Imputing missing groundwater observations

Abstract

In this paper, we consider the problem of completing missing records of annual water levels. The water levels records are taken once a year, in a group of neighboring wells. The collected records are assembled into a data matrix, where each column refers to a different well and each row refers to a different year. Yet some entries of the matrix are unknown and we want to assign appropriate values to these entries. The need for solving such problems arises in many applications, as many models and programs require a complete set of data. Traditional approaches for handling missing groundwater records are based on statistical techniques for treating missing data. The current paper introduces a new approach for solving this problem. One that is able to take advantage of the ‘matrix structure’ of annual water levels. This type of ‘matrix imputing methods’ has been proved successful in many modern areas, but it has not yet been tested in hydrology. Special attention is given to the question of assessing the quality of the imputed water levels. The proposed methods are examined on a number of test cases.