Parameterization of Pilot Point Methodology for Supplementing Sparse Transmissivity Data

Aditya Kapoor,Deepak Kashyap

doi:10.3390/w13152082

Abstract

Pilot point methodology (PPM) permits estimation of transmissivity at unsampled pilot points by solving the hydraulic head based inverse problem. Especially relevant to areas with sparse transmissivity data, the methodology supplements the limited field data. Presented herein is an approach for estimating parameters of PPM honoring the objectives of refinement of the transmissivity (T) interpolation and the model calibration. The parameters are the locations and number of pilot transmissivity points. The location parameter is estimated by defining a qualifying matrix Q comprising weighted sum of the hydraulic head-sensitivity and the kriging variance fields. Whereas the former component of Q promotes the model calibration, the latter one leads to improved T interpolation by locating pilot points in un-sampled tracts. Further, a three-stage methodology is proposed for an objective determination of the number of pilot points. It is based upon sequential upgradation of the Variogram as the pilot points are added to the data base, ensuring its convergence with the head-based optimal Variogram. The model has been illustrated by applying it to Satluj-Beas interbasin wherein the pumping test data is not only sparse, but also unevenly distributed.

Highlights

Distributed models are nowadays routinely employed for regional planning of groundwater development
The present practice in respect of the Pilot point methodology (PPM) parameters is oriented solely towards enhancing the calibration with almost no thought given to the interpolation aspect
In strategy 3, the pilot points have filled up the unsampled tracts, though not as effectively as strategy 2

Summary

Introduction

Distributed models are nowadays routinely employed for regional planning of groundwater development. An important input in this regard is the transmissivity (T) field which is known to influence the long-term model predictions significantly. These fields are usually generated by interpolating cell transmissivities from the sampled T values that are typically obtained through the pumping tests. The interpolation is mostly based upon kriging [2,3,4], finite element linked basis functions, spline function, and polynomial approximation [5,6,7] Such T fields may not be credible on account of the sparseness of sampled T values and resulting models may lack predictive capability. Conducting an adequate number of pumping tests may not always be possible due to their high cost and difficult logistics

Methods

Results

Discussion

Conclusion