# Soil Moisture Estimates in a Grass Field Using Sentinel-1 Radar Data and an Assimilation Approach

^{*}

## Abstract

**:**

## 1. Introduction

- -
- To test the potential of Sentinel 1 for soil moisture estimation in a grass field characterized by typical Mediterranean water-limited conditions;
- -
- To compare and revise some common retrieval models for soil moisture estimation from Sentinel 1 data, proposing a simplified and robust solution to account for vegetation attenuation effects on radar backscattering using simultaneous Sentinel 2 optical data;
- -
- To develop and test an operational approach to assimilate Sentinel 1 observations in a land surface model, to demonstrate the potential of the use of the new satellite sensors in soil moisture predictions in a grass field.

## 2. Materials and Methods

#### 2.1. Sardinian Case Study

^{3}and a porosity of 53% [17]. The grass root density was 0.5–1.0 kg/m

^{3}.

^{3}m

^{−3}) near the probes. Micrometeorological observations from 2003 onwards are also available for the Orroli site [17,47].

^{3}, and a porosity of 45%. This secondary case study provided the opportunity to further validate the proposed method for soil moisture estimation from Sentinel 1 data.

#### 2.2. Satellite Data

^{0}

_{vv}backscattering coefficients from S1A and S1b images were acquired.

#### 2.3. Methods for Soil Moisture Retrieval from Sentinel 1 Data

^{0}

_{vv}directly, while the Dubois et al. [27] and Fung et al. [23] methods compute the ε dielectric constant from σ

^{0}

_{vv}, so that a further step is needed to estimate θ from ε. To relate θ with ε through the Γ operator, we used the common Topp et al. [76] equation [36,41,77]:

#### 2.3.1. The Revised Change Detection Method

^{0}

_{dry}) and maximum (σ

^{0}

_{wet}) backscatter values observed over the investigated period; these are considered to be equivalent to the dry and wet soil references, respectively [5]. The method’s assumption is that factors influencing the radar backscatter signal vary over time, with vegetation and surface roughness affecting long-term changes in σ

^{0}

_{vv}, whereas short-term variations of backscattering are associated with moisture variations. The high temporal resolution of Sentinel-1 SAR time series is a precondition for the use of the method. We revised the Urban et al. [5] method:

_{min}) and a maximum (the saturated soil moisture condition, θ

_{s}) amount of soil moisture, which were characteristics of the soil type, and could be determined from the observed soil moisture; σ

^{0}

_{dry}and σ

^{0}

_{wet}were estimated from the lowest and the highest backscatter values observed over the investigated period, respectively [5]. Hereafter, we indicated with “CD” the revised change detection method.

#### 2.3.2. The Semi-Empirical Model of Dubois et al. 1995

^{0}

_{vv}radar observations, knowing surface roughness and the specific radar configuration parameters (wavelength and incidence angle). While radar configuration parameters were known, σ was undetermined.

^{0}

_{vv}from ε we estimated σ by inverting (3) at each satellite pass. In this way, the variability of σ with grass growth was investigated. We hereafter refer to the Dubois et al. [27] model as “DU”.

#### 2.3.3. The Physical Model of Fung et al., 1992

_{z}is equal to k cos β, and k

_{x}is equal to k sin β. The term ${I}_{vv}^{n}$ is given:

_{v}is the surface reflection coefficient given by the Fresnel reflection equation as a function of the local incident angle and the dielectric constant based on the polarization sensor, and ${W}^{n}\left(-2{k}_{x},0\right)$ is the Fourier transform of the nth power of the surface autocorrelation function, which is related to CL by an exponential distribution.

^{0}

_{vv}observations, Equation (4) (together with (5)–(7)) needs to be inverted, and two parameters, σ and CL, need to be defined. Usually, prescribed or field estimated values of σ and CL are used, assuming that they are constant over time. When field soil moisture observations are available, Equation (4) can be used in inverse mode to estimate σ and CL for each satellite pass, using simultaneous radar observations. Indeed, from θ measured in the field, a “measured” ε dielectric constant can be derived inverting (1), and ε can be used in (4), to obtain σ and CL from σ

^{0}

_{vv}observations. However, since two parameters are unknown, two equations are needed. Sentinel 1 provided two daily passes (S1A and S1B), so that two σ

^{0}

_{vv}were available daily, and two Equation (4) could be used. Indeed, assuming that the soil moisture measured at the field remained approximately constant throughout the day, the system of two Equation (4) could be solved to estimate the two unknown parameters at each satellite pass. We investigated the time variabilities of σ and CL with grass growth at the field site, relating them to simultaneous NDVI observations.

