Estimation of Seasonal Evapotranspiration for Crops in Arid Regions Using Multisource Remote Sensing Images

An accurate estimation of evapotranspiration (ET) from crops is crucial in irrigation management, crop yield assessment, and optimal allocation of water resources, particularly in arid regions. This study explores the estimation of seasonal evapotranspiration for crops using multisource remote sensing images. The proposed estimation framework starts with estimating daily evapotranspiration (ETd) values, which are then used to calculate ET estimates during the crop growing season (ETs). We incorporated Landsat images into the surface energy balance algorithm over land (SEBAL) model, and we used the trapezoidal and sinusoidal methods to estimate the seasonal ET. The trapezoidal method used multitemporal ETd images, while the sinusoidal method employs time-series Moderate Resolution Imaging Spectroradiometer (MODIS) images and multitemporal ETd images. Experiments were implemented in the agricultural lands of the Kai-Kong River Basin, Xinjiang, China. The experimental results show that the obtained ETd estimates using the SEBAL model are comparable with those from the Penman–Monteith method. The ETs obtained using the trapezoidal and sinusoidal methods both have a relatively high spatial resolution of 30 m. The sinusoidal method performs better than the trapezoidal method when using low temporal resolution Landsat images. We observed that the omission of Landsat images during the middle stage of crop growth has the greatest impact on the estimation results of ETs using the sinusoidal method. Based on the results of the study, we conclude that the proposed sinusoidal method, with integrated multisource remote sensing images, offers a useful tool in estimating seasonal evapotranspiration for crops in arid regions.


Introduction
Water is an essential resource, especially for agriculture in arid and semiarid regions [1,2]. One vital component to describe the hydrological cycle in ecological systems and to estimate water balance is evapotranspiration (ET). ET is the process by which water is transported from the earth's surface to the atmosphere by the evaporation from surfaces (soils and wet vegetation) and by the transpiration from plants through the stomata present in the plant leaves [3,4]. Crop evapotranspiration is a fundamental variable in the hydrological cycle and is thus significant for the management of irrigation and water resources [5]. However, accurately assessing ET for crops is challenging because of its high spatial and temporal variability.
Many studies have been conducted to estimate ET using methods such as sap flow [6], lysimeters [7,8], the Bowen ratio [9], and eddy covariance [10,11]. These traditional methods rely on (3) A sinusoidal method is proposed to derive ETs from ETd using multisource remote sensing images. The remainder of this paper is structured as follows. Section 2 describes the study area and datasets. Section 3 discusses the proposed methodology for ETd and ETs estimation. Section 4 presents the experimental results, followed by the discussion and conclusions in Sections 5 and 6, respectively.

Study Area
The agricultural land of the Kai-Kong River Basin in Xinjiang, China, was selected as the study area ( Figure 1). Located in Northwestern China, Xinjiang is characterized as having an extreme arid climate [56] and is considered as an important region for crop production. The agricultural lands of the Kai-Kong River Basin are important planting regions for crops in Xinjiang. The Kai-Kong River Basin is located at 40°48′-43°20′N and 82°56′-88°12′E, covering an area of around 5.7×10 4 km 2 . It includes the Kaidu River Basin in the upstream and the Kongque River Basin in the downstream. The terrain is characterized as rugged in the northwest and flat in the southeast, and the altitude ranges from 600 to 4800 meters [57]. Figure 1 shows the agricultural land of the Kai-Kong River Basin, which is delineated by a red line. The area includes 1.02×10 3 km 2 agricultural lands of Bosten Lake, 2.46×10 3 km 2 agricultural lands of the Kaidu River, and 2.79×10 3 km 2 agricultural lands of the Kongque River [58]. The study area is characterized by an arid continental climate with a long sunshine time, a large temperature difference between day and night, frequent climate fluctuations, sparse rainfall, and severe evaporation. The precipitation in this area is concentrated from April to July, with maximum precipitation at 20-40 mm. The agricultural land of the Kai-Kong River Basin provides a representative area for research on crop evapotranspiration in arid regions. The major crops in the study area are wheat, corn, cotton, chili, and pear, and the cropping period runs from March to October. The cropping system is one crop per annum, and the crop phenology includes the following: wheat and pear are cultivated and turn green in mid-March and mature in July and October; chili is planted in mid-April and harvested in late September; corn and cotton emerge in early May and mature in September and October.

