Low-Frequency Effects on Eddy Covariance Fluxes ... - AMS Journals

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JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY

VOLUME 46

Low-Frequency Effects on Eddy Covariance Fluxes under the Influence of a Low-Level Jet THARA V. PRABHA, MONIQUE Y. LECLERC,

AND

ANANDAKUMAR KARIPOT

The University of Georgia, Griffin, Georgia

DAVID Y. HOLLINGER U.S. Department of Agriculture Forest Service, Durham, New Hampshire (Manuscript received 21 September 2005, in final form 22 June 2006) ABSTRACT Turbulent bursts observed over a tall forest canopy during the initiation of a nocturnal low-level jet (LLJ) are studied with the help of wavelet analysis. The burst of turbulence is observed in response to a shear instability associated with the initiation of LLJ. Turbulent kinetic energy, momentum, and CO2-rich cold air are transferred downward by large eddies with length scales that are higher than the LLJ height. Microfronts are observed over the canopy as a secondary instability that enhances the mixing processes within and above the canopy. The scale-dependent wavelet correlation analysis reveals that countergradient fluxes result from low frequencies, whereas cogradient flux is associated with high-frequency turbulent motions. The countergradient flux is initially noted at low frequencies, and, through coherent motions, it is transferred to smaller scales with a nearly 20-min delay. The countergradient flux dominates at the initiation of the event and reduces net flux, whereas enhanced cogradient flux at the decay of the event increases the net flux. The wavelet correlation coefficient corresponding to cogradient and countergradient fluxes is applied to segregate three regions of the spectra corresponding to “turbulent,” “coherent,” and “noncoherent” large scales. These findings are used to examine the implications on eddy covariance flux measurements.

1. Introduction Nocturnal respiratory release of carbon dioxide (CO2) is an integral component of the ecosystem carbon balance. Several studies (Goulden et al. 1996; Greco and Baldocchi 1996; Lindroth et al. 1998; Chen et al. 1999; Hollinger et al. 1999; Aubinet et al. 2000; Saleska et al. 2003) have reported an underestimation of CO2 fluxes often associated with inadequate mixing in the stable boundary layer (SBL). Sporadic outbreaks of turbulence are also a common occurrence in the SBL and enhance the mixing but at the same time introduce uncertainties in measured fluxes. Information about how sporadic outbreaks of turbulence and enhanced vertical diffusion near the surface (Nappo 1991) contribute to significant changes in nocturnal fluxes is criti-

Corresponding author address: M. Y. Leclerc, Laboratory for Environmental Physics/Biometeorology Program, The University of Georgia, 1109 Experiment St., Griffin, GA 30223. E-mail: [email protected] DOI: 10.1175/JAM2461.1 © 2007 American Meteorological Society

JAM2461

cal in the understanding of factors that underlie large uncertainties in nocturnal carbon flux estimates. SBLs are characterized by a host of atmospheric phenomena that contribute to intermittent turbulence (Nappo 1991; Coulter and Doran 2002; Doran 2004), such as wave– turbulence interactions (Einaudi and Finnigan 1993), shear-flow instability (Newsom and Banta 2002), density currents (Sun et al. 2002), downward-propagating solitary and internal gravity waves (Sun et al. 2004), and low-level jets (LLJs; Banta et al. 2002). In the presence of an LLJ, SBLs are often coupled with upside-down boundary layers (Mahrt 1999; Mahrt and Vickers 2002). The turbulence is generated at elevated layers by high wind shear, and turbulent kinetic energy (TKE) is transported downward (Banta et al. 2002, 2003). Several studies (Wu and Raman 1998; Corsmeier et al. 1997; Reitebuch et al. 2000; Beyrich 1994; Kalthoff et al. 2000; Mathieu et al. 2005) have linked the transport of trace gases and the presence of nocturnal concentration maxima at the surface to the downward transport during LLJ events. The dynamics

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of jets in laboratory and geophysical flows (Thorpe and Guymer 1977) has been well documented, but far less attention has been given to the interaction between the LLJ and the underlying vegetated surface. In the presence of an accelerating LLJ above the surface, the wind speed in the lower layers of the atmosphere also increases. Instabilities over the tall forest canopy increase with increasing wind speed and amplify canopy waves (Pulido and Chimonas 2001). Waveturbulence events in the canopy are observed to be a venting mechanism for CO2 accumulated within the canopy (Fitzjarrald and Moore 1990). Karipot et al. (2006) reported that LLJs could influence CO2 fluxes over a tall forest by introducing intermittent turbulent periods within the canopy. Measurements at the Howland Forest “AmeriFlux” site in Maine have shown anomalously high nocturnal CO2 respiration (Hollinger et al. 2004) when turbulent periods are preceded by calm periods. This large efflux was presumed to be closely associated with the mixing of accumulated CO2rich subcanopy air with the air above. Our analysis at this site showed that CO2 concentration gradients in the roughness layer are significantly modified during moderately strong and weak LLJs and are characterized by turbulent bursts (Prabha et al. 2006, manuscript submitted to Bound.-Layer Meteor.). Some of these turbulence events have the potential to contribute to vertical advection from the residual boundary layer as the air is brought down to lower layers with little dilution (Nappo 1991). The eddy covariance (hereinafter EC) CO2 fluxes during such occasions have signatures attributed to atmospheric dynamics, in addition to the true biological contribution. In this paper, we present a case in which low-frequency events are found to penetrate the roughness sublayer and introduce bursts over the canopy at the initiation of an LLJ. Spectral characteristics of the event observed over the canopy and small-scale intermittent events associated with it are examined with the help of wavelet analysis. Scaledependent characteristics of energy, downward flux of energy, friction velocity u , and CO2 flux are examined * to elucidate observed events. Wavelet correlation coefficients of odd and even quadrants representing the exchange efficiency are introduced as a new approach to separate the noncoherent low-frequency, coherent, and turbulence contributions to flux and energy. This approach is applied in this study to discuss implications of LLJ-induced low-frequency events on flux estimates.

