Estimation of Crop Evapotranspiration Using Satellite Remote Sensing-Based Vegetation Index

Irrigation water is limited and scarce in many areas of the world, including Comarca Lagunera, Mexico. Thus better estimations of irrigation water requirements are essential to conserve water. The general objective was to estimate crop water demands or crop evapotranspiration (ETc) at different scales using satellite remote sensing-based vegetation index. The study was carried out in northern Mexico (Comarca Lagunera) during four growing seasons. Six, eleven, three, and seven clear Landsat images were acquired for 2013, 2014, 2015, and 2016, respectively, for the analysis. The results showed that ETc was low at initial and early development stages, while ETc was high during mid-season and harvest stages. These results are not new but give us confidence in the rest of our ETc results. Daily ETc maps helped to explain the variability of crop water use during the growing season. Based on the results we can conclude that ETc maps developed from remotely sensed multispectral vegetation indices are a useful tool for quantifying crop water consumption at regional and field scales. Using ETc maps at the field scale, farmers can supply appropriate amounts of irrigation water corresponding to each growth stage, leading to water conservation.


Introduction
Irrigation water is limited and scarce in many areas of the world. Agriculture is the major consumer of fresh water [1,2], but it is not necessarily used efficiently due to farmers supplying more water than is consumed by the crop. Thus, better estimation of irrigation water requirements is essential to use water efficiently so water is available for use in the future. To achieve water conservation, it is necessary that farmers adopt new technologies for estimating crop water demands more accurately.
Crop evapotranspiration (ET c ) represents crop water requirement and is affected by weather and actual crop conditions [3,4]. A useful method to estimate ET c or crop water requirements is to multiply reference evapotranspiration (ET r ) by a crop coefficient ( c ) (see (1)). ET r is estimated based on meteorological information (e.g., solar radiation, air temperature, wind, and air vapor pressure deficit) from a local weather station. The Penman-Monteith equation has been advanced as the standard method for estimating reference ET [5,6]. c is typically taken from literature values and is affected by crop variety and growth stage [5][6][7]. ET c has been estimated or measured using other methods, for example, weighing lysimeters, evaporation pan, soil water balance, atmometer, Bowen Ratio Energy Balance System (BREBS), and Eddy Covariance (EC). However, these methods are recognized as the point-based measurements. Satellite-based remote sensing is an alternative to estimate crop water requirement and its spatial and temporal distribution on a field-by-field basis at a regional scale. These remote sensingbased methods have been shown to be accurate [8][9][10][11]:  Remote sensing is a technology that can estimate ET c at regional and local scale in less time and with less cost [9,10]. Remote sensing can also estimate crop coefficients based on spectral reflectance of vegetation indices (VIs) [5,12]. The normalized difference vegetation index (NDVI) is the most common VIs [13]. NDVI takes into account the reflectance of red and near-infrared wavebands [14], where red waveband is strongly absorbed by chlorophyll in leaves of the top layers, while near-infrared wavebands is reflected by the mesophyll structure in leaves, penetrating into deeper leaf layers in a healthy vegetation [15,16]. High values of NDVI are related to healthy and dense vegetation, which presents high reflectance values in the NIR waveband and low reflectance values in the red waveband [17]. Crop coefficients generated from VIs determine ET c better than a tabulated c because it represents the actual crop growth conditions and capture the spatial variability among different fields [2,18,19].
The objectives of this study were to (1) calculate NDVI values for each corn field for each growing season, (2) develop a simple linear regression model between NDVI derived from satellite-based remote sensing and tabulated c obtained of alfalfa-based crop coefficient from ASCE Manual 70, (3) generate c maps using the linear regression equation obtained between NDVI and c values, and (4) create ET c maps with high spatial resolution at regional and field scales.

