Parameterization of a two-layer model for estimating vineyard evapotranspiration using meteorological measurements

Agricultural and Forest Meteorology 150 (2010) 276–286

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Parameterization of a two-layer model for estimating vineyard evapotranspiration using meteorological measurements S. Ortega-Farias a,*, C. Poblete-Echeverrı´a a, N. Brisson b a b

Research and Extension Center for Irrigation and Agroclimatology (CITRA), Universidad de Talca, Casilla 747, Talca, Chile Institut National de la Recherche Agronomique (INRA), Unite´ Climat, Sol et Environnement, Domaine St Paul, Site Agroparc, 84914 Avignon Cedex 9, France

A R T I C L E I N F O

A B S T R A C T

Article history: Received 29 September 2008 Received in revised form 20 November 2009 Accepted 23 November 2009

The Shuttleworth and Wallace (SW) model with variable canopy resistance was evaluated to estimate evapotranspiration (ETv) from a drip-irrigated Merlot (Vitis vinifera L.) vineyard trained on a vertical shootpositioned (VSP) system. This vineyard is located in the Talca Valley, Region del Maule, Chile (358250 LS; 718320 LW; 125 m a.s.l). The performance of the SW model was evaluated using the eddy-covariance method on a 30 min time interval. Also, sub-models to estimate net radiation (Rn) and soil heat flux (G) were used in the SW model. A good agreement between observed and estimated values of Rn was found with a root mean square error (RMSE) of 33 W m2 and a mean absolute error (MAE) of 24 W m2. Also, the SW model was able to estimate latent heat flux with RMSE and MAE of 34 and 21 W m2, respectively. On a daily basis, results indicate that the SW model was able to predict the ETv with RMSE and MAE values of 0.51 and 0.41 mm d1, respectively. These results suggest that it is possible to directly estimate ETv over unstressed grapevines using meteorological data and soil moisture measurements. ß 2009 Elsevier B.V. All rights reserved.

Keywords: Canopy resistance Energy balance Vine Evapotranspiration

1. Introduction The main viticultural areas of Chile have experienced more ˜ a’’-Southern Oscillation frequent droughts related to the ‘‘La Nin (ENSO) events during the last 10 years (Meza et al., 2003). For this reason, the drip irrigation system has been widely adopted by farmers to optimize water application in vineyards. Additionally, drip-irrigated vineyards require a correct irrigation scheduling in order to maintain existing production levels and wine quality. A key to achieve these targets is the estimation of actual evapotranspiration (ETa) according to nonlinear interactions of soil, vines and atmospheric conditions. In this regard, Sene (1994) and Ortega-Farias et al. (2007) suggested using the two-layer model of Shuttleworth and Wallace (SW) to directly estimate ETa using meteorological data measured over a non-irrigated and dripirrigated vineyard, respectively. Furthermore, during the last decade, the SW model has been widely used to estimate ETa in different types of sparse crops and climatic conditions (Alves and Cameira, 2002; Anadranistakis et al., 2000; Kato et al., 2004; Zhou et al., 2006; Gardiol et al., 2003; Fisher et al., 2005). In the SW model, ETa is calculated as the sum of the Penman–Monteith equation for evaporation and transpiration, weighted by a set of coefficients that represent the combination of soil and canopy resistances (Shuttleworth and Wallace, 1985).

* Corresponding author. Fax: +56 71 200212. E-mail address: [email protected] (S. Ortega-Farias). 0168-1923/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.agrformet.2009.11.012

However, the direct estimation of ETa is complex because vineyard water use is controlled by energy absorbed by vines and soil surface. Vineyards consist of widely spaced plants that allow for deep penetration of sunlight into the canopy. As a result, the soil contribution to the energy balance is considerable (Spano et al., 2000). This depends highly on management practices that determine vine vigour and, hence, water-use (Yunusa et al., 2004). The vigour of the vine is manifested through the canopy size, leaf area index (LAI), and fraction of soil surface covered by vegetation (fc). In commercial vineyards, canopy cover is generally incomplete as a result of the canopy geometry generated by training systems. According to canopy structure and vegetation coverage, sensible heat flux (H) generated at the soil surface can be a major contributor to the vineyard energy balance which plays a key role in vine transpiration and evaporation. For this reason, the incomplete canopy cover is considered a major cause of the relatively low rate of transpiration by grapevines in commercial vineyards since the majority of the incident radiation is not captured, but transmitted to the bare soil surface (Yunusa et al., 2004). Therefore, the application of the SW model for irrigation scheduling requires an adequate characterization of canopy geometry and training system, which control the energy absorbed by vines and soil surface. For a drip-irrigated Cabernet Sauvignon vineyard, Ortega-Farias et al. (2007) indicated that the SW model simulated latent heat flux (LE) and ETa with a mean absolute error (MAE) of 22 W m2 and 0.36 mm d1, respectively. According to this study, the parameterization of LAI and canopy resistance is critical in order to

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increase confidence in the accuracy of the SW model. Also, the SW model was able to predict LE over a furrow-irrigated vineyard with a MAE value of 39 W m2 (Zhang et al., 2008). Unlike to these studies, our research consists of evaluating the application of SW model to directly simulate LE and ETa using weather data (air temperature, relative humidity, wind speed, and solar radiation) generated by an automatic meteorological station installed over a drip-irrigated Merlot vineyard. Also, this study includes the evaluation of a sub-model for estimating the net radiation (Rn) and soil heat flux (G) using only conventional meteorological data. Finally, the canopy resistance ðrsc Þ was simulated using weather information in combination with soil water content measurements in the root-zone, and soil surface resistance ðrss Þ was calculated only as a function of soil water content in the top layer of soil. 2. Theory The daytime and nighttime variation of latent heat flux from vine transpiration and soil evaporation is computed by the following expressions (Shuttleworth and Wallace, 1985):

lETv ¼ LE ¼ T þ E

(1)

T ¼ Cc

DA þ ððra c p D  Drac As Þ=ðraa þ rac ÞÞ D þ g ð1 þ ðrsc =ðraa þ rac ÞÞÞ

(2)

