Introduction

Advances in information technologies have facilitated the storage of large amounts of data in the last years (Tan et al., 2005). However, the methods to retrieve useful information from those sources have not evolved at the same rate. Possibly, the traditional tools and techniques for data analysis may not be appropriate or sufficient for processing the information influx (Sumathi and Sivanandam, 2006). An important amount of data is continually generated by satellites orbiting the Earth. These instruments acquire different types of territorial information, with large spatial/temporal cover from oceans, the atmosphere and land surface (Tan et al., 2005). Likewise, the information obtained from meteorological stations provides the real measure of the environmental conditions at a given site. Combining both information fluxes is a challenge posed by the use of modern technologies for data gathering and processing. Thus, it becomes a tool for transforming satellite data into useful information for monitoring environmental variables (Lillesand et al., 2014). Here, we develop and evaluate a model that uses data from remote sensors and weather stations to estimate real evapotranspiration (ETR) at pixel scale.

Evapotranspiration (ET) is the process that describes water transport from the different land surfaces (soil, vegetation, water bodies, etc.) to the atmosphere (Njoku and Njoku, 2014). This process is divided (Stancalie and Nertan, 2012) into a physical component (direct evaporation) and a biological component (transpiration occurring in the stomatal pores of plants). It has been estimated that more than 60% of precipitation returns to the atmosphere in the form of ET, being one of the most important fluxes in the hydrological cycle (Zeng et al., 2012). The energy used for ET, referred to in the literature as latent heat flux, is one of the main consumptions of solar energy by the land surface (Yao et al., 2013). This phenomenon is strongly associated with meteorological variables (temperature, humidity and wind speed), vegetative vigor of plants and soil available moisture (Allen, 2006; Atchley and Maxwell, 2011). The latter variable is a limiting factor, even when the remaining variables favor the ET process (Mauser and Schadlich, 1998).

There are two approaches (Allen, 2006) to deal with the ET concept: ET of the reference crop (ET0) and real ET of the crop (ETr). ET0 indicates the amount of water used by a crop (reference crop) under determined conditions. UN Food and Agriculture Organization (FAO) experts defined the hypothetical reference crop as an area cultivated with alfalfa (Medicago sativa L.) and raygrass (Lolium multiflorum Lam.) of 12cm in height, without water deficit and growing under no nutrition or health limiting conditions (Allen, 2006). Since this is a hypothetical crop, this variable is mostly related to climate, because it expresses the evaporating power of the atmosphere (Allen et al., 2003). However, ET0 is a theoretical concept that assumes water availability and plant growth states that do not often occur in the real situation. Real evapotranspiration (ETr), sometimes named crop evapotranspiration (ETc), involves evaporation from the soil and transpiration that really occurs in a given period under conditions different from those of the reference crop (Allen et al., 2007). The relationship between ET0 and ETr is expressed by a dimensionless coefficient known as kc, which incorporates phenological and management factors (Allen et al., 2015).

Since direct measurement of ET is not easy and requires costly equipment, different methods have been developed to estimate the amount of water that is lost through ET. These methods can be classified as empirical (Thornthwaite, 1948; Blaney et al., 1952) or physics-based (e.g. Penman, 1948; Monteith, 1981 and FAO Penman Montheith, in Allen (2006)). The FAO Penman Montheith method is considered the standard model for estimating ET in agriculture (Zeleke and Wade, 2012). This model is useful to estimate ET0 as it requires only weather data for the calculations (Allen, 2006). Then, to obtain an actual measure of the water consumed by ET, it is necessary to incorporate some measurements of the current vegetation state into the model. A feasible alternative for solving this problem is to use satellital information to complement the models based on meteorological data (Bastiaanssen et al., 1998a). Here, we present and evaluate a model using the FAO Penman Monteith equation to calculate ET0, then it calculates the ET fraction (similar to kc) using an energy balance model. This model is based on the surface energy balance algorithm for land (SEBAL) and incorporates a method for automatically selecting pixels by thresholds. Moreover, an equation recommended by the International Committee on Weights and Measures (CIPM) to calculate air density is incorporated.

