Weighting functions

Overview

Weighting functions define how input how forcing data shifts the groundwater head up or down at a given time point. The forcing data can be an input time-series (e.g. rainfall or pumping rate) or a time-series derived from a forcing transformation funtion. Importantly, the selected weighting function should match the type of forcing. For example input pumping data should be weighted by a function simulate draw-down mechanisms such at responseFunction_FerrisKnowles.

Additionally, once a weighting function is defined within a HydroSight model then it can be used as an input to a another class of weighting function called derived weighting functions. This allow, for example, a Pearsons weighting function used to weight precipitation to be input to a derived weighting function that rescales the Pearsons weights and applies it to a different forcing time-series. The advantage of this is that a second forcing can be simulated with only one additional model parameter and that the second forcing would have the same lag time as the precipitation.

Weighting Functions

The following weighting functions for each forcing data time series:

Name	Purpose	No. Param.	Options	Comments
Bruggeman	Streamflow influence on head. See von Asmuth et al. (2008).	TBC	(none)	This function is still to be tested and must be used with caution.
FerrisKnowles	Pumping drawdown for a confined aquifer. See Shapoori et al. (2015a, 2015b).	2	Recharge and non-flow boundary conditions can be set.	The equation is an instantaneous version for the Theis drawdown equation.
FerrisKnowlesJacobs	Pumping drawdown for a unconfined aquifer. See Shapoori et al. (2015b).	3	As for FerrisKnowles.	An unconfined aquifer is simulated using the Jacob's correction. To be effective drawdown should be a moderate fraction of the saturated thickness.
Hantush	Pumping drawdown for a confined leaky aquifer.	3	As for FerrisKnowles.	Shapoori et al. (2015a)
Pearsons	Climatic influences that increase the head, e.g. recharge. See Peterson and Western (2014).	3	Parameter bounds for calibration.
PearsonsNegative	As for Pearsons, but for climatic influences that lower the head, e.g. ET. See Peterson and Western (2014).	3	As for Pearsons

Derived Weighting Functions

The above weighting functions can also be used as inputs to the following derived weighting functions. This allow, for example, the impact from ET to be simulated not as an additional weighting function but by simply re-scaling the Pearson's weighting function used for recharge, and hence eliminating two model parameters from the model.

• derivedweighting_UnconstrainedRescaled : rescales an input weighting function whereby the recsaling can be positive or negative. This function can be used to simulate the impacts of, say, revegetation by rescaling responseFunction_Pearsons used to simulate recharge.
• derivedweighting_PearsonsNegativeRescaled : similar to derivedweighting_UnconstrainedRescaled but only to be used to rescale responseFunction_Pearsons. The function uses a normalised Pearson's function and then applies a scaling parameter. This may reduce the parameter covariance between the input weighting function and the rescaling and hence contribute to reliable calibration.
• derivedweighting_PearsonsPositiveRescaled : as for responseFunction_Pearsons but using a negative rescaling.