Study Area.
The study was carried out in northern Mexico (Comarca Lagunera) during four growing seasons. Comarca Lagunera had an average latitude of 25 ∘ 40 N and longitude of 103 ∘ 18 W and elevation of 1115 m above mean sea level ( Figure 1). In Comarca Lagunera, forage crops (alfalfa, corn, sorghum, and oat (planted in the winter season)) occupied more than 75% of the total irrigated area [35]. Silage corn is the most important crop after alfalfa in this region. Five silage corn fields in each growing season were selected for NDVI calculations. The corn fields were irrigated using surface irrigation systems. The plant population density was 78,000 plants ha −1 . Silage corn is typically planted from late March to early April and chopped for silage from late July to early August, depending on the crop variety. The corn fields selected ranged between 10 and 20 hectares in size. The soil texture for this region is clay loam soil. The mean annual maximum temperature is 28 ∘ C, minimum 13 ∘ C, and mean 21 ∘ C [36]. The mean annual precipitation is 200 mm, while the annual potential evapotranspiration is 2,000 mm [37]. EROS performed the atmospheric corrections on the images. Also the wedge-shaped gaps appearing within the Landsat 7 images as a result of the SLC-off issue were removed using the Imagine built-in focal analysis tool [11]. Six, eleven, three, and seven clear Landsat images were acquired for 2013, 2014, 2015, and 2016, respectively ( Table 1). The satellite images were processed using the Model Maker tool of ERDAS Imagine Software.

Pixel Selection.
Ten pixels for each corn field and each season were selected and extracted from NDVI maps. The pixels were located in the center of each corn field for each overpass date during the four growing seasons. The same pixels were observed throughout the corn growing season. We assumed that the pixels are representative of the entire corn field. All corn fields had flat terrain. The number of pixels per year is presented in Table 2.

NDVI Calculations.
The NDVI is the difference between near-infrared (NIR) and red waveband reflectances divided by their sum [13]. NDVI values range between −1 and +1, where water presents negative values and dense canopy presents high positive values [17,38,39]. The NDVI was calculated for each overpass date and for each growing season using Model Maker tool of ERDAS Imagine Software as shown in the next equations: For Landsat 7, NDVI was calculated as follows:  For Landsat 8, NDVI was calculated as follows: where NIR band and Red band are the near-infrared and red wavebands, respectively. Reyes-González et al. [40] made some comparisons of NDVI derived from satellite remote sensing and derived from GreenSeeker in the Comarca Lagunera, Mexico. The results showed that the NDVI values derived from satellite were within 95% of the in situ values (data not shown).

Crop Coefficient ( ) Values from Manual 70.
The c values were taken from ASCE Manual 70 (Appendix E) [7] and were adjusted according to different corn growth stages throughout the growing season. For c estimations the ASCE Manual 70 divides the growing season into two periods, namely, percent of time from planting to effective cover and days after effective cover to harvest. The effective cover and harvest of corn in our study occurred around 55 and 105 DAP, respectively, based on the crop phenology.

Relationship between NDVI and and Maps
Development. The relationships between NDVI derived from Landsat images and tabulated c 's values obtained from ASCE Manual 70 (Appendix E) [7], corresponding to each satellite overpass date for 2013, 2014, 2015, and 2016 corn growing seasons, were established. These relationships were used to generate a single linear regression equation for entire period of study.

Reference Evapotranspiration (
) Calculations. The meteorological information was taken from an automated weather station. The weather station was located at the National Institute of Forestry, Agriculture, and Livestock Research (INIFAP), Matamoros, Coahuila, Mexico (Figure 1).
The ET r values were taken from the weather station, where ET r was calculated using the Penman-Monteith equation [5,41].

Crop Evapotranspiration
The c values from the c maps were multiplied by ET r (see (1)) to create ET c maps with high spectral resolution (30 m) for 2014 growing season, using Model Maker tool of ERDAS Imagine Software and ArcGIS version 10.3.1. The ET c maps are generated to monitor the spatial distribution and temporal evolution of the crop water requirements during the growing season.

Flowchart of ET c Estimation.
A summary of ET c estimation using satellite remote sensing-based vegetation index is shown in Figure 2. The Landsat images and weather data are the two major inputs parameters in the vegetation index method.

