Parameterization of the Satellite-Based Model ( METRIC ) for the Estimation of Instantaneous Surface Energy Balance Components over a Drip-Irrigated Vineyard

A study was carried out to parameterize the METRIC (Mapping EvapoTranspiration at high Resolution with Internalized Calibration) model for estimating instantaneous values of albedo (shortwave albedo) (αi), net radiation (Rni) and soil heat flux (Gi), sensible (Hi) and latent heat (LEi) over a drip-irrigated Merlot vineyard (location: 35°25′ LS; 71°32′ LW; 125 m.a.s. (l). The experiment was carried out in a plot of 4.25 ha, processing 15 Landsat images, which were acquired from 2006 to 2009. An automatic weather station was placed inside the experimental plot to measure αi, Rni and Gi. In the same tower an Eddy Covariance (EC) system was mounted to measure Hi and LEi. Specific OPEN ACCESS Remote Sens. 2014, 6 11343 sub-models to estimate Gi, leaf area index (LAI) and aerodynamic roughness length for momentum transfer (zom) were calibrated for the Merlot vineyard as an improvement to the original METRIC model. Results indicated that LAI, zom and Gi were estimated using the calibrated functions with errors of 4%, 2% and 17%, while those were computed using the original functions with errors of 58%, 81%, and 5%, respectively. At the time of satellite overpass, comparisons between measured and estimated values indicated that METRIC overestimated αi in 21% and Rni in 11%. Also, METRIC using the calibrated functions overestimated Hi and LEi with errors of 16% and 17%, respectively while it using the original functions overestimated Hi and LEi with errors of 13% and 15%, respectively. Finally, LEi was estimated with root mean square error (RMSE) between 43 and 60 W·m−2 and mean absolute error (MAE) between 35 and 48 W·m−2 for both calibrated and original functions, respectively. These results suggested that biases observed for instantaneous pixel-by-pixel values of Rni, Gi and other intermediate components of the algorithm were presumably absorbed into the computation of sensible heat flux as a result of the internal self-calibration of METRIC.


Introduction
Nowadays drip irrigated viticulture in semi-arid zones is under political and economic pressure to optimize irrigation strategies, considering the persistent diminishing water supply, due to increased consumption, mismanagement and pollution.In this regard, irrigation strategies such as regulated deficit irrigation or partial root drying have emerged as potential ways to increase water savings [1][2][3].Therefore, it is critical to know the vineyard water use or actual evapotranspiration (ETa) during the entire growing season with the aim of planning and maintaining adequate water management [4][5][6][7].Accurate estimation of ETa is a key to understand a range of hydrological, climatic, and ecosystem processes [8,9].Presently, there are various methods to obtain ETa based on the measurements of the surface energy balance (SEB) [10,11] such as the Eddy Covariance (EC) and Bowen ratio (BRES) systems, which have been widely used in research to quantify ETa of a vineyard [7,[12][13][14][15][16][17].However, these systems do not provide spatial trends of ETa because these measurements represent a point influenced by a small footprint area [18,19].
During the last 20 years, satellite-based remote sensing (SBRS) tools have emerged as a low-cost, yet reliable alternative to estimate ETa over large areas and wide range of vegetation types [10,11,[20][21][22][23][24].These remote sensing tools estimate ETa based on algorithms which compute the SEB components using remotely sensed surface reflectance in the visible (VIS) and near-infrared (NIR) wavebands and surface temperature (radiometric) from the infrared (IR) thermal bands [19,24,25].In this manner, using satellite based data and ground-based weather measurements; ETa for each pixel is computed as a residual from the surface energy balance (RSEB) equation: where λ is the latent heat of vaporization (J•kg −1 ); ETi is the instantaneous evapotranspiration

and
Hi is sensible heat flux (W•m −2 ).Subscripts "i" denote measurements at the time of satellite overpass.
Most of the RSEB models available in the literature are one-source modeling approaches.One of the most cited algorithms is METRIC (Mapping EvapoTranspiration at high Resolution with Internalized Calibration) [26] which was derived from the SEBAL (Surface Energy Balance Algorithm for Lands) model [9].SEBAL estimates the energy partitioning at a field scale using minimal requirements of field data over relatively flat landscapes with and without irrigation.As an improvement from SEBAL, METRIC was designed to estimate ETa for irrigated crops incorporating ground-based reference Penman-Monteith evapotranspiration by assuming a one-source resistance transfer scheme [22].According to [27,28] the internal self-calibration of METRIC removes a substantial amount of systematic biases in the ETa estimate by calibrating the sensible heat flux for two extreme conditions (hot pixel and cold pixel) or "anchor pixels".Consequently, daily ETa can be obtained at high spatial resolution (e.g., 30 m × 30 m for Landsat scenes) as follow: where ETa_M is the daily ETa computed for each pixel (mm•d −1 ); ETo is the daily Penman-Monteith reference evapotranspiration (mm•d −1 ) [29]; Fi_M is the reference evapotranspiration fraction developed from the near-instantaneous image time and assumed to be constant across the day for well-watered agricultural crops (dimensionless); ETi_M is the instantaneous ETa computed for each pixel (mm•h −1 ) [30][31][32]; ETo_i is the instantaneous ETo (mm•h −1 ).
According to [33] a disadvantage of the energy balance approach employed in METRIC is that the computation of the latent heat flux (and subsequently the estimated evapotranspiration) is only as accurate as the estimates of net radiation, soil heat flux and sensible heat flux.Several researchers have indicated that METRIC could present absolute errors between 5% and 20% in the estimation of daily or seasonal ETa of several fully covered crops such as alfalfa, bean, pea, potato, sugar beet, spring grain, winter grain, corn, soybean and sorghum [22,24,26,28,34].On the other hand, the application of satellite-based models like METRIC to sparse crops such as vineyards has recently been applied with promising results [32,[35][36][37][38][39].Generally, vineyards have widely spaced rows that affect the partitioning and spatial distribution of net radiation.Thus, in a drip-irrigated vineyard, the partitioning of net radiation into sensible, latent and soil heat fluxes is conditioned to the surrounding soil, canopy training system and plant density, where the sensible heat flux is the principal component of the vineyard SEB [14,40].Consequently, understanding the behavior of SEB components over drip-irrigated vineyard could provide insights into sources of error in the quantification of water and energy exchanges considering that canopies are geometrically and thermally heterogeneous.In this respect, [28] indicated that although daily values of SEB fluxes are generally more helpful and practical than instantaneous energy fluxes derived at the satellite overpass, it is important to identify the systematic model bias in the energy balance components on the image and attribute biases to correct the causes.
As far as we known, there are very few studies that evaluate the trends of SEB components over a drip-irrigated vineyard derived from remote-sensing techniques.Thus, it is necessary to evaluate the accuracy of RSEB models to estimate the energy balance components over sparse canopies such as vineyards.In this regard, the main goal of this research is to parameterize the METRIC model for estimating instantaneous values of Rni, Gi, Hi and LEi over a drip-irrigated Merlot vineyard under Mediterranean semi-arid climatic conditions.Also, the specific sub-models to estimate G, LAI and zom were calibrated for the Merlot vineyard as an improvement of the original algorithm of METRIC.

