Calibration and validation of a remote sensing ...

Irrig Sci DOI 10.1007/s00271-012-0381-x

ORIGINAL PAPER

Calibration and validation of a remote sensing algorithm to estimate energy balance components and daily actual evapotranspiration over a drip-irrigated Merlot vineyard Carlos Poblete-Echeverrı´a • Samuel Ortega-Farias

Received: 14 August 2011 / Accepted: 12 April 2012 Ó Springer-Verlag 2012

Abstract A study was carried out to calibrate and validate a remote sensing algorithm (RSA) for estimating instantaneous surface energy balance components and daily actual evapotranspiration (ETa) over a drip-irrigated Merlot vineyard located in the Maule Region of Chile (35° 250 LS; 71° 320 LW; 125 m.a.s.l.). ETa was estimated as a function of instantaneous evaporative fraction and average daily net radiation (Rnday) using meteorological variables in combination with reflectance data measured by a handheld multi-spectral radiometer. The sub-models used to estimate the instantaneous net radiation (Rnins), soil heat flux (Gins), and Rnday were calibrated and validated using measurements of the surface energy balance components, incoming longwave radiation ðL #ins Þ, outgoing longwave radiation ðL "ins Þ, and surface albedo (a). The validations of instantaneous sensible heat flux (Hins), latent heat flux (LEins), and ETa were carried out using turbulent energy fluxes obtained from an eddy correlation (EC) system. For reducing the moderate EC imbalance (about 11 %), turbulent energy fluxes were recalculated using the Bowen ratio method. The validation analysis indicated that the calibrated sub-models of the RSA were able to estimate Rnins, Gins, Hins, and LEins with a root-mean-square error (RMSE), mean absolute error (MAE), and index of agreement (IA) ranging between 16–54, 13–44 W m-2, and 0.72–94, respectively. Also, the RSA was able to estimate ETa with RMSE = 0.38 mm day-1, MAE =

Communicated by E. Fereres. C. Poblete-Echeverrı´a  S. Ortega-Farias (&) Research and Extension Center for Irrigation and Agroclimatology (CITRA), Universidad de Talca, Talca, Chile e-mail: [email protected]

0.32 mm day-1 and IA = 0.96. These results demonstrate the potential use of reflectance and meteorological data to estimate ETa of a drip-irrigated Merlot vineyard.

Introduction Irrigation scheduling is a critical aspect of successful grape production and wine quality (Sivilotti et al. 2005; Shellie 2006; Intrigliolo and Castel 2008). In order to obtain optimal irrigation scheduling, it is necessary to have a reliable method to quantify the water consumption of the plants, that is, daily actual evapotranspiration (ETa). For this purpose, the use of remote sensing techniques to estimate ETa is becoming an important tool for studying water consumption on a field and a regional scale (Allen et al. 2007; Gowda et al. 2008). Remote sensing energy balance methods provide instantaneous estimations of evapotranspiration (ETins), which are then used in the estimation of ETa (Chavez et al. 2008). Numerous remote sensing algorithms that use the principle of surface energy balance for estimating ETa have been developed in order to make use of remote data acquired by sensors on airborne and satellite platforms, for example: SEBI (Surface Energy Balance Index) (Menenti and Choudhury 1993), TSM (Two-source model) (Norman et al. 1995), SEBAL (Surface Energy Balance Algorithm for Land) (Bastiaanssen 1995, 2000; Bastiaanssen et al. 1998a), S-SEBI (Simplified Surface Energy Balance Index) (Roerink et al. 2000), SEBS (Surface Energy Balance System) (Su 2002), METRIC (Mapping Evapotranspiration at high Resolutions with Internal Calibration) (Tasumi 2003; Allen et al. 2007), MEBES (Surface Energy Balance to Measure Evapotranspiration) (Ramos et al. 2009) and ReSET (Remote Sensing of ET) (Elhaddad and Garcia

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2011; Elhaddad et al. 2011). In general, energy balance methods use remotely sensed surface reflectance data in the visible (VIS) and near-infrared (NIR) regions of the electromagnetic spectrum to determine the NDVI and infrared (IR) thermal band thereby estimating the surface temperature (radiometric temperature) (Gowda et al. 2008). These methods consist of the estimation of: (1) net radiation (Rn) using the associated surface albedo and emissivity fractions for shortwave and longwave radiation; (2) soil heat flux (G) using surface temperature, albedo, and the normalized difference vegetation index (NDVI); and (3) sensible heat flux (H), as a function of the temperature gradient above the surface, surface roughness, and wind speed (Senay et al. 2007). In the algorithms of surface energy balance methods, the latent heat flux (LE) is estimated as the residual of the simple surface energy balance equation (assuming no advection of energy into the area): LE ¼ Rn  G  H

ð1Þ

where LE, Rn, G, and H are all in W m-2. Energy balance methods in special SEBAL and METRIC have been tested extensively in different parts of the world with positive results (Bastiaanssen et al. 1998b, 2005; Gowda et al. 2008). However, the aircraft or satellite images may not be available for management decisions during critical phenological stages. The availability of airborne sensors is constrained by weather conditions, revisit frequency, and elaborate data processing (Stamatiadis et al. 2006). Recent developments in optical remote sensing equipment have made it possible to use ground-based sensors to measure reflectance on small spatial scales with high frequency (Boelman et al. 2003). Ground-based sensors are designed to overcome many of the limitations associated with satellite or aircraft-based sensing systems for field conditions (Stamatiadis et al. 2004). Therefore, we propose the use of a hand-held multi-spectral radiometer as an alternative for obtaining reflectance values over vineyards (vines and soil separately). With this instrument, it is possible to estimate instantaneous values of Rn, G, H, and LE. Remote sensing energy balance algorithms use several empirical equations to estimate the instantaneous surface energy balance components. These empirical equations are related to the type of surface and atmospheric conditions. In general, these empirical equations were developed for full cover crops (Teixeira et al. 2009). Therefore, local parameterization of any remote sensing equations can improve the accuracy of the model (Duchemin et al. 2006). The main objective of this study was to calibrate and validate a remote sensing algorithm (RSA) to estimate instantaneous surface energy balance components and ETa over a drip-irrigated Merlot vineyard trained on a vertical shoot-positioning system (VSP) under semi-arid conditions

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using meteorological and reflectance data. The sub-models used to estimate instantaneous values of net radiation (Rnins), soil heat flux (Gins), sensible heat flux (Hins), and average daily net radiation (Rnday) were calibrated and validated with respect to local conditions of the vineyard using ground-truth measurements. Moreover, ETa values were computed as a function of daily net radiation (Rnday) and instantaneous evaporative fraction (Kins).

