Bistatic Electromagnetic Scattering from Randomly Rough Surfaces

This letter aimed to validate the advanced integral equation model (AIEM) through different correlation length parameterizations using radar imagery for field-scale studies in a semi-arid environment. This letter compared backscattering coefficients simulated from the AIEM and retrieved from the synthetic aperture radar imagery of a study site in Sardinia. Two treatments for the correlation length were adopted, i.e., in situ measurements and empirically based correlation length estimation. The results showed an overestimation of backscattering coefficients of 2.5 dB with a root mean square error (RMSE) of 3.1 dB for HH and VV polarizations and an underestimation of 27.7 dB and an RMSE of 31.0 dB for HV polarization from the AIEM parameterized by in situ measurements. When using the AIEM with an empirical correlation length, a bias of less than 1.0 dB was found with an RMSE of 1.7 dB for HH and VV polarizations and an overestimation of 1.1 dB and an RMSE of 5.1 dB for HV polarization. Better results were obtained with surface soil moisture (SSM) measured at 10 cm than at 5 cm. Promising soil moisture data retrieval from the SAR imagery is expected from using the empirical correlation length-parameterized AIEM for field-scale purposes in semi-arid environments.

Abstract. Radar remote sensing has demonstrated its applicability to the retrieval of basin-scale soil moisture. The mechanism of radar backscattering from soils is complicated and strongly influenced by surface roughness. Additionally, retrieval of soil moisture using AIEM (advanced integrated equation model)-like models is a classic example of underdetermined problem due to a lack of credible known soil roughness distributions at a regional scale. Characterization of this roughness is therefore crucial for an accurate derivation of soil moisture based on backscattering models. This study aims to simultaneously obtain surface roughness parameters (standard deviation of surface height σ and correlation length cl) along with soil moisture from multi-angular ASAR images by using a two-step retrieval scheme based on the AIEM. The method firstly used a semi-empirical relationship that relates the roughness slope, Zs (Zs = σ2/cl) and the difference in backscattering coefficient (Δσ) from two ASAR images acquired with different incidence angles. Meanwhile, by using an experimental statistical relationship between σ and cl, both these parameters can be estimated. Then, the deduced roughness parameters were used for the retrieval of soil moisture in association with the AIEM. An evaluation of the proposed method was performed in an experimental area in the middle stream of the Heihe River Basin, where the Watershed Allied Telemetry Experimental Research (WATER) was taken place. It is demonstrated that the proposed method is feasible to achieve reliable estimation of soil water content. The key challenge is the presence of vegetation cover, which significantly impacts the estimates of surface roughness and soil moisture.

In this paper, an empirical methodology to retrieve bare soil moisture by Synthetic Aperture Radar (SAR) is developed. The model is based on Advanced Integral Equation Model (AIEM). Since AIEM cannot express cross-polarized backscattering coefficients accurately, we propose an empirical model to retrieve soil moisture for bare farmland only with co-polarized SAR data. The soil moisture can be obtained by solving an equation of HH and VV polarized data without any field measurements. Both simulated and real SAR data are used to validate the accuracy of the model. This method is especially effective in a large area where the surface roughness is difficult to be completely measured.

In general, the diving dynamics of an autonomous underwater vehicle (AUV) has been derived under various assumptions on the motion of the vehicle in vertical plane. Usually, pitch angle of AUV is assumed to be small in maneuvering, so that the nonlinear dynamics in the depth motion of the vehicle could be linearized. However, a small-pitch-angle is a somewhat strong restricting condition and may cause serious modeling inaccuracies of AUV’s dynamics. For this reason, many researchers concentrated their interests on the applications of adaptive control methodology to the motion control of underwater vehicle. In this chapter, we directly resolve the nonlinear equation of the AUV’s diving motion without any restricting assumption on the pitch angle in diving model. The proposed adaptive neuro-fuzzy sliding mode controller (ANFSMC) with a proportional + integral + derivative (PID) sliding surface is derived so that the actual depth position tracks the desired trajectory despite uncertainty, nonlinear dynamics and external disturbances. In the proposed control structure, the corrective term is approximated by a continuous fuzzy logic control and the equivalent control is determined by a feedforward neural network. The weights of the neural network are updated such that the corrective control term of the ANFSMC goes to zero. The adaptive laws are employed to adjust the output scaling factor and to compute PID sliding surface coefficients. Finally, the lyapunov theory is employed to prove the stability of the ANFSMC for trajectory tracking of diving behaviors. Simulation results show that this control strategy can attain excellent control performance.

In this paper we propose a bistatic scattering model which is an extension to the advanced integral equation model. The z-related phase factor in the spectral representation of the Green's function is retained. Yet through rigorous evaluation of the expected value of the exponential which include this z-related phase factor, we find that an error function with complex argument is introduced, which definitely possesses an imaginary part. Its effect may not be overlooked when either the surface roughness or the air-ground permittivity contrast is not too small. We regard the error function related terms as correction terms to both the Kirchhoff-comlementary and the complementary scattering coefficients. Explicit formula for the former term is given in this paper. The validity of this extended bistatic scattering model is demonstrated through the excellent agreements between model predictions and measurement data for statistically known surfaces. Keyword- AIEM; bistatic scattering; error function.

