The study area is located in the Duero Basin, northwest in Spain (Figure 1A). The geographical location of the study area is 41°06′N-41°32′N, 5°01′W-5°45′W (Figure 1B) and corresponding area is about 1,300 km². The climate of the area belongs to the mediterranean climate, and the annual average temperature is 12°C. The main land-use types are farmland, forest, city and water areas. The main types of crop include wheat, cereal, maize, grape and cotton. The REMEDHUS soil moisture network is established in the study area, which has 24 soil moisture observation stations (Hydra Probes, Stevens Water Monitoring System) and belongs to the International Soil Moisture Network (Dorigo et al., 2011; Dorigo et al., 2013; Campus, 2019). Probes measure 0–5 cm soil moisture and temperature every hour.

The geological substrate of the study area include sandstones, conglomerates, detritic limestones, and fluvial deposits of conglomerates, gravels and sands. 13 in 24 soil moisture monitoring stations were selected (Figure 1B), and other 11 fields were excluded because their observations are vegetation-related or lack of soil moisture content during the measurement period. These 13 fields consist of two clay texture fields, six loam texture fields and five sand texture fields. A supplementary dataset which include four monitoring stations in southern France were also selected. Figures 1C–E show the bare farmland surface of clay, loam and sand texture which have been cultivated. The spacing between ridge in the fields is approximately 0.5 m. Figure 1F shows the uncultivated field, the surface roughness of these part of fields is relatively small. Some fields contain straw, which will have a certain effect on the backscattering coefficients (Figure 1G), the data in these fields needs to be excluded.

104 Sentinel-1 and 23 Sentinel-2 images, over the study area, between 2017 and 2018 were obtained from the Copernicus Open Access Hub (Copernicus, 2018). The acquisition modes of Sentinel-1 data are the interferometric (IW) mode and the level 1 ground range detected (GRD) product type, the spatial resolution of images are 20 × 22 m (4.4 equivalent number of looks). The details of Sentinel-1 data are shown in Table 1. The observed Sentinel-2 data are level 1C or level 2A products. By performing atmospheric correction on S2 level 1C data, the level 2A data were obtained. The local incidence angle is calculated using SRTM 1 s DEM data, which has a spatial resolution of 30 m.

The soil moisture content data were obtained from the ISMN. To reduce the impact of measurement errors, the hourly observation data in every day were averaged to obtain the daily soil moisture content. Global Satellite Mapping of Precipitation (GsMap) was obtained from Google Earth Engine, which provides a global hourly rain rate with a 0.1 × 0.1° resolution (Gorelick et al., 2017).

Sentinel-1 images were preprocessed by the following steps: 1) introducing the orbit file to eliminate orbit error; 2) obtaining the backscattering coefficients based on the calibration for Sentinel-1 images; 3) A 5 × 5 Lee Sigma speckle filter was used to eliminate the speckle noise in the backscattering-coefficients image; 4) terrain-flattening, to eliminate radiation errors caused by spheroids and terrain fluctuations; and 5) Applying terrain correction to eliminate the geometrical error caused by spheroids and terrain fluctuations. To eliminate the variation in the backscattering coefficients caused by the different terrains and local incidence angles, a Gamma0 ( γ 0 ) images of the study area were obtained based on above steps (Small, 2011). The average γ 0 and local incidence angle of selected fields were calculated. Soil texture data over 17 field fields were obtained, as shown in Table 2 (Ceballos et al., 2004). Soil texture is classified according to the international soil texture classification standard. The average value such as backscattering coefficients and the local incidence angle of the fields were calculated where the monitoring stations are located. The local incidence angle was calculated using SRTM 1 s DEM data, which has a spatial resolution of 30 m. This data can match Sentinel-1 data well because the study fields are all larger than 30 × 30 m.

