Calculating Vegetation Index-Based Crop Coefficients for Alfalfa in the Mesilla Valley, New Mexico Using Harmonized Landsat Sentinel-2 (HLS) Data and Eddy Covariance Flux Tower Data

Abstract

The goal of this study is to investigate the usefulness of the relatively new 30 m spatial and <5.7-day temporal resolution Harmonized Landsat Sentinel-2 (HLS) dataset for calculating vegetation index-based crop coefficients (K_cVI) for estimating field scale crop evapotranspiration (ET_c). Increased spatial and temporal resolution ET_c estimates are needed for improving irrigation scheduling, monitoring impacts of water conservation programs, and improving crop yield. The crop coefficient (K_c) method is widely used for estimating ET_c. Remote sensing vegetation indices (VI) are highly correlated to Kc and allow the creation of a K_cVI but the approach is limited by the availability of high temporal and spatial resolutions. We selected and calculated sixteen commonly used VIs using HLS data and regressed them against field-measured ET for alfalfa in the Mesilla Valley, New Mexico to create linear K_cVI models. All models showed good agreement with K_c (r² > 0.67 and RMSE < 0.15). ET_c prediction resulted in an MAE ranging between 0.35- and 0.64-mm day⁻¹, an MSE ranging between 0.20- and 0.75-mm day⁻¹ and an MAPD ranging between 10.0 and 16.5%. The largest differences in predicted ET_c occurred early in the growing season and during cutting periods when the spectral signal could be influenced by soil background or irrigation events. The results suggest that applying the K_cVI approach to the HLS dataset can help fill in the data gap in remote sensing ET tools. Future work should focus on assessing additional crops and integration into other tools such as the emerging OpenET platform.

1. Introduction

Accurate estimates of evapotranspiration (ET) at both regional and field scales are crucial for gaining insights into the spatiotemporal distribution of agricultural water usage. They are particularly important for regions that suffer from chronic drought, as they can inform water management decisions. Furthermore, these measurements can provide essential context for guiding precision agriculture. In this regard, locally calibrated ET measurements play a vital role in enhancing our understanding of agricultural water use and its impact on the environment.

Remote sensing models for field scale estimates of ET tend to use a physical approach that employs thermal imagery to calculate a surface energy balance to solve for latent energy, which is then converted to evapotranspiration, as a residual in the energy balance (e.g., SEBAL [1], ALEXI/DisALEXI [2], METRIC [3], SSEBop [4]). However, the availability of high spatial (<30 m) and temporal resolution (<8 days) thermal imagery is limited, thus potentially missing several weeks of measurements during the growing period. Conversely, data harmonization of spectral bands between satellites provides high spatial resolution imagery delivered <5.7 days, thus creating new opportunities for the use of empirical methods that utilize the spectral bands for creating vegetation index (VI)-based crop coefficients (K_cVI) and provides water managers another tool for decision making. The objective of this research is to better understand the utility of K_cVI from the Harmonized Landsat Sentinel (HLS) dataset for estimating ET_c at the field scale.

Obtaining measurements of ET across space and time is challenging and field measurements using lysimeters, Bowen ratio, and eddy covariance techniques, or scintillometers, are expensive and require well-trained research personnel who can exploit the demanding accuracy of the measurements. Crop evapotranspiration (ET_c) can be estimated using the K_c method, which multiplies a locally calculated standardized reference ET (ET_sz) value by an empirically determined K_c value (Equation (1))—the resultant equation is the standardized FAO-56 crop coefficient method [5] (Equation (2)), which allows for the comparison of ET_c for different time periods and regions.

$${\mathrm{K}}_{\mathrm{c}}={\displaystyle \frac{{\mathrm{E}\mathrm{T}}_{\mathrm{a}}}{{\mathrm{E}\mathrm{T}}_{\mathrm{s}\mathrm{z}}}}$$

(1)

$${\mathrm{E}\mathrm{T}}_{\mathrm{c}}={\mathrm{E}\mathrm{T}}_{\mathrm{s}\mathrm{z}}\times {\mathrm{K}}_{\mathrm{c}}$$

(2)

where

ET_sz is reference evapotranspiration (short grass) (mm day⁻¹);

K_c is the crop coefficient (unitless);

ET_a is the measured actual evapotranspiration (mm day⁻¹);

ET_c is the crop evapotranspiration (mm day⁻¹);

One of the strengths of using the K_c approach is the inclusion of measurements that capture localized weather and plant-specific conditions. ET_sz incorporates weather parameters supplied by a nearby weather station to capture the evaporation power of the atmosphere. K_c is a single value representing soil evaporation and plant transpiration [5] and integrates site-specific information such as the farm irrigation and management practices [6] and physiological characteristics of a crop such as light absorption and canopy roughness during different stages of the growth cycle [7]. K_c values are derived from field experiments where the ET_a for a specified crop is measured under optimal growing conditions using a weighing lysimeter, soil water balance approach, or eddy covariance method and divided by ET_sz (Equation (2)). The FAO-56 report published general K_c values for many crops for three different stages of the growing season. Applying the K_c method can potentially overestimate ET_c because of uncertainties in precipitation effectiveness [8], and because K_c values are developed under ideal growing conditions, have morphological and physiological differences for different varieties, thus it is important to modify K_c for local conditions and cultural practices [9]. The FAO method does suggest using a crop stress coefficient (K_s) to adjust for suboptimal growing conditions; however, it requires information on the soil matric potential, hydraulic conductivity, soil type, and the associated field capacity. The published K_c values in FAO-56 do not capture the spatiotemporal variability of K_c at resolutions sufficient for precision agricultural management decisions. In contrast, the sensitivity of the spectral bands of satellite imagery to changes in vegetation health makes remote sensing a viable solution for relating vegetation index (VI) values to K_c and estimating plant ET.

