Determination of Crop Coefficients for Flood-Irrigated Winter Wheat in Southern New Mexico Using Three ETo Estimation Methods

Abstract

Crop coefficient (K_c), the ratio of crop evapotranspiration (ET_c) to reference evapotranspiration (ET_o), is used to schedule an efficient irrigation regime. This research was conducted to investigate variations in ET_c and growth-stage-specific K_c in flood-irrigated winter wheat as a forage crop from 2021 to 2023 in the Lower Rio Grande Valley of southern New Mexico, USA, and evaluate the performances of two temperature-based ET_o estimation methods of Hargreaves–Samani and Blaney–Criddle with the widely used Penman–Monteith method. The results indicated that the total ET_c over the whole growth stage for flood-irrigated winter wheat was 556.4 mm on a two-year average, while the average deep percolation (DP) was 2.93 cm and 2.77 cm, accounting for 28.8% and 27.2% of applied irrigation water in the 2021–2022 and 2022–2023 growing seasons, respectively. The ET_o over the growing season, computed using Penman–Monteith, Hargreaves–Samani, and Blaney–Criddle equations, were 867.0 mm, 1015.0 mm, and 856.2 mm in 2021–2022, and 785.6 mm, 947.0 mm, and 800.1 mm in 2022–2023, respectively. The result of global sensitivity analysis showed that the mean temperature is the main driving factor for estimated ET_o based on Blaney–Criddle and Hargreaves–Samani methods, but the sensitivity percentage for Blaney–Criddle was 76.9%, which was much higher than that of 48.9% for Hargreaves–Samani, given that Blaney–Criddle method is less accurate in ET_o estimation for this area, especially during the hottest season from May to August. In contrast, wind speed and maximum temperature were the main driving factors for the Penman–Monteith method, with sensitivity percentages of 70.9% and 21.9%, respectively. The two-year average crop coefficient (K_c) values at the initial, mid, and late growth stage were 0.54, 1.1, and 0.54 based on Penman–Monteith, 0.51, 1.0 and 0.46 based on Blaney–Criddle, and 0.52, 1.2 and 0.56 based on Hargreaves–Samani. The results showed that the Hargreaves–Samani equation serves as an alternative tool to predict ET_o when fewer meteorological variables are available. The calculated local growth-stage-specific K_c can help improve irrigation water management in this region.

1. Introduction

Wheat is the main cereal crop that supplies essential food for the world population, and winter wheat contributes approximately 80% of global wheat production [1]. The United States of America (USA) is a major producer and the third-largest wheat exporter worldwide [2]. Winter wheat (Triticum aestivum L.) is commonly grown in the southern Great Plains of the USA, including Oklahoma, Kansas, New Mexico, and Texas, as a dual-purpose crop for grain and forage production [3]. In 2020, winter wheat production in the USA totaled 31.8 million tons, of which production in New Mexico was estimated at 87.6 thousand tons, representing a decrease of 2% compared to 2019 [4]. According to the 2022 report on crop progress and conditions in New Mexico, 84% of the winter wheat harvested for grain was in very poor or poor condition across a limited area, compared with 57% in 2021, while the 5-year average was 33% [5]. The water scarcity in the drier areas of the western US, especially the increasing water shortage in irrigated agriculture, is the main reason for the reduction of yield. Although planting strategies and the yield of different winter wheat cultivars have been documented in the Southeast and Great Plains of the USA [6,7], detailed information on winter wheat water use (evapotranspiration) and crop coefficient is still lacking, which is required for managing crop water demands for the Lower Rio Grande Valley of New Mexico. In this region, Harkey (coarse-silty, mixed, calcareous, and thermic Typic Torrifluvents) and Glendale (fine-silty, mixed, calcareous, and thermic Typic Torrifluvents) soils are prevalent [8], and the climate is arid continental [9]. The New Mexico Interstate Stream Commission (NMISC) has completed and accepted the Lower Rio Grande Regional Water Plan to meet regional water needs for the next 40 years since 2003 [9].

Irrigation is required to maintain cereal production in arid and semi-arid regions. The actual evapotranspiration (ET_c) is a key parameter in estimating water requirements for efficient irrigation. To date, many methods for ET_c measurements have been established directly or indirectly using lysimeters [10], eddy covariance [11], Bowen-ratio energy balance [12], soil water balance [13], sap flow coupled with micro-lysimeters [14], and remote sensing energy balance [15] or satellite-based ET_c with vegetation indices [16]. Numerous mathematical models have been developed to estimate ET_c as the product of the specific crop coefficient (K_c) and reference evapotranspiration (ET_o) [17,18,19]. Generally, the tabulated K_c values provided by Allen et al. [20] are used for ET_c estimation in different locations and seasons; however, the adjusted K_c based on local conditions can further meet the need for precise irrigation scheduling [21]. To the best of our knowledge, no previous studies have investigated variations in ET_c and local K_c for flood-irrigated winter wheat in southern New Mexico, which in turn affect the accuracy of irrigation amounts supplied on demand throughout the crop’s growing season in this region.

