Empirically Adopted IEM for Retrieval of Soil Moisture From Radar Backscattering Coefficients

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 in situ 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^deg and 60- - ^deg, soil dielectric constants between 4 and 42, surface rms height from 4 to 31 mm, and correlation length from 50 to 250 mm.