Correct Form of Hall Technique for Border Irrigation Advance

Abstract

The Hall technique for computing stream advance down an irrigated border strip is shown to be inconsistent in the selection of numerical parameters for approximating infiltrated volume. This inconsistency leads to violation of mass conservation and to error in computed advance. By viewing it in dimensionless terms, the behavior of this error is demonstrated over the practical range of variation of border‐irrigation parameters with a Kostiakov infiltration formula and Manning roughness formula. It is shown to vary from insignificant magnitudes under 1% to well over 10%. A correction term to neutralize the inconsistency is presented. An alternate formulation free of the inconsistency and suitable for modern high‐speed computers working with a reasonably large number of significant figures is presented. Errors stemming from the basic physical assumption—constant average depth of surface water—are not addressed.