Materials and Methods

Study area

The application of the surface energy balance model was carried out in two test sites (Figure 1). The first one in the south of the province of Buenos Aires (Lobería, 38°11'1.47"S, 58°52'22.89"W) and the second one in the Paraná Department, Entre Ríos Province (31°51'14.26"S, 60°28'18.87"W); both in Argentina. For the Lobería area (application 1), meteorological data (Table I) were used from Agricultural School No. 1, located 7.8km from the studied site (38°7'0.44"S, 58°51'8.37"W). For Paraná area (application 2), meteorological data were used from the Paraná Station, National Institute of Agricultural Technology (EEA-INTA), located 6.1km from the center of the analyzed image (31°49'51.56"S, 60°31'8.40"W).

Meteorological and satellite data

Landsat 5TM images were downloaded from the GLOVIS server provided by the USGS-NASA (USGS 2016). For Lobería, a subset of the image was generated (date 29/01/2009; 225/086 path/row), its area was 2.34km² (1.54×1.52km). For Paraná site, image (date 23/01/2011; 227/082 path/row) an area of 13.6km2 (4.7×2.9km) was used. These sites were chosen within a coverage area of the meteorological station demarcated by a buffer of 10km radius.

The model requires, as inputs, daily means of temperature (ºC), wind speed (m·s^-1), relative humidity (%), also maximum and minimum values of those variables and an estimate of the reference evapotranspiration (ET0) calculated with the FAO-Penman-Monteith method.

Model description

To compute parameters that compose the model we first present the energy balance equation (EBE), and then we develop the equations and procedures that structure the whole model.

Energy Balance Equation (EBE)

Net Radiation (Rn)

Net radiation is the term of highest magnitude within the EBE and represents the amount of energy available for physical and biological processes occurring on the land surface. Its calculation requires a balance between the outgoing (↑) and incoming (↓) energy fluxes for the shortwave (S= 0.25 to 3μm) and longwave (L= 3 to 100μm) radiation fractions (Stancalie and Nertan 2012). This balance can be made from satellite data using the following equation (Bastiaanssen et al., 1998a):

The energy corresponding to incoming shortwave radiation (RS↓) that reaches the earth’s surface is that which has still not been returned to the atmosphere through reflection. This reflected energy is known as surface albedo (α) and depends on the cover type (Chuvieco, 2010). To calculate α, the following equation was used (Robinove, 1981;Duguay and LeDrew, 1992):

where albedo at the top of the atmosphere (αtoa) is calculated from reflectivity (ρλ) of each band, except for the thermal band (Bastiaanssen et al., 1998a):

To do this, participation of mean solar exo-atmospheric irradiance of each band should be calculated (ESUNλ) using its weighting coefficient ϖλ:

The calculation of the reflectivity of each band requires converting the digital numbers (DN) to spectral radiance values (Lλ) using the satellite calibration constant (Chander and Markham, 2003). Then, reflectivity is calculated for each band, as follows:

where θ: solar incidence angle and dr: the earth-sun distance, calculated using the Julian Day (JD) (Duguay and LeDrew, 1992; Chuvieco, 2010).

Furthermore, αpath_radiance is a mean fraction of the incoming solar radiation that is back-scattered before it reaches the earth’s surface (Bastiaanssen, 2000). Atmospheric transmissivity (τsw) is a dimensionless value that indicates the incoming radiation fraction that actually reaches the earth’s surface. This phenomenon occurs due to absorption and diffusion of radiation by particles suspended in the atmosphere. In this model, this fraction is calculated as a function of the height of the site (z) (Allen, 2006):

The term RS↓ refers to the direct and diffuse solar radiation flux that actually reaches the earth’s surface, and is measured in W·m-²:

Gsc is the solar constant (1367W·m^-2) and the remaining components are the same factors used for the calculation of reflectances and albedo at the top of the atmosphere (Duffie et al., 2013).