#### 2.3.4. Removal of Grass Cover Contribution from Radar Backscattering

_{veg}) and the soil (σ°

_{soil}), and the two way attenuation of the vegetation layer (τ

^{2}). For a given incidence angle, the backscattering is expressed as:

_{1}and W

_{2}are vegetation descriptors, which we assumed to be equal to the NDVI following Baghdadi et al. [50], and A and B are fitted parameters of the model that depend on the vegetation descriptors. To apply the WCM with known A and B, we computed ${\sigma}_{veg}^{0}$ and ${\tau}^{2}$ from (9) and (10) using Sentinel 2-based observations of the NDVI, and derived ${\sigma}_{soil}^{0}$ from (8) using ${\sigma}_{vv}^{0}$ from Sentinel 1. Soil moisture was estimated from ${\sigma}_{soil}^{0}$ using the three soil moisture retrieval models (CD, DU, and FU) assuming model parameters were constant over time.

^{0}

_{vv}observations of S1A and S1B Sentinel, and estimated the σ and CL for each satellite pass. Because simultaneous NDVI data were available from satellite observations, we related the estimated σ and CL with the NDVI to obtain the σ

_{F}(NDVI) and CL

_{F}(NDVI) relationships. In this way, the FU model parameters varied with NDVI, and the σ

_{F}(NDVI) and CL

_{F}(NDVI) relationships were used in (4) to retrieve soil moisture information.

_{D}(NDVI) relationship. In this way, using the DU model, σ varied with the NDVI using the proposed σ

_{D}(NDVI) relationship, and σ

_{D}(NDVI) was used in (3) with simultaneous ${\sigma}_{vv}^{0}$ Sentinel 1 observations to derive the dielectric constant. The soil moisture was estimated from the dielectric constant using (1).

#### 2.4. Data Assimilation Approach

#### 2.4.1. The Land Surface Model

_{rz}is the root zone depth, I is the infiltration rate, q

_{D}is the rate of drainage out of the bottom of the root zone, which is estimated using the unit head gradient assumption [78,81] E

_{bs}is the rate of bare soil evaporation, and E

_{t}is the rate of transpiration. As in the original Noilhan and Planton [79] model, the throughfall rate was modeled through a balance equation of the intercepted water by the canopy reservoir (its capacity is a function of the LAI), which produces throughfall when the reservoir is saturated. The infiltration model is based on the Philip’s infiltration equation. The evapotranspiration components were estimated using the Penman-Monteith equation ([82], p. 224), with aerodynamic resistances estimated as a function of wind velocity through the transfer coefficient for water vapor according to the Monin-Obukhov similarity theory and accounting for atmosphere stability [83]. The potential evaporation (PE) was estimated using the Penman equation ([82]). Details are provided in Montaldo and Albertson [78] and Montaldo et al. [17].

#### 2.4.2. The Assimilation Approach Using the EnKF

_{j}

_{e}, with N

_{e}the size of the ensemble) model predictions is propagated in parallel using (13). Each ensemble member is updated separately using the $\overrightarrow{\delta}\left({t}_{j}\right)$ observation and the diagnosed state error covariance $\overrightarrow{{P}^{-}}\left({t}_{j}\right)$ (e.g., Ref. [66], Equation (6b)). The superscript ‘−’ will be used to indicate the modeled state variable value before the updating, and the superscript ‘+’ for the value after the updating at time t

_{j}. The optimal updating is given by (Reichle et al., 2002)

_{s}), the minimum stomatal resistance (r

_{s,min}), and the limiting soil moisture of grass (θ

_{lim}). The ensemble of soil moisture initial values was generated by altering a particular value of soil moisture through the addition of a normally distributed perturbation with mean zero and SD

