Surface soil moisture (M_{s}) is an important factor in many fields of study, such as meteorology, hydrology, and ecology (Pultz et al., 1997 ; Dirmeyer, 2000; Le HégaratMascle et al., 2002 ; Yang et al., 2016 ); it also has important applications in estimating crop yield and drought monitoring (McNairn et al., 2012 ). With the development of the economy in the arid area of Northwest China, where rainfall is scant, the shortage of water resources is becoming more and more severe, making it more important to obtain timely distribution of the soil moisture in a certain range. Remotesensing technology has shown great ability to estimate soil moisture, as compared to optical and passive microwave remote sensing. Active remote sensing has its own special advantage in soilmoisture estimation, and many empirical and semiempirical models have been developed to estimate soil moisture (Oh et al., 1992 ; Dubois et al., 1995 ; Shi et al., 1997 ). Current empirical and semiempirical models are suitable for a certain range of surface roughness. Recently, the integral equation model (IEM) was developed and widely used in simulating backscattering of bare soil or sparsely vegetated landscapes. Based on the model, surface soilmoisture information can be obtained (Fung, 1994; Rahman et al., 2008 ). Based on IEM, Chen et al. (2003) developed the Advance Integral Equation Model (AIEM) to simulate backscattering of bare soil or sparsely vegetated landscapes, with a good result showing that it is useful for soilmoisture estimation over a bare soil surface. Generally, when using AIEM to simulate backscattering of bare soil, two important input parameters—soil moisture and surface roughness—are unknown; and other input parameters such as radar configuration are known. To estimate soil moisture, the impact of surface roughness on backscattering must be removed, using multiangle and multipolarized data to establish the relationship between backscattering and surface roughness (Zribi and Dechambre, 2003; Baghdadi et al., 2006 ; Gherboudj et al., 2011 ). The objective of this study is to present a method to estimate soil moisture over bare agricultural fields, using RADARSAT2 high and lowincidenceangle mode data, based on the AIEM.
2 Study area and data processing 2.1 Study areaThe study area is located in the city of Dunhuang, west of the Hexi Corridor, in Northwest China (Figure 1a). Dunhuang falls in an arid climatic zone, with an annual average rainfall of about 39.9 mm; but the annual mean evaporation reaches 2,486 mm. Dunhaung oasis is surrounded by the Gobi Desert, water needed for both daily and irrigation depending on glaciermelt water from the Qilian Mountains. The shortage of water resources has become an important problem in this area, making it important to be able to estimate surface soil moisture over agricultural fields in this arid area (Liu et al., 2017 ).
RADARSAT2 was launched in December of 2007 by the Canadian Space Agency. It is an earthobserving satellite offering powerful technical advancements that enhance marine surveillance, ice monitoring, disaster management, environmental monitoring, resource management, and mapping, RADARSAT2 works at Cband (5.405GHZ), providing 11 kinds of beam mode data, with different resolutions and incidence angles. The incidence angles range from 10° to 60°. Two RADARSAT2 images were acquired over the Dunhuang study area: the highincidenceangle mode data (May 13, 2015), with a 53.3° average incidence angle, HH polarization; and the lowincidentangle mode data (May 12, 2015), with a 16.5° average incidence angle, HH polarization. The image data are singlelook complex (SLC) data; the image digital numbers (DN) are in units of amplitude; and the DN value should be converted to backscattering values (σ) before using. The computation of σ is
$\sigma = 10 \times \lg \left[\left(\frac{{D{N^2} + {A_0}}}{{{A_1}}}\right)\times \sin (I)\right]$  (1) 
where σ is the radar backscattering coefficient in decibel units (dB), DN is the image digital numbers, A_{0} and A_{1} are the automatic gain control, and I is the incidence angle. The NEST (Next ESA SAR Toolbox) software was used on the image for radiometric calibration.
A median filter consisting of a 9pixel moving window was applied to reduce RADARAT2 SAR data speckle (Thoma et al., 2006 ). Based on the 1:50,000 relief maps, ground control points were chosen; and the RADARSAT2 backscattering image data were georectified.