The next term, necessary to solve the net radiation equation, is the outgoing longwave radiation (RL↑) emitted from the earth’s surface. To obtain this parameter it is necessary to compute the vegetation indices NDVI (normalized difference vegetation index) and SAVI (soil-adjusted vegetation index). Then, LAI (leaf foliar area index) is calculated based on SAVI (Bannari et al., 1995). Two emissivity values are computed: Thermal emissivity within the spectral range of band 6 (εNB) and Emissivity in the broad thermal spectrum (ε0). To calculate emissivity values, the following equations and logical operations are used (Allen et al., 2002):

The following step consists of computing radiation emitted by the earth in the thermal spectrum (Rc), correcting the values of radiance of band 6 (L6) (Wukelic et al., 1989):

To solve this equation, three parameters related to the state of the atmosphere are necessary: Thermal radiance emitted by the atmosphere in the direction of the satellite (Rp), air transmisivity (τNB) and thermal radiance emitted by the atmosphere in the direction of the earth (Rsky) (Barsi et al., 2003). Values for Rp and τNB require using a simulation model for atmospheric radiation transfer (e.g. MODTRAN; Berk et al., 1999). In extreme cases of lack of data for these terms, fixed values 0, 1 and 0 are assigned to parameters Rp, τNB and Rsky, respectively (Allen et al., 2002). This converts Rc into an uncorrected radiance of band 6. Not correcting L6 results in an underestimation of surface temperature Ts in 5º. However, in further steps of this model, a function must be generated to determine the difference between surface temperature and air temperature (Bastiaanssen et al., 1998b). For this reason, the error of L6 estimation has a low effect on the final value of ET calculated by the model (Allen et al., 2002).

Once Rc, is calculated, surface temperature (ºK) is obtained from the equation based on Planck’s law:

where K₁ (607.76mW·cm-²·sr^-1 ·µm^-1) and K₂ (1260.56mW·cm^-2 ·sr^-1·µm^-1) are constants for Landsat 5 band 6 (Markham and Barker, 1986). To complete this step, outgoing long wave radiance (RL↑) is calculated using Stefan-Boltzmann’s equation:

where σ is the Stefan-Boltzmann constant (5.67×10-8W·m^-2·K^-4).

To complete the calculation of the parameters necessary for solving Rn equation, incoming long wave radiance (RL↓) is calculated:

To solve this equation, the Tcold, referred to mean temperature of cold pixels is calculated. For this, a process for selecting ‘cold’ and ‘hot’ pixels is conducted, which is explained below in the calculation of sensible heat flux (H).

Soil heat flux (G)

Soil heat flux (G) refers to the energy stored in the soil and vegetation and is transferred through conduction. To obtain this parameter, the G/Rn relation is computed using the following equation (Bastiaanssen et al., 1998b):

where Ts: surface temperature (ºC) obtained from the image on band 6 of the sensor and, α: surface albedo. Then, knowing the values for Rn, G must be solved for.

Sensible heat flux (H)

H represents the energy fraction that heats the air through convection and conduction. This parameter is the most difficult to model and is usually the factor differentiating the diverse models available for remote sensors. In SEBAL, the driver of this energy flux is the temperature difference between the soil surface and the air (dT) (Bastiaanssen, 2000). Parameter dT is estimated from a linear function calculated with the information of the cold and hot pixels. These pixels correspond to contrasting energy balance situations within the image, where H and λ ET are assumed as known (Bastiaanssen et al., 1998a; Allen et al., 2002).

Here, we incorporate logical operators that impose conditions for automating the pixel selection process. The ‘cold’ pixels represent a wet soil surface, with irrigated crops and good plant cover. The selection condition is that surface temperature should be between the 10th and 20th percentiles of its distribution and NDVI should be between 0.7 and 0.8. ‘Hot’ pixels are representative of a dry surface with low plant cover, where ET is close to 0. It is assumed that surface temperature in cold pictures is similar to air temperature, whereas the maximum difference between them is given by hot pixels (Allen et al., 2002). The condition for selecting hot pixels is that surface temperature should be between the 80th and 90th percentiles and the NDVI between 0.2 and 0.3.

