Estimating Evapotranspiration of Pomegranate Trees Using Stochastic Configuration Networks (SCN) and UAV Multispectral Imagery

Evapotranspiration (ET) estimation is important in precision agriculture water management, such as evaluating soil moisture, drought monitoring, and assessing crop water stress. As a traditional method, evapotranspiration estimation using crop coefficient (Kc) has been commonly used. Since there are strong similarities between the Kc curve and the vegetation index curve, the crop coefficient Kc is usually estimated as a function of the vegetation index. Researchers have developed linear regression models for the Kc and the normalized difference vegetation index (NDVI), usually derived from satellite imagery. However, the spatial resolution of the satellite image is often insufficient for crops with clumped canopy structures, such as vines and trees. Therefore, in this article, the authors used Unmanned Aerial Vehicles (UAVs) to collect high-resolution multispectral imagery in a pomegranate orchard located at the USDA-ARS, San Joaquin Valley Agricultural Sciences Center, Parlier, CA. The Kc values were measured from a weighing lysimeter and the NDVI values were derived from UAV imagery. Then, the authors established a relationship between the NDVI and Kc by using a linear regression model and a stochastic configuration networks (SCN) model, respectively. Based on the research results, the linear regression model has an R2 of 0.975 and RMSE of 0.05. The SCN regression model has an R2 and RMSE value of 0.995 and 0.046, respectively. Compared with the linear regression model, the SCN model improved performance in predicting Kc from NDVI. Then, actual evapotranspiration was estimated and compared with lysimeter data in an experimental pomegranate orchard. The UAV imagery provided a spatial and tree-by-tree view of ET distribution.