2. The site characteristics Continuous EC measurements have been carried out over a coniferous forest canopy at the Howland Ameri-

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Flux site (45.204°N, 68.740°W) since 1996 (Hollinger et al. 1999). The site is located in a seemingly homogeneous terrain (Hollinger et al. 2004) over an 80-kmwide basin of the Penobscot River and in the lee of the northern Appalachian Mountain range, with elevations varying between 1 and 2.9 km. There is a hill situated 4 km northwest of the site with an elevation of approximately 150 m. The evidence of LLJs in this region has been documented in the climatic data (Bonner 1968) of the nearby radiosonde stations at Caribou and Portland. The jet likely originates from a combination of baroclinic and sea-breeze frontal influences, because the site is only 100 km away from the Atlantic Ocean.

3. Measurements The canopy was 20 m tall during 2001, and EC measurements were made at 29 m above the ground using a three-dimensional sonic anemometer (Model SAT-211/ 3K; Applied Technologies, Inc., of Boulder, Colorado) and a fast-response CO2/water infrared gas analyzer (Model LI-6262; Li-Cor, Inc., of Lincoln, Nebraska). Data were sampled at 5 Hz. Ambient concentrations of CO2 at 5, 12, 19, and 29 m were recorded with a Li-Cor nondispersive infrared gas analyzer (Model 6251). Details pertaining to instrumentation, data collection, and postfield signal processing have been presented earlier (Hollinger et al. 1999, 2004). During August of 2001, wind profile measurements were carried out with a boundary layer sodar (PA2; Remtech, Inc., of Velizy, France) up to a height of 1 km and a vertical resolution of 20 m. The sodar was setup approximately 150 m away from the flux tower.

4. Methods of data analysis Wavelet analysis of EC data is used to examine time– frequency characteristics of a strong turbulent burst after the evening transition. Wavelet analysis is extensively used to study intermittent and coherent eddies of the canopy turbulence (Collineau and Brunet 1993; Gao and Li 1993; Turner et al. 1994; Qiu et al. 1995; Katul et al. 1998; Brunet and Irvine 2000; Thomas and Foken 2005). The approach is efficient in identifying scale-dependent intermittency and intensity of turbulence (Anandakumar and Kailas 1999; Terradellas et al. 2001), which is relevant in analyzing features of the event studied here. The wavelet analysis is carried out on detrended, 6-h time series of velocities, temperature, and CO2 concentration (u, ␷, w, T, and CO2). Details of the analysis are presented in the appendix. A three-axis coordinate rotation (Kaimal and Finnigan 1994) was performed on

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the wind components for each 1-h period to remove the effect of instrument tilt and terrain irregularities. Derived parameters from the wavelet analysis constitute spectral (Katul et al. 1998; Cuxart et al. 2002) and cospectral analysis. More details on the application of wavelet analysis for intermittent events, nonstationary turbulence, and identification of small-scale and coherent structures of lower frequency in the SBL are given by Terradellas et al. (2001). We introduce a scale-dependent wavelet correlation coefficient WCC, defined as w,x

WCC

共n, s兲 ⫽

冋

|s⫺1CWnw,x共n, s兲|2 |s⫺1W nw共n, s兲|2 |s⫺1W nx共n, s兲|2

册

1Ⲑ2

.

共1兲

WCC is a ratio of the cospectra CWn and corresponding variance spectra Wn at scale s as described in the appendix. WCC is a measure of phase coherence between vertical velocity w and x (where x is u, ␪, or CO2). We have considered the real part of CWn in the analysis to relate the results with cospectra. WCC is similar to the spectral correlation coefficient introduced by McBean and Miyake (1972) as a measure of transfer efficiency. The scale (frequency) dependency of WCC allows us to examine the exchange efficiency at different scales of interest. This approach is further extended with the help of quadrant analysis to isolate the turbulent exchange associated with an event that contributes positive or negative flux. The turbulent vertical exchange of CO2 is partitioned into four quadrants (Shaw 1985) depending on the sign of wavelet coefficients (Giostra et al. 2002; Cava et al. 2005) corresponding to the w and CO2 concentration. The four quadrants representations are quadrant 1 with positive CO⬘2 and positive w⬘, quadrant 2 with positive CO⬘2 and negative w⬘, quadrant 3 with negative CO⬘2 and negative w⬘, and quadrant 4 with negative CO⬘2 and positive w⬘. Quadrants 1 and 3 contribute to a positive (cogradient) flux, and quadrants 2 and 4 contribute to a negative (countergradient) flux. The value of WCC varies between ⫺1 and ⫹1, depending on the dominance of countergradient and cogradient flux contributions at a specific frequency. In the case of CO2 flux, the positive contribution refers to exchange in which an eddy moving upward carrying CO2-rich air (ejections) or a downward-moving eddy with CO2-depleted air (sweeps) contributes to net flux. In the negative contribution, upward-moving CO2depleted air or downward-moving CO2-rich air causes the exchange. We use relative importance of the cogradient and countergradient fluxes at a range of frequencies/scales to isolate contributions to fluxes from noncoherent low-frequency (wavelength ␭ k H, where H is LLJ height), coherent low-frequency, and turbulent

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motions. A combination of WCC and bandpassfiltering property (Terradellas et al. 2001) of wavelet is used to filter the TKE, vertical flux of TKE, and the CO2 flux associated with large eddies (␭ ⱖ H ), coherent eddies, and finescale turbulence. The correlation of energy between adjacent scales (Yamada and Ohkitani 1991) is used to elucidate the cascade of CO2 variance and is defined as Rj ⫽ 2j

兺␤

j,kⲐ2␤j⫹1,k,

共2兲

where ␤ is scale-dependent normalized signal energy variation and j and k represent the index of scale and time, respectively; Rj is interpreted as a similarity measure, which represents a pseudo–correlation coefficient between scales (Yee et al. 1996). This information is used to explore the modulation of canopy-scale motions by low-frequency events. The reconstructed time series of u and CO2 flux at * a range of low frequencies is also examined. The original signal is retrieved from the inverse transform using the Dirac delta function (Farge 1992). The TKE and fluxes are computed for different frequency bands using the approach described in Terradellas et al. (2001) and Cuxart et al. (2002) using the bandpass-filtering property and multiresolution decomposition of the spectra (Mallat 1989).

