Stochastic Simulation Methods for Precipitation and Streamflow Time Series

One major acknowledged challenge in daily precipitation is the inability to model extreme events in the spectrum of events. These extreme events are rare but may cause large losses. How to realistically simulate extreme behavior of daily precipitation is necessary and important. To that end, a hybrid probability distribution is developed. The logic of this distribution is to simulate the low to moderate values by an exponential distribution and extremes by a generalized Pareto distribution. Compared with alternatives, the developed hybrid distribution is capable of simulating the entire range of precipitation amount and is much easier to use. The hybrid distribution is then used to construct a bivariate discrete-continuous mixed distribution, which is used for building a daily precipitation generator. The developed generator can successfully reproduce extreme events. Compared with other widely used generators, the most important advantage of the developed generator is that it is apt at extrapolating values significantly beyond the upper range of observed data.

The major challenge in monthly streamflow simulation is referred to the underrepresentation of inter-annual variability. The inter-annual variability is often related with sustained droughts or periods of high flows. Preserving inter-annual variability is thus of particular importance for the long-term management of water resources systems. To that end, variables conveying such inter-annual signals should be used as covariates. This requires models that must be flexible at incorporating as many covariates as necessary. Keeping this point in mind, a joint conditional density estimation network is developed. Therein, the joint distribution of streamflows of two adjacent months is assumed to follow a specific parametric family. Parameters of the distribution are estimated by an artificial neural network. Due to the seasonal concentration of precipitation or the joint effect of rainfall and snowmelt, monthly streamflow distribution sometimes may exhibit a bimodal shape. To reproduce bimodality, nonparametric models are often preferred. However, the simulated sequences from existing nonparametric models represent too close a resemblance to historical record. To address this issue, while retaining typical merits of nonparametric models, a multi-model regression-sampling algorithm with a few weak assumptions is developed.

Collecting hydrometric data is the first step for building hydrologic models, and for planning, design, operation, and management of water resource systems. In this dissertation, an entropy-theory-based criterion, termed maximum information minimum redundancy, is proposed for hydrometric monitoring network evaluation and design. Compared with existing similar approaches, the criterion is apt at finding stations with high information content, and locating independent stations.