A formalism (North and Nakamoto, 1989) is employed to estimate the sampling error, both numerically and analytically, of the soil moisture field under different sampling schemes. In this formalism, the mean square error consists of two factors, a design dependent filter and space-time spectral density of soil moisture field. The factors are integrated over all frequencies and wave numbers. The space-time spectral density of soil moisture can be estimated from observed records or based upon solutions of a stochastic soil moisture model tuned by the observed data. The lack of temporal measurements of the soil moisture field makes it difficult to estimate the spectra directly from observed records, thus the space-time soil moisture spectra is based on a stochastic model.
A stochastic model is used to force a soil moisture model to investigate the impact of precipitation and soil heterogeneities on soil moisture evolution. The parameters for the stochastic model are estimated by using SGP '97 data. The mean value of precipitation and soil properties is significant in the sampling error estinaton of soil moisture field. The change of correlation structure with the same mean value is not important in sampling error estimation. The impact of partial coverage on soil moisture mapping is insignificant in sampling error estimation.