Satellite remote sensing data are widely accepted as a solution for estimating the spatiotemporal distribution of various biophysical attributes of the Earth’s surface, including evapotranspiration. Satellite data are useful because of the availability of free imagery, long periods of historic coverage, and due to most satellite data often having a high level of systematic calibration applied before being distributed [10]. The relationship between electromagnetic radiation (EMR) and vegetation provides the theoretical foundation for remote sensing as a method for measuring ET, where the physical and physiological properties of the plants determine the amount of EMR absorbed, transmitted, reflected, and emitted [11]. In healthy vegetation, EMR wavelengths between 380 and 710 nm, referred to as photosynthetically active radiation, are absorbed by pigments in the chloroplasts, whereas near-infrared wavelengths between 700 and 1200 nm are reflected or transmitted by the spongy mesophyll [12]. As plants decrease chlorophyll production and/or are under stress, there is a reduction in absorption of photosynthetically active radiation [12] which leads to the plants using less water. The relationship between changes in these wavelengths and vegetation characteristics can be realized through the use of VIs.

VIs are dimensionless transformations of measurements of specific wavelengths of electromagnetic energy, typically in the visible, near-infrared, and mid-infrared wavelengths, and are used to highlight features of interest and contain up to 90 percent of spectral information of vegetation [13]. VIs correlate to changes in vegetation health (e.g., water uptake, diseases, nutrients, and pests) and are representative of plant productivity [7]. Because of the similarities to K_c in terms of changes in response to the plant growth cycle and plant stress, K_cVI values can be estimated through regression of a VI derived from reflectance data from an in situ radiometer [9] or from satellite and aerial sensors (e.g., [14,15,16]) to ground measured data. Many factors can influence the reflectance values recorded at the sensor including the range of wavelengths the sensor is recording, atmospheric conditions, background soil reflectance, soil moisture, and vegetation disease or stress.

Numerous VIs were developed for different applications. The most commonly applied index is the Normalized Difference Vegetation Index (NDVI) [17]. The NDVI tends to saturate around 0.8 with healthy vegetation and is sensitive to differences in soil background [18]. Several indices were created as variations of the NDVI to incorporate adjustment factors to create a more dynamic response, such as the Renormalized Difference Vegetation Index (RDVI) [19], or to adjust for the soil background effects, such as the Modified Soil-Adjusted Vegetation Index (MSAVI) [20]. Some indices were developed to use only information within the visible spectrum to estimate vegetation conditions such as the Normalized Green Red Difference Index (NGRDI) [21] or the Green-NDVI (GNDVI) [22] and are sensitive to chlorophyll concentration and can have a higher dynamic range compared to the NDVI. Other indices incorporate information from the mid-infrared range because of the response to moisture in vegetation [23] and the ability to indicate drought [24]. While examples exist [25], there are a limited number of studies that compare the effectiveness of multiple VIs for the purpose of calculating K_c. Thus, there is still a need for investigating different VIs for K_c development because the different band combinations and adjustments within the equations provide the potential to improve the dynamic range of the index and reduce background noise, leading to a better representation of K_c. There is also an importance in calculating K_cVI with minimal adjustments based on ad hoc manual measurements if these methods are to be operationalized by the agricultural community.

Until recently, a lag in processing, inadequate temporal resolution, and accessibility of data have hindered the operational use of high spatial resolution satellite ET measurements for field scale management decisions. Forage crops such as alfalfa are cut numerous times throughout a growing season and satellites like Landsat may not coincide to capture the average growing conditions [26]. One advancement is the HLS dataset, which capitalizes on the spectral and spatial resolution similarities between Landsat and Sentinel-2 satellites. The result is a dataset that increases the theoretical temporal resolution of data capable of field scale measurements to between 3.2 and 5.7 days [27]. HLS data are available on the internet and have near real-time processes of the most current imagery. The improved temporal resolution of the HLS data makes it an appealing potential solution for use for a K_cVI approach for field scale ET measurements.

This study assesses the usefulness of the HLS dataset for creating empirically derived K_cVI values and subsequently predicting ET_c for an alfalfa (Medicago sativa) crop in the Mesilla Valley of the Rio Grande basin in New Mexico, USA. The objectives of this study are: (1) to create linear regression models from 16 different VIs, and (2) to test the performance of these equations in predicting ET_c using regression error metrics.

2. Description of the Study Site and Methodology

2.1. Site Description and Alfalfa Crop

The study site is a 35.2 ha privately owned alfalfa field (32°12′3.07″N, 106°44′09.90″W, central coordinates) located in the Mesilla Valley of southern New Mexico (Figure 1). The Mesilla Valley lies within the Chihuahua Desert and exemplifies agricultural conditions in a semi-arid desert environment. The region’s historical precipitation is less than 230 mm year⁻¹ and 75% of it falls during summer monsoonal months of July, August and September, and the average monthly temperature ranges between 5.5 and 26.6 °C with diurnal temperature of 17.8 °C [28]. The winds in the Valley are moderately strong with occasional gusts in winter and spring and usually light during summer. The potential evaporation of the region exceeds the precipitation, and from 1980 to 2020, the region has experienced an increase of between 135 and 235 mm in evaporative demand [29].

Mesilla Valley is 80 km long and varies in width from a few kilometers to 10 km wide. It is a highly productive agricultural corridor along the Rio Grande in Doña Ana County, New Mexico. Doña Ana County has an area of about 21,400 hectares dedicated to farming and is one of the most productive agricultural regions in New Mexico. The valley supports a variety of forage crops (e.g., alfalfa and winter wheat) and annual row crops (e.g., green chile, onions, and cotton). Over the past few decades, however, the Valley has evolved into one of the largest pecan-producing areas in the United States [30].

