Transfer function‐noise modeling in continuous time using predefined impulse response functions

Abstract

[1] A method of transfer function-noise (TFN) modeling is presented that operates in continuous time and uses a predefined family of impulse response (IR) functions. The resulting class of models is referred to as predefined IR function in continuous time (PIRFICT). It provides a useful tool for standardized analysis of time series, as it can be calibrated using irregularly spaced data and does not require a model identification phase prior to calibration. In section 2, the discrete Box-Jenkins (BJ) model is presented and transformed into continuous time to obtain the PIRFICT model. The discrete transfer function of a BJ model, which is made up of a variable number of parameters, is replaced by a simple analytical expression that defines the IR function. From the IR function, block response functions are derived that enable the model to handle irregularly spaced data. In the example application, the parameter estimates and performance of the BJ and PIRFICT model are compared using a data set of 15 piezometers and a simulated series. It was found that the estimated transfer and BR functions of both models follow the same general pattern, although the BJ transfer functions are partly irregular. The performance of both models proves to be highly comparable for all piezometers.

A time-series analysis framework for the flood-wave method to estimate groundwater model parameters

“…Convolution of a stress with its corresponding response function provides the effect of that stress on the head. From a time-series modeling perspective, the method proposed is a variation of the method of predefined response functions (Von Asmuth et al 2002). The response functions of the extended flood-wave method are to be compared with the well function of a pumping test: they translate observed heads into aquifer parameters with a minimum of parameters.…”

“…Time series analysis is performed with the method of predefined response functions (Von Asmuth et al 2002). Transfer functions, a term widely used in system theory and time series analysis, can be considered as synonymous to response functions.…”

The need of data harmonization to derive robust empirical relationships between soil conditions and vegetation

“…To analyze long time series of daily groundwater level data, the groundwater level series were extended to the period 1970-2000 and interpolated to daily values with Menyanthes (von Asmuth et al 2002). The interpolation was needed to calculate MSL values accurately.…”

Transfer function-noise modeling and spatial interpolation to evaluate the risk of extreme (shallow) water-table levels in the Brazilian Cerrados

“…In this approach, the spatial differences in water-table dynamics are determined by the spatial variation in the system properties, while its temporal variation is driven by the dynamics of the input into the system. The PIRFICT-model (predefined impulse response function in continuous time) is an alternative to discrete-time transfer function-noise (TFN) models (Von Asmuth et al 2002). An important advantage in the use of the PIRFICT-model, compared with discrete-time TFN models, is that it can deal with input and output series which have different observation frequencies and irregular time intervals (Von Asmuth and Bierkens 2005).…”