In ‘cold’ pixels, it is assumed that ET is 5% higher than ET0; therefore, sensible heat flux is defined as:

For ‘hot’ pixels, where there is scarce vegetation and humidity, it is assumed that there is no ET, hence:

Then, dT is computed for the selected pixels:

For this, it is necessary to obtain the aerodynamic resistance to heat transport (rah), air density (ρ) and Cp, the specific heat of the air (1004J·kg^-1·K^-1) The resistance rah is related to wind speed (ux) and to the friction of the air layer that interacts with the surface (Zom). In principle, its magnitude is calculated for conditions of neutral atmosphere stability. Then, the instability conditions are simulated via a process of iterations (Bastiaanssen et al., 1998a).

To obtain the parameter ρ, an equation recommended by the International Committee for Weights and Measures (CIPM) was introduced: CIPM 1981/91(Davis, 1992):

where p: atmospheric pressure (101325 Pascals), Ma: molar mass of dry air (0.0289635 kg·mol^-1), Z: dimensionless compressibility factor, R: molar constant of gases (8.31451 J·kmol^-1), T: air temperature in ºK, Xv : dimensionless molar fraction of vapor and, Mv: molar mass of water vapor (0.0180154 kg·mol^-1).

Once the difference in temperature for the selected pixels is computed, a linear regression plot is performed between dT and Ts. The coefficients of the trend line of this regression (slope and intercept) will be used to compute dT for all the pixels of the image as a function of their surface temperature:

When all the parameters are calculated for all the image pixels, the following equation is solved:

Latent heat flux (λET)

As already mentioned, λET (W·m^-2) is calculated as a residual of the energy balance. However, the previously computed energy fluxes (H, G and Rn) are instantaneous; hence, the estimations must be extrapolated to daily values. To solve this problem, the concept of evaporative fraction is used, which is the energy used for the evaporation process over the total of energy available for the process (Brutsaert and Sugita, 1992):

Then, assuming that evaporative fraction is constant along the day (ΛInst= Λ24hs ≈Kc), daily values of real ET (ETr) can be obtained using the following equation:

Model evaluation

Two proofs of the model were carried out to evaluate its results. When moving from Lobería (application 1) to Paraná (application 2), the number of types of ground cover and the number of pixels in the image were increased.

To evaluate the results produced by the model, the estimated Kcs were compared with the bibliographic ones for each type of coverage. To do this, the pixels of the selected images were classified. The sub-scene of the Lobería area, comprises a region with an irrigation pivot and a field bordering a stubble. The image of Lobería was classified by clusters based on the NDVI and the surface temperature derived from band 6 of the satellite. From this classification the pixels were grouped within the classes ‘Irrigation’ and ‘Stubble’ (Table II).

For the Paraná area (application 2), image pixels were classified into five land cover types that were generated through two classification stages. The first stage involved a supervised classification based on the visual analysis of the image, which originated three classes (crop, bare soil and natural vegetation; Chuvieco, 2010). The second stage included a classification by clusters using the k-means algorithm on NDVI values, surface temperature and the three classes generated during the first stage as classification variables. The aim of this second stage was to split vegetation types in six clusters. Clusters 5 and 6, were unified as ‘Bare soil” class. For vegetation types, a higher NDVI refers to higher vegetation vigor and a lower Ts means a better hydric condition. For this reason, the classes ‘Natural vegetation’ and ‘Crop’ were subdivided into ‘+’ for pixels of best vegetation condition and ‘-’ for those of worst conditions. Then, different Kc values for each class (theoretical Kc) were selected from the literature (Allen 2006) (Table III).

After verifying the normality and homoscedasticity assumptions, an ANOVA was performed to evaluate the presence of significant differences in the mean ETr values of the classes.

H0: μ Kc(Clase A) = μ Kc(Clase B) = μKc(Clase C)

H1: μ Kc(Clase A) ≠ μ Kc(Clase B) ≠ μKc(Clase C)

Then, the correspondence of theoretical Kc values with the Kc estimated by the model was tested. To do this, the probability of obtaining a Kc value equal to the theoretical one for a population that has the distribution parameters of the Kc of each class (mean and variance) was calculated with a t test.