The field was laser-leveled and alfalfa was seeded in 2014. The alfalfa field was flood-irrigated 11 times during the 2017 growing season at a 24-day mean interval and received a total of 1874 mm of irrigation and 232 mm of precipitation (

Table 1. Cumulative irrigation and precipitation depths between irrigation events.

Irrigation Event	Date	DOY	Irrigation (mm)	Precipitation (mm)
1	3 March 2017	62	202	0
2	21 March 2017	80	141	0
3	4 April 2017	94	142	2
4	3 May 2017	123	137	0
5	16 May 2017	136	173	5
6	11 June 2017	162	160	1
7	7 July 2017	188	176	154
8	16 August 2017	228	134	43
9	15 September 2017	258	222	1
10	25 September 2017	268	188	15
11	1 November 2017	305	199	11

). In 2017, the alfalfa was healthy, uniform, and monotypic. It was harvested seven times during the growing season (

Table 2. Alfalfa harvesting dates for the study site during the 2017 growing season. DOY is the day of the year.

Cutting Event	Cut Date	DOY
1	20 April 2017	110
2	2 June 2017	153
3	29 June 2017	180
4	6 August 2017	218
5	4 September 2017	247
6	18 October 2017	291
7	27 November 2017	331

). The average harvest interval for the first five harvests was 12 days and approximately 30 days for the final end-of-season harvest.

The growing season for alfalfa at the study site was determined using growing degree days (GDD) at a base temperature of 5 °C (41 °F) to mark the beginning of the growing season. Accumulation of GDD began on 21 March 2017, or day of the year (DOY 80), when the air temperature reached and stayed above 5 °C (41 °F) for five consecutive days [31]. The end of the growing season was determined to be 7 December 2017 (DOY 341), where the minimum temperature dropped below −4.4 °C (24 °F) for more than two hours [31].

The soil texture at the study site was classified by Boyko et al. [32] as silt loam in the top 30 cm, sandy loam below it up to 60 cm, and then sand up to 180 cm. In 2017, Boyko et al. [32] measured volumetric soil moisture in the upper 30 cm ranging between 20.9% and 45.6% with an average of 40%.

2.2. Evapotranspiration Using the Eddy Covariance Method

All field measurements used in this study are from the previously published work by Boyko, et al. [32]. Climate data for calculating reference evapotranspiration (ET_sz) were collected from the Leyendecker III weather station (32°12′21.46″N, 106°44′50.74″W, elevation 1176 m AMSL). The weather station is located approximately 620 m west of the alfalfa field. Data recorded during site maintenance were removed from daily ET_sz calculations. The American Society for Civil Engineers Standardized Reference Evapotranspiration [33] was used to calculate ET_sz because it is widely used and accepted and provides the ability to transfer crop coefficients to other geographic locations.

Actual evapotranspiration (ET_a) was measured by applying the energy balance method to data collected from an eddy covariance flux tower installed in the center of the alfalfa field (Figure 1). Bawazir, et al. [34] present the methodology used for measuring net radiation, soil heat, and sensible heat fluxes and determining latent heat as a residual of the energy balance. Net radiation (Rn) was measured using a NR-Lite (CSI, Logan, UT, USA). Soil heat flux (G) was measured using two HFT3 plates (CSI, Logan, UT, USA) in combination with a CS 616 soil moisture sensor (CSI, Logan, UT, USA) and two CAV averaging soil temperature thermocouples (CSI, Logan, UT, USA). Sensible heat (H) was measured using a CSAT3 (CSI, Logan, UT, USA) three-dimensional sonic anemometer. The equivalent depth of water in mm was calculated by dividing the latent heat flux by the latent heat of vaporization of water (2.45 MJ/kg at 20 °C) and the density of water (1000 kg/m³). An open path LICOR 7500 (LI-COR^® Biosciences, Lincoln, NE, USA) was used to directly measure latent heat from May to August as a check for energy balance closure. The fetch distance of the eddy covariance ranged from 2 m to 234 m. The mean energy balance closure was 0.96 for the growing period. See Boyko, et al. [32] for a more detailed description of field measurements and methods carried out.

2.3. Satellite Data

The Harmonized Landsat Sentinel-2 (HLS) dataset is produced to create a virtual constellation of satellites to increase temporal coverage for better monitoring of agricultural and water management among other land monitoring applications [27]. Native Sentinel-2 data have a spatial resolution of 10–20 m and Landsat has a spatial resolution of 30 m. Co-registration of the two satellites is obtained by resampling HLS Sentinel-2 data to 30 m and resampling Landsat data to a common reference grid [27]. The two satellites have similar spectral bands in regard to center wavelengths and bandwidths (

Table 3. Spectral characteristics of satellite bands prior to harmonization (nm).

		Landsat OLI	Sentinel-2
Center wavelength	Blue	482.04	492
	Green	561.41	560
	Red	654.59	665
	Near Infrared	864.47	833
	Shortwave Infrared 1	1608.86	1614
	Shortwave Infrared 2	2220.0	2190
Bandwidth	Blue	60.04	66
	Green	57.33	36
	Red	37.47	31
	Near Infrared	28.25	106
	Shortwave Infrared 1	84.7	91
	Shortwave Infrared 2	175	180

), and both satellites have 12-bit radiometric resolution. The slight differences between satellites require the data to be harmonized and delivered as surface reflectance products so that changes in the spectral responses are due to actual changes in surface reflectance and not a result of the differences between sensors and/or differences in atmospheric conditions. We utilized the HLS data version 2.0 satellite scenes which used Landsat OLI and Sentinel-2 data for the 2017 growing season. These data were acquired through the National Aeronautics and Space Administration (NASA) https://hls.gsfc.nasa.gov/ accessed on 4 January 2023.

