Seasonal and Regional Variability of Parameters for Stochastic Daily Precipitation Models: South Dakota, U.S.A.

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Abstract
Fourier series are used to describe the seasonal variation of the five parameters for a stochastic model of daily precipitation utilizing a first‐order Markov chain for the occurrence process and a mixed exponential distribution for the daily precipitation amounts (MCME model). Spatial variability of the means of each parameter for 16 stations in South Dakota has been illustrated by mapping isopleths. MCME parameters for 4 stations not included in the analysis are more closely described by the arithmetic mean of parameters for the 6 nearest stations than by using parameters for the nearest neighboring station or parameters estimated by spline fitting or linear interpolation. However, MCME parameters estimated by all interpolation methods were significantly different from parameters identified for each of the four stations by maximum likelihood techniques. The principal source of this spatial variability at distances of on the order of 100 km is data inconsistency due to methodological differences affecting small precipitation amounts and apparently related to observation time. Sampling error, possible parameter identifiability problems, and real differences in the precipitation regime on a scale smaller than the station spacing also contribute to the observed variability.