5. Observed characteristics in the roughness sublayer During hours after the evening transition, EC measurements showed several bursts of turbulence with diversity in its duration and strength. In Fig. 1 we present a characteristic event lasting nearly an hour [1913–2013 local standard time (LST)] after sunset at 1821 LST 28 August 2001. The event characterizes intense velocity fluctuations, a change in wind direction from southeasterly to northeasterly, a slight decrease in temperature, and an initial increase in CO2 concentration followed by a decrease. There are two separate events divisible in this period with frontlike characteristics, each with a quiescent period, a sharp change in wind velocities, and a turbulent period with intense velocity variance. Because of these characteristics we denote these events as microfronts, with one beginning at 1913 LST and lasting 13 min and a second one beginning at 1930 LST and lasting 23 min. Similar changes in wind velocities are noted in a short-duration density current during the “Microfronts” experiment (Blumen et al. 1999), whereas drastic temperature changes (by 4 K) noted in that study are not found here. We notice a temperature drop of 1 K attributed to combined effects

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FIG. 2. Temporal variation of CO2 concentration at 5 (filled square) and 29 (open circle) m, temperature gradient between 29 and 19 m (filled circle), and u (bars) observed at 29 m above the * surface. Periods I–IV, as defined in section 7, are indicated on the top axis.

FIG. 1. Time series of three wind velocity components, air temperature, and CO2 concentration from EC measurements above the canopy (29 m above the surface) during initiation of the event (1913–2013 LST) on 28 Aug 2001.

of cold-air advection during the event and radiational cooling. The temperature and the CO2 concentration also show several ramp-like structures with small durations. The variation of observed CO2 concentrations, temperature gradient, and u are presented in Fig. 2 during * a 5-h period on the night of 28 August 2001 to illustrate influences of the event within and just above the canopy. As seen in Fig. 2, the CO2 concentration gradient between the canopy bottom (5 m) and above canopy (29 m) gradually increases up to 18 ppmv until 1830 LST as the SBL is formed after the evening transition. The gradient decreases drastically during 1900– 2000 LST (period II) and approaches zero shortly after 2000 LST. This is an indication that the event introduces enhanced mixing in the roughness sublayer, influencing the CO2 storage. The friction velocity is also high during period II. Hourly averages of turbulence observations at 29 m above the surface are presented in Table 1. The TKE (e) and downward vertical flux of TKE (w⬘e) during the period with events discussed above (period II) are considerably higher than during other periods. Such large

TKE values are sometimes found at distances far away from the mountain (Panofsky and Dutton 1984) ranges attributed to leeside cyclogenesis. The enhanced TKE may also be due to the enhanced shear at the inflection point of the canopy. Other observed features include a decrease in stability, a decrease in Brunt–Väisälä frequency, an increase in the standard deviation of velocity components (␴u, ␴␷, and ␴w) and standard deviation of CO2 concentration (␴c), and a decrease in the integral time scale Tw. There is no appreciable change in the standard deviation of temperature (␴␪). The kurtosis of u and w velocity components approaches 16 and 5, respectively, indicating high intermittency.

6. Evolution of mean state The mesoscale weather pattern during the study period characterizes that of an approaching cold front along the northern Appalachians associated with low pressure over Canada. Figure 3a gives a vector representation of the sodar wind profiles in the boundary layer recorded at 15-min intervals. The hourly averaged (the exception is period II for which only one profile was available) wind speed, w standard deviation (␴w), and wind shear during the 5-h period (1800–2200 LST; periods I–IV) are presented in Figs. 3b–d, respectively. Weak and steady southwesterly wind is prevalent before the study period with variable winds above 300 m. The ␴w values are roughly constant (0.4 m s⫺1) below 100 m, vary in the layers between 150 and 300 m, and continue to increase with height beyond 300 m (Fig. 3c), indicating a highly turbulent layer aloft. During the first half of period I, the wind shear increases at all levels

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TABLE 1. Mean wind speed U and the turbulence characteristics {TKE e; vertical flux of TKE w⬘e; stability parameter (z ⫺ d)/L (where d is displacement height); Brunt–Väisälä frequency [N ⫽ (g/␪)(⳵␪/⳵z), where g is acceleration due to gravity and ␪ is potential temperature]; standard deviation of velocities (␴u, ␴␷, and ␴w), temperature (␴␪), and CO2 concentration (␴c); and integral time scale (Tw)} observed at z ⫽ 29 m above the surface for the five hourly periods. Time (LST) (period) 1700–1800 1800–1900 1900–2000 2000–2100 2100–2200

(I) (II) (III) (IV)

U (m s⫺1)

e (m2 s⫺2)

w⬘e (m3 s⫺3)

(z ⫺ d)/L

N ⫽ (g/␪)(⳵␪/⳵z) (Hz)

␴u (m s⫺1)

␴␷ (m s⫺1)

␴w (m s⫺1)

␴␪ (K)

␴c (ppmv)

Tw (s)