Study Data
Three kinds of data were used in this study: remote sensing images, meteorological data, and ancillary data. Remote sensing data include Landsat and MODIS images acquired in 2016. The Landsat images were obtained from Landsat 7 Enhanced Thematic Mapper Plus (ETM+) and Landsat-8 Operational Land Imager and Thermal Infrared Sensor (OLI/TIRS) (Path = 143, Row = 31). In total, we collected 13 cloud-free multitemporal Landsat images during the 2016 cropping season with a level correction 1T (terrain corrected) from the USGS Earth Explorer site

Study Data
Three kinds of data were used in this study: remote sensing images, meteorological data, and ancillary data. Remote sensing data include Landsat and MODIS images acquired in 2016. The Landsat images were obtained from Landsat 7 Enhanced Thematic Mapper Plus (ETM+) and Landsat-8 Operational Land Imager and Thermal Infrared Sensor (OLI/TIRS) (Path = 143, Row = 31). In total, we collected 13 cloud-free multitemporal Landsat images during the 2016 cropping season with a level correction 1T (terrain corrected) from the USGS Earth Explorer site (https://earthexplorer.usgs.gov/). The spatial resolution of visible bands is 30 m, and the spatial resolution of the thermal infrared bands of Landsat 7 ETM+ and Landsat-8 OLI/TIRS is 60 and 100 m, respectively. Details of the Landsat images are presented in Table 1. The Landsat images were preprocessed by applying radiometric calibration, atmospheric correction, and clipping. Due to the banding phenomenon caused by the failure of the satellite scan line corrector for the Landsat 7 ETM+ images acquired after 31 May 2003, stripping processing was required for Landsat 7 ETM+ images. For the MODIS data, we downloaded 46 time-series MOD16A2 images, with the spatial and temporal resolutions of 500 m over 8 days, for 2016 from the NASA Earth Data site (http://earthdata.nasa.gov). We preprocessed the MODIS data by applying project transformation (sinusoidal projection to UTM_Zone_45N), format conversion (HDF to TIF), band extraction (ET band), real value calculation (valid_data × scale_factor), image clipping, and S-G filtering [59,60]. For the digital elevation model (DEM), we downloaded 18 ASTER Global Digital Elevation Model 2 (ASTGTM2) images with 30 m resolution from the website (http://www.gscloud.cn/), whose processing consisted of image mosaic and clipping operations.
For the meteorological dataset, we obtained data for wind speed, air temperature, average air pressure, precipitation, air humidity (vapor pressure or dew point temperature), solar radiation, and meteorological station characteristics (height of wind measurement and vegetation height). The daily meteorological dataset was downloaded from the China Meteorological Data Sharing Service Network (http://data.cma.cn/). Ancillary data, which include crop sample points, planting structure, and phenology information, were also collected for the study. A detailed description of these data can be found in our previous study [61].

Methods
The proposed framework for ET s estimation is shown in Figure 2. The SEBAL model was applied to obtain instantaneous evapotranspiration values (ET inst ) using multitemporal Landsat images, meteorological data, and DEM data, which were then converted into ET d . A trapezoidal method and a sinusoidal method were then used to upscale the ET d to the ET s . The trapezoidal method estimates ET s based only on the multitemporal ET d images derived by SEBAL, while the sinusoidal method estimates ET s using multisource remote sensing images. For the trapezoidal method, the formula for the trapezoidal area was applied to estimate ET s for crops. For the sinusoidal method, we used time-series MOD16A2 images to obtain the change in the crops' ET between phenological dates (day of year, DOY). Multitemporal ET d images were then used to calculate the ET s for crops.
Remote Sens. 2020, 12, x FOR PEER REVIEW 5 of 20 Figure 2. The proposed framework of the ETs (seasonal evapotranspiration) estimation for crops using multisource remote sensing images.

ETd Estimation Based on the SEBAL Model
SEBAL is a flux algorithm based on a complete radiation and energy balance, along with resistances for momentum, heat, and water vapor transport for every pixel [62,63]. It estimates ET through a simplified land surface energy balance method. When using SEBAL, the values for albedo, normalized difference vegetation index (NDVI), land surface temperature (TS), and emissivity from Landsat images are calculated first. Together with meteorological and DEM data, these values are used to estimate key variables in the energy balance equation, including net radiation flux (Rn), soil heat flux (G), and the sensible heat flux (H). We can obtain the latent heat flux (LE) as a residual using the equation: Based on the latent heat flux (LE), the instantaneous evapotranspiration (ETinst) is defined as follows [64][65][66]:

ET d Estimation Based on the SEBAL Model
SEBAL is a flux algorithm based on a complete radiation and energy balance, along with resistances for momentum, heat, and water vapor transport for every pixel [62,63]. It estimates ET through a simplified land surface energy balance method. When using SEBAL, the values for albedo, normalized difference vegetation index (NDVI), land surface temperature (T S ), and emissivity from Landsat images are calculated first. Together with meteorological and DEM data, these values are used to estimate key variables in the energy balance equation, including net radiation flux (Rn), soil heat flux (G), and the sensible heat flux (H). We can obtain the latent heat flux (LE) as a residual using the equation: Based on the latent heat flux (LE), the instantaneous evapotranspiration (ET inst ) is defined as follows [64][65][66]: where λ indicates the latent evaporation heat. Previous studies have shown the effectiveness of the sine method to convert ET inst to ET d using this expression [67,68]: where N is the number of daily ET hours, and t is the time interval between sunrise and data-collecting time of the Landsat satellite. This equation is inspired by the ET inst change curve on a clear day, which closely conforms to a sine relation. In this paper, we use the same method to convert ET inst into ET d .