2.3 Ground observationsField campaign measurements of soilsurface roughness and soil moisture were conducted when the RADARSAT2 satellite passed over on May 12, 2015. Soilsurface roughness was measured using a 1.5m profile of a pin meter. For the 26 experimental sites, roughness was computed by averaging the roughness parameters (the root mean square height (s) and the correlation length (l)) obtained from three sparsely distributed measurement points. Soil moisture at the surface was measured for three depths: 0–7.5 cm, 0–12 cm and 0–20 cm using the TDR300 at the time of the RADARSAT2 overpasses. The three different depths of soil moisture were also computed by averaging the soilmoisture readings obtained from three sparsely distributed measurement points.
The correlation between radar backscattering and soil moisture of different depths was analyzed, as shown in Table 1. It is shown that lowincidenceangle SAR data are more sensitive to soil moisture. For high and lowincidenceangle radar backscattering, there is a better relationship between SAR data and moisture in the top 0–20 cm of soil.
In this paper, we use AIEM to simulate radar backscattering. The values of the main input parameters—including soil moisture, roughness, incidence angle, and soil temperature—were set based on the ground experiment. The soil temperature was set at 20 °C. The incidence angle was set according to lowincidencemode RADARSAT2 data, which was 16.5°. Seven different s values were chosen, ranging from 0.1 cm to 1.3 cm; three different l values were chosen, ranging from 5 cm to 11 cm; and five different M_{s} values were chosen, ranging from 10% to 60%. Based on the input parameters, the HH polarization backscattering was simulated using AIEM.
In earlier studies, the influence of soil roughness on backscattering considered only the root mean square height (s), neglecting the effect of l. Based on comprehensive consideration of the influence of s and l on the radar backscattering, a roughness parameter was used, where Z_{s}=s^{2}/l (Zribi and Dechambre, 2003). Figure 2 shows the effect of s (Figure 2a) and Z_{s} (Figure 2b) on radar backscattering; the mixedroughness parameter Z_{s} is more accurate to simulate radar backscattering.
To analyze the influence of soil moisture and soil roughness on radar backscattering, the l was set to one value (l=8 cm), which can simplify the analysis of the relationship. Considering one value for the l has no influence on our conclusions in this section. Then, the influence of soil moisture and roughness on radar backscattering is simulated, as shown in Figure 3.
As shown in Figure 3, the influence of soil moisture on backscattering is approximately independent of the soilroughness parameter; and the influence of roughness on radar backscattering is also approximately independent of the soil moisture. Our conclusions are similar to those of Zribi et al. (2005) . We also find that the relationship is logarithmic between the radar backscattering (σ) and soil moisture (M_{s}) and soil roughness (Z_{s}) for the RADARSAT2; and radar backscattering (σ) can expressed as a function of M_{s} and Z_{s}, where
$\sigma = a\ln {M_s} + b\ln {Z_s} + c$  (2) 
In section 2.3, we found that lowincidentangle mode data are more suitable for obtaining soil moisture; so the RADARSAT2 lowincidentangle radar backscattering can be written by
${\sigma _{\rm {low}}} = a\ln {M_s} + b\ln {Z_s} + c$  (3) 
Based on AIEM, the highand lowincidenceangle SAR backscattering was simulated. It was also found that the difference in backscattering with two different incidence angles, independent of soil moisture, has a relationship on its own with soil roughness, as shown in Figure 4. Our conclusions are similar to those of Zribi and Dechambre (2003). For the RADARSAT2 high and lowincidentangle mode simulated data, the difference (Δσ=σ_{low}−σ_{high}) between lowincidenceangle radar backscattering (σ_{low}) and highincidenceangle radar backscattering (σ_{high}) shows a logarithmic relationship with Z_{s}, where
${Z_s} = d \times \ln \Delta \sigma + f$  (4) 
Therefore, the ln(M_{s}) can be written as Equations (3) and (4):
$\ln ({M_s}) = \frac{1}{a}{\sigma _{\rm {low}}}  \frac{b}{a}\ln d  \frac{b}{a}\ln (\ln \Delta \sigma + \frac{f}{d})  \frac{c}{a}$  (5) 
In Equation (4), we expand
$\ln {M_s} = {k_1}{\sigma _{\rm {low}}} + {k_2}\ln \Delta \sigma + {k_3}{(\ln \Delta \sigma )^2} + {k_4}$  (6) 
where k_{1}, k_{2}, and k_{3} are the coefficients; and k_{4} is the constant. The ln(M_{s}) is the function of σ_{low} and Δσ(σ_{low}–σ_{high}); the coefficients and constant can be calculated by the leastsquare fitting method, based on the measured data and RADARSAT2 high and lowincidenceangle backscattering data.