1.76 2.35 3.50 2.00 2.40

0.150 0.345 4.217 0.857 0.839

⫺0.002 ⫺0.067 ⫺0.512 ⫺0.310 ⫺0.171

0.76 0.267 0.028 0.028 0.043

0.033 0.052 0.041 0.02 0.024

0.256 0.577 2.250 0.978 1.098

0.461 0.553 1.771 0.733 0.596

0.148 0.223 0.478 0.420 0.322

0.151 0.212 0.215 0.084 0.207

0.469 1.335 3.404 1.300 1.658

1.46 1.94 1.14 1.63 1.29

below 200 m and reaches a maximum (0.026 s⫺1) at 1845 LST. The turbulence generated by shear instability at higher levels in the BL is transferred downward at this time. The wind speed profile during period II shows a well-developed jet (6 m s⫺1), with the jet nose at 262 m. The wind shear decreases to a minimum value below the jet nose, and ␴w increases in the lower 200 m. The wind veers (Fig. 3a) with height (⬇70° within 900 m). During periods III and IV, northeasterly flow becomes predominant (Fig. 3a) below 400 m, the jet (6 m s⫺1 at 250 m) is well established, and the wind

backs with height. These sequences of events depict cold-frontal characteristics with relatively colder, northeasterly air pooling over the site as the jet establishes. A weak decoupling exists at a higher elevation (around 200 m), where minimum turbulence intensity (␴u/U and ␴w/U ) is noted. Intensity ␴w/U decreased with height up to 200 m (0.1 at the surface to 0.05 at 200 m) and then continued to increase with height. The existence of such a layer with weak turbulence and enhanced shear above indicates that the layer served as a

FIG. 3. (a) Vectorial representation of wind velocity during 1600–2300 LST; temporal variation of (b) wind speed, (c) standard deviation of vertical velocity, and (d) wind shear with height during 1700–1800 LST (line with open circles) and the four periods on 28 Aug 2001. Vector scale is given at top-right corner of (a); LLJ height H is indicated in (a) with a thick line.

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less turbulent layer, above which flow accelerated (between 250 and 320 m) to form the jet. Considerable variation in ␴w between 100 and 300 m indicates continued transport of momentum across this layer as a result of the interaction with upper-layer flow. As a result, an “upside-down boundary layer” (Mahrt 1999) is observed throughout the study period as evidenced by the downward TKE flux (Table 1). The TKE and downward flux of TKE over the canopy is maximum (Table 1) during period II and remains at a slightly lower value during periods III and IV, that is, after the jet is well developed (Fig. 3). Unlike in the typical collapse of the surface-layer turbulence (Businger 1973; Smedman et al. 1995), the turbulence is not totally collapsed over the canopy because of continued downward transport of momentum and TKE and enhanced shear production associated with the canopy drag. The downward propagation of the instability leads to recoupling of upper-level flow with the moderately turbulent lower layers and to turbulent bursts over the canopy (Fig. 1) and reduction of CO2 concentration and temperature gradients in the canopy layer (Fig. 2). It is to be emphasized that the event examined here is visualized as a low-frequency, shearinduced perturbation that originated in the residual layer aloft, propagated downward, and moved past the EC flux tower. A time–frequency analysis of this phenomenon will give information on the contributions to variances and flux from a number of periodic and nonperiodic events, their interactions, and exchange of energy.

7. Wavelet power spectra and cospectra The wavelet analysis is carried out on velocity components during the 6-h period 1700–2300 LST, and four periods from this analysis (I: 1800–1900 LST, II: 1900– 2000 LST, III: 2000–2100 LST, and IV: 2100–2200 LST) are used in the following discussions. Spectral characteristics of velocity variances and the cospectral characteristics of momentum, heat, and CO2 fluxes are examined. The cospectra are analyzed as a frequencydependent correlation coefficient (WCC). The cogradient and countergradient contributions to WCC corresponding to CO2 flux are also presented.

a. Characteristics of velocity spectra The time-averaged wavelet spectra (WS) for three velocity components corresponding to the four periods are presented in Fig. 4a. The comparison of Fourier spectra (FS) and WS (Fig. 4a, periods I and III) show several spurious fluctuations in FS. The WS are smoother than the FS and allow a better identification

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of different small-scale events. As seen in the Fig. 4a, an enhancement of wavelet power is noticed at a number of periodicities during periods II and III. The spectra represent those of a mixture of turbulence and waves (Stull 1988) with a low-frequency (depending on the peak variance) wave source, a buoyancy subrange (showing a ⫺2 slope), an energy gap, and an inertial subrange (following ⫺2⁄3 slope). The Brunt–Väisälä frequency observed close to the canopy during period I is 0.052 Hz (2.25h), which is lower than the high-frequency peak (0.13 Hz ⬇ 0.9h) in the w spectra, an indication that temperature variations are also forced by canopy-scale turbulent eddies (here h is canopy height). The u and ␷ component spectra during period I show a prominent low-frequency maximum at 0.001 Hz. It is useful to mention that the event is noted 2 min earlier at a tower situated 770 m west of the measurement location, which implies that the event propagated at a speed of 6.4 m s⫺1, which is close to the LLJ speed during this period. A buoyancy subrange is noted for frequencies between 0.004 and 0.002 Hz and a ⫺2 slope (indicating wave motion) is visible in the u and ␷ component spectra; it is less prominent in the w spectrum because of suppression of vertical motion. The temperature and CO2 variance spectra (not presented) also showed a buoyancy subrange similar to that of horizontal velocities, and variances peaked at low frequencies. An energy gap is noted between 0.002 and 0.008 Hz. The inertial subrange with a ⫺2⁄3 slope is visible in the w and ␷ spectra and for a small range of u spectra. The ratio of spectral energies of w and u components in the inertial subrange gives a much higher value (2.7) than that of the isotropic (1.3) case (Panofsky and Dutton 1984). Period II characterizes isotropic conditions. There is a prominent low-frequency peak at 0.0008 Hz. The buoyancy subrange is found between 0.0008 and 0.001 Hz, and the energy gap is between 0.001 and 0.003 Hz. There are three peaks (0.003, 0.009, and 0.039 Hz ⬇ 1.17 km, 389 m, and 89 m, respectively) in the horizontal velocity spectra at frequencies higher than the energy gap, indicating secondary instabilities formed by the wave source. The w spectral peak shifts to a lower frequency at 0.029 Hz (⬇6h), which is lower than the Brunt–Väisälä frequency (0.041 Hz), indicating the presence of larger-scale eddies (kh) attributed to w variance. It also indicates that these wave-type motions propagate in the vertical and horizontal directions. The variance contributed by intermediate frequencies increases, indicating transfer of energy from lower frequencies. Period III details isotropic conditions with a considerable increase in the variance at intermediate frequencies of all three wind components. Meanwhile,

