = 5 were realised in only 15 % of TH. Under unstable atmospheric conditions the intermittency of the momentum transfer was most pronounced whereas it was least pronounced under neutral atmospheric conditions. Mean HFH showed the highest level under neutral atmospheric conditions, but intermittency was most pronounced under stable atmospheric conditions. In MP2 the effects of different atmospheric stability conditions on SH and HFH were more distinct than in MP1whereas TH remained relatively uniform with increasing hole size. Lowest SH values were observed under neutral atmospheric stability conditions (Fig. 5.27). Under these atmospheric stability conditions large amounts of the momentum transfer occurred in the smallest cumulative time fractions. Highest SH values up to H = 30 were seen under stable atmospheric conditions, but they also occurred during the largest cumulative time fractions, and therefore, momentum transfer was least intermittent under these atmospheric stability conditions. HFH and corresponding TH values decreased fastest under unstable atmospheric conditions with increasing hole size above the Hartheim Scots pine forest canopy. Turbulent sensible heat transfer was most intermittent under these conditions. Inversely, under neutral atmospheric stability conditions turbulent sensible heat transfer above the Scots pine forest canopy was least intermittent. The results obtained by quadrant analysis for the different kinds of turbulence above and below the Hartheim Scots pine forest canopy are in general agreement with the results obtained for other forest canopies.

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1.0 0.8

z/h = 1.94

0.8

0.6

0.6

0.4

0.4

0.2

0.2 z/h = 1.94

0.0

0.0

1.0

1.0 z/h = 0.32

0.8

0.8

0.6

0.6

0.4

0.4

0.2

cum. time fraction T H

cum. momentum flux fraction S H

1.0

unstable neutral stable

0.2

z/h = 0.32

0.0

0.0 0

5

10 15 20 25 30 0

5

10 15 20 25 30

hole size H

Fig. 5.25: Cumulative momentum flux fractions SH and cumulative time fractions TH above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) 1.0 0.8

z/h = 1.94

0.8

0.6

0.6

0.4

0.4 0.2

0.2 z/h = 1.94

0.0

0.0

1.0

1.0 z/h = 0.32

0.8

0.8

0.6

0.6

0.4

0.4

0.2

cum. time fraction T H

cum. heat flux fraction HFH

1.0

unstable neutral stable

0.2

z/h = 0.32

0.0

0.0 0

5

10 15 20 25 30 0

5

10 15 20 25 30

hole size H

Fig. 5.26: Cumulative heat flux fractions HFH and cumulative time fractions TH above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions MP1 (2002–11–01 to 2003–01–31)

1.0

1.0

unstable neutral stable

0.8

0.8

0.6

0.6

0.4

0.4 0.2

0.2 z/h = 1.94

0.0

0.0

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0

cum. time fraction T H

cum. heat flux fraction HFH cum. stress fraction S H

98

0.0 0

5

10 15 20 25 30 0

5

10 15 20 25 30

hole size H

Fig. 5.27: Cumulative momentum (stress) flux fractions SH, heat flux fractions HFH, and time fractions TH above (z/h = 1.94) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP2 (2003–07–01 to 2003–07–31)

Using quadrant analysis, BALDOCCHI and HUTCHISON (1987), BERGSTRÖM and HÖGSTRÖM

(1989), MAITANI and SHAW (1990), LEE and BLACK (1993a), and LEE and

BLACK (1993b) have also shown that a large amount of momentum and sensible heat is transferred in rather small fractions of time above and below various forest canopies.

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6.

DISCUSSION

6.1

Turbulence measurements over tall plant canopies

KAIMAL and FINNIGAN (1994) assume that much of the turbulence data collected in tall plant canopies during the recent decades cannot give reliable information on airflow characteristics. Especially airflow measurements within plant canopies are subject to serious uncertainties because normally no spatial averaging is done and within−canopy turbulence is very variable. Most studies investigating airflow characteristics over tall plant canopies are single−point measurements concentrating on selected time series (LU and FITZJARRALD, 1994). Nonetheless, it could be shown in numerous studies based on single−point statistics of turbulence that turbulent airflow over tall plant canopies is dominated by large coherent structures and exhibits more similarities with airflow in a plane mixing layer than in a boundary layer (FINNIGAN, 2000). As most of the experimental studies carried out in real plant canopies, results of turbulence measurements presented in this work represent single−point measurements and are not spatially averaged. But in contrast to most of the turbulence studies reported in literature two comparatively long measurement periods, MP1 (2002−11−01 to 2003−01−31) and MP2 (2003−07−01 to 2003−07−31), were chosen. MP1 and MP2 cover a broad range of atmospheric stability conditions as well as different seasons and provide more general results for the turbulence characteristics over the horizontally relative homogeneous Scots pine forest canopy at the forest meteorological experimental site Hartheim.

6.2

Experimental setup

6.2.1

In situ measurements

Results are presented of turbulence measurements above and below (height range: z/h = 0.14 to z/h = 2.08) a Scots pine forest canopy using a combination of two sonic anemometers and a profile of eight cup anemometers. Data collected under different atmospheric stability conditions are compared to the turbulence characteristics determined for other tall plant canopies, in particular to forests. The most significant implications concerning the ground–based instrumentation are summarised as follows:

100

-

A better vertical resolution of fast three−dimensional turbulence measurements, especially in the upper part of a forest canopy and at a forest canopy top, enables a better association of turbulence parameterisation with the detailed canopy architecture (VILLANI et al., 2003). The two employed sonic anemometers (z/h = 0.32 and z/h = 1.94) are the minimum instrumentation to fulfil the requirements needed to characterise the turbulence structure of a tall plant canopy.

-

The below–canopy sonic measurement height (z/h = 0.32) suffers from the very low wind speeds. Very low wind speeds are reality at this experimental site within the subcanopy trunk space of the Hartheim Scots pine forest.

-

Further improvement of the interpretation of variations in canopy turbulence can be achieved by the separate determination of above– and within−canopy stability conditions. It has been shown that atmospheric stability conditions above and within the same plant canopy as well as between different canopy types (sparse and dense canopies) differ (e.g. JACOBS et al., 1992; KRUIJT et al., 2000; MAHRT et al., 2000).