Among the mathematical equations used to obtain ET_o, the Penman–Monteith method has been reported to be very precise under different environmental conditions [16,22,23,24]. However, the application of the Penman–Monteith equation requires several meteorological variables, which are often not available [25,26,27]. Alternatively, simple temperature-based equations are used for ET_o estimation at the local scale. Notably, air temperature is the earliest monitored meteorological variable among the inputs of ET_o computation, and it has been reported that changes in temperature and solar radiation resulted in at least 80% of ET_o variability [28]. The available temperature-based equations include the well-known Hargreaves–Samani [29] and Blaney–Criddle equations [30]. The Blaney–Criddle equation was first developed for New Mexico in 1942 to calculate consumptive water use for limited crops, such as alfalfa, cotton, and deciduous trees in the NM Pecos River Valley [31,32]. The Hargreaves–Samani equation has been recommended as accurate and simple in several studies [33,34]. Some studies have calibrated and validated both equations under diverse local conditions; however, the applications of the two equations have yielded contrasting conclusions in different studies, as both equations can under- or overestimate ET_o for specific crops under certain climates [35,36]. To our knowledge, no prior studies have applied these two equations for ET_o estimation in the Lower Rio Grande Valley of southern New Mexico. Therefore, the specific objectives of this study were to (1) evaluate the performances of temperature-based equations of Hargreaves–Samani and Blaney–Criddle in the Lower Rio Grande Valley of southern New Mexico by comparing their outputs with those from the Penman–Monteith method, (2) determine the influence of meteorological variables on simulated ET_o using global sensitivity analysis for all three ET_o estimation approaches, (3) estimate crop evapotranspiration for flood-irrigated winter wheat grown for forage using the water balance method, and (4) investigate the local crop coefficient (K_c) of winter wheat in the study area.

2. Materials and Methods

2.1. Experimental Site

This study was conducted at the Leyendecker Plant Science Research Center (Latitude 32°12.326′ N, Longitude 106°44.781′ W at an altitude of 1174 m above sea level) of New Mexico State University, located 14.5 km south of Las Cruces, from 2021–2023. The experimental site is 1.2 acres in size. Winter wheat seeds (Weathermaster, supplied by West Gaines Seed, Inc., Seminole, TX, USA) were sown on 29 September 2021 and 30 September 2022 and were harvested on 20 May 2022 and 22 May 2023, respectively. The seeds were planted using a plot drill (John Deere 450, Grand Detour, IL, USA) at a seeding rate of 70 lbs/acre with a drill spacing of 0.15 m for both years. The preharvest plant height was 92.3 ± 1.2 cm and 81.6 ± 0.8 cm for the 2021–2022 and 2022–2023 seasons, respectively. The physical properties of the soil in the study area are given in

Table 1. Soil particle size distribution and textural class at 4 random locations, and soil physical properties at 3 random locations covering the whole experimental winter wheat plot at Leyendecker farm, Las Cruces, NM. The data are average values + standard error of three replicates.

Depth (cm)	Particle Size Distribution (%)			Texture
	Sand	Silt	Clay
0–20	24.0 ± 0.6	23.0 ± 0.5	53.0 ± 0.4	clay
20–40	32.3 ± 0.9	16.2 ± 0.7	51.5 ± 0.6	clay
40–60	17.8 ± 0.9	20.4 ± 0.9	61.8 ± 0.3	clay
60–80	30.3 ± 1.3	40.1 ± 1.0	29.6 ± 1.4	clay loam
80–100	58.4 ± 2.0	23.7 ± 1.5	17.9 ± 1.4	sandy loam
Depth (cm)	BD	Ks	FC	WP
0–15	1.34 ± 0.16	0.066 ± 0.17	0.38 ± 0.05	0.21 ± 0.04
15–30	1.35 ± 0.16	0.066 ± 0.17	0.38 ± 0.05	0.21 ± 0.05
30–50	1.39 ± 0.15	0.001 ± 0.00	0.39 ± 0.04	0.23 ± 0.00
50–80	1.29 ± 0.16	0.255 ± 0.33	0.34 ± 0.10	0.17 ± 0.11

Note: BD = bulk density (g cm⁻³), K_s = saturated hydraulic conductivity (cm h⁻¹), FC = soil water content at field capacity at 30 kPa (cm³ cm⁻³), and WP = soil water content at wilting point at 1500 kPa (cm³ cm⁻³).