H0: μ Kc(Clase A) = μ Kc(Teórico Clase A)

H1: μ Kc(Clase A) ≠ μ Kc(Teórico Clase A)

Finally, the model ability to detect changes in vegetation state and soil hydric condition was evaluated for Paraná area (application 2). For this purpose, a simple linear regression analysis was performed for the two satellite variables related to NDVI and surface temperature.

Results

For Lobería area (application 1), the ANOVA produced a p-value that remained outside the acceptance zone of the null hypothesis (Table IV); the same result was obtained in Paraná area (Table V).

For Lobería land coverage, the p-value associated with the one parameter t-test was lower than the significance level (α= 0.05) for the ‘Irrigation’ class and higher for the ‘Stubble’ class (Table VI). However, the mean value estimated in each class is within the 25th and 75th percentiles (Table VI,Figure 2).

For the Paraná region (application 2), p values associated with the statistic do not fall in the rejection region of the null hypothesis for any of the classes (Table VII, Figure 3).

Regression analysis between NDVI and the calculated ETr, shows a positive linear relationship between these variables (p<0.0001), although with a low adjustment level (R²= 0,37) (Table VIII, Figure 4).

Finally, regression analysis between surface temperature and the calculated ETr also showed a significant, although opposite, linear relationship between these variables, but with high adjustment (R²= 0,91) (Table IX, Figure 5).

Discussion

The ANOVA that evaluated the effect of classes on ETr yielded a lower value at a significant level of 0.05 for both areas studied. This suggests the rejection of the hypothesis of mean equality, indicating the existence of an effect of cover type on ETr estimated by the model. For both places, the theoretical Kc was always within the 25th and 75thpercentiles, which is close to the mean and the median for all the classes. The real ET values obtained by the model are closely related to those expected for the different cover types found in the image. As expected, estimated ET values are higher than those found on surfaces that present low vegetal coverage in both locations.

In the Paraná area, mean ET was higher in crop class than in natural vegetation, and in the latter it was higher than in bare soil. Within vegetation covers, pixels classified as ‘+’ due to their better vegetation condition (mean NDVI ≈0.75) and water status (lower surface temperature) showed significantly higher ETr values than those classified as ‘-’.

Kc values for each class found in the literature (theoretical Kc) did not differ statistically from those estimated by the model. However, a more exhaustive validation of the model can be made if the crops phenological conditions are known, with the aim of finding more accurate theoretical Kc.

Finally, the ETr was evaluated in relation to the NDVI and soil moisture (Surface temperature) to evaluate the capacity of the model to detect changes in the vegetation state and soil hydric conditions. A positive linear relationship has been found between ETr and vegetation vigor measured (through NDVI). Nevertheless, the low fit (r²= 0.37) indicates that ETr is not completely dependent on plant state, as the capacity of a plant to absorb water can be limited due to the soil moisture content. The inverse relationship with high fit (r²= 0.91) found between ETr and surface temperature, confirms this assumption.

The model presented aims to be a tool to integrate large environmental information that are permanently generated by satellite and meteorological measuring instruments. The generated script allowed us to combine procedures proposed by different authors into a single process in which the user only needs to enter crude data. The feasibility of applying models of this type to regional-scale studies is mainly limited by availability of meteorological stations. By contrast, at the site level, the limiting factor is the availability of intermediate and high resolution images with a visiting frequency that allows to describe phenological changes in crops and natural vegetation.

From the statistical analysis we conclude that the aims of the research have been satisfactorily met. The model was validated and will be useful to make estimations of evapotranspiration adjusted to site-specific variation.

Acknowledgements

This work was carried out at CICyTTP (Diamante, Entre Ríos), ICyTE- UNMDP (Mar del Plata, Argentina) and Regional Center of Geomatics (CEREGEO), with funds provided by Comisión Nacional de Investigaciones Científicas y Tecnológicas de la República Argentina (CONICET). The authors are especially grateful to Instituto Nacional de Tecnología Agropecuaria (INTA) and United States Geologycal Survey (USGS) for their free distribution policy of weather and satellite data, respectively.

ENERGY BALANCE MODEL AS REAL EVAPOTRANSPIRATION ESTIMATOR WITH SATELLITE AND METEOROLOGICAL DATA

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Author notes

acenolaza@gmail.com