Materials and methods Study location The data set used to calibrate and validate the RSA was collected from a drip-irrigated Merlot vineyard located in the Talca Valley, Region del Maule, Chile (35° 250 LS; 71° 320 LW; 125 m above sea level) during the 2007/2008 (season 1, calibration), 2008/2009 (season 2, validation), and 2009/2010 (season 3, validation) growing seasons. The climate of the area is Mediterranean and semi-arid with an average daily temperature of 19.4 °C (for the study period) and an average annual rainfall of 679 mm. The summer period is usually dry and hot (receiving 2.2 % of the annual rainfall), while the spring is wet (receiving 16 % of the annual rainfall). The soil in the vineyard is classified as Talca series (Fine family, mixed, thermic Ultic Haploxeralfs) with a clay loam texture and average bulk density of 1.5 g cm-3. For the effective rooting depth (0–60 cm), the average volumetric soil water content at field capacity (hfc) and wilting point (hwp) were 0.36 and 0.22 m3 m-3, respectively. The vineyard was irrigated daily using drippers (4 l h-1) spaced at intervals of 1.5 m. The Merlot vines were planted in 1999 in north–south rows, 2.5 m apart, with 1.5 m within-row spacing (plant density of 2,667 plants ha-1) and were trained on a vertical shoot-positioning system (VSP) with the main wire 1 m above the soil surface. The shoots were maintained in a vertical plane by three wires with the highest wire located 2 m above the soil surface. Field measurements The irrigation management of the Merlot vineyard was carried out using a maximum allowed depletion (MAD) of 0.29 m3 m-3. In addition, the volumetric soil water content (h) at a rooting depth of (0.6 m) (hrd) was monitored weekly at 12 sampling points distributed throughout the vineyard plot using a portable TDR unit (TRASE, Soil Moisture Corp., Santa Barbara, CA, USA). Vine water status was evaluated weekly using the midday stem water potential (wx) as measured by a pressure chamber (PMS 600, PMS Instrument Company, Corvallis, OR, USA).

Irrig Sci

wx was measured on 12 young, fully expanded leaves (2 leaves per vine), which were first wrapped in aluminum foil and then encased in plastic bags at least 2 h before measurements were taken (Chone et al. 2001). The leaf area index (LAI) was estimated as a function of the shoot length which was correlated with its total leaf area using an empirical equation developed by Poblete-Echeverria and Ortega-Farias (2009). The average fractional cover (fc) for the vineyard was estimated through measurements of the projected area of the vine (i.e., the shaded area at midday). Meteorological and micrometeorological measurements The vineyard plot (4.25 ha) used for the meteorological and micrometeorological measurements was mostly homogeneous and flat. The soil surface was maintained free of weeds or cover crops during the validation and calibration periods. Furthermore, the experimental vineyard plot is surrounded by other vineyard plots with similar management and conditions (Total extension of the commercial vineyard = 97 ha). Latent (LEEC) and sensible (HEC) heat fluxes were measured with an eddy covariance (EC) system mounted to a tower located 4.7 m over the soil surface and facing to the predominant wind directions (S–W and S–E). The EC system used in this study consisted of a fast response, openpath, infrared gas analyzer IRGA (LI-7500, LI-COR Inc., Lincoln, Nebraska, USA) and a three-dimensional sonic anemometer (CSAT3, Campbell Scientific Inc., Logan, UT, USA) (Table 1). To minimize flux loss and flow distortion, IRGA was mounted a few centimeters below the CSAT3 volume center (Campbell Scientific, Inc. 2006). Footprint was calculated using the analytical 1D footprint model proposed by Schuepp et al. (1990). The upwind fetch was about 550 m in length for the prevailing wind directions. The EC fluxes were sampled and stored in a datalogger (CR5000, Campbell Scientific Inc., Logan, UT, USA) at 10 Hz. The average values of LEEC and HEC were calculated and recorded with an output frequency of 30 min. Finally, the raw, high-frequency data (10 Hz) were post-processed using the EdiRe software package developed at the University of Edinburgh, including coordinate rotation using the planar fit method (Wilczak et al. 2001), sensible heat flux correction (Schotanus et al. 1983), and latent heat flux correction (Webb et al. 1980). Net radiation was measured by a Fritchen type net radiometer (Q7.1, Campbell Sci., Logan, UT, USA) (RnQ7.1). Also, the components of net radiation over the vineyard (albedo, incoming shortwave radiation, outgoing shortwave radiation, incoming longwave radiation and outgoing longwave radiation) were measured by a fourway net radiometer (CNR1, Kipp & Zonen, Delft, The

Netherlands) which consists of two pyranometers (CM-3) and two pyrgeometers (CG-3) (Table 1). Soil heat flux (GHFT3) was measured by eight soil heat flux plates buried at a depth of 0.08 m (HFT3, Campbell Scientific Inc., Logan, UT, USA) (Table 1). Four plates were used to measure soil heat fluxes under canopy, and four additional plates were used to measure the soil heat flux between rows. This arrangement was established in order to account the row shade effect during the course of the day. Variation of the average soil temperature was measured by two soil thermocouples (TCAV, Campbell Scientific Inc., Logan, UT, USA) positioned at depths of 0.02 and 0.06 m above each heat flux plate. The heat stored above the plates was added algebraically to the fluxes measured by the soil heat flux plates (Oliphant et al. 2004; Ortega-Farias et al. 2010). Measurements of soil heat fluxes and soil temperatures were recorded every 10 s by a datalogger (CR1000, Campbell Scientific Inc., Logan, UT, USA) and the average was recorded every 30 min. Moreover, the energy balance closure was evaluated using a linear regression between turbulent energy fluxes (HEC ? LEEC) and available energy (RnQ7.1 - GHFT3) for a 30-min period (Wilson et al. 2002). Finally, values of LEEC and HEC from the EC system were recalculated using the Bowen Ratio (b = HEC/LEEC) (Twine et al. 2000; Chavez et al. 2005; Martinez-Cob and Faci 2010): RnQ7:1  GHFT3 1þb

ð2Þ

bðRnQ7:1  GHFT3 Þ 1þb

ð3Þ

LEBR ¼ HBR ¼

A second meteorological station was used to collect air temperature (Ta), soil temperature (Tsoil), canopy temperature (Tc) (measured with a Vaisala sensor installed inside of the canopy), relative humidity (RH), wind speed (u), and incoming solar radiation ðK #Þ (Table 1). Reflectance measurements Reflectance measurements obtained by a hand-held multispectral radiometer were used to calculate the average normalized difference vegetation index of the vineyard plot (NDVI) as follows: NDVI ¼ fc NDVIr þ ð1  fc ÞNDVIbr

ð4Þ

where fc is the average fractional cover (dimensionless), NDVIbr is the normalized difference vegetation index measured from soil between rows (dimensionless), and NDVIr is the normalized vegetation index measured over vine canopy (dimensionless). The NDVIbr and NDVIr were calculated using the standard equation developed by Rouse et al. (1974):

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Irrig Sci Table 1 List of sensors used for micrometeorological and meteorological measurements

Instrument Eddy covariance

a

o.f. is the output frequency; b Eight locations; cTwo depths per each location

NDVIr ¼

NIRr  REDr NIRr þ REDr

NDVIbr ¼

NIRbr  REDbr NIRbr þ REDbr

Variables

Sensors

Scan rate/o.f.a

Installation height (m)

10 Hz/30 min

4.7

Sensible heat flux

CSAT3 (Campbell Sci.)

Latent heat flux

LI-7500 (LI-COR)

Net radiometer

Net radiation

Q7.1 (Campbell Sci.)

10 s/30 min

4.7

Four-way net radiometer

Albedo, incoming and outgoing shortwave and longwave radiation

CNR1 (Kipp and Zonen)

10 s/30 min

4.7

Soil heat flux plates and thermocouples

Soil heat flux

HFT-3 (Campbell Sci.)b

10 s/30 min

-0.08

Soil temperature

TCAV (Campbell Sci.)c

Automatic meteorological station

Air and canopy

HMP-35 and 45 (Vaisala)

Temp/R. Humidity Wind speed/direct.