_{θ}standard deviation. At each time step, the ensemble of precipitation was generated by multiplying the recorded precipitation value by a normally distributed random variable. An ensemble of saturated hydraulic conductivity values (${k}_{s}^{l}$) was generated as being log

_{10}normally distributed with mean of $log({\widehat{k}}_{s})$ (indicating with ${\widehat{k}}_{s}$ the base (i.e., best guess) value of the ${k}_{s}^{l}$ ensemble) and the standard deviation of SD

_{logks}. An ensemble of minimum stomatal resistance (${r}_{s,min}^{l}$) was generated as being normally distributed with mean of ${\widehat{r}}_{s,min}$ and standard deviation of SD

_{rsmin}. Finally, an ensemble of limiting soil moisture values (${\theta}_{lim}^{l}$) was generated as being normally distributed with mean of ${\widehat{\theta}}_{lim}$ and standard deviation of SD

_{θlim}.

## 3. Results

#### 3.1. Soil Moisture Estimation from Radar

^{0}

_{dry}= −16 dB, σ

^{0}

_{wet}= −9 dB, θ

_{min}= 0.05, θ

_{s}= 0.53), soil moisture was poorly estimated during the 2016 and 2017 dry seasons, with θ being higher (>0.14) than observed, especially in the summer of 2016 (Figure 3), when the effect of grass was not removed. In the summer of 2017, the estimated θ reached the lowest values only in mid-June, while the observed θ was already ~0.1 in May. The θ estimates were more reasonable in the spring and summer of 2018 when soil moisture was mainly wet, even though θ estimates could not follow the steep shifts of the observed θ (Figure 3). The effects of grass cover were not sufficiently removed from the radar signal using the WCM (fitted parameter values: A = 0.05 and B = 0.5) with the CD method (Figure 3). In 2017, θ was estimated to be slightly better (rmse = 0.09, R

^{2}= 0.53, and p < 0.01, slope of the regression line = 0.63), while θ was poorly estimated for the other two observed years (rmse = 0.09, R

^{2}= 0.38, and p < 0.01, slope of the regression line = 0.46 in 2016; rmse = 0.12, R

^{2}= 0.11, and p > 0.1, slope of the regression line = 0.20 in 2018, Table 1).

_{D}(NDVI), considering the 2017 growing–dying period of grass only (Figure 4b). In March, σ started out low with the highest NDVI (up to 0.7 cm), then increased and reached the highest values (up to 2.5 cm) for NDVI ≈0.5, and then decreased with decreasing NDVI due to the dry summer conditions (Figure 4b). A significant parabolic curve (with concavity facing down) relating σ and the NDVI, σ

_{D}(NDVI), was estimated (σ

_{D}= −11.96 NDVI

^{2}+ 11.44 NDVI − 0.5982, with R

^{2}= 0.70 and p < 0.001). To estimate θ, we used (3) with surface roughness given by σ

_{D}(NDVI) during the March-September period, and an equal 0.5 cm for the rest of the year. θ was well estimated for all the three years although σ

_{D}(NDVI) was estimated using 2017 data only (Figure 4c), confirming the robustness of the approach (rmse = 0.07, R

^{2}= 0.67, and p < 0.001, slope of the regression line = 0.78 in 2016; rmse = 0.04, R

^{2}= 0.93, and p < 0.001, slope of the regression line = 0.99 in 2017; rmse = 0.13, R

^{2}= 0.03, and p > 0.1, slope of the regression line = 0.10 in 2018; Table 1). We also tested the DU model using the WCM to account for the effects of grass cover on radar backscattering, and a constant σ value of 2 cm for that soil type. Using this approach, the model performance was lower and θ was not well estimated during both the dry and wet periods (Figure 4c) thus not capturing the seasonal dynamics (Table 1). Similar poor results (not reported here for brevity) were obtained using other constant σ values (=0.5 cm and 1 cm) in conjunction with the WCM in DU.