Validation of the SEBAL Algorithm Performance
We used the Penman-Monteith (PM) model proposed by the Food and Agriculture Organization (FAO) in 1998 [69] to verify the accuracy of the ET d obtained by the SEBAL model. The actual evapotranspiration (ET c , mm·day −1 ) of the crops is calculated using the formula: where K c is the crop coefficient, and ET 0 is the reference evapotranspiration (mm·day −1 ). The ET c obtained by the PM model has generally been used to verify the accuracy of ET d estimated by other models [3,70], which is why the PM model was selected to validate the results of this study.

ET s Estimation Based on the Trapezoidal Method
We propose a trapezoidal method to estimate the ET of crops using multitemporal ET d images derived by SEBAL. Suppose that multitemporal Landsat images are acquired during the crop growing season. Let D m , m ∈ {1, . . . , n}, be the acquired time (DOY) of the m th Landsat image, and n is the total number of the acquired images. Let ET k be the ET d estimated at different periods, ET m as the ET d of Landsat image on the m th period, and ∆d as the time difference between adjacent images. The ET d change curves with the DOY of crops during the growing season are shown in Figure 3. The blue trapezoid area in Figure 3 is bounded by the ET d curve of crop 1 between two adjacent dates D m and D m+1 . The default value of ET 0 is 0, and the area of the trapezoid is then (ET m +ET m+1 ) × ∆d m /2. The calculated area is regarded as the cumulative ET for D m to D m+1 . To obtain the ET s , the areas of all trapezoids during the crop growing season were aggregated for the crops. The formula of the trapezoidal method is given in Equation (6), as follows: According to the definition, the estimation accuracy of the trapezoidal method is dependent on the intensity of the ET d time-series. Th e ET s can be derived with a high estimation accuracy when a sufficient number of Landsat images is used. The ETd change curves with the DOY of crops during the growing season are shown in Figure 3. The blue trapezoid area in Figure 3 is bounded by the ETd curve of crop 1 between two adjacent dates Dm and Dm+1. The default value of ET0 is 0, and the area of the trapezoid is then (ETm+ETm+1) × Δdm /2. The calculated area is regarded as the cumulative ET for Dm to Dm+1. To obtain the ETs, the areas of all trapezoids during the crop growing season were aggregated for the crops. The formula of the trapezoidal method is given in Equation (6), as follows:

ET s Estimation Based on the Sinusoidal Method
Acquiring over 15 Landsat images with satisfactory quality for a specific area within a year is usually difficult due to low temporal resolution and meteorological factors, such as cloud and rain. To deal with this problem, we propose a new method to estimate the ET of crops during the growing season using multisource remote sensing images. MOD16A2 images have high temporal resolution, i.e., eight days, and can reflect the change of crop ET during the year and crop growing season, while Landsat images have a relatively high spatial resolution, i.e., 30 m, and can estimate ET at a finer level. The proposed method, referred to as the sinusoidal method in this paper, estimates the ET s of crops using time-series MOD16A2 images and the ET d images produced by SEBAL. The workflow of the sinusoidal method is shown in Figure 4.
According to the definition, the estimation accuracy of the trapezoidal method is dependent on the intensity of the ETd time-series. The ETs can be derived with a high estimation accuracy when a sufficient number of Landsat images is used.

ETs Estimation Based on the Sinusoidal Method
Acquiring over 15 Landsat images with satisfactory quality for a specific area within a year is usually difficult due to low temporal resolution and meteorological factors, such as cloud and rain. To deal with this problem, we propose a new method to estimate the ET of crops during the growing season using multisource remote sensing images. MOD16A2 images have high temporal resolution, i.e., eight days, and can reflect the change of crop ET during the year and crop growing season, while Landsat images have a relatively high spatial resolution, i.e., 30 m, and can estimate ET at a finer level. The proposed method, referred to as the sinusoidal method in this paper, estimates the ETs of crops using time-series MOD16A2 images and the ETd images produced by SEBAL. The workflow of the sinusoidal method is shown in Figure 4. We first randomly selected ten sample points from each crop as the training points and the remaining sample points as testing points. We used the training points to extract the ET from 46 timeseries MOD16A2 images and obtain the ET change curve of the five main crops, which intuitively, is similar to the shape of a trigonometric curve. Based on the conversion method (ETinst to ETd) discussed We first randomly selected ten sample points from each crop as the training points and the remaining sample points as testing points. We used the training points to extract the ET from 46 time-series MOD16A2 images and obtain the ET change curve of the five main crops, which intuitively, is similar to the shape of a trigonometric curve. Based on the conversion method (ET inst to ET d ) discussed in Section 3.1, we assumed that the ET d change meets the form of a sine function (Equation (7)) within a year and is given by the expression: where y is the ET d of crops, and x represents the image acquisition date (DOY). The coefficients y 0 , A, x c , and w were then determined by the time-series ET d for every pixel. To verify our assumption, we used the testing points to extract the ET from 46 time-series (MOD16A2) images and obtained the ET values for the five crops. We applied the sine function (Equation (7)) to the ET data and obtained the y 0 , A, x c , w, and the coefficient of determination (R 2 ) for each crop. If the R 2 ∈ [0.60, 1], we considered that the pattern of the change of the ET d can be formulated as a sine function. We then applied the sine function form to the multitemporal ET d images and obtained the fitted sine function for each pixel at the same coordinate. Finally, we integrated the fitted sine function to obtain ET s for each pixel and acquired the distribution of ET s by calculating every pixel in the multitemporal ET d images.

