Downscaling of Soil Moisture Fields Using a Modified Fractal Interpolation Scheme

The scaling analysis of the soil moisture from the Southern Great Plains Hydrology experiment (SGP'97) showed that the scaling behavior of soil moisture fields violates the scale invariance at large-scale and this characteristic can be explained by field parameters related water holding capacity. Therefore, ancillary data were incorporated in to the fractal interpolation method as vertical scaling parameters to replicate the spatial characteristic of soil moisture from the existing characteristics of field parameters. Even though previous works related random fractal downscaling method can generate more deterministion output as the number of observations is increased, the output is a single realization of many. Therefore, they have limitation for practical application. A modified fractal interpolation method using a contraction mapping approach was used to construct unique fractal interpolated surfaces. We applied the modified fractal interpolation method for downscaling the retrieved soil moisture from the SGP'97 experiment. The results demonstrate that the downscaling model can capture all the basic statistics of soil moisture at higher-resolution as well the dual-scaling behavior for spatial scales above and below 10 km for a wide range of environmental conditions including very wet and dry soils.