Statistical Interpolation of Groundwater Hydrographs

Abstract

Groundwater observation bores are often monitored irregularly and infrequently. The resulting groundwater hydrographs are consequently less informative for understanding groundwater level trends, seasonality, flow directions, drawdown, and recovery. This paper presents an approach to temporally interpolate a groundwater hydrograph that has an irregular observation frequency to daily time steps. The approach combines nonlinear transfer function noise modeling with temporal kriging of the model residuals to produce an interpolated hydrograph that honors all water level observations input to the modeling and accounts for meteorological forcing between the observations. The reliability of the approach was evaluated using six observation bores having extended periods of daily data and by resampling them to six observation frequencies ranging from weekly to annually. The analysis showed that for weekly to monthly resampled data, >90% of the observed daily variability can be simulated at four of six bores. The performance declined with observation step size, as expected, but even at a biannual time step the error corrected interpolation can explain >70% of the variance at three of six bores. Additionally, an application shows that (1) the probability of a water level depth being exceeded can be estimated from quarterly resampled data and (2) the median annual water level range can be estimated from monthly resampled data. Supplementing less frequent observations with 6 and 12 months of daily data was also examined, with the addition of a 12-month period significantly improving interpolation results at three of the four analyzed bores. The approach has been incorporated into the HydroSight toolbox http://peterson-tim-j.github.io/HydroSight/.