E ¼ Cs

DA þ ððra c p D  Dras ðA  As ÞÞ=ðraa þ ras ÞÞ D þ g ð1 þ ðrss =ðraa þ ras ÞÞÞ

(3)

where ETv = actual evapotranspiration over a vineyard (mm d1); l = latent heat of vaporization (J kg1); LE = latent heat flux from vineyard (W m2); T = latent heat flux from vine transpiration (W m2); E = latent heat flux from soil evaporation (W m2); Cc = canopy resistance coefficient; Cs = soil surface resistance coefficient; D = slope of the saturation vapor pressure curve at the mean temperature (kPa K1); A = available energy leaving the complete canopy (W m2); cp = specific heat of the air at constant pressure (1013 J kg1 K1); ra = air density (kg m3); D = water vapor pressure deficit at the reference height (kPa); rac ¼ bulk boundary layer resistance; of the vegetative elements in the canopy ðs m1 Þ; As = available energy at the soil surface (W m2); raa ¼ aerodynamic resistance between canopy source height and reference level ðs m1 Þ; g = psychrometric constant (kPa K1); rsc ¼ canopy resistance ðs m1 Þ; ras ¼ aerodynamic resistance between the soil and canopy source height ðs m1 Þ; and rss ¼ soil surface resistance ðs m1 Þ.

277

which corresponded to a normalized soil water content value (F4) of 0.51. The Merlot vines were planted in 1999 in north-south rows 2.5 m apart, with 1.5 m within-row spacing. The vines were trained on a vertical shoot-positioned (VSP) system with a foliage height of 2.0 m and canopy width of 0.5 m. The canopy geometry of this training system was similar to a parallelepiped which was conserved after bloom (about mid-November) by hedging two or three times during the summer. Typical vine trunk diameters were about 11.7 cm (0.8 cm) and soil surface was maintained free of weeds or cover crop during the experiment. 3.2. Irrigation management and plant measurements Irrigation water was delivered twice a week in the morning using 4.0 L h1 drippers spaced at intervals of 1.5 m along the rows. Weekly measurements of soil water content (ui) at the rooting depth (0–60 cm) were taken using a portable TDR unit (TRASE, Soil Moisture Corp., Santa Barbara, CA) with 12 pairs of rods inserted below the drippers. Also, the volumetric soil water content (ug) in the top layer of soil (0–20 cm) was measured under vine canopy (4 points) and between rows (6 points). The average value of ug was weighted by a fractional cover of 0.3 which was estimated by measuring dimension of canopy 10 times during each season. Vine water status was evaluated using the midday stem water potential (cx) measured with a pressure chamber (Soil Moisture Equipment, Santa Barbara, CA). cx was measured on 12 fully expanded leaves, wrapped in aluminum foil and encased in plastic bags at least 2 h before measurement. Stomatal resistance (rst) was measured using a portable infrared gas analyzer (model LI-6400, LI-COR, Lincoln, NE). Measurements of cx and rst were done at midday (approximately 11:00–14:00 h) from sunlit and shaded leaves situated on both sides of the vine rows. Leaf area index (LAI) was estimated as a function of the shoot length which was correlated with its total leaf area (Ortega-Farias et al., 2007): Pi

LAsh Av ¼ 616:7 þ 35:1Lsh

LAI ¼ LAsh

1

(4) (5)

where LAsh = total leaf area per shoot (cm2); Av = area of vines (cm2); i = total shoot number per vine; and Lsh = shoot length (cm). To develop the correlation between LAsh and Lsh, leaves of each shoot were scanned so that leaf area was measured using an image analysis. On four vines the total shoot length per vine was measured once a week during the experiment.

3. Materials and methods 3.3. Energy balance measurements 3.1. General description The experiment was conducted during the 2006/2007 and 2007/2008 growing seasons on a drip-irrigated commercial Merlot (Vitis vinifera L.) vineyard located in the Talca Valley, Regio´n del Maule, Chile (358250 LS; 718320 LW; 125 m a.s.l.). The climate in this area is a typical Mediterranean semiarid climate with an average daily temperature of 17.1 8C between September and March (between spring and summer periods). Average annual rainfall in the region is about 676 mm falling mainly during the winter months. The summer period is usually dry (2.2% of annual rainfall) and hot while the spring is on average wet (16% of annual rainfall). The soil at the vineyard is classified as the Talca series (family Fine, mixed, thermic Ultic Haploxeralfs) with a clay loam texture. For the effective rooting depth (0–60 cm), the volumetric soil water content at field capacity (uFC) and at wilting point (uWP) were 0.36 m3 m3 (216 mm) and 0.22 m3 m3 (132 mm), respectively. The management allowed depletion (MAD) was 29% (174 mm),

An automatic weather system was installed at the Merlot vineyard to measure energy balance components and meteorological variables at 30-min interval. Wind speed (u) and wind direction ðwÞ were monitored by a cup anemometer and a wind vane (03101-5, Young, Michigan, USA) and precipitation (Pp) was measured by a rain gauge (A730RAIN, Adcon Telemetry, Austria). Air temperature (Ta) and relative humidity (RHa) were measured using a Vaisala probe (model HMP45C). Net radiation (Rn), incoming (Rsi) and outgoing (Rso) solar radiation were measured by a four-way net radiometer (CNR1, Kipp&Zonen Inc., Delft, Netherlands). Sensors of u, w, Pp, Ta, RHa, Rn, Rsi, and Rso were installed at 4.7 m above the soil surface. Also a Vaisala probe for measuring temperature (Tc) and relative humidity (RHc) within canopy was installed inside the foliage at 1.6 m above the soil surface. Rn at the soil surface was measured by a Fritchen type net radiometer (REBS-Q7, Campbell Sci., Logan, UT) at a 0.5 m height. Additionally, the sensor inter-comparison over a grass surface

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indicated that differences between the CNR1 and REBS-Q7 were less than 30 W m2, which is within sensor accuracy. Latent heat flux (LE) and sensible heat flux (H) were measured using an eddy-covariance (EC) system mounted at a height of 4.7 m and oriented towards the predominant wind direction (South). The system consisted of a fast response open-path infrared gas analyzer (LI-7500 IRGA; LI-COR, Inc., Lincoln, Nebraska, USA) and a three dimensional sonic anemometer (CSAT, Campbell Sci., Logan, UT). The minimum fetch-to-instrument-height ratio was about 200:1, sufficiently large to preclude horizontal advection. Also, estimates of LE from the LI-7500 IRGA were corrected for air density (Webb et al., 1980), and H estimates were corrected for sonic temperature (Schotanus et al., 1983). LE and H measurements were made at 10 Hz, and means, standard deviations, and covariances were calculated for 30-min periods by Reynolds block averaging. Soil heat flux was estimated using eight flux plates installed on either side of the rows (6 and 2 plates into the inter-row and below row, respectively). This arrangement takes into account the row shade effect during the course of the day. The flux plates of constant thermal conductivity (HFT3, Campbell Sci., Logan, UT) were placed at a 0.08 m depth (d). Also, two averaging thermocouple probes (TCAV, Campbell Sci., Logan, UT) to measure soil temperature (Tsoil) were installed above each flux plate at depths of 0.02 and 0.06 m. At each position, the soil heat flux was calculated by adding the measured flux at 0.08 m to the heat stored (S) in the layer above the heat flux plates. Values of S are given by: S ¼ ðrb C d þ u g rw C w Þ

