Synthetic streamflow generation: 1. Model verification and validation

Abstract

A part of the streamflow construction and simulation process is the verification that a stochastic streamflow model reproduces those statistics which by design it should reproduce; the use of unbiased statistics is shown to be advantageous in this exercise. In addition, if a model reproduces statistics not used in the model-parameter estimation process, its credibility is further enhanced. These concepts are illustrated, and the performance of a wide range of monthly streamflow models are compared using data for the upper Delaware River basin in New York State. INTRODUCTION Stochastic monthly streamflow models are often used in simulation studies to evaluate the likely future performance of water resource systems. The development and use of a stochastic streamflow model can involve all of the following basic steps: (1) obtain streamflow records and other information, (2) select models to describe the marginal probability distributions of flows in different seasons and estimate the models' parameters, (3) select an appropriate model of the spatial and temporal dependence of the streamflows, (4) verify that the computer implementation of the model performs as specified, (5) validate the model for water resource system simulation, and (6) use the model. First, one collects the data to be used for parameter estimation, model verification, and any model validation. Then an appropriate model of the temporal and spatial dependence of flows and the marginal distribution of flows at each site in each period is selected, and its parameters are estimated. The fourth and fifth steps involve model verification and validation. An important distinction between these two activities has been drawn in the simulation literature [Fishman and Kiviat, 1968; Mihram, 1972; Schlesinger et al., 1979]. Schlesinger et al. [1974] describe verification asthe certification that the model is implemented on the computer in a manner that truly depicts the idealized model.

Multivariate modelling of water resources time series using artificial neural networks

“…These include autoregressive moving average (ARMA) models (Box & Jenkins, 1970), disaggregation models (Valencia & Schaake, 1973), models based on the concept of pattern recognition (Panu & Unny, 1980). Stedinger & Taylor (1982) studied the performance of five different models for streamflow simulation. All these models have their merits and have also been criticized.…”

An Introduction to Probability, Statistics, and Uncertainty

“…Definition of resemblance in terms of moments can also lead to confusion over whether the population parameters should equal the sample moments, or whether the fitted model should generate flow sequences whose sample moments equal the historical values-the two concepts are different because of the biases (as discussed in Sect. 6.7) in many of the estimators of variances and correlations (Matalas and Wallis 1976;Stedinger 1980Stedinger , 1981Stedinger and Taylor 1982a).…”

An empirical‐stochastic, event‐based program for simulating inflow from a tributary network: Framework and application to the Sacramento River basin, California

“…Its methods later became more formalized using statistical theories to develop autoregressive models for monthly rainfall data [Hannan, 1955]. Since that time, stochastic statistical theory has been applied to empirical streamflow simulation primarily to synthetically extend the historical record of annual maximum series at a particular gauging point [e.g., Stedinger and Taylor, 1982] and to generate synthetic series for ungauged basins using regional parameters [e.g., Benson and Matalas, 1967].…”