Introduction

Viticulture plays an important role in the economics in the Mediterranean zone of southern Europe (Sene 1994), America, and Oceania where productivity improvements are directly associated with the vineyard water consumption or actual evapotranspiration (ETa). The correct determination of ETa is a key factor for improving water-use efficiency (WUE) and establishing irrigation strategies such as the regulated deficit irrigation (RDI) that has been successfully applied to increase the WUE and grape quality (Nadal and Arola 1995; Basinger and Hellman 2007; Acevedo-Opazo et al. 2008). Therefore, accurate ETa estimation is the first step in developing irrigation strategies to optimize water application, yields, and quality (Heilman et al. 1996; Yunusa et al. 2000; Campos et al. 2010; Galleguillos et al. 2011). ETa can be measured by using lysimeters, Bowen ratio method (BREB), or eddy covariance (EC) systems. In the absence of direct measurements, ETa is usually estimated empirically by multiplying the reference evapotranspiration (ETo) by a single crop coefficient (K c). This method provides a simple and convenient way to estimate crop water requirements. The major uncertainty of this approach is that many K c values reported in the literature often do not apply to local conditions because K c values depend on nonlinear interactions among plants architecture, soil and climate conditions (Jagtap and Jones 1989; Annandale and Stockle 1994). In general, vineyards present sparse canopies with high spatial variability of soil and vine vigor that affect vineyard energy and water balances (Ortega-Farias et al. 2009). Consequently, K c extrapolation from individual experimental sites to a large area may generate erroneous ETa estimations.

To account for the spatial variability of soil and vigor, optical satellite-based remote sensing technology could be a reliable alternative for estimating ETa and K c for vineyards. Also, satellite-based technology provides accurate measurements at a reasonable frequency over a large area allowing the monitoring of the water management practices and the evaluation of the impact of different strategies (Bastiaanssen and Bos 1999; Su 2002; Tasumi et al. 2005; Santos et al. 2008; Kleissl et al. 2009; Singh and Irmak 2009; Teixeira et al. 2009a, b). Optical satellite and thermal-based ETa and K c estimates at the field scale for several crops have been documented in the literature (Bausch 1995; Tasumi et al. 2005; Kalma et al. 2008; Barbagallo et al. 2009; Samani et al. 2009; Singh and Irmak 2009; Teixeira et al. 2009a, b; Campos et al. 2010; Galleguillos et al. 2011). These provide evidence about the capability of remote sensing techniques to integrate the different variability sources.

ETa and K c optical satellite-based estimations are based on (a) reflectance methods and (b) land surface energy balance methods (LSEB) (Tasumi et al. 2005; Gowda et al. 2008). Reflectance methods commonly use vegetative indexes (VI) such as the normalized difference vegetation index (NDVI) and the soil-adjusted vegetation index (SAVI) (Campos et al. 2010). Alternatively, the LSEB methods estimate ETa as a residual component of the surface energy balance (Gowda et al. 2008). According to the literature, ETa and K c estimates based on the LSEB models outperform those based on VI models. Presumably, this is because the LSEB models utilize strong theoretical and physical relationships and additional information from the satellite thermal band that reflects the plant water status, specific crop characteristics, and soil water management (Seguin et al. 1994; Allen et al. 2007a).

One widely applied LSEB model is METRIC (mapping evapotranspiration at high resolution with internalized calibration) (Allen et al. 2007a), which was developed from the SEBAL model (surface energy balance algorithm for land) (Bastiaanssen et al. 1998). METRIC uses a self-calibration procedure that involves ground based hourly ETo measurements and the selection of extreme (hot and cold) pixels within agricultural surfaces (Gowda et al. 2008). Using METRIC, ETa estimates have been found to be accurate and robust allowing the production of “ETa maps” for several crops on a field by field basis. METRIC has been used to estimate seasonal crop water budgets and to plan water rights management, water resource planning, and water regulation among other applications (Tasumi et al. 2005).