Temporal-Spatial Variation of ET inst and ET d Obtained by the SEBAL Model
We used the SEBAL model to obtain ET inst and ET d using Landsat images ( Figure 5). The figure shows high consistency for both the ET inst and ET d , ranging between 0-1.20 mm·h −1 and 0-8.00 mm·d −1 , respectively. We then used sample points for the five main crops to extract the ET from the ET d images, and we obtained the change curve of ET d , as shown in Figure 6. where y is the ETd of crops, and x represents the image acquisition date (DOY). The coefficients y0, A, xc, and w were then determined by the time-series ETd for every pixel. To verify our assumption, we used the testing points to extract the ET from 46 time-series (MOD16A2) images and obtained the ET values for the five crops. We applied the sine function (Equation (7)) to the ET data and obtained the y0, A, xc, w, and the coefficient of determination (R 2 ) for each crop. If the R 2 ∈ [0.60, 1], we considered that the pattern of the change of the ETd can be formulated as a sine function. We then applied the sine function form to the multitemporal ETd images and obtained the fitted sine function for each pixel at the same coordinate. Finally, we integrated the fitted sine function to obtain ETs for each pixel and acquired the distribution of ETs by calculating every pixel in the multitemporal ETd images.

Temporal-Spatial Variation of ETinst and ETd Obtained by the SEBAL Model
We used the SEBAL model to obtain ETinst and ETd using Landsat images ( Figure 5). The figure shows high consistency for both the ETinst and ETd, ranging between 0-1.20 mm·h −1 and 0-8.00 mm·d −1 , respectively. We then used sample points for the five main crops to extract the ET from the ETd images, and we obtained the change curve of ETd, as shown in Figure 6.  Based on the phenological information of the five main crops in the study area, we divided the DOY into three stages: the initial stage of growth from 97 to 137, the middle stage from 137 to 249, and the late stage from 249 to 305. In Figure 5, the ETinst and ETd values gradually increased with the growth of crops in the initial stage and reached their peaks in the middle stage. The range of the ETinst and ETd values are similar to that in the initial stage but gradually decreased at the late stage. Based on the crop planting structure in the study area, the high ETinst and ETd values were concentrated in  Based on the phenological information of the five main crops in the study area, we divided the DOY into three stages: the initial stage of growth from 97 to 137, the middle stage from 137 to 249, and the late stage from 249 to 305. In Figure 5, the ETinst and ETd values gradually increased with the growth of crops in the initial stage and reached their peaks in the middle stage. The range of the ETinst and ETd values are similar to that in the initial stage but gradually decreased at the late stage. Based on the crop planting structure in the study area, the high ETinst and ETd values were concentrated in Based on the phenological information of the five main crops in the study area, we divided the DOY into three stages: the initial stage of growth from 97 to 137, the middle stage from 137 to 249, and the late stage from 249 to 305. In Figure 5, the ET inst and ET d values gradually increased with the growth of crops in the initial stage and reached their peaks in the middle stage. The range of the ET inst and ET d values are similar to that in the initial stage but gradually decreased at the late stage. Based on the crop planting structure in the study area, the high ET inst and ET d values were concentrated in the pear fields, while the low values were concentrated in the cotton fields. Wheat was the first to be planted and the earliest to mature. The ET d associated with wheat started to increase on DOY 79 and began to decrease on DOY 177 (see Figure 6). Pear had the longest growing period, which was sown the earliest and was the last to mature. The ET d of pear started to increase on DOY 97 and had the slowest rate of decrease among the five main crops. Chili was sown after wheat and pear, which was then followed by corn and cotton. The ET d of chili started to increase on DOY 105 while the ET d of corn and cotton started to rise on DOY 113.