Based on Equation (6), M_{s} is obtained using Equation (7).
${M_s} = \exp [{k_1}{\sigma _{\rm {low}}} + {k_2}\ln \Delta \sigma + {k_3}{(\ln \Delta \sigma )^2} + {k_4}]$  (7) 
In section 1.3, the lowincidenceangle SAR backscattering has a better relationship with moisture in the top 20 cm of the soil. Based on the measured data of 26 sites in the Dunhuang study area and the RADARSAT2 data, k_{1}, k_{2}, k_{3}, and k_{4} are calculated using SPSS19.0. The ln(M_{s}) is given by
$\ln {M_s} = 0.126{\sigma _{\rm {low}}}  0.139\ln \Delta \sigma + 0.068{(\ln \Delta \sigma )^2} + 5.892$  (8) 
Then, the soil moisture of the top 20 cm of soil is obtained by Equation (9):
${M_s} = \exp [0.126{\sigma _{\rm {low}}}  0.139\ln \Delta \sigma + 0.068{(\ln \Delta \sigma )^2} + 5.892]$  (9) 
As shown in Figure 5a, the coefficient of determination between obtained soil moisture and measured soil moisture is 0.85; the RMSE is 4.02%. A linear empirical model describing the relationship between soil moisture and lowincidentangle backscattering data was also built by a regression method based on the 26 plot measurements. The model obtained an RMSE of 7.11% and a correlation coefficient of 0.51. The results show the potential of this method to estimate soil moisture with a high accuracy.
A simple soilmoisture estimation method is proposed in this paper. Radar backscattering is mainly influenced by soil moisture and roughness, so soil moisture is a function of radar backscattering and soil roughness. For bare agricultural fields in an arid area, the backscattering of lowincidenceangle RADARSAT2 data is more sensitive to soil moisture; and a better relationship is found between radar backscattering and the amount of moisture in the top 20 cm of soil. The difference between low and highincidentangle radar backscattering shows a logarithmic relationship with soil roughness. Therefore, the estimate of soil moisture is a function of lowincidenceangle backscattering and the difference of low and highincidentangle radar backscattering. The natural logarithm of soil moisture is deduced by combining the roughness model and the backscattering model based on the simulated data. By expanding the natural logarithm of soil moisture into a Taylor series, soil moisture can be obtained using the leastsquare method without having soilroughness measurements. The results show that the method is useful for estimating soil moisture. Further study is needed with regard to the accuracy of roughness measurements.
Acknowledgments:The study was supported by the National Natural Science Foundation of China (41401408 and 41371027) and the Opening Fund of Key Laboratory of Desert and Desertification, Chinese Academy of Sciences. The authors would like to thank all the experts and editors.
Baghdadi N, Holah N, Zribi M. 2006. Soil moisture estimation using multiincidence and multipolarization ASAR data. International Journal of Remote Sensing, 27(10): 19071920. DOI:10.1080/01431160500239032 
Chen KS, Wu TD, Tsang L, et al. 2003. Emission of rough surfaces calculated by the integral equation method with comparison to threedimensional moment method simulations. IEEE Transactions on Geoscience and Remote Sensing, 41(1): 90101. DOI:10.1109/TGRS.2002.807587 
Dirmeyer PA. 2000. Using a global soil wetness dataset to improve seasonal climate simulation. Journal of Climate, 13(16): 29002922. DOI:10.1175/15200442(2000)013<2900:UAGSWD>2.0.CO;2 
Dubois PC, van Zyl J, Engman T. 1995. Measuring soil moisture with imaging radars. IEEE Transactions on Geoscience and Remote Sensing, 33(4): 915926. DOI:10.1109/36.406677 
Fung AK, 1994. Microwave scattering and emission models and their applications. Norwood, MA, USA: Artech House, pp. 10–45.

Gherboudj I, Magagi R, Berg AA, et al. 2011. Soil moisture retrieval over agricultural fields from multipolarized and multiangular RADARSAT 