. The soil at the experimental site is classified as Glendale; the typical surface for Glendale soil is clay, and the layers below are clay loam and very fine sand [8]. The soil has low hydraulic conductivity in root zone layers. The average bulk density, water content at field capacity, and wilting points are 1.34 g cm⁻³, 0.37 cm³ cm⁻³, and 0.21 cm³ cm⁻³, respectively (Table 1). A chemical analysis of the soil and irrigation water is given in

Table 2. Chemical properties of pre-tilling soil at 5 different depths within the winter wheat plot, as well as irrigation water chemical properties during the winter wheat growing season. The data are average values + standard error of three replicates.

Properties	Unit	Soil					Irrigation Water
		0–20 cm	20–40 cm	40–60 cm	60–80 cm	80–100 cm
pH		8.13 ± 0.03	8.13 ± 0.09	7.93 ± 0.09	8.03 ± 0.03	8.20 ± 0.26	7.73 ± 0.40
Electrical conductivity	dS/m	1.67 ± 0.32	1.84 ± 0.54	3.46 ± 0.23	2.74 ± 0.92	1.84 ± 0.70	1.01 ± 0.11
Sodium	ppm	518.3 ± 127.6	719.7 ± 200.9	1071.7 ± 354.8	940.0 ± 41	454.7 ± 120.6	96.3 ± 15.4
Chloride	ppm	121.9 ± 13.5	108.4 ± 33.1	142.6 ± 61.2	190.3 ± 76.6	111.6 ± 57.8	93.5 ± 2.40
Calcium	ppm	5581.0 ± 32.5	5482.0 ± 52.2	6952.7 ± 511.0	5685.7 ± 905.0	3865.0 ± 1468.8	95.8 ± 21.3
Magnesium	ppm	578.3 ± 10.1	639.7 ± 23.0	795.7 ± 60.6	567.7 ± 134.2	360.0 ± 128.5	18.5 ± 2.02
Potassium	ppm	430.0 ± 38.2	407.3 ± 23.7	381.3 ± 44.5	198.7 ± 42.0	171.0 ± 80.6	6.25 ± 0.25
Nitrate	ppm	31.4 ± 9.7	10.83 ± 2.04	7.63 ± 2.40	4.47 ± 1.73	4.33 ± 1.87	34.1 ± 18.5
Sulfur	ppm	219.6 ± 61.7	236.0 ± 76.5	1156.4 ± 240.6	1347.1 ± 601.7	630.7 ± 279.4	70.8 ± 3.38

. The electrical conductivity of the 40–60 and 60–80 cm soil layers is much higher than in other layers, which is consistent with the concentrations of sodium and chloride (Table 2). The crop was flood-irrigated with well water. A total of 8 and 7 irrigation events were applied throughout the 2021–2022 and 2022–2023 growing seasons, respectively, according to local farm practices. A flow meter was installed at the outlet of the pump to measure the irrigation flow rate and volume. The pump delivers 2500 gallons of water per minute, and each irrigation event lasts 45 min. The irrigation interval was about 30 days for the first three irrigations from the beginning of the growing season until mid-November. After that, irrigation occurred once every 20 days from February until late May. The crop received 101.6 mm of water during each irrigation event, with a total of 812.8 and 711.2 mm applied during the growing seasons of 2021–2022 and 2022–2023, respectively. The observed groundwater table at the Rio Grande riverbed was 3.34 m during the winter of 2021.

2.2. Measurements and Data Collection

2.2.1. Soil Physical Properties

Soil samples from the experimental plot were collected at five depths (0–20 cm, 20–40 cm, 40–60 cm, 60–80 cm, and 80–100 cm) from 4 locations in 2021 to determine soil texture. The depth-wise samples were analyzed separately for each location. The percentages of clay, silt, and sand in each sample were determined in the laboratory using the hydrometer method [37]. Soil textures were identified based on the USDA textural triangle. Soil bulk density was determined using the core method [38]. Individual soil cores (5 cm in diameter and 5 cm in height) were partitioned into depth intervals of 0–15 cm, 15–30 cm, 30–50 cm, and 50–80 cm at three locations. Saturated hydraulic conductivity was determined using the constant head method [39], and soil water retention was measured using the pressure chamber method [40]. The volumetric water content at 30 kPa and 1500 kPa was defined as field capacity and wilting point water content, respectively. The chemical analysis of soil and irrigation water was tested in Ward Laboratories, Inc., Kearney, NE, USA.

