Peter F Rasmussen

Prediction in partial duration series with generalized pareto‐distributed exceedances

As a generalization of the common assumption of exponential distribution of the exceedances in partial duration series the generalized Pareto distribution has been adopted. Estimators for the parameters are presented using estimation by both method of moments and probability-weighted moments. The corresponding estimators for the T-year event are given and approximate expressions for bias and variance of the estimators are derived in both cases. Using the mean square error of the T-year event estimator as a performance index it is shown that the method of moments is preferable to the probability-weighted moments. Maintaining the generalized Pareto distribution as the parent exceedance distribution the T-year event is estimated assuming the exceedances to be exponentially distributed. For moderately long-tailed exceedance distributions and small to moderate sample sizes it is found, by comparing mean square errors of the T-year event estimators, that the exponential distribution is preferable to the correct generalized Pareto distribution despite the introduced model error and despite a possible rejection of the exponential hypothesis by a test of significance. For moderately short-tailed exceedance distributions (with physically justified upper limit) the correct exceedance distribution should be applied despite a possible acceptance of the exponential assumption by a test of significance.

Estimation and validation of contemporaneous PARMA Models for streamflow simulation

Seasonal streamflow series generally exhibit periodicity in the autocovariance structure. Such periodicity can be represented by PARMA models, i.e., autoregressive moving average (ARMA) models with parameters that vary with the seasons. Statistical properties of low-order models such as the PARMA(2,2) model are examined. The periodic moment equations are derived; they can be used to compute the periodic covariance structure of a given model. Simulation of streamflow at several sites can be done using the contemporaneous PARMA model. The main problem in using such models is to determine the covariance matrices of innovations. Traditionally, this has been done by the method of maximum likelihood. However, this method generally leads to significant underestimation of the cross correlation of flows. A moment estimator is developed herein for the contemporaneous PARMA(2,2) model along with three approximate moment-based estimators for those cases where a feasible moment solution cannot be obtained. The applicability of the proposed methods is illustrated by fitting PARMA models to weekly flow data for two catchments in the Ottawa River basin.