Random, but Uniform Please: Requirements for Synthetic Precipitation Generation for Computer Simulations in Agriculture

Abstract

Observed weather records are often too short or discontinuous for long-term simulation of hydrologic processes. These shortcomings can be remedied with computer-generated synthetic weather. Generation of synthetic weather involves the use of random numbers (RN) to simulate the stochastic nature of daily weather. In arid and semi-arid regions, sometimes only a few RNs are needed for the generation of daily precipitation amount because rainfall events are scarce and infrequent. However, small samples of RNs are not always uniformly distributed as assumed by the precipitation model. This can lead to generated daily precipitation amounts that have distribution statistics different from those of the observed precipitation, which, in turn, can affect subsequent model simulations that use the synthetic precipitation. A random number resampling procedure (called RANSAM) was developed to ensure that as few as 50 RNs would approximate both mean and standard deviation of the uniform distribution within 5% of theoretical values, while retaining essential random characteristics. The adherence of RNs to the uniform distribution led to generated daily precipitation amounts that have statistics close to those of the underlying observed precipitation. Without RANSAM, about 300 or more conventional RNs would be needed to obtain a uniform distribution of similar level of accuracy. RANSAM was verified with precipitation data at four weather stations in the western United States. It demonstrated that precipitation amounts generated with RNs by RANSAM were consistently closer and converged faster to observed precipitation statistics than for precipitation generated with conventional RNs. Thus, in dry climates when only few RNs are needed to generate daily precipitation amount and uniformity of RNs is an issue, RANSAM offers an alternate source of RNs that more consistently adhere to the uniform distribution as assumed by the precipitation model.