-

The application of the eddy covariance method is not without drawbacks, especially below the Scots pine forest canopy. The underlying theory relies on both spatial homogeneity and temporal stationarity (KAIMAL and FINNIGAN, 1994; FOKEN and WICHURA, 1996). Below the Scots pine forest canopy these conditions were rarely realised.

6.2.2

Sodar measurements above the Hartheim Scot pine forest

Sodar measurements were carried out at the top of TL (z/h = 1.27), i.e. just above the Scots pine forest canopy. The Scintec FAS64 was operated throughout MP1 and MP2 continuously. So far no reliable results of sodar measurements above a forest canopy are documented in literature and known to the author. Thus, (1) no experimental guidelines on the subject are established, and (2) limited knowledge exists on the airflow structure above forests up to heights exceeding in situ instrumentation based on experimental data. However, since very few data passed simple data quality and plausibility checks a very low percentage of sodar data could be used for further analysis. In MP2 the FAS-

101

run version 2.0.0 p40 improved wind data availability up to 520 a.g.l. considerably, but a negligible percentage of these data were comparable in magnitude to the in situ measurements. All data measured in MP2 had to be discarded. Reasons for the poor sodar data quality may be: -

background noise: e.g. traffic (SANTOVASI, 1986), trees (SANTOVASI, 1986; KURZEJA,

1994), aircrafts (PARRY et al., 1975), birds and insects (PARRY et al., 1975,

MASTRANTONIO et al., 1999), -

noise due to fixed echoes: e.g. meteorological tower (WITTICH, 1990), trees (KURZEJA, 1994; VOGT and THOMAS, 1994),

-

noise due to high wind speeds (FINKELSTEIN et al., 1986; MELAS, 1991),

-

noise due to the impact of raindrops (SANTOVASI, 1986; FINKELSTEIN et al., 1986),

-

neutral stratified ABL in the late afternoon (SANTOVASI, 1986; ANTONIOU et al., 2003),

-

errors due to theoretical limitations, instrumental errors, systematic refraction effects, errors due to vertical velocities introduced by horizontal wind vector components because of infinite antenna beamwidth (SPIZZICHINO, 1974; NEFF and COULTER, 1986; MELAS, 1990; THOMAS and VOGT, 1993a; COULTER, 1997; ITO, 1997; ANTONIOU et al., 2003),

-

error introduced by spatial and temporal pulse volume separation of individual sodar measurements (KRISTENSEN and GAYNOR, 1986; GAYNOR and KRISTENSEN, 1986; GAYNOR, 1994),

-

reduction of emitted acoustic power during selected periods (e.g. nighttime) in the vicinity to inhabited areas (PIRINGER, 1994; THOMAS and VOGT, 1993b; VOGT and THOMAS, 1994).

A serious problem at the experimental site Hartheim seems to be the degradation of sodar signals due to background noise, most likely caused by the nearby autobahn to the east of the experimental site. Together with the reduction of the emitted acoustic power during nighttime due to complaints of the inhabitants of Hartheim and the employed small enclosure, background noise accounts at least partially for the poor sodar data

102

quality. Another problem must be fixed echoes, i.e. the sound of side lobes of the emitted acoustic beams propagating near the forest canopy, which is reflected off stationary objects because a considerable amount of data exhibited a zero Doppler shift. It is not clear which object could have reflected sound waves to cause fixed echoes since the FAS64 was placed purposely above the Hartheim Scots pine forest canopy. With regard to the turbulence parameter σw, noise reduces the signal−to−noise ratio (SNR), which must be large enough throughout the measurement period to produce plausible results. If values from only a portion of the sample period are included due to small values of SNR, the variance is likely to be overestimated because the more turbulent portions of the signal that are associated with larger values of SNR are preferentially sampled (COULTER, 1997). No clear conclusion can be drawn concerning the influence of the elevated position of the sodar and the background noise induced by tree swaying.

6.3

Family portrait of canopy turbulence

Turbulence characteristics determined in MP1 and MP2 above and below the Hartheim Scots pine forest canopy are primarily compared to the turbulence characteristics presented in the ‘family portrait’ of canopy turbulence (RAUPACH et al., 1996). The ‘family portrait’ results (1) show that there is a broad agreement in turbulence characteristics among various types of tall plant canopies, and (2) lead to the argument that the plane mixing layer analogy rather than the boundary layer analogy is the appropriate model for air mass exchange near the top of tall plant canopies (FINNIGAN, 2000). The results of the ‘family portrait’ are nonetheless limited by three factors (BRUNET and IRVINE, 2000): -

turbulence characteristics of the compiled studies are not calculated in a consistent manner,

-

data runs are limited to only one representative point per plant canopy providing no measure of variability,

-

only near neutral atmospheric stability conditions are investigated.

103

6.4

Turbulence characteristics

6.4.1

Turbulence statistics

RAUPACH et al. (1996) compared airflow statistics in the vicinity of tall plant canopies to the airflow statistics of a plane mixing layer and found that the statistics of both types of airflows are analogues in many respects. Important common characteristics of these types of flow are, e.g. the presence of an inflexion point in the mean wind speed profile, the relative role between ejection and sweep events, and the turbulent scales of the active coherent motions. Results obtained for both measurement periods (MP1 and MP2) concerning the mean wind speed profile measurements show that the -

normalised wind speeds profiles are inflected near the top of the Hartheim Scots pine forest,

-

normalised shear length scales Ls/h at the canopy top are slightly lower than 0.5h as proposed by RAUPACH et al. (1996), except under unstable atmospheric conditions in MP2.

Fast turbulence measurements within the subcanopy trunk space (z/h = 0.32) of the Hartheim Scots pine forest canopy illustrate that -

wind direction regimes above and below the Scots pine forest canopy differ,

-

normalised standard deviations σu/ u * and σw/ u * are in the range as observed for other tall plant canopies (RAUPACH et al., 1996),

-

normalised mean momentum flux − u´w´ / u *2 values are (close to) 0 at this measurement height,

-

as a result of the low wind speeds mean Tiu and Tiw values are very high with Tiu values higher than 2, and Tiw around 1,

-

mean Sku values are generally near 0,

-

mean Skw values are negative under all atmospheric stability conditions with the most negative value under neutral atmospheric stability conditions,

104

-

mean Kru values are close to 0, mean Krw values are positive and rather high (1.33 to 2.09),

-

Lu/h as well as Lw/h vary in a small range under different atmospheric stability conditions and are in general accordance with results reported for other forests (RAUPACH et al., 1996).

