The volumetric SM content (cm³ cm⁻³) is obtained from the trapezoidal geometry of the transformed SWIR reflectance (TR_SWIR)—vegetation index feature space (Sadeghi et al., 2017) as conceptually shown in Figure 1. For this study, we replaced the previously applied NDVI with the SAVI because it is generally more sensitive to sparse vegetation cover (i.e., the initial and development stages of agricultural crops) as it corrects for the influence of soil brightness when vegetation density is low. This leads to independence of the OPTRAM parameters from soil type. The volumetric SM is calculated as:

with

and

Where i and s are the intercept and slope of the dry- and wet-edge, respectively (Figure 1), n is the soil porosity, L is the soil brightness correction factor, and R_Red, R_NIR, and R_SWIR denote the reflectances within the Red (636–673 nm), NIR (760–823 nm), and SWIR (2,110–2,290 nm) spectral bands captured with the TERRA-REF Vis-NIR and SWIR imaging systems. The average spectral frequencies of the applicable bands were used to derive R_Red, R_NIR, and R_SWIR. The value of L varies with the extent of the green vegetation cover. For dense vegetation L = 0, and for bare soil L = 1. Generally, L = 0.5 is applied as the default value. When L = 0, then the SAVI equals the NDVI.

The optical observations (i.e., Vis-NIR, and SWIR) for calculation of the SAVI, TR_SWIR, and SM (Equations 1–3) were acquired at ultrahigh spatial resolution with the TERRA-REF platform (Figure 2a). This state-of-the-art instrument located in Maricopa, Arizona consists of a 30-ton steel gantry with suspended instrument box that contains various imaging systems and sensors, including hyperspectral Vis-NIR and SWIR cameras (Figure 2b) with their specifications listed in Table 1. The robot autonomously moves along two 200-meter steel rails and continuously images the soil and crop below, providing reflectance measurements while the land surface transitions from bare soil to full plant canopy (Burnette et al., 2018).

The hyperspectral imagers (Headwall Photonics, Bolton, MA, USA) are push-broom sensors that acquire 939 (Vis-NIR) and 275 (SWIR) spectral bands within the 380–1,000 nm and 900–2,500 nm electromagnetic frequency ranges, respectively (Figure 2c). The distance between the soil surface and the hyperspectral cameras was 2-m. The Vis-NIR hyperspectral images for calculation of the SAVI were radiometrically calibrated using real-time down-welling irradiance captured with a spectral irradiance meter (Ocean Optics, Largo, FL, USA) mounted on top of the gantry, which covers the range from 337 to 823 nm. The SWIR images were calibrated with white and gray reference panels with known spectral reflectance values placed at the 2-m distance below the imaging system (Figure 3). Prior to irradiance-based calibration, the dark current was subtracted from the raw image to correct for detector artifacts. Hyperspectral bands over each domain were averaged and used for analysis.

The OPTRAM-estimated SM values were then evaluated based on soil moisture reference measurements with state-of-the-art time domain reflectometry (TDR) sensors (True TDR-315, Acclima, Inc., Meridian, ID, USA) installed at three locations within the scanner field at 2, 10, and 50 cm depths (Figure 2d). The TDR-315 sensor houses the entire measurement circuitry, including a microprocessor, within the sensor head and communicates with a datalogger for transfer of processed data via the SDI-12 protocol. The TDR-measured soil moisture data were recorded at 15-min intervals with CR1000 dataloggers (Campbell Scientific, Inc., Logan, UT, USA). The data used for this study are from an energy sorghum phenotyping experiment conducted from September 1 to October 28, 2018.

The TR_SWIR-SAVI trapezoidal space was generated via integration of five scenes collected at the initial stage (i.e., bare soil), during sorghum development, and at the final growth stage (i.e., before harvest) from the beginning of September to the end of October, 2018. The advantages of the integrated trapezoid are increased computational efficiency and independence of dry- and wet-edge parameters from the growth stage. The dry- and wet-edges and their associated parameters (Figures 1 and 4) were determined via manual fitting. This is justifiable because of the very distinct geometry exhibited by the measured TR_SWIR-SAVI relationship during the sorghum experiment (Figure 4). Furthermore, Babaeian et al. (2018) demonstrated with a thorough sensitivity analysis that the selection of the dry- and wet-edge locations does not need to be overly precise for the OPTRAM to accurately estimate surface soil moisture. It should be noted that the more homogeneous soil and vegetation cover conditions in agricultural fields in conjunction with ultrahigh spatial resolution observations alleviate problems with OPTRAM parameterization occasionally experienced for large scale, coarse-resolution satellite observations, such as oversaturation of the wet-edge or uncertainty associated with image pixels that neither belong to the soil nor to vegetation (e.g., surface water bodies, roads, or buildings) (Sadeghi et al., 2017).

To evaluate the accuracy of the OPTRAM SM estimates, they were compared with the TDR reference measurements at the three sensor nest locations. The SM contents measured with the TDR sensors throughout the growth period ranged from 0.029 to 0.465 cm³ cm⁻³. The OPTRAM SM was obtained by averaging the pixels directly covering the TDR sensor locations (i.e., an area of 30 times 50 cm). It is interesting to note that because of the ultrahigh resolution, the data volume generated for such a small area with the TERRA-REF Vis-NIR and SWIR imaging systems exceeds several gigabytes for a single scene. Figure 5 depicts the correlation between OPTRAM-determined SM and the TDR reference measurements at 2, 10, and 50 cm depths, with correlation coefficients (R) ranging from 0.66 to 0.83 and root mean square errors (RMSE) from 0.045 to 0.057 cm³ cm⁻³, which is considered reasonably accurate for remote sensing of SM (Entekhabi et al., 2014). Because of the limited penetration depth of Vis-NIR and SWIR electromagnetic radiation it was expected that the OPTRAM SM estimates better match the near-surface (2-cm) TDR reference measurements. However, there is also an obvious correlation between the OPTRAM estimates and root-zone SM (Figure 5), which contradicts the common presumption that surface soil moisture is decoupled from the root-zone (Qiu et al., 2014, 2016; Tayfur et al., 2014). Our results support findings in Sadeghi et al. (2019) and Koster et al. (2018), who established links between near-surface SM and the SM in deeper depths, and are in line with results shown in Wu and Dickinson (2004) and Ford et al. (2014), who demonstrate that root-zone SM can be accurately inferred from SWIR remote sensing observations. It is interesting to note that the OPTRAM SM estimates can be applied to directly calculate crop water consumption with a new analytical approach based on inversion of the linearized Richard's equation (Sadeghi et al., 2019). Furthermore, OPTRAM SM time series could be coupled with numerical water flow models to simulate root-zone moisture dynamics considering plant water uptake.

Figure 6 depicts the OPTRAM soil moisture distributions across sensor nest location 1 at ultrahigh spatial resolution (i.e., 2-mm pixel size) for the early stage of sorghum development (September 28), close to maturity (October 9), and short before harvest (October 18). The maps clearly indicate the OPTRAM's capability to capture soil moisture variations when parameterized with ultrahigh resolution Vis-NIR and SWIR observations, not only for single scenes, but also for various soil moisture states related to irrigation and plant development stage. This instills confidence that the proposed method is amenable for parameterization with high-resolution UAS observations, which opens new avenues for farm scale precision irrigation management to increase crop water use efficiency while alleviating the risk of environmental contamination and contributing to conservation of strained water resources in water-limited regions of the world.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.