Location and characteristics of the study site

We conducted the study during the production cycle from April to September 2014, in a vineyard cv Shiraz of seven years old, owned by the Vinícola San Lorenzo, Parras de la Fuente, Coahuila, Mexico. This location is 25° 30’ N, 102° 11’ W, and 1505 m altitude and with a dry and semiarid climate with average temperature of 14 to 18 °C. The average annual rainfall is 366 mm, with dominant easterly winds (^{INIFAP, 2015}) during the months in which the study was performed.

In the vineyard, we delimited two sections of 5.2 ha each, (204 m in the E-W direction, and 256 m in direction N-S). Plant lines were aligned in the N-S direction, 1.5 m spacing between plants and 2.5 m between rows, with a density of 2620 plants/ha. Water is applied for 2 h d^-1 with a drip irrigation system, for the emitter rate of 2.1 L h^-1, and wet width (0.40 m) was a water depth of 7 mm. The crop received the agronomic management (pruning, fertilization and phytosanitary control) in accordance with the standards established by the Vinícola San Lorenzo.

Instrumentation and measurements

The eddy covariance method was used to determine the current daily ET rate (ETa) (April to September) of each section of the vineyard. For this, we estimated the latent heat (LE) and sensitive (H) flux with the following equations (^{Ham and Heilman, 2003}):

(1)

(2)

where L is the heat of water vaporization, w is the vertical wind speed, ρ_wv is the density of water vapor in the air, ρ _a, C_p and Ta are the density, heat capacity and air temperature, respectively; and Ts is the sonic temperature. The prime symbol on the variables mean deviations from the mean, and the horizontal bar over two variables denotes the covariance between the variables for a particular time segment (30 min).

We measured the vertical wind speed and sonic temperature with a three-dimensional sonic anemometer (CSI-CSAT3, Campbell Scientific, Inc., Logan, Utah, USA); to obtain ρ_wv we used an open path infrared carbon dioxide analyzer (Open Path CO₂/H₂O analyzer, LI-7500. LI-COR, Lincoln, Nebraska, USA). Air temperature (Ta) was measured with a temperature and relative humidity sensor (HP45C, Vaisala, Inc., Woburn, MA, USA). We mounted the sensors on a pole at 3 m above ground surface (1 m above the plant canopy) in the west end and midpoint of the plant rows of each section.

The three-dimensional sonic anemometer was oriented towards the east, so that the wind had a minimum of 200 m contact with the plants surface in the direction E-W and 125 m in the direction N-S, before contact with the sensors. The measurement frequency of the sensors was 10 Hz, the flows were obtained as averages of 30 min, and the data stored in memory module cards of a CR1000 datalogger (Campbell, Cientific, Inc., Logan, Utah, USA.).

To assess the accuracy of measurements of the H and LE flows, we determined the energy balance over the plant surface (^{Zermeño-González et al., 2010}; ^{Shapland et al., 2012}) with the following relationship:

(3)

where Rn is net radiation, H is the sensible heat flux, LE is the latent heat flux, and G is the heat flux at soil surface; units of all variables were expressed in W m^-2. The Rn was measured with a net radiometer (LITE, Keep and Zonen, Inc., Delft, Netherlands) placed 1 m above the canopy of the vineyard of each section. We obtained the heat flow in the soil surface (G), weighted average in each section by measuring G with a heat transducer (HFT3 model, Campbell Scientific, Inc., Logan, Utah, USA) at 0.08 m below the soil surface at the midpoint of one of the rows, at the center of two plants beneath the canopy, and another one over the center of a corridor (bare ground). The change in energy accumulated in the soil layer (over the transducer), due to changes of temperature at 0.02 and 0.06 m below the surface, obtained with a thermocouple (chromel-constantan) of 4 rods, was added to the heat flux measured a 0.08 m (^{Kustas et al., 2000}; ^{Payero et al., 2005}; ^{Balbontín-Nesvara et al., 2011}). The sensible (H) and latent (LE) heat flux were corrected by the effect of density difference between the masses of rising and falling air (^{Webb et al., 1980}).