The application of METRIC to develop K c and ETa maps for seasonal vineyard water budgets is still under development, and application of remote sensing to the vineyard irrigation management is an emerging research area. For drip-irrigated vineyards, Campos et al. (2010) published a method to assess the estimation of daily ETa and crop coefficients based on the basal crop coefficient derived from satellite-based VI adjusted by the soil and water stress coefficients. Comparisons between modeled and measured ETa showed coefficients of determination (R 2) of 0.67 and 0.79, for daily and weekly averages, respectively. For nonirrigated vineyards, Galleguillos et al. (2011) applied the S-SEBI (simplified surface energy balance index) model (Roerink et al. 2000) and showed a root mean square error (RMSE) of 0.83 mm d−1 between modeled and measured ETa, which was similar to the one reported over simpler canopies with full ground cover.

However, the potential use of METRIC to estimate the water use of drip-irrigated vineyards has not been evaluated under semiarid climatic conditions. Consequently, the aim of this research was to evaluate the METRIC model to estimate single crop coefficients and ETa for the main phenological stages of a drip-irrigated Merlot vineyard under semiarid climatic conditions.

Theory

The daily ETa using the METRIC model is computed as follows (see “List of symbols”):

$$ {\text{ET}}_{{{\text{a}}\_{\text{M}}}} = {\text{ET}}_{\text{o}} \times F_{{{\text{i}}\_{\text{M}}}} $$
(1)

where ETa_M is the daily ETa computed for each pixel (mm d−1); ETo is the daily reference evapotranspiration (mm d−1); and F i_M is the reference evapotranspiration fraction (F o) at the time of satellite overpass. Values of ETo are calculated as follows (Allen et al. 1998; ASCE-EWRI 2005):

$$ {\text{ET}}_{\text{o}} { = }\sum\limits_{{i{ = 1}}}^{ 2 4} {{\text{ET}}_{\text{oh}} } $$
(2)
$$ {\text{ET}}_{\text{oh}} = \frac{{0.408 \cdot \Updelta \cdot \left( {R_{{{\text{n\_o}}}} - G_{\text{o}} } \right) + \gamma \cdot \frac{37}{{\left( {T_{{{\text{a\_o}}}} + 273.16} \right)}} \cdot u_{2} \cdot {\text{VPD}}}}{{\Updelta + \gamma \cdot \left( {1 + C_{\text{d}} \cdot u_{2} } \right)}} $$
(3)

where EToh is the hourly reference evapotranspiration computed by the Penman–Monteith model (mm h−1); R n_o is the net radiation over a short reference (grass) (MJ m−2 h−1); G o is the soil heat flux for short reference (MJ m−2 h−1); γ is the psychrometric constant (kPa °C−1); T a_o is air temperature for short reference surface (°C); u 2 is the mean wind speed at 2-m height (m s−1); VPD is the vapor pressure deficit (kPa); Δ is the slope of the saturation curve (kPa °C−1); and Cd is the denominator conversion factor (0.24 and 0.96 for daytime and nighttime, respectively). Values of F i_M are calculated as:

$$ F_{{{\text{i\_M}}}} = K_{{{\text{c\_M}}}} = \frac{{{\text{ET}}_{{{\text{i\_M}}}} }}{{{\text{ET}}_{{{\text{oh\_i}}}} }} $$
(4)

where ETi_M is the instantaneous ETa calculated for each pixel (mm h−1); EToh_i is the hourly reference evapotranspiration at the time of satellite overpass (mm h−1). F i_M is the same as the crop coefficient (K c_M) because it is assumed that F i_M is equal to the mean values of hourly F o for the daytime period (Tasumi et al. 2005; Colaizzi et al. 2006; Trezza 2006; Allen et al. 2007b; Gowda et al. 2008). Using METRIC, ETi_M is calculated as a residual of the surface energy balance at the time of satellite overpass:

$$ {\text{ET}}_{{{\text{i\_M}}}} = \frac{{3,600 \cdot {\text{LE}}}}{{\lambda \cdot \rho_{\text{w}} }} $$
(5)
$$ {\text{LE}} = R_{\text{n}} - G - H $$
(6)

where LE is the latent heat flux (W m−2); 3,600 is a time conversion factor from seconds to hour; λ is the latent heat of vaporization (J kg−1); ρw is the water density (≈1,000 kg m−3); R n is the net radiation flux (W m−2); H is the sensible heat flux (W m−2); and G is the soil heat flux (W m−2). For each pixel, net radiation is obtained using:

$$ R_{\text{n}} = \left( {1 - \alpha } \right) \cdot R_{{{\text{s}} \downarrow }} + R_{{{\text{L}} \downarrow }} - R_{{{\text{L}} \uparrow }} - \left( {1 - \varepsilon_{0} } \right) \cdot R_{{{\text{L}} \downarrow }} $$
(7)

where α is the broadband surface albedo (dimensionless); R s↓ is the incoming shortwave radiation (W m−2); R L↓ and R L↑ are the incoming and outcoming longwave radiations (W m−2), respectively; and εo is the surface emissivity that accounts for reflectance of incoming longwave radiation at the land surface.

