Assessment of sampling error associated with soil moisture estimation designs

A spectral formalism was developed and applied to quantify the sampling errors due to spatial and/or temporal gaps in soil moisture measurements. A design filter was developed to compute the sampling errors for discrete measurements in space and time. This filter has as its advantage a general form applicable to various types of sampling design. The lack of temporal measurements of the two-dimensional soil moisture field made it difficult to compute the spectra directly from observed records. Therefore, the wave number frequency spectra of soil moisture data derived from stochastic models of rainfall and soil moisture were used. Parameters for both models were estimated using data from the Southern Great Plains Hydrology Experiment (SGP97) and the Oklahoma Mesonet. The estimated sampling error of the spatial average soil moisture measurement by airborne L-band microwave remote sensing during the SGP97 hydrology experiment is estimated to be 2.4 percent. Under the same climate conditions and soil properties as the SGP97 experiment, equally spaced ground probe networks at intervals of 25 and 50 km are expected to have about 16 percent and 27 percent sampling error, respectively. Satellite designs with temporal gaps of two and three days are expected to have about 6 percent and 9 percent sampling errors, respectively.