Accuracy Assessment of ET d Obtained by the SEBAL Model
In this study, we referred to existing studies to obtain the crop coefficients of cotton for accuracy assessment because of the difficulty in the acquisition of field data of K c . Cotton is the most widely planted crop in Xinjiang. Most of the related studies focused on cotton but few on the derivation of crop coefficients for other crops. It is therefore hard to obtain the validation data of other crops for the accuracy assessment. Here, we referred to the K c of cotton from related studies and used the FAO model to verify the accuracy of ET d derived from the SEBAL model. We estimated ET c using meteorological data and the crop coefficient (K c ) for cotton, where the K c of cotton was provided by [71]. The estimation accuracy of the SEBAL model is defined as 1-(|ET c -ET d |/ET c ). Accuracy verification for cotton's ET d was obtained using the SEBAL model, as summarized in Table 2. This table shows that the difference between the ET d obtained using the SEBAL model and the actual evapotranspiration (ET c ) derived using the PM model was within one mm·day −1 , and the accuracy of ET d was more than 80%.

Validation Results of the Sinusoidal Method
We used the testing points to extract the ET from 46 time-series MOD16A2 images and obtain the ET values for the five main crops. We also used the MOD16A2 images covering the crop growing season to extract the ET values during the crop growth period based on crop phenology. We then applied the sine function (Equation (7)) to obtain the ET change curves for the entire year (Figure 7a) and the growing season (Figure 7b). The function fitting formula and the coefficient of determination (R 2 ) for each crop are shown in Table 3. The results show that the coefficients of determination (R 2 ) for the main crops during the entire year are greater than 0.80, while the R 2 values of the fitting functions during the crop growing season were over 0.85 except for cotton in both cases. The sinusoidal function of cotton had low fitting accuracy, and the shape of the fitted curve was different from other crops. This is mainly due to some missing pixels in the cotton region of the MODIS images, which resulted from the low image quality. When using the sample points of cotton to extract ET values from the time-series MOD16A2 images, there were about 47% null values in the missing pixels. These missing pixels may affect the accuracy of function fitting for cotton.
The results show that the coefficients of determination (R 2 ) for the main crops during the entire year are greater than 0.80, while the R 2 values of the fitting functions during the crop growing season were over 0.85 except for cotton in both cases. The sinusoidal function of cotton had low fitting accuracy, and the shape of the fitted curve was different from other crops. This is mainly due to some missing pixels in the cotton region of the MODIS images, which resulted from the low image quality. When using the sample points of cotton to extract ET values from the time-series MOD16A2 images, there were about 47% null values in the missing pixels. These missing pixels may affect the accuracy of function fitting for cotton.

Distribution of ET during Crop Growing Season
The use of the trapezoidal method in estimating ETs is dependent on the date of acquisition (DOY) of the Landsat images and requires that the estimation interval is discrete. In contrast, the