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FIG. 4. (a) The variance spectra of u, ␷, and w components during the four periods. Spectra are normalized with the variance of respective wind component during each 1-h period. The thin line in the plots for periods I and III corresponds to vertical velocity variance spectra from Fourier spectral analysis. (b) The WCC of momentum (labeled “uw”), heat (“w␪”), and CO2 (“wc”) flux during the four periods. (c) The WCC as a function of frequency for cogradient [labeled “(⫹) wc”] and countergradient [(⫺) wc] CO2 fluxes during the four periods.

the peak energy of the wave source at the lowest frequencies decreases, and the buoyancy subrange (0.0008–0.0015 Hz) becomes less divisible. The wave energy from low frequencies has propagated to higher frequencies (further insights into this aspect are presented in section 9) and peaks at 0.006 and at 0.014 Hz (corresponding to wavelengths 333 m and 142 m) for all three velocity variances. This result indicates that ed-

dies that are comparable to the LLJ height H have contributed to the variance. During period IV, the lowfrequency wave source reappears with higher energy at 0.0009 Hz, and a better isotropic condition is noted (spectral energy ratio of w and u in the inertial subrange region is 1.7). The comparison of spectra during the first three periods indicates that there is a delay for the event to

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appear in all three velocity components, with quasitwo-dimensional eddies during period I changing to a three-dimensional disturbance during period III. This delay may be due to the fact that three-dimensional features appear in the flow only after the primary disturbance saturates, as noted in the direct numerical simulations of Kelvin–Helmholtz instabilities (Werne and Fritts 1999) and observations of a shear-flow instability during the Cooperative Atmosphere–Surface Exchange Study (CASES-99; (Newsom and Banta 2002). They also noted that, once the energy is transferred through vertical momentum flux, the wave disturbance grows at the expense of mean shear. In our observations, this phenomenon is evidenced by a decrease in wind shear (Fig. 3d, period II) and subsequent development of wave motions (Fig. 4a, period III).

b. Exchange efficiency WCC (a measure of exchange efficiency for momentum, heat, and CO2) as a function of frequency is shown in Fig. 4b during the same periods as in Fig. 4a. A situation with a negative value for w–CO2 correlation and a positive value for momentum or heat represents a countergradient contribution at the corresponding frequencies. The phase difference (Stull 1988) between the w and CO2 [␾wc⫽ tan⫺1(Q/Co), where Co is quadrature spectrum and Q is cospectrum from CWw,c n ] varied between 120° and 180° at low frequencies ( f ⬍ 0.001 Hz), attributed to a countergradient flux. A phase difference of 90° between the w and CO2 concentration or temperature time series is generally expected for gravity waves (Stull 1988). Although we notice the gravity wave (wave source) at f ⫽ 0.001 Hz with a ␾wc of 90° during period I, considerable variation in ␾wc occurs during subsequent periods. The |␾wc| varies between 20° and 180° in the intermediate frequencies ( f ⬇ 0.000 54–0.006 Hz), signifying combination of nonlinear waves (Finnigan et al. 1984) as well as turbulent motions. Corresponding wavelengths are higher than the height of the LLJ, and associated countergradient fluxes are attributed to nonlinear wave interactions. We will examine the time evolution of fluxes in section 8 to know more about the nonzero flux. Countergradient flux and ␾wc higher than ⫾90° were also observed over canopies (Lee et al. 1996) at higher frequencies than noticed here. A few other points to note from Fig. 4b are 1) the countergradient flux (for CO2 and heat) at low frequencies dominates throughout the 4-h period; 2) the presence of positive heat flux at low frequencies is due to convective-type instability, which propagates to intermediate frequencies; 3) the peak cogradient CO2 flux shifts toward higher frequencies from period I to period

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IV, successively; and 4) correlations decrease to nearzero values for CO2 flux beyond 0.5 Hz. The peak cogradient flux of momentum and scalars is noticed at the same frequency as in the three velocity spectra peaks during periods II and III, which indicates that energycontaining three-dimensional eddies (␭ ⬇ H ) take part in the exchange. However, cospectral frequencies during periods I (␭ ⬇ h) and IV (␭ ⬇ 4h) correlate with that of energy-containing vertical motion. The cogradient momentum exchange efficiency decreases during the initiation (period II) of the event at all frequencies and increases considerably at all frequencies after the event (periods III and IV), as observed in the variation of u (Fig. 2). *

c. Exchange efficiency of cogradient and countergradient CO2 transfer The exchange efficiencies in the odd (countergradient transfer) and even quadrants (cogradient transfer) are examined in Fig. 4c for all four periods. For the discussions in subsequent sections, we divide the spectra into three regions: a noncoherent, low-frequency region (|␾wc| ⬎ 90°); a coherent region (|␾wc| ⬇ 20°– 180°); and a noncoherent, turbulent region (|␾wc| ⬍ 20°). The exchange efficiencies associated with cogradient contribution are nearly zero at noncoherent low frequencies. This fact implies that the action of CO2rich sweeps and CO2-depleted ejections associated with large eddies (␭ k H ) are responsible for large exchange efficiencies, resulting in a negative flux contribution. In the coherent cospectral region, both cogradient and countergradient exchange efficiencies have equal importance. There is dominant exchange of positive flux in this region during period I. The flux in the even and odd quadrants is equally important in subsequent periods, signifying that the wave source at low frequency contributed to the enhanced coherent motion. In the turbulent region, the exchange efficiency leading to positive flux is highest at wavelengths corresponding to LLJ height [where we notice a peak for all three velocity variances (Fig. 4a)], and for ␭ ⬇ h. The positive WCC decreases and negative WCC increases at higher frequencies (␭ ⬍ h), and both are equal at the highest frequencies in response to uniform mixing and isotropic conditions.