G for each pixel is estimated using two empirical relations depending of the leaf area index according to Tasumi (2003):

$$ \frac{G}{{R_{\text{n}} }} = 0.05 + 0.18 \cdot e^{{ - 0.52{\text{LAI}}}} \quad ({\text{if}}\quad {\text{LAI}} \ge 0.5) $$
(8)
$$ \frac{G}{{R_{\text{n}} }} = 1.8 \cdot \frac{{\left( {T_{\text{s}} - 273.16} \right)}}{{R_{\text{n}} }} + 0.84\quad ({\text{if}}\quad {\text{LAI}} < 0.5) $$
(9)

where T s is the surface temperature (°K), and LAI is the leaf area index (m2 m−2) calculated for each pixel.

The H estimations are obtained for each pixel assuming a linear relation between the aerodynamic resistance and the surface to air temperature difference (Seguin et al. 1994; Trezza 2002; Tasumi 2003) according to:

$$ H = \frac{{\rho_{\text{air}} \cdot C_{\text{p}} \cdot \Updelta T_{\text{s}} }}{{r_{\text{ah}} }} $$
(10)

where ρair is the air density (kg m−3); C p is the specific heat capacity of air (1,004 J kg−1 K−1); r ah is the aerodynamic resistance to heat transport (s m−1); and ΔT s is the linear empirical function that represents the near surface to air temperature difference (°K). Values of r ah and ΔT s are internally calibrated for each scene by using several anchor pixels (cold and hot) selected by the user and an iterative process that involves Monin–Obukhov similarity theory. For more details about the METRIC model (including image handling and processing), read Allen et al. (2007a, 2010).

Materials and methods

The study was carried out in a 97 ha vineyard located in the Talca Valley, Maule Region, Chile (35°25′ LS; 71°32′ LW; 125 m.a.s.l) during the 2007–2008 and 2008–2009 growing seasons. Within this vineyard, an area of 4.25 ha of a drip-irrigated commercial cv. Merlot vineyard (Vitis vinifera L.) was used as experimental plot (Fig. 1). The climate is classified as Mediterranean semiarid with an average daily temperature of 17.1 °C between September and March (spring–summer). Average rainfall in the region is about 676 mm falling mainly throughout the winter season. The summer period is usually dry and hot (2.2 % of annual rainfall), while the spring is wet (16 % of annual rainfall). The soil at vineyard is classified as Talca series (family Fine, mixed, thermic Ultic Haploxeralfs) with a clay loam texture. The effective rooting depth is between 0 and 60 cm where the volumetric soil content at field capacity (θFC) and wilting point (θWP) were 0.36 m3 m−3 (216 mm) and 0.22 m3 m−3 (132 mm), respectively. Also, the maximum allowed depletion (MAD) was 29 % (174 mm).

Fig. 1
figure 1

Image of the drip-irrigated Merlot vineyard. The experimental plot is highlighted in the square. Yellow borders show the field contour (Talca Valley, Maule Region, Chile) (color figure online)

Full size image

The Merlot vines were planted in 1999 in north–south rows with a plant density of 2,667 plants ha−1 (2.5 m between rows and 1.5 m between vines). The vines were trained on a vertical shoot positioned (VSP) system and the soil surface was maintained free of weeds and cover crops during the study. A constant shape of the canopy (a parallelepiped) was maintained with LAI ranging between 0.8 and 1.2 m2 m−2 and soil surface covered by vegetation (f c) between 28 and 31 % during the two study periods, especially after full flowering. The vineyard was drip irrigated using 4.0 L h−1 drippers spaced at 1.5 m along the rows. Soil water status was monitored weekly with volumetric soil water content measurements (θi) at the effective rooting depth (0–60 cm) using a portable TDR (Trase System, 6050X1, Santa Barbara CA, USA). Also, the midday stem water potential (Ψx) using a pressure chamber (PMS instruments, model 600, Albany OR, USA) was conducted on 12 fully expanded leaves that had been wrapped in aluminum foil and encased in plastic bags for at least 2 h before the measurements.