Distribution of ET during Crop Growing Season
The use of the trapezoidal method in estimating ET s is dependent on the date of acquisition (DOY) of the Landsat images and requires that the estimation interval is discrete. In contrast, the sinusoidal method is not constrained by the image acquisition date and has the advantage of continuous estimation interval. In this study, we designed three experiments to test the estimation results using the trapezoidal and sinusoidal methods. To estimate the ET s for five main crops, we used the ET d images covering the growth period of each crop to estimate the ET s based on their different phenological information. In Experiments A and B, the estimation intervals were set up using similar acquisition dates and crop phenology to compare the ET s results using the two methods. The discrete estimation intervals (DOY) of the trapezoidal method were set as follows: wheat (97, 105, 113, 137, 153, 177 105, 113, 137, 153,  177, 209, 217, 249, 265, 281, 289, 305). The distribution of ET s by the trapezoidal method is shown in Figure 8a. For the sinusoidal method, the continuous estimation intervals were set as follows: wheat (97,281) corn (113,281) cotton (113,305) chili (105,281) and pear (97,305) The spatial distribution of ET s is shown in Figure 8b. In Experiment C, we changed the estimation intervals from Experiment B based on the growth period mentioned in Section 4.3. This was to evaluate the influence of the estimation interval on the ET s estimates from the sinusoidal method. The estimation intervals were set as follows: wheat (81,281) corn (121,281), cotton (121,313) chili (105,281) and pear (81,313) The distribution of ET s is shown in Figure 8c. The calculation process of ET s was implemented through Interactive Data Language (IDL) programming, and the frequency distribution of ET s is shown in Figure 9.
sinusoidal method is not constrained by the image acquisition date and has the advantage of continuous estimation interval. In this study, we designed three experiments to test the estimation results using the trapezoidal and sinusoidal methods. To estimate the ETs for five main crops, we used the ETd images covering the growth period of each crop to estimate the ETs based on their different phenological information. In Experiments A and B, the estimation intervals were set up using similar acquisition dates and crop phenology to compare the ETs results using the two methods. The discrete estimation intervals (DOY) of the trapezoidal method were set as follows: wheat ( 105, 113, 137, 153, 177, 209, 217, 249, 265, 281, 289, 305). The distribution of ETs by the trapezoidal method is shown in Figure 8a. For the sinusoidal method, the continuous estimation intervals were set as follows: wheat (97,281) corn (113,281) cotton (113,305) chili (105,281) and pear (97,305) The spatial distribution of ETs is shown in Figure 8b. In Experiment C, we changed the estimation intervals from Experiment B based on the growth period mentioned in Section 4.3. This was to evaluate the influence of the estimation interval on the ETs estimates from the sinusoidal method. The estimation intervals were set as follows: wheat (81,281) corn (121,281), cotton (121,313) chili (105,281) and pear (81,313) The distribution of ETs is shown in Figure 8c. The calculation process of ETs was implemented through Interactive Data Language (IDL) programming, and the frequency distribution of ETs is shown in Figure 9.  The distribution shape of the ETs obtained by the trapezoidal method was consistent with that of the sinusoidal method, as shown in Figures 8 and 9. In both methods, ETs values in pear fields were found with relatively high values, mainly because it had the longest growing period. There were some noticeable differences between the ETs obtained from the trapezoidal and sinusoidal methods. Under the same estimation intervals, the ETs estimates from the trapezoidal method are higher than that of the sinusoidal method, as presented in Figure 8a,b. Based on the results of Experiments B and C, the ETs estimates change when the estimation intervals are modified. When estimation intervals are set based on the crop phenology, more accurate ETs estimates can be obtained. sinusoidal method is not constrained by the image acquisition date and has the advantage of continuous estimation interval. In this study, we designed three experiments to test the estimation results using the trapezoidal and sinusoidal methods. To estimate the ETs for five main crops, we used the ETd images covering the growth period of each crop to estimate the ETs based on their different phenological information. In Experiments A and B, the estimation intervals were set up using similar acquisition dates and crop phenology to compare the ETs results using the two methods. The discrete estimation intervals (DOY) of the trapezoidal method were set as follows: wheat (97, 105,  113, 137, 153, 177, 209, 217, 249, 265, 281), corn (113, 137, 153, 177, 209, 217, 249, 265, 281), cotton (113,  137, 153, 177, 209, 217, 249, 265, 281, 289, 305), chili (105, 113, 137, 153, 177, 209, 217, 249, 265, 281), and pear (97, 105, 113, 137, 153, 177, 209, 217, 249, 265, 281, 289, 305). The distribution of ETs by the trapezoidal method is shown in Figure 8a. For the sinusoidal method, the continuous estimation intervals were set as follows: wheat (97,281) corn (113,281) cotton (113,305) chili (105,281) and pear (97,305) The spatial distribution of ETs is shown in Figure 8b. In Experiment C, we changed the estimation intervals from Experiment B based on the growth period mentioned in Section 4.3. This was to evaluate the influence of the estimation interval on the ETs estimates from the sinusoidal method. The estimation intervals were set as follows: wheat (81,281) corn (121,281), cotton (121,313) chili (105,281) and pear (81,313) The distribution of ETs is shown in Figure 8c. The calculation process of ETs was implemented through Interactive Data Language (IDL) programming, and the frequency distribution of ETs is shown in Figure 9.  The distribution shape of the ETs obtained by the trapezoidal method was consistent with that of the sinusoidal method, as shown in Figures 8 and 9. In both methods, ETs values in pear fields were found with relatively high values, mainly because it had the longest growing period. There were some noticeable differences between the ETs obtained from the trapezoidal and sinusoidal methods. Under the same estimation intervals, the ETs estimates from the trapezoidal method are higher than that of the sinusoidal method, as presented in Figure 8a,b. Based on the results of Experiments B and C, the ETs estimates change when the estimation intervals are modified. When estimation intervals are set based on the crop phenology, more accurate ETs estimates can be obtained. The distribution shape of the ET s obtained by the trapezoidal method was consistent with that of the sinusoidal method, as shown in Figures 8 and 9. In both methods, ET s values in pear fields were found with relatively high values, mainly because it had the longest growing period. There were some noticeable differences between the ET s obtained from the trapezoidal and sinusoidal methods. Under the same estimation intervals, the ET s estimates from the trapezoidal method are higher than that of the sinusoidal method, as presented in Figure 8a,b. Based on the results of Experiments B and C, the ET s estimates change when the estimation intervals are modified. When estimation intervals are set based on the crop phenology, more accurate ET s estimates can be obtained. Figure 10 presents the box plots of ET s values for wheat, corn, cotton, chili, and pear, while the average ET s for the five crops are shown in Table 4. The results show pear had the highest evapotranspiration during the growing season, followed by chili. The ET s of wheat, corn, and cotton were found to be similar. Under the same estimation interval, the ET s estimates derived using the trapezoidal method were higher than those obtained using the sinusoidal method. Comparing the average ET s values from Experiments B and C, the change in the estimation interval resulted in different Remote Sens. 2020, 12, 2398 13 of 20 ET s estimates using the sinusoidal method. For wheat, the estimation interval expanded from (97,281) in Experiment B to (81,281) in Experiment C, and its average ET s increased from 634.57 to 660.18 mm. Similarly, the estimation interval for pear was extended from (97,305) to (81,313), and its average ET s increased from 891 to 943.81 mm. For corn, the contraction of the estimation interval by eight days, from (113,281) to (121,281), caused a slight decrease in the average ET s from 645.53 to 641.43 mm. For chili, the estimation interval in Experiments B and C was identical, and the average ET s were almost the same. Figure 10 presents the box plots of ETs values for wheat, corn, cotton, chili, and pear, while the average ETs for the five crops are shown in Table 4. The results show pear had the highest evapotranspiration during the growing season, followed by chili. The ETs of wheat, corn, and cotton were found to be similar. Under the same estimation interval, the ETs estimates derived using the trapezoidal method were higher than those obtained using the sinusoidal method. Comparing the average ETs values from Experiments B and C, the change in the estimation interval resulted in different ETs estimates using the sinusoidal method. For wheat, the estimation interval expanded from (97,281) in Experiment B to (81,281) in Experiment C, and its average ETs increased from 634.57 to 660.18 mm. Similarly, the estimation interval for pear was extended from (97,305) to (81,313), and its average ETs increased from 891 to 943.81 mm. For corn, the contraction of the estimation interval by eight days, from (113,281) to (121,281), caused a slight decrease in the average ETs from 645.53 to 641.43 mm. For chili, the estimation interval in Experiments B and C was identical, and the average ETs were almost the same.