2.2.2. Soil Water Content

At the center of the experimental site, 4 Teros 12 sensors (METER Group, Pullman, WA, USA) were installed horizontally at depths of 15, 30, 50, and 80 cm to continuously monitor diurnal volumetric soil water content. According to the particle size distribution for 0–100 cm soil depths at 4 locations covering the whole plot, the soil variability through the profile (CV = 7.14% for clay; CV = 11.3% for sand on a five-layer average) within the plot was small. Therefore, we decided to place one set of soil moisture sensors at the center of the plot. A second set of sensors at the same depths was installed about 3.5 m from the first location, and the difference in soil moisture content was low (the average CV = 1.60%, 4.55%, 5.62%, and 3.16% for soil depths of 15, 30, 50, and 80 cm, respectively, during one irrigation cycle). All sensor data were automatically broadcast on Lora frequencies across different channels using Ebyte22 hardware. A linear equation was suggested by the Meter group in the manual for the calibration of mineral soil types with saturated paste extract EC_s ranging from 0 dS/m to 8 dS/m. Volumetric water content is calculated using the following equation:

$$\theta =C_0\times RAW+C_1,$$

(1)

where θ is the volumetric water content (cm³ cm⁻³); RAW is the raw sensor output, and C₀ and C₁ are the calibration coefficients (C₀ = 3.879 × 10⁻⁴, C₁ = −0.6956).

Soil-specific calibration equations usually perform better than the manufacturer’s [41]. Concurrently, all of the devices required separate calibrations for different soil horizons [42]. In our study, the gravimetric method was used to calibrate the volumetric water content data measured with Teros 12 sensors. Undisturbed and loose soil samples were collected from depths of 15, 30, 50, and 80 cm at 4 locations near the Teros 12 sensors at two-to-five-day intervals during the period from 16 February to 20 May. Thus, the sample size used for calibration was 52. After that, the soil samples were weighed and oven-dried at 105 °C until reaching a constant weight. Calibration was performed for 4 different soil horizons at 15, 30, 50, and 80 cm. New coefficients C₀ and C₁ for Equation (1) were derived for each sensor depth, and the calibration Equation (1) was fitted using the nonlinear least-squares approach. The estimated coefficients C₀ and C₁ for Equation (1) at the 15, 30, 50, and 80 cm sensor depths are shown in

Table 3. Estimated coefficients C₀ and C₁ for the calibration of Teros 12 sensors (Equation (1)) at each soil depth of 15, 30, 50, and 80 cm.

Sensor Depths (cm)	New Coefficients for Calibration Equation (1)		R2 *
	C0	C1
15	3.771 × 10−4	−0.6677	0.916
30	3.558 × 10−4	−0.6065	0.867
50	3.503 × 10−4	−0.5929	0.817
80	3.700 × 10−4	−0.6551	0.769

Note: * Coefficient of determination for volumetric water contents measured using Teros 12 sensors using the new calibration versus volumetric water contents converted by the measurements with the gravimetric method.

.

The Teros 12 determined volumetric water contents were recalculated from the measured raw data and the estimated coefficients using Equation (1). The coefficients of determination (R²) between the modified volumetric water contents and the gravimetrically determined volumetric water contents were always greater than 0.80 at depths of 15, 30, and 50 cm, while at 80–100 cm depth, R² was 0.77 (Figure 1 and Table 3).

2.2.3. Meteorology

The climate of the experimental area is classified as semi-arid, with an annual precipitation of 203–255 mm and an average annual temperature of 16–24 °C [9]. An ATMOS-41 weather station (METER Group, Pullman, WA, USA) was installed 300 m northwest of the experimental site to record daily precipitation, air temperature, relative humidity, wind speed, and solar radiation at 15-minute intervals. The average daily relative humidity (RH), vapor pressure deficit (VPD), air temperature (T_a), and solar radiation (R_s) over the two growing periods of winter wheat were 48.2 ± 1.1% and 52.6 ± 1.1%, 1.02 ± 0.04 kPa and 0.83 ± 0.03 kPa, 11.3 ± 0.4 °C and 10.8 ± 0.4 °C, and 188.3 ± 4.4 W/m² and 174.6 ± 4.6 W/m², respectively (Figure 2).

2.3. Crop Coefficients Approach

The crop coefficient K_c is defined as the ratio of crop evapotranspiration (ET_c) to reference evapotranspiration (ET_o). It varies throughout the crop growth stage with the surface resistance and aerodynamic properties of the crop and the reference crop [17]. Generally, K_c is calculated using single or dual approaches as outlined in FAO56, with the derivation of K_c consistent with the growth change of the crop, such as height, leaf area, and albedo of the crop–soil surface [17]. However, we chose to calculate K_c as the ratio of ET_c to ET_o because we had an estimate of ET_c using the water balance method. Several previous studies have also estimated K_c using water balance [43,44,45]:

$$k_c=E{T}_c/E{T}_o.$$

(2)

The average daily ET_c was estimated using the water balance equation [46]:

$$E{T}_c=\left[{\displaystyle \frac{(I+P-DP+{\displaystyle {\sum }_{i=1}^n({\theta }_1-{\theta }_2})\Delta S_i}{\Delta t}}\right],$$

(3)

where I is irrigation depth (mm), P is precipitation (mm), DP is deep percolation below the upper 80 cm soil depth (mm), ΔS is the thickness of each soil layer (mm), which are 150, 150, 200, and 300 mm in this study, θ₁ and θ₂ are the volumetric soil water content at times one and two (%), and Δt is the time interval between two consecutive irrigation events in days. In this study, surface runoff is 0, and capillary rise from the groundwater table is 0 since the groundwater table is below 3 m and the soil in the deeper layer is sandy.