DT soil d Dt

(6)

where rb = soil bulk density (1600 kg m3); rw = density of water (1000 kg m3); Cd = specific heat capacity of soil (890 J kg1 K1); Cw = specific heat capacity of the soil water (4190 J kg1 K1); DTsoil = change in soil temperature (K); Dt = time intervals (s). Half-hour averages of all signals were recorded on an electronic datalogger (CR 5000, Campbell Sci., Logan, UT). Every 15 days, soil evaporation (E) was measured with microlysimeters which were made from PVC tubes of 75 mm i.d. and 150 mm in length (Yunusa et al., 2004). Four microlysimeters were installed on either side of the vines into the inter-row and two microlysimeters were installed within the drip-line (one below drip and the other one between drippers). 3.4. Data quality control Wilson et al. (2002) indicated that the eddy correlation (EC) system could present systematic errors in the measurements of turbulent energy fluxes (LE and H). Therefore, it is very important to avoid systematic energy imbalances and errors in the direct EC measurements used for model validations. For this reason, entire days that clearly exhibited persistent noisy behavior due to instrumental problems, flow distortion through the tower, or adverse meteorological conditions (for example rainy days) were discarded. For this reason, days that presented an energy balance ratio (EBR) of (H + LE) to (Rn  G) between 0.90 and 1.10 were excluded for the validation model. Major problems were associated with power failure and 46 days were eliminated for the 2-year data set when EBR values were <0.90 or >1.10. Also, when 5 or more of the 48 observations were missing, that day of data was excluded. If fewer than five observations were missing, data were linearly interpolated to complete the time series (Brotzge and Crawford, 2003; Laubach and Teichmann, 1999). In this case, most of the interpolations were applied during the early morning and late afternoon, especially on cloudy days.

Data were collected from November 15 (Day of year (DOY) 319) 2006 to March 15 (DOY 74) 2007 for the first season and October 19 (DOY 292) 2007 to February 28 (DOY 59) 2008 for the second season. After data quality control was applied as described above, a total of 96 days were available for which all energy balance data (Rn, H, LE and G) were complete from the experimental site. However, much longer datasets were available for Rn, G and meteorological variables. 3.5. Parameterization of available energy and resistances The available energy at the crop canopy is computed as: A ¼ Rn  G

(7) 2

where Rn = net radiation above the vineyard canopy (W m ); G = soil heat flux (W m2). On 30-min intervals, values of Rn were computed as follows (Ortega-Farias et al., 2000): Rne ¼ ð1  aÞRsi þ ea s Ta4  es s Ts4

(8)

where a = albedo; Rsi = incoming solar (short-wave) radiation (W m2); ea = atmospheric emissivity; s = Stefan–Boltzman constant (5.67  108 W m2 K4), es = emissivity of the surface (0.98); Ta = air temperature (K); Ts = surface temperature (K). In this study, Ts was estimated from measured soil (Tsoil) and canopy (Tc) temperatures weighted by fractional area (fc) of vegetation (Norman et al., 1995; Ezzahar et al., 2007): qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 (9) T s ¼ 4 f c Tc4 þ ð1  f c ÞTsoil where Tsoil and Tc are in Kelvin. The fractional area of the vineyard was 0.30 (0.04) and assumed constant during both seasons. Values of ea were computed from air temperature and vapor pressure as (Brutsaert, 1982): rffiffiffiffiffiffi e ea ¼ f 7 w (10) Ta where ew = air vapor pressure (kPa); f = calibration coefficient. Values of f were 1.51 for Rsi > 0 and 1.91 for Rsi  0. These values were suggested by Carrasco and Ortega-Farı´as (2008) for a drip-irrigated Cabernet Sauvignon vineyard trained on the VSP system. The soil heat flux was computed as a linear function of Rn: Ge ¼ 38:5 þ 0:25Rn

(11)

ðcoefficient of determination ðR2 Þ ¼ 0:89Þ

The intercept and slope were different from those found by Sene (1994) and Yunusa et al. (2004), indicating that a local calibration is necessary to get accurate estimates of G on half and hourly basis. It is important to indicate that Eq. (11) was obtained using 20 independent days which were randomly selected from the two growing seasons. The available energy at the soil surface was computed as As ¼ Rns  G

(12)

Rns ¼ Rn expðC LAIÞ

(13) 2

where Rns = net radiation at the soil surface (W m ); LAI = leaf area index (m2 m2); C = extinction coefficient of the canopy for net radiation. Using daily values of Rns and Rn, the extinction coefficient was estimated as 0.38  0.05. Many studies have been conducted to estimate stomatal resistance, which has been generally expressed as a function of the solar radiation, water vapor deficit, air temperature, leaf water potential and soil moisture content (Anadranistakis et al., 2000; Kaufmann, 1982; Torula and Heikinheimo, 1998). Using the Jarvis

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approach, values of rsc can be estimated by the following equations (Noilhan and Planton, 1989): r s min F 1 LAI F 2 F 3 F 4

rsc ¼ F1 ¼ f ¼

(14)

1þ f f þ ðr s min =r s max Þ

(15)

0:55Rsi 2 Rsl LAI

(16)

F 2 ¼ 1  0:0025D

(17)