Performance of the Proposed Methods for Different Acquisition Frequency of Landsat Images
Obtaining time-intensive Landsat images is often challenging for areas with high precipitation and frequent cloud cover. To explore the impact of missing images at various stages of growth on the accuracy of ETs estimates, the trapezoidal and sinusoidal methods proposed in this paper were used to estimate ETs using different combinations of multitemporal Landsat images. The experimental design is shown in Table 5. Three

Performance of the Proposed Methods for Different Acquisition Frequency of Landsat Images
Obtaining time-intensive Landsat images is often challenging for areas with high precipitation and frequent cloud cover. To explore the impact of missing images at various stages of growth on the accuracy of ET s estimates, the trapezoidal and sinusoidal methods proposed in this paper were used to estimate ET s using different combinations of multitemporal Landsat images. The experimental design is shown in Table 5.
Three . We used a similar method to set estimation intervals for other crops in the three experiments. The estimation interval is continuous for the sinusoidal method, and the setting of the integration interval was the same as that in Section 4.4 Experiment C. Figure 11a shows the distributions of ET s for the three experiments, while the frequency distributions are presented in Figure 11b.
√ refers to images that need to be involved in the estimation.
Remote Sens. 2020, 12, x FOR PEER REVIEW 14 of 20 The estimation interval is continuous for the sinusoidal method, and the setting of the integration interval was the same as that in Section 4.4 Experiment C. Figure 11a shows the distributions of ETs for the three experiments, while the frequency distributions are presented in Figure 11b. Note: √ refers to images that need to be involved in the estimation.  The tests with excluded images showed lower ET s results compared with the estimates using all 13 Landsat images (see Figure 8a) using the trapezoidal method, whereas higher ET s results were found using the sinusoidal method compared with the estimates using all 13 Landsat images (see Figure 8c). Results showed that the frequency of ET s estimated using 9 Landsat images had a significant difference from the frequency using 13 Landsat images (Figure 9) for the trapezoidal method. The frequency of estimated ET s , however, was similar for the sinusoidal method when using either 13 or 9 Landsat images covering the early stage (Test 1) and final stage (Test 3) of crop growth period. This indicates that the sinusoidal method performed better than the trapezoidal method when using Landsat images with low temporal resolution. Moreover, in Test 2 using the sinusoidal method, the ET s of wheat, corn, and chili were higher, as indicated by vast areas of land shown in orange and red (Figure 11a). This suggests that the effect of missing images at the middle stage of crop growth on ET s estimation is more significant than that of missing images at the early or final stages.