Vineyard phenological stages

Five vineyard key phenological stages were identified: bud break (B), flowering (FL), fruit set (FS), veraison (V), and harvest (H). Based on visual inspection, a starting stage was assumed when almost 50 % of the plants had reached a new phenological state (Table 1).

Table 1 Key phenological stages of a drip-irrigated Merlot vineyard (Talca Valley, Maule Region, Chile)
Full size table

Meteorological and energy balance measurements

ETo values were estimated from hourly data of incoming solar radiation (R si_o), relative humidity (RHa_o), T a_o, and u 2 obtained from an automatic weather station (AWS) (Adcon Telemetry, A733GSM/GPRS, Klosterneuburug, Austria) that was placed in the middle of 1 ha covered with well-watered grass at the “Panguilemo” experimental station (35°22′ LS; 71° 35′ LW; 124 m.a.s.l). Another AWS was installed at the Merlot vineyard to measure energy balance components and meteorological variables at 30-min intervals on average. Wind speed (u) and wind direction (wdir) were monitored by a cup anemometer and a wind vane (Young, 03101-5, MI, USA). Air temperature (T a) and relative humidity (RHa) were measured by a combined probe (Vaisala, HMP45C, MA, USA). Net radiation (R n), incoming (R si), and outgoing solar radiation (R so) were measured by a four-component net radiometer (Kipp&Zonen Inc., CNR1, Delft, The Netherlands) only for the 2007–2008 growing season. A net radiometer (REBS, Q7.1, SEA, USA) was installed as backup. For the 2008–2009 seasons, the four-way net radiometer was removed and the measurements continued using two REBS Q7.1 net radiometers. Sensors to measure u, wdir, T a, RHa, R n, R si, and R so were placed at 4.7 m over the soil surface.

Latent (LE) and sensible (H) heat fluxes were measured using an EC system mounted at a height of 4.7 m and oriented toward the predominant wind direction (South). LE and H were measured by a fast response, open-path infrared gas analyzer (IRGA) (LI-COR Inc., LI7500, Lincoln, NE, USA) and a three-dimensional sonic anemometer-thermometer (Campbell Sci., CSAT3, Logan UT, USA). The footprint analysis showed that under unstable conditions, 90 % of cumulative normalized flux measurements is obtained at about 280 m distance upwind, representing a fetch-to-height ratio (r FR) of about 60:1. On the other hand, the existing upwind fetch of the prevailing wind direction (South) was more than 550 m with r FR of 117:1. G was measured by soil heat flux plates buried at a depth of 0.08 m (HFT3, Campbell Scientific Inc., Logan, UT, USA). Four plates were used to measure soil heat fluxes under plant rows, and four other plates were used to measure the soil heat flux between rows. Soil temperature and heat storage were measured by four soil thermocouples (TCAV, Campbell Scientific Inc., Logan, UT, USA) positioned at 0.02 and 0.06 m depth above each heat flux plate. Measurements of climatic variables and energy balance components were recorded every 10 s by two data loggers (CR5000 and CR1000, Campbell Scientific Inc., Logan, UT, USA) and averaged every 30 min.

The post-processing of raw 10 Hz EC data included the sonic temperature correction (Schotanus et al. 1983), density correction (Webb et al. 1980), and coordinate rotation (Wilczak et al. 2001) and statistical analysis for quality control. (For more details, read Poblete-Echeverria and Ortega-Farias (2009).) For the quality control, the energy balance closure was considered using the ratio of turbulent fluxes (H + LE) to available energy (R n − 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 (Ortega-Farias et al. 2010). According to (Twine et al. 2000), LE and H values from the EC system were recalculated using the Bowen ratio (β = H/LE) for the two growing seasons.