The observed mean below–canopy turbulence statistics lead to the conclusion that intense turbulent sweep events are not very dominate within the Hartheim Scots pine forest canopy down to z/h = 0.32. The effectiveness in mean momentum transfer is low under unstable and stable atmospheric conditions at this height. Nonetheless, one has to bear in mind that the presented mean turbulence statistics are the result of comparatively long periods with very low mean wind speeds, which alternate with shorter periods with higher wind speeds. Turbulence statistics under neutral atmospheric stability conditions are most pronounced but for many quantities at the low end of the results presented by RAUPACH et al. (1996). Statistics of the fast turbulence measurements above the Hartheim Scots pine forest canopy (z/h = 1.94) in MP1 and MP2 reveal that -

mean − u´w´ / u *2 values vary little with atmospheric stability conditions exhibiting greatest mean values under neutral atmospheric stability conditions,

-

mean σu/ u * and σw/ u * values are greater than 1, but rather low compared to the results reported for other forests (RAUPACH et al., 1996),

-

mean Tiu values cluster around 0.3 under all atmospheric stability conditions,

-

mean Tiw values cluster around 0.2 under all atmospheric stability conditions,

-

mean Sku values are generally positive and near 0,

-

mean Skw values are close to 0 and not for all atmospheric stability conditions negative,

-

mean Kru values are close to 0 and always negative,

-

mean Krw values exhibit greater values than Kru which are always positive,

-

mean Lu/h values are greatest under neutral atmospheric stability conditions,

105

-

mean Lw/h values are greatest under neutral atmospheric stability conditions in MP1 and under unstable stratification in MP2.

Results obtained for the turbulence statistics above the Hartheim Scots pine forest canopy indicate that the turbulent air mass transfer at z/h = 1.94 is riddled with large structures and intense turbulent events accounting for a substantial amount of air mass exchanged. Sundry atmospheric stability conditions lead to differences in turbulence statistics. Since the chosen atmospheric stability classes are quite crude the differences in turbulence statistics are sometimes marginal. Apart from different absolute mean values observations in different seasons exhibit no significant changes in the stability dependent pattern of turbulence statistics. In conclusion it can be stated that the turbulence statistics determined above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy in MP1 and MP2 are in general agreement with results presented for other tall plant canopies for the same height ranges. In order to gain deeper insight in turbulence structures more turbulence measurement heights are needed.

6.4.2

Spectral analysis

Important features of turbulence spectra and cospectra just above and within tall plant canopies are the location of the spectral peak frequencies of the wind velocity components and the slope of the inertial subrange. In MP1 the results of the spectral analysis below the Hartheim Scots pine forest canopy show that -

fˆmax (w), and fˆmax (uw) values are lowest under unstable atmospheric conditions

indicating largest eddy scales, -

under neutral atmospheric conditions both Sˆmax (u) and Sˆmax (w) exhibit greatest values,

-

the slopes of the inertial subranges of both u– and w–spectra are steeper at mid−frequencies than the slope of the inertial subranges above the Scots pine forest canopy under all atmospheric stability conditions,

106

-

mean fˆmax (u) values are shifted towards higher frequencies under all atmospheric stability conditions compared to above−canopy results,

-

mean Sˆmax (u), Sˆmax (w), Sˆmax (uw), and Sˆmax (wtsv) values are slightly greater than above the canopy under all atmospheric stability conditions.

LIU et al. (2001) state that the shift of fˆmax (u) is due to higher contributions from smaller eddies in the horizontal velocity spectra because the large eddies from the mean airflow above the forest canopy are broken down into small−scale eddies by the plant elements when transferred down to below the canopy. The shift of fˆmax (w) towards higher frequencies below the Hartheim Scots pine forest canopy in consequence of (1) approaching the Scots pine forest floor and the subsequent limitation of the eddy scales (FINNIGAN, 1979a), and (2) the transfer of energy to smaller scales through action of form drag by the foliage elements (RAUPACH and SHAW, 1982; RAUPACH et al., 1986) is not observed. RAUPACH and SHAW (1982) explain the steeper drop−off at mid−frequencies of the below−canopy u– and w–spectra by the generation of wake−turbulence caused by form drag on canopy elements. AMIRO and DAVIS (1988) speculate that under stable atmospheric within−canopy conditions an inertial subrange cannot be established. The second peak in their spectra seems to be caused by wake turbulence. AMIRO (1990b) suggests that near the bottom of a forest canopy Kolmogorov scaling theory does not hold because mean airflow is low, turbulence intensities are high, and turbulence is intermittent. FITZJARRALD and MOORE (1990) suggest that under nighttime conditions TKE is being created by buoyancy in the unstable lower canopy during their study. GARDINER (1994) shows that the tree resonant frequencies lie in the region where energy is being lost from the turbulence spectra. KRUIJT et al. (2000) give two possible explanations for the pattern of the within−canopy u– and w–spectra. First, a relatively high level of instrument noise, and second, new turbulent energy is being created at high frequencies. Since both the streamwise and the vertical spectra show a similar shape KRUIJT et al. (2000) suggest that new turbulent energy was being created in the lower canopy at their forest site. The reason for such

