An event-oriented hourly precipitation model

Abstract

A simulation model of hourly rainfall amounts was developed to provide hourly precipitation input to a water balance model. The hourly rainfall model consists of four parts: (1) daily rainfall occurrence, (2) event rainfall amount, (3) hourly rainfall occurrence within an event, and (4) hourly rainfall amounts within an event. An event is defined as a consecutive number of wet days preceded by at least one day of no rainfall and followed by at least one day of no rainfall. Daily rainfall occurrence in the model is simulated using a two-state Markov chain. The order of the chain was defined using Akaike's information criterion. Fourier coefficients were estimated for each Markov chain parameter to describe the seasonal variations in daily rainfall occurrence. A probability distribution generates the rainfall amount of an event. The exponential, the mixed exponential, the lognormal, the gamma, and the Weibull probability distributions were examined to determine which would be most suitable for modeling the event rainfall amounts. Fourier coefficients were estimated for the parameters of the appropriate probability distribution to describe seasonal variations in event rainfall amounts. Another two-state Markov chain is used to generate occurrence of wet hours and dry hours within the rainfall event. A third-order Markov chain best defined the occurrence of wet hours and dry hours for the developmental data set. For each wet hour, an hourly index is generated using another probability distribution. Hourly rainfall indexes were created from the developmental data by dividing each wet hour by the event rainfall amount. Fourier coefficients were estimated for each of the Markov chain and the probability distribution parameters to describe the hourly variations of rainfall occurrence and rainfall amount in a rainfall event. The hourly indexes are then summed over the event and divided by the sum to give the distribution of rainfall within an event. Finally, the total rainfall amount generated previously for the event is multiplied by each of the derived normalized indexes, resulting in generated hourly rainfall amounts for each hour of the rainfall event.