Also, the reference evapotranspiration fraction (F i_EC) and crop coefficient (K c_EC) were calculated using LE obtained by the EC system:

$$ F_{{{\text{i\_EC}}}} = \frac{{{\text{ET}}_{{{\text{i\_EC}}}} }}{{{\text{ET}}_{{{\text{oh\_i}}}} }} $$
(11)
$$ K_{{{\text{c\_EC}}}} = \frac{{{\text{ET}}_{{{\text{a\_EC}}}} }}{{{\text{ET}}_{\text{o}} }} $$
(12)

where ETi_EC is the hourly ETa at the instant of satellite image (mm d−1); ETa_EC is the ETa calculated as:

$$ {\text{ET}}_{{{\text{a\_EC}}}} = \sum\limits_{i = 1}^{24} {{\text{ET}}_{\text{ah}} } $$
(13)

where ETah is the hourly ETa obtained from the EC system. Also, the mean values (F mean) of hourly F o from 8:00 to 18:00 h were included in the study to test the METRIC assumption (F c_M = F i_M).

Landsat satellite data sets

Two Landsat 5 (TM) and eleven Landsat 7 (+ETM) cloud free satellite images (path 233, row 85) were obtained from USGS Glovis (http://glovis.usgs.gov) with available scenes every 16 days. The Landsat scenes were acquired including a default standard terrain correction (Level 1T). Since 2003, the +ETM images have gaps owing to failures in the satellite scan line corrector (slc-off), only scenes without gaps in the study area were processed (Table 2). According to the Landsat 7 handbook (NASA 2010) and METRIC operation manual (Allen et al. 2010), atmospheric corrections in visible and infrared bands were applied to obtain values representative for the earth’s surface. Pixel selection followed previous research (Bastiaanssen et al. 1998; Tasumi et al. 2005; Singh and Irmak 2009), but to avoid the contamination by pixels outside the experimental area (due to buildings, trees, vineyard streets and the Lircay River), a perimeter of 30 m from the field edges inward was excluded when calculating field-scale averages.

Table 2 Acquisition dates of Landsat 5 (TM) or 7 (ETM+) cloud free images used in the analysis (path 233, row 35)
Full size table

For each image, the sensible heat flux at the cold anchor pixel was defined as H cold = R n_cold − G cold − 1.20EToh. The factor 1.20 was applied considering that ET of the fully covered alfalfa (ETr) was 20 % greater than that of grass. According to the literature, the ratio of ETr to ETo ranges from 1.20 to 1.40 (Tasumi 2003; Folhes et al. 2009). On the other hand, several “hot” anchor pixels were selected for each image, considering surfaces inside the agricultural settings with no vegetation cover and with little soil evaporation. To ensure that the EToh from the hot pixels’ candidates was near zero, the FAO-56 available soil water balance model was applied (Allen et al. 1998).

Statistical comparison between measured and estimated values

Daily ETa_M and K c_M were computed by averaging 36 (30 × 30 m) pixels within the 4.25 ha experimental plot. K c_M and ETa_M values were compared with those obtained by the EC system (K c_EC and ETa_EC). Daily comparisons include the ratio (b) of K c_M to K c_EC, index of agreement (d), RMSE, and mean absolute error (MAE) (Willmott et al. 1985; Mayer and Butler 1993). Also, the t test was used to check whether the ratio was significantly different from unity at the 95 % confidence level. Similar statistical parameters were used for the comparison between ETa_M and ETa_EC on a daily basis. For validating the METRIC assumption (F i_M = K c_M), values of F i_EC were compared with those of F mean.