Wind sentry 3001 (Young) LI-200X (LI-COR)

Pyrgeometers (CG-3) -0.06, -0.04 10 s/30 min

4.7 1.5, 4.7 4.7

Solar radiation

ð5:1Þ

Table 2 Hand-held multi-spectral radiometer bands used to calculate normalized difference vegetation index (NDVI) Wavelengths

Band

Spectrum region

630–690

B4

Visible red

820–880

B6

Near infrared

ð5:2Þ

where NIR is the near-infrared (%) and RED is the visible red (%). Both variables corresponded to their respective reflectance in the light band. Sub-indexes r and br correspond to values measured over vine canopy and from soil between rows, respectively. Thirty-two dates were chosen for calculating NDVI during the three growing seasons at different phenological stages (Flowering, Fruit set, Veraison and Harvest). In this study, 64 sampling points (regular grid of 20 9 20 m) were used to calculate average NDVI values from the influence area of the EC system (footprint). The location of each sampling point was recorded using a Trimble Global Positioning System (GPS) (with differential correction) (Trimble, Inc., Sunnyvale, CA). The multispectral reflectance readings (percentage of incoming solar radiation in each wavelength band) over the vine canopy and soil surface between rows were recorded using a handheld multi-spectral radiometer equipped with sun angle cosine correction capacity (MSR16R, CropScan Inc., Rochester, MN). The multi-spectral radiometer was manually transported and a support pole was used to position the radiometer at the desired level above the canopy. This sensor utilizes narrowband interference filters to select discrete bands in VIS and NIR regions of the electromagnetic spectrum. In this study, nine bands were measured within the 485–1,650 nm range of which Bands 4 and 6 (Table 2) were used to calculate NDVI (Eq. 2). Hand-held multi-spectral radiometer calibrations were conducted with an opal glass diffuser using the two-point (2 Point Up/Down) method (Cropscan Inc. 2001). The view

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Pyranometers (CM-3)

Wavelengths expressed in nm

angle of the hand-held, multi-spectral radiometer was constant, facing vertically downward with a 28° field of view (FOV) for reflected radiation. The measurements were carried out at 0.5 m above the vine canopy and 2.5 m above the soil surface, which resulted in a projected view area of 0.05 m2 with a diameter of 0.25 m for vine and projected view area of 1.22 m2 with a diameter of 1.25 m for soil. Furthermore, the hand-held multi-spectral radiometer was equipped with an external infrared (IR) thermometer (IRt/c.2-K-80F/27C, Exergen Corporation, Watertown, MA, USA) to obtain surface temperature (Tsurf_IR). Measurements were made under clear conditions at midday (13:00–15:00) to minimize the effect of diurnal changes in solar zenith angle. Remote sensing algorithm (RSA) The evaluation of the RSA was performed through two steps: (1) calibration (2007/2008 season) and validation (2008/2009 and 2009/2010 seasons) of the sub-models used to estimate instantaneous energy balance components and Rnday; and (2) validation of the extrapolation method based on Kins and Rnday for estimating daily actual evapotranspiration using meteorological and reflectance data.

Irrig Sci

Instantaneous net radiation

4 L "ins ¼ e0 rTsurf

The estimated instantaneous net radiation (Rnins) expressed in W m-2 was calculated using the following equation (Allen et al. 2007; Samani et al. 2007):

where Tsurf is the estimated surface temperature (K) and e0 is the estimated surface thermal emissivity (dimensionless). e0 was calculated as follows (Van der Griend and Owe 1993):

Rnins ¼ ð1  aÞK #ins þ L #ins  L "ins  ð1  e0 ÞL #ins ð6Þ where K #ins is the measured instantaneous incoming shortwave radiation (W m-2); a is the estimated surface albedo (dimensionless). L #ins is the estimated instantaneous incoming longwave radiation (W m-2), L "ins is estimated instantaneous outgoing longwave radiation (W m-2), and e0 is the estimated surface thermal emissivity (dimensionless). In this study, the surface albedo for the whole sparse vineyard (rows and between rows) was estimated using RED and NIR bands reflectance according to the simple model proposed by Brest and Goward (1987) weighted by the factional cover: a ¼ fc ðc1 REDr þ c2 NIRr Þ þ ð1  fc Þðc1 REDbr þ c2 NIRbr Þ ð7Þ where fc is the measured fractional cover (dimensionless), NIRr is the average near-infrared wavelength measured over the vine canopy (dimensionless), NIRbr is the average near-infrared wavelength measured between rows (dimensionless), REDr is the average visible red light measured above the vine canopy (dimensionless), REDbr is the average visible red light measured between rows, and c1 and c2 are empirical coefficients. Equation 7 was calibrated using instantaneous values of surface albedo measured by the four-way net radiometer CNR1 (aCNR1). L #ins was calculated as follows (Allen et al. 2007; Bastiaanssen et al. 1998a): L #ins ¼ eatm rTa4ins

ð11Þ

where NDVI is the normalized difference vegetation index obtained from the Eq. 4 (dimensionless), c5 and c6 are empirical coefficients that were calibrated inverting Eq. 10 and using the observed surface thermal emissivity and surface temperature measured by an infrared thermometer. Tsurf was estimated using measurements of soil and canopy temperatures (Norman et al. 1995; Ezzahar et al. 2007): qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 4 Tsurf ¼ c7 fc Tc4 þ ð1  fc ÞTsoil ð12Þ where Tsoil is the measured soil temperature (K), Tc is the measured canopy temperature (K), and c7 is an empirical coefficient that was calibrated using surface temperature measured by an infrared thermometer (Tsurf_IR). Instantaneous soil heat flux The estimated instantaneous soil heat flux (Gins) expressed in W m-2 was estimated using the following equation developed by Bastiaanssen (2000):   ð13Þ Gins ¼ Rnins Tsurf ðc8 a þ c9 Þ 1  0:98NDVI4 where c8 and c9 are empirical coefficients. The estimated instantaneous soil heat flux was calibrated using the soil heat flux measured in 8 locations (4 locations below the vine canopy and 4 between rows).

ð8Þ

where r is the Stefan-Boltzmann constant (W m-2 K-4); Tains is the measured instantaneous air temperature (K); and eatm is the estimated atmospheric emissivity (dimensionless). eatm was calculated using the following equation (Bastiaanssen 1995; Bastiaanssen et al. 1998a): eatm ¼ c3 ð lnðssw ÞÞc4

e0 ¼ c5 þ c6 lnðNDVIÞ

ð10Þ

ð9Þ

where sSW is the atmospheric transmissivity calculated as a ratio of incoming shortwave radiation to terrestrial solar radiation (dimensionless) (Allen et al. 1998), and c3 and c4 are empirical coefficients. These coefficients were calibrated inverting Eq. 8 and using the observed atmospheric emissivity and air temperature measured by the meteorological station. L "ins was calculated as follows (Bastiaanssen et al. 1998a; Samani et al. 2007; Allen et al. 2007):