FAO Penman-Monteith method

The determination of the reference ET by the FAO Penman-Monteith procedure is based on the application of the original Penman Monteith equation (^{Novák, 2012}) to a large area of 0.12 m high turgid pasture without soil moisture deficit and under neutral atmosphere conditions (^{Allen et al., 2006}; ^{Almorox et al, 2012}).

To determine the daily reference latent heat flux (LE_PM) when meteorological measurements correspond to the average or integrated values of ET rate peak hours (8:00 to 20:00 h), the Penman Monteith equation is written as:

(4)

where S is the slope of the curve of vapor pressure at saturation vs temperature for a given temperature (kPa K^-1), Rn is net radiation (MJ m^-2 d^-1), G is the heat flux on the soil surface (MJ m^-2 d^-1), ρa is the air density (kg m^-3), Cp is the heat capacity of air (MJ kg^-1 K^-1), δe is the average vapor pressure deficit in the time considered (kPa), g is the psychrometric constant of the locality (kPa K^-1), ra is the average aerodynamic air resistance to the water vapor flow for the same time segment (s m^-1), and rs is the canopy resistance (s m^-1).

In determining the reference latent heat flux by the FAO Penman-Monteith method, the aerodynamic resistance (ra) for a large area of grass of 0.12 m high in a neutral atmosphere is determined by the relationship:

(5)

where u2 is the average wind speed (m s^-1) at 2 m above the surface. For the same grass, a value of 70 s m^-1 is assigned to the canopy resistance. The heat flux in the soil surface is estimated as 10% of the value of net radiation (G=0.10*Rn). The Rn is estimated for a vegetated surface of full coverage of an albedo (reflectivity index of solar radiation) of 0.23, based on the total incident solar radiation and making a balance of short and long wave radiation over the grass canopy (^{Allen et al., 2006}).

Wind speed was measured with a three-dimensional sonic anemometer (3-D sonic anemometer, Campbell Sci., Logan, Utah, USA), the total incident solar radiation with a Sylicon Pyranometer (LI-200X, Lincoln, Nebraska, USA). The deficit vapor pressure (δe) was obtained from the temperature and relative humidity that were measured with a temperature and humidity probe (HC2S3) (temperature and relative humidity probe, Campbell, Sci., Logan, Utah). Measurements were performed at a frequency of 1 s, and averages were obtained every 30 min.

The daily reference ET rate (ETr) was obtained by dividing the daily latent heat reference flux (LE_PM) by the heat of water vaporization (L). Measurement of ETr by the FAO Penman-Monteith method is for a grass that covers the entire surface; therefore, for crops grown in rows and that do not cover the entire soil surface a cover relationship factor should be considered. To estimate the ETa rate from ETr, monthly adjustment coefficients for crop development (Kc) were obtained according to the following relationship:

(6)

So, the value of the monthly Kc (which varies with the phenological development of the crop) was obtained by dividing the total monthly ETa corresponding to one of the sections of the vineyard (measured with the method of the eddy covariance) by the total ETr of the same month, measured with the FAO Penman Monteith method. Here we expect to have a better estimate of ETa, as the FAO 56 manual only describes the value of two Kc coefficients, one for the maximum value and the other for the final value.

Statistical evaluation

We performed the validation of the FAO Penman Monteith method by comparing the current ET data measured daily (with the eddy covariance method), with that estimated with the FAO Penman-Monteith method. For this we applied the non-parametric Wilcoxon test for paired populations (Wilcoxon, p≤0.05).

Energy balance on the vineyard canopy

The energy balance over the plant surface shows that the sum of the flows for turbulence (H+LE) were on average 15% lower than the available energy (Rn-G) (Figure 1). This small imbalance is within the acceptable margin of difference of the energy balance when H and LE are measured with the eddy covariance method (^{Twine et al., 2000}; ^{Ham and Heilman, 2003}; ^{Foken, 2008}). In similar studies by ^{Tonti et al. (2013}) in a soybean crop (Glycine max), the sum of H+LE was on average 22 % less than the Rn-G energy available, whereas for a vine planting ^{Balbontín-Nesvara et al., 2011}) reported a 19 % difference in the same context.