Theoretical Basis
The instantaneous net radiation for each pixel at the time of the satellite overpass is estimated using the following equation: where αi is the broadband surface albedo (dimensionless); Rs↓ is the incoming shortwave radiation (W m −2 ); RL↓ and RL↑ are the incoming and outgoing longwave radiation, respectively and εo is the surface emissivity that accounts for reflectance of incoming longwave radiation at the land surface [34].The broadband albedo is computed by the integration of the surface reflectances for the visible and near infrared (NIR) bands using a weighting coefficient as [41]: where ρs,bd is at-surface "s" reflectance for each "bd" band (dimensionless) and wbd is the weighting coefficient of the Landsat bands for calculating broad-band surface albedo (dimensionless).To compute the instantaneous soil heat flux, three empirical relations depending on the leaf area index (LAI) can be used.These functions were originally developed for annual crops as follows [27,42].
where Tsi is the radiometric temperature (in °C) computed from the thermal infrared waveband (TIR); LAI is expressed in (m 2 •m −2 ); 0.0074 and 0.0038 are empirical coefficients and NDVI is the normalized difference vegetation index (dimensionless).The leaf area index is computed in METRIC using the next empirical relations [27]: ( ) where SAVI is the soil adjusted vegetation index (dimensionless) [43] calculated for each pixel [42].
Instantaneous pixel-by-pixel sensible heat fluxes are obtained for each scene as follows: where ρair is the air density (kg•m −3 ); Cp is the specific heat capacity of air (1004 Previous studies [9,26] have demonstrated that ΔTs can be spatially approximated as a simple linear function: where β0 and β1 are empirical calibration coefficients for each satellite scene.Tsi is expressed in °K. Considering that the values of Ta above each pixel are unknown, the determination of β0 and β1 involves an iterative process, which is based in the selection of several well-known anchor pixels (wet and dry) at each scene.These anchor points are recognizable because they ideally represent the conditions of an agricultural field with full and active transpiration vegetation close to reference conditions (cold pixel) and a surface with no vegetation cover (hot pixel) with little or residual evaporation from soil [44].In this manner, the SEB of the cold pixel can be computed as: where Hcold, Rncold and Gcold represent the sensible heat, net radiation and soil heat fluxes for each cold pixel located inside the image at the time of satellite overpass (W•m −2 ); ϕ is an adjustment factor which incorporates the probability of wet soil surface beneath the vegetation canopy that may increase the total ETo_i [30].In the same way, the SEB of the hot pixel within each image can be calculated using the Equation (13), assuming that ETo_i is near to zero.In this manner, the values of β0 and β1 obtained from the anchor pixels are then used in the estimation of Hi for each pixel by an iterative process that involves the Monin-Obukhov similarity theory [22,25,26].The self-calibration of METRIC involves the inverse calibration of the SEB via the sensible heat flux computed by specifying the evapotranspiration at the two anchor pixels.This process removes systematic biases embedded in the estimations of Rni, Gi and other intermediate components of the METRIC algorithm, which are common to nearly all satellite-based calculations.These biases are in turn removed in the computation of the ETa, considering that the process is executed for millions of pixels contained inside each scene [27].For more details about METRIC data processing and physical-mathematical algorithms, refer to [26] and the METRIC application-manual [27].

Materials and Methods
The study was carried out in a drip-irrigated vineyard located in the Talca Valley, Maule Region, Chile (35°25′ LS; 71°32′ LW; 125 m.a.s.l) during the 2006-2007, 2007-2008 and 2008-2009 growing seasons (Figure 1).The vineyard was planted in 1999 and it had a surface of 97 ha where approximately 57.3 ha are planted and the remainder is covered by buildings, roads, trees, gardens and a plant nursery.Inside the vineyard, a plot with Merlot vines (Vitis vinifera L.) of 4.25 ha was selected (Figure 2).This experimental plot was flat and surrounded by another vineyard field with similar characteristics.The climate of the area is classified as Mediterranean semiarid, with an annual mean temperature of 17.4 °C.The minimum and maximum yearly temperatures are 8.2 and 22.3 °C, respectively.Annual precipitation is around 700 mm concentrated in the fall and winter.The cumulative reference evapotranspiration is approximately 1100 mm, from spring to summer.The soil type at the experimental plot is classified as Talca series (family Fine, mixed, thermic Ultic Haploxeralfs) with a clay loam texture.The volumetric soil content was measured as 0.36 m 3 •m −3 (216 mm) and 0.22 m 3 •m −3 (132 mm) for field capacity (θFC) and wilting point (θWP), respectively, considering a root depth of 0.6 m.The maximum allowed depletion (MAD) of the soil was 174 mm.
The training system of the Merlot vineyard was vertical shoot positioned (VSP) with a plant density of 2667 plants•ha −1 (2.5 m between rows and 1.5 m between vines).The canopy width and foliage height were 0.5 and 2.0 m, respectively.The canopy was maintained as a parallelepiped where the values of LAI and fractional cover (fc) were between 0.8-1.2m 2 •m −2 and 0.28-0.31m 2 •m −2 , respectively, particularly after bloom (about mid-November) by hedging two or three times during the summer.The vineyard was drip-irrigated using emitters of 4.0 L•h −1 spaced at 1.5 m along the rows.It is important to note that vines were maintained under non-water stress conditions during the study period.This condition was evaluated using weekly measurements of volumetric soil water content (θi) at the effective rooting depth and midday stem water potential (Ψx).Measurements of θi and Ψx were done using a portable Time Domain Reflectometry (TDR, Trase System, 6050X1, Santa Barbara CA, USA) and a pressure chamber (PMS instruments, model 600, Albany OR, USA), respectively.Five key phenological stages were identified according to [45]: Bud break (B), Flowering (FL), Fruit set (FS), Veraison (V) and Harvest (HA).Based on visual inspection, the start of a stage was assumed to occur when 50% of vines had reached a new phenological state.