Selection criteria were applied within the NASA website to download satellite images for use in the analysis. The selection criteria for the satellite images were acquired during the growing season between 21 March 2017 (DOY 80) and 7 December 2017 (DOY 341), cloud cover of less than 20 percent, and in path/row 33/38 for Landsat and tile T13SCR for Sentinel-2. Further sorting of imagery was performed by visual analysis and assessment of the Fmask band to ensure no clouds were over the study site. After sorting, 26 images (10 Landsat and 16 Sentinel-2) were determined to be useful for analyzing vegetation indices and alfalfa crop coefficients in the Mesilla Valley for the 2017 growing season (Appendix A). The pixels in all but four of the images used in the analysis were assessed to have low or moderate aerosol levels using the Fmask. The average days between satellite passes was 9.1 days and the minimum and maximum days were 1 day and 20 days.

2.4. Spectral Indices

A systematic selection process was used to identify potentially useful vegetation and water indices from the hundreds of spectral indices in use for various earth monitoring applications. A summary of different vegetation indices, their potential uses, advantages, and disadvantages can be found in [35,36,37]. A table of 118 vegetation indices provided by Xue and Su [35] were assessed for inclusion in this study based on whether (1) the spectral bands are available on both HLS satellites; (2) the index does not require manual input, particularly in regards to correction coefficients; and (3) they have some foundation in spectroscopy. From the list of 118 vegetation indices, we selected 16 indices (

Table 4. Equations of spectral indices selected for use in the vegetation index-based crop coefficient index (K_cVI) analysis.

Name	Equation	Reference
Atmospherically Resistant Vegetation Index	$ARVI={\displaystyle \frac{\left({\rho }_{NIR}-(2\times {\rho }_{red}\right)+{\rho }_{Blue})}{\left({\rho }_{NIR}+(2\times {\rho }_{red}\right)+{\rho }_{Blue})}}$	[38]
Enhanced Vegetation Index	$EVI=2.5{\displaystyle \frac{{\rho }_{NIR}-{\rho }_{red}}{1+{\rho }_{NIR}+6{\rho }_{red}-7.5{\rho }_{Blue}}}$	[39]
Excess Green Index	$ExG=2\times {\rho }_{green}-{\rho }_{red}-{\rho }_{Blue}$	[40]
Global Environment Monitoring Index	$\begin{array}{ll}GEMI=& \eta (1-0.25 \eta )-{\displaystyle \frac{{\rho }_{red}-0.125}{1-{\rho }_{red}}}\\ & \eta ={\displaystyle \frac{{2 \left({\rho }_{NIR}^2-{\rho }_{red}^2\right)+1.5 \rho }_{NIR}+0.5{\rho }_{red}}{{\rho }_{NIR}+{\rho }_{red}+0.5}}\end{array}$	[41]
Green NDVI	$GNDVI={\displaystyle \frac{{({\rho }_{NIR}-\rho }_{green})}{({\rho }_{NIR}+{\rho }_{green})}}$	[22]
Green Ratio Vegetation Index	$GRVI={\displaystyle \frac{{\rho }_{NIR}}{{\rho }_{green}}}$	[42]
Infrared Index	$II={\displaystyle \frac{{({\rho }_{NIR}-\rho }_{MidIR})}{({\rho }_{NIR}+{\rho }_{MidIR})}}$	[23]
Modified Soil Adjusted Vegetation Index	$MSAVI2={\displaystyle \frac{\left(1\times {\rho }_{NIR}+1-\sqrt{{(2\times {\rho }_{NIR}+1)}^2-8\times ({\rho }_{NIR}-{\rho }_{red})}\right)}{2}}$	[20]
Moisture Stress Index	$MSI={\displaystyle \frac{{\rho }_{MidIR}}{{\rho }_{NIR}}}$	[43]
Normalized Green-Red Difference Index	$NGRDI={\displaystyle \frac{{({\rho }_{green}-\rho }_{red})}{({\rho }_{green}+{\rho }_{red})}}$	[21]
Normalized Difference Vegetation Index	$NDVI={\displaystyle \frac{\left({\rho }_{NIR}-{\rho }_{red}\right)}{\left({\rho }_{NIR}+{\rho }_{red}\right)}}$	[17]
Normalized Multi-band Drought Index	$NMDI={\displaystyle \frac{{\rho }_{NIR-}\left({\rho }_{1640}-{\rho }_{2130}\right)}{{\rho }_{NIR}+{(\rho }_{1640}-{\rho }_{2130})}}$	[24]
Renormalized Difference Vegetation Index	$RDVI={\displaystyle \frac{{\rho }_{NIR}-{\rho }_{red}}{\sqrt{{\rho }_{NIR}+{\rho }_{red}}}}$	[19]
Transformed Difference Vegetation Index	$TDVI=\sqrt{0.5+\left[{\displaystyle \frac{\left({\rho }_{NIR}-{\rho }_{red}\right)}{\left({\rho }_{NIR}+{\rho }_{red}\right)}}\right]}$	[44]
Visible Atmospherically Resistant Index	$VARI={\displaystyle \frac{\left({\rho }_{green}-{\rho }_{red}\right)}{\left({\rho }_{green}+{\rho }_{red}+{\rho }_{blue}\right)}}$	[21]
Visible-band Difference Vegetation Index	$VDVI={\displaystyle \frac{\left(2\times {\rho }_{green}-{\rho }_{red}-{\rho }_{blue}\right)}{\left(2\times {\rho }_{green}+{\rho }_{red}+{\rho }_{blue}\right)}}$	[45]

). Of the indices that were excluded, 56 used spectral bands not included on Landsat satellites, at least 8 required some form of posteriori input, several indices were duplicated with different names, and some were not peer-reviewed or well-grounded in spectroscopy. It should be noted that several of the citations in [35] were incorrect or did not point to the original source of the indices. Of the 16 selected indices, seven used variations of the relationship between red and near-infrared, four incorporated shortwave infrared wavelengths, three indices used only the bands within the visible spectrum, and two used the relationship between green and near-infrared wavelengths.

