Improved evaluation procedure for heat-pulse soil water flux density method

Analytical solutions of the heat equation must be evaluated in order to imp lement the heat-pulse method for measuring soil water flux density, We deve loped an improved procedure for evaluating the integrals in these solutions by recognizing that they can be reduced to a single function, W,known as t he well function for leaky aquifers, The evaluation procedure was improved further by developing an efficient method to approximate W. This method, wh ich involves summing the first few terms of an infinite series, also provid es a simple means of determining the approximation error. For a wide range of input parameters, at most two terms of the series are needed to approxim ate W with error less than 10(-4) in absolute value. Thus, numerical integr ation is not required in order to implement the heat-pulse method for measu ring soil water flux density. Our results regarding the evaluation of W are relevant to other problems in soil science and groundwater hydrology in wh ich the function W appears.