_{F}(NDVI) and CL

_{F}(NDVI) relationships (Figure 5a,b). Although the relationships of σ and CL with NDVI were not significant, we estimated the relationships of σ

_{F}(NDVI) and CL

_{F}(NDVI) (σ

_{F}= −10.83 NDVI

^{3}+ 5.58 NDVI

^{2}+ 1.88 NDVI + 0.87, R

^{2}= 0.14, p > 0.1, and CL

_{F}= 37.85 NDVI

^{3}− 97.48 NDVI

^{2}+ 63.1 NDVI − 8.24, R

^{2}= 0.11, p > 0.1), and used the two relationships to make the two parameters variable with the NDVI and estimate θ. During the spring and summer of 2017 that were very dry, θ was well estimated but it was underpredicted in the fall of 2017 and in 2018, which were instead wet (Figure 5 and Table 1). The θ estimates were even worse using the WCM to account for the effects of grass cover on radar backscattering, and constant values of σ (=1 cm) and CL (=0.5 cm) in (4) (Figure 5 and Table 1).

_{D}(NDVI) relationship, which made the σ parameter variable over time with grass cover, reaching the lowest rmse in 2016 and 2017 (Table 1), which were the years with longer dry conditions. Considering the 2016–2017 period only, θ estimates from radar (θ

_{R}) using the DU method were significantly related with the θ measured at the field (θ

_{obs}) (Figure 6a; R

^{2}= 0.80 and p < 0.001), and the slope of the fitted line between θ

_{R}and θ

_{obs}was close to one (= 0.9, Figure 6a). Instead, using the FU method θ

_{R}was still significantly related with observed soil moisture (R

^{2}= 0.41 and p < 0.001) but it was underestimated especially under wet conditions (Figure 6a). Using FU, the differences between θ

_{R}and observed soil moisture (Δθ

_{R,O}) were significantly negatively correlated with the observed soil moisture itself (Figure 6b, R

^{2}= 0.65 and p < 0.001). Using the CD method, θ

_{R}was still significantly related with the observed soil moisture (Figure 6a; R

^{2}= 0.51 and p < 0.001), but soil moisture was overpredicted under dry conditions and underpredicted under wet conditions. This behavior is well depicted by the fitted curved line between Δθ

_{R,O}and θ

_{obs}(Figure 6b), which highlighted a θ

_{R}overprediction of ≈0.1 for drier θ

_{obs}(~<0.2), and a θ

_{R}underprediction of the same amount for wet θ

_{obs}(~>0.3; Figure 6b).

_{D}(NDVI) relationship estimated at the Orroli site (Figure 7). Also for this test site, θ was well estimated (rmse = 0.04, R

^{2}= 0.79, and p < 0.01, slope of the regression line = 0.73 in 2017; and rmse = 0.36, R

^{2}= 0.44, and p > 0.1 slope of the regression line = −1.43 in 2018), especially during the spring of 2017 (rmse = 0.019, R

^{2}= 0.94, and p < 0.01, slope of the regression line = 0.93) (Figure 6).

#### 3.2. Soil Moisture Assimilation in a Land Surface Model

_{e}) was 100 members [68], which was a sufficiently large number to ensure accurate estimates with the EnKF, as demonstrated by the sensitivity analysis by Reichle et al. [66]. The measurement error in ε was assumed to be zero mean with a standard deviation 0.1 that corresponded to an error of about 5% in the θ observations. The ensembles of initial ${\theta}^{l}$ were generated from a Gaussian distribution with a mean of 0.2, intentionally lower (20%) than the observed value, and a standard deviation of 0.05, a higher value than those presented in the literature (e.g., [63,85]). At each time step the ensemble of precipitation was generated by multiplying the recorded precipitation value by a normally distributed random variable with mean zero and a standard deviation equal to 20%. Model errors were achieved: (1) generating an ensemble of ${k}_{s}^{l}$ with a lower ${\widehat{k}}_{s}$ value of 5 × 10

^{−7}m/s than the calibrated value of 5 × 10

^{−6}m/s, and SD

_{logks}of 0.98; (2) generating an ensemble of ${\theta}_{lim}^{l}$ with a higher ${\widehat{\theta}}_{lim}$ value of 0.25 than the calibrated value of 0.2, and SD

_{θlim}of 0.05; (3) generating an ensemble of ${r}_{s,min}^{l}$ with a higher ${\widehat{r}}_{s,min}$ value of 200 s/m than the calibrated value of 100 s/m, and SD

_{rsmin}of 20 s/m. The range of the k

_{s}values exceeded one order of magnitude. Note that the errors of the initial model states and parameters were uncorrelated.