Introduction
Evapotranspiration (ET) estimation is important in precision agriculture water management [1,2]. ET is known as the main outgoing water flux from the surface on the earth [3]. ET is a combination of two separate processes, evaporation and transpiration. Evaporation is the process whereby liquid water is converted to water vapor [4]. Then, the water vapor removes from the evaporating surface. Transpiration is the process of the vaporization of liquid water contained in plant tissues and the vapor removal to the atmosphere [4]. The following three steps constitute the current theory for transpiration. First, the conversion of liquid-phase water to vapor water causes canopy cooling from latent heat exchange. Thus, canopy temperature can be used as an indicator of ET. Second, diffusion of water vapor from inside plant stomata on the leaves to the surrounding atmosphere. Third, atmospheric air mixing by convection or diffusion transports vapor near the plant surfaces to the upper atmosphere or offsite away from the plant canopy. Usually, evaporation and transpiration occur simultaneously. There are direct and indirect methods for ET estimation. For direct methods, there are lysimeters [5] and water balance methods [6]. For indirect methods, there are energy balance methods [3], Pan evaporation methods [6,7], and remote sensing methods [8]. For energy balance methods, Bowen ratio [9,10] and eddy covariance [11] have been widely used for ET estimation.
Using crop coefficient (K c ) for ET estimation is a commonly used method for water irrigation management. The crop evapotranspiration (ET c ) is calculated by the K c approach whereby the effect of the various weather conditions are incorporated into reference ET (ET o ) and the crop characteristics into the K c [4]: The curve of K c is the crop coefficient distribution during a whole growing season. At the beginning of the growing season, K c starts increasing from a small value. When the canopy cover is full, the K c reaches a maximum around the mid-season. Then, the K c starts decreasing before the end of the growing season.
The normalized difference vegetation index (NDVI) has been widely used for vegetation monitoring, such as water stress detection [12,13], crop yield assessment [14], and ET estimation [15,16]. The NDVI is calculated by where ρ NI R is the reflectance of the near-infrared band. The parameter ρ R is the reflectance for the red waveband. NDVI is a standardized method to measure healthy vegetation.
When the NDVI has a higher value, it means the vegetation has a high level of photosynthesis. Estimating crop coefficient values using satellite-derived NDVI has been commonly used in many studies. [17][18][19]. For instance, Trout et al. [20] and Zhang et al. [21] used NDVI to estimate canopy ground cover for generating K c . Kamble et al. [17] established a relationship between NDVI and K c by linear regression model. Although satellite images can provide spatially distributed measurements, they cannot acquire useful spatio-temporal resolution imagery for precision agriculture applications [22]. The satellite overpass time is not always consistent with research requirements. For example, the Landsat 8 visible and nearinfrared image resolution is at the 30-meter level, with a 16-day revisit time. The thermal band resolution for the Landsat is at a 100-meter level. Some other satellites, such as GOES and MODIS, also have thermal sensors. The thermal imagery provided by MODIS is 500 m per pixel. The GOES has a thermal resolution of 5 km per pixel. For many agricultural applications, the revisit time and resolution are unacceptable when considering the weather conditions, such as cloud cover. The spatial resolution may also not be available for detecting the field variability [23] and is only useful for large scale studies. Although there are new satellite platforms, such as Sentinel-2, which provide a significant improvement in revisit time and multispectral capability, the timing of satellite overpass is not always synchronous with research requirements [24].
As a new remote sensing platform, researchers are more and more interested in the potential of small UAVs in precision agriculture [25][26][27][28], especially on heterogeneous crops, such as vineyard and orchards [29,30]. Compared with the satellite, UAVs can be operated at any time if the weather is within operating limitations. The satellite has a fixed flight path, UAVs are more mobile and adaptive for site selection. Mounted on the UAVs, lightweight sensors, such as RGB cameras, multispectral cameras, and thermal infrared cameras, can be used to collect high-resolution images. The higher temporal and spatial resolution images, relatively low operational costs, and nearly real-time image acquisition make the UAVs ideal for mapping and monitoring ET.
The contribution of this research was to investigate the methods for estimating K c and ET using UAV-based NDVI for an experimental pomegranate orchard. The novelty is that a regression model was established between the NDVI and K c by using the SCN algorithm, which was first proposed by the authors. The pomegranate has been widely planted in the world. The pomegranate also has drought resistance and high economic value. There is approximately 11,000 ha of pomegranate in the semi-arid and arid areas of California [21]. The spatial and temporal variability of K c and NDVI were analyzed by using the SCN model, which made tree-by-tree ET estimation becomes possible. The performance of the proposed regression model was evaluated by the data collected by the UAVs.
The rest of the paper is organized as follows. Section 2 introduces MATERIAL AND METHODS for ET estimation, such as the pomegranate study site, the UAV platform and sensors being used, UAV image processing technology, and the SCNs. Results and discussions are presented in Section 3. A simple regression model and SCN model are used to demonstrate the ET estimation method. In Section 4, concluding remarks are presented.

The UAV Platform and Multispectral Camera
In this research, the authors used a UAV platform, called "Hover" (Fig. 2). The "Hover" was equipped with a Pixhawk flight controller, GPS, telemetry antennas. It can fly over the field by waypoints mode (designed by using Mission Planner software). The lithium polymer battery has a capacity of 9500 mAh, which can support a 30-minute flight mission with cameras mounted on it. The "Hover" Fig. 2 The "Hover". The "Hover" was equipped with a Pixhawk flight controller, GPS, telemetry antennas. It can fly over the field by waypoints mode (designed by using Mission Planner software). The lithium polymer battery has a capacity of 9500 mAh, which can support a 30-minute flight mission with cameras mounted on it The Rededge M camera (MicaSense, Seattle, WA, USA) was being used for collecting the multispectral imagery, which had five different bands. The five bands are Blue, Green, Red, Near-infrared, and Red edge. The Rededge M also has a spectral resolution of 1280 × 960 pixel, with a 46 • field of view. With a Downwelling Light Sensor (DLS), which is a 5-band light sensor that connects to the camera, the Rededge M can measure the ambient light during a flight mission for the five bands. Then, the DLS can record the light information in the metadata of the images captured by the camera. After the image calibration, the information detected by the DLS can be used for correcting lighting changes during a flight, such as changes in cloud cover during a UAV flight.

