Introduction

The procedure described in the FAO-56 Manual is the most widely used to calculate crop evapotranspiration (ET_c), which is the product of a crop coefficient (K_c) by reference evapotranspiration (ET₀) (^{Allen et al., 2006}). ^{Wright (1982)} proposed the dual method, where K_c is the product of the crop basal coefficient (K_cb) and the coefficient associated with soil evaporation (K_e). The K_cb component represents crop evaporation conditions under conditions where the soil surface is dry (direct evaporation from soil surface is minimal), and crop growth is not limited by water stress, phytosanitary, climatological or physiological factors (^{Rocha et al., 2011}). Currently, K_cb is widely used to estimate actual evapotranspiration, which represents the potential baseline K_c value (^{Allen et al., 2006}). The main reference on this subject is the FAO-56 Manual compendium; however, it has certain limitations, because it only provides K_cb values at three main stages for each crop and under standard conditions, which are non-existent in true applications (^{Mhawej et al., 2021}).

The crop coefficient methodology is used to estimate ET_c and schedule irrigation (^{Escarabajal et al., 2015}). However, its application calls for the determination of K_cb for each crop and stage of development, which requires a variety of methods, many of which are time-consuming, destructive, and expensive in terms of time and money. For this reason, it has been decided to simplify their determination using variables such as leaf area index (^{Kirk et al., 2009}), plant cover fraction (^{López-Urrea et al., 2009}) or crop canopy reflectivity (^{Neale et al., 1989}), among others.

The empirical relationship between biophysical variables and K_cb with vegetation indices is increasingly used due to the wide availability of remote sensing information (^{Odi-Lara et al., 2013}). Currently, there are several equations or algorithms estimating K_cb for herbaceous crops (maize, wheat and grapevine, among others) using vegetation indices, such as the normalized difference vegetation index (NDVI) and the soil-adjusted vegetation index (SAVI), which are the most widely used because they are easy to calculate and derivable from a multispectral sensor (^{Candiago et al., 2015}). Remote sensing allows estimations of large areas since they provide reliable spatial and temporal information over the crop growth period (^{Chaudhary & Srivastava, 2021}).

Satellites have aroused great interest in the scientific community due to their multiple applications and high spatial, temporal, spectral and radiometric resolution (^{Borràs et al., 2017}). The most widely used are those that provide free and easily accessible information, such as the Sentinel-2 satellite. In addition, satellite imagery, combined with geographic information technologies, are used with the objective of optimizing agricultural productivity, by considering spatial variability, as it is associated with each production plot (^{Lizarazo-Salcedo & Alfonso-Carvajal, 2011}).

The Lagunera Region, where irrigation district (RD) 017 is located, is one of the main dairy basins at the national level, and livestock is fed mainly alfalfa, silage and concentrates. Maize silage is the most common, as it can account for 30 to 40% of the diet (on a dry basis) of production cows (^{González-Castañeda et al., 2005}). Maize silage is a crop with high productivity, low protein content and good energy value (^{Núñez-Hernández et al., 2003}). This has led to an increase in the areas planted with this crop, since it is also one of the forages that require less water (^{Arreola et al., 2016}). In the last four years, this has been the main crop in the region, with a current area of 54 000 ha (^{Reyes-González et al., 2022}), out of a total irrigated area of 167 000 ha.

The region has two sources of water for crop irrigation: surface water (river water) and groundwater (well water), but both sources are limited and have low availability. This situation forces producers to implement strategies to increase the efficient use of irrigation water, such as canal rehabilitation, pond construction, land leveling, and land irrigation technification, among others. However, all these efforts will not give the best results if they do not start from the principle of applying only the water requirements of the crops. Therefore, it is essential to make practical and operative estimates of K_cb throughout the growing season, to later calculate ET_c and schedule irrigation with an efficient use of water.

The use of spectral information from Sentinel-2 satellite imagery is an alternative to the FAO-56 method to calculate K_cb. Therefore, the objective of this study was to evaluate nine algorithms (six using NDVI and three using SAVI) to estimate the K_cb of forage maize during the whole vegetative cycle in two plots with different water sources and different irrigation management. The algorithms with the best accuracies were identified when compared with the K_cb derived from tables in the FAO-56 Manual (^{Allen et al., 2006}).