_{D}(NDVI) relationship, we assimilated those estimates in the EnKF. The skill of the filter can be evaluated in Figure 8, where the mean ($\overline{\theta}$) and the 5th and 95th percentiles of the ${\theta}^{l}$ ensemble predicted by EnKF are plotted with radar-based soil moisture estimates. The spread of the EnKF ensemble decreased rapidly through time, as shown by the reduction of the distance between the 5th and the 95th percentiles of the ensemble of ${\theta}^{l}$ (Figure 8a). The EnKF guided $\overline{\theta}$ towards observations from the radar (Figure 8), correcting the EnOL especially in spring and early-summer, the key seasons for water resources management (rmse of 0.08 using EnOL and rmse of 0.02 using EnKF when $\overline{\theta}$ was compared with radar-based observations). This is well depicted by Figure 8b, where the rmse of $\overline{\theta}$ with respect to radar-based soil moisture observations was computed every ten days for a forward 90-day error calculation window (across Figure 8a), showing that rmse using EnKF was lower than 0.05, mostly lower than 0.02 in 2016/17 fall-spring, and always lower than the rmse using EnOL (up to 31%). To further test the EnKF a validation 2018–2020 period was also included (Figure 8), confirming the robustness of the approach with rmse still lower than 0.03 using EnKF.

## 4. Discussion

#### 4.1. Soil Moisture Estimation from Radar Satellite Observations

_{D}(NDVI) relationship was estimated for the 2017 spring-summer period only, when used for the whole 2016–2018 period, the results were very encouraging, reaching the lowest errors in soil moisture estimates (rmse of 0.04 and 0.07 in 2017 and 2016, respectively, Figure 4). Note that the results were acceptable even for the highest values of NDVI (>0.7), although the σ

_{D}(NDVI) relationship was estimated for lower NDVI (0.1–0.7). With the objective of simplifying the parameterization of the retrieval models the use of the proposed σ

_{D}(NDVI) allowed to integrate vegetation effects in the roughness parameter, as previously suggested by Capodici et al. [52]. Note that, recently, Hamze et al. [92] estimated soil roughness from L-band images, improving significantly soil moisture mapping derived using C-band SAR data. In addition, El Hajj et al. [93] demonstrated that the use of L-band images can be attractive for high NDVI (>0.7) in several crops, overcoming the limitations of C-band. Nowadays, L-band images are not available with high revisit time, in contrast with the C-band images of Sentinel 1, and, therefore, are not appropriate for operational soil moisture mapping [92]. In the next future, L-band images should be available at higher revisit time with the new SAR missions (e.g., NISAR (NASA-ISRO SAR), and Tandem-L; [92]), becoming attractive for operational approaches.

_{F}(NDVI) and CL

_{F}(NDVI) relationships, with results being even worse than with the change detection method for the wettest soil conditions (Figure 6b).

_{D}(NDVI) relationship was estimated at the Orroli site. Hence, due to the low computational burden and the improvements in soil moisture estimation, the DU approach with the proposed σ

_{D}(NDVI) relationship can be recommended for operational soil moisture mapping from Sentinel 1 data.

#### 4.2. Soil Moisture Assimilation in a Land Surface Model

## 5. Conclusions

_{D}(NDVI) relationship, in more sites with different soil and climate conditions.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Daily time series at the Sardinian grass field during the 2016–2018 period of (

**a**) observed soil moisture (θ) and precipitation (P), (

**b**) radar backscattering in VV polarization (σ

^{o}

_{vv}) from the Sentinel 1 satellite, (

**c**) normalized difference vegetation index (NDVI) estimated from the Sentinel 2 satellite (note that few a NDVI from Landsat were used to improve the NDVI time series).