2.5. Vegetation Indices-Based Crop Coefficients

Each of the 26 individual HLS images suitable for analysis was processed into 16 vegetation indices and then processed into K_cVI values. An area of interest (AOI) of the entire field was digitized into a shapefile using ArcMap version 10.8.1 and 30 cm base map imagery acquired by MAXAR (Westminster, CO, USA) on 14 November 2021 and provided as service layer by ESRI. The shapefile was reduced by a 30 m buffer around the perimeter to reduce the potential influence of edge effects on the spectral indices. Given the uniform irrigation, growth of the field, and cutting cycle, information derived from the imagery pixel values within the AOI was assumed to be representative of the field conditions. Python programming was used to extract zonal statistics of the alfalfa AOI from each vegetation index file including the count, minimum, maximum, mean, and median pixel values. A visual analysis of the histograms revealed the distribution of pixel values was skewed to the left, thus the median value was the better measure of central tendency and used in the subsequent analyses. The median pixel values of each VI from the study field were regressed using an ordinary least squares linear regression against the in situ derived K_c values (i.e., ET_a/ET_sz) to develop equations for predicting K_c from each VI referred to here as K_cVI. The sixteen linear equations were then applied to their respective vegetation index images and then multiplied by the daily ET_sz estimate to calculate ET_c for each image.

The general process for the study is outlined in Figure 2.

2.6. Statistical Analysis

Adapting the methodology in Hunsaker, et al. [9], common regression metrics were used to assess how well each linear equation predicted the K_c value. The coefficient of determination (r²) was used to measure the proportion in the K_c predicted by each regression equation. The root means square error (RMSE) was used to assess the Euclidean distance from the predicted Kc values to the field-measured K_c values, the lower values indicating lower error. p-values were used to indicate statistical significance of each regression equation. An F-test was used to determine if there was a statistical difference between linear equations produced separately using only Landsat and only Sentinel data for each VI.

The robustness of each linear regression model was assessed using two methods: (1) determining if there is a statistical difference between predicted and measured ET_c using a Wilcoxon rank-sum test, and (2) a cumulative ranking of the K_cVI model performance in terms of r². Ten different model runs were performed on the 16 different indices for a total of 160 model outputs with the data partitioned into a 60/40 split of training and testing data using a random selection function in Python—each model run was made up of different sets of randomly selected training and testing data. The Wilcoxon rank-sum test was used to test for statistically significant differences assuming non-parametric data with a 0.05 significance level. The null hypothesis (H_o) assumed no statistical differences between the field-measured and predicted ET_c and the alternative hypothesis (H_a) that there is a significant difference. The r² values for each K_cVI regression equation were assigned an ordinal ranking from 1 to 16 for each of the 10 model runs with the higher ranking assigned to the higher r² values, and were subsequently summed to determine a ranking of which models consistently performed better with the data used in this study.

The relationship between ET_c from the eddy covariance tower and the estimated ET_c using the spectral indices and the K_cVI method were assessed using correlation statistics. The mean absolute error (MAE), the mean squared error (MSE), the mean absolute percent difference (MAPD) relative to the observed mean, and relative root mean squared error (rRMSE) were determined. The MAE assesses the magnitude of error in ET_c by using the K_cVI equations when comparing the measured ET_a, the MSE measures the average squared differences between observed and predicted ET values, the MAPD provides an average of differences between predicted and observed values divided by the observed values, and rRMSE provides a measure of prediction accuracy relative to the range of values for a variable.

2.7. Comparison to OpenET

The agreement between the estimated ET_c from the 16 K_cVI models and estimated ET_a from the OpenET Ensemble model was assessed for 20 additional alfalfa fields located in the Mesilla Valley to address the lack of additional field measurements for comparison. The emerging OpenET platform provides daily, monthly, and annual estimates of ET_a for individual field polygons and at a 30 m spatial resolution grid from six remote sensing ET models and a combined Ensemble model [46]. Accuracy assessments of the OpenET models indicate the Ensemble model typically provides a high agreement with eddy covariance data for all croplands (r² = 0.81, MBE = −0.35 mm day⁻¹) [47], alfalfa (r² = 0.65, MBE = −12.2 mm month⁻¹) [48], and pecan (r² = 0.95, MBE = 7 mm month⁻¹) [49]. An additional 20 alfalfa fields were identified using the 2017 USDA Cropland Data Layer and selected to represent the variability in area and distribution throughout the valley. We applied a negative 30 m buffer to the fields to reduce the effects of edge pixel influence on the estimated values. The estimated daily ET_a Ensemble model values for each of the 20 alfalfa fields were retrieved through the OpenET Python API.

The 16 K_cVI equations were applied to the HLS data for each of the 20 fields to estimate the K_c values and were subsequently multiplied by the corresponding daily ET_sz from the Leyendecker III weather station to estimate daily ET_c. The data from all 20 fields were combined for each of the 16 K_cVI models and then assessed for agreement with the OpenET Ensemble model in terms of r², MAE, MSE, and MAPD.