Materials and methods

The study was conducted during the spring-summer 2021 cycle in two forage maize plots located in the municipality of Francisco I. Madero, Coahuila, Mexico. Both plots are part of the irrigated area of Module XII of DR 017 Región Lagunera (Table 1; Figure 1). The climate is dry warm desert, with rainfall in summer and cool winter. Average annual rainfall is 258 mm and average annual evaporation is 2 000 mm, so the precipitation – evaporation ratio is 1:10. The average annual temperature is 21 °C, with a maximum of 33.7 °C and a minimum of 7.5 °C (^{García, 2004}).

Figure 1. Study area. 

In both plots, seven seeds per linear meter were sown, with a row spacing of 0.76 m; this resulted in a sowing density of about 92 thousand plants∙ha^-1. In Plot 1, five irrigations were applied: one pre-planting irrigation and four auxiliary irrigations. This property has surface (river) and groundwater (well) rights. The pre-sowing irrigation and the first auxiliary irrigation were applied with well water, and river water was used for the rest of the irrigation. In Plot 2, only surface water was used, and a pre-planting irrigation and two auxiliary irrigations were applied during the vegetative cycle.

Statistical analysis

To evaluate the precision of the estimated K_cb of forage maize compared to the K_cb of tables in the FAO-56 Manual, three statistical indicators were used: 1) coefficient of determination (R²), which reflects the goodness of fit of a model to the variable it seeks to explain (Equation 16); 2) mean squared error (MSE), which measures the variation of the values estimated compared to the observed ones (Equation 17), and 3) average relative error (ARE), which indicates in percentage of the approximation of the value estimated compared to the real value, the lower the value the better the approximation (Equation 18).

where y_iobt are the K_cb data from FAO-56 Manual tables, ( yiobt ) is the average of the K_cb data from FAO-56 Manual tables, y_iest is the K_cb data estimated with the algorithms using IV, ( yiest ) is the average of the K_cb data estimated with the algorithms proposed in this study (which use IV and Sentinel-2 satellite images), and n is the number of observations.

Results and discussion

Growth stages of forage maize, as determined by tables of the FAO-56 Manual, are shown in Table 3. For both plots, the vegetative cycle was 122 days. Harvesting was carried out when the crop reached 34 and 35 % dry matter in Plot 1 and Plot 2, respectively; that is, when the maize was in the R₃ and R₄ stages of development, and the grain was identified in a milky state in Plot 2 and in a pasty state in Plot 1. ^{Núñez-Hernández et al. (2005)} recommends harvesting at 28 to 35 % dry matter to promote good fermentation during the maize silage process. In addition, in this range, forage losses during harvesting are minimal.

A difference of 196.5 DDD at the final stage of crop growth (K_{cb fin}) was recorded between the two plots, with Plot 2 accumulating the largest amount of thermal energy. This depends on the sowing dates and geographic location of the plots, but also on irrigation management, which influences water availability and affects temperature, which decreases both water and thermal stress. Thus, forage maize is especially sensitive at the grain filling stage (^{Zhu & Burney, 2022}). ^{Núñez-Hernández et al. (2005)} reported a value of 1 470 DDD, accumulated in 103 days of vegetative cycle of a forage maize hybrid evaluated in the same study area.

LAI of Plot 1 was higher than that of Plot 2 from the development stage (K_{cb dev}) to the final stage of the crop (K_{cb fin}), which is due to the higher number of irrigations and better distribution of these in Plot 1, resulting in lower depletion of available soil moisture (ASM) (Figure 2) and, consequently, lower water stress. Higher water stress has an impact on lower foliage production per unit area and lower biomass accumulation due to lower photosynthetically active radiation interception, which eventually leads to lower yield (^{Song et al., 2019}). ^{Montemayor-Trejo et al. (2007}) reported maximum IAF values of 3.4 at 78 DAS of forage maize (development stage), in Comarca Lagunera, Mexico, when gravity irrigation was applied. However, in another study conducted in the same region, maximum values of IAF of 5 were reported in this same crop, values similar to those found in this study, but with drip irrigation (^{Montemayor-Trejo et al., 2012}).