**Figure 2.**Statistics of the seasonal (

**a**) precipitation (P), and (

**b**) potential evaporation (PE) at the Sardinian site in relation to the 2003–2018 period (in each box, the red line indicates the median, the box and whiskers represent quartilies, and outliers are depicted individually). The seasonal values of 2016, 2017, and 2018 years are indicated.

**Figure 3.**At the grass field: (

**a**) soil moisture estimates using the revised change detection method (CD) and the revised change detection method after the WCM vegetation effect removal (CD,WCM), compared with the soil moisture observed in the field (obs); (

**b**) soil moisture using the CD,WCM method (θ

_{CD,WCM}) versus soil moisture observed in the field (θ

_{obs}) (dotted lines are the linear regressions, with equations θ

_{CD,WCM}= 0.5 θ

_{obs}+ 0.1, R

^{2}= 0.69 p < 0.01 in 2016; θ

_{CD,WCM}= 1.42 θ

_{obs}−0.005; R

^{2}= 0.74, p < 0.01 in 2017; θ

_{CD,WCM}= 0.2 θ

_{obs}+ 0.17, R

^{2}= 0.31, p > 0.1 in 2018; the solid line is the linear regression for the whole 2016–2018 period, with equation θ

_{CD,WCM}= 0.2 θ

_{obs}+ 0.41, R

^{2}= 0.12, p < 0.001).

**Figure 4.**The results using the DU method at the grass field for the 2016–2018 period of: (

**a**) estimated roughness length (σ) time series for the three years; (

**b**) estimated σ versus corresponding NDVI, and fitted line of equation: σ

_{D}= −11.96 NDVI

^{2}+ 11.44 NDVI − 0.5982; (

**c**) comparison of soil moisture observed at the Orroli field site (obs), and soil moisture estimated using DU with the WCM (DU, WCM) (with σ = 2 cm), and soil moisture estimated using DU and the proposed σ

_{D}(NDVI) relationship (DU, σ

_{D}(NDVI)).

**Figure 5.**The results using the FU method at the grass field for the 2016–2018 period of: (

**a**) estimated roughness length (σ) versus corresponding NDVI, and fitted line of equation σ

_{F}= −10.83 NDVI

^{3}+ 5.58 NDVI

^{2}+ 1.88 NDVI + 0.87; (

**b**) estimated correlation length (CL) versus corresponding NDVI, and fitted line of equation CL

_{F}= 37.85 NDVI

^{3}− 97.48 NDVI

^{2}+ 63.1 NDVI − 8.24; (

**c**) comparison of soil moisture observed at the Orroli field site (obs) with soil moisture estimated from Sentinel 1 data using FU and constant σ and CL values (FU, σ = 1, CL = 0.5), using FU and constant CL (= 0.5 cm) and the proposed σ

_{F}(NDVI) relationship (FU, σ

_{F}(NDVI), CL = 0.5), and using FU and the proposed σ

_{F}(NDVI) and CL

_{F}(NDVI) relationships (FU, σ

_{F}(NDVI), CL

_{F}(NDVI)).