Instantaneous sensible heat flux The estimated instantaneous sensible heat flux (Hins) expressed in W m-2 was calculated by the following equation (Allen et al. 2007): Hins ¼

qair Cp dT rah

ð14Þ

where qair is the moist air density (kg m-3), Cp is the specific heat of air (J kg-1 K-1), rah is the aerodynamic surface resistance (m s-1), and dT is the air temperature gradient (K). Because both rah and Hins are unknown, an iterative solution is required. Instantaneous sensible heat flux as initial conditions Hinsi was calculated as follows: Hinsi ¼

qair Cp ðTsurf  Tains Þ rahi

ð15Þ

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Irrig Sci

rahi ¼

  1 zr  d ln kui zoh

ku  b  d ln zzbom   d ur ln zzbom   ub ¼ ln zzr d om

ui ¼

ð16Þ ð17Þ

ð18Þ

zom ¼ c10 h

ð19Þ

d ¼ c11 h

ð20Þ

where h is the height of the vine canopy (m) and c10 and c11 are empirical coefficients. A single-level sonic anemometer (CSAT3) was used to calibrate the coefficients c10 and c11 using the methodology proposed by Martano (2000). This methodology reduces the problem of finding joint values of both zom and d to a simpler least squares procedure for one variable. For subsequent iterations, corrected values for u* were computed taking into account the stability corrections for momentum and heat transport based on Monin–Obukhov similarity theory (Allen et al. 2007; Bastiaanssen et al. 1998a). The longitude of Monin–Obukhov as initial condition (Li) was computed as follows: ð21Þ

Next, the consecutive iterations of instantaneous sensible heat flux (Hinsn ) were calculated as follows: qair Cp ðTsurf  Tains Þ rahn   1 zr  d ¼  ln  whn ku1 zoh

Hinsn ¼ rahn

un ¼

ku  b zb d ln zom  wmn

Ln ¼

ð24Þ

ð27Þ ð28Þ ð29Þ

Instantaneous latent heat flux The estimated instantaneous latent heat flux (LEins) expressed in W m-2 was calculated as a residual of surface energy balance components using the following equation: LEins ¼ Rnins  Gins  Hins

ð30Þ

Finally, the estimated instantaneous evaporative fraction (Kins) was computed as follows: Kins ¼

LEins Rnins  Gins

ð31Þ

This approach assumes that instantaneous evaporative fraction is constant on a daily basis. Daily actual evapotranspiration Once the Kins is calculated and assuming that average daily soil heat flux (Gday) is negligible, estimated daily actual evapotranspiration (ETa) expressed in mm day-1 can be calculated by using the extrapolation method based on Kins and average daily net radiation (Rnday) (Bastiaanssen et al. 1998a; Chavez et al. 2008): ETa ¼

ð23Þ

ð26Þ

qair Cp u3 n Tsurf kgHinsn

ð22Þ

where n indicates the consecutive number of iteration, g is the gravitational acceleration (9.8 m s-2), wh is the

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   zr  d 0:25 1  16 Ln     1 þ v2mn 1 þ vmn wmn ¼ 2ln þ ln 2 2   p  2 arctan vmn þ 2   0:25 zb  d vmn ¼ 1  16 Ln

vh n ¼

where rahi is the aerodynamic surface resistance as initial conditions (m s-1), zr is the reference height (m), k is the von Karman’s constant (0.41 dimensionless), Tains is the instantaneous air temperature (K), zom is the momentum roughness length (m), d is the zero-plane displacement height (m), ub is the wind speed at a blending height zb (m s-1), ur is the measured wind speed at zr (m s-1), zoh is the roughness height for heat transfer (m) (taken as 0.1 zom), and ui* is the friction velocity for initial conditions (m s-1). The estimated aerodynamic parameters zom and d were calculated by the simple equation proposed by Brutsaert (1982):

q Cp u3 i Tsurf Li ¼ air kgHinsi

integrated stability for heat, and wm is the integrated stability for momentum. wh and wm were calculated under the instable condition (L \ 0) using a formulation developed by Paulson (1970): ! 1 þ v2hðbÞ whn ¼ 2 ln ð25Þ 2

86; 400; 000Kins ðRnday Þ kqw

ð32Þ

k ¼ 2; 501; 000  2; 361Taday

ð33Þ -1

where k is the latent heat of vaporization (J kg ), qw is the water density (kg m-3), 86,400,000 is a conversion factor, Taday is the measured daily average air temperature (°C), and Rnday is the average daily net radiation (W m-2). Rnday was calculated as follows (Bastiaanssen et al. 1998a):

Irrig Sci

Rnday ¼ ð1  aÞK #day c12 ssw day

ð34Þ

where c12 is an empirical coefficient, K #day is the measured daily incoming shortwave radiation (W m-2) and ssw day is the daily atmospheric transmissivity (dimensionless) calculated as follows: ssw day ¼

K #day K #exo day #exo day

d ¼ 0:006918  0:399912 cosðda Þ þ 0:070257senðda Þ  0:006758 cosð2da Þ þ 0:000907  senð2da Þ  0:002697  cosð3da Þ þ 0:00148  senð3da Þ

Mean bias error

MBE MAE

-2

Root-meansquare error

RMSE

Index of agreement

IA

ð37Þ

xsday ¼ ar cosð tanð/Þ tanðdÞÞ

Symbol

Mean absolute error

E0 ¼ 1:00011 þ 0:034221 cosðda Þ þ 0:001218 sinðda Þ þ 0:000719 cosð2da Þ þ 0:000077 sinð2da Þ 2pðJ  1Þ 365

Statistical parameters

ð35Þ

is the daily terrestrial solar radiation (W m ). where K Equation 34 was calibrated using measurements from a Q7.1 net radiometer (RnQ7.1). Values of K #exo day were calculated as follows (Iqbal 1983):    24 Gsc E0 sinð/Þ sinðdÞ xsday  tan xsday K #exo day ¼ 11:574 p ð36Þ

da ¼

Table 3 Statistical parameters to evaluate the performance of the remote sensing algorithm

ð38Þ

Equation

1 N 1 N

N P

Optimum 0

ðEi  Oi Þ

i¼1 N P

0

j Ei  O i

i¼1

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P N

i¼1

0

ðEi Oi Þ2 N

  PN ðEiOiÞ2 1  PN i¼1 2 ½jEiOjþjOiOj i¼1

1

Ei = estimated; Oi = observed; N = number of data pairs

standard values: (1) LEEC, HEC, and ETaEC and (2) LEBR, HBR, and ETaBR EC fluxes corrected by the Bowen Ratio. Finally, a sample t test was used to compare observed (KBR) and estimated (Kins) values of instantaneous evaporative fraction.