F 3 ¼ 1  0:0016ð298  T a Þ2

(18)

where F1, F2, F3, and F4 take into account the effect of photosynthetically active radiation (PAR), vapor pressure deficit, air temperature, and soil water stress, respectively. rs min = minimum stomatal resistance (s m1); rs max = maximum stomatal resistance (2000 s m1); Rsl = threshold radiation value above which the stomata open (30 W m2). The term 2/LAI expresses the shading between leaves, while the factor 0.55 represents the PAR portion of solar radiation flux density. For this study, the daily mean value (from 11:00 to 14:00 h) of stomatal resistance and rs min were 216 (54) and 144 s m1, respectively. The daily mean value of rs min was obtained from well-watered vines with cx > 0.5 MPa (Williams and Trout, 2005). The effect of soil water stress on canopy resistance was calculated using the normalized soil water (F4) (Calvet et al., 1998; Ortega-Farias et al., 2004): F4 ¼

ui  uWP uFC  uWP

(19)

where uFC = volumetric soil moisture content at field capacity (fraction); uWP = volumetric soil moisture content at wilting point (fraction); ui = volumetric soil moisture content in the root-zone (fraction). Also, values of rac are given by: rac ¼

rb LAI

(20)

where rb = mean boundary layer resistance (25 s m1) (Shuttleworth and Wallace, 1985). A general description of aerodynamic resistance, Cs and Cc is found in Shuttleworth and Wallace (1985) and Ortega-Farias et al. (2007). Values of raa and ras are estimated by the following expressions: raa ¼

LAI a 4  LAI a r ðaÞ þ ra ð0Þ 4 a 4

(21)

ras ¼

LAI s 4  LAI s r ðaÞ þ ra ð0Þ 4 a 4

(22)

ras ð0Þ ¼ raa ð0Þ ¼ ras ðaÞ ¼

raa ðaÞ ¼

lnðx=z0o Þ lnfðd þ zo Þ=z0o g uk

2

lnðx=z0o Þ lnðx=z0o Þ uk

2

 ras ð0Þ

h nðh  dÞ     d þ zo  exp n  exp n 1  h

(23)

(24)

lnððx  dÞ=zo Þ uk

2

(25)

lnððx  dÞ=zo Þ 2

uk         xd h d þ zo þ exp n 1  1  ln hd nðh  dÞ h (26)

279

where raa ðaÞ ¼ value of raa for a crop with complete canopy cover ðLAI ¼ 4Þ ðs m1 Þ; raa ð0Þ ¼ value of raa for bare soil ðs m1 Þ; ras ðaÞ ¼ value of ras for a crop with complete canopy cover ðLAI ¼ 4Þ ðs m1 Þ; ras ð0Þ ¼ value of ras for bare soil ðs m1 Þ; x = reference height above the crop where meteorological measurements are available (4.7 m); h = canopy height (2.0 m); d = zero plane displacement of crop with complete canopy cover (0.67 h); zo = roughness length of crop with complete canopy cover (0.05 h); z0o ¼ roughness length of the bare soil ð0:01 hÞ; u = wind speed at the reference height (m s1); k = von Ka´rma´n’s constant (0.41); n = eddy diffusivity decay constant in a crop with complete canopy cover (2.5). The soil surface is the resistance to water vapor movement from the interior to the soil surface and was computed as follows. rss ¼ 19



us ug

3:5

(27)

where rss ¼ soil surface resistance ðs m1 Þ; ug = volumetric soil water content in the top layer of soil (0–20 cm); us = saturated volumetric soil water content at the 20 cm depth (0.53 m3 m3). Eq. (27) (with R2 = 0.67) was developed using measurements of E and ug from an independent data set of 20 days. In this case, a regression analysis was done between rss and us/ug where rss values were obtained by solving Eq. (3). 3.6. Statistical analysis In order to assess the validity of the estimation of latent heat flux (or vineyard evapotranspiration), as computed from the Shuttleworth and Wallace model, our calculations were compared to latent heat flux measured by the eddy-covariance method. Daily and 30-min comparisons include the ratio (roe) of observed to estimated values, index of agreement (Ia), root mean square error (RMSE) and mean absolute error (MAE) (Mayer and Butler, 1993; Willmott, 1981). Also, the Z-test was used to check whether the value of roe was significantly different from unity at the 95% confidence level. Similar statistical parameters were used to compare the observed and estimated values of net radiation on a 30-min and daily basis. 4. Results and discussion Skies were mostly clear for both seasons with daily values of Rsi and Rn between 5–35 MJ m2 d1 and 4–19 MJ m2 d1, respectively (Fig. 1a and b). Daily mean air temperatures were similar during both seasons, but atmospheric conditions during the second season were drier than those found during the first season. In this case, maximum mean values of D during 2007/2008 were greater than those for 2006/2007 (Fig. 1e and f). Also, daily mean values of u were 1.9 (0.6) m s1 and 0.9 (0.5) m s1 during 2006/2007 and 2007/2008, respectively (Fig. 1g and h). In both seasons, the top layer of soil (0–20 cm) was very dry where daily mean value of soil evaporation was 0.8 (0.2) mm d1 during the first season and 0.5 (0.1) mm d1 during the second season, according to measurements of the microlysimeters. Using the same measurements, Ortega-Farias et al. (2008) indicated that SW model predicted soil evaporation (Eq. (3)) with RMSE of 0.2 mm d1 and vine transpiration measured by the sapflow method accounted for 75–80% of ETv obtained by the EC system. It is important to indicate that no rainfall was observed during this study and wetted area of the drip-irrigated vineyard was only about 3%. Rainfall amounts from DOY 295 to DOY 62 in the first and second seasons were 34.4 and 11.6 mm, respectively. Energy balance closure was evaluated using a linear regression between turbulent energy fluxes (H + LE) and available energy (Rn  G) (Wilson et al., 2002; Laubach and Teichmann, 1999) (Fig. 2). The linear regression between (H + LE) and (Rn  G) was

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Fig. 1. Daily values of solar radiation (Rsi), net radiation (Rno), air temperature (Ta), vapor pressure deficit (D) and wind speed (u) for the 2006/2007 and 2007/2008 growing seasons.

similar for the 2006/2007 and 2007/2008 seasons with an overall value of R2 equal to 0.96. The overall analysis of the selected days indicates that the intercept (15 W m2) was statistically equal to zero and slope (0.96) was significantly different from unity,

indicating that turbulent energy fluxes were lower than available energy by about 4%. These results indicate that the eddycovariance method was providing accurate estimates of LE and H on the selected days during both seasons (Spano et al., 2000;

Fig. 2. A regression analysis between turbulent energy fluxes (H + LEo) from eddy correlation system and available energy (Rn  Go) for a drip-irrigated Merlot vineyard. The solid line represents the 1:1 line.