107

patterns could be wake production where low frequency TKE is broken down by drag on canopy elements and transferred to higher frequencies (AMIRO and DAVIS, 1988; KAIMAL and FINNIGAN, 1994; FINNIGAN, 2000). w–spectra especially support the idea of a source of smallest scale turbulence, which may be attributed to wake generation (MAZZONI, 1996; KRUIJT et al., 2000). As stated by KRUIJT et al. (2000) this effect should be considered as important in the forest canopy where the vegetation area is highest. In the subcanopy trunk space of the Hartheim Scots pine forest (z/h = 0.32) the plant area density is very small. KRUIJT et al. (2000) speculate that the observed pattern might be attributable to the low overall level of turbulence close to the forest floor where high frequency pressure fluctuations or remnants of wakes behind canopy elements become relatively more visible in the spectra. BALDOCCHI and HUTCHISON (1988) and BALDOCCHI and MEYERS (1988b) explain the steepness of the inertial subrange within their plant canopies in terms of a short−circuiting of the energy cascade (‘spectral short cut’) due to the breaking up of large−scale eddies by canopy elements and the subsequent shift of turbulent energy directly to higher frequency wake turbulence. VILLANI et al. (2003) tend to attribute the high frequency pattern observed in within−canopy velocity spectra to the relative increase of instrument noise, at least during stable atmospheric conditions when turbulence is suppressed. Effects of atmospheric stability conditions on mean fˆmax (u) and fˆmax (w) as observed by LIU et al. (2001) are apparent above the Hartheim Scots pine forest canopy only in MP2 for unstable atmospheric conditions. Mean fˆmax (u) is shifted towards a lower peak frequency indicating that larger eddies than under neutral and stable atmospheric conditions dominate the turbulence structure above the Scots pine forest canopy. Under stable atmospheric conditions within the subcanopy trunk space of the Scots pine forest a shift of fˆmax (u) and fˆmax (w) towards higher frequencies is observable.

The relationship of the peak frequencies of the streamwise and vertical velocity components above and below tall plant canopies is important in the light of the discussion of coherent turbulence structures. Compared to the peak frequency values above the Hart-

108

heim Scots forest canopy, below−canopy mean fˆmax (u) values are shifted towards higher frequencies whereas below−canopy fˆmax (w) values are shifted towards lower frequencies. Invariance of fˆmax (u) and fˆmax (w) would indicate a common mechanism in which eddies pass through the forest (RAUPACH et al., 1996). Since this is not observed for other tall plant canopies RAUPACH et al. (1996) postulate that large eddies above the canopy modify the streamwise wind velocity but have no significant effect on vertical motions. The application of spectral analysis to identify dominating and especially coherent turbulence structures is not satisfactory because (1) the turbulent flow field should have to be a pure superposition of waves (FARGE, 1992), (2) the occasional sweep and ejection events form only a part of the information that contributes to the atmospheric turbulence spectrum but this information cannot be identified as dominant frequency within the wide range that encompasses the spectrum (MARSHALL et al., 2002).

6.4.3

Conditional sampling

Results of mean joint probability distributions and quadrant analysis correspond to the results obtained by the turbulence statistics. Below the Hartheim Scots pine forest canopy (z/h = 0.32) contour plots of the mean normalised joint probability distributions of (u´, w´) and quadrant analysis confirm that -

under all stability conditions the nature of turbulence looks rather Gaussian, and indicates that there is no obvious structure to the momentum transport at this measurement height,

-

the contour plots of mean normalised joint probability distributions of (w´, tsv´) as well as the quadrant analysis reflect that under unstable atmospheric conditions an upward transfer of sensible heat takes place (quadrants I and III).

Above the Hartheim Scots pine forest canopy (z/h = 1.94) contour plots of the mean joint probability distributions of (u´, w´) as well as the quadrant analysis indicate that -

in MP1 and MP2 mean momentum transfer is dominated by coherent motions under all atmospheric stability conditions, i.e. by ejection and sweep events (quad-

109

rants II and IV) with the most pronounced pattern under neutral atmospheric stability conditions, -

in MP1 and MP2 mean joint probability distributions of (w´, tsv´) show a mean upward heat transfer under unstable atmospheric conditions,

-

in MP1 a mean downward heat transfer is exhibited under neutral and stable atmospheric conditions,

-

in MP2 under unstable atmospheric conditions a pronounced mean upward heat transfer occurs.

The phenomenon of increasing importance of the interaction quadrants I and III in momentum transfer below plant canopies as observed within the Hartheim Scots pine forest canopy was also observed in other tall plant canopies. BALDOCCHI and HUTCHISON (1987) attribute the greater magnitude of the interaction events within an almond orchard to either sloshing of the air near the ground or to the existence of systematic wake circulations within the canopy. LEE and BLACK (1993a) as well as GREEN et al. (1995) attribute the increasing importance of the interaction events to the small and sometimes negative momentum flux densities in the lower forest canopy. In contrast to that SHAW et al. (1983), GAO et al. (1989), MAITANI and SHAW (1990), and for artificial plant canopies in the wind tunnel RAUPACH et al. (1986) as well as NOVAK et al. (2000) observed that sweep events are the major contributors to the total momentum transfer within the respective plant canopies. The results of conditional sampling lead to the conclusion that the air mass exchange above and below the Hartheim Scots pine forest canopy can be characterised as intermittent. For the turbulent momentum transfer intermittency appears to be lower at the subcanopy measurement height than above the Hartheim Scots pine forest canopy whereas the turbulent sensible heat transfer seems to be more intermittent at this height. The variability of the conditionally sampled momentum flux with atmospheric stability conditions is exhibited by the quadrant analysis showing that intermittency is greatest under stable atmospheric conditions with minor differences between MP1 and MP2. GAO et al. (1992) found a decrease of the strength of ejection and sweeps events from unstable to slightly stable conditions, KRUIJT et al. (2000) report the highest degree of intermittency under neutral atmospheric stability conditions above a forest canopy.

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6.5

Plane mixing layer analogy

The results of this work concerning the turbulence characteristics above and below the Hartheim Scots pine forest canopy are in general agreement with observations in other tall plant canopies (RAUPACH et al., 1996; KRUIJT et al., 2000; VILLANI et al., 2003). Most notably are the: -

inflexion of the mean wind speed profile near the Scots pine forest canopy top responsible for hydrodynamical instabilities,

-

order of the normalised shear length scale as the vertical length scale associated with strong vertical air mass exchange,

-

indications towards organised motions above and below the Scots pine forest canopy.