Results and discussion

Atmospheric conditions were very dry and hot for both growing seasons since clear days prevailed during the experiment (Fig. 2). The highest values of T a_o, R si_o, ETo, and VPD were recorded at the end of December and beginning of January (summer in the southern hemisphere). Maximum and minimum air temperatures were between 35 and 17 °C, respectively, for both growing seasons (Fig. 2a). R si_o ranged from 33 MJ m−2d−1 for clear days to 4.3 MJ m−2d−1 for partly cloudy days (Fig. 2a). Cumulative rainfall was 11.4 mm per year for the two study periods. Rainfall events were concentrated in late April for the first growing season and the beginning of September for the second season (Fig. 2a). Daily mean u 2 was between 0.5 and 1.5 m s−1 and maximum u 2 reached values between 2.5 and 3.5 m s−1 (Fig. 2b). Under these weather conditions, the VPD ranged between 0.1 and 1.7 kPa (Fig. 2c). Daily ETo ranged between 0.8 and 8.4 mm d−1 from September (spring–summer) to April (summer–fall) (Fig. 2c) with a mean value of 6.2 mm d−1 for the driest period (December to January). Under these atmospheric conditions, vines were irrigated twice a week according to measurements of soil water content that was maintained between 0.29 and 0.35 m3 m−3 (Fig. 3a) with mean values of θi = 0.32 (±0.01) and 0.31 (±0.02) m3 m−3 for the first and second period, respectively. Under these soil water conditions, Ψx ranged from −0.4 to −1.02 MPa (Fig. 3b), indicating that the drip-irrigated vineyard was maintained under well-irrigated conditions during the two study period (Schultz and Matthews 1993). Total water applications were 217 and 255 mm year−1 for the first and second period, respectively.

Fig. 2
figure 2

Daily values of maximum (T a_o max) and minimum (T a_o min) air temperature, solar radiation (R si_o), rainfall, wind speed (u 2), vapor pressure deficit (VPD), and daily reference evapotranspiration (ETo) for the 2007–2008 and 2008–2009 growing seasons (Talca Valley, Maule Region, Chile)

Full size image
Fig. 3
figure 3

Monthly averaged values of a volumetric soil moisture (θi) and b midday stem water potential (Ψx), for the 2007–2008 and 2008–2009 growing seasons (Talca Valley, Maule Region, Chile)

Full size image

The vineyard hourly energy balance closure indicates that turbulent fluxes (H + LE) were less than the available energy (R n − G) (Fig. 4). The linear regression through the origin indicated that the coefficient of determination (R 2) was 0.90 for days where satellite images were available. The slope of the regression line was different from unity at the 95 % confidence level and turbulent fluxes were less than the available energy by about 11 %. The level of closure of the energy balance is in agreement with previous applications of EC system in sparse crops. Such measurements are considered sufficient to provide accurate estimates of ETa (Oliver and Sene 1992; Laubach and Teichmann 1999; Kordova-Biezuner et al. 2000; Testi et al. 2004; Ortega-Farias et al. 2007). To close the energy balance, hourly LE values from the EC system were recalculated using the Bowen ratio. The Bowen ratios were between −0.26 to 2.36 and −0.13 to 3.66, for the 2007–2008 and 2008–2009 growing seasons, respectively.

Fig. 4
figure 4

Ratio of hourly turbulent energy fluxes (LE + H) to available energy (R n − G) from eddy covariance system for a drip-irrigated Merlot vineyard for the 2007–2008 and 2008–2009 periods (Talca Valley, Maule Region, Chile)

Full size image

For the two study periods, the comparisons between F i_EC versus F mean and K c_EC versus F i_EC are shown in Figs. 5 and 6, respectively, which indicate that points are close to the 1:1 line. The comparison between F i_EC and F mean indicated that d, MAE, and RMSE were 0.89, 0.05, and 0.06, respectively (Table 3). In addition, the t test indicated that the ratio of F i_EC to F mean was not different from unity at the 95 confidence level. Similarly, the t test indicated that F i_EC values were statistically similar to those of K c_EC with d = 0.84, MAE = 0.05, and RMSE = 0.07. For the drip-irrigated Merlot vineyard, these results suggested that the instantaneous F o at the satellite image time can be used to derive daily crop coefficients.

Fig. 5
figure 5

Comparisons between instantaneous (F i_EC) and mean (F mean) reference evaporative fraction obtained from eddy correlation measurements. F mean is the mean value of hourly F o from 8:00 to 18:00 h, and F i_EC is the hourly F o at the time of satellite overpass

Full size image
Fig. 6
figure 6

Comparison between instantaneous reference evaporative fraction (F i_EC) and daily crop coefficient (K c_EC) obtained from eddy correlation measurements for a drip-irrigated Merlot vineyard (Talca Valley, Maule Region, Chile). K c_EC is the daily ratio of actual to reference evapotranspiration

Full size image
Table 3 Statistical analysis of reference evapotranspiration fraction (F o), single crop coefficient (K c), and actual evapotranspiration (ETa) of a drip-irrigated Merlot vineyard
Full size table