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281

Fig. 3. Daily values of normalized soil water (F4) and midday stem water potential (cx) for a drip-irrigated Merlot vineyard.

Fig. 4. Daily mean values of canopy resistance ðrsc Þ (averaged values from 11:00 to 15:00 h) and leaf area index (LAI) for a drip-irrigated Merlot vineyard.

Ortega-Farias et al., 2007). Also, Oliver and Sene (1992) found daily ratios of turbulent energy fluxes to available energy in the range of 0.9–1.2 with average values of about 1.06 for a non-irrigated Airen vineyard. For the 2-year data set, average values of daytime and nighttime energy balance closure were 15 (40) and 18 (15) W m2, respectively. However, R2 value was 0.27 for nighttime fluxes indicating that EC measurements were erratic. Fortunately, the average value of (Rn  G) during nighttime was 26 (15) W m2 which is within sensor accuracy. Values of cx ranged from 0.5 to 0.9 MPa and from 0.4 to 1.0 MPa for the 2006/2007 and the 2007/2008 season, respectively (Fig. 3). These values indicate that the Merlot vineyard was well irrigated and vine water status was adequate during both simulation periods (Williams and Trout, 2005). In this study, irrigation started on 08 November 2006 (DOY 312) in the first season and 19 November 2007 (DOY 323) in the second season when the soil water content reached a value near MAD (F4 = 0.5) (Fig. 3). Using this irrigation strategy, the normalized soil water content (F4) during both seasons was between 0.35 and 0.83 (Fig. 3) and the Merlot vineyard received a seasonal irrigation amount of 224 mm and 215 mm for 2006/2007 and 2007/2008, respectively. The lowest values of F4 (0.34) and cx (1.0 MPa) were observed between 16 and 20 January 2008 (Fig. 3b) where water application was reduced because of pump malfunction. During both seasons, LAI was less than 0.8 m2 m2 from DOY 292 to DOY 365 after which LAI was kept almost constant, between 1.0 and 1.22 m2 m2, until harvest by mechanical trimming (Fig. 4). Under these irrigation and canopy managements, daily mean values of canopy resistance (Eq. (13))

ranged between 250 and 567 s m1 for LAI < 1.0 m2 m2 and between 131 and 250 s m1 for LAI > 1.0 (Fig. 4). Fig. 5 shows that daily values of Rn and Rso accounted for 37–57 and 16–21% of Rsi, respectively, during both simulation periods. For these periods, a daily mean albedo of 0.19 was used to compute daytime variation of net radiation (Eq. (8)). Pieri and Gaudille`re (2003) indicated that vineyard albedo depends on the geometrical dimensions (ratio of row spacing (R) to canopy height (r)), shape of rows, and row azimuth. These authors computed an a value = 0.20 for a traditional vineyard in Bordeaux (one single vertical plane of foliage of nearly rectangular shape) with a ratio of R to r equal to 1.1. For a non-irrigated Airen vineyard grown on free standing bushes, Sene (1994) indicated that daily mean albedo was 0.27 and hourly average values dropped as low as 0.18. For an Italian vineyard grown on a trellis system, Vieira de Azevedo et al. (1997) found that daily mean values of albedo changed from 0.18 in the first days after bud shooting to 0.23 after blooming, falling to 0.20 in the period of fruit development. Also, Fig. 5 shows that the mean ratio of G to Rn was less than 0.026, indicating that soil heat flux did not significantly affect the vineyard energy balance on a daily basis. Similarly, Yunusa et al. (2004) and Trambouze et al. (1998) on Sultana and Shiraz vineyards, respectively, indicated that daily G accounted for 8–11% of Rn. On the other hand, Heilman et al. (1996) reported that G was about 29% of Rn for a Chardonnay vineyard. Results indicate that there was good agreement between observed (Rno) and estimated (Rne) values of net radiation during both the 2006/2007 and 2007/2008 season with similar values of RMSE, MAE, and Ia (Table 1). On a 30-min basis, overall values of Ia,

Fig. 5. Daily ratios of outgoing solar radiation (Rso) and net radiation (Rn) to incoming solar radiation (Rsi) for a drip-irrigated Merlot vineyard. Also, daily ratio of soil heat flux (G) to Rno are included.

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282

Table 1 Statistical validation of net radiation (Rn) model applied to a drip-irrigated Merlot vineyard. 30-min comparison

RMSE (W m2)

MAE (W m2)

reo

Ia

Z-Test

2006/2007 season 2007/2008 season

33 33

23 25

0.99 1.03

0.99 0.99

T T

Overall

33

0.99

T

24 2

d

1

)

1.01 2

MAE (MJ m

d

1

)

reo (MJ m

2

1

Daily comparison

RMSE (MJ m

Ia

Z-Test

2006/2007 season 2007/2008 season

1.5 1.1

1.1 0.8

0.94 0.98

d

)

0.90 0.96

F F

Overall

1.3

0.95

0.94

0.94

F

RMSE = root mean square error; MAE = mean absolute error; roe = ratio of observed to estimated values of net radiation on 30-min and daily basis; Ia = index of agreement; T = true hypothesis (b = 1); F = false hypothesis (b 6¼ 1).

Fig. 6. Comparison between estimated (Rne) and observed (Rno) net radiation at a 30 min interval for a drip-irrigated Merlot vineyard. The solid line represents the 1:1 line.

RMSE and MAE were 0.99, 33 W m2 and 24 W m2, respectively. The Z-test indicated that the value of roe was not significantly different from 1.0, suggesting that values of Rne and Rno were similar. However, Fig. 6 indicates that the Rn model tended to overestimate for Rno > 600 W m2 and underestimate for Rno < 200 W m2, especially during the second season. Daily comparison indicated that Rn model during 2007/2008 presented a better performance than that during 2006/2007 season (Table 1). Major departures from the 1:1 line were observed on cloudy days that presented daily values of net radiation less than 6 MJ m2 d1 (or 2.4 mm d1) (Fig. 7a). The greater disagreements were observed on DOY 74, which presented a Rn/Rsi ratio of 0.54. On this day, maximum difference between Rne and Rno were 105 W m2 and 5 MJ m2 d1 on a 30-min and daily basis, respectively. The overall analysis indicates that the model was able to simulate daily net radiation with overall values of RMSE and MAE equal to 1.3 and 0.95 MJ m2 d1, respectively. For both simulation periods, the roe values were statistically different from 1.0 suggesting that the model underestimated net radiation with an error of 6%. Similar results have been reported by Carrasco and Ortega-Farı´as (2008) in a drip-irrigated Cabernet Sauvignon vineyard, where the Rn model showed the largest errors under cloudy atmospheric conditions with maximum MAE and RMSE values equivalent to 40 and 61 W m2, respectively. According to Brotzge and Deuchon (2000) and Brotzge and Crawford (2003), the

