Tests for detecting a shift in the mean of hydrological time series

Maximum likelihood parameter estimation of hydrologic spatial processes by the Gauss-Newton method

Alternative approaches suggested for modeling multiseries of water resources systems are reviewed and compared. Most approaches fall within the general framework of multivariate ARMA models. Formal modeling procedures suggest a three-stage iterative process, namely: model identification, parameter estimation and diagnostic checks. Although a number of statistical tools are already available to follow such modeling process, in general, it is not an easy task, especially if high order vector ARMA models are used. However, simpler ARMA models such as the contemporaneous and the transfer-function models may be sufficient for most applications in water resources. Two examples of modeling bivariate and trivariate streamflow series are included. Alternative modeling procedures are used and compared by using data generation techniques. The results obtained suggest that low order models, as well as contemporaneous ARMA models, reproduce quite well the main statistical characteristics of the time series analyzed. It is assumed that the same conclusions apply for most water resources time series.

Approaches to multivariate modeling of water resources time series1

The structure of disaggregation models places severe constraints on the feasible values of the lagged covariance of generated flow vectors. A new and simple class of disaggregation models is presented which employ the Valencia-Schaake disaggregation model structure but allow the models' innovations to be serially correlated. These models can reproduce (1) the covariance matrix of the disaggregated flows, (2) their covariance with the upper level flows, and (3) reasonable approximations to the lag one covariance of the disaggregated flow vectors given the constraints imposed by a disaggregation approach. The Mejia-Rousselle disaggregation model is shown, in general, to fail to reproduce the anticipated variances and covariances of the disaggregated flows because the model and its parameter estimators are not self-consistent. The paper closes with a discussion of practical modeling considerations and of staged disaggregation procedures which reduce the size of multisite multiseason models.

Disaggregation Procedures for Generating Serially Correlated Flow Vectors

Here we review the main thrusts of rainfall-runoff modelling with an eye toward the advantageous use of the massive date sets being accumulated and the modern computers capable of dealing effectively with such sets. More than a tutorial, this study is aimed at providing a unifying structure for analyzing available techniques. The closing section draws attention to the existence of an alternative methodology.

Rainfall-runoff forecasting methods, old and new

In time series modeling of hydrologic systems the model structure either is determined a priori from physical considerations or is identified statistically. This paper sets forth a maximum likelihood procedure for estimating the parameters of a class of statistical models (linear time-invariant state-space) once a suitable member of the class has been identified. Using the innovation form of the state-space model, the parameters of the transition, input weighting, gain and output, or measurement matrices are estimated as well as the innovation covariance matrix. Procedures for estimating process and measurement covariances in the state-space model, and the parameters of the equivalent multivariate autoregressive moving average with exogenous inputs (ARMAX) model are also developed. A convergent and asymptotically efficient on-line method of estimation is derived from the off-line algorithm. Four examples are presented: daily rainfall-runoff forecasting, four-site monthly streamflow, seasonal model, and river flow input-output model with a tributary.

Parameter estimation of multiple input‐output time series models: Application to rainfall‐runoff processes

The problem of linear model structure identification for multivariate time series or multiple input-output models is presented and solved The identification is obtained using canonical correlations to determine model order The equivalence between state-space model structure and multivariate autoregressive moving average with exogenous inputs (ARMAX) models is presented The class of models open to analysis includes rainfall-runoff models, multivariate streamflow models, and time invariant state-space models used in Kaiman filtering Examples include a rainfall-runoff model using three precipitation inputs, a four-site monthly streamflow model, and a four-season streamflow model

Identification of multivariate time series and multivariate input‐output models

This paper deals with the problem in which it is necessary to infer the probabilistic characteristics of a streamflow variable yt (e.g., annual peak discharge, or accumulated streamflow during some time interval) given a correlated longer record xt (e.g., annual peak discharge at a gaging site with longer record; rainfall during the same time interval). In particular, it is necessary to estimate probabilities of the form P(y ≥ y0) for given Y0. Conventional methods make assumptions about the joint probability distribution of xt and yt; the methods developed in this paper require no such assumption, being distribution free. Estimates of P(y ≥ Y0) are also obtained by Bayesian methods.

David M. Cooper

Papers

Parameter estimation of multiple input‐output time series models: Application to rainfall‐runoff processes

Identification of multivariate time series and multivariate input‐output models

Distribution-Free Methods for Estimating Flood and Streamflow Exceedance Probabilities by Correlation

Model identification and parameter estimation for hydrologic input/output models

Theory and application of model identification and parameter estimation algorithm for hydrologic models.