Decoupling of modeling and measuring interval in groundwater time series analysis based on response characteristics W.L. Berendrecht a, * , A.W. Heemink a , F.C. van Geer b , J.C. Gehrels b,c a Department of Applied Mathematical Analysis, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands b Netherlands Institute of Applied Geoscience TNO, National Geological Survey, P.O. Box 80015, 3508 TA Utrecht, The Netherlands c Department of Watermanagement, Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands Received 20 March 2002; accepted 28 February 2003 Abstract A state – space representation of the transfer function – noise (TFN) model allows the choice of a modeling (input) interval that is smaller than the measuring interval of the output variable. Since in geohydrological applications the interval of the available input series (precipitation excess) is often smaller than the interval of the output series (groundwater head), the state – space model opens the way to a more detailed description of the system. This paper evaluates the influence of the reduction of the modeling interval on the performance of the state – space time series model while keeping the measuring interval fixed. In order to obtain general conclusions of the relation between the modeling interval and the model performance, a large number of groundwater time series are generated and modeled with the state – space time series model. The results show that a reduction of the modeling interval noticeably improves the model performance. The degree of improvement depends on aspects like the response time of the system, the length of the time series and the amount of noise. A case study illustrates the effect of reducing the modeling interval as well as that of adding high-frequency measurements to the time series. q 2003 Elsevier Science B.V. All rights reserved. Keywords: Time series analysis; Modeling interval; Transfer function; Groundwater; Kalman filter 1. Introduction Time series models (Box and Jenkins, 1970), and especially transfer function–noise (TFN) models, have been applied to analyze hydrological systems for many years (Hipel and McLeod, 1994; Van Geer and Zuur, 1997; Young et al., 1997). In groundwater hydrology, the main applications of TFN modeling are decomposition of groundwater level fluctuations into natural and anthropogenic fluctuations (Van Geer and Defize, 1987; Gehrels et al., 1994) and prediction of the effects of interventions (Knotters and Bierkens, 2000). Besides the TFN model form proposed by Box and Jenkins, there is an alternative way to describe a dynamic system, namely by using the state – space form (Schweppe, 1973; Maybeck, 1979). This formulation is a very powerful and flexible representation of a system and has been successfully 0022-1694/03/$ - see front matter q 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-1694(03)00075-1 Journal of Hydrology 278 (2003) 1–16 www.elsevier.com/locate/jhydrol * Corresponding author. E-mail address: w.berendrecht@nitg.tno.nl (W.L. Berendrecht).