A derivation of roughness correlation length for parameterizing radar backscatter models

Surface roughness is a key parameter of radar backscatter models designed to retrieve surface soil moisture (θ_S) information from radar images. This work offers a theory‐based approach for estimating a key roughness parameter, termed the roughness correlation length (L _c). The L _c is the length in centimetres from a point on the ground to a short distance for which the heights of a rough surface are correlated with each other. The approach is based on the relation between L _c and h _RMS as theorized by the Integral Equation Model (IEM). The h _RMS is another roughness parameter, which is the root mean squared height variation of a rough surface. The relation is calibrated for a given site based on the radar backscatter of the site under dry soil conditions. When this relation is supplemented with the site specific measurements of h _RMS, it is possible to produce estimates of L _c. The approach was validated with several radar images of the Walnut Gulch Experimental Watershed in southeast Arizona, USA. Results showed that the IEM performed well in reproducing satellite‐based radar backscatter when this new derivation of L _c was used as input. This was a substantial improvement over the use of field measurements of L _c. This new approach also has advantages over empirical formulations for the estimation of L _c because it does not require field measurements of θ_S for iterative calibration and it accounts for the very complex relation between L _c and h _RMS found in heterogeneous landscapes. Finally, this new approach opens up the possibility of determining both roughness parameters without ancillary data based on the radar backscatter difference measured for two different incident angles.