For neutral atmospheric stability conditions RAUPACH et al. (1996) predict a ratio of streamwise spacing of the dominant coherent eddies (Λx) to the shear length scale (Ls) near the top of tall plant canopies of Λx/Ls ≈ 8.1 ± 0.3. Nevertheless, despite all the similarities in turbulence characteristics determined at the forest meteorological experimental site Hartheim and other tall plant canopies the evaluation of the plane mixing layer analogy based on the presented results fails. The physical picture of the turbulent structure in tall plant canopies proposed by RAUPACH et al. (1996) requires the determination of turbulence characteristics at the plant canopy top. In MP1 and MP2 no turbulence measurements were available at the Hartheim Scots pine forest canopy top.

6.6

Plant canopy characteristics

The detailed knowledge of the structure and architecture of a plant canopy is a prerequisite to understand the canopy turbulence characteristics just above and within tall plant canopies because canopy turbulence characteristics depend on both canopy characteristics and near−ground atmospheric dynamics (FINNIGAN, 2000). Although RAUPACH et al. (1996) show that after suitable scaling there is a broad agreement between measurements of turbulence statistics within and above various real and artificial plant canopies a close relation between the turbulence characteristics and varying canopy characteristics is reported by AMIRO (1990a), GREEN et al. (1995), KATUL et al. (1999), FINNIGAN

111

(2000), KRUIJT et al. (2000), NOVAK et al. (2000), and MARKKANEN et al. (2003). For example, GREEN et al. (1995) report for three differently thinned Sitka spruce stands a horizontal variation in the range of 20 % to 90 % in turbulence statistics depending on tree density. NOVAK et al. (2000) state that the variations in turbulence characteristics in their field and wind tunnel studies can be explained by systematic differences in canopy morphology. A detailed description of canopy characteristics is beyond the scope of the present work. The Hartheim Scots pine forest canopy is described by the vertical distribution of the vegetation area density. For the present work this simple canopy description is sufficient and acceptable because the canopy structure and architecture of the Hartheim Scots pine forest is rather homogeneous. Existing parameterisations of plant canopy characteristics in various plant canopy airflow models (WILSON and SHAW, 1977; MEYERS and PAW U, 1986; KATUL and ALBERTSON,

1998; MASSMAN and WEIL, 1999) are mainly based on the vertical profile of

the cumulative leaf drag area (ζ) which subsumes the effects of leaf area density (a), drag coefficient (Cd), and aerodynamic sheltering (Pm) on the wind field (THOM, 1971, MASSMAN, 1997). Improvement of these parameterisations and the subsequent effects on canopy turbulence might be achieved by use of optical measurements of gap fraction (MARCOLLA et al., 2003; CESATTI and MARCOLLA, 2004).

112

113

7.

CONCLUSIONS

Results of field measurements of airflow characteristics obtained above and below a horizontally homogeneous Scots pine forest canopy in two comparatively long measurement periods were presented. The results, especially those obtained above the Scots pine forest, are in general agreement with measurements made over various other tall plant canopies particularly the ‘family portrait’ of canopy turbulence (RAUPACH et al., 1996). The below–canopy results are partially in contrast to the results of other studies. This discrepancy is seen to be mainly due to the effects of very low wind speeds below the Scots pine forest canopy over rather long periods and its effects on all analysed turbulence variables. The effects of the low wind speeds are consequently echoed in the mean values of all turbulence characteristics determined for different stability conditions. Turbulence statistics, spectral analysis, and conditional sampling indicate that air mass between the Scots pine forest and the atmosphere at the forest meteorological experimental site Hartheim is to a considerable degree exchanged by large, intermittent turbulence structures. To confirm the findings of this work and to gain a more detailed view of canopy turbulence characteristics at the experimental site Hartheim, it is necessary to -

measure turbulence characteristics at more heights with sonic anemometers, especially in the vicinity of and directly at the Scots pine forest canopy top,

-

find a way to employ remote sensing devices in the Scots pine forest to be able to analyse airflow characteristics to heights exceeding the roughness sublayer,

-

parameterise the characteristics of the Scots pine forest canopy in more detail,

-

establish a more selective atmospheric stability classification to avoid undesirable averaging effects on mean turbulence variables,

-

establish methods like the wavelet analysis (COLLINEAU and BRUNET, 1993; GAO and LI, 1993; LU and FITZJARRALD, 1994; FEIGENWINTER, 2000; BRUNET and IRVINE,

2000; MARSHALL et al., 2002) which complement the detection of coherent

structures over tall plant canopies.

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To gain a more general view of canopy turbulence, it is furthermore necessary to conduct canopy turbulence studies under non–ideal conditions, e.g. in complex terrain as has already been done by TURNIPSEED et al. (2003) and VAN GORSEL et al. (2003).

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125

LIST OF ABBREVIATIONS

ABL

atmospheric boundary layer

a.g.l.

above ground level

CBL

convective boundary layer

CI

capping inversion

CL

canopy layer

CML

canopy mixing layer

EC

eddy covariance

EL

equilibrium layer

EZ

entrainment zone

FA

free atmosphere

FAS64

flat array sodar with 64 transducers

FFT

fast Fourier transform

IBL

internal boundary layer

ISL

inertial sublayer

LAI

leaf area index

LES

large eddy simulation

ML

mixed layer

MPx

measurement period (x = 1, 2)

NBL

nocturnal boundary layer

PBL

planetary boundary layer

PML

plane mixing layer

RL

residual layer

RSL

roughness sublayer

SBL

stable boundary layer

SL

surface layer

SNR

signal–to–noise ratio

sodar

sound detection and ranging

Thigh

higher tower at the experimental site Hartheim

Tlow

lower tower at the experimental site Hartheim

126

127

LIST OF SYMBOLS

a

leaf area density

(m2 m–3)

cp

specific heat of air at constant pressure

(J kg–1 K–1)

d

zero plane displacement

(m)

dp

sonic anemometer measuring path length

(m)

dd

wind direction

(°)

f

frequency

(Hz)

fc

cyclic frequency

(Hz)

fˆ

normalised frequency

g

acceleration due to gravity

(m s–2)

h

mean plant canopy height

(m)

k

wavenumber

(m–1)

kB

Bragg wavenumber

(m–1)

l

size of inhomogeneities of the acoustic refractive index in the atmosphere

(m)

m

empirical constant

p

air pressure

(hPa)

q

specific moisture

(g kg–1)

q*

surface layer humidity scale

(kg kg–1)

r

distance separating two measurements

(m)

ruw

correlation coefficient

rv

distance between sodar antenna and scatter volume

(m)

t

time

(s)

tsp

sampling period

(s)

tsv

acoustic virtual (sonic) temperature

(K)

u

longitudinal wind velocity component

(m s–1)

ur

radial wind velocity component

(m s–1)

u*

friction velocity

(m s–1)

v

lateral wind velocity component

(m s–1)

w

vertical wind velocity component

(m s–1)

z

height above ground

(m)

z0

aerodynamic roughness length

(m)

