Estimation of the number of frequencies and bandwidth for the surface measurement of soil moisture as a function of depth

The feasibility of obtaining estimates in situ of volumetric soil moisture as a function of depth using measurements of radio wave reflection at the soil surface at several discrete frequencies was demonstrated through computer simulation. By deriving empirical relationships between the number of frequencies, the frequency range, and the number of soil layers for which the soil moisture is estimated, the number of frequencies and measurement bandwidth have been determined. The soil moisture profile was obtained to a depth of 1.5 m by inverting, through function optimization, a simulation of the reflection coefficient from layered dielectric materials. The dielectric properties of soil-water mixtures mere obtained from the models of (1962) and (1980) and the function optimization was done with Powell´s direction set method (1992). The number of soil layers in which soil moisture could be resolved was found to be twice the number of frequencies used. The required bandwidth increased with the number of soil layers from 20 MHz for six layers to 140 MHz for 16 layers. Within some assumptions about the nature of the radio wave propagation, the theoretical accuracy of the estimate depended only on the quantization error introduced by having to consider discrete layers of uniform soil with finite thicknesses