Fitting Daily Precipitation Amounts Using the SB Distribution

Lloyd W. Swift Jr. Coweeta Hydrologic Laboratory, U.S.D.A. Forest Service, Otto, NC 28763

Search for other papers by Lloyd W. Swift Jr. in
Current site
Google Scholar
PubMed
Close
and
Hans T. Schreuder Rocky Mountain Forest and Range Experiment Station, U.S.D.A. Forest Service, Fort Collins, CO 80526

Search for other papers by Hans T. Schreuder in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The log-normal, gamma, Weibull, S8 and beta distributions were fit to daily precipitation amounts foreach calendar month for a 38-year period. Data are from the high precipitation zone of the southernAppalachian Mountains. The S8 distribution, a generalization of the log-normal, consistently fit the databest. There was no striking evidence that precipitation distribution differed by month. The SB distributionalso was best when fit to all precipitation days without regard to date. The gamma distribution fit rainfallamounts accumulated for two and three consecutive wet days best.

Higher order Markov chains, up through the fifth order, described our data better than lower orderchains. Thus, the probability of precipitation on any day depends on what happened on at least the fiveprevious days. The SB distribution of precipitation amounts on all dates preceded by dry days is differentfrom the distribution of amounts on all dates preceded by precipitation days. The SBB distribution, a simplebivariate extension of the S8, showed low correlations between amounts of precipitation on consecutive wetdays and between amounts on the first and third days of three consecutive days with precipitation. Thecumulative amounts of precipitation over n days are normally distributed for large n with mean O.53n cmand standard deviation 1.55n2 cm.

Abstract

The log-normal, gamma, Weibull, S8 and beta distributions were fit to daily precipitation amounts foreach calendar month for a 38-year period. Data are from the high precipitation zone of the southernAppalachian Mountains. The S8 distribution, a generalization of the log-normal, consistently fit the databest. There was no striking evidence that precipitation distribution differed by month. The SB distributionalso was best when fit to all precipitation days without regard to date. The gamma distribution fit rainfallamounts accumulated for two and three consecutive wet days best.

Higher order Markov chains, up through the fifth order, described our data better than lower orderchains. Thus, the probability of precipitation on any day depends on what happened on at least the fiveprevious days. The SB distribution of precipitation amounts on all dates preceded by dry days is differentfrom the distribution of amounts on all dates preceded by precipitation days. The SBB distribution, a simplebivariate extension of the S8, showed low correlations between amounts of precipitation on consecutive wetdays and between amounts on the first and third days of three consecutive days with precipitation. Thecumulative amounts of precipitation over n days are normally distributed for large n with mean O.53n cmand standard deviation 1.55n2 cm.

Save