**Figure 6.**At the grass field for the 2016–2017 period: (

**a**) comparison of soil moisture estimates from Sentinel 1 (θ

_{R}) using the CD method with WCM (CD,WCM), the DU method with the proposed σ

_{D}(NDVI) relationship (DU, σ

_{D}(NDVI)), and the FU method with the proposed σ

_{F}(NDVI) and CL

_{F}(NDVI) relationships (FU, σ

_{F}(NDVI), CL

_{F}(NDVI)) with measured soil moisture at the field (θ

_{obs}) (regressions dashed lines are: θ

_{CD,WCM}= 0.55 θ

_{obs}+ 0.09 with R

^{2}= 0.45 and p < 0.01, θ

_{DU}= 0.90 θ

_{obs}+ 0.02 with R

^{2}= 0.80 and p < 0.01, θ

_{FU}= 0.45 θ

_{obs}+ 0.03 with R

^{2}= 0.41 and p < 0.001, respectively); (

**b**) differences between θ

_{R}and θ

_{obs}(Δθ

_{R,o}) versus θ

_{obs}(regression dashed lines are: Δθ

_{CD,WCM,o}= (−7.83 × 10

^{3}θ

_{obs}

^{4}+ 3.55 × 10

^{4}* θ

_{obs}

^{3}− 2.52 × 10

^{4}* θ

_{obs}

^{2}+ 5385 θ

_{obs}− 307.4)/(θ

_{obs}

^{2}+ 2106 θ

_{obs}+ 194.4) with R

^{2}= 0.65 and p < 0.001, Δθ

_{DU,o}= 0.10 θ

_{obs}+ 0.02 with R

^{2}= 0.05 and p = 0.06, Δθ

_{FU,o}= −0.55 θ

_{obs}+ 0.03 with R

^{2}= 0.51 and p < 0.001).

**Figure 7.**At the second grass field site, the comparison between observed soil moisture (obs), and estimated soil moisture from Sentinel 1 using the DU method and the proposed σ

_{D}(NDVI) relationship (DU, σ

_{D}(NDVI)).

**Figure 8.**Soil moisture assimilation results at the grass field site: (

**a**) assimilated soil moisture observations from Sentinel 1 (using DU and the proposed σ

_{D}(NDVI) relationship) (obs., radar), ensemble mean soil moisture predicted in the ensemble open loop comparison configuration (EnOL), and the ensemble mean soil moisture predicted by the assimilation approach using the Ensemble Kalman filter (EnKF) (the 95% confidence interval of the EnKF soil moisture assimilation is shown as a gray band); (

**b**) the evolution of the rmse of ensemble mean soil moisture predicted by EnOL and EnKF with respect to the observed radar-based soil moisture using a 90-day window translated in 10-day increments.

**Table 1.**Statistical index of method performance for soil moisture estimation from Sentinel 1 observations at the Sardinian site [CD, change detection method; CD, WCM, change detection method using the water cloud model; DU WCM, DU method using the Water Cloud Model; DU σ

_{D}(NDVI), DU method using the proposed σ

_{D}(NDVI) relationship; FU, σ = 1, CL = 0.5, FU method using constant σ and CL; FU, σ

_{F}(NDVI), CL = 0.5, FU method using constant CL and the proposed σ

_{F}(NDVI) relationship; FU, σ

_{F}(NDVI), CL(NDVI), FU method using the proposed σ

_{F}(NDVI) and CL

_{F}(NDVI) relationships; rmse, root mean square error; R

_{μ}, mean ratio; R

_{σ}, standard deviation ratio; slope and intercept of the regression line between soil moisture field observations and soil moisture estimates].

Statistical Index | Year | CD | CD, WCM | DU WCM | DU s_{D}(NDVI) | FU, s = 1, CL = 0.5 | FU, s _{F} (NDVI),CL = 0.5 | FU, s _{F} (NDVI), CL_{F}(NDVI) |
---|---|---|---|---|---|---|---|---|