Vine Surface Energy Balance Measurements
A tower of 4.7 m of height was installed over the Merlot vineyard to measure the meteorological variables and energy balance components.Height and sensor characteristics are indicated in Table 1.
To measure the net radiation, incoming (Rsin) and outgoing solar radiation (Rso) a four-component net radiometer (Kipp&Zonen Inc, CNR1, Delft, The Netherlands) was installed above the canopy.Values of Rso and Rsin were also used to compute the vineyard albedo (α = Rsin/Rso).Additionally as backup, a net radiometer (REBS, Q7.1, Seattle, WA, USA) was installed next to the tower at the same height.For the 2008-2009 seasons the four-component net radiometer was removed and the measurements continued using only the REBS Q7.1 net radiometer.Surface soil heat flux at 0.08 m depth was measured by eight soil heat flux plates (HFT3, Campbell Scientific Inc., Logan, UT, USA) regularly distributed along the space between the inter-row and inter-plant.Surface soil heat fluxes were computed by correcting the soil heat fluxes at 0.08 m using thermal storage computed from four pairs of soil temperature thermocouples (TCAV, Campbell Scientific Inc., Logan, UT, USA).These allowed the better integration of the higher values from the sun-exposed area and the lower values from the shadowed area considering the path of the sun from the morning to the afternoon.Sensible and latent heat fluxes were measured using an Eddy Covariance system mounted at a height of 4.7 m (Table 1) and oriented towards the predominant wind direction (South).Sensible heat fluxes were calculated by a three-dimensional sonic anemometer/thermometer (CSAT 3, Campbell Scientific Inc., Logan, UT, USA) and latent heat fluxes were computed by a fast response open path infrared gas analyzer (IRGA) (LI-COR Inc., LI7500, Lincoln, NE, USA) as follows [46]: where ' q ' w is the covariance between the instantaneous variation of the vertical wind speed (w') (m•s −1 ) and humidity (q')•(kg•kg −1 ); ' T ' w is the covariance between w' and the instantaneous sonic temperature (T') (°K).
The footprint analysis indicated that 90% of cumulative normalized fluxes were close to 550 m (rFR ≈ 117:1) at the time of satellite overpass (Figure 2c,d).Also, the wind-rose from Figure 2e,f shows the existing upwind fetch of the prevailing wind direction (South).Raw data of H and LE were post-processed considering corrections of density [47], sonic temperature [48] and coordinate rotation [49].These data were computed over 30 min intervals.For the quality control, the energy balance closure was computed using the ratio (Cf) of turbulent fluxes (H + LE) to available energy (Rn − G).When the daily ratios were outside the range between 0.8 and 1.2, the entire day was excluded to reduce the uncertainty associated with errors in the LE and H measurements [40].Assuming that the measurements of Rn and G were representative of the available energy in the vineyard, the fluxes of H and LE were forced to close the energy balance using the Bowen ratio [13,50,51]: (17) where β (= H/LE) is the hourly Bowen ratio (dimensionless).Subscript β indicates that the turbulent energy fluxes were forced to close the energy balance using the Bowen ratio.
Raw net radiation, CSAT, and IRGA data were sampled and stored in a datalogger at 10 Hz (CR5000, Campbell Scientific Inc., Logan, UT, USA).Data of the surface soil heat flux plates and soil temperature thermocouples were also sampled and stored in a separate datalogger (CR1000, Campbell Scientific Inc., Logan, UT, USA).

Ground Measurements of Vineyard Reflectance
During the growing seasons 2007-2008, 2008-2009 and 2009-2010, weekly ground measurements of reflectance for the near infrared (NIR) and red (R) wavebands (similar to Landsat) were collected for the space occupied for the canopy (r) and the bare soil (br).These measurements were taken in 64 grid points regularly spaced at 20 × 20 m 2 inside the experimental plot as previously indicated by [52].The measurements of NIR and R wavebands were done using a handheld multi-spectral radiometer (CropScan Inc., MSR16R, Rochester, MN, USA).During the 2008-2009 growing season a thermal infrared thermometer (Exergen Corporation, IRt/c.2-K80F/27C,Watertown,MA, USA) was acquired to measure the thermal infrared waveband.Both sensors were mounted on a 3 m pole.Measurements were conducted near the satellite overpass time and allowed to obtain NDVI and Ts.

Landsat Satellite Datasets and Image Processing
Two Landsat 5 (TM) and thirteen Landsat 7 (+ETM) satellite scenes (Path 233, Row 85) were downloaded from USGS Glovis [53] (Table 2).Scenes used in this research considered only days with less than 30% cloud cover.Additionally, taking into account that since 2003 the +ETM images have shown gaps owing to failures in the satellite scan line corrector (slc-off), only scenes without gaps at the experimental plot were processed (Table 2).Maps of the complete vineyard's surface energy balance components were drawn by using the same scenes aforementioned.All Landsat scenes used in this research were acquired including a default for the systematic radiometric and geometric corrections which consider ground control points and a Digital Elevation Model (DEM) for topographic accuracy standard terrain correction (Level 1T-precision and terrain correction) [54].An area of study (AOS) of approximately 2804.7 km 2 was delimited from each satellite image (Figure 1) and several anchor pixels (cold/dry) were selected according to the method proposed in literature [27,42].Following the selection criteria suggested by [27,42,55] several pairs of anchor pixels were used for each satellite scene.Cold pixels were located within well-known green areas inside the AOS.For hot pixels selection, several points were tested considering agricultural fields that were bare at the time of satellite overpass.Also, a spreadsheet with the two-stage slab model described in the FAO-56 manual [56] was applied to ensure the assumption that the ETa from the soil hot pixels candidates of each image were near zero.For each image, the sensible heat flux at the cold anchor pixel was defined as it was indicated in Equation (14).In this study, a value of ϕ = 1.2 (Equation ( 14)) was used to estimate the Hcold considering that the ratio of reference evapotranspiration for alfalfa (ETr) to ETo ranges from 1.2 to 1.4 [42,57].

