*5.3. Approximants*

The study showed that the transfer functions for both 1D and 2D were able to be approximated by an exponential function with a reference time. The best-fit coe fficient for the exponential was consistent across the 2D modelling, but variable for the 1D modelling. However, the analytical value was reasonable for five of the six 1D outputs, suggesting that one value may be a reasonable approximation for most situations. If so, this requires only for the reference time and the time delay (the time at which recharge, and the exponential approximation begins). This was not investigated in this study. However, PerTy3 appears to be able to estimate the time delay and the change in recharge at that time, so it may become a matter of finding how this could be simplified or how these parameters change in response to di fferent model parameters. The exponential function can be derived from a linear reservoir model in which the total recharge is linear with respect to the mass of water in the perched water table.

The use of approximants and superposition may lead to simplification of the estimation of recharge. The approximants form a step towards considering transfer functions as conceptual models that are fitted by the groundwater response. This has been done previously [16,18] for situations where response times are quicker and individual events are independent. These are then used for calibration. For the situations considered here, the response from di fferent actions gradually accumulate into one single evolving groundwater response. This can be used to calibrate the transfer function, where there

is no rejected recharge and provided transfer functions do not vary greatly for di fferent actions. Where there is rejected recharge, drainage can be used for calibration.