A

sodar antenna area

(m2)

128

(m s–1)

C

speed of sound

Cd

drag coefficient

C T2

temperature structure function

(k2 m2/3)

C 2v

velocity structure function

(m4/3 s–2)

EHF

ratio of uncorrelated to organised contributions of the turbulent momentum flux densities

ES

ratio of uncorrelated to organised contributions of the turbulent heat flux densities

FH

turbulent sensible heat flux

(W m–2)

G

global radiation

(W m–2)

H

hole size

HFH

cumulative heat flux fractions

HF(i,H) heat flux fraction in quadrant i for hole size H (K m s–1)

Hs

turbulent kinematic surface heat flux

I

instrument function

I(i,H)

conditioning function

Kh

turbulent diffusion coefficient for heat in the ISL

(m2 s–1)

Km

turbulent diffusion coefficient for momentum in the ISL

(m2 s–1)

Kq

turbulent diffusion coefficient for water vapour in the ISL

(m2 s–1)

Kri

kurtosis (i = u, v, w)

K*h

turbulent diffusion coefficient for heat in the RSL

(m2 s–1)

K*m

turbulent diffusion coefficient for momentum in the RSL

(m2 s–1)

K*q

turbulent diffusion coefficient for water vapour in the RSL

(m2 s–1)

L

Obukhov length

(m)

Li

single–point Eulerian integral length scale (i = u, v, w)

(m)

Ls

shear length scale

(m)

M

wind vector

(m s–1)

MKE

mean kinetic energy

(kg m2 s–2)

Ls

shear length scale

(m)

PAI

plant area index

Pe

emitted acoustic power

Pm

sheltering factor

Pr

received acoustic power

(W)

Rn

net radiation

(W m–2)

(W)

129

Si

spectral energy density (i = u, v, w)

(m2 s–1)

Suw

cospectral energy density for momentum flux

(m–2 s)

Swtsv

cospectral energy density for sensible heat flux

(m K)

SH

cumulative momentum flux fractions

Sˆ

normalised spectral energy density

Ski

skewness (i = u, v, w)

S(i,H)

momentum flux fraction in quadrant i for hole size H

T

absolute temperature

(K)

TKE

turbulent kinetic energy

(kg m2 s–2)

Tr

atmospheric transmission

Ta

air temperature

(°C)

Th

air temperature at z = h

(°C)

Ti

single–point Eulerian integral time scale (i = u, v, w)

Tv

virtual temperature

TH

cumulative time fractions

T*

surface layer temperature scale

T(i,H)

time fraction in quadrant i for hole size H

U

horizontal wind speed

(m s–1)

Uh

wind speed at z = h

(m s–1)

U0

wind speed on the low–speed side of a PML

(m s–1)

Vd

wind velocity component along the sonic anemometer measuring path

(m s–1)

Vn

wind velocity component normal to the sonic anemometer measuring path

(m s–1)

WKE

wake kinetic energy

(kg m2 s–2)

X

empirical constant

αi

tilt angles (i = N, E, S, W)

β

nondimensional factor

γ

ratio of wind velocity component normal to sonic path to speed of sound

δw

vorticity thickness

(m)

ε

viscous dissipation rate of TKE

(m2 s3)

ζ

leaf drag area

η

Kolmogorov microscale

(K) (°C)

(°)

(m)

130

θ

potential temperature

κ

von Karman constant

λ

wavelength

(m)

ρ

air density

(kg m–3)

σi

standard deviation of wind vector components (i = u, v, w)

(m s–1)

τ

time lag

(s)

υ

kinematic viscosity of air

(m2 s–1)

φh

nondimensional SL function for heat

φm

nondimensional SL function for momentum

φq

nondimensional SL function for water vapour

∆z

Range resolution

(m)

χ

scattering cross–section

(m–1)

Θ

scatter angle

(°)

Λ

integral length scale of turbulence

(m)

Λx

streamwise spacing between successive coherent turbulent structures

(m)

Ψm

nondimensional stability function

(K)