Calibration of LAI, zom and G functions
It is acknowledged that originally the METRIC model was developed for annual crops and it may not apply well to sparse crops such as vineyards with low fractional cover and heterogeneous canopy.For this reason, LAI, zom and G functions were calibrated using ground data collected from the vineyard.In this regard, the estimation of LAI was done using the Weibull function (determination coefficient (R 2 ) = 0.85): ( ) where LAI_M is the Leaf Area Index modeled by satellite scene at each pixel (m 2 •m −2 ) This model was developed using values of LAI obtained from an allometric correlation [5,58] and NDVI computed from the handheld multi-spectral radiometer.It is important to indicate that values of NDVI calculated from Landsat scenes were significantly similar to those obtained from the handheld multi-spectral radiometer (R 2 = 0.99; MAE = 0.03; RMSE = 0.04).According to [59], the Weibull function provides good estimations of growth because it assumes a monotonically increasing sigmoid growth similar to biological systems.The flexibility of this function is attributable to the parameters showed in Equation ( 18): parameter 1.2 represents the upper asymptote defined as the average maximum measured LAI.The parameters 3.08 and 2013.35 are both empirical constants, which define the shape of the pattern of growth.The parameter 6.41 determines the inflexion point.
The Perrier function for estimating zom has been suggested by other authors [27,38] as an alternative to compute zom in sparse crops such as vineyards.In this study, values of zom were estimated using the following calibrated function (R 2 = 0.96): where h is the canopy height (m).In this regard, [12,52,60] indicated that values of the roughness length represents between 3% and 10% of plant height [12,52,60].
For soil heat flux, the calibration of Equation ( 8) was based on ground measurements of net radiation, soil heat flux and albedo.Also, values of NDVI and radiometric temperature were obtained using the hand-held radiometer.In this case, the calibration Equation (8) results in (R 2 = 0.89):

Statistical Comparison between Measured and Estimated Values
Instantaneous satellite-based estimates of momentum roughness length (zom_M), leaf area index (LAI_M), albedo (α_M), net radiation (Rn_M), soil heat flux (G_M), sensible heat flux (H_M), and latent heat flux (LE_M) were computed by averaging values of 36 (30 m × 30 m) pixels that fell within the 4.25 ha experimental plot.To avoid the "contamination" caused by pixels outside the experimental plot a perimeter of 30 m from the edges inward was excluded when calculating field-scale averages SEB fluxes [9,34,61].
The validation of sub-models that compute the instantaneous energy balance components (Rn_M, G_M, H_M and LE_M ), α_M, LAI_M and zom_M was carried out using the ratio of estimated to observed values (b), mean absolute error (MAE), root-mean-square error (RMSE) and index of agreement (d).The student's t-test analysis was applied to check whether b was significantly different from unity at the 95% confidence level.For the validation, hourly measurements of α, Rn, G, Hβ and LEβ between 1100 and 1200 h were linearly interpolated to obtain the instantaneous values (αi, Rni, Gi, Hβi and LEβi) at the satellite overpass time (about 1125 h).Values of MAE, RMSE and d were respectively computed as follows [62][63][64]: where n is the number of pairs; i y and ∧ i y are the observed and modeled values, respectively.

Results and Discussion
Generally the weather was hot and dry during the study period.Daily mean values of air temperature (Ta) and vapor pressure deficit (VPD) were 19.3 °C and 1.1 kPa, respectively.Maximum values of Ta and VPD were 35 °C and 4.1 kPa, respectively, which were reached near to 1800 h.For this study, the volumetric soil water content at rooting depth ranged from 0.25 to 0.32 m 3 •m −3 and mean Ψx was between −0.4 and −1.0 MPa indicating that the Merlot vineyard was not under water stress during the three growing seasons [32,[65][66][67].
The accuracy of the EC measurements above the vineyard was checked using the energy balance closure, which presented a coefficient of determination of 0.9 for the study period.Also, the hourly ratio of (H + LE) to (Rn − G) was equal to 0.9 indicating that the vineyard SEB was systematically imbalanced by about 10% [32].On the other hand, Table 3 shows that the energy balance closure was 0.86 (±0.16) at the time of satellite overpass.According to [50], these uncertainties are modest and can be corrected using the Bowen-ratio approach (β = H/LE).In this manner, the correction of the turbulent energy fluxes increased the hourly values of latent heat flux and sensible heat fluxes by about 4% and 6%, respectively.Table 3. Energy balance closure (Cf), Bowen ratio (β) and instantaneous ratios of latent (LEβi), sensible (Hβi) and soil (Gi) heat fluxes to net radiation (Rni) for a drip-irrigated vineyard at the satellite overpass.Instantaneous ratio of Rni to incoming solar radiation (Rsin_i) is also included.Where DOY is the day of the year.Subscript "i" denotes instantaneous values and subscript "β" denotes that the fluxes were corrected using the Bowen-ratio approach.
The hourly variation of the albedo, Bowen ratio, Rn, G, Hβ and LEβ over the Merlot vineyard is presented in Figure 3.During early morning, hourly values of albedo were close to 0.4 and decreased gradually reaching an almost constant value between 1000 and 1800 h with a mean α of 0.19 (±0.05) (Figure 3a).After 1800 h, hourly albedo increased reaching values similar to those observed during early morning.At the time of satellite overpass, the measured albedo ranged from 0.12 to 0.18 for the drip-irrigated Merlot vineyard, which presented a ratio of vine row spacing (rs) to canopy height (hc) equal to 1.25.Using rs/hc = 1.6, the model of [68] estimated hourly albedos ranging between 0.18 and 0.2 for a vertical trellis system.
The diurnal variation of the Bowen ratio at the experimental plot is indicated in Figure 3b, which shows that hourly β described an almost parabolic trend skewed to the left.At the time of satellite overpass, β varied between 0.68 and 3.17 for the dataset (Table 3).Similar results were found by [69] who indicated that hourly β was between 1.25 and 0.62 for a drip-irrigated vineyard cv.Sultana trained on a T-trellis system (rs = 3.3 m, fc = 0.3−0.5).[46] for irrigated grapevines (hc = 1.5 m, rs = 2.9 m) pointed out that hourly β described an almost parabolic trend during the daytime where hourly β ranged from 0.3 to 0.75 during 1000-1700 h.Also, [70] observed values of hourly Bowen ratio between 0.2 and 0.7 during the daytime for sunny days in table grapes cv.Niagara rosada trained on vertical shoot positioned system (hc = 1.5 m, rs = 2.0 m).