The aim of this letter is to discuss the influence of radar frequency on the relationship between surface soil moisture and the nature of radar backscatter over bare soils. In an attempt to address this issue, the advanced integral equation model was used to simulate backscatter from soil surfaces with various moisture vertical profiles, for three frequency bands, namely, L, C, and X. In these computations, we investigated the influence of the vertical heterogeneity of soil moisture on the characteristics of the backscattered signals. The influence of radar frequency is clearly demonstrated. A database produced from Envisat ASAR and TerraSAR-X data, which was acquired over bare soils with in situ measurements of moisture content and ground surface roughness, was used to validate the utility of taking the soil moisture heterogeneity into account in the backscatter model.

Emission and backscattering signals of land surfaces at different frequencies have distinctive responses to soil and vegetation physical states. The use of multi-frequency combined active and passive microwave signals provides complementary information to better understand and interpret the observed signals in relation to surface states and the underlying physical processes. Such a capability also improves our ability to retrieve surface parameters and states such as soil moisture, freeze-thaw dynamics and vegetation biomass and vegetation water content (VWC) for ecosystem monitoring. We present here a prototype Community Land Active Passive Microwave Radiative Transfer Modelling platform (CLAP) for simulating both backscatter (σ0) and emission (TB) signals of land surfaces, in which the CLAP is backboned by an air-to-soil transition model (ATS) (accounting for surface dielectric roughness) integrated with the Advanced Integral Equation Model (AIEM) for modelling soil surface scattering, and the Tor Vergata model for modelling vegetation scattering and the interaction between vegetation and soil parts. The CLAP was used to simulate both ground-based and space-borne multi-frequency microwave measurements collected at the Maqu observatory on the eastern Tibetan plateau. The ground-based systems include a scatterometer system (1–10 GHz) and an L-band microwave radiometer. The space-borne measurements are obtained from the X-band and C-band Advanced Microwave Scanning Radiometer 2 (AMSR2) radiation observations. The impacts of different vegetation properties (i.e., structure, water and temperature dynamics) and soil conditions (i.e., different moisture and temperature profiles) on the microwave signals were investigated by CLAP simulation for understanding factors that can account for diurnal variations of the observed signals. The results show that the dynamic VWC partially accounts for the diurnal variation of the observed signal at the low frequencies (i.e., S- and L-bands), while the diurnal variation of the observed signals at high frequencies (i.e., X- and C-bands) is more due to vegetation temperature changing, which implies the necessity to first disentangle the impact of vegetation temperature for the use of high frequency microwave signals. The model derived vegetation optical depth τ differs in terms of frequencies and different model parameterizations, while its diurnal variation depends on the diurnal variation of VWC regardless of frequency. After normalizing τ at multi-frequency by wavenumber, difference is still observed among different frequencies. This indicates that τ is indeed frequency-dependent, and τ for each frequency is suggested to be applied in the retrieval of soil and vegetation parameters. Moreover, τ at different frequencies (e.g., X-band and L-band) cannot be simply combined for constructing accurate long time series microwave-based vegetation product. To this purpose, it is suggested to investigate the role of the leaf water potential in regulating plant water use and its impact on the normalized τ at multi-frequency. Overall, the CLAP is expected to improve our capability for understanding and applying current and future multi-frequency space-borne microwave systems (e.g. those from ROSE-L and CIMR) for vegetation monitoring.

Parametric exponentially correlated surface emission model for L-band passive microwave soil moisture retrieval

The capability of COSMO-SkyMed (CSK) in monitoring vegetation has been investigated in this paper. SAR data from CSK were collected on two agricultural areas in Italy from 2010 to 2012, at different dates during the vegetation cycle. X-band data have been compared to accurate ground truth measurements of soil and vegetation parameters carried out simultaneously to satellite passes. Significant sensitivity of backscatter to vegetation water content of agricultural crops was observed. However, the backscattering showed an opposite trend as a function of biomass of wheat and sunflower, which belong to two very different vegetation types, namely narrow-leaf and broad-leaf crops. Similar trends emerged at lower frequencies (i.e., C and L bands) for the same crop types. In order to investigate the role of different parameters of soil and vegetation (e.g., surface roughness and moisture, plant density and height, dimensions of leaves, stem diameter, and water content) on the backscatter behavior for these two different crop types, model simulations were performed using a discrete element radiative transfer model for vegetation, whereas soil was modeled using the advanced integral equation model (AIEM). A sensitivity analysis of the model was carried out by varying the dimensions of vegetation components within the range of parameters directly measured on ground during the experimental campaigns. The model simulations were successively compared with experimental data of backscattering. The good agreement found between experimental and simulated data encouraged the follow-up of the research toward the implementation of inversion algorithms, which can be able to retrieve vegetation biomass from SAR data and from an operative point of view.

