Comparison of univariate and transfer function models of groundwater fluctuations (original) (raw)

1993, Water Resources Research

Seasonal autoregressive integrated moving average (SARIMA) univariate models and single input-single output transfer function (SARIMA with externalities or SARIMAX) models of groundwater head fluctuations are developed for 21 Upper Floridan aquifer observation wells in northeast Florida. These models incorporate empirical relationships between rainfall input and head response based on historical correlations and cross correlations between these two time series. The magnitude of the forecast error terms indicates that the SARIMA and SARIMAX models explain an average of 84-87% of the variation observed in the monthly piezometric head levels for 1-month lead forecasts. Thus the models account for the dominant processes which affect temporal groundwater fluctuations. Both the SARIMA and SARIMAX models provide unbiased forecasts of piezometric head levels; however, the SARIMAX models produce more accurate forecasts (i.e., smaller forecast probability limits) than the SARIMA models, particularly as lead time increases. Modeling efforts reveal consistent model structures over the study region, with local hydrologic and geologic conditions causing site-specific variability in the time series model parameters. INTRODUCTION The management of surface water and groundwater resources requires the use of modeling techniques which recognize the variability and uncertainty of hydrologic inputs. Rainfall, streamflow, evapotranspiration, and groundwater flow are all unpredictable processes which affect the design, operation, and management of water resource systems. Time series modeling techniques have been shown to provide a systematic empirical method for simulating and forecasting the behavior of uncertain hydrologic systems and for quantifying the expected accuracy of the forecasts. Time series modeling of suspended sediment concentration in rivers has been conducted by Sharma et al. [1979], Sharma and Dickinson [1980], Fitzgerald and Karlinger [1983], Gurne!l and Fenn [1984], Caroni et al. [1984], La Barbera et al. [1985], and Lemke [1990]. Their studies have shown that time series models provide an improved methodology for predicting suspended sediment concentrations in comparison with traditional simple regression models. Lernke [1991] developed single input-single output and multiple input-single output transfer function models for predicting daily suspended sediment concentrations and found that these models provided a good representation of dynamic fluvial processes. Matalas and Wallis [1976], O'Connell [1977], Stedinger [1981], Stedinger and Vogel [1984], and $tedinger et al. [1985] used multivariate time series models to simulate synthetic streamflows that exhibit long-term persistence. Jackson et al. [1973], Law [1974], Houston [1983], and Changnon et al. [1988] used time series analysis to examine climatological and hydrogeological variables associated with groundwater fluctuations in a variety of shallow unconfined aquifer systems. More recently, Ada