Integral Equation Model Model Research Articles

Characteristics of Saline Soil in Extremely Arid Regions: A Case Study Using GF-3 and ALOS-2 Quad-Pol SAR Data in Qinghai, China

Soil salinization is a global problem, which seriously damages the ecological environment and considerably reduces agricultural productivity, especially in arid regions. Synthetic aperture radar (SAR) has been widely used in remote sensing due to its weather and sunlight independence. Polarimetric SAR has great potential for large-scale mapping and monitoring salt-affected soils. In this study, we investigate the characteristics of saline soil in extremely arid regions using dual-band quadrature-polarimetric (quad-pol) SAR images acquired by GF-3 (C-band) and ALOS-2 (L-band). Firstly, the effectiveness of the modified dielectric mixing model and integral equation model (IEM) in describing saline soil is evaluated. Secondly, the potential relationships between polarimetric parameters and salinity are discussed in both the C- and L-band, respectively, such as co-polarization ratio, scattering entropy H, and scattering angle α. Finally, a linear regression model for monitoring salt content is established. The main contributions of this article are as follows: (1) Simulation results suggest that the radar backscattering coefficient is a weak function of salinity at low water content, but our experimental data show that soil salinity significantly contributes to the radar backscattering coefficient, which indicates the modified dielectric mixing model and IEM model is not applicable in extremely arid areas. (2) A negative correlation between the co-polarization ratio and salinity is observed, and the correlation coefficients are 0.64 (C-band) and 0.71 (L-band). Besides, scattering entropy and scattering angle exhibit a positive correlation with salinity in the C-band with correlation coefficients 0.686 and 0.669, respectively, whereas a negative correlation is found in the L-band with correlation coefficients 0.682 and 0.680, respectively. This can be attributed to the different penetration depths and sensitivity to the surface roughness of the electromagnetic waves at two frequencies. (3) A regression model for salinity estimating based on radar backscattering coefficient, co-polarization ratio, and scattering entropy is established, with a determination coefficient (R2) of 0.79 and a root mean square error (RMSE) of 6.56%, allowing us to determine soil salinity from quad-pol SAR images without using backscattering models. Therefore, our results can be a reference for future soil salinity monitoring and inversion.

Evaluation of Backscattering Models and Support Vector Machine for the Retrieval of Bare Soil Moisture from Sentinel-1 Data

The main objective of this work was to retrieve surface soil moisture (SSM) by using scattering models and a support vector machine (SVM) technique driven by backscattering coefficients obtained from Sentinel-1 satellite images acquired over bare agricultural soil in the Tensfit basin of Morocco. Two backscattering models were selected in this study due to their wide use in inversion procedures: the theoretical integral equation model (IEM) and the semi-empirical model (Oh). To this end, the sensitivity of the SAR backscattering coefficients at V V ( σ v v ∘ ) and V H ( σ v h ∘ ) polarizations to in situ soil moisture data were analyzed first. As expected, the results showed that over bare soil the σ v v ∘ was well correlated with SSM compared to the σ v h ∘ , which showed more dispersion with correlation coefficients values (r) of about 0.84 and 0.61 for the V V and V H polarizations, respectively. Afterwards, these values of σ v v ∘ were compared to those simulated by the backscatter models. It was found that IEM driven by the measured length correlation L slightly underestimated SAR backscatter coefficients compared to the Oh model with a bias of about − 0.7 dB and − 1.2 dB and a root mean square (RMSE) of about 1.1 dB and 1.5 dB for Oh and IEM models, respectively. However, the use of an optimal value of L significantly improved the bias of IEM, which became near to zero, and the RMSE decreased to 0.9 dB. Then, a classical inversion approach of σ v v ∘ observations based on backscattering model is compared to a data driven retrieval technic (SVM). By comparing the retrieved soil moisture against ground truth measurements, it was found that results of SVM were very encouraging and were close to those obtained by IEM model. The bias and RMSE were about 0.28 vol.% and 2.77 vol.% and − 0.13 vol.% and 2.71 vol.% for SVM and IEM, respectively. However, by taking into account the difficultly of obtaining roughness parameter at large scale, it was concluded that SVM is still a useful tool to retrieve soil moisture, and therefore, can be fairly used to generate maps at such scales.

