Correcting the Volume Balance Equation for Shape Factors During Advance

The volume balance model has been an important tool in the evaluation and design of surface irrigation systems. Perhaps it's most useful application has been in evaluating the intake parameters of a sloping border or furrow during the advance phase of irrigation. Unfortunately, these volume balance estimates of intake parameters may not provide a unique enough solution to allow accurate simulation of runoff and recession. There are three important problems with a volume balance approach. First, the inflow during the advance phase must be steady. This is often difficult to achieve in the field. Second, if an intake equation with steady-state or cracking terms is used, the related parameters must be determined outside of the volume balance analysis and then input. These values are difficult to measure accurately in the field. And third, unless the analysis specifically ignores the surface volume during advance, these models use a uniform flow equation, like Manning, to describe the cross-sectional area of flow at the field inlet and then an assumption regarding the shape of the flow profile downstream — generally assuming the cross-sectional area is constant. The assumption of a constant cross-sectional area is known to introduce substantial errors.