Results and Discussion
3.1. NDVI Curves. The NDVI average values (10 pixels) selected and extracted from NDVI maps for five corn fields and for different corn growing seasons are shown in Figure 3. The figures show similar NDVI curves for 2014 and 2016, while, for 2013 and 2015, the curves are incomplete due to lack of clear sky images during the growing seasons. In general, NDVI values at initial stage were low around 0.15 in early April (DAP ∼ 8). Then the NDVI values increase as the crop develops reaching its maximum value (0.8) at mid-season stage followed by plateau from late May to middle July (DAP 55-95). At the end of the season the NDVI values are slightly decreasing (∼0.7) by the end of July (DAP 105). Several researchers reported similar seasonal NDVI curves for corn (e.g., [17,20,24,30,[42][43][44][45][46][47]). All NDVI curves developed by these researchers showed low values at early stages, then increasing at mid-season stages and then slightly declining at late stages. However, Thomason et al. [44] reported that NDVI curves of forage corn gradually increased from initial to mid-season and then remained constant until the end of the season.
In this study, the NDVI values derived from Landsat 8 (L8) were greater than NDVI values derived from Landsat 7 (L7) in mid-season (Figure 3 (2014 and 2016)) and early stages (Figure 3 (2013)). The differences between L8 and L7 ranged from 0.03 to 0.09 (data not shown). Those differences are in agreement with values reported by Flood [48] (0.04) and Ke et al. [49] (0.06), but greater than reported by Roy et al. [50] (0.02). The difference between L8 and L7 was because L8 has a narrower near-infrared waveband (L7 = 0.77-0.90 m, L8 = 0.85-0.88 m), higher signal to noise ratio, and higher 12-bit radiometric resolution [48,49,51,52]. These features provide more precise measurements that are less influenced by atmospheric conditions and more sensitive to surface reflectance [48,49,52]. Although the comparison of NDVI between L8 and L7 was not an objective of this study, it is important to mention that inconsistent or unreliable values of NDVI can produce poor estimates of crop evapotranspiration [49].

Relationship between NDVI and .
The NDVI values were taken from NDVI maps generated as an output using The linear regression equations for the four years were compared using the -test method to test statistical difference between two independent regressions [56]. Table 3 shows the results of all comparisons, where all values were less than tabulated values, which means that there were no statistical differences between linear regression equations. Based on these results all data from the four years were pooled and a single linear equation was generated ( Figure 5). This linear equation was used to create c maps for 2014 growing season ( Figure 6).

3.3.
Maps and Curve. Previous empirical linear equation between NDVI and c was used to generate c maps using Landsat images processed in ERDAS Imagine Software    [53], and Reyes-González et al. [54], who reported maps of daily spatial distribution of c for six, four, seven, and four overpass dates, respectively.  The c values obtained from c maps based on the average of ten selected pixels within each of five corn fields for each overpass date throughout the 2014 growing season is shown in Figure 7. In general, the minimum c value (0.24) was presented in early season, while the maximum c value (1.00) was presented in the mid-season stage. The standard deviation (vertical bars) values of c were lower than 0.07 throughout the growing season (Figure 7), this means that planting dates, management practice, and maturity dates among corn fields did not affect too much the c values during the season.
The relationship between c calculated from c maps and c from tables is shown in Figure 8. A strong relationship was found with 2 = 0.96. This means that c values derived from vegetation index ( c calculated) can be a robust parameter to calculate actual crop evapotranspiration. The main difference between c calculated and c tabulated is that the c tabulated comes from well-water reference crop (e.g., alfalfa), whereas c calculated comes from the actual crop growth conditions, where some c values derived from reflectance of vegetation were reduced by soil water content. Similar results were reported by Singh and Irmak [45] and Kamble et al. [30]. They found that limited moisture content decreased c values. Those low c values occurred around 15 days previous to start the mid-season stage. In our study the little difference between c calculated and c tabulated was

ET c Maps and ET c Values.
ET c maps of 30 m resolution were generated as an output of c maps multiplied by ET r values for corresponding day using ERDAS Imagine Software (Model Maker) for 2014 growing season (Figure 9). The ET c maps showed low ET c values (2.0 mm day −1 ) (light green color) at initial stage and high ET c values (8.0 mm day −1 ) (red color) at mid-season stage. These two seasons were characterized because in the initial stage crop needs smaller water requirements, whereas in the mid-season crop needs higher water requirements, as we can see in the next section. The ET c maps created in this study are in agreement with other researchers; for example, in [2,4,58,59], they generated ET c maps using c derived from remote sensing-based vegetation  indices. Other researchers reported that c derived from canopy reflectance based vegetation index had the potential to estimate crop evapotranspiration at regional and field scales, for example, in [17,18,29,55,60,61].