probable causes of potential errors in the estimation of Rn on cloudy days were associated with the parameterization of the air emissivity, which depends on vapor pressure and air temperature at the reference level. Also, Ezzahar et al. (2007) and Ortega-Farias et al. (2000) indicated that the use of the Brutsaert’s formula may create an important scatter for low values of net radiation. A good comparison between observed (LEo) and estimated (LEe) values of LE was observed for the Merlot vineyard during the 2006/2007 and 2007/2008 seasons (Fig. 8). Similar values of Ia, RMSE and MAE were found for both simulation periods, but the roe value for 2006/2007 was lower than that for 2007/2008 (Table 2). Results of the Z-test indicate that roe value was significantly different from 1.0, suggesting that the SW model tended to underestimate and overestimate during the first and second season, respectively. The overall analysis indicated that the SW model overestimated latent heat flux with RMSE and MAE by 34 and 21 W m2, respectively. On a daily basis, the performance of the SW model was similar during the two seasons with RMSE values< 0.55 mm d1 (Table 2). The overall analysis suggested that the SW model was able to simulate ETv with Ia and RMSE of 0.88 and 0.51 mm d1 (1.25 MJ m2 d1), respectively. It is important to indicate that differences between Rno and Rne did not significantly affect the performance of the SW model for simulating ETv on cloudy days (Fig. 7). For cloudy days, observed (LEo) and estimated (LEe) values of LE were less than 100 W m2 (Fig. 9a and b) and the

Fig. 7. Comparison between estimated (e) and observed (o) values of net radiation (Rn) and vineyard evapotranspiration (ETv) at a daily interval. The solid line represents the 1:1 line.

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283

Fig. 8. Comparison between estimated (LEe) and observed (LEo) latent heat flux over a drip-irrigated Merlot vineyard. The solid line represents the 1:1 line.

Table 2 Statistical validation of latent heat flux (LE) and vineyard evapotranspiration (ETv) over a drip-irrigated Merlot vineyard estimated by the Shuttleworth and Wallace model.

(a) LE 2006/2007 season 2007/2008 season Overall

(b) ETv 2006/2006 season 2007/2008 season Overall

RMSE (W m2)

MAE (W m2)

roe

Ia

Z-Test

31 36

19 22

0.97 1.09

0.98 0.97

F F

1.03

0.97

F

34

21

RMSE (mm d1)

MAE (mm d1)

roe (mm d1)

Ia

Z-Test

0.47 0.55

0.37 0.44

0.97 1.01

0.87 0.88

F T

0.51

0.41

1.01

0.88

T

RMSE = root mean square error; MAE = mean absolute error; roe = ratio of observed to estimated values of latent heat flux or vineyard evapotranspiration; Ia = index of agreement; T = true hypothesis (b = 1); F = false hypothesis (b 6¼ 1).

Fig. 9. Observed (o) and estimated (e) values of latent heat flux (LE), net radiation (Rno), soil heat flux (Go) for cloudy days. The turbulent energy fluxes (H + LEo), available energy (Rno  Go), incoming solar radiation (Rsi), and albedo are included for a reference.

284

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SW model was able to predict ETv with RMSE values less than 15 W m2. Fig. 9c and d illustrates that values of Rno were greater than those of Rne during nighttime and daytime, but differences between estimated (ETve) and observed values (ETvo) of vineyard evapotranspiration were 0.5 and 0.35 mm d1 for DOY 74 and DOY 361, respectively. Also, values of turbulent energy fluxes and available energy were very close and albedo ranged between 0.17 and 0.21 from 11:00 to 14:00 h. For clear days, the best agreement between LEo and LEe was observed on DOY 40 (2007/2008) (Fig. 10b), where the maximum values of Ta and D were 28 8C and 2.61 kPa, respectively. Also, the daily Rn/Rsi ratio was 0.48 and albedo ranged between 0.17 and 0.20 from 10:00 to 18:00 h. On DOY 40, the roe was not significantly different from unity, indicating that values of LEo were similar to those of LEe. In this case, RMSE and MAE values were less than 20 W m2. Fig. 10d indicates that Rno and Rne presented a similar pattern during the day, but values of Rne were greater than those of Rno from 13:00 to 15:00 h. Also, values of turbulent energy fluxes (H + LEo) were close to available energy (Rno  Go) during daytime and nighttime with value of energy balance residue (Reb = Rno  Go  H  LEo) ranging between 53 and 58 W m2 (Fig. 10f). On DOY 40, daily values of ETvo and ETve were 3.4 and 3.5 mm d1, respectively and accounted for 58% of Rn. Greatest disagreements between LEo and LEe were observed on DOY 363 (Fig. 10a) where the SW model tended to underestimate

latent heat flux over the Merlot vineyard under clear sky conditions (Rn/Rsi ratio = 0.55 and albedo = 0.19). Under these conditions, the maximum values of Ta and D were 31.2 8C and 2.94 kPa, respectively (Figs. 1c and 2e). Also, soil surface on DOY 363 was wetted by rainfall (17.2 mm) observed on DOY 358. Major disagreements were observed between 12:00 and 20:00 h, where values of u were between 4.7 and 7.1 m s1 (Fig. 1g). RMSE value was 102 W m2 with a maximum difference between LEo and LEe of 197 W m2. Daily values of ETvo and ETve were 5.1 and 3.7 mm d1, respectively, for the vineyard with a midday stem water potential of 0.59 MPa. Also, a good energy balance closure was observed on DOY 363 where daytime values of Rne and Rno were similar, except at midday. In general, the greatest disagreements were observed on clear days after rainfall, especially under high atmospheric demand for water vapor. A similar study was done by Ortega-Farias et al. (2007) who indicated that the SW model was able to simulate latent heat flux (LE) over a drip-irrigated Cabernet Sauvignon vineyard under dry atmospheric conditions with a root mean square error (RMSE) and mean absolute error (MAE) of 29 and 22 W m2, respectively. Also, this study indicated that the SW model was very sensitive to errors in leaf area index and mean stomatal resistance, but it was not affected by errors in the estimation of aerodynamic resistances. Recently, Zhang et al. (2008) indicated that the SW model simulated LE over a furrow-irrigated vineyard (fc = 0.35) with MAE of 39 W m2.