This paper presents a new scheme to retrieve precipitable water vapor (PWV) over land using AMSR-E brightness temperatures (TB) without the help of ancillary data. A surface emission model, Advanced Integral Equation Model (AIEM) and an one-dimensional atmosphere transfer model (1DRTM) were combined to generate a database. Through analysis of the simulated dataset, it is found that the ratio of the polarization difference obtained from 23.8 and 18.7 GHz (ΔT B (23.8) / ΔT B (18.7), called PDR_PWV later) is sensitive to PWV. Compared to the GPS results, the RMSE of our algorithm is 9 mm. There are regional consistency between the results from MODIS and our algorithm. Furthermore, on the surfaces covered by cloud where MODIS cannot be used to retrieve PWV, our algorithm can also give reasonable results.

Both passive and active microwave sensors have long been used in retrieving the soil moisture, however, only the SAR can provide the high spatial resolution data (10 m~1 km) suitable for watershed scale hydrological studies. In this paper, we took a preliminary study on deriving the catchment scale soil moisture content and their spatial variations in a typical semi-arid rangeland located at the Loess Plateau of China with active microwave remotely sensed data. The Advanced Integral Equation Model (AIEM) was coupled with the Envisat ASAR images by using the simulated surface roughness information retrieved from the multi-angle (15deg a 31deg) ASAR data as constraining condition to estimate the surface soil moisture content within the studied watershed, the Jinhe River Basin. In general, the soil moisture map derived from this study shows high wetness in most part of the basin, which is in agreement with the actual rainy condition in the study region.

In this paper, we investigated the bistatic scattering of soil moisture and surface roughness of bare soil surfaces. We generated database by using an advanced integral equation model (AIEM). For better understanding the bistatic scattering characteristics of bare soil surfaces, we adopted single polarized simulations and combination of dual angular simulations. To explore the sensitivity of bistatic scattering to soil moisture, we applied a defined sensitivity index. The results shown that the scattering coefficients of VV polarization are more sensitive to soil moisture compared with the HH polarized scattering coefficients. Moreover, the forward direction is the most sensitive to soil moisture in all cases. Besides, the dual angular observations show good sensitivity to soil moisture, especially when the differences of the two incident angles are large.

In this paper, an attempt is made to identify the optimal bistatic configurations for the retrieval of bare soil moisture at L-band based on a global sensitivity analysis using the extended Fourier amplitude sensitivity test (EFAST) algorithm. For this purpose, we apply the Advanced Integral Equation Model (AIEM), which is a well-established theoretical scattering model, to simulate complete sets of bistatic scattering coefficients, over a wide range of surface roughness and dielectric parameters. The sensitivities of radar response to soil moisture and surface roughness are identified and quantified in terms of bistatic geometries and radar parameters. The results show that the autocorrelation functions (ACFs), which significantly affect the distribution of sensitivity indices of surface roughness, do not exert distinct effects on the bistatic sensitivity pattern of soil moisture. In bistatic scattering, $VV$ polarization shows higher sensitivity to soil moisture than $HH$ polarization, particularly at large incident angles. As incident angle increases, in cases of small azimuth scattering angles and large scattering angles, the sensitivity zone expands and tends to move to the forward region at $VV$ polarization. This feature persists regardless of the ACFs, and thus offers promising configurations for soil moisture retrieval. For $HH$ polarization, in contrast, the sensitivity zone gradually moves to the backward region as the incident angle increases.

Effect of vegetation index choice on soil moisture retrievals via the synergistic use of synthetic aperture radar and optical remote sensing

The integral equation model (IEM) is considered as a promising algorithm for soil moisture retrieval from active microwave data over bare soil and sparsely vegetated conditions. However, the soil dielectric constant is implicitly embedded in the complicated IEM; inversion of soil moisture is often accomplished through iteration and is thus computationally expensive, particularly when it is applied to retrieve soil moisture from active microwave data on a large scale. To simplify the inversion process of soil moisture directly from the active microwave data, basic math functions were adopted to fit the simulation results of the original IEM so that the radar backscattering coefficient becomes an explicit function of soil dielectric constant or the soil dielectric constant is an explicit function of radar backscattering coefficient. Soil moisture is then calculated directly from radar backscattering coefficient without iteration. We called this model empirically adopted IEM (EA-IEM). The accuracy of the EA-IEM to the original IEM and its applicability are analyzed through three processes: model intercomparison, sensitivity analysis, and model comparison with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">situ</i> measurements. The average differences of backscattering coefficients between the EA-IEM and the original IEM are 0.14 dB for HH-polarization and 0.12 dB (Gaussian correlation function) and 0.2 dB (exponential correlation function) for VV-polarization. The sensitivity of soil moisture variation is examined under the consideration of absolute and relative calibration errors. A comparison between the soil moisture estimated and the measurements is performed, and the root-mean-square (rms) error is found to be 3.4%, suggesting that the EA-IEM performs well in these real cases. All these analyses indicate that the EA-IEM is a good representative of the original IEM and can be used to retrieve soil moisture under the tested range of model parameters: incidence angles between 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deg</sup> and 60 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deg</sup> , soil dielectric constants between 4 and 42, surface rms height from 4 to 31 mm, and correlation length from 50 to 250 mm.