Application of seasonal parametric linear stochastic models to monthly flow data

Abstract

Stochastic linear models are fitted to hydrologic data for two main reasons: to enable forecasts of the data one or more time periods ahead and to enable the generation of sequences of synthetic data. These techniques are of considerable importance to the design and operation of water resource systems. Short sequences of data lead to uncertainties in the estimation of model parameters and to doubts about the appropriateness of particular time series models. A premium is placed on models that are economical in terms of the number of parameters required. One such family of models is multiplicative seasonal autoregressive integrated moving average (Arima) models that have been described by G. E. P. Box and G. M. Jenkins. In this paper we illustrate the process of identifying the particular member of the family that fits logarithms of monthly flows, estimating the parameters, and checking the fit. The seasonal Arima model accounts for the seasonal variability in the monthly means but not the seasonal variability of the monthly standard deviations: for this reason its value is limited. The forecasting of flows one or more months ahead is described with an example.

Drought forecasting using stochastic models

“…An inherent advantage of the SARIMA family of models is that few model parameters are required for describing time series, which exhibit non-stationarity both within and across the seasons. Some useful applications of these models in seasonal river flow forecasting are reported in McKerchar and Dellur (1974), Panu et al (1978), Cline (1981), Govindaswamy (1991) and Yurekli et al (2005). Hydrologists have also widely used stochastic analogy for the analyzing and modeling of hydrologic time series.…”

Generating and forecasting monthly flows of the Ganges river with PAR model

“…An inherent advantage of the SARIMA family of models is that few model parameters are required for describing time series, which exhibit nonstationarity both within and across seasons. Some useful applications of these models in seasonal river flow forecasting are reported in McKerchar and Delleur (1974); Panu et al (1978); Cline (1981); Govindasamy (1991); Sidhu (1995 Kavvas and Delleur (1975) have shown, both from analytical and empirical results, that seasonal and/or nonseasonal differencing, although very effective in the removal of hydrologic periodicities, distorts the original spectrum, thus making it impractical or impossible to fit an ARMA model for hydrologic simulation or synthetic generation. McKerchar and Delleur (1974); Delleur et al (1976) have shown that the forecasting capabilities of seasonally differenced models may be impaired by the fact that they may not take into account the seasonal variation in the seasonal standard deviations.…”

Development of Flow Forecasting Models in the Bow River at Calgary, Alberta, Canada

“…Auto-regressive (AR) and auto-regressive integrated moving average (ARIMA) models were applied to forecast monthly flows in Wabash River, Indiana, USA [20]. Noakes et al [13] assessed the forecasting ability of ARMIA, auto-regressive moving average (ARMA) and AR models in forecasting monthly flows in 30 rivers in North and South America.…”