Results and discussion

ð39Þ General conditions of the vineyard during calibration and validation seasons ð40Þ

where Gsc is the solar constant (1,367 Wm-2), J is the number of the day in the year, E0 is the eccentricity correction factor for a day, xsday is the daily sunrise hour angle (rad), da is the day angle (rad), / is the latitude of the site (rad), and d is the solar declination (rad). Statistical analysis In this study, the calibration analysis was carried out using a nonlinear optimization method, where the empirical coefficients were determined by minimizing the root-meansquare error (RMSE). The validation of sub-models that compute the instantaneous energy balance components (Rnins, Gins, Hins, and LEins) and ETa was carried out using the ratio of estimated to observed values (reo), mean bias error (MBE), index of agreement (IA), mean absolute error (MAE), and root-mean-square error (RMSE) (Legates and McCabe 1999; Mayer and Butler 1993; Willmott 1982) (Table 3). Student’s t test analysis was applied to check whether the value of reo was significantly different from unity at the 95 % confidence level. It is important to indicate that the simulations of LEins, Hins, and ETa from the remote sensing algorithm (RSA) using two approaches as

In general, the atmospheric conditions at the drip-irrigated Merlot vineyard during calibration and validation seasons were dry and hot. Values of daily average air temperature (Taday) were 20.9, 20.8, and 20.4 °C, while daily average soil temperatures were 26.6, 25.8, and 23.1 °C for the 2007/2008, 2008/2009, and 2009/2010 seasons, respectively. The daily average values of the vapor pressure deficit (VPD) were -1.07, -0.91, and -0.89 kPa for the 2007/2008, 2008/2009, and 2009/2010 seasons, respectively. Values of hrd registered by TRD were very similar during calibration and validation seasons, ranging from 0.27 to 0.36 with an average of 0.31 m3 m-3 for the three seasons (Fig. 1a, c, e). This range indicated that the Merlot vineyard was well irrigated because hrd was maintained between volumetric soil water content at field capacity (hfc) and MAD during the growing seasons. There were only a few exceptions in which hrd reached values lower than MAD (Fig. 1a, c, e). Also, values of wx were used to evaluate the vine water status during calibration and validation seasons, following the water stress classifications proposed by Sibille et al. (2007). During the calibration season (2007/2008), average values of wx ranged between -0.42 and -1.0 MPa (Fig. 1b). These results indicate that the vineyard was under mild to moderate water stress. During the validation seasons (2008/2009 and 2009/2010), average values of wx ranged between -0.30 and -1.2 MPa

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Irrig Sci

(a)

(b)

0.50 0.45

Season 2007/2008

-0.2 -0.4

0.35

-0.6

ψ x (MPa)

0.30 0.25 0.20 Field capacity

0.10

MAD

0.05

Wilting point

325 331 345 352 362 8 14 22 28 31 36 39 43 50 57 63 64 70 71 78 85 91

317 323 331 345 352 362 8 14 21 28 31 35 42 49 56 63 72 80 85 91

(d) Season 2008/2009

0.0 -0.2

0.40

-0.4

0.35

-0.6

0.30

ψ x (MPa)

θ rd (m 3 m -3 )

Day of year

0.25 0.20

I II III

-1.0 -1.2

0.15

Field capacity

0.10

MAD

0.05

Wilting point

IV

-1.4

V

-1.6 -1.8

301 309 315 316 322 336 351 365 6 13 27 41 48 69 76 83

301 316 323 337 344 357 364 5 12 20 26 33 40 47 54 62 68 75 82

Day of year

(f)

0.50

Season 2009/2010

0.0 -0.2

0.40

-0.4

0.35

-0.6

0.30

ψ x (MPa)

0.25 0.20

Season 2009/2010 I II

-0.8

III

-1.0 -1.2

0.15

Field capacity

0.10

MAD

0.05

Wilting point

IV

-1.4

V

-1.6 -1.8

302 310 314 330 337 344 351 358 363 7 12 19 26 33 40 48 54 75 77 82

0.00

Day of year Fig. 1 Evolution of volumetric soil water content at the rooting depth (hrd) and midday steam water potential (wx) for the drip-irrigated Merlot vineyard. Values of field capacity (hfc), wilting point (hwp),

316 330 337 344 349 356 5 7 12 19 26 33 40 47 54 68 75 82

θ rd (m 3 m -3 )

Season 2008/2009

-0.8

Day of year

123

V

-1.6 -1.8

0.50

0.45

IV

-1.4

0.00

(e)

III

-1.0

Day of year

0.45

II

-0.8

-1.2

0.15

0.00

(c)

Season 2007/2008 I

0.40

θ rd (m 3 m -3 )

0.0

Day of year and management allowed depletion (MAD) are included as a reference. I, II, III, IV, and V correspond to correspond to absent, mild, moderate, strong, and severe water stress, respectively

Irrig Sci

2010). In this regard, Twine et al. (2000) proposed as a method for reducing moderate EC imbalance, the use of the BR method for recalculating the turbulent energy fluxes obtained from the EC system (Eqs. 2, 3). In this study, the HEC and LEEC were recalculated using the Bowen ratio which ranged between 0.87–1.88 and 0.62–1.78 for the 2008/2009 and 2009/2010 seasons, respectively.

800 700

H EC +LE EC = 0.89(Rn Q7.1 - G HFT3 ) R² = 0.91 n=1536

H EC + LE EC (W m -2 )

600 500 400 300

Calibration of the empirical coefficients

200 100 0 -100 -200 -200 -100

0

100

200

300

400

500

Rn Q7.1 - GHFT3 (W

600

700

800

m -2 )

Fig. 2 Sensible heat flux plus latent heat flux (HEC ? LEEC) versus net radiation minus soil heat flux (RnQ7.1 - GHFT3) over 30-min intervals. The dashed line represents 1:1 line

(Fig. 1d, f). These values indicate that the vineyard was under mild to moderate water stress during most of the season, with just 3 days registering values below the threshold of moderate water stress (-1.1 MPa). The average values of LAI registered during the 2007/08, 2008/09, and 2009/10 seasons were 1.09 (±0.43), 1.10 (±0.45), and 1.12 (±0.47), respectively. A constant average value of fc (30 %) was observed because the canopy geometry (similar to a parallelepiped) of the Merlot vineyard was maintained after full bloom by hedging during the summer. Measured surface energy balance components The analysis of the footprint model showed that under unstable conditions 90 % of cumulative normalized flux measurement is obtained at nearly 280 m lengths. Thus, the upwind fetch (550 m) of the prevailing wind direction was large enough to avoid horizontal advection. Furthermore, in order to analyze the reliability of measurements based on the EC system, energy balance closure was evaluated. Figure 2 shows the linear comparison between available energy (RnQ7.1 - GHFT3) and turbulent energy fluxes (HEC ? LEEC) for a 30-min period. The linear analysis through the origin indicated that the slope (b) was 0.89, and coefficient of determination (R2) was 0.91 (Fig. 1). The slope indicates that turbulent energy fluxes were less than available energy, suggesting an imbalance of about 11 %, which is acceptable according to the literature for vineyards (Spano et al. 2000, 2004; Ortega-Farias et al. 2007,

The calibration of the empirical coefficients from c1 to c12 (Table 4) was done by using data collected during the 2007/2008 growing season. The empirical coefficients for the surface albedo (Eq. 7) c1 and c2 calibrated in this study were 0.674 and 0.398, respectively (Table 4). These coefficients were slightly different from the values presented by Brest and Goward (1987) (c1 = 0.512 and c2 = 0.418). These differences can be attributed to the methodology used to measure RED and NIR values with the hand-held multi-spectral radiometer. In this study, RED and NIR were measured separately for vine canopy and soil between rows. Furthermore, the fc value was used as a weighted factor to scale up the measurements, taking into account the proportion of soil between rows and vine canopy. The calibrated empirical coefficients c3 and c4 obtained for the estimated atmospheric emissivity (Eq. 9) were 1.020 and 0.236, respectively (Table 4). These values were similar to the coefficients (c5 = 1.08 and c6 = 0.265) presented by Bastiaanssen (1995) for western Egypt. However, different coefficients have been registered in diverse conditions. For example Allen et al. (2000) registered values of c3 = 0.85 and c4 = 0.09 for data collected over alfalfa fields in Idaho (USA). Moreover, Teixeira et al. (2009) registered values of c3 = 0.942 and c4 = 0.103 in a study carried out over natural Caatinga vegetation in the Low-Middle Sao Francisco River Basin (Brazil). For the estimation of the surface thermal emissivity (Eq. 11) c5 was 1.016 and c6 was 0.049 (Table 4). These values were similar to the coefficients presented by Bastiaanssen (1995) (c5 = 1.009 and c6 = 0.047) and Teixeira et al. (2009) (c5 = 1.004 and c6 = 0.059). The calibrated value of c7 for the vineyard conditions used for calculating surface temperature (Eq. 12) was 1.063 (Table 4). Using a similar data set as that of the present study, Ortega-Farias et al. (2010) applied the equation proposed by Norman et al. (1995) without any calibration (i.e. c7 = 1). However, in this study, the original model without calibration presented an underestimation of approximately 6.3 %. The necessity to adjust Eq. 12 is a result of the methodology used to measure temperature (Tc and Tsoil). In the original model, Norman et al. (1995) used two infrared thermometers to measure Tc and Tsoil, one pointed at the soil surface