3. Results and Discussion

3.1. Regression Equations for K_cVI

The linear regressions between the VIs and the Kc values from the in situ field measurements suggest that all of the VIs selected for this study have high correlation coefficients (r² between 0.67 and 0.90) for the 2017 growing season and predictions of Kc fall within 0.09 to 0.17 RMSE (

Table 5. Linear regression equations derived from vegetation indices and field-measured Kc values for alfalfa with r² and RMSE values (dimensionless).

VI	KcVI	r2	RMSE	VI	KcVI	r2	RMSE
ARVI	1.59 × ARVI + 0.54	0.72	0.16	MSI	−0.89 × MSI + 1.52	0.85	0.12
EVI	1.28 × EVI + 0.2	0.74	0.15	NDVI	1.48 × NDVI − 0.12	0.88	0.10
EXG	14.2 × EXG + 0.33	0.81	0.13	NGRDI	1.65 × NGRDI + 0.69	0.90	0.09
GEMI	1.72 × GEMI − 0.42	0.67	0.17	NMDI	2.16 × NMDI + 0.11	0.76	0.15
GNDVI	2.26 × GNDVI − 0.59	0.82	0.13	RDVI	1.77 × RDVI + 0.07	0.76	0.15
GRVI	0.11 × GRVI + 0.3	0.70	0.16	TDVI	3.16 × TDVI − 2.53	0.88	0.10
II	1.29 × II + 0.62	0.82	0.13	VARI	2.17 × VARI + 0.69	0.90	0.10
MSAVI	1.34 × MSAVI + 0.22	0.74	0.15	VDVI	−4.55 × VDVI + 1.82	0.76	0.15

). The slope and intercept for the NDVI (1.48 and −0.12) are similar to the results found in the literature. For example, Kamble, et al. [15] estimated K_c for rainfed and irrigated agriculture as 1.4571 × NDVI − 0.1725 and obtained an r² of 0.91. The linear regression equations derived by Campos, et al. [14] for estimating the basal crop coefficient (K_cb) used the soil-adjusted vegetation index (SAVI) for maize (K_cb = 1.414 × SAVI − 0.02) and soybeans (K_cb = 1.258 × SAVI − 0.006) with r² values between 0.805- and 0.868. The two best-performing Kc MAE ranged between 0.35- and 0.64-mm day⁻¹, MSE ranged between 0.20- and 0.75-mm day⁻¹, and MAPD ranged 10.0- and 16.5%. The visible atmospherically resistant index (VARI), the normalized green-red difference index (NGRDI), and the normalized difference vegetation index (NDVI) showed the highest correlation and lowest errors when compared to the measured values. Out of the seven VIs that exploit the slope of reflectance between red and near-infrared, the NDVI and the TDVI both had an r² of 0.88 and the other four equations were less than 0.76. Some of the lowest correlations were found in VIs that corrected for atmospheric and soil background (ARVI, EVI, and MSAVI). The results of an F-test between linear models created separately with Landsat and Sentinel data revealed no significant differences between the linear models of each respective VI, thus suggesting good harmonization between the two sensors (

Table A2. Statistical comparison of linear models derived separately from Landsat and Sentinel using F-test where p < 0.05 indicates a significant difference. None of the linear models showed a significant difference, which suggests good data harmonization between the two satellites.

VI	F-Statistic	p-Value	VI	F-Statistic	p-Value
ARVI	0.61	0.72	MSI	1.88	0.20
EVI	1.58	0.27	NDVI	1.67	0.25
EXG	1.69	0.24	NGRDI	−0.49	1.00
GEMI	2.27	0.14	NMDI	0.86	0.56
GNDVI	1.52	0.28	RDVI	1.41	0.32
GRVI	0.03	0.47	TDVI	2.04	0.17
II	1.10	0.44	VARI	−0.18	1.00
MSAVI	2.09	0.16	VDVI	1.12	0.43

).

The distribution of field-measured K_c was clustered into low values directly after harvesting (~0.3 to 0.5) and higher values when the alfalfa plants were fully developed (>1.0) during a period typically less than seven days after cutting (Figure 3a). Even with HLS providing a hypothetical return interval of <5 days, there were only a few opportunities during the growing season to capture imagery during early season growth and in the period between cut and canopy closure, and even fewer opportunities due to clouds. This resulted in the inclusion of only seven satellite images during the cut and rapid growth period (Figure 3b). Furthermore, the distribution can be seen on plots of VIs and measured K_c, where the data appear to have two clusters—one related to data acquired during the cut period and another where the alfalfa canopy has closed (Figure 4). Only one data point falls between these clusters.

3.2. Comparisons of Estimated and Measured ET_c

The Wilcoxon signed-rank test results of different combinations of training and testing data results suggest the linear model ET_c predictions have a closer agreement with the eddy covariance data when data represent all periods of the growth cycle. The 10 model runs of randomized data produced 160 linear models. Of the 160 models, 26 were statistically significantly different (p < 0.05) when compared to measured ET_a (

Table 6. Summary of K_cVI models that resulted in significant differences in the Wilcoxon signed-rank test between measured ET_a and predicted ET_c. for 10 model runs for each VI.

Index	Count	Index	Count
ARVI	2	MSI	1
EVI	2	NDVI	1
EXG	3	NGRDI	3
GEMI	2	NMDI	1
GNDVI	0	RDVI	2
GRVI	1	TDVI	2
II	1	VARI	3
MSAVI	2	VDVI	2

). The model runs that indicated a significant difference were caused by a random selection in the training data of either a majority of low index values (low vegetation cover) or conversely, not including enough low index values. Three models (ExG, NGRDI, and VARI) were more sensitive to changes in training data, which suggests that these models may require larger training datasets. None of the model runs were significantly different between the GNDVI and the field-measured K_c.