131

LIST OF FIGURE CAPTIONS

page Fig. 3.1 Fig. 3.2

Fig. 3.3 Fig. 4.1 Fig. 4.2 Fig. 4.3 Fig. 4.4 Fig. 4.5 Fig. 5.1 Fig. 5.2 Fig. 5.3

Fig. 5.4 Fig. 5.5

Fig. 5.6

Daytime structure of the troposphere over a forest with a meteorological measurement tower (after MONCRIEFF et al., 2000) .................. Idealised energy spectrum in the atmospheric boundary layer showing the energy containing range (A), the inertial subrange (B), and the dissipation range (C). Si (i = u, v, w) is the spectral energy density, k the wavenumber, Λ the integral length scale of turbulence and η the Kolmogorov microscale (adopted from KAIMAL and FINNIGAN, 1994)...................................................................................................... Idealised development of a plane mixing layer (PML) above a tall plant canopy (FINNIGAN, 2000) ............................................................. Location of the forest meteorological experimental site Hartheim in the southern Upper Rhine Valley .......................................................... Normalised vegetation area density function a(z/h)/amax(z/h) at the forest meteorological experimental site Hartheim in the year 2003 ..... Scots pine forest with micrometeorological tower Thigh (z/h = 2.11) at the forest meteorological experimental site Hartheim in August 2002 ....................................................................................................... Micrometeorological tower TL (z/h = 1.35) with the flat array sodar FAS64 on top at the forest meteorological experimental site Hartheim in the year 2002 ............................................................................ Quadrants (I, II, III, IV) and hyperbolic excluded regions (grey region) for the streamwise and vertical velocity fluctuations (u´ and w´) (adapted from SHAW et al., 1983) ................................................... Hourly mean horizontal wind speeds U(z) at different heights at the forest meteorological experimental site Hartheim in December 2002.. Hourly mean horizontal wind speeds U(z) at different heights at the forest meteorological experimental site Hartheim in July 2003 ........... Combined mean wind speed profiles U(z) under different atmospheric stability conditions (number of profiles: unstable: 20; neutral: 7; stable: 78) at the forest meteorological experimental site Hartheim up to z/h = 14.08 (200 m a.g.l.) in MP1 (2002–11–01 to 2003–01– 31).......................................................................................................... Normalised mean wind speed profiles U(z)/Uh under different atmospheric stability conditions in (a) MP1 (2002–11–01 to 2003–01– 31) and (b) MP2 (2003–07–01 to 2003–07–31) up to z/h = 2.08 ......... Normalised mean wind speed differences (U29.6–U6.0)/U29.6 at the experimental site Hartheim as a function of friction velocity u * and surface layer temperature scale T* in MP1 (2002–11–01 to 2003– 01–31).................................................................................................... Normalised mean wind speed differences (U29.6–U6.0)/U29.6 at the experimental site Hartheim as a function of friction velocity u * and surface layer temperature scale T* in MP2 (2003–07–01 to 2003– 07–31)....................................................................................................

20

25 29 37 38 39 40 45 49 49

50 51

53

54

132

page Fig. 5.7

Fig. 5.8

Fig. 5.9

Fig. 5.10

Fig. 5.11

Fig. 5.12

Fig. 5.13

Fig. 5.14

Fig. 5.15

Comparison of wind directions above (dd27.5m) and below (dd4.5m) the Hartheim Scots pine forest canopy in MP1 (2002–11–01 to 2003–01–31). (a) comparison of all available wind direction data, (b–f) comparison of wind direction data for different classes of friction velocity u * ..................................................................................... (a) Mean streamwise and vertical turbulence intensities Tiu and Tiw, (b) normalised mean streamwise and vertical standard deviations σu/ u * and σw/ u * above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31)................... (a) Normalised mean momentum flux densities − u´w´ / u *2 , (b) normalised mean streamwise and vertical integral length scales Lu/h and Lw/h above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31)................................. Mean correlation coefficient –ruw above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01– 31).......................................................................................................... (a) Mean streamwise and vertical velocity skewnesses Sku and Skw, (b) mean streamwise and vertical velocity kurtoses Kru and Krw above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) ...................................................... Normalised mean streamwise and vertical spectral energy densities f Si(f)/ σi2 (i = u, w) above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31). The f–2/3 lines indicate the expected inertial subrange drop–off.......................... Normalised mean streamwise and vertical spectral energy densities f Si(f)/ σi2 (i = u, w) above (z/h = 1.94) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07– 31). The f–2/3 lines indicate the expected inertial subrange drop–off .... Normalised mean streamwise and vertical cospectral energy densities f Suw(f)/ u´w´ and f Swt sv (f)/ w´t sv ´ above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01– 31). The f–4/3 lines indicate the expected inertial subrange drop–off .... Normalised mean streamwise and vertical cospectral energy densities f Suw(f)/ u´w´ and f Swt sv (f)/ w´t sv ´ above (z/h = 1.94) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003– 07–01 to 2003–07–31). The f–4/3 lines indicate the expected inertial subrange drop–off..................................................................................

56

60

62

64

65

68

70

72

73

133

page Fig. 5.16 Mean σi–normalised (i = u, w) joint probability distributions of the fluctuations of the streamwise and vertical velocity components (u´, w´) above (z/h = 1.94) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) (a–c) and MP2 (2003–07–01 to 2003–07–31) (d–f). Contour lines stand for 0.002 probability intervals............................... Fig. 5.17 (a–c) Mean σi–normalised (i = u, w, tsv) joint probability distributions of the fluctuations of the streamwise and the vertical velocity components (u´, w´), (d–f) w´ and the sonic temperature (w´, tsv´) below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31). Contour lines stand for 0.002 probability intervals ....... Fig. 5.18 Mean σi–normalised (i = w, tsv) joint probability distributions of the fluctuations of the vertical velocity component and the sonic temperature (w´, tsv´) above (z/h = 1.94) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) (a–c) and MP2 (2003–07–01 to 2003– 07–31) (d–f). Contour lines stand for 0.002 probability intervals ........ Fig. 5.19 Mean turbulent momentum flux fractions S(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions above (z/h = 1.94) the Hartheim Scots pine forest canopy in MP1 (2002–11–01 to 2003–01–31) ............................................................... Fig. 5.20 Mean turbulent momentum flux fractions S(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions above (z/h = 1.94) the Hartheim Scots pine forest canopy in MP2 (2003–07–01 to 2003–07–31) ............................................................... Fig. 5.21 Mean turbulent momentum flux fractions S(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions below (z/h = 0.32) the Hartheim Scots pine forest canopy in MP1 (2002–11–01 to 2003–01–31) ............................................................... Fig. 5.22 Mean turbulent heat flux fractions HF(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions above (z/h = 1.94) the Hartheim Scots pine forest canopy in MP1 (2002–11–01 to 2003–01–31) ............................................................... Fig. 5.23 Mean turbulent heat flux fractions HF(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions above (z/h = 1.94) the Hartheim Scots pine forest canopy in MP2 (2003–07–01 to 2003–07–31) ............................................................... Fig. 5.24 Mean turbulent heat flux fractions HF(i,H) (i = I, II, III, IV) for various hole sizes H under different atmospheric stability conditions below (z/h = 0.32) the Hartheim Scots pine forest canopy in MP1 (2002–11–01 to 2003–01–31) ............................................................... Fig. 5.25 Cumulative momentum flux fractions SH and cumulative time fractions TH above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) .........................................