Fig. 10. Observed (o) and estimated (e) values of latent heat flux (LE), net radiation (Rno), soil heat flux (Go) for clear days. The turbulent energy fluxes (H + LEo), available energy (Rno  Go), incoming solar radiation (Rsi), and albedo are included for a reference.

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In this study, the parameterization for the SW model was so well defined that, under dry soil conditions, the only input data required were direct measurements of climatic variables (Ta, u, RHa and Rsi), soil water content and leaf area index. It is important to acknowledge that the parameterization of Rn, G, rsc and rss depend on the training system, irrigation system and vine water status. The training system affects the vine vigor which is manifested through the canopy size, leaf area index (LAI), and fraction of soil surface covered by vegetation (fc). Therefore training systems have a substantial effect on soil energy balances, mainly by changing the partitioning of vineyard net radiation into its soil and canopy components (Heilman et al., 1996). According to canopy structure and vegetation coverage, sensible heat flux (H) generated at the soil surface can be a major contributor to the vineyard energy balance which plays a key role in vine transpiration and evaporation. For the drip-irrigated Merlot vineyard, canopy cover was generally incomplete as a result of the regimented structure imposed by the VSP system. This training system consists of widely spaced vines that allow for deep penetration of sunlight and air turbulence into the canopy. A constant shape of the canopy (a parallelepiped) was maintained with LAI ranging between 0.8 and 1.22 m2 m2and fc values of 0.3 (0.04) during the two growing seasons, especially after full bloom. Under this constant shape, daily ratios of Rso to Rsi were quite constant (a = 0.19  0.023), allowing a good performance of the Rn model during the two study periods. Also, during these two seasons, the top layer of soil (0–20 cm) was very dry and soil surface wetted by drip emitters was 3%. Under this canopy and soil water conditions, the soil contribution to the vineyard energy balance is considerable, especially under high atmospheric demand for water vapor. Under these atmospheric conditions, soil surfaces of a drip-irrigated vineyard could produce more sensible heat flux than that of a flood-irrigated vineyard because wetted surfaces are less than 3% of the total area of the vineyard. Consequently, soil heating that increases H depends on training and irrigation system. The parameterization of Rn, G, and rss seems adequate for the drip-irrigated Merlot vineyard trained on VSP, but further study is required for overhead systems (fc = 1) that completely shade the ground. In this case, the vineyard canopy of the overhead system behaves as a big-leaf and a one-layer model such as Penman– Monteith could be applied to simulate ETv (Rana and Katerji, 2008). Finally, values of midday steam water potential indicated that the Merlot vineyard was well irrigated during both simulation periods. Under these conditions, the Jarvis model, without any local calibration, seems correct for the unstressed Merlot vines. However, a calibration of Javis model could be required for vineyards under moderate or severe water stress. 5. Conclusions The SW model was successfully validated with LE and ETv measured from an eddy correlation system installed over a dripirrigated Merlot vineyard under well-irrigated conditions. In this regard, the SW model simulated latent heat flux at 30-min intervals with a RMSE and MAE of 34 and 21 W m2, respectively. For the vineyard evapotranspiration, RMSE was 0.51 mm d1 and MAE was 0.41 mm d1. In addition, the index of agreement was 97% and 88% for LE and ETv, respectively. These results suggest that it is possible to directly estimate ETv using meteorological information in combination with soil moisture measurements. However, It is important to acknowledge that the parameterization of SW model depends on the training system, irrigation system and vine water status. Future research will be centered on the effect of the training system and vine water status on the parameterization of Rn, G, rsc and rss . Also, we will explore the application of remote sensing to simulate the ground surface area cover which depends on vine vigor and canopy geometry.

285

Acknowledgements The research leading to this report was supported by the Chilean project FONDECYT N8 1071040 and a program for cooperation between Chile and France under project ECOSCONICYT N8 C04U03. We would like to thank Prof. Sharon Goulart for her assistance in editing the manuscript.