Discussion
In this study, we investigated the estimation of seasonal evapotranspiration for crops in the arid region using multisource remote sensing images. We applied the SEBAL model to estimate the ET d and proposed a trapezoidal method and a sinusoidal method to estimate evapotranspiration of crops during the growing season. We found that the estimation results from the SEBAL model using Landsat images can reasonably reflect the ET d of cotton in the study area. We also learned that the sinusoidal method performed better than the trapezoidal method when using Landsat images with low temporal resolution. When we tried excluding images in the analysis, we found that the omission of images during the middle stage of crop growth has the greatest impact on the estimation results of ET s using the sinusoidal method. Based on these results, we found that the sinusoidal method integrated with multisource remote sensing images offers a useful tool to estimate ET s with a spatial resolution of 30 m.
The change of ET d is related to the stages of growth and phenology of the crops (see Figure 6). In the initial stage of growth, while the crops grow fast, the ET d steadily increases. In the middle stage, when the crops reach their maximum growth, the ET d reaches its peak. In the late stage, the crops mature and are harvested, resulting in the decrease of ET d values. Estimated ET values of cotton derived from the SEBAL model were close to the actual ET values obtained using the Penman-Monteith model (see Table 2). This means that the results derived from the SEBAL model were able to properly estimate the ET d of cotton in the agricultural lands of the Kai-Kong River Basin. However, this study validated the accuracy of the ET d that is only based on one crop due to the lack of K c data for other crops. Future research can be conducted to further assess the estimation accuracy of the SEBAL model by using the crops coefficients for other crops. In addition, we used the Gapfill extension tool implemented in the ENVI software to deal with the stripping errors of Landsat 7 ETM+ images. Nevertheless, some error pixels still exist in the strips. Since these pixels only account for a small portion (i.e., less than 10%) of the total image pixels, the estimated ET d and ET s might be influenced only slightly by stripping errors.
The actual ET d is generally difficult to measure due to the high spatial and temporal variability. During the crop growing season, obtaining field measurements of evapotranspiration is often highly problematic. In the absence of actual measurements, previous studies validated their ET d estimates by comparing them with the data provided in the literature [72]. Similarly, we also used the results from related studies to verify the accuracy of our ET s estimates, due to the lack of actual field data. Previous studies showed that the average annual water requirement for cotton was 679.00 mm in the Tarim River Basin in Xinjiang from 1989 to 2010, and the average annual effective rainfall was 63.00 mm [73]. Thus, the average annual evapotranspiration for cotton is about 743.00 mm in the Tarim River Basin, which is composed of nine river systems, including the Kai-Kong River Basin. The average annual water requirement for cotton in the Kai-Kong River Basin ranges from 555.70 to 810.20 mm from 1963 to 2012 in another research [74], where the average annual evapotranspiration was about 618.70-873.20 mm. The estimated ET s of cotton were 725.18, 638.52, and 690.61 mm all within the range, indicating that the estimated results are reasonable. Future work can be conducted to further evaluate the accuracy of the proposed methods using actual measurements from lysimeters.
In this paper, we used 13 Landsat images to estimate ET s , and we achieved good results via both the trapezoidal and sinusoidal methods. To evaluate the performance of the proposed methods for the different acquisition frequencies of the Landsat images, we designed three sets of experiments that excluded images in the early stage, the middle stage, and the final stage of crop growth. The results indicate that the trapezoidal method is suitable when using Landsat images with high temporal resolution, while the sinusoidal method is suitable when using Landsat images with low temporal resolution. Furthermore, the middle stage of crop growth is an important integral component of ET estimation for the sinusoidal method. When obtaining time-intensive Landsat images is difficult, the sinusoidal method can still be used to estimate ET s even with the absence of some images in the early or final stages of the crop growing season. The sinusoidal method, integrated with multisource remote sensing images, offers a useful tool to estimate ET s with a spatial resolution of 30 m for crops in the study area. Moreover, we used the sine function to fit the time-series ET data, extracted from MOD16A2 images, mainly inspired by the method of extending ET inst to ET d estimates in this paper. In future endeavors, we will apply the polynomial function and other functional forms to the time-series ET data, and we will compare the fitting accuracy of the sine function.
Compared with other methods for estimating ET s , the main advantage of the proposed sinusoidal method is that it estimates ET s for crops using remote sensing images only covering the crop growth period within one year. In this paper, we applied the sinusoidal method to estimate the ET s in the arid region of the agricultural land of the Kai-Kong River Basin in Xinjiang. This method also has the potential to be applied in semiarid or temperate regions. The ET d derived from the SEBAL serves as an input for the estimation of ET s by the sinusoidal method. Since the SEBAL has been widely used in arid and semiarid regions, as well as temperate regions [75], we believe that the sinusoidal model can also be used to estimate ET s in semiarid and temperate regions based on the multitemporal ET d images derived from the SEBAL model and time-series of MOD16A2 images. Nonetheless, future research can be conducted to further test the applicability of the sinusoidal method in these regions. In addition, the spatial resolution of the ET s obtained for crops depends on the resolution of the input of multitemporal ET d images, i.e., 30 m resolution in this paper. Theoretically, the proposed method can also be used to obtain ET s with different resolutions when using ET d images with different resolutions, leading to our future work.

Conclusions
This study investigated the estimation of seasonal evapotranspiration for crops in an arid region using multisource remote sensing images. We applied the SEBAL model to estimate the ET d in the agricultural lands of the Kai-Kong River Basin, Xinjiang, China. We proposed a trapezoidal and a sinusoidal method to upscale ET d values to ET s . Based on the results of the study, we conclude the following: (1) The SEBAL model is effective in estimating the ET d of cotton using Landsat images in the agricultural lands of the Kai-Kong River Basin, Xinjiang, China. (2) Compared with the trapezoidal method, the sinusoidal method can obtain more accurate ET s when using Landsat images with low temporal resolution.