ET c Maps at a Field Scale.
ET c maps at filed scale help to explain the variability of crop water requirements during the growing season as shown in Figure 10. These images at a field scale level show the corresponding ET c values according to each growth stage; this indicates that each stage requires different amount of water throughout the season. For example, minimum water requirements (2.0 mm day −1 ) are needed at the initial stage, whereas maximum water requirements are needed at mid-season stage (8.0 mm day −1 ). Understating different crop growth stages and applying the accurate amount of volumetric water, farmers can improve their irrigation scheduling, improve water management, and enhance irrigation water sustainability. Similar ET c maps at a field scale for agricultural crops including corn were reported by Farg et al. [32], Zipper and Loheide [62], and Senay et al. [63], they reported minimum and maximum ET c values at different crop growth stages, where the higher evapotranspiration rates were found at the mid-season growth stage and lowest evapotranspiration rates were found at early growth stage.

Comparison between ET r and ET c .
The ET r values were taken directly from a local weather station, while ET c values were derived from ET c maps. Figure 11 shows the comparison between ET r and ET c for 214 growing season. This figure illustrated that the daily ET r values were higher than the daily ET c outputs at the beginning of the growing season, but similar values were recorded at mid-season stage. In early stage (DAP 1-20) the ET r values were around 6.0 mm day −1 , while the ET c values were around 2.0 mm day −1 . In development stage (DAP 20-55) the ET r values continue around 6 mm day −1 , while ET c values increase from 2 to 6 mm day −1 . In the midseason stage (DAP 55-95) both ET r and ET c values were very similar around 7.0 mm day −1 . At the end of the growing season (DAP 95-105) the ET r values were slightly greater than ET c values by 0.5 mm day −1 . From early to mid-development stage the ET c values were lower than ET r values, this means that in those particular stages farmers can save irrigation water (grey wide column in the graph), because in those stages the crop needs small water requirements, due to the fact that the crop canopy is no yet fully developed. In short, the ET c values from ET c maps could be used by farmers in their irrigation scheduling programs because it shows when and how much water is required by the crop during different growth stages.
Reyes-González et al. [54] reported that the farmers should use ET c instead of ET r for irrigation scheduling in arid and semiarid region where irrigation water is scarce. USDA-NASS [64] reported that the farmers in the United States use four primary methods to determine when to irrigate: the first was visual observation of crop condition method (41%), the second was the soil feel method (21%), the third was personal calendar schedule method (11%), and the fourth was daily crop evapotranspiration method (4%). Methods for deciding when to irrigate need to be more accurate because of the competition for irrigation water increases and its value increases. Farmers must use scientific irrigation scheduling methods (e.g., ET method) instead of empirical methods (e.g., crop condition, feel of soil, and personal calendar) to save water and protect the environment. The ET method is based on climatic demands and is more accurate than empirical methods for irrigation scheduling [65]. ET maps and atmometers are methods to estimate crop water requirements with high accuracy [11].

Conclusions
The general objective of this study was to estimate crop evapotranspiration using satellite remote sensing-based vegetation index in northern Mexico.
The relationships between NDVI derived from Landsat images and tabulated c obtained from ASCE Manual 70 (Appendix E) were established for four growing seasons. These empirical linear regression equations were used to generate a single linear regression equation.
ET c maps were created as an output of c maps multiplied by ET r values. The ET c values ranged from 1.40 to 7.41 mm day −1 during the period of study. The results showed that ET c values were low at initial and early development stages, while ET c values were high during mid-season and harvest stages. Daily ET c maps helped to explain the variability of crop water use throughout the growing season.
Farmers in northern Mexico region use empirical methods in their irrigation scheduling methods. The results indicate that farmers could reduce their seasonal water application amounts by 18% just by using ET c appropriately in their irrigation scheduling methods.
The information generated in this study is essential for irrigation scheduling because it shows when and how much water is required by the crop during different crop growth stages.
According to our results we can conclude that ET c maps developed from remotely sensed multispectral vegetation indices are a useful tool for quantifying accurate crop water consumption or crop evapotranspiration at regional and field scales.

Conflicts of Interest
The authors declare that they have no conflicts of interest.