Figure 3.
Hourly variation of albedo (α), Bowen ratio (β), net radiation (Rn), soil heat flux (G), sensible heat flux (Hβ) and latent heat flux (LEβ) measured above a drip-irrigated vineyard for the days when satellite scenes were available.Dotted rectangles denote the satellite overpass hour (about 1124 h).Subscript "β" denotes that the fluxes were corrected using the Bowen-ratio approach.Figure 3c shows that the net radiation describes a bell shaped pattern where hourly fluxes increased during the morning until reaching a peak of 650 (±44) W•m −2 at 1400 h.Then, Rn decreased gradually reaching values close to zero at 2000 h.Similar patterns and values of Rn were described in previous studies for vineyards [14,16,[70][71][72][73].For this study, mean ratio of Rni to instantaneous solar radiation (Rsi) was 0.67 (±0.05) at the time of satellite overpass (Table 3).
The hourly G followed a curve skewed to the right, in comparison with the shape of Rn (Figure 3d), starting at 800 h with values close to −100 W•m −2 and reaching at 1500 h maximum values between 100 and 400 W•m −2 .These trends could be associated to the row orientation, canopy architecture and the soil dampness effect on the surface temperature.For the daytime (between 800 and 1800 h), the mean values of soil heat flux were 2.6 (±3) MJ•m −2 •d −1 which was larger than those observed by [69] (1.28 MJ•m −2 •d −1 ).For our study, values of G accounted for 11%-37% of Rn during daytime (data not shown).For this period, [12] indicated that G accounted for as much as 38%-44% of Rn for a drip irrigated Cabernet Sauvignon vineyard.Our results also differed from [7,16,69,74] who indicated that mean values of G accounted for 11%-29%, 7%-11%, 5%-8% and 9%-11% of net radiation, respectively.Differences aforementioned presumably were due to differences in canopy geometry, plant density, and the number of sensors used to compute G. Instantaneous values of Gi averaged 123 (±31) W•m −2 (Figure 3d) accounting for 16%-38% of Rni.
Hourly H was small in the morning and increased near solar noon, reaching its maximum close to 400 W m −2 between 1400 and 1500 h (Figure 3e).[16,70,73] found hourly maximum values of H between 300-400, 200-300 and 100-200 W•m −2 , respectively.In our experiment, daytime Hβ accounting for 22%-60% of Rn while [12,69] indicated that H accounted for 25%-48% of Rn.Additionally, Hβi ranged between 185 and 330 W•m −2 at the satellite overpass (Figure 3e).Ratios of Hβi to Rni, were between 0.30 and 0.63 at about 1130 h, indicating that almost half of the available energy of the vineyard was dissipated into sensible heat flux at the time of satellite overpass.
Hourly value of LEβ increased smoothly from 800 h reaching its peak (400 W•m −2 ) between 1500 and 1600 h (Figure 3f).Daytime ratio of LEβ to Rn was between 0.22 and 0.52 while the instantaneous ratio of LEβi to Rni was between 0.20 and 0.44.In general, results indicated that LEβ was smaller than Hβ showing consistent results in comparison to previous studies carried out in a drip irrigated vineyard in the same path-row area [12] where LE accounted for 20%-40% of Rn.In this regard [69] for a drip irrigated Sultana vineyard conducted on T-trellis system (fc = 0.4 ± 0.1) reported that the daytime ratio of LE/Rn increased from 0.43 in warm-dry periods to 0.57 in cool-humid periods.For a drip irrigated Chardonnay vineyard training on a bilateral cordon trellis, [74] indicated that the ratios of LE and H to Rn ranged between 0.46-0.67 and 0.13-0.37,respectively, concluding that the canopy architecture may have a substantial effect on soil and canopy energy balance, mainly by changing the partitioning of vineyard net irradiance into its soil and canopy components.Finally, [75] for agricultural and natural areas suggested that the partitioning of available energy is affected by water availability and vegetation cover.In our case, as aforementioned a constant shape of the canopy (a parallelepiped) was maintained without weeds between rows with LAI ranging between 0.8 and 1.2 m 2 •m −2 and fc values of 0.3 (±0.02) during the complete evaluated periods, especially after full bloom.Also, during these seasons, the top layer of soil (0-20 cm) in the inter-rows was very dry and soil surface wetted by drip emitters was 3%.Under these canopy and soil water conditions, the soil contribution to the vineyard energy balance was considerable, especially under high atmospheric demand for water vapor.Under these conditions, sensible heat flux generated at the soil surface could be a major contributor to the vineyard energy balance which plays a key role in vine transpiration and evaporation [40].