Improved discrimination of geological units via geomorphological classification of synthetic aperture radar images

Geological mapping usually requires field visits, but the processing and interpretation of hyperspectral satellite images can also be very beneficial for this task. Microwave or radar remote sensing can obtain surface morphologies using synthetic aperture radar (SAR) images and reduce the duration of field visits dramatically by discriminating geological units based on lithology and texture. This requires the surface roughness to be modeled against microwave signal backscattering. The integral equation model (IEM) is the most well-known rough scattering model, in which surface roughness is calculated using the roughness height statistical parameter (rms-height); however, this study uses an improved IEM based on power-law geometry. The roughness map of the Anaran anticline (located between Dehloran and Ilam in Iran) using TerraSAR images is computed and classified to generate a morphological map. Calculating the roughness map requires training the IEM model and the formation of the look-up-table for pure lithological sites. In situ microtopography measurement was performed on seven different sites containing the main lithologies in the study area, using total station surveying, to train the mathematical model and compare and evaluate the results. Comparing this roughness map with ground-truth data at test sites indicates that computations using the new IEM model results in a misclassification of <10 % of the samples in the map. This error is acceptable, indicating that the new model could, in many cases, reduce the duration of field visits.

Evaluation of Radar Backscattering Models IEM, OH, and Dubois using L and C-Bands SAR Data over different vegetation canopy covers and soil depths

Abstract. Several algorithms have been proposed in the literature to invert radar measurements to estimate surface soil moisture. The objective of this paper is to compare the performance of the most common surface back scattering models including the theoretical integral equation model (IEM) of Fung et al. (1992), and the semi-empirical models of Oh et al. (1992, 1994, 2002 and2004) and Dubois et al. (1995). This analysis uses four AIRSAR data in L and C band together with in situ measurements (soil moisture and surface roughness) over bare soil and vegetation covers area and three different soil depths. The results show that Dubois model tend to over-estimate the radar response in both bands while IEM model and Oh model frequently over-estimate the radar response in L band but under-estimate them in C band. By evaluating of all models in different soil depths, the best results were obtained in 0–3 cm depths. For vegetation area poor correlation between models backscatter simulation and radar response was observed.

A Comparison of IEM and SPM Model for Oil Spill Detection Using Inversion Technique and Radar Data

The purpose of this work is to verifying L band wave behavior for oil spill detection over oceans from satellite remote sensing sensors. Moreover, evaluation of the optimum theoretical backscattering model for this application is considered. This objective was realized by performing an inversion technique which uses neural networks and backscattering model to estimate ocean surface parameters like roughness and dielectric constant. The normalized measure of the radar signal that backscattered to the antenna (sigma zero) includes specific characteristics of the target such as roughness and dielectric constant. Although, in radar imagery, surface roughness is the dominant factor in determining the amplitude of the return signal, this study, most often focus on the dielectric properties because there is a significant difference between dielectric constant of water and oil and therefore they can be distinguished easily by estimating dielectric constant parameter. The neural networks were first trained with a simulated data set generated from the integral equation model (IEM) and second with metadata from small perturbation model (SPM). It used a fast learning algorithm for training a multilayer feed forward neural network. A theoretical database was used for the learning stage. The proposed approach was applied with ALOS-PALSAR images from the Philippine Sea and output are presented in binary images.

Effect of multiple scattering on the phase signature of wet subsurface structures: applications to polarimetric L- and C-band SAR

We propose a two-layer integral equation model (IEM) model including multiple-scattering terms to reproduce the phase signature of buried wet structures that we observed on L-band synthetic aperture radar (SAR) images. We have good agreement between the extended (single+multiple scattering) IEM model and previous results obtained using a single-scattering IEM model combined with finite-difference time-domain simulations. We show that the multiple scattering not only significantly influences the copolarized phase difference but can also be related to the soil moisture content. In order to assess the validity of our extended model, we performed radar measurements on a natural outdoor site and showed that they could be fairly well fitted to the extended model. A parametric analysis presents the dependence of the copolarized phase difference on roughness parameters (rms height and correlation length) and radar parameters (frequency and incidence angle). Our study also shows that the phase signature should allow detection of buried wet structures down to a larger depth for C-band (3.8 m) than for L-band (2.6 m). This signature could then be used to map subsurface moisture in arid regions using polarimetric SAR systems.