3.3. Differences between ET Measurements Based on Vegetation Indices

Modeled results were compared to daily ET_a measured from the eddy covariance system to assess the MAE, MSE, and MAPD (

Table 7. Statistical comparison results of predicted ET_c using the K_cVI method and observed ET_a.

VI	MAE (mm/day)	MSE (mm/day)	MAPD (%)	rRMSE (%)	VI	MAE (mm/day)	MSE (mm/day)	MAPD (%)	rRMSE (%)
ARVI	0.62	0.64	15.7	17.2	MSI	0.49	0.35	13.1	12.8
EVI	0.60	0.61	15.0	16.8	NDVI	0.41	0.26	12.0	11.0
EXG	0.51	0.42	14.0	13.8	NGRDI	0.35	0.20	10.0	9.5
GEMI	0.63	0.75	16.3	18.6	NMDI	0.57	0.51	14.4	15.3
GNDVI	0.51	0.39	13.9	13.3	RDVI	0.58	0.57	14.7	16.2
GRVI	0.64	0.60	16.5	16.6	TDVI	0.42	0.28	12.3	11.3
II	0.51	0.40	13.0	13.5	VARI	0.36	0.21	10.0	9.7
MSAVI	0.59	0.61	14.8	16.7	VDVI	0.52	0.42	16.3	13.9

). The MAE was between 0.35- and 0.64-mm day⁻¹ for all VIs, which suggests the use of any of these models for longer time periods of analysis (e.g., monthly or annual) would be appropriate. However, the MAE metric averages out the peaks in higher and lower ET predictions on the daily time scale. This is particularly important to consider during the early growth and cut periods when ET is much lower and the percentages of those errors relative to the measured values can be much higher. The MSE was between 0.20- and 0.75-mm day⁻¹ for all models with the VARI, NGRDI, and NDVI models having better accuracy than the other models. The results of the MAPD suggest the VARI, NGRDI, and NDVI models produce the smallest absolute percent difference from the observed values (<12.0%) on average. Similar results were found by French, et al. [16], where the NDVI was used to calculate K_c for wheat crops in Arizona. French et al. found a MAPD of 28 to 41 percent during the early growth and between 13 and 18 percent during mid-season growth for wheat. The rRMSE was <10% for the NGRDI and the VARI, which are generally considered excellent models; all other models were <20%, which are also considered good models [50,51].

The autocorrelation of the field-derived Kc values used in the VI regression models was based on the ratio of eddy covariance ET_a and the weather station ET_sz was not an issue impacting the K_cVI models. The results of the Wilcoxon signed-rank test, where the data were partitioned into training and testing sets, suggest that there were only significant differences between measured ET_a and K_cVI predicted ET_c when image dates did not capture the early growth stages. Therefore, we argue these comparisons are still accurate, but may not be precise. Future work would benefit from having multiple years of data from different locations.

The difference between higher and lower estimation for the ET_a values when compared to eddy covariance measurements was ±2 mm day⁻¹ for all models (Figure 5). For the NDVI, NGRDI, VARI, and VDVI, the predicted values were within approximately ± 1 mm day⁻¹. Although ±2 mm day⁻¹ might be a good estimate in some cases, it is important to consider the percentage error relative to the observed value. All models produced a higher ET_c at the first data point and nearly all models produced a lower ET_c during the cutting periods by around 1 mm day⁻¹.

The trends of ET_c derived using the K_cVI followed closely with the measured ET_a largest errors in predicting ET_c occurred in the early growing season and during cut periods (Figure 6). The lower ET predictions during the cutting periods are likely due to the spectral bands not capturing irrigation events after a cut when soil evaporation is the dominate component of ET and is cited as a downfall in spectral remote sensing approaches for measuring ET [52,53,54].

The resultant equations can be applied to spectral imagery to calculate a crop coefficient and then applied to Equation (2) to estimate daily ET_c. An example map of ET_c can be seen in Figure 7 using the NGRDI where the range of ET is between 3.3- and 8.2-mm day⁻¹. The lower ET values are mixed pixels of alfalfa and the narrow dirt access roads.

3.4. Agreement with OpenET Ensemble

The daily estimated ET_c for the 20 additional alfalfa fields derived from the K_cVI models, aside from the VDVI, demonstrated agreement with the daily estimated OpenET Ensemble model ET_a (

Table 8. Statistical comparison results of predicted ET_c from the 20 additional alfalfa fields using the K_cVI method and estimated ET_a from the OpenET Ensemble model.

VI	r2	MAE (mm/day)	MSE (mm/day)	MAPD (%)	rRMSE (%)	VI	r2	MAE (mm/day)	MSE (mm/day)	MAPD (%)	rRMSE (%)
ARVI	0.71	0.71	0.98	30.42	25.1	MSI	0.79	0.59	0.71	24.91	21.5
EVI	0.76	0.66	0.82	29.55	23.1	NDVI	0.75	0.68	0.85	26.41	23.4
EXG	0.75	0.69	0.87	26.99	23.7	NGRDI	0.75	0.68	0.84	30.95	23.3
GEMI	0.68	0.73	1.10	33.44	26.7	NMDI	0.75	0.67	0.86	34.96	23.6
GNDVI	0.71	0.73	0.99	29.65	25.3	RDVI	0.76	0.66	0.82	27.91	23.0
GRVI	0.73	0.73	0.94	34.16	24.7	TDVI	0.74	0.69	0.87	25.94	23.8
II	0.78	0.61	0.74	27.88	21.9	VARI	0.75	0.69	0.86	31.20	23.6
MSAVI	0.76	0.67	0.84	29.64	23.3	VDVI	0.28	1.19	2.46	61.87	39.9