For selected days, the Fig. 7 shows the hourly (F h_EC) and mean (F mean) values of reference evapotranspiration fraction (F o) obtained from the EC system for the stages from bud break (B) to flowering (FL), FL to fruit set (FS), FS to veraison (V), and V to harvest (H). On DOY 334 (FL–FS stage, 2007–2008 season), Fh_EC was relatively constant before noon ranging between 0.31 and 0.55, but F h_EC increased up to 1.1 due to clouds between 16:00 and 18:00 h. On this day, F mean was 0.49 and F i_EC was 0.36. On DOY 337 (2008–2009 season), F h_EC was between 0.23 and 0.78 during the daytime with F i_EC equal to F mean (0.57). For the FS–V stage, F h_EC was relatively constant during the daytime with F mean = 0.49 and F i_EC = 0.57 for DOY 25, while F mean = 0.59 and F i_EC = 0.65 for DOY 03. For the V–H stage, F h_EC ranged between 0.43 and 0.99 for DOY 49 and between 0.21 and 0.65 for DOY 67. Values of F mean and F i_EC were 0.66 and 0.62 for DOY 49, while those were 0.33 and 0.43 for DOY 67, respectively. These results indicate that F h_EC was approximately constant during the daytime for main phenological stages under clear sky conditions. Also, the measurements suggest that the reference evapotranspiration fraction (F o) is more variable on partly cloudy days. Colaizzi et al. (2006) indicated that F o appeared more stable throughout the day in comparison with other up-scaling methods based on the evaporative fraction, incoming solar radiation, and ratio of net to incoming solar radiation. To extrapolate from instantaneous to daily values of ETa, Chávez et al. (2008) found that the F o method performed better for transpiring crops with nonsoil water stress and for advective and homogeneous surface conditions. Furthermore, Allen et al. (2007a) and Gowda et al. (2007) indicated that F o is able to account for impacts of advection and changing wind and humidity conditions during the day.

Fig. 7
figure 7

Hourly reference evapotranspiration fraction (F h_EC) and actual evapotranspiration (ETah) obtained from eddy correlation measurements for the main phenological stages of a drip-irrigated Merlot vineyard (one representative day per phonological stage). The large circles show the mean values (F mean) of F h_EC from 8:00 to 18:00 h. DOY day of year and EToh hourly reference evapotranspiration

Full size image

Table 3 indicates that the crop coefficients of METRIC differed from the EC measurements with MAE = 0.08, RMSE = 0.10, and d = 0.70. The ratio of K c_M to K c_EC was significantly different from unity, and METRIC overestimated the crop coefficient by about 10 % (Fig. 8). These results showed acceptable levels of accuracy (differences <20 %) in agreement with the typical errors found in the literature when remote sensing models were applied to estimate K c. In Idaho, Tasumi et al. (2005) indicated that the average error in the estimation of K c was near 5 % when METRIC was applied in crops such as alfalfa, bean, corn, pea, sugar beet, and grain. Using NDVI obtained from satellite images, Singh and Irmak (2009) simulated K c in corn with RMSE ranging between 0.13 and 0.2.

Fig. 8
figure 8

Comparison between the crop coefficients obtained by the eddy correlation system (K c_EC) and estimated by METRIC model (K c_M) for a drip-irrigated Merlot vineyard for the 2007–2008 and 2008–2009 growing seasons (Talca Valley, Maule Region, Chile)

Full size image

In general, values of K c_M were close to those of K c_EC for the B–FL and FL–FS stages (Fig. 9). Mean values of K c_EC and K c_M were 0.41 and 0.46 for the B–FL stage and 0.53 and 0.54 for the FL–FS stage, respectively. For the FS–V stage, mean K c_EC was 0.56 and mean K c_M was 0.59. Finally, Fig. 9 shows that K c_M was greater than K c_EC during the V–H stage where the mean values of K c_EC and K c_M were 0.46 and 0.62, respectively. In Spain, Campos et al. (2010) indicated that K c values of drip-irrigated vineyard were 0.5 for the period between flowering and fruit set and were 0.47 after pruning. In Brazil, Teixeira et al. (2007) found that mean weekly values of K c were in the range from 0.65 to 0.82 and from 0.63 to 0.87, for the first and second growing cycle of a drip-irrigated vineyard, respectively. In Spain, Balbontin-Nesvara et al. (2010) indicated that the mean K c from bud break to veraison was 0.2 and 0.3 as measured by EC and BREBS systems, respectively. After veraison, averaged values of K c were 0.52 for BREBS and 0.49 for EC system. Finally, the FAO 56 manual (Allen et al. 1998) recommends values of K c = 0.30, 0.70, and 0.45 for the initial (K c_ini), mid-season (K c_mid), and late (K c_late) season stages, respectively. Considering the FAO-56 seasonal stages, mean values of K c_M for the 13 satellite images were 0.46, 0.57, and 0.62, while K c_EC were 0.41, 0.55, and 0.46 for the initial, mid-, and late stages, respectively.