UAV Image Collection and Processing
The authors used the Mission Planner to program all flight missions. The flight height was set up as 60 m. The overlapping of UAV imagery was set up as 80%, so that the UAV imagery of the pomegranate could be stitched together during image processing. A bi-weekly UAV flight schedule was suggested to collect sufficient data. If there is a UAV crash, unexpected weather conditions, hardware issues, or unknown reasons, data may not be collected successfully. If data is missed, people may have to wait for another year. Therefore, the authors flew the UAV bi-weekly over the pomegranate field at noon during the growing season in 2019 (Table 1).
To minimize the shading effect on the images, the UAVs are usually flying at noon with clear sky conditions. Because each pixel in a UAV image is a percentage of the reflected light, pixel values need to be calibrated by using a known reflectance value. Therefore, the image of a calibration board needs to be taken before and after the flight missions, servicing as the reflectance reference (Fig. 3). It is important to take pictures of the reference panel immediately before and after the flight missions because the solar angle and light intensity can change [12], which causes inaccurate experiment results. UAV images usually have higher radiometric homogeneity than aircraft or satellite images because of the lower flight altitude [31]. However, there are also special UAVs image quality problems. For Fig. 3 The image of a calibration board needs to be taken before and after the flight missions, servicing as the reflectance reference. It is important to take pictures of the reference panel immediately before and after the flight missions because the solar angle and light intensity can change [12], which causes inaccurate experiment results. UAV images usually have higher radiometric homogeneity than aircraft or satellite images because of the lower flight altitude [31]  Preselection is recommended because it can speed up the processing of large datasets. Building the dense cloud can reconstruct a more accurate surface, which can improve the quality of the final orthomosaic. Higher quality usually can result in a more accurate surface, which means a greater number of points. However, higher quality is not recommended because of longer data processing time. Medium quality is sufficient for UAVs image processing, especially for low variations field. Building Digital Elevation Model (DEM) allows generating an accurate surface, which can be used as a source for the orthomosaic generation. This will shorten the data processing time compared with Build Mesh operation because Build Mesh is usually used for a more complex surface. he source data for building DEM is the dense cloud. For the interpolation method, Extrapolated option is selected because it can generate a surface without gaps being extrapolated to the bound box sides. The default option for Interpolation is Enabled, which is not recommended because it will leave the valid elevation values only for fields that are seen from at least one aligned camera.

Stochastic Configuration Networks (SCNs)
The stochastic configuration networks (SCNs) was proposed by Wang et al. in 2017 [33]. The SCNs has a powerful capability for regression and classification analysis. Traditionally, it is quite challenging to correctly determine an appropriate architecture for a neural network so that the trained model can achieve excellent performance for both learning and generalization. Compared with the known randomized learning algorithms for neural networks, the SCNs randomly assign the input weights and biases of the hidden nodes in the light of a supervisory mechanism. Randomness plays a significant role in both exploration and exploitation. A good neural networks architecture with randomly  For example, the maximum times of random configuration T max was set as 100. The scale factor Lambdas in the activation function, which directly determined the range for the random parameters, was examined by performing different settings (0.5 -200). The tolerance was set as 0.001. For the other parameters in the SCNs model, please refer to [33] assigned weights can easily outperform a poorer architecture with finely tuned weights [34,35]. The output weights are analytically evaluated in a constructive or selective method. In contrast with the known randomized learning algorithms, such as the Randomized Radial Basis Function (RBF) Networks [36] and the Random Vector Functionallink (RVFL) [37], SCNs can provide good generalization performance at a faster speed. Concretely, there are three types of SCNs algorithms, which are SC-I, SC-II, and SC-III. SC-I algorithm uses a constructive scheme to evaluate the output weights only for the newly added hidden node [38]. All of the previously obtained output weights are kept the same. The SC-II algorithm recalculates part of the current output weights by analyzing a local least squares problem with user-defined shifting window size. The SC-III algorithm finds all the output weights together by solving a global least-squares problem. SCNs algorithms have been widely used in many areas such as image data analytics [16,39], prediction of component concentrations in sodium aluminate liquor [40], and etc. [41,42]. The linear regression can only plot the best fit line, but the data may have a non-linear pattern. Therefore, in this research, the SCNs is applied to derive better regression model than the linear regression model.