Deep percolation (DP, cm) was calculated using the method proposed by Doorenbos and Pruitt [30] expressed as

$$DP=\left\{\begin{array}{c}0\\ SWC-SW{C}_{FC}\end{array}\begin{array}{c}\\ \end{array}\begin{array}{c}if\\ if\end{array}\begin{array}{c}\\ \end{array}\begin{array}{c}SWC<SW{C}_{FC}\\ SWC>SW{C}_{FC}\end{array}\right\},$$

(4)

where SWC is the in situ soil water stored in the root zone (cm), and SWC_FC is the soil water stored at field water holding capacity for the same depth (cm). DP was calculated using soil water content and field water holding capacity data for depths of 15, 30, 50, and 80 cm.

2.3.1. Methods of Reference Evapotranspiration Estimation

Selecting a proper method for computing reference evapotranspiration depends on the type, quality, and length of the available climatic data.

The Penman–Monteith method is recommended when temperature, humidity, wind speed, and solar radiation data are available because of its accuracy in any environment. It is obtained using the following Equation [47]:

$$E{T}_o={\displaystyle \frac{\left[0.418\Delta (R_n-G)+\gamma \frac{900}{T+273}{u}_2(e_s-e_a)\right]}{\Delta +\gamma (1+0.34u_2)}},$$

(5)

where R_n is the net radiation at the crop surface (MJ m⁻² day⁻¹), calculated using the equations based on Allen et al. [20], resulting in its Julian day dependence. G is the soil heat flux density (MJ m⁻² day⁻¹), Δ is the slope of the vapor pressure curve (kPa °C⁻¹), γ is the psychrometric constant (kPa °C⁻¹), T is the mean daily air temperature at 2 m height (°C), e_s-e_a is the saturation vapor pressure deficit (kPa), and u₂ the wind speed at 2 m height (m s⁻¹). The computation of all parameters required for the ET_o calculation follows the method outlined by Allen et al. [20].

The temperature-based Blaney–Criddle method for estimating ET_o has been widely used in the western USA, as described by Doorenbos and Pruitt [30]. This method can be commonly described as [48]

$$E{T}_o=c_e(a_t+b_{t}pT).$$

(6)

The unit of ET_o in this equation is inch/d, T is the mean air temperature for the period (°F), p is the mean daily percent of annual daytime hours, and a_t and b_t are adjustment factors based on the climate of this region, and c_e is an adjustment factor based on elevation above sea level. The calculations for these three factors are given as

$$c_e=0.01+3.049\times {10}^{-7}{E}_{lev},$$

(7)

$$a_t=3.937\left(0.0043R{H}_{\min }-{\displaystyle \frac{n}{N}}-1.41\right),$$

(8)

$$b_t=b_n+b_u,$$

(9)

$$b_n=0.82-0.0041R{H}_{\min }+1.07{\displaystyle \frac{n}{N}}-0.006R{H}_{\min }{\displaystyle \frac{n}{N}},$$

(10)

and

$$b_u=(1.23U_d-0.0112R{H}_{\min }{U}_d)/1000,$$

(11)

where E_lev is the elevation above sea level (ft), RH_min is the mean daily minimum relative humidity (%), n/N is the ratio of actual to possible sunshine hours, with n/N = 0.7 in this study area, and U_d is the mean daytime wind speed at 2 m above the ground (mile/d).

Another temperature-based method was defined using Hargreaves and Samani [29]:

$$E{T}_o=0.0023\times 0.408R_a(T_{mean}+17.8){(T_{\max }-T_{\min })}^{0.5},$$

(12)

where R_a is the extraterrestrial radiation (MJ m⁻² d⁻¹) obtained from a set of equations [34]; therefore, it is Julian day dependent. T_mean, T_max, and T_min are the mean, maximum, and minimum air temperatures during the calculation period (°C).

Growing degree days (GDDs, °C day) were computed as follows [49]:

$$GD{D}_i=T_{avg}-T_b.$$

(13)

GDD_i is the growing degree days for the day i (°C day). If T_avg < T_b, GDD = 0, T_avg is the daily mean temperature (°C), and T_b is the crop-specific base air temperature, taken as 0 °C for winter wheat [50]. The accumulated GDD can reflect the seasonal variations of crop ET_c, which is beneficial for explaining the potential trend of K_c throughout the growing period of winter wheat.