8. Multiscale decomposition and interaction at low frequencies The observation of anomalously high nocturnal CO2 respiration after a low u as we note for the current *

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FIG. 5. (a) Multiscale resolution of u s for Fourier periods of 3000, 400, 200, 150, 100, and 50 s during 1900–2030 LST. (b) Same as * (a), but for multiscale resolution of CO2 flux. The arrows on the x axis correspond to the times of maximum countergradient flux.

event (Fig. 2) is observed at several occasions at the Howland flux site (Hollinger et al. 2004). Other studies (Baldocchi et al. 2000) have also reported an increase in the flux following sporadic outbreaks of turbulence, resulting in a net increase in the flux. To investigate the mechanism underlying these observations, the multiscale decomposition approach is employed for u and * CO2 flux during 1900–2030 LST (Fig. 5b). The u cor* responding to different Fourier periods are presented in Fig. 5a; u

*s

⫽ 关共u⬘w⬘兲2s ⫹ 共␷⬘w⬘兲2s兴1Ⲑ4,

共3兲

where s corresponds to wavelet scale. A total of 140 scales with a resolution of 0.08 are used for this analysis. The scales are converted to respective Fourier periods, and u for selected periodicities are presented in the * figure. In response to the primary low-frequency disturbance, u has a value of 0.09 m s⫺1. This eddy with a * size much larger than the LLJ height (␭ ⬇ 6–10 km) is noted throughout the study period. The u associated * with smaller periodicity increases, and a delay (nearly 20 min) exists in the u peaks as periodicity decrease * from 400 s (␭ ⬇ 0.8–1.4 km) to 100 s (␭ ⬇ 0.2–0.35 km, including the LLJ height). The increase in u at these *

periodicities is due to the increase in downward transfer of momentum from the primary disturbance above the jet nose. The positive CO2 flux at 150 (␭ ⬇ 0.4–0.7 km), 100 (␭ ⬇ 0.2–0.35 km), and 50 (␭ ⬇ 0.1–0.17 km) s increases simultaneously with the appearance of a negative-fluxcontributing event at 3000-s periodicity. The result also shows that there is a delay in the appearance of negative-flux-contributing events for periodicities in the range of 400–100 s, and the duration decreases and the amplitude increases with decreasing periodicity. At 100-s periodicity, countergradient flux is noted at 2000 LST with duration close to 10 min, which is followed by a large cogradient flux. The secondary disturbances initiated by the large eddy propagate at a lower speed than the primary disturbance at 4.5 m s⫺1. This difference introduces further instabilities at smaller periodicities, contributing to large flux. The presence of large flux at smaller scales during this time may be attributed to the propagation of waves to strong regions of turbulence and conversion of wave energy to TKE (Stull 1988). It can be inferred that during initial stages of the event a near-equal contribution of cogradient and countergradient fluxes reduces the resultant flux or

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gives a countergradient net flux, whereas at a later stage enhancement of the cogradient flux at smaller scales results in higher (net positive) fluxes. The strong shear layer associated with LLJ might be serving as a barrier to the penetration and propagation of external disturbances and have contributed to transient countergradient contribution to fluxes at low frequencies. The transient nature, along with a nonsymmetric wave contribution to flux, leads to a nonzero value to the net flux. The countergradient contribution in CO2 fluxes can be misinterpreted as an “uptake” if proper care is not practiced while analyzing and interpreting the nocturnal data. This is important especially during sporadic outbreak of turbulence as observed at the Howland AmeriFlux site. Anomalous uptakes of CO2 during nocturnal conditions are reported in recent studies (Baldocchi et al. 2000; Cava et al. 2004; Hollinger et al. 2004). Baldocchi et al. (2000) noticed an unusual uptake of CO2 in the EC measurements during dormant periods at the Oak Ridge forest, in contrast to the chamber-based CO2 flux measurements. Based on the understanding of countergradient fluxes, we suggest that anomalous nocturnal uptake may not be biological but rather is caused by nonlocal (␭ k h) transport. This argument is supported by earlier studies on ozone and air-pollutant transport that demonstrate the role of LLJs in horizontal and vertical transport from distant locations (Corsmeier et al. 1997; Reitebuch et al. 2000; Beyrich 1994; Kalthoff et al. 2000).

9. Influence on the small-scale variance Large-scale motions that contribute to “inactive” turbulence are presumed to have negligible contribution to the net flux. Raupach et al. (1996) suggested that the main role of the inactive eddies is to make the active canopy-scale motions intermittent. However, the features of countergradient flux (␭ k H ) discussed in the previous sections suggest that large-scale (we denote large scale because eddies with ␭ k H that are of mesoscale origin in this context also contributed to the flux at the EC tower) perturbations also contribute to active turbulence. In the following analysis, we examine how large-scale (␭ k H ) perturbations influence smallerscale variance (energy) and possible energy cascade. We use interscale transfer of scalar variance derived from the wavelet spectra of CO2 concentration for this analysis. To elucidate the interscale transfer of scalar variance (energy), the pseudocorrelation (Rj) of CO2 variance between different scales is examined. In pseudocorrelation analysis (Yee et al. 1996), the correlation be-

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FIG. 6. The correlation of CO2 concentration variance between adjacent frequencies during the four periods.

tween energy corresponding to consecutive scales of motion is found. Pseudocorrelation Rj (Fig. 6) increases with decreasing wavelength, suggesting transfer of energy from larger to smaller eddies. The Rj increases during the initiation of the event (period II) for ␭ ⫽ 0.6–1.6 km. The Rj peaks during period III at ␭ ⬇ 4 km, ␭ ⬇ H, and ␭ ⬇ h. The presence of high correlation indicates that the event introduces a series of cascading eddies, which result in the transfer of energy from large to small scales. The large correlation at ␭ ⬇ H and ␭ ⬇ h during period III is a clear indication that mixing between the air parcels from and above H with the roughness sublayer air is considerably increased. The high correction in the wavelength band 0.5h–3h indicates enhanced canopy-scale transfer during period III. The Rj decreases at most of the lower wavelengths except for ␭ ⬇ H after the passage of the event (period IV). These results suggest that, during the event, energy transfer from LLJ (␭ ⬇ H ) to smaller scales continued to exist, which could influence the CO2 fluxes.

