Comparative assessment of surface soil moisture simulations by the coupled wcm-iem vs. data-driven models using the Sentinel 1 and 2 satellite images

Abstract

Radar satellite imagery has been widely used to obtain soil moisture (SM) estimates of high accuracy. However, obtaining the best accuracy of SM estimates requires investigating the contribution of vegetation canopy to the accuracy of retrieved SM. We used the Integral Equation Model (IEM) coupled with the Water Cloud Model (WCM) (herein referred to as the IWCM) to estimate surface SM using radar and multi-spectral images. Accordingly, Sentinel-1 and Sentinel-2 images corresponding to calibration (2017) and validation (2016) periods were used to obtain VV-polarized radar data (where radar transmits and receives vertical polarization), Leaf Area Index, and Normalized Difference Vegetation Index at the SM measurement stations. SM measurements from eleven stations in the Walnut Gulch watershed, USA, were used as in situ data. Investigating the relationship between the simulation error on various variables revealed a dependence of error on precipitation received on the day before soil moisture measurement was carried out. Next, two data-driven models (DDMs), i.e., Support Vector Machine (SVM) and the Regression Tree (RT), were used to obtain SM estimates at stations using radar signal and vegetation indices as their input features. Accordingly, the RT model showed the best performance with validation error of 0.071 m³/m³ and 0.074 m³/m³ for the LAI and NDVI-based models, respectively. Based on the RT results, precipitation of the previous day, followed by the Julian date had the highest values of importance in predicting the the soil moisture. The RT model was consequently used to calculate regionalized estimates for the watershed due to its higher accuracy in estimating SM in the measurement stations. The results indicated the feasibility of using DDMs to obtain regionalized surface SM measurements at the watershed scale.

Appendices

Appendix 1

Fig. 10

Results of the IWCM-L model for a station 13, b station 14, c station 28, d station 34, e station 37, f station 46, g station 57, h station 69 i station 82, j station 89, k station 100

Fig. 11

Results of the IWCM-N model for a station 13, b station 14, c station 28, d station 34, e station 37, f station 46, g station 57, h station 69 i station 82, j station 89, k station 100

Table 8 Sentinel 1 acquisition dates

Table 9 Sentinel 2 acquisition dates

Appendix 2

The transition reflection coefficient (${R}_{\mathrm{tv}}$) can be computed as:

$${R}_{\mathrm{tv}}={R}_{\mathrm{v}}\left(\theta \right)+({R}_{\mathrm{vo}}-{R}_{\mathrm{v}}\left(\theta \right))(1-{S}_{\mathrm{t}}/{S}_{\mathrm{to}})$$

(26)

$${S}_{t}=\frac{{\left|{F}_{t}\right|}^{2}\sum_{n=1}^{\infty }\frac{{\left(ks\mathrm{cos}\left(\theta \right)\right)}^{2n}}{n!}{w}^{\left(n\right)}(2k\mathrm{sin}\left(\theta \right))}{\sum_{n=1}^{\infty }\frac{{\left(ks\mathrm{cos}\left(\theta \right)\right)}^{2n}}{n!}\left|{F}_{t}+\frac{{2}^{n+2}{R}_{\mathrm{vo}}}{{e}^{{(ks\mathrm{cos}\left(\theta \right))}^{2}\mathrm{cos}(\theta )}}\right|{w}^{\left(n\right)}(2k\mathrm{sin}\left(\theta \right))}$$

(27)

$$F_t=8R_{\mathrm{vo}}^2\sin^2(\theta)\left(\frac{\cos\left(\theta\right)+\sqrt{{\varepsilon_r-\sin}^2\left(\theta\right)}}{\cos\left(\theta\right)\sqrt{{\varepsilon_r-\sin}^2\left(\theta\right)}}\right)$$

(28)

$$\mathrm{lim}{S}_{t},ks\to 0:{S}_{\mathrm{to}}={\left|1+\frac{8{R}_{\mathrm{vo}}}{{F}_{t}\mathrm{cos}(\theta )}\right|}^{-2}$$

(29)

where ${R}_{\mathrm{vo}}$ is the vertical reflection coefficient at the specular angle (zero incidence angle) and other variables are similar to those in Eqs. 6 to 13. If the exponential function is selected for the ACF, the surface spectrum function takes the following form (Fung et al. 2010).

$${w}^{\left(n\right)}\left(2k\mathrm{sin}\left(\theta \right)\right)=\frac{2\pi n{l}^{2}}{{\left\{{n}^{2}+{(2kl\mathrm{sin}(\theta ))}^{2}\right\}}^{1.5}}$$

(30)

where $k$, $l$, and $\theta$ are wave number, surface correlation length, and incidence angle, respectively.