Comparison between Measured and Estimated Variables
Results showed that the Weibull model (Equation ( 18)) estimated LAI with values of MAE = 0.2 m 2 •m −2 and RMSE = 0.3 m 2 •m −2 (Table 4a).Also, the t-test indicated that b was significantly equal to unity indicating that estimated and observed values of LAI were similar.In contrast, the original approaches (Equations ( 9) and ( 10)) underestimated LAI by about in 58% with values of RMSE and MAE both equal to 0.6 m 2 •m −2 (Table 4b).The good results obtained with the Weibull model can be associated to the constant shape of the canopy (a parallelepiped) that was maintained with fc values of 0.3 (±0.04) during the study period, especially after full bloom.Also, the soil surface was kept without weeds, because the top layer of soil (0-20 cm) was very dry and soil surface wetted by drip emitters was 3%.Under these constant shape and soil water conditions, NDVI may be a valid input to estimate LAI, allowing a good performance of the Weibull model.In this manner, NDVI was selected because of its simplicity and robustness against other vegetation indices based on similar studies carried out on vineyards [76,77].On the other hand, [77] indicated that the use of NDVI computed from images of low-spatial-resolution such as Landsat (pixel resolution: 900 m 2 ) could generate poor estimations of LAI because pixels contain mixed pixels reflectance information from the surface occupied by plants (row) and the between row space.Recently, in two vineyards, [58] indicated that the LAI can be overestimated up to 17% when contrasting geo-referenced LAI data from cover photography method against NDVI obtained from the satellite World-View 2 (pixels resolution: 2 m 2 ).Vineyard satellite-based estimations of zom using the Perrier function (Equation ( 19)) generated zom values ranging between 0.05 and 0.11 m, which are within the values indicated by [12,60].Validation analysis indicated that RMSE and MAE where both equal to 0.01 m (Table 4a).Also, b was significantly equal to unity suggesting that estimated and observed values of zom were similar.The original function (Equation ( 12)) used in METRIC algorithm [27] underestimated zom by about 81% with RMSE and MAE both equal to 0.08 m (Table 4b).These results suggest that canopy shape and rs/hc ratio can plays a key role in the parameterization of zom.
For the albedo, the statistical t-test indicated that the ratio of estimated to observed values were significantly different from the unity indicating an underestimation of 21% (Table 4b).In this case, the values of MAE and RMSE were both equal to 0.04.For the drip-irrigated vineyard, mean value of αi was 0.2 (±0.13) while that of α_M was 0.13 (±0.02).[35] indicated an albedo of 0.2 for seven sites corresponding to rainfed vineyards, which presented similar trellis structure as our experiment (rs = 2.5 m, hc = 1.5 m).For a non-irrigated vineyard (cv.Airen) trained on free standing bushes (fc = 0.3, hc = 0.9 m, rs = 2.5), [14,60] obtained a mean albedo of 0.27 which dropped as low 0.18 during a rain event.Differences aforementioned could be associated to the training systems, rs/hc ratio and fc, which affect the level of solar radiation reaching the soil surface.
Figure 4 shows the comparisons between observed and estimated values of the energy balance components at the time of satellite overpass.In this case, estimated values from METRIC were calculated using the calibrated functions of LAI, zom and G.For the net radiation (squares) all points were over the 1:1 line with RMSE and MAE of 69.4 and 63 W•m −2 , respectively.The t-test indicated that Rn_M/Rni ratio (b =1.11) was significantly different from unity (one) indicating that METRIC overestimated Rn by approximately 11% (Table 4a).[78] showed values of RMSE and MAE equal to 51 and 25 W•m −2 , respectively when a simplified residual SEB model was applied over a heterogeneous landscape in China.For corn, [28] reported that SEBAL overestimated Rni by 7% with a RMSE = 65 W•m −2 .For sorghum and corn, [79] indicated that a two-source energy balance model underestimated Rni by about 4% with RMSE = 44.2W•m −2 .
The comparison between measured and modeled soil heat fluxes (diamonds) in Figure 4 shows that the points were grouped below the 1:1 line.In this case, the calibrated and original functions underestimated the instantaneous soil heat flux by about 17 and 5%, respectively, with similar values of RMSE and MAE (Table 4).Similar studies carried out by [80] indicated that METRIC estimated Gi with RMSE = 19 W•m −2 over a corn and soybean production region.[28] pointed out that SEBAL significantly overestimated Gi for corn with RMSE = 79.8W•m −2 .Also, [81] estimated the soil heat fluxes with RMSE = 23 W•m −2 (error of 19%) by the application of a remote sensing method over a heterogeneous surface.These authors suggested that errors could be attributable to the difference of spatial/temporal scales between satellite data and measurements.
The comparison between measured and estimated sensible heat fluxes during satellite overpasses (Figure 4-circles) shows that the points were over the 1:1 line.In this case, METRIC using the calibrated functions of LAI, zom and G overestimates the instantaneous sensible heat fluxes by about 16% with RMSE, MAE and d equal to 67 W•m −2 , 57 W•m −2 and 0.52, respectively (Table.4a).When using the original function, METRIC overestimated the instantaneous sensible heat fluxes by about 13% (RMSE = 51 W•m −2 ; MAE = 43 W•m −2 and d = 0.68) (Table 4b).For corn and soybean, [80] indicated that METRIC tends to overestimate Hi by about 80 W•m −2 with RMSE = 57 W•m −2 .For corn, [28] indicated that instantaneous values of H were underestimated by nearly 50%.Over heterogeneous surfaces [78] indicated that the RMSE was 23 W•m −2 when a simplified residual SEB model was applied to estimate the sensible heat flux at the time of satellite overpass.According to [26,44,82], biases in the estimation of sensible heat fluxes are necessary because calculations (iterations) of H_M absorb the biases obtained previously in the computation of net radiation and soil heat fluxes.As a consequence the accuracy of the complete model in the estimation of LE_M strongly depends on the anchor pixel selection (end members), which determines the self-calibration of H_M.  4a).When using the calibrated functions, the ratio of LE_M/LEi was significantly different to the unity suggesting that instantaneous values of LE_M were overestimated by about in 17%.When using original functions, METRIC significantly overestimated (15%) the latent heat flux over the drip-irrigated vineyard with values of RMSE, MAE and d equal to 43, 35 W•m −2 and 0.8, respectively (Table 4b).For drip-irrigated vineyards, [83] found errors of 18% in the estimation of LEi when using a two-source energy balance (TSEB) model and Landsat scenes.In spite of this error, the TSEB model estimated daily ETa with RMSE equal to 0.5 mm•d −1 .In this regard, [32] observed that errors of 15% in the estimation of LEi produced an ETa overestimation of 9% with a RMSE = 0.62 mm•d −1 for the same Merlot vineyard.For fully covered crops, [28,80] found values of RMSE equal to 108 in corn and 55 W•m −2 in soybean, respectively.In general, the literature indicates that most of the remote sensing models applied over full or sparse canopies to estimate daily ETa presented errors between 0.5 and 0.8 mm•d −1 which are acceptable for irrigation management [22,35,83].
METRIC with original (grey bars) and calibrated (white bars) functions both overestimated the instantaneous net radiation by about 63 (±30) W•m −2 during the growing cycle (Figure 5a).In this regard, the calibrated function of LAI did not produce a significant effect on the computation of the surface emissivities, which are used by METRIC to estimate the outgoing long wave radiation and surface temperature [27].Values of H_M, LE_M and G_M using the calibrated functions showed biases of 35 (±50), 43 (±53) and −15 (±31) W•m −2 , respectively; while those using the original functions presented biases of 29 (±33), 33 (±40) and 2 (±35) W•m −2 , respectively.These results suggest that errors in the estimation of LAI_M, zom_M and G_M were balanced by the self-calibration of METRIC to estimate the instantaneous turbulent energy fluxes.Also, errors in estimations of Rni (Figure 5a) and Gi (Figure 5b) were typically balanced by bias in Hi (Figure 5c).This buffer effect significantly influenced the estimations of latent heat fluxes at the time of satellite overpasses (Figure 5d).
In this respect, sensitivity analysis studies applied to METRIC model indicated that variations on intermediate parameters (albedo, NDVI, LAI, G and roughness length) indirectly could affect the accuracy of LEi and subsequently ETa estimation [84,85], but the most important effect is attributable to the end member selection [82,[85][86][87][88][89].On this point, [90] indicated that the spatial distribution of Hi in the image is based on Hi estimation between two anchor pixels.So, if LEi at the anchor pixel is overestimated then H will be underestimated throughout the satellite scene.On the contrary, if LEi is underestimated, Hi will be overestimated.According to [27] the selection of the two "anchor" pixels requires knowledge, thoughtfulness and skill of the operator.These points have been indicated as controversial inside the ET research community because selection is subjective and depends of the ability of the operator in search and isolate of the most appropriates hot and cold pixels [55,87,88].

