Stochastic analysis of California's recent precipitation drought in the context of the last one hundred years

Abstract:

Approximately one hundred years of daily precipitation data have been analyzed at thirteen stations in California. Seasonal markovian stochastic models accounting for daily occurrence and depth are constructed using a generalized linear modeling framework. A probit link function is used to model the seasonally varying probability of daily precipitation, and a reciprocal link is used to model the (seasonally varying) mean of a gamma distribution for daily
precipitation depth. Short-term memory is accounted for with lagged indicator variables of precipitation occurrence. In this framework, the model is flexible enough to well capture the variability of daily precipitation, and its parameters are readily estimated using standard methods. Simulated realizations of centuries of daily data, however, do not capture the measured variance of precipitation at seasonal to annual time scales, indicating that low frequency variations in the underlying processes are present, which, by construct, are not accounted for. To account for this a clustering algorithm is developed that separates the years of data into distinct clusters (with associated parameters) in an optimal fashion with respect to the likelihood of the fitted generalized linear models. Typically three clusters are found to adequately be able to reproduce the aggregated (i.e. annual) rainfall statistics (e.g. the variance and also the probability distribution of annual rainfall). The final estimated models are again used to simulate hundreds of ensembles of the last century of rainfall, and are used to assess how unusual, or not, the calendar year 2013 drought was. At 10 of 13 stations, the annual 2013 rainfall was not statistically unusual, in the sense that a year as dry as 2013 would be expected to occur at least once in each century in ten percent of the ensembles. At 3 stations, however, the simulations reproduced 2013 levels of rainfall (in each simulated century) less than ten percent of the time. From these preliminary results, we conclude that the null hypothesis, i.e. that 2013 precipitation was produced by the same stochastic process as has occurred for the past 100 years, is rejected at the p=0.1 level at 3 stations.