Figure 2. Temporal distribution of available soil moisture (ASM) depletion of the two study plots. RP = pre-sowing irrigation; RA = relief irrigation 

Figure 2 shows the ASM of the soil profile determined by gravimetric moisture content sampling before and after irrigation, and average values of available moisture at a depth of 120 cm (15.4 % for Plot 1 and 13.5 % for Plot 2). Plot 2 showed the highest ASM (0 %) before applying the first relief irrigation (1.R.I.), which was applied 63 days after applying the pre-sowing irrigation (R.P.) and at 55 DAS. The programming of DR 017 is based on the requirements of the cotton crop, but it is not suitable for forage maize, which is reflected in low yields and low forage quality. In Plot 1 the highest ASM (34 %) was observed before 3.R.I., which was applied 29 days after 2.R.I. The rest of the irrigations, in both plots, were applied between 88 and 53 % of the ASM of the soil. The consumption of 50 % of available moisture is the optimum criterion for applying gravity irrigation to the study plots.

Table 4 shows the comparison of the K_cb estimated by the algorithms used in this study and the K_cb reported in the FAO-56 Manual during the initial, development, middle and final stages of the forage maize crop established in Plot 1. It is observed that the measure of central tendency showing lower values of error in the estimation of K_cb in all the algorithms used was the average at the melga level. Also, the Campos K_cbNDVI algorithm had the lowest MSE value, both at the initial stage (K_{cb ini}) and at the development stage (K_{cb dev}). With reference to the middle stage (K_{cb mid}), the Glez-Dugo K_cbSAVI algorithm had the lowest MSE value, and for the final stage (K_{cb fin}) it was the Glez-Piqueras K_cbNDVI algorithm. When considering the four growth stages of forage maize, the Allen FAO-56 K_cbNDVI and Argolo K_cbSAVI algorithms showed the lowest MSE values. However, the Campos K_cbNDVI algorithm presented, in each of the growth stages, values lower than 22 % of ARE, and in the whole vegetative cycle a ARE of 11.6 %, reaching an accuracy of 88.4 %. The above is satisfactory for estimating ET_c using vegetation indices, since, according to ^{Alfieri et al. (2017)}, an accuracy of 80 % is required.

Table 5 shows that the mode had lower MSE values in most of the algorithms used to calculate K_cb in Plot 2, except for the equations Campos K_cbNDVI, Argolo K_cbNDVI and Allen FAO-56 K_cbNDVI. In these expressions, the average had lower MSE value. The Argolo K_cbSAVI algorithm had lower MSE values in the K_{cb ini} and K_{cb dev} stages. For K_{cb mid} and K_{cb fin} stages, the lowest MSE value was with Choudhury K_cbNDVI. However, when considering the whole maize growing cycle, the Argolo K_cbSAVI algorithm had the lowest MSE value, but Argolo K_cbNDVI algorithm had values lower than 13 % of ARE at the four stages of maize growth, and 8.3 % of ARE in the whole growing cycle, resulting in an accuracy of 91.7 %.

The Campos K_cbNDVI algorithm had the lowest ARE values in the two plots studied, both by growth stage and in the whole vegetative cycle, except for K_{cb ini} and K_{cb dev} stages in Plot 2. Thus, this algorithm is reliable for estimating K_cb of forage maize with different surface irrigation management.

Figures 3 and 4 show the distribution of the calculated K_cb and the K_cb reported in the FAO-56 Manual of crop growth. In Plot 1 it is observed that in the K_{cb ini} and K_{cb dev} stages of the crop most of the algorithms overestimate K_cb. In the K_{cb ini} stage the algorithms overestimated K_cb from 60 to 239 %, and in the K_{cb dev} stage they overestimated K_cb from 10 to 69 %. In contrast, at the K_{cb mid} stage most algorithms underestimated K_cb from 4 to 40 %, and at the K_{cb fin} stage most overestimated K_cb from 2 to 60 %. Five irrigations were applied throughout the vegetative cycle of the crop, which were distributed in a pre-sowing or aniego irrigation, and four auxiliary irrigations applied at 19, 58, 87 and 105 DAS, with an accumulated gross irrigation lamina of 93.4 cm (Figure 3).

Figure 3. Distribution of K_cb estimated by the algorithms used and the K_cb obtained from the FAO-56 Manual of forage maize grown in Plot 1. 

Figure 4. Distribution of the K_cb estimated by the algorithms used and the K_cb obtained from the FAO-56 Manual of forage maize grown in Plot 2. 