2.3.2. Statistical Indicators

The statistical indicators used to evaluate the performance of the methodologies against the reference evapotranspiration computed using the Penman–Monteith method were the Nash–Sutcliffe model efficiency coefficient (CE), the mean bias error (MBE), the mean absolute error (MAE), and the root mean square error (RMSE):

$$CE=1-{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n{(E{T}_i-E{T}_{PMi})}^2}}{{\displaystyle {\sum }_{i=1}^n{(\overline{E{T}_{PMi}}-E{T}_i)}^2}}},$$

(14)

$$MBE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n(E{T}_i-E{T}_{PMi})},$$

(15)

$$MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|E{T}_i-E{T}_{PMi}\right|},$$

(16)

and

$$RMSE={\left[{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{(E{T}_i-E{T}_{PMi})}^2}\right]}^{0.5}$$

(17)

where ET_PM and ET_i are the reference evapotranspiration (ET_o) values of the day i, calculated using the Penman–Monteith method and the other methods (Blaney–Criddle or Hargreaves–Samani), respectively. $\overline{E{T}_{PM}}$ is the average over the data period, while n is the sample size. The smaller the indices of MAE, MBE, and RMSE, the better the agreement between ET_o computed using other methods and ET_o computed using the Penman–Monteith method. The values of CE range from −∞ to 1, with CE = 1 being the optimal value. Values between 0 and 1 indicate acceptable levels of performance, whereas values less than 0 indicate unacceptable performance.

2.4. Global Sensitive Analysis

A global sensitivity analysis was conducted for all three ET_o estimation approaches to determine the influence that measured parameters had on simulated ET_o. Crystal Ball (Oracle Inc., Redwood City, CA, USA), based on the Sobol method [51], was used to quantify the contribution of each input parameter to the change in the simulated results. The sensitivity percentages of input meteorological variables for each ET_o estimation method were displayed in the result section. The parameter interactions were considered in this approach. A Monte Carlo simulation [52] was implemented to provide natural random variation in each parameter within their observed ranges. During the simulation, each parameter was subsampled 10,000 times, represented by their mean values and standard deviations across all observations under an assumed normal distribution [53]. After analyzing the pattern of these 10,000 trials of data derived from Monte Carlo simulation, a distribution of predicted ET_o was shown (Figure 3). In this study, the mean standard deviations of predicted ET_o were 2.13 mm, 2.81 mm, and 2.27 mm for the Penman–Monteith, Blaney–Criddle, and Hargreaves–Samani methods, respectively. Finally, the software produced the contribution of each input parameter to the variability of the predicted ET_o. The greater the percentage, the more sensitive a model output variable is to that parameter. The sensitivity rankings of input parameters will be presented in the results section later.

3. Results

3.1. Temporal Variations in Soil Water Content (SWC) and Deep Percolation (DP)

Significant fluctuations in soil moisture at each depth were caused by each irrigation event (Figure 4). The average SWC at 15, 30, 50, and 80 cm were 33.2 ± 0.4%, 36.4 ± 0.2%, 39.8 ± 0.1%, and 39.9 ± 0.4% for the 2021–2022 growing season, respectively, and 34.0 ± 0.3%, 35.4 ± 0.2%, 35.8 ± 0.04%, and 37.5 ± 0.1% for the 2022–2023 growing season. The average soil moisture depletion (ΔSWC) values before and after irrigation at 15, 30, 50, and 80 cm were 13.8%, 5.3%, 2.4%, and 6.4% for the 2021–2022 season, and 15.0%, 11.8%, 1.7%, and 4.7% for the 2022–2023 season, respectively. The high values of depletion at 80 cm indicate that deep percolation cannot be negligible in this study. In our study, an additional irrigation event was applied during the 2021–2022 growing season for the 2022–2023 growing season when intense precipitation occurred in October (Figure 4). DP for each irrigation event ranged from 9.8% to 39.7% of the irrigation amount throughout the 2021–2022 season and from 17.8% to 33.0% throughout the 2022–2023 season.

3.2. Reference Evapotranspiration Using the Three Methods

The total ET_c during the whole growing season was 564.2 mm and 548.6 mm for 2021–2022 and 2022–2023, respectively. The ET_o computed using the Penman–Monteith, Blaney–Criddle, and Hargreaves–Samani methods were 867.0 mm and 785.6 mm, 1015.0 mm and 947.0 mm, and 856.2 mm and 800.1 mm, respectively, over the two periods of winter wheat growth stage (Figure 5). Compared to the Penman–Monteith method, Blaney–Criddle overestimated ET_o by 17.1% and 20.5% for the 2021–2022 and 2022–2023 seasons, respectively, while Hargreaves–Samani underestimated ET_o by 1.2% in the 2021–2022 season and overestimated ET_o by 1.8% in the 2022–2023 season. The goodness-of-fit indicators confirmed the better performance of the Hargreaves–Samani method, which had higher CE and smaller MBE, MAE, and RMSE for both growing seasons (

Table 4. Goodness-of-fit indicators for the comparison between the Blaney–Criddle and Hargreaves–Samani methods against the Penman–Monteith equation for calculating reference evapotranspiration. CE: Nash–Sutcliffe model efficiency coefficient, MBE: mean bias error, MAE: mean absolute error, and RMSE: root means square error.