Spatial Variability of the Estimated Surface Energy Balance Components for the Complete Vineyard
At the time of satellite overpass, Figure 6 shows the maps with the spatial variability of the satellite-based energy balance components estimated by METRIC using the calibrated functions.For the entire vineyard (97 ha), the maps were generated for the phenological stages of bud break (B), flowering (FL), fruit set (FS), veraison (V) and harvest (HA).Average values of Rn_M for the pixels inside the vineyard were 565 (±16), 565 (±16), 619 (±17), 632 (±17), 613 (±15) and 537 (±17) W•m −2 for B, FL, FS, V and HA, respectively (Figure 6a-e).In this case, the coefficient of variation (less than 5%) indicated that the spatial variability of Rn_M was not important.For B, FL, FS, V and HA G_M ranged between 50 and 190 W•m −2 with maximum and minimum values observed in veraison and fruit set, respectively (Figure 6f-j).Average values of H_M were 326 (±64), 311 (±78), 280 (±63), 281 (±59) and 296 (±44) W•m −2 (Figure 6k-o) while those of LE_M were 135 (±86), 180 (±98), 223 (±81), 209 (±76) and 155 (±70) W•m −2 (Figure 6p-t) for B, FL, FS, V and HA, respectively.In Figures 6k-o nearly a third of the complete vineyard can be clearly identified inside a dark blue area (387 W•m −2 ) corresponding to the old part of the vineyard where the training system shown more separated vines than the described for Merlot occupied in this study.The effect of distance inside this area presumably could increase the sensible heat flux due the bare soil beneath vines, considering that during this period the vineyard did not reach its complete foliage cover.Also, the highest and lowest values of H_M (400 W•m −2 ) and LE_M (30 W•m −2 ) were observed in areas without plants (bare soil and winery).The highest values of Rn_M (726 W•m −2 ) and LE_M (300-500•W m −2 ) were observed in the vineyard contours reflecting the presence of trees, natural bushes and the influence of the "Lircay" River.The low spatial variability of G_M, H_M and LE_M observed for each phenological stage was associated with the uniform canopy shape of the vineyard where the values of LAI and fractional cover (fc) were maintained between 0.8-1.2m 2 •m −2 and 0.28-0.31,respectively, particularly after the full bloom soil surface was very dry and maintained free of weeds (cover crops) during October and March for all evaluation period in which rainfall was less than 3.0 (±2.4) mm.