76

77

80

82

82

83

87

88

88

93

134

page Fig. 5.26 Cumulative heat flux fractions HFH and cumulative time fractions TH above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions MP1 (2002–11–01 to 2003–01–31) ...................................................... Fig. 5.27 Cumulative momentum (stress) flux fractions SH, heat flux fractions HFH, and time fractions TH above (z/h = 1.94) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP2 (2003–07–01 to 2003–07–31) ..................................................

93

94

135

LIST OF TABLE CAPTIONS

page Table 4.1 Table 4.2

Table 5.1

Table 5.2

Table 5.3

Table 5.4

Table 5.5

Table 5.6

Table 5.7

Main stand characteristics of the Hartheim Scots pine forest in the years 2002 and 2003........................................................................... Measurement heights of different wind measuring systems at the two micrometeorological towers (Thigh and Tlow) at the forest meteorological experimental site Hartheim during the measurement periods MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31)................................................................................... Mean values of global radiation G, net radiation Rn, air temperature at z = h Th, wind speed at z = h Uh, friction velocity u * , and the surface layer temperature scale T* at the forest meteorological experimental site Hartheim in the measurement periods MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31)....................................................................................... Number of hourly mean values of different atmospheric stability conditions (unstable, neutral, and stable) at the forest meteorological experimental site Hartheim in the measurement periods MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07– 31)....................................................................................................... Mean shear length scale Ls at the canopy top of the Hartheim Scots pine forest under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07– 31)....................................................................................................... Compilation of cited turbulence studies, which were conducted in tall plant canopies and to which the results of this work are compared (several of the cited studies are part of the ‘family portrait’ of canopy turbulence (RAUPACH et al., 1996))................................... Mean turbulence statistics above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01– 31) and MP2 (2003–07–01 to 2003–07–31) ...................................... Number of hourly (co)spectra used to calculate mean (co)spectra above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31)....................................................................................... Normalised spectral peak frequencies ( fˆmax ) and normalised spectral peak energy densities ( Sˆ ) for the streamwise and vertical

38

41

47

48

55

58

61

67

max

velocity component (u and w) above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01– 31) and MP2 (2003–07–01 to 2003–07–31) ......................................

69

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Table 5.8

Table 5.9

Table 5.10

Table 5.11

Table 5.12

Table 5.13

Table 5.14

Table 5.15

Normalised cospectral peak frequencies ( fˆmax ) and normalised cospectral peak energy densities ( Sˆmax ) for the u´w´– and w´tsv´– cospectra above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003– 07–01 to 2003–07–31)........................................................................ Mean proportions (%) of σi −normalised (i = u, w) joint probability distributions of the fluctuations of the streamwise and the vertical velocity components (u´, w´) in the quadrants I to IV above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07– 31)....................................................................................................... Mean proportions (%) of σi −normalised (i = w, tsv) joint probability distributions of the fluctuations of the vertical velocity component and the sonic temperature (w´, tsv´) in the quadrants I to IV above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31)....................................................................................... Mean momentum flux fractions S(i,H) (i = I, II, III, IV) for hole size H = 0 above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07– 01 to 2003–07–31).............................................................................. Mean momentum flux fraction ratios S(IV,H)/S(I,H), S(IV,H)/S(II,H), and S(IV,H)/S(III,H) for H = 0 above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31) .................. Mean ratios of uncorrelated to organised contributions (ES) to the turbulent momentum transfer above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01– 31) and MP2 (2003–07–01 to 2003–07–31) ...................................... Mean turbulent heat flux fractions HF(i,H) (i = I, II, III, IV) for H = 0 above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31)....................................................................................... Mean turbulent heat flux fraction ratios HF(III,H)/HF(I,H), HF(III,H)/ HF(II,H), and HF(III,H)/HF(IV,H) for H = 0 above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07– 31).......................................................................................................

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page Table 5.16 Mean ratios of uncorrelated to organised contributions (EHF) to the turbulent sensible heat transfer above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01– 31) and MP2 (2003–07–01 to 2003–07–31) ...................................... Table 5.17 Cumulative turbulent momentum flux fractions SH, heat flux fractions HFH, and time fractions TH for the hole sizes H = 5, 10, 20 above (z/h = 1.94) and below (z/h = 0.32) the Hartheim Scots pine forest canopy under different atmospheric stability conditions in MP1 (2002–11–01 to 2003–01–31) and MP2 (2003–07–01 to 2003–07–31).......................................................................................

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Berichte des Meteorologischen Institutes der Universität Freiburg Nr. 1:

Fritsch, J.: Energiebilanz und Verdunstung eines bewaldeten Hanges. Juni 1998.

Nr.2:

Gwehenberger, J.: Schadenpotential über den Ausbreitungspfad Atmosphäre bei Unfällen mit Tankfahrzeugen zum Transport von Benzin, Diesel, Heizöl oder Flüssiggas. August 1998.

Nr. 3:

Thiel, S.: Einfluß von Bewölkung auf die UV-Strahlung an der Erdoberfläche und ihre ökologische Bedeutung. August 1999.

Nr. 4:

Iziomon, M.G.: Characteristic variability, vertical profile and modelling of surface radiation budget in the southern Upper Rhine valley region. Juli 2000.

Nr. 5:

Mayer, H. (Hrsg.): Festschrift „Prof. Dr. Albrecht Kessler zum 70. Geburtstag“. Oktober 2000.

Nr. 6:

Matzarakis, A.: Die thermische Komponente des Stadtklimas. Juli 2001.

Nr. 7:

Kirchgäßner, A.: Phänoklimatologie von Buchenwäldern im Südwesten der Schwäbischen Alb. Dezember 2001

Nr. 8:

Haggagy, M.E.-N.A.: A sodar-based investigation of the atmospheric boundary layer. September 2003

Nr. 9:

Rost, J.: Vergleichende Analyse der Energiebilanz zweier Untersuchungsflächen der Landnutzungen “Grasland“ und „Wald“ in der südlichen Oberrheinebene. Januar 2004

Nr. 10: Peck, A.K.: Hydrometeorologische und mikroklimatische Kennzeichen von Buchenwäldern. Juni 2004 Nr. 11: Schindler, D.: Characteristics of the atmospheric boundary layer over a Scots pine forest. Juni 2004