STOCHASTIC ANTI-ALIASING OF WATER-TABLE HYDROGRAPHS TO DETERMINE LONG-TERM RECHARGE

One method of quantifying recharge variations is to calibrate models to water-table hydrographs. Estimating recharge from model calibration allows researchers to account for a range of spatial scales (tens to hundreds of mm per year), and temporal scales (days to years). However, aliasing (anomalous low-frequency component due to a low sampling rate) is an inherent problem in analyzing water-table hydrographs because it is often impractical to sample water-table elevations at a rate greater than the highest-frequency stress on the aquifer. Moreover, sampling an unfiltered signal at a specified sampling rate presumes that one knows the highest frequency of the input signal.

To address the aliasing problem, we use a stochastic anti-aliasing algorithm in which we generate a stochastic hydrograph that (1) matches the data points on the observed hydrograph, and (2) has a fractal dimension consistent with that of the observed hydrograph. This approach allows us to generate synthetic hydrographs with arbitrarily high frequencies that are used in inverse models to estimate recharge. We use a Monte Carlo approach to estimate the statistical distribution of groundwater recharge.

We have applied this approach to estimating recharge from water-table hydrographs using a one-dimensional finite-difference model that uses the Boussinesq equation. We tested the inversion method by generating synthetic recharge signals to generate synthetic water-table hydrographs. Because the method works well with the synthetic data, we have applied these methods to water-table hydrographs measured on Hatteras Island, North Carolina. Our water-table hydrographs have been measured in several monitoring wells at different sampling rates (every ten minutes versus twice daily).