Growing Season	Method	CE (%)	MBE (mm)	MAE (mm)	RMSE (mm)
2021–2022	Blaney–Criddle	79.8	0.59	0.73	0.92
	Hargreaves	80.2	−0.07	0.67	0.91
2022–2023	Blaney–Criddle	54.9	0.61	0.85	1.13
	Hargreaves	67.9	0.03	0.70	0.96

).

3.3. Input Parameters’ Assessment for the Three ET_o Estimation Methods

The results of the global sensitivity analysis are displayed in Figure 6, which reports the sensitivity percentage of input meteorological variables based on Crystal Ball analysis for three ET_o estimation methods. For Penman–Monteith, wind speed and maximum temperature were the driving factors affecting ET_o the most, with sensitivity percentages of 70.9% and 21.9%, respectively. Solar radiation ranked third, with a sensitivity percentage of 4.0%.

Regarding the two temperature-based methods, mean temperature, percent sun, and minimum relative humidity were the first three factors influencing the simulated ET_o based on Blaney–Criddle; their sensitivity percentages were 76.9%, 15.4%, and 6.6%, respectively. Mean temperature, Julian day, and minimum temperature, with sensitivity percentages of 48.9%, 26.3%, and 15.9%, respectively, affected the simulated ET_o based on Hargreaves–Samani.

3.4. Crop Coefficients

Crop coefficients (K_c) for the two seasons were consistent with the general trend that K_c values were lower during the early-season stages and late-season stages toward harvest but gradually increased during the mid-season stages in spring (Figure 7). The K_c exhibited a single-peak curve throughout the 2021–2022 growing season. Average K_c values were 0.50, 0.46, and 0.47 for the early season, 1.25, 1.12, and 1.41 for the mid-season, and 0.53, 0.48, and 0.59 for the late season, according to the Penman–Monteith, Blaney–Criddle, and Hargreaves–Samani methods, respectively. However, during the 2022–2023 season, K_c showed a bimodal curve over time; average K_c values were 0.58, 0.56, and 0.57 for the early season, 0.90, 0.84, and 0.99 for the mid-season, 0.54, 0.43, and 0.53 for the late season, according to the Penman–Monteith, Blaney–Criddle, and Hargreaves–Samani methods, respectively.

4. Discussion

ET_o represents the primary weather-induced influences on the evapotranspiration rate of the grass reference crop [17]. The Penman–Monteith equation was found to be the most precise method for estimating ET_o across a wide range of climatic conditions [16,22,23,24,54,55], whereas the Hargreaves–Samani and Blaney–Criddle equations are two temperature-based and alternative widely used approaches that produce acceptable estimations under diverse climates using limited meteorological data [56,57]. Among these, Hargreaves–Samani has been reported to perform poorly in extremely windy and humid conditions [58]. In our study, the motivation for selecting the two temperature-based methods is that we expected this study could provide new insights into ET_o estimation with low-cost or less availability of data. Unlike Penman–Monteith, which requires more meteorological inputs, both Hargreaves–Samani and Blaney–Criddle needed only temperature as input. Hargreaves–Samani is more widely used than Blaney–Criddle, but the Blaney–Criddle method was first developed in 1942 for New Mexico to calculate consumptive water use for crops in the NM Pecos River Valley. However, the results indicated that, compared to the Penman–Monteith method, the Blaney–Criddle method overestimated ET_o by 18.7% on a 2-year average, whereas the Hargreaves–Samani method overestimated ET_o by 0.2%. Hafeez et al. [36] reported that Blaney–Criddle and Hargreaves–Samani overestimated ET_o by 23.78% and 37.93%, respectively, compared to the Penman–Monteith method in a humid subtropical climate. Valipour [59] compared 11 temperature-based models with the PM method and found that the modified Hargreaves–Samani method estimated ET_o better than other models in most provinces of Iran. Therefore, the input variables and output accuracy vary among different methods, and selecting a suitable ET_o estimation method benefits site-specific water consumption predictions.