10. Bandpass-filtered TKE and CO2 flux The characteristics of the exchange efficiencies (Fig. 4c) described earlier are used to separate the contribution to fluxes from the large-scale (which also show a countergradient flux), coherent-scale (both cogradient and countergradient flux are present) and turbulentscale (there is net cogradient flux leading to intermittent and noncoherent finescale structures) motions. The bandpass-filtering capability of wavelet transform and reconstructed time series of TKE, vertical flux of

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the second microfront, indicating an overturning. The high-frequency upward transport is prevalent during both microfronts. The countergradient CO2 flux dominates at large scale (␭ k H ) during 1900–2000 LST. The cogradient flux in the turbulent scales increases simultaneously with the countergradient flux at large scale. The negative flux in the coherent-scale motions is observed with a delay and characterizes a countergradient flux during 1930–1950 LST, followed by a positive flux during 1950–2010 LST.

b. Influence on flux estimates

FIG. 7. (top) TKE, (middle) the vertical flux of TKE, and (bottom) the vertical flux of CO2 for turbulent scales (thin line) with wavelength ⬍ 2h, coherent scales (dashed line) with wavelengths of 2h–13h, and noncoherent, large scales (thick line) for wavelength of 13h–28h. Data for periods I–III are shown; hatched area corresponds to the part of time series in Fig. 1.

TKE, and CO2 flux are used in this analysis. Also, implication of countergradient flux to the short-period and long-period time-averaged flux is discussed.

a. Large, coherent, and turbulent scales There is a twofold increase in energy at all three scales during the event (Fig. 7). The TKE associated with turbulence and coherent scale is nearly equal, partly associated with the shear production and possibly also because of the conversion of wave energy to TKE. The increase in TKE associated with lowfrequency motions is mainly due to the increase in horizontal velocity variances and contributes to a single peak in TKE. The peak for w component is noticed at 1950 LST (not shown), and the peak for horizontal velocity is at 1926 LST. This time lag indicates that the low-frequency perturbation is initially two-dimensional, and it introduces a three-dimensional disturbance in the roughness sublayer at a later stage. There are two peaks in turbulent contributions during the event attributed to two microfronts (Fig. 1) formed as a secondary instability at small scales. The vertical flux of TKE and CO2 concentration for large-, coherent-, and turbulent-scale motions is presented in the middle and lower panels of Fig. 7, respectively. The downward vertical flux of TKE for ␭ k H dominates between 1915 and 2045 LST, associated with the first microfront (Fig. 1), followed by upward flux in

Figures 8a and 8b shows the fraction of total TKE and total CO2 flux attributed to the three spectral bands. The fraction of energy in the noncoherent low frequencies is higher (0.4–0.8) than that of turbulent and coherent scales during the first half of the periods shown. After the initiation of the event, the fraction of energy at coherent scales increases up to 0.5 followed by increase of 0.5–0.7 in the turbulent scales. The fraction of CO2 flux is given in Fig. 8b. The countergradient flux at lower frequencies is of similar magnitude to the turbulent flux. Nappo and Chimonas (1992) pointed out that internal gravity waves generated by gentle topographic features are capable of introducing fluxes of nearly equal magnitude as that generated by turbulence. Finnigan et al. (1984) reported similar observation for heat flux partitioned into wave and turbulent flux contributions. They also showed that turbulence of that high intensity could not exist without the presence of wave motion. The waves propagating to regions of strong turbulence will be absorbed by turbulence, and wave energy is converted to TKE (Stull 1988) and that might explain high TKE values. The coherent scale shows a delayed and minor increase in negative flux, but it is an important component because the largescale flux and turbulent-scale flux are approximately equal. The cogradient and countergradient flux contribution decreases after the event as the wind shear acts to reduce the countergradient flux at large scales in an SBL (Komori and Nagata 1996). The countergradient flux contribution is 40%–45% during this event, which leads to a resultant negative flux (Fig. 9a) when the trend in 1-h data is retained. It is a usual practice to do short-period averages during intermittent events in the SBL. To illustrate the influence of short as well as long averaging period, we consider three types of analysis—first by removing the 15min trend and finding the averages, second by removing the 30-min trend and finding the average flux, and third by removing the 1-h trend and finding 30-min averages. The removal of 15- or 30-min trends in the

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349

FIG. 8. Fraction of (a) total TKE and (b) total CO2 flux at noncoherent large-scale (open triangles), coherent-scale (open circles), and turbulent-scale (filled squares) motions.

time series results in a large positive flux by filtering out the countergradient flux. When the 1-h detrended data are used to find hourly or half-hourly fluxes, a resulting countergradient flux is noted. These findings have interesting consequences in defining a correct averaging time as demonstrated in Fig. 9b. Here we follow the approach of Oncley et al. (1996) to determine the averaging time from the cumulative integral of the cospectrum (ogive function). The cumulated wavelet cospectra are used to find the frequency at which there is no additional contribution to the covariance. The re-

ciprocal of this frequency is used as the minimum averaging time required, including all flux contributions from various frequencies. In a similar way, the ogives of the respective periods are presented in Fig. 9b. Fluxes do not reach a constant value at low frequencies for periods I–III because of the dominating influence of the countergradient flux at lower frequencies. The ogives decrease because of the appearance of the countergradient contribution at higher frequencies, after 0.001 18 Hz (14.12 min), 0.0062 Hz (2.68 min) and 5.1 ⫻ 10⫺4 Hz (32.7 min) respectively for periods I, II and III. This

FIG. 9. (a) The CO2 flux calculated after removing 60- (open circles; A), 30- (plus signs; B), and 15-min (times signs; C) trend and averaging for corresponding periods; 30-min-averaged flux (filled circles; D) estimated after removing 1-h trend. (b) The distribution of cumulated flux (ogive) at different frequencies for four periods. The hatched area corresponds to coherent scales.