Conclusions
Empirical functions of METRIC to estimate LAI, zom and Gi were calibrated for a drip-irrigated vineyard under non-water stress (midday Ψx > −1.0 MPa).Results indicated that LAI, zom and Gi were estimated using the calibrated functions with errors of 4%, 2% and 17% while those were computed using the original functions with errors of 58%, 81%, and 21%, respectively.At the time of satellite overpass, the original METRIC underestimated the satellite-based albedo by about 21% and overestimated net radiation by 11%.Using the calibrated functions, METRIC overestimated instantaneous latent and sensible heat fluxes by about 17% and 16%, respectively.Using the original functions, it overestimated LE and H with errors of 15% and 13%, respectively.Results of this research indicated that the calibration of Gi, LAI and zom did not produce significant effects on the estimation of the turbulent energy fluxes because of the self-calibration employed in the estimation of H_M.Also, biases observed for instantaneous pixel-by-pixel values of Rn_M and G_M, were presumably absorbed into H_M as a result of the self-calibration method of METRIC, which is highly dependent on the hot and cold pixels selection.Finally, future research needs to be performed considering a sensitivity analysis of intermediate variables and the use of an automatized method to optimize the selection of anchor pixels (wet and dry) at each scene.
Definition Cf Ratio of turbulent fluxes to available energy or energy balance closure (= (H + LE)/(Rn − G)) (dimensionless) Cp Specific heat capacity of air (1004 J kg −1 •K −1 ) d Zero plane displacement for heigth (m) ETa Actual evapotranspiration (mm•d −1 ) ETa_M ETa computed for METRIC for each pixel (mm•d −1 ) ETi ETa at the instant of satellite overpass (mm•h −1 ) ETi_M Instantaneous ETa calculated for METRIC for each pixel (mm•h −1 ) ETo Penman-Montetith reference evapotranspiration computed for grass (mm•d −1 ) ETo_i Hourly reference evapotranspiration at the time of satellite overpass (mm•h −1 ) ETr Reference evapotranspiration (for alfalfa) (mm•d −1 ) fc Fractional cover (fraction) Fi_M Reference evapotranspiration fraction computed by METRIC at the time of satellite Overpass (= ETi_M/EToh) (dimensionless) G Soil heat flux (W•m −2 ) G_M Soil heat flux estimated by METRIC at the time of satellite overpass (W•m −2 ) Gi Soil heat flux at the instant of satellite overpass (W•m −2 ) H Sensible heat flux (W•m −2 ) H_M Sensible heat flux estimated by METRIC at the time of satellite overpass (W•m −2 ) hc Canopy heigth (m) Hcold Sensible heat flux at the instant of at the time of satellite overpass for the cold Pixel (W•m −2 ) Hi Sensible heat flux at the instant of satellite overpass (W•m −2 ) Hβ Sensible heat flux forced to close the energy balance using the Bowen ratio (W•m −2 ) LAI Leaf Area Index (m 2 •m −2 ) LAI_M Leaf Area Index estimated by satellite scene at each pixel (m 2 •m −2 ) LE Sensible heat flux (W•m −2 ) LE_M Latent heat flux estimated by METRIC at the time of satellite overpass (W•m −2 ) LEi Sensible heat flux at the instant of at the time of satellite overpass (W•m −2 ) LEβ Latent heat flux forced to close the energy balance using the Bowen ratio (W•m −2 ) NDVI Normalized Difference Vegetation Index (dimensionless) q' Humidity (kg•kg −1 ) rah Aerodynamic resistance to heat transport (s•m −1 ) RHa_o Relative humidity for a short reference surface (fescue grass) (%) RL↑ Outgoing longwave radiation (W•m −2 ) RL↓ Incoming longwave radiation (W•m −2 ) Rn_M Net radiation estimated by METRIC at the time of satellite overpas (W•m −2 ) Rncold Net radiation flux at the instant of at the time of satellite overpass for the cold pixel (W•m −2 ) Rni Net radiation at the instant of satellite overpass (W•m −2 ) rs Row spacing (m) Rs↓ Incoming shortwave radiation (W•m −2 ) Rsin Measured incoming solar radiation radiation (W•m −2 ) Rsin_o Incoming solar radiation in reference conditions (fescue grass) (W m −2 •h −1 ) Rso Measured outgoing solar radiation radiation (W•m −2 ) SAVI Soil Adjusted Vegetation Index (dimensionless) T Instantaneous sonic temperature (°K) Ta Air temperature over the vineyard (fescue grass) (°C) Ta_o Air temperature for short reference surface (fescue grass) (°C) Taz1 and Taz2 Near surface air temperature (°K) Ts Surface radiometric temperature (°C or °K) Tsi Instantaneous surface radiometric temperature calculated for each pixel (°C or °K) u2 Mean wind speed at 2-m height in reference conditions (fescue grass) (m•s −1 ) VPD Vapor pressure deficit (kPa) w' Wind speed (m•s −1 ) wbd Weighting coefficient of the Landsat bands for calculating broad-band surface Albedo (dimensionless) zom Aerodynamic roughness length for momentum transfer (m) zom_M Aerodynamic roughness length for momentum transfer computed by METRIC (m) α Surface albedo (dimensionless) α_M Broadband surface albedo at the time of satellite overpass computed by METRIC (dimensionless) αi Surface albedo at the instant of satellite overpass (dimensionless) β Bowen ratio (= H/LE) (dimensionless) ΔTs Near-surface air temperature gradient (ΔTs = Taz1 − Taz2) above each pixel, where Taz1 and Taz2 are near surface air temperature at heights z1 and z2 (m), respectively (°K) ε0 Surface emissivity (dimensionless) θFC Volumetric soil water content at field capacity (m 3 •m −3 ) θi Measured volumetric soil water content (m 3 •m −3 ) θWP Volumetric soil water content at wilting point (m 3 •m −3 ) λ Latent heat of vaporization (J•kg −1 ) ρair

Figure 2 .
Figure 2. Site detail showing: (a) vine varieties distribution scheme; (b) image that shows the experimental plot (vineyard block N°22A indicated as a segmented square).White dot inside the experimental plot indicates the Eddy Covariance system position; (c,d) show the analytical footprint model for all evaluated days under unstable conditions in terms of relative and cumulative contribution, respectively; (e) and (f) depict the wind-rose for unstable conditions at the peak (Xpeak) of the footprint function and during the time of satellite overpasses, respectively.

81 F
LAI = leaf area index; z om = momentum roughness length; α = surface albedo; R n = net radiation; G = soil heat flux; H = sensible heat flux and LE = latent heat flux.Sub indexes "i" denotes instantaneous ground measured values, "β" denotes that the fluxes were corrected using the Bowen-ratio approach and "M" denotes modeled values using METRIC.RMSE = root mean square error; MAE = mean absolute error; b = ratio of observed to computed values; d = index of agreement; T = null hypothesis (b = 1) True; F = alternative hypothesis (b ≠ 1) False.

Figure 4 .
Figure 4. Comparisons at the time of satellite overpass between observed (axis X) and estimated (axis Y) values of net radiation (Rn), soil heat flux (G), sensible heat flux (H), and latent heat flux (LE) for a drip irrigated Merlot vineyard.Estimated values were obtained using METRIC with the calibrated functions.Subscript "i" denotes instantaneous values.

Figure 5 .
Figure 5. Comparisons between the measured (black bars) and modeled values using METRIC with the original (grey bars) and calibrated (white bars) functions to estimate (a) net radiation (Rni); (b) soil heat flux (Gi); (c) sensible heat flux (Hi); and (d) latent heat flux (LEi) at the time of satellite overpass.Modeled values correspond to average from pixels inside the experimental plot.DOY is the day of the year.Subscript "i" denotes instantaneous values.
[27]Ts is the near-surface air temperature gradient (ΔTs = Ta z1-Ta z2) above each pixel, where Ta z1 and Ta z2 are near surface air temperature (°K) at heights z1 and z2 above the elevation of d + zom, where d is zero plane displacement height (all in m).rah is the aerodynamic resistance to heat transport (s•m −1 ).Originally, METRIC estimates the values of zom based on the height (h) of annual agricultural crops by assuming that the crop height vary proportionally with the LAI[27].Thus for agricultural areas, zom can be

Table 1 .
Sensor heights and configuration inside the experimental plot.

Table 2 .
Images selected for processing surface energy balances over a drip-irrigated Merlot vineyard.
* DOY = day of the year following the calendar day.

Table 4 .
Validation of sub-models that compute the instantaneous values of energy balance components, albedo, leaf area index and momentum roughness length for a drip-irrigated Merlot vineyard.