Transfer function-noise modelling of irregularly observed groundwater heads using precipitation data

Time series data on precipitation rates and groundwater heads are used for transfer function-noise (TFN) models which are employed to analyse and predict fluctuations in groundwater levels around a hilly site hosting underground gas storage caverns. The time series of groundwater heads, however, has been collected at irregular intervals and, in some cases, it has missing values at various points. It is necessary to use a method of times series analysis that is capable of filling in these observational gaps. For the irregularly observed time series, Kalman filtering is applied. To apply the Kalman filter, the TFN models must first be written as a state space in vector notation. Then the Kalman filter is combined with a maximum likelihood criterion to estimate the parameters of the TFN model. The Kalman filtering equation is iteratively calculated using appropriate initial parameters. The filtering procedure incorporates the recursive ‘prediction–correction’ form using a maximum likelihood criterion. After validating TFN models estimated using recursive filtering, these models are used to forecast and predict the values at non-observed time steps. The comparison between the predicted heads and the observed heads in the validation period show reasonably good matches.