123

Irrig Sci Table 4 Calibrated empirical coefficients of the remote sensing algorithm used to compute the surface energy balance components and daily actual evapotranspiration using meteorological data in combination with reflectance measurements Variable (Units)

Symbol

Equation

Empirical coefficients

Surface albedo (dimensionless)

a

a ¼ fc ðc1 REDr þ c2 NIRr Þ þ ð1  fc Þðc1 REDbr þ c2 NIRbr Þ

Atmospheric emissivity (dimensionless)

eatm

eatm ¼ c3 ð lnðssw ÞÞc4

Surface thermal emissivity (dimensionless)

e0

e0 ¼ c5 þ c6 ln ðNDVIÞ

ð7Þ

c1 = 0.674 c2 = 0.398

ð9Þ

c3 = 1.020 c4 = 0.236

ð11Þ

c5 = 1.016

p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 4 fc Tc4 þ ð1  fc ÞTsoil ð12Þ   ¼ Rnins Tsurf ðc8 a þ c9 Þ 1  0:98NDVI4 ð13Þ

c6 = 0.049

Surface temperature (K)

Tsurf

Tsurf ¼ c7

c7 = 1.063

Instantaneous soil heat flux (W m-2)

Gins

Gins

c8 = 0.0068 c9 = 0.0081

Momentum roughness length (m)

zom

zom ¼ c10 h ð19Þ

Zero-plane displacement height (m)

d

d ¼ c11 h ð20Þ

Average daily net radiation (W m-2)

Rnday

Rnday ¼ ð1  aÞK #day c12 ssw day

c10 = 0.11 c11 = 0.52 ð34Þ

c12 = 135

fc is the fractional cover (dimensionless), NIRr is the average near-infrared wavelength measured over the vine canopy (dimensionless), NIRbr is the average near-infrared wavelength measured between rows (dimensionless), REDr is the average visible red measured above the vine canopy (dimensionless), REDbr is the average visible red measured between rows, ssw is the atmospheric transmissivity (dimensionless), NDVI is the normalized difference vegetation index (dimensionless), Tsoil is the measured soil temperature (K), Tc is the measured canopy temperature (K), Rnins is the instantaneous net radiation (W m-2), h is the height of the vine canopy (m), sswday is the daily atmospheric transmissivity (dimensionless) and K #day is the measured daily incoming shortwave radiation (W m-2)

and the other at the vegetation. However, in this study, Tsoil was measured using soil thermocouples and Tc was measured using a Vaisala sensor installed inside of the canopy. The calibrated values of c8 and c9 used to estimate instantaneous soil heat flux (Eq. 13) were 0.0068 and 0.0081, respectively (Table 4). These values are very different from those presented by Bastiaanssen (2000) (c8 = 0.0074 and c9 = 0.0038) in the irrigated Gediz Basin (Turkey) and by Texeira et al. (2009) (c8 = -0.11 and c9 = 0.002) for irrigated fruit crops (table-grape, winegrape and mango orchard) and for non-irrigated natural vegetation at Caatinga (Brazil). The calibrated empirical coefficients c10 and c11 used for calculating momentum roughness length and zero-plane displacement height were 0.11 and 0.52, respectively (Table 4). These values are different from those presented by Brutsaert (1982) (c10 = 0.13 and c11 = 0.67). For estimating average daily net radiation, the calibrated empirical coefficient c12 obtained in this study was 135. This value is higher than the value presented by Bastiaanssen et al.f (1998a) (c12 = 110) in the Netherlands and lower than the average value presented by Teixeira et al. (2009) (c12 = 143) in the Low-Middle Sao Francisco River Basin in Brazil. The calibration procedure indicated that the majority of the sub-models required a minor correction of the empirical coefficients. The major corrections were carried out in the empirical coefficients used to estimate instantaneous soil heat flux and aerodynamic parameters (momentum roughness length and zero-plane displacement height). In the case of the instantaneous soil heat flux, the differences can

123

be explained by specific conditions of the vineyard, such as canopy geometry, fc, row spacing and irrigation. The vineyards trained on VSP had an incomplete canopy cover with a large portion of the soil surface exposed. Incomplete canopy cover is considered a major cause of the relatively low rates of transpiration in commercial vineyards since the majority of the incident radiation is transmitted to the bare soil surface (Oliver and Sene 1992; Yunusa et al. 2004). In this study, the exposed soil surface (1 - fc) was approximately 70 % of total surface. As a result, the soil contribution to the energy balance was considerable, especially at midday. Measured data showed that at midday soil, heat flux represents approximately 27 % of net radiation. Teixeira et al. (2009) reported that soil heat flux is a difficult term to estimate and should be checked against field measurements. Allen et al. (2007) indicated that several applications of METRIC have required a modification of the empirical functions for estimating instantaneous soil heat flux. In the case of zom and d calculated as a simple function of the vegetation height (Eqs. 19, 20), Brutsaert (1982) indicated values of c10 = 0.13 and c11 = 0.67, for agricultural crops and forest in humid areas covering most of the ground surface (fc close to 1) with homogeneous conditions. However, for sparse vineyards (trained on VSP), the relationship between c10 and c11 with respect to the vegetation height can be very different since diverse parameters such as the canopy architectures play an important role in the calculation of aerodynamic parameters. For example, in vineyards, Riou et al. (1987) found c10 = 0.13 and c11 = 0.50, Van den Hurk (1996) found

Irrig Sci Table 5 Validation of sub-models to estimate the instantaneous values of net radiation (Rnins), soil heat flux (Gins), sensible heat flux (Hins), and latent heat flux (LEins) Simulated variable

RMSE

MAE

Rnins

24 (3.8 %)

21 (3.2 %)

Gins

16 (9.4 %)

13 (7.8 %)

MBE

IA

reo

t test

-2 (0.2 %)

0.94

1.00

T

3 (1.6 %)

0.82

1.01

T

(a) Validation using eddy correlation fluxes as a standard for comparison Hins

59 (26.0 %)

50 (22.0 %)

38 (16.7 %)

0.59

1.13

F

LEins

54 (27.2 %)

44 (22.4 %)

12 (4.2 %)

0.72

1.03

F

0.86 0.75

1.05 0.95

F F

(b) Validation using EC fluxes recalculated by Bowen ratio method as a standard for comparison Hins LEins

34 (13.5 %) 46 (20.8 %)

27 (10.7 %) 37 (16.8 %)