rmse | 2016 | 0.10 | 0.09 | 0.22 | 0.07 | 0.15 | 0.16 | 0.16 |

2017 | 0.10 | 0.09 | 0.24 | 0.04 | 0.12 | 0.18 | 0.08 | |

2018 | 0.12 | 0.12 | 0.23 | 0.13 | 0.16 | 0.06 | 0.19 | |

2016–2018 | 0.10 | 0.10 | 0.23 | 0.08 | 0.14 | 0.16 | 0.14 | |

R_{m} | 2016 | 0.94 | 1.11 | 0.53 | 0.96 | 2.06 | 1.43 | 2.14 |

2017 | 0.80 | 0.95 | 0.47 | 1.01 | 1.66 | 1.47 | 1.31 | |

2018 | 0.90 | 1.06 | 0.54 | 1.24 | 1.94 | 0.92 | 1.87 | |

2016–2018 | 0.88 | 1.04 | 0.51 | 1.03 | 1.88 | 1.34 | 1.70 | |

R_{s} | 2016 | 1.71 | 1.33 | 2.94 | 1.05 | 2.67 | 1.69 | 1.83 |

2017 | 1.34 | 1.15 | 2.25 | 0.97 | 2.05 | 1.86 | 1.30 | |

2018 | 1.87 | 1.60 | 3.50 | 1.84 | 3.10 | 0.93 | 0.86 | |

2016–2018 | 1.54 | 1.29 | 2.68 | 1.09 | 2.43 | 1.61 | 1.31 | |

R^{2} | 2016 | 0.28 | 0.38 | 0.36 | 0.67 | 0.31 | 0.07 | 0.16 |

2017 | 0.57 | 0.53 | 0.45 | 0.93 | 0.55 | 0.01 | 0.80 | |

2018 | 0.12 | 0.11 | 0.09 | 0.03 | 0.12 | 0.57 | 0.06 | |

2016–2018 | 0.35 | 0.37 | 0.33 | 0.58 | 0.34 | 0.01 | 0.22 | |

Slope | 2016 | 0.31 | 0.46 | 0.20 | 0.78 | 0.21 | −0.16 | 0.22 |

2017 | 0.56 | 0.63 | 0.30 | 0.99 | 0.36 | −0.06 | 0.69 | |

2018 | 0.19 | 0.20 | 0.08 | 0.10 | 0.11 | 0.82 | −0.29 | |

2016–2018 | 0.38 | 0.47 | 0.21 | 0.70 | 0.24 | −0.06 | 0.36 | |

Intercept | 2016 | 0.17 | 0.10 | 0.38 | 0.06 | 0.06 | 0.19 | 0.05 |

2017 | 0.14 | 0.09 | 0.36 | 0.00 | 0.05 | 0.16 | 0.01 | |

2018 | 0.21 | 0.17 | 0.41 | 0.16 | 0.09 | 0.05 | 0.19 | |

2016–2018 | 0.17 | 0.11 | 0.38 | 0.06 | 0.06 | 0.17 | 0.05 |

Parameter | Description | Value | |
---|---|---|---|

Grass | WV | ||

r_{s,min} [s m^{−1}] | Minimum stomatal resistance | 100 | 280 |

T_{min} [°K] | Minimum temperature | 272.15 | 272.15 |

T_{opt} [°K] | Optimal temperature | 295.15 | 292.15 |

T_{max} [°K] | Maximum temperature | 313.15 | 318.15 |

θ_{wp} [–] | Wilting point | 0.08 | 0.05 |

θ_{lim} [–] | Limiting soil moisture for vegetation | 0.20 | 0.15 |

ω [HPa^{−1}] | Slope of the f_{3} relation | 0.01 | 0.01 |

z_{om,v} [m] | Vegetation momentum roughness length | 0.05 | 0.5 |

z_{ov,v} [m] | Vegetation water vapor roughness length | z_{om}/7.4 | z_{om}/2.5 |

z_{om,bs} [m] | Bare soil momentum roughness length | 0.015 | |

z_{ov,bs} [m] | Bare soil water vapor roughness length | z_{om}/10 | |

θ_{s} [–] | Saturated soil moisture | 0.53 | |

b [–] | Slope of the retention curve | 8 | |

k_{s} [m/s] | Saturated hydraulic conductivity | 5 × 10^{−6} | |

∣ψ_{s}∣ [m] | Air entry suction head | 0.79 | |

d_{rz} [m] | Root zone depth | 0.19 |

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Montaldo, N.; Fois, L.; Corona, R.
Soil Moisture Estimates in a Grass Field Using Sentinel-1 Radar Data and an Assimilation Approach. *Remote Sens.* **2021**, *13*, 3293.
https://doi.org/10.3390/rs13163293

**AMA Style**

Montaldo N, Fois L, Corona R.
Soil Moisture Estimates in a Grass Field Using Sentinel-1 Radar Data and an Assimilation Approach. *Remote Sensing*. 2021; 13(16):3293.
https://doi.org/10.3390/rs13163293

**Chicago/Turabian Style**

Montaldo, Nicola, Laura Fois, and Roberto Corona.
2021. "Soil Moisture Estimates in a Grass Field Using Sentinel-1 Radar Data and an Assimilation Approach" *Remote Sensing* 13, no. 16: 3293.
https://doi.org/10.3390/rs13163293