Figure 1 Relationship between the sum of the surface flows (H + LE) and the available energy (Rn-G) (30 min average values) over the canopy of a vineyard (cv Shiraz). 

Relationship between ET measured in the vineyard and the reference using the FAO Penman-Monteith method

The ETa rate measured with the method of eddy covariance presented the same pattern of variation than the ETr rate obtained with the FAO Penman-Monteith method (Figure 2). Note that over the months of the crop production cycle, the ETr rate was greater than ETa, but with the same pattern of variation (for being affected by the same weather conditions). On average, in the months mentioned, the ETr was 4.73 mm d^-1, whereas the current ET was 1.48 mm d^-1, so the difference was 31.3 %. This difference was because the ETr considered a full coverage vegetated surface (grass 0.12 m tall), whereas the vineyard with 2.5 m between rows and 0.80 m wide of the plant canopy only covered 32 % of the total area. By adjusting the ETr by the coverage factor (0.32), the daily rate of ETa was very similar to the ETr and the average difference was only 1.93%. (Figure 3).

Figure 2 Daily evapotranspiration rate measured by the method of eddy covariance (ETa) and reference (ETr) with the FAO Penman Monteith method in a vine crop (cv Shiraz). 

Figure 3 Daily evapotranspiration rate measured by the method of eddy covariance (Eta) and that obtained with the FAO Penman Monteith method modified by the ratio of coverage factor (ETraj). 

Relationship between the measured current ET rate and current estimated

The daily rate of ETa was obtained by multiplying the ETr rate corrected by the coverage ratio for the monthly adjustment coefficients of crop development (Kc) obtained in this study. Table 1 shows that the value of Kc increases from April to June, remains slightly greater than 1 in July and August and decreases in September. This variation coincides with the plant development of the crop and the subsequent process of senescence of the plants. Similar variation patterns of Kc were observed in different annual crops (^{Li et al, 2008}; ^{Villagra et al, 2014}; ^{de Guimaraes et al., 2015}).

Table 1: Monthly evapotranspiration rate measured by the method of eddy covariance (Eta), and the reference measured by the FAO Panman Monteith method modified by the coverage factor (ETr) and determination of the monthly adjustment coefficients for crop development (Kc) 

The daily ETa rate measured by the method of eddy covariance and ETa estimated from the reference ET (FAO Penman-Monteith method) was very similar throughout the months of the vineyard production cycle (Figure 4). Wilcoxon test for paired populations indicated that these populations are statistically equal (p≤0.01). This result allows us to reconfirm the implementation of the FAO Penman Monteith method to estimate the ETa rate of the vineyard from the ETr. The meteorological information required by the FAO Penman-Monteith method can be obtained from the nearest weather stations to the cultivation area; thus its application is free compared to methods that require sensors for in situ measurements (such as the eddy covariance method) to determine the daily rate of ET. Other studies in different crops also recommend the application of this method to determine the current rate of ET in different regions. ^{Trezza et al. (2008}) measured the ETa of a sugar cane crop from reference ET for a better irrigation program, which resulted in higher crop yield. ^{Er-Raki et al. (2009}) report a better determination of the ETa of an orchard of orange trees (Citrus sinensis) using the FAO Penman-Monteith method when the Kc values were obtained from measurements of crop ET with the eddy covariance method. According to ^{Lage et al. (2003}), the ET measured (with the method of lysimeter) in rice was very similar to the ET of the same crop obtained with the FAO Penman Monteith method; besides, they point out to a slight underestimation of the method due to the entry of advective energy from adjacent areas.

Figure 4 Current daily rate of evapotranspiration (ETa) measured with the eddy covariance method and estimated from the reference evapotranspiration (FAO Penman Monteith method) during the months of production (April to September 2014) in a vineyard (cv Shiraz) in the Vinícola San Lorenzo, Parras, Coahuila.