The soil dielectric constant is closely related to soil particle size, soil porosity and soil moisture. Retrieving soil moisture using microwave remote sensing depends on the characteristics of microwave, which is sensitive to the dielectric constant, so an accurate retrieval method should involve an accurate dielectric constant model. The following formula can be used to establish the relationship between soil moisture content and soil dielectric constant (Stogryn, 1971; Dobson et al., 1985): ε α = 1 + ( ρ b ρ s ) ( ε s α − 1 ) + m v β ε f w α − m v (1) where ε is the dielectric constant of solid soil particles and the water mixture; ε s is the dielectric constant of solid soils, which is equal to 4.70; ε f w is the dielectric constant of free water; ρ b is the bulk density of soil; ρ s is the specific density; m v is the soil volumetric water content; α is a constant factor that equals 0.65; and β is the soil texture-dependent coefficients. The real part of β can be expressed as follows: β = 127.48 − 0.519 S − 0.152 C (2) where S is the sand content, and C is the clay content. When only the real part is considered, ε f w can be written as: ε f w = ε w ∞ + ε w 0 − ε w ∞ 1 + ( 2 π τ w f ) 2 (3) where ε w ∞ equals 4.9, which is the high-frequency limit of ε w ; ε w 0 is the static dielectric constant of water; τ w is the relaxation time of water; and f is the frequency in hertz. 2 π τ w and ε w 0 can be calculated using the following formulas: 2 π τ w ( T , N ) = 2 π τ w ( T , 0 ) b ( N ,   T ) (4) b ( N ,   T ) = 0.1463 × 10 − 2 N T + 1.000 − 0.04896 N − 0.02967 N 2 + 5.644 × 10 − 3 N 3 (5) ε w 0 ( T , N ) = ε 0 ( T , 0 ) α ( N ) (6) ε 0 ( T , 0 ) = 87.24 − 0.4008 T + 9.398 × 10 − 4 T 2 + 1.410 × 10 − 3 T 3 (7) α ( N ) = 1.000 − 0.2551 N + 5.151 × 10 − 2 N 2 − 6.889 × 10 − 3 N 3 (8) N = S [ 1.707 × 10 − 2 + 1.205 × 10 − 5 S + 4.058 × 10 − 9 S 2 ] (9) where T is the temperature in °C and N is the normality of the solution. According to data from the Harmonized World Soil Database (HWSD, FAO/IIASA/ISRIC/ISSCAS/JRC, 2012), the conductivity of the soil in the study area is between 0.1–0.7 ds/m, so the soil in the study area can be regarded as non-saline soil. So S equals 0 and α ( N ) equals 1. Since the temperature has little effect on the dielectric constant under positive temperature conditions, it can be assumed that the temperature is 10°C.

In this study, the Dubois model is modified to retrieve the soil moisture content. The Dubois model is developed based on multiple ground-measured frequencies, multiple polarizations, and multiple-incidence angle scatterometer data. The model can be expressed as follows: σ h h 0 = 10 − 2.75 ( cos 1.5 ⁡ θ sin 5 ⁡ θ ) 10 0.028 ε t a n θ ( k s ⁡ sin ⁡ θ ) 1.4 λ 0.7 (10) σ v v 0 = 10 − 2.35 ( cos 3 ⁡ θ sin 3 ⁡ θ ) 10 0.046 ε t a n θ ( k s ⁡ sin ⁡ θ ) 1.1 λ 0.7 (11) where σ h h 0 and σ v v 0 are the backscattering coefficients of the Horizontal transmit and Horizontal receive (HH) and VV polarizations; θ is the incidence angle; k is the wavenumber; λ is the wavelength; and s is the Rms height. The radiation terrain correction method can be used to eliminate the radiation difference caused by topography. The corrected backscattering coefficients is expressed as γ v v 0 . Due to lacking of Sentinel-1 HH polarization data over the study area, only the VV polarization formula was selected. Thus, the final retrieval model can be expressed as: γ v v 0 = 10 − 2.35 ( cos 3 θ ′ sin 3 θ ′ ) 10 0.046 ε t a n θ ( k s ⁡ sin ⁡ θ ′ ) 1.1 λ 0.7 (12) where θ ′ is the incidence angle after radiation terrain correction.