The global sensitivity analysis indicated the influence of input parameters on simulated ET_o for all three methods. The sensitivity percentage of average temperature for Blaney–Criddle was 76.9%, much higher than the 48.9% for Hargreaves–Samani (Figure 6), given that the ET_o estimated via Blaney–Criddle is more fluctuant and less accurate compared to ET_o estimated using Hargreaves–Samani during the growing season, especially in an arid area such as the Lower Rio Grande Valley, where the monthly average temperature is over 20 °C from May to September, and seasonal variation is large (Figure 2). This conclusion is also consistent with the results of statistical indicators (Table 4 and Figure 5). Thus, Hargreaves–Samani is suggested as an alternative method in the study area, especially when only temperature sensors are in the field or in areas with lower financial resources. Moreover, compared to the Penman–Monteith method, the Blaney–Criddle method is much less sensitive to wind speed; therefore, the areas lacking wind speed data will be beneficial from using this method. Nowadays, more advanced technologies and methods such as remote sensing and machine learning models are used to estimate ET_o [60,61]; in our future study, we will further use these advanced methods and compare the scope of applicability of different methods in our study area.

The crop coefficient (K_c), defined as the ratio of ET_c/ET_o, represents specific crop characteristics. It is affected by crop varieties, irrigation management, and environmental conditions but varies little with climate change [62]. Various authors reported K_c values for winter wheat in various locations and irrigation methods. Some reported that the K_c value of winter wheat in monoculture ranges between 0.26–0.80, 0.91–1.44, and 0.27–0.98 at the initial, mid, and late growth stages, respectively, in Northern China [43,63,64,65], while the K_c values for winter wheat at the initial, mid-, and end-season stages were 0.77, 1.35, and 0.26, respectively, in Southwest Iran [57]. Site-specific measurements and observations of crop growth are expected to be more accurate in estimating crop water use and optimizing irrigation scheduling [66]. To the best of our knowledge, no precise information on K_c has been reported for southern New Mexico. Our study presents daily values of K_c from equations (Figure 7), which are very useful for the efficient management of irrigation water [67]. The two-year average K_c values were 0.54, 0.51, and 0.52 for the early season, 1.1, 1.0, and 1.2 for the mid-season, and 0.54, 0.46, and 0.56 for the late-season crop growth stages according to the Penman–Monteith, Blaney–Criddle, and Hargreaves–Samani methods, respectively (Figure 7). In comparison with the K_c values reported for Uvalde, Texas [21], our values are similar at the early and mid-growth stages to those of 0.53 and 1.15 and slightly larger at the late growth stage compared to 0.40. Howell et al. [50] reported K_c values for winter wheat at Bushland, Texas, High Plains, where the peak value of K_c was 0.94, and initial and late K_c were 0.29 and 0.30, respectively.

The K_c curve represents variations in K_c over the crop growing season [20]; it showed unimodal and bimodal trends for the 2021–2022 and 2022–2023 seasons, respectively, in this study (Figure 7). K_c values for the mid-season first decreased and then gradually increased during the period from 16 February to 8 March in the 2022–2023 season, which resulted from much lower calculated ET_c during this period compared to the 2021–2022 season. This finding might be explained by the reason that the accumulated growing degree days (GDDs) during this period ranged from 513.0 °C to 705.8 °C in the 2022–2023 season, which was lower than that of the 2021-2022 season (543.1 °C to 725.7 °C) (Figure 8), consequently giving the lower ET_c for the period from February 16 to March 8 in 2022–2023 season. Moreover, the irrigation date after the winter season in the 2022–2023 season was 6 February 2023, which was 10 days in advance than in the 2021–2922 season (16 February 2022); this practice also exacerbated the decrease in ET_c. This phenomenon indicates that irrigation time is critical in the establishment of irrigation regimes to meet the specific water needs of individual crops and ensure optimal water-saving [68]. In our future study, more detailed crop growth datasets will be observed in leaf area, crop height, leaf age and conditions, and the fraction of ground covered by the vegetation; we will further calculate K_c with FAO56 methods based on its theoretical background and compare the K_c values with those calculated using the ratio of ET_c to ET_o.

5. Conclusions

In this study, three ET_o estimation methods—Penman–Monteith, Blaney–Criddle, and Hargreaves–Samani—were evaluated, and a global sensitivity analysis was conducted for all three approaches to determine the influence of input parameters on simulated ET_o. Both Blaney–Criddle and Hargreaves–Samani overestimated ET_o by 18.7% and 0.2%, respectively, compared to the Penman–Monteith method on a 2-year average. The global sensitivity analysis also showed that average temperature accounted for 76.9% of sensitivity for the Blaney–Criddle method, which was much higher than that for Hargreaves–Samani (48.9%). This suggests that the Hargreaves–Samani equation could be a reliable alternative tool for predicting ET_o accurately when a lower number of meteorological variables are available in this area. Unlike Penman–Monteith, which requires more meteorological inputs, the Hargreaves–Samani method enables a very low-cost estimation of ET_o, which benefits areas with lower financial resources or only temperature sensors in the field.