Seasonal K c and NDVI
The values of K c and NDVI were shown in Fig. 5. The values of K c were derived using (1). The ET c was recorded by the weighing lysimeter in the center of the pomegranate field. The ET o was calculated by the California Irrigation Management Information System The values of K c were derived using equation (1). The ET c was recorded by the weighing lysimeter in the center of the pomegranate field. The ET o was calculated by the California Irrigation Management Information System (CIMIS) near the pomegranate field. The NDVI was derived by image processing tools in MATLAB 2020b Fig. 6 Linear regression model for K c and NDVI. There was a strong correlation between the K c and NDVI. A simple linear regression model was built using the NDVI values derived from the UAV imagery and the K c from field measurement (CIMIS) near the pomegranate field. The NDVI was derived by image processing tools in MATLAB 2020b.
A strong correlation was shown between the K c and NDVI during the growing season in 2019. The maximum values of K c and NDVI were 1.0069 and 0.8429 on July 25 th (DOY 206), respectively. The high values of K c and NDVI showed that the trees in the lysimeter were in a wellirrigated condition. The K c increased fast at the beginning Fig. 7 The SCNs training model performance. Since the dataset of K c and NDVI was not large, in this study, SCNs model was used for building the regression model between K c and NDVI. Four out of seven days of data were used for training the SCNs regression model. All the data points were fitted very well in the trained model Fig. 8 The SCNs model evaluation performance. Three days of data were used to evaluate the trained model. The value of R 2 was 0.995. The value of RSME was 0.046. Both of them showed good performance for estimating K c by using NDVI. The variations of K c were well explained by using the NDVI from UAV images of the growing season. After the peak of the mid-season, K c started decreasing. Both K c and NDVI had very low values on October 29 th (DOY 302). The reason was that most leaves fell off the pomegranate trees after the harvest. Therefore, the data of DOY 302 was not used for the data analysis.

Regression Models for K c and NDVI
As shown in Fig. 6, there was a strong correlation between the K c and NDVI. A simple linear regression model was built using the NDVI values derived from the UAV imagery and the K c from field measurement, where 4.6666 and -2.9277 were the slope and intercept coefficients, respectively. The correlation coefficient (R 2 ) was 0.975. The root mean square error (RSME) was 0.05. With the development of machine learning technology, many neural networks have been applied for agricultural applications [30,43]. Since the dataset of K c and NDVI was not large, in this study, SCNs was used for building the regression model between K c and NDVI. Four out of seven days of data were used for training the SCNs regression model. All the data points were fitted very well in the trained model, as shown in Fig. 7. The weights and bias were shown in Table 3. The parameter L meant that there were four hidden nodes of the trained SCNs model. For the other parameters in the SCNs model, please refer to [33].
Three days of data were used to evaluate the trained model, as shown in Fig. 8. The value of R 2 was 0.995. The value of RSME was 0.046. Both of them showed good performance for estimating K c by using NDVI. The variations of K c were well explained by using the NDVI from UAV images. The trained model was used to generate the K c . For example, the spatial mapping of NDVI and K c on September 19 th were shown in Fig. 9. The spatial mapping of ET on September 19 th was shown in Fig. 10.

Conclusions
In this article, UAV flight missions were conducted to collect remote sensing multispectral images in a pomegranate orchard at USDA. Using the NDVI derived from the multispectral imagery, the authors could apply a SCNs for a regression model between NDVI and K c . The parameters of the SCNs model was shown in Table 3. The K c represented the actual growth conditions in the field. Therefore, K c could be used for estimating the ET temporally and spatially in the pomegranate field.
The simple linear regression model was K c (NDV I ) = 4.6666NDV I − 2.9277. Compared with the simple linear regression model, the SCNs model could better fit the data points in the training dataset. The simple linear regression model had R 2 and RMSE of 0.975 and 0.05, respectively. The SCNs regression model had R 2 and RMSE of 0.995 and 0.046. The SCNs showed a better performance than the linear regression model.
Although only the data of 2019 was used for analysis, the study had provided evidence that variations of NDVI from UAV imagery could be used to explain the variations of K c . In the future, the data of 2017 and 2018 will be added to train a more robust SCNs model. article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons. org/licenses/by/4.0/.