The Rms height was used as a unique parameter to describe surface roughness. The Rms height can be expressed as a linear function of the backscattering coefficients or cross-polarization ratio, which is equal to σ V H 0 ( d B ) − σ V V 0 ( d B ) (Srivastava et al., 2008). Rms   height = A 1 + B 1 × σ V H 0 ( d B ) (13) Rms   height = A 2 + B 2 × [ σ V H 0 ( d B ) − σ V V 0 ( d B ) ] (14) where σ V H 0 ( d B ) is the cross-polarization backscattering coefficients expressed in decibel. A 1 and B 1 are equal to 4.71 and 0.14, respectively, A 2 and B 2 are equal to 4.27 and 0.22, respectively. The above formula is obtained from farmland located in the states of Uttar Pradesh and Uttarakhand in India by Srivastava. To eliminate the influence of terrain, the backscattering coefficients can be expressed as γ 0 . The following formula can be used to calculate the Rms height. Rms   height = 4.71 + 0.14 × γ V H 0 ( d B ) (15) Rms   height = 4.27 + 0.22 × [ γ V H 0 ( d B ) − γ V V 0 ( d B ) ] (16) where γ V H 0 ( d B ) and γ V V 0 ( d B ) are VH and VV polarization backscattering coefficients, respectively, which eliminate the local incidence angle effect.

To avoid the effect of crops on soil moisture retrieval, it is necessary to filter the data during the research period. NDVI was used as a major indicator that judges whether the ground surface is bare. NDVI was calculated using Sentinel-2 data by the following formula: NDVI = N I R − R E D N I R + R E D = B 8 A − B 4 B 8 A + B 4 (17) where NIR is the near-infrared band reflectance; RED is the red band reflectance; and B 8 A and B 4 are the near-infrared and RED bands of Sentinel-2. The fields were evaluated to determine whether they are bare based on the NDVI value. NDVI values below 0.25 represent bare surface. Even so, under the condition of NDVI below 0.25, the fields contains straw and grapevines. In such a case, the backscattering value will be disturbed. To eliminate these values, the Google Earth, ESRI ArcGIS living atlas and Sentinel-2 datasets were used.

To discuss the retrieval accuracy under different climatic conditions, the data were divided into datasets with or without rain. The condition of rain refers to precipitation in 48 h and lasted at least 2 h before the observation of Sentinel-1.

Rain affects the soil moisture as well as the backscattering coefficients. However, the trend of change in backscattering coefficients with soil moisture is closely related to soil texture. Three typical fields (i.e., clay, loam, and sand) in cultivated and uncultivated areas are chosen to analyze. To confirm that there was no surface changes during the analysis period, Google Earth, ESRI ArcGIS living atlas and the visible light bands of Sentinel-2 data were used.

Figure 3 presents the change of the soil moisture content before and after rain. The results show that sand has a relatively lower moisture content than loam and clay regardless of rain conditions because of its large porosity and weak moisture content capacity. Owing to a lowest porosity and a strongest moisture retention capacity, Clay has highest moisture content. The soil moisture content of loam is between that of clay and sand. The soil moisture content of these three types of texture soil increased with the rain. The soil moisture content of sand changes little after rain, which is caused by the low saturated moisture content of sand.

The backscattering coefficients of clay, loam and sand all exhibit an obvious upward trend with the appearance of rain (Figure 4). Under the condition of no rain, the backscattering coefficients of sand is slightly lower than that of clay and loam. The range of γ V V 0 is more uniform than that of γ V H 0 , indicating that the VH backscattering coefficients exhibits a degree of randomness. Although the soil moisture content of the sand changes little after rain, the backscattering coefficients changes obviously. This phenomenon may be because sand has a higher dielectric constant under the same water content compared with loam and clay. VV backscattering coefficients of clay and loam increased more than VH after rain except for sand, indicating that VV backscattering coefficients of loam and clay are more sensitive to changes in soil moisture than VH.

Figure 5 present the variation of soil moisture, backscattering coefficients and cross-polarization with rain. By excluding changes of the surface in the fields, each of them can be considered as no change in the surface roughness during the illustrated period. The results show that the impact of different rain degrees on soil moisture and backscattering coefficients are significantly different. The slight rain significantly increased the backscattering coefficients, but there is no significant change in soil moisture. It can be seen that rain is an important factor affecting the backscattering coefficients and soil moisture retrieval.

According to ground surface conditions of the fields, they can be divided into cultivated and uncultivated fields which represent rough surface (Figures 5A,C,E) and flat surface (Figures 5B,D,F). The backscattering coefficients of cultivated fields are larger than uncultivated fields, which is mainly due to greater roughness of the cultivated fields. When the soil moisture changes less, there is a degree of fluctuation in the backscattering coefficients, as shown in Figures 5A,F. Besides rain, these fluctuations are related to changes of incidence direction and penetration depth of microwave signal. The fluctuation of cultivated fields is greater than that of uncultivated fields because the status of the cultivated fields are more complex. The changes of γ V H 0 and γ V V 0 are very similar while γ V H 0 − γ V V 0 has a quite different from γ V V 0 . In this case, when the slight rain is not taken into account and ground surface roughness is considered to be unchanged, the variation of γ V V 0 can be seen as a result of systemic changes, such as incidence direction and penetration depth, γ V H 0 can be considered as a valid parameter to reflect systematic fluctuations.

