This study focuses on the statistical characterization of the spatial structure of L band microwave radiobrightness temperature fields retrieved during the Southern Great Plains hydrology experiment of 1997 (SGP97). It is found that the radiobrightness temperature observations of interest can be considered nonstationary scaling processes that exhibit persistence or long memory. This implies that the spatial dependence of observations decays very slowly at large separation distances such that models with exponentially decaying autocorrelation (e.g., autoregressive moving average models or exponential models commonly used in geostatistics) are not appropriate. It is further shown that the radiobrightness temperature fields retrieved during SGP97 exhibit distinct scaling behaviors along the horizontal (west to east) and vertical (south to north) directions. A two-dimensional implementation of the fractionally integrated moving average (FIMA) time series model is shown capable of capturing the spatial autocovariance structure of the observations. The results presented evince that the FIMA paradigm allows for robust estimation of distinct scaling exponents along the horizontal and vertical directions both in stationary and nonstationary situations. Comparisons to alternative heuristic methods for determining the scaling exponent(s) further demonstrate that FIMA models yield estimates with superior accuracy. Additionally, within the FIMA framework it is possible to jointly and accurately model the spatial dependence of radiobrightness temperature for observations separated by short and long distances.