A parameterized surface reflectivity model and estimation of bare-surface soil moisture with L-band radiometer

Soil moisture is an important parameter for hydrological and climatic investigations. Future satellite missions with L-band passive microwave radiometers will significantly increase the capability of monitoring Earth's soil moisture globally. Understanding the effects of surface roughness on microwave emission and developing quantitative bare-surface soil moisture retrieval algorithms is one of the essential components in many applications of geophysical properties in the complex Earth terrain by microwave remote sensing. We explore the use of the integral equation model (IEM) for modeling microwave emission. This model was validated using a three-dimensional Monte Carlo model. The results indicate that the IEM model can be used to simulate the surface emission quite well for a wide range of surface roughness conditions with high confidence. Several important characteristics of the effects of surface roughness on radiometer emission signals at L-band 1.4 GHz that have not been adequately addressed in the current semiempirical surface effective reflectivity models are demonstrated by using IEM-simulated data. Using an IEM-simulated database for a wide range of surface soil moisture and roughness properties, we developed a parameterized surface effective reflectivity model with three typically used correlation functions and an inversion model that puts different weights on the polarization measurements to minimize surface roughness effects and to estimate the surface dielectric properties directly from dual-polarization measurements. The inversion technique was validated with four years (1979-1982) of ground microwave radiometer experiment data over several bare-surface test sites at Beltsville, Maryland. The accuracies in random-mean-square error are within or about 3% for incidence angles from 20/spl deg/ to 50/spl deg/.

Monostatic and bistatic statistical shadowing functions from a one-dimensional stationary randomly rough surface: II. Multiple scattering

The integral equation model (IEM) has been developed over the last decade and it has become one of the most widely used theoretical models for rough-surface scattering in microwave remote sensing. In the IEM model the shadowing function is typically either omitted or a form based on geometric optics with single reflection is used. In this paper, a shadowing function for one-dimensional rough surfaces which incorporates multiple scattering, finite surface length and both monostatic and bistatic configurations is developed. For any uncorrelated process, the resulting equation can be expressed in terms of the monostatic statistical shadowing function with single reflection, derived in the preceding companion paper. The effect of correlation between the surface slopes and heights for a Gaussian surface is studied to illuminate the range over which such correlations can be ignored. It is found that while the correlation between surface slopes and heights in the monostatic statistical shadowing function with single reflection can be ignored, when calculating the average shadowing function with double reflection the correlation between slopes and heights between points must be incorporated.

Prediction of IEM Model for Backscattering Enhancement

Predictions for scattering from randomly very rough surfaces are developed and compared with experimental data. The integral equation method with multiple scattering is developed to predict this backscattering enhancement phenomenon. The backscattering enhancement can be predicted from the constructive interference of multiple surfaces scattering from a very roughly random surface. For specialized surfaces involving roughness large compared with the incident wavelength, the backscattering enhancement takes place. In this paper we show that the phenomenon of backscattering enhancement becomes evident for both the normalized surface height > 1.5 and the surface root mean square slope > 0.5. Further, we also show that the incident angle is a factor for the backscattering enhancement. The derivation of the basic surface scattering model is provided and a computer simulation is also provided to compare with measurement. The phenomenon of backscattering enhancement is observed in both the integral equation model (IEM) model prediction and experimental data. In comparing the IEM model with measured data over a wide range of frequency and angle, excellent agreement is found. The difference between the model prediction and data is less than a dB.