11 (4.2 %) -10 (-4.0 %)

RMSE is the root-mean-square error (W m-2); MAE is the mean absolute error (W m-2); MBE is the mean bias error (W m-2) and IA is the index of agreement (dimensionless); reo is the ratio of estimated to observed values (dimensionless). The values in brackets for RMSE, MAE, and MBE represent relative root-mean-square error (rRMSE), relative mean absolute error (rMAE), and relative mean bias error (rMBE), respectively. T = true hypothesis (reo = 1); F = false hypothesis (reo = 1)

c10 = 0.09 and c11 = 0.34, and Weiss and Allen (1976) found c10 = 0.125 and c11 = 0.70. Validation of instantaneous energy balance components The sub-models used in this study to calculate instantaneous energy balance components (Rnins, Gins, Hins, and LEins) were validated using ground-truth field data collected during the 2008/2009 and 2009/2010 growing seasons. In the first term, the calibrated Eq. 6 was able to estimate the instantaneous net radiation with a RMSE, MAE, MBE, and IA equal to 24 W m-2 (3.8 %), 21 W m-2 (3.2 %), -2 W m-2 (0.2 %), and 0.94, respectively (Table 5). Also, the reo value was not significantly different from unity, indicating that values of RnQ7.1 were similar to those of Rnins. These results are within the 5–10 % error margin of the typical net radiation measurements (Blonquist et al. 2009). Also, these results were similar to those reported by Chavez et al. (2009) using the two-source energy balance model (TSM) and multispectral airborne imagery over corn and sorghum. They reported a good estimation of the instantaneous net radiation with RMSE = 44 W m-2 (7.1 % error) and MBE = -24 W m-2 (-4.0 % error). The comparison between measured and estimated values of the instantaneous net radiation is presented in Fig. 3a, which shows that points were very close to a 1:1 line. Figure 3b shows that values of GHFT3 and Gins ranged between 140 and 200 W m-2 and points were close to the 1:1 line. The t test indicated that reo (1.01) was statistically equal to unity indicating that values of GHFT3 and Gins were similar at the 95 % confident level (Table 5). In addition, the calibrated Eq. 13 simulated the instantaneous soil heat flux for the vineyard conditions with RMSE = 16 W m-2 (9.4 %), MAE = 13 W m-2 (7.8 %) and MBE = 3 W m-2 (1.6 % error). These results are similar to those

registered by Teixeira et al. (2009) who indicated RMSE = 13 W m-2 and an average deviation = 6 % for a local conditions. The average ratio of Gins to Rnins simulated by the calibrated equations (Gins/Rnins = 0.26) was similar to the measured ratio (GHFT3/RnQ7.1 = 0.27). In the literature, the recommended values for the ratio G/Rn range from 0.15 to 0.40, with typical values of around 0.30 for sparse canopies (Brutsaert 1982; Humes et al. 1994; Kustas and Goodrich 1994). Comparisons between HEC versus Hins and HBR versus Hins are shown in Fig. 4a, which indicates that the data points were close to the 1:1 line, especially when HBR was used as a standard (observed value) for comparison. The Hins/HEC and Hins/HBR ratios were statistically greater than unity suggesting that the RSA tended to overestimate the instantaneous sensible heat flux between 5 and 13 %. Also, the ratio of Hins to HEC was greater than that of Hins to HBR by about 8 % (Table 5). Values of RMSE and MAE were 59 (26.0 %) and 50 W m-2 (22 %) when HEC was used as an observed value, while those when HBR was used as a standard for comparison were 34 (13.5 %), 27 W m-2 (10.7 %), respectively. Similar errors were obtained by Teixeira et al. (2009) who found RMSE values and an average deviation equal to 42 W m-2 and equal to 3 %, respectively. The validation of RSA to simulate instantaneous latent heat flux indicated that the reo values were significantly different from unity suggesting that LEins was greater than LEEC by about 3 % and LEins was less than LEBR by about 5 %. Furthermore, Fig. 4b shows that few points presented deviations between 100 and 150 W m-2 from the 1:1 line. Values of RMSE and MAE were 54 (27.1 %) and 44 W m-2 (22.4 %), respectively, when LEEC was used as a standard for comparison. Using LEBR as observed value, RMSE was 46 W m-2 (20.8 %) and MAE was 37 W m-2 (16.8 %). Chavez et al. (2005) indicated that LE estimated

123

Irrig Sci

(a) 900

(b) 300

850 250

800

200

700

G ins (W m-2 )

Rn ins (W m -2 )

750

650 600

150

100

550 500

50

450 0

400 400

450

500

550

600

650

700

750

800

850

0

900

50

100

150

200

250

300

G HFT3 (W m -2 )

Rn Q7.1 (W m -2 )

Fig. 3 Comparison between measured and estimated values of instantaneous net radiation and soil heat flux. RnQ7.1 and GHFT3 were measured at field conditions, and Rnins and Gins were estimated using the remote sensing algorithm (RSA). The dashed line represents 1:1 line

(a)

(b)

500 450 400

EC

450

BR

400

EC BR

350

LE ins (W m-2 )

350

H ins (W m -2 )

500

300 250 200

300 250 200

150

150

100

100

50

50 0

0 0

50

100

150

200

250

300

350

400

450

500

H EC and HBR (W m -2 )

0

50

100

150

200

250

300

350

LE EC and LE BR (W

400

450

500

m -2 )

Fig. 4 Comparison between observed and estimated values of instantaneous sensible and latent heat fluxes. HEC and LEEC were obtained from the eddy correlation (EC) system; HBR and LEBR were

obtained from EC fluxes corrected by the Bowen ratio; and Hins and LEins were estimated using the remote sensing algorithm (RSA). The dashed line represents 1:1 line

by remote sensing has a better agreement with LE adjusted for closure than when LE is not adjusted for closure, reducing RMSE values by around 7 W m-2 (reduction of 14 %). Furthermore, errors found in our study were similar to those obtained by Teixeira et al. (2009) who found a RMSE value equal to 34 W m-2 and an average deviation equal to 10 %.

using remote sensing data (Crago and Brutsaert 1996; Bastiaanssen et al. 1998a; Colaizzi et al. 2006). Moreover, the extrapolation method assumes that instantaneous and daily values of the evaporative fraction are similar (Bastiaanssen et al. 1998a). In this regard, the observed (KBR) and estimated (Kins) values of instantaneous evaporative fractions are indicated in Fig. 5. Also, the daily evaporative fraction (KBRday) computed as a function of daily average values of RnQ7.1, GHFT3, and LEBR was included in this figure. In this study, average values of Kins, KBR and KBRday were 0.44 (±0.12), 0.46 (±0.07), and 0.47 (±0.12), respectively. These average values were significantly similar at the 95 % according to the independent sample

Validation of the daily actual evapotranspiration The extrapolation method used in this study was based on Kins and Rnday. This method is one of the more commonly used in the estimation of daily actual evapotranspiration

123

Irrig Sci 1.0 ins Λ ins

0.9

Λ BR Λ BRday BRday BR

0.8

Evaporative fraction

Fig. 5 Observed (KBR) and estimated (Kins) values of instantaneous evaporative fraction during the study period. Also, the daily evaporative fractions (KBRday) were estimated as a function of daily average values of net radiation (RnQ7.1), soil heat flux (GHFT3), and latent heat (LEBR)