References Alves, I., Cameira, M.D., 2002. Evapotranspiration estimation performance ofroot zone water quality model: evaluation and improvement. Agric. Water Manage. 57, 61–73. Anadranistakis, M., Liakatas, A., Kerkides, P., Rizos, S., Gavanosis, J., Poulovassilis, A., 2000. Crop water requirement model tested for crops grown in Greece. Agric. Water Manage. 42, 371–385. Brutsaert, W., 1982. Evaporation in the Atmosphere: Theory, History, and Application. D. Reidel, Higham, MA, 229 pp. Brotzge, J., Crawford, K., 2003. Examination of the surface energy budget: a comparison of eddy correlation and Bowen ratio measurements systems. J. Hydrometeorol. 4, 160–178. Brotzge, J., Deuchon, C., 2000. A field comparison among a domeless net radiometer, two four-component net radiometers, and a domed net radiometer. J. Atmos. Ocean. Technol. 17, 1569–1582. Calvet, J., Noilhan, J., Roujean, J., Bessemoulin, P., Cabelguenne, M., Olioso, A., Wigneron, J., 1998. An interactive vegetation SVAT model tested against data from six contrasting site. Agric. For. Meteorol. 92, 73–79. Carrasco, M., Ortega-Farı´as, S., 2008. Evaluation of a model to simulate net radiation over a vineyard cv. Cabernet Sauvignon. Chilean J. Agric. 68, 156–165. Ezzahar, J., Chehbouni, A., Hoedjes, J.C.B., Er-Raki, S., Chebouni, A.H., Boulet, G., Bonnefond, J.M., Bruin, H.A.R., 2007. The use of the scintillation technique for monitoring seasonal water consumption of olive orchards in a semi-arid region. Agric. Water Manage. 89, 173–184. Fisher, J.B., DeBiase, T.A., Qi, Y., Xu, M., Goldstein, A.H., 2005. Evapotranspiration models compared on a Sierra Nevada forest ecosystem. Environ. Model. Software 20, 783–796. Gardiol, J.M., Serio, L.A., Della Maggiora, A.I., 2003. Modelling evapotranspiration of corn (Zea mays) under different plant densities. J. Hydrol. 271, 188–196. Heilman, J.L., McInnes, K.J., Gesch, R.W., Lascano, R.J., Savage, M.J., 1996. Effects of trellising on the energy balance of a vineyard. Agric. For. Meteorol. 81, 79–93. Kaufmann, M., 1982. Leaf conductance as a function of photosynthetic photon flux density and absolute humidity difference from leaf to air. Plant Physiol. 69, 1018–1022. Kato, T., Kimura, R., Kamichika, M., 2004. Estimation of evapotranspiration, transpiration ratio and water-use efficiency from a sparse canopy using a compartment model. Agric. Water Manage. 65, 173–191. Laubach, J., Teichmann, U., 1999. Surface energy budget variability: a case study over grass with special regard to minor inhomogeneities in the source area. Theor. Appl. Climatol. 62, 9–24. Mayer, D.G., Butler, D.G., 1993. Statistical validation. Ecol. Model. 68, 21–31. Meza, F.J., Wilks, D.S., Riha, S.J., Stendiger, J.R., 2003. Value of perfect forecasts of sea temperatures anomalies for selected rain-fed agricultural locations of Chile. Agric. For. Meteorol. 116, 117–135. Noilhan, J., Planton, S., 1989. A simple parameterization of land surface processes for meteorological models, American Meteorological. Mon. Wea. Rev. 177, 536– 549. Norman, J.M., Kustas, W.P., Humes, K.S., 1995. A two-source approach for estimating soil and vegetation energy fluxes from observations of directional radiometric surface temperature. Agric. For. Meteorol. 77, 263–293. Oliver, H.R., Sene, K.J., 1992. Energy and water balances of developing vines. Agric. For. Meteorol. 61, 167–185. Ortega-Farias, S., Antonioletti, R., Olioso, A., 2000. Net radiation model evaluation at an hourly time step for mediterranean conditions. Agronomie 20 (1), 157–164 (INRA-Francia). Ortega-Farias, S., Olioso, A., Antonioletti, R., Brisson, N., 2004. Evaluation of the Penman–Monteith model for estimating soybean evapotranspiration. Irrig. Sci. 23, 1–9. Ortega-Farias, S., Carrasco, M., Olioso, A., Acevedo, C., Poblete, C., 2007. Latent heat flux over a Cabernet Sauvignon vineyard using the Shuttleworth and Wallace model. Irrig. Sci. 25, 161–170. ˜ iga, M., 2008. Evaluation of a two-layer model to Ortega-Farias, S., Poblete, C., Zun estimate vine transpiration and soil evaporation for vineyards. In: Proceeding of the World Environmental and Water Resources Congress. Honolulu, Hawai (ASCE-EWRI). Pieri, P., Gaudille`re, J.P., 2003. Sensitivity to training system parameters and soil surface albedo of radiation intercepted by vine rows. Vitis 42, 77–82. Rana, G., Katerji, N., 2008. Direct and indirect methods to simulate the actual evapotranspiration of an irrigated overhead table grape vineyard under Mediterranean conditions. Hydrol. Process. 22, 181–188. Schotanus, P., Nieuwstadt, F., de Bruin, H., 1983. Temperature measurement with a sonic anemometer and its application to heat and moisture fluxes. Boundary Layer Meteorol. 26, 81–93.

286

S. Ortega-Farias et al. / Agricultural and Forest Meteorology 150 (2010) 276–286

Sene, K.J., 1994. Parameterisations for energy transfers from a sparse vine crop. Agric. For. Meteorol. 71, 1–18. Spano, D., Snyder, R.L., Duce, P., Paw, U.K.T., 2000. Estimating sensible and latent heat flux densities from grapevine canopies using surface renewal. Agric. For. Meteorol. 104, 171–183. Shuttleworth, W.J., Wallace, J.S., 1985. Evaporation from sparse crops-an energy combination theory. Quart. J. R. Meteorol. Soc. 111, 839–855. Torula, T., Heikinheimo, M., 1998. Modelling evapotranspiration from a barley field over the growing season. Agric. For. Meteorol. 91, 237–250. Trambouze, W., Bertuzzi, P., Voltz, M., 1998. Comparison of methods for estimating actual evapotranspiration in a row-cropped vineyard. Agric. For. Meteorol. 91, 193–208. Vieira de Azevedo, P., Heriberto de Castro, A., Barbosa da Silva, B., Monteiro, J., Monteiro, F.A., 1997. Evaliac¸a˜o da reflecta˜ncia e do saldo de radiac¸a˜o sobre um cultivo de videira Europe´ia. Rev. Brasileira Agrometeorol. 5, 1–7. Webb, E.K., Pearman, G.I., Leuning, R., 1980. Correction of flux measurements for density effects due to heat and water vapour transfer. Quart. J. Meteorol. Soc. 106, 85–100.

Wilson, K., Goldstein, A., Falge, E., Aubinet, M., Baldocchi, D., Berbigier, P., Bernhofer, C., Ceulemans, R., Dolman, H., Field, C., Grelle, A., Ibrom, A., Law, B.E., Kowalski, A., Meyers, T., Moncrieff, J., Monson, R., Oechel, W., Tenhunen, J., Valentini, R., Verma, S., 2002. Energy balance closure at FLUXNET sites. Agric. For. Meteorol. 113, 223–243. Williams, L.E., Trout, T.J., 2005. Relationships among vine- and soil-based measures of water status in a Thompson seedless vineyard in response to high-frequency drip irrigation. Am. J. Enol. Viticult. 56, 357–366. Willmott, C.J., 1981. On the validation of models. Phys. Geogr. 2, 184–194. Yunusa, I.A.M., Walker, R.R., Lu, P., 2004. Evapotranspiration components from energy, sapflow and microlysimetry techniques for an irrigated vineyard in inland Australia. Agric. For. Meteorol. 127, 93–101. Zhang, B., Kang, S., Li, F., Zhang, L., 2008. Comparison of three evapotranspiration models to Bowen ratio-energy balance method for a vineyard in an arid desert region of northwest China. Agric. For. Meteorol. 148, 1629–1640. Zhou, M.C., Ishidaira, H., Hapuarachchi, H.P., Magome, J., Kiem, A.S., Takeuchi, K., 2006. Estimating potential evapotranspiration using Shuttleworth-Wallace model and NOAA-AVHRR NDVI data to feed a distributed hydrological model over the Mekong River basin. J. Hydrol. 327, 151–173.