Multifrequency Soil Moisture Inversion from SAR Measurements with the Use of IEM

This study focuses on the development of a consistent methodology for soil-moisture inversion from synthetic aperture radar (SAR) data with the use of the integral equation model (IEM), developed by A. K. Fung and colleagues, without the need to prescribe time-varying land-surface attributes as constraining parameters. Specifically, the dependence of backscatter coefficients obtained from synthetic aperture radar (SAR) on the soil dielectric constant, surface-roughness height, and correlation length was investigated. The IEM was used in conjunction with an inversion model to retrieve soil moisture by using multifrequency and multipolarization data (L-, C-, and X-bands) simultaneously. The results were cross validated with gravimetric observations obtained during the Washita '94 field experiment in the Little Washita Watershed, Oklahoma. The average error in the estimated soil moisture was of the order of 3.4%, which is comparable to that expected due to noise in the SAR data. The retrieval algorithm performed very well for low incidence angles and over bare soil fields, and it deteriorated slightly for vegetated areas and overall for very dry soil conditions. Although the original IEM model was developed for bare soil conditions only, one important result of this study was the fact that the retrieval algorithm performed well for vegetated conditions, as demonstrated by the fact that the convergence ratio varied between 92% (dry conditions) and 98% (wet conditions) of all pixels for all days of the experiment. The sensitivity of soil-moisture estimates to spatial aggregation of remote-sensing data before and after the retrieval also was investigated. The results suggest that there is potential to improve the operational utility of high-resolution SAR data for soil-moisture monitoring by compressing the SAR data (preaggregation) to a spatial resolution at least one order of magnitude above that of measurement.

Backscattering behavior and simulation comparison over bare soils using SIR-C/X-SAR and ERASME 1994 data over Orgeval

During April 1994, the three-frequency radar system flew on the Space Shuttle Endeavour, known as SIR-C/X-SAR mission (Shuttle Imaging Radar C/X-Synthetic Aperture Radar). Over the Orgeval watershed (France), the ground condition stayed very wet throughout the 5-day SAR mission. The SAR imagery allows a data collection over a range of roughness conditions on bare soils. Three classes were identified: very smooth sowings with crusted top layer, cloddy surfaces, and different ploughed fields for future crops. To complement the Shuttle Radar data (three frequencies L, C, X, incidence range from 44° to 57°), the helicopter-borne scatterometer ERASME (C- and X-bands, copolorized configurations) was used. Merging of the two databases was possible. As a result, incidence angles ranging from 25° to 50° are available in C- and X-bands for the copolarized cross sections. Then the major objective of the article is, over this available data collection, to begin the validation of current surface backscattering models to natural surfaces, the theoretical integral equation model (IEM) of Fung et al. (1992) and the empirical model of Oh et al. (1994). It shows adequacies and limits. The IEM model reproduces well radar scatter over smooth surfaces, but fails over rough surfaces, predicting a flatter response with incidence angle than the observed signals in C- and X-bands. Difference in backscatter response due to direction angles (perpendicular and parallel to the row direction) is difficult to reproduce over smooth surfaces by this model integrating anisotropic surface but may be due to the unadequacy of the surface representation. The Oh algorithm agrees well with the backscatter response over rough surfaces at medium incidence angle, but fails with a systematic underestimation over smooth conditions. As a conclusion, further developments are necessary on derivation of theoritical solutions over rough surfaces and on validation of semiempirical algorithms over data sets of various training sources (radar and natural conditions).

A simple model for retrieving bare soil moisture from radar-scattering coefficients

A simple algorithm based on a rough surface scattering model was developed to invert the bare soil moisture content from active microwave remote sensing data. In the algorithm development, a frequency mixing model was used to relate soil moisture to the dielectric constant. In particular, the Integral Equation Model (IEM) was used over a wide range of surface roughness and radar frequencies. To derive the algorithm, a sensitivity analysis was performed using a Monte Carlo simulation to study the effects of surface parameters, including height variance, correlation length, and dielectric constant. Because radar return is inherently dependent on both moisture content and surface roughness, the purpose of the sensitivity testing was to select the proper radar parameters so as to optimally decouple these two factors, in an attempt to minimize the effects of one while the other was observed. As a result, the optimal radar parameter ranges can be chosen for the purpose of soil moisture content inversion. One thousand samples were then generated with the IEM model followed by multivariate linear regression analysis to obtain an empirical soil moisture model. Numerical comparisons were made to illustrate the inversion performance using experimental measurements. Results indicate that the present algorithm is simple and accurate, and can be a useful tool for the remote sensing of bare soil surfaces.