Fig. 9
figure 9

Daily values of crop coefficient obtained by the eddy correlation system (K c_EC) and calculated (K c_M) by METRIC model for the main phenological stages of a drip-irrigated Merlot vineyard (Talca Valley, Maule Region, Chile). Phenological stages: bud break (B), flowering (FL), fruit set (FS), veraison (V), and harvest (H)

Full size image

Our results suggest that it is possible to estimate daily ETa as a function of F i_M and ETo (Eq. 1). The comparisons between daily ETa_M and ETa_EC are indicated in Fig. 10 and Table 3 for each day when satellite images were available. METRIC estimated the daily ETa for the drip-irrigated vineyard with RMSE and MAE = 0.62 and 0.50 mm d−1, respectively. The ratio of ETa_M to ETa_EC was different from unity at a 95 % confidence level indicating that METRIC overestimated the daily ETa with an error of 9 % (Fig. 10). Folhes et al. (2009) observed that METRIC estimated ETa of banana fields with RMSE = 0.4 mm d−1. To predict daily ETa of maize, Singh and Irmak (2011) found a RMSE between 1.1 and 1.7 mm d−1. In vineyard, Galleguillos et al. (2011) published values of RMSE = 0.83 mm d−1, when applying the S-SEBI model to estimate the daily ETa. In Brazil, Teixeira et al. (2009a) observed that SEBAL predicted ETa for natural vegetation and irrigated crops (wine grapes, table grapes, and mango orchards) with errors <18 % and RMSE of 0.38 mm d−1.

Fig. 10
figure 10

Comparison between actual evapotranspiration (ETa_EC) obtained by the eddy correlation system and estimated by METRIC (ETa_M) model for a drip-irrigated Merlot vineyard (Talca Valley, Maule Region, Chile)

Full size image

The worst performance of the METRIC crop coefficients was observed from veraison to harvest (Fig. 9), where RMSE and MAE were 0.17 and 0.16, respectively. The major disagreements between K c_M and K c_EC were associated with errors in the estimation of instantaneous values of the energy balance components, especially with Rn. For the V–H stages, RMSE were 60, 35, and 19 W m−2 for R n, H, and G at the satellite overpass, respectively. According to Allen et al. (2011), a disadvantage of the residual energy balance approach is that the computation of LE is only as accurate as the estimates of R n, H, and G. METRIC attempts to overcome this disadvantage by focusing internal calibration on LE and using H to absorb intermediate estimation errors and biases.

Conclusions

For a drip-irrigated Merlot vineyard under well-irrigated conditions (midday Ψx > −1.0 MPa), METRIC estimated crop coefficient with RMSE and MAE = 0.1 and 0.08, respectively. Using the reference ETo fraction as a method for scaling up from instantaneous to daily values, METRIC computed ETa with RMSE = 0.62 mm d−1 and MAE = 0.5 mm d−1. In addition, the indexes of agreements were 0.7 and 0.85 for crop coefficient and ETa, respectively. Major disagreements between K c_M and K c_EC were observed from veraison to harvest, where METRIC overestimated K c and ETa with RMSE = 0.16 and 0.89 mm d−1, respectively. However, those errors did not significantly affect the overall performance of METRIC during the study period. Future research will focus on the detection of variables that most significantly affect the METRIC performance, considering canopy geometry, LAI, and the parameterization of surface energy balance components. Because of the long interval between Landsat scenes, it will also be necessary to check the applicability of METRIC using other satellites that regularly collect thermal imagery at high spatial resolution, such as ASTER.