0.7

Season 2009/2010

Season 2008/2009

0.6 0.5 0.4 0.3 0.2 0.1 68

84

47

41

35

23

14

344

316

337

288

76

62

69

41

27

14

337

351

323

315

309

0.0

Day of year

(a) 7.0

Actual evapotranspiration (mm day -1)

6.0 5.0

ETa EC

Season 2008/2009

ETa BR ETa

4.0 3.0 2.0 1.0 41

62

69

41

47

68

76

27 35

Day of year

(b) 7.0 6.0 5.0 4.0

ETa EC

Season 2009/2010

ETa BR ETa

3.0 2.0

84

23

14

344

337

0.0

316

1.0 288

Actual evapotranspiration (mm day -1 )

14

351

337

323

315

0.0 309

Fig. 6 Evolution of actual evapotranspiration obtained by the eddy correlation (EC) system (ETaEC), obtained from EC fluxes corrected by the Bowen ratio method (ETaBR) and estimated using the remote sensing algorithm (RSA) (ETa) during the 2008/2009 (a) and 2009/2010 (b) seasons

Day of year

t test. Nichols and Cuenca (1993) and Crago and Brutsaert (1996), using measurements of surface energy balance components, indicated that evaporative fraction is almost constant during the daytime hours under clear skies. Also, Li et al. (2008) indicated that the instantaneous evaporative fraction at midday (14:00–15:00 h) was approximately equal to the daily evaporative fraction with RMSE of 0.08. However, it is important to indicate that under non-fair

weather conditions, the instantaneous evaporative fraction is not necessarily constant during daytime (Lhomme and Elguero 1999; Gentine et al. 2007). Several studies have suggested that daily average soil heat flux (Gday) values tend toward zero (e.g., Chemin and Alexandridis 2004; Brutsaert 2005; Allen et al. 1998). Thus, Gday was assumed negligible to calculate ETa using RSA. In this study, measured Gday values o were very close

123

Irrig Sci 6.0 EC

ETa (mm day -1 )

5.0

BR

4.0

3.0

2.0

1.0

0.0 0.0

1.0

2.0

3.0

4.0

ETa EC and ETa BR (mm

5.0

6.0

day -1 )

Fig. 7 Comparison between observed and estimated values of daily actual evapotranspiration. ETaEC were obtained by the eddy correlation (EC) system data; ETaBR were obtained from EC fluxes corrected by Bowen ratio (BR) method; and ETa was estimated using the remote sensing algorithm (RSA). The dashed line represents 1:1 line

to zero with an average value = 11 (±15) W m-2. Therefore, the estimation of ETa was calculated only as a function of Rnday and Kins (Eq. 32). In this study, mean values of ETaEC, ETaBR, and ETa were 2.84 (±0.78), 2.81 (±0.83), and 2.55 (±0.81) mm day-1, respectively (Fig. 6a, b). These values are in agreement with those presented in several studies of vineyard water requirements (Oliver and Sene 1992; Evans et al. 1993; Yunusa et al. 1997, 2004; Ortega-Farias et al. 2007; Trambouze et al. 1998; Rana and Katerji 2008; Williams and Ayars 2005). The comparison between ETaEC versus ETa and ETaBR versus ETa is presented in Fig. 7 which shows that the points were close to the 1:1 line, especially when LEBR was

used as a standard for comparison. The ETa/ETaEC and ETa/ETaBR ratios were significantly different from unity, suggesting that the RSA underestimated the daily actual evapotranspiration with an error margin less than 9 % (Table 6). Values of RMSE, MAE, and MBE for the comparison between ETaEC and ETa were 0.45 (15.8 %), 0.40 (14 %), and -0.24 (-8.5 %) mm day-1, while those for the comparison between ETaBR and ETa were 0.38 (13.4 %), 0.32 (11.3 %), and -0.21 (-7.4 %) mm day-1, respectively. Errors found in this study are similar to those presented by Teixeira et al. (2009), who estimated ETa using Landsat images with a RMSE value of 0.38 mm day-1 and Chavez et al. (2008), who estimated ETa using multispectral images over corn and soybean fields with a RMSE value of 0.35 mm day-1. The worst performance of the RSA was observed on DOY337 (season 2008/2009) where ETa, ETaEC, and ETaBR were 2.1, 2.83, and 2.87 mm day-1, respectively (Fig. 6a). Major disagreements between observed and estimated values were associated with errors in the estimation of the evaporative fraction and instantaneous latent heat flux. In this case, values of KBR and Kins were 0.52 and 0.3, while those of LEins and LEBR were 147 and 230 W m-2, respectively. In general, the underestimation of LEins was observed when levels of solar radiation rapidly changed in short period of time. On DOY 337, solar radiation at midday was reduced in less than 1 h by about 200 W m-2 due to clouds.

Conclusion The calibration analysis indicated that the empirical coefficients of the sub-models to estimate the surface albedo (a), atmospheric emissivity (eatm), surface thermal emissivity (e0), and surface temperature (Tsurf) required a minor correction. The major corrections were done in the empirical coefficients used to estimate instantaneous soil heat flux

Table 6 Validation of the remote sensing algorithm to compute the daily actual evapotranspiration using meteorological and reflectance data obtained from a hand-held multi-spectral radiometer Validation method

RMSE

MAE

MBE

IA

reo

t test

ECa

0.45

0.40

-0.24

0.92

0.91

F

(15.8 %)

(14.0 %)

(-8.5 %)

0.38

0.32

-0.21

0.96

0.92

F

(13.4 %)

(11.3 %)

(-7.4 %)

BRb a

EC is the validation using observed values obtained from eddy covariance system

b

BR is the validation using observed values obtained from eddy covariance system corrected by Bowen ratio method. RMSE is the root-meansquare error (mm day-1); MAE is the mean absolute error (mm day-1); MBE is the mean bias error (mm day-1); IA is the index of agreement (dimensionless). reo is the ratio of estimated to observed values (dimensionless). The values in brackets for RMSE, MAE, and MBE represent relative root-mean-square error (rRMSE), relative mean absolute error (rMAE), and relative mean bias error (rMBE), respectively. T = true hypothesis (reo = 1); F = false hypothesis (reo = 1)

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(Gins) and aerodynamic parameters (momentum roughness length (zom) and zero-plane displacement height (d)). The validation analysis of instantaneous fluxes indicated that calibrated sub-models were able to estimate instantaneous net radiation, soil heat flux, sensible heat and latent heat with a RMSE, MAE and IA ranging between 16–54, 13–44 W m-2, and 0.72–0.94, respectively. Using the EC turbulent energy fluxes recalculated by the Bowen ratio method, the validation analysis indicated that the remote sensing algorithm was able to estimate daily actual evapotranspiration with RMSE = 0.38 mm day-1, MAE = 0.32 mm day-1, and IA = 0.96. It is important to indicate that the relative root-mean-square error (rRMSE) were reduced by about 12.5, 6.4, and 2.4 % in the estimation of Hins, LEins, and ETa, respectively, when EC fluxes were recalculated using the Bowen ratio approach. Finally, the results obtained in this study demonstrate the potential use of reflectance data in combination with meteorological measurements to estimate energy balance components and daily actual evapotranspiration over a drip-irrigated Merlot vineyard trained on VSP under semi-arid conditions. Acknowledgments This study was supported by the Chilean government through the projects CONICYT (No 79090035) and FONDECYT (No 1071040 and 3100128).

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