). The r² ranged between 0.68 and 0.79 for all the models except the VDVI (r² = 0.28). The daily MAE ranged between 0.59- and 0.73-mm day⁻¹, which is similar to the values reported by Volk, et al. [47] for OpenET Ensemble compared to eddy covariance data in croplands (0.83 mm day⁻¹). The daily MSE ranged between 0.61- and 1.10 mm day⁻¹ for all models except the VDVI (2.46 mm day⁻¹). The daily MAPD ranged between 24.9% and 34.1% for all the K_cVI models except the VDVI (61.9%) compared to the OpenET Ensemble. The higher MAPD in this analysis could be due to the VI-based models being influenced by cutting events, irrigation events following cutting events, and/or the HLS data containing clouds over some of the fields. The rRMSE ranged between 21.5% and 26.7% for all models except for the VDVI, which had an rRMSE of 39.9% suggesting that all but the VDVI were fair-performing models [51]. This analysis only assesses the agreement between the K_cVI model estimated ET_c and OpenET Ensemble estimated ET_a and does not assess the accuracy of either for the 20 additional alfalfa fields. Thus, it is possible that the K_CVI estimates better reflect ET_c and the errors are from the OpenET Ensemble model estimates. Five of the six models in the OpenET Ensemble depend on thermal data from Landsat ETM+ and OLI, which have larger spans of days without satellite coverage, thus interpolation of these data could miss cutting and irrigation events that are captured by the HLS products and subsequently captured by the K_CVI estimates of ET_c.

3.5. Evaluation and Next Steps

This study demonstrated promising results for using several different K_cVI equations for predicting ET_c; however, there are several limitations. The results of this study are specific to alfalfa grown in the Mesilla Valley using the HLS dataset. The results might not be translatable to other sensors with different spectral bandwidths and center wavelengths and not calibrated to surface reflectance. Furthermore, this study used one year of data and, although some of the comparisons separated the data into training and testing sets, there is an inherent autocorrelation between the in situ data and the K_cVI-derived ET_c. We attempted to address this shortcoming by the inclusion of an analysis that assesses the agreement of the K_cVI model estimates with the OpenET Ensemble model estimates for 20 additional alfalfa fields, which provided evidence that the K_cVI approach using HLS data could fill in some of the ET data gaps at the field scale left by the lower temporal resolution of models reliant on Landsat thermal data. Future studies would benefit from having additional years of data and multiple fields with instrumentation to measure in situ ET_a.

As outlined in Pôças, et al. [55], experimental conditions such as crop type, irrigation management, and climate conditions introduce variability in empirical relationships for developing K_cVI. Although there are additional VIs that could be calculated from the addition of red-edge bands included on the sentinel satellite, these bands are not included on Landsat and, therefore, were not considered in this analysis.

In this study, there were not enough clear satellite observations during the cut and early growth periods to assess whether any of the VIs, particularly those that account for soil background, are able to reduce the error in predicted ET_c. Although clouds were not present over the study site for the image dates used, three images did have low/moderate aerosol levels and one image had high aerosol levels which can affect VI calculations, thus caution should be used when calculating VIs from HLS data. Where bare soil is present, differences in soil types across locations will likely have an impact on the regression coefficients [9,16]. Future research could address this objective by separating out imagery taken during the early growth periods and running a statistical analysis to assess whether any of the K_cVI models more accurately predict ET_c during lower vegetation cover. There could be a vegetation cover threshold where an ensemble model could switch between K_cVI models based on cover. This would require more image dates during the early growth/cut periods.

Two notable advancements are addressing these issues and creating new opportunities for operational remote sensing ET products. The relatively new OpenET web application provides estimated ET_a at the field scale at daily, monthly, and annual time steps for six ET models and an Ensemble model for agricultural areas in the western United States [46]. There is still a need within the OpenET platform to increase the satellite imagery inputs in order to reduce the interpolations between image dates—perhaps the HLS dataset can help improve the temporal coverage. Secondly, as new commercial satellite constellations with multispectral sensors become more common, there advancements in data harmonization that could lead to producing satellite based ET estimates at high spatial and temporal resolution using data such as the Planet Lab constellation of satellites or incorporating data from UAVs [56].

4. Conclusions

We used the HLS dataset to calculate 16 VIs and used linear regression to calculate crop coefficients by regressing field-measured K_c on the different VIs. All the VIs produced linear models that showed high correlations with the measured K_c values and some of the models produced ET_a errors close to ±1 mm day⁻¹. The results suggest that the HLS dataset is an important dataset for filling in the data gap with a higher temporal frequency of satellite data to improve the accuracy of satellite ET_a estimates and it can reduce the need to interpolate between missing satellite overpasses. This is particularly important for crops like alfalfa that have multiple harvests during a growing season and when missing one or two Landsat images can cause the omission of nearly an entire cutting period. The results also suggest that when crops are past the initial growth period the K_cVI approach can be used to provide accurate ET data at monthly and yearly time scales. Another interesting finding was two vegetation indices that used only spectral bands within the visible spectrum for predicting K_c produced the highest agreement with eddy covariance data. This opens the door for harmonizing other higher spatial resolution satellites or aerial sensors that only collect visible spectra and for applying similar methods for calculating K_c. This approach could be further explored for use on properly calibrated unmanned aerial systems (UAS).