In general, it was observed that in the two study plots the algorithms used had a lower adjustment in the initial and final periods of the crop. This is because the crop cover values are lower and soil evaporation, not considered by K_cb, has a greater effect (^{Allen et al., 2006}), so there is greater variation in the daily values of K_{cb ini} and K_{cb fin} depending on the water status of the surface soil layer (^{Rocha et al., 2011}).

Figures 5 and 6 show the K_cb maps generated with the Campos K_cbNDVI algorithm in the two study plots at pixel scale. This algorithm had the best statistical indices when comparing the estimated K_cb with the K_cb from tables in the FAO-56 Manual. Plot 1 showed a K_cb variation from 0.13 to 0.32 in the initial stage (Julian day 77), from 0.25 to 0.59 in the development stage (Julian day 107), from 0.82 to 1.05 in the middle stage (Julian day 142) and from 0.77 to 0.96 in the final stage (Julian day 172) (Figure 5).

Figure 5. Spatial and temporal distribution of K_cb of forage maize grown in Plot 1 in the stages: a) initial (77 Julian day), 

Figure 6. Spatial and temporal distribution of K_cb of forage maize grown in Plot 2 in the stages: a) initial (127 Julian day), 

Plot 2 had K_cb variations from 0.33 to 0.57 in the initial stage (Julian day 127), from 0.32 to 0.88 in the development stage (Julian day 147), from 0.86 to 1.11 in the middle stage (Julian day 172) and from 0.70 to 1.12 in the final stage (Julian day 212) (Figure 6). It is observed that Plot 2 had greater variation in K_cb values in all growth stages of forage maize. This could be due to factors such as crop type (hybrid), soil texture, irrigation management or microclimate, individually or in combination. The maps allow to identify areas with irrigation stress or poor nutrition, irrigation system malfunction or other environmental stress (^{Knipper et al., 2019}).

The K_cb estimated by the Campos K_cbNDVI algorithm were similar to those reported by ^{Gao et al. (2009)} in two maize growth stages (initial and mid), with values from 0.36 to 0.37 in the K_{cb ini} stage, from 1.18 to 1.19 in the K_{cb mid} stage and from 0.22 to 0.28 in the K_{cb fin} stage. The values of the last stage were different from those reported in this study, since the first K_cb values concern maize for grain. ^{Ojeda et al. (2006)} obtained K_c values, using a model based on accumulated DDD, from 0.05 to 0.3 in emergence (V_E), from 0.4 to 0.45 in vegetative stage with four leaves (V₄), from 1 to 1.12 in panicle stage (V_T), from 1.15 to 1.25 in reproductive stage with stigmas appearance (R₁), from 1.1 to 1.2 in reproductive stage with granulation (R₂), from 1 to in reproductive stage with milky grain (R₃) and from 0.8 to 1 in reproductive stage with doughy grain (R₄). ^{Reyes-González et al. (2019)} found K_cb values of 0.22 to 0.40 at the K_{cb ini} stage, 1.00 at the K_{cb mid} stage and 0.80 at the K_{cb fin} stage, in the same study area.

The K_cb derived from the spectral information of the Sentinel-2 images are independent from the parameters of time, sowing day and effective coverage, and represent the evolution of crops in quasi-real time. Hereby, the difference corresponds only to the time lapse in collecting the satellite imagery and processing the information (1-2 days), which facilitates irrigation scheduling in a large region, since neither sowing dates nor assumed effective coverage are required (^{Rocha et al., 2011}).

Conclusions

The use of spectral information from the red and near infrared bands recorded in Sentinel-2 satellite imagery is a viable and adequate alternative to the FAO-56 Manual method for calculating the basal crop coefficient (K_cb) of forage maize. In addition, by combining the use of this technology with the collection of information in the field, it is possible to analyze its behavior more precisely and make more accurate estimates, as specific information is available for the crop cycle and study site. This makes it possible to monitor its evolution in quasi-real time and, consequently, to schedule irrigation in a convenient way in time and space, thus increasing the efficiency of water use.

The Campos K_cbNDVI algorithm had the best accuracies for estimating the K_cb of forage maize in the two different conditions of field irrigation, both in its growth stages and in its entire crop cycle, obtaining an average accuracy of 88 %.