The backscattering coefficients of fields present a rising trend in the summer and autumn, and are more obvious in cultivated fields, but the soil moisture show downward trend. The moisture content of the surface soil in farmland areas is not only related to rain and irrigation, but also related to temperature and evaporation. The monthly temperature changes in the study area are shown in Figure 6. The results show that temperatures in the study area increased from January to August and gradually declined after September, evaporation is significantly greater in summer than in winter. In addition, the study area is located in the Mediterranean region, the winter precipitation is significantly greater than the summer precipitation, leading to significant reduction of the soil moisture in the summer and autumn. From May to October, when soil moisture decreases, the γ V H 0 increases. The reason is microwave signal’s penetration depth increases when the soil moisture declines, the amount of volume scattering increases. But within the same time period, γ V V 0 does not significantly change. In such a case, we can still assume that γ V H 0 is a parameter that reflects the penetration depth, and the increase in value can explain γ V V 0 is stable and soil moisture decreases.

For the soil with different textures, the backscattering coefficients of sand is more volatile than that of clay and loam, but the moisture of soil fluctuate least, reflecting the different backscattering characteristics of different soil textures. Backscattering coefficients of sand is more susceptible to the condition of soil surfaces, and its penetration depth is more likely to produce random scattering. However, regardless of soil texture, γ V H 0 and γ V V 0 changing trends were consistent.

Through the above analysis, it can be seen that in addition to the rain, the γ V H 0 is also related to systematic factors, such as the incidence direction and penetration depth. The γ V H 0 is more closely related to these systematic states than γ V H 0 − γ V V 0 , so γ V H 0 can be considered to reflect these systemic parameters more fully. Table 3 shows the correlation between backscattering coefficients and soil moisture, and the results show that the correlation between γ V V 0 and soil moisture is higher than that of γ V H 0 and γ V H 0 − γ V V 0 . Therefore, combined with the above analysis, γ V V 0 is more suitable for describing soil moisture, γ V H 0 is more suitable for describing soil roughness and other systematic fluctuations.

The main parameters of the Dubois model include the incidence angle, surface roughness and soil moisture. According to γ 0 , which is used as the backscattering coefficients, it can be considered that the influence of terrain and the incidence angle are eliminated. Therefore, parameter θ in the formula can be simplified and replaced with a constant. In addition, considering that the VH backscattering coefficients reflects the volume scattering component of the target and have a high correlation with the VV backscattering coefficients, γ V H 0 was used to depict parameters representing the surface roughness and systematic fluctuations. The relationship between γ V V 0 simulated by the Dubois model under different incidence angles and the actual value is shown in Figure 7. The incidence angle range of the measured data is basically distributed between 30–50°. Therefore, it can be considered that when the incidence angle in the model is 40°, the model matches the measured value best. However, there is a large angle between the trend line and the 40° model line, indicating that in this situation, the accuracy of the model is low when γ V H 0 has a large value, so the model needs to be further modified.

The roughness term coefficients and constant term in the model can be parameterized, and consider Eq. 15. The modification model can be shown as follows in dB form. γ v v 0 = − 23.327 + 0.386 ε + 27.297 l o g 10 ( 1.16 ( 4.71 + 0.14 γ V H 0 ) ) (18)

The relationship between the modified model and the measured value is shown in Figure 8.

The soil moisture map of the study area on September 19, 2018 is shown in Figure 11. The spatial resolution of the map is 22 m. When NDVI is greater than 0.25, it can be considered as vegetation area, which are the green parts in the map. The bare soil area uses seven grades color to describe the moisture content. The soil moisture content of the entire study area is higher in the east than in the west. This is because the soil texture of the east region is mainly the loam and clay, and the west is the sand area. Compared with sand, clay and loam have higher soil moisture content. In addition, Due to proximity to the Duero River and its tributaries, some areas in the west also have high soil moisture content.