ESTIMATION OF PARAMETERS CHARACTERIZING FREQUENCY DISTRIBUTIONS OF TIMES BETWEEN STORMS

Abstract

Long records of precipitation data of the order of minutes are often needed for hydrology studies, but few such records exist over widespread areas. Storm simulation is an alternative approach to meet this need. One element of storm simulation is modeling the durations of dry periods between storms (storm–occurrence modeling). However, simple methods of characterizing storm occurrences and estimating simulation parameters are needed for practical storm simulation. One method for characterizing times between storms (TBS) is by using the “exponential method.” This method assumes that TBS greater than a minimum TBS follows an exponential distribution. Two parameters are necessary in the exponential method, the minimum time between independent storms (called critical time between storms, or CTBS), and the average time between independent storms (ATBS). Methods for estimating these parameters were explored using 34 recording rain gauges over a 225,000 km2 area encompassing the Plains area of eastern Colorado and its periphery. Monthly CTBS values ranged from 0.2 d to 2.5 d with a median of 0.8 d. Monthly ATBS ranged from 2.0 d to 13.0 d with a median of 4.5 d. Monthly mapping of CTBS and ATBS allows estimation of these two parameters and incorporates observed spatial and temporal variation. All regressions of CTBS vs. average monthly precipitation (Pmo), ATBS vs. Pmo, and CTBS vs. ATBS using collapsed monthly data yielded poor correlations. However, analysis of monthly data at individual stations yielded good log–linear correlations between ATBS and Pmo, and fair linear correlations between CTBS and ATBS. Intercept and slope parameters for each of the two regressions were correlated across the study area. The results suggest that further categorization of raw precipitation data into “wet,” “dry,” and “normal” categories may minimize errors in computing CTBS and ATBS. Subsequent mapping of regression parameters may improve the CTBS– and ATBS–estimating methods discussed in this article. A fixed CTBS (e.g., 6 hr often used in precipitation analyses) did not capture the month–to–month variability observed in measured data, and was much shorter than required for statistical independence between storms (6 hr is only 22% to 36% of values of CTBS found in this study). PRISM (parameter–elevation regressions on independent slopes model) maps of Pmo across the U.S. are a source of readily available Pmo data for use in the regressions investigated. The methods developed for estimating CTBS and ATBS are a promising simple parameterization framework for quantifying the temporal and spatial characteristics of independent storms and frequency distributions of TBS for stochastic–storm generation and other hydrological investigations.