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analysis shows that even a very short averaging time would account for the countergradient flux introduced by the event.

11. Summary and conclusions A wavelet analysis technique is used to analyze the time–frequency characteristics of an episodic burst observed during the initiation of an LLJ prior to the incidence of a cold front. Our analysis at the Howland AmeriFlux site shows that the roughness-layer turbulence has a direct link with the turbulent burst events during the LLJ activity. The downward transfer of TKE, momentum, and CO2 during this upside-down boundary layer regime (Mahrt and Vickers 2002) is associated with large eddies having length scales higher than the LLJ height (H ) and their interaction with canopy-scale motions. Microfronts are formed as a secondary instability, which enhances the mixing processes within and above the canopy. A new approach based on the cogradient and countergradient wavelet correlation coefficient is applied to the eddy covariance data to separate flux contributions from turbulence, coherent, and noncoherent lowfrequency (␭ k H ) motions. Our results emphasize the role of low-frequency flux contributions under nocturnal conditions and their direct influence on the roughness-sublayer turbulence. We notice a countergradient net CO2 flux at the initiation of the event and an increase in net flux after the initiation due to enhanced turbulent-scale cogradient flux. These findings help to explain the anomalously high nocturnal CO2 respiration observed at the site (Hollinger et al. 2004) during turbulent periods preceded by calm periods. The wavelet decomposition of u and CO2 flux suggests a delay * in the introduction of countergradient flux at lower frequencies (for ␭ k H to ␭ ⬇ H ). A correlation between the CO2 concentration variance at neighboring scales shows a transfer of energy from large-scale motions (␭ k H ) to canopy scale, causing enhanced turbulence. Large-scale motions (␭ k H ) introduce a convectivetype instability and countergradient fluxes are caused by the CO2-depleted warm air within the canopy being displaced by comparatively CO2 rich, descending cold air. Because this happens just after evening transition, the CO2 in the daytime residual layer is brought down with large-scale motions (␭ k H ), which lasts for nearly 3 h after the evening transition and displaces CO2depleted air in the lower layers. This large-scale contribution is of approximately equal magnitude to that of the turbulent-scale contribution before and during the initial stages of the event, thus making the coherent flux contribution very important. Furthermore, our study suggests that CO2 fluxes are modified up to 40%–45%

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during such events as a result of the countergradient contribution. One important aspect of the current study is that the findings on low-frequency countergradient fluxes help to explain anomalous nocturnal CO2 uptake by the canopy reported at some of the flux sites. The burst events introduce not only a random flux error associated with intermittency, but also a systematic error in the flux estimations resulting from the countergradient flux contribution at low and intermediate frequencies. This study highlights the need for detailed analysis of eddy covariance fluxes, especially in the presence of nocturnal phenomena, such as LLJs, which are a common feature at several sites. The interaction of the lowfrequency events associated with the LLJ and the canopy-scale motions is elusive and needs further insights from measurements. This study also highlights the need for an improved flux estimation method based on scale-dependent characteristics, which may also help to explain in part the large uncertainties in the nocturnal flux measurements using the eddy covariance technique. Acknowledgments. This work is funded by the U.S. Department of Energy (DOE), Office of Science, Terrestrial Carbon Processes (TCP) through a grant to Prof. M. Y. Leclerc of The University of Georgia. We thank the International Paper Company, Ltd., for providing access to The research site in Howland, Maine. We thank H. Hughes, J. Lee, and J. Walsh for their expert technical assistance. The Howland flux research is supported by the Office of Science (BER), U.S. DOE, through the Northeast Regional Center of the National Institute for Global Environmental Change (NIGEC) under Cooperative Agreement DE-FC0390ER61010. Findings and conclusions are the sole responsibility of the authors and do not necessarily represent views of the NIGEC, DOE, or of International Paper, Ltd. We thank two anonymous reviewers for several valuable suggestions.

APPENDIX Details of the Wavelet Analysis Continuous wavelet transform (Farge 1992; Daubechies 1993; Torrence and Compo 1998) of a discrete time series is given by W x共n, s兲 ⫽

1

公|s|

冕

x共t兲 ␺*

冉冊

t⫺n dt, s

共A1兲

where s is the wavelet scale, dt is the time interval between data points in time series x(t) with N data points, and ␺* is the transforming function. A wavelet is a waveform with effectively limited duration and an av-

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erage value of zero. The Morlet wavelet function (Grossman and Morlet 1984) used in this study has been successfully applied to nocturnal turbulence analysis to isolate the low-frequency events (Terradellas et al. 2001; Cuxart et al. 2002) and is given by ⌿0共t兲 ⫽ ␲⫺1Ⲑ4ei␻0te⫺t

2Ⲑ2

,

共A2兲

which satisfies the admissibility condition [␺0(t) must be wavelike with zero mean and finite energy] and has a nondimensional frequency of ␻0 ⫽ 6. The approximate Fourier period T corresponding to oscillations within the Morlet wavelet is 1.03 times the scale s. The scale s, period T, frequency f, and wavelength ␭ are used in the discussions to represent wavelet scale, corresponding Fourier period, frequency, and wavelength. The intermittent and localized features in the time series could effectively be identified in a wavelet cospectrum, and low-frequency variations are well resolved (Hudgins et al. 1993). The wavelet cross spectrum is given by CWnw,x共n, s兲 ⫽ W nw共n, s兲W nx*共n, s兲,

共A3兲

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