Date of Award:


Document Type:


Degree Name:

Doctor of Philosophy (PhD)


Biological and Irrigation Engineering


Gary P. Merkley


A robust mathematical model of one-dimensional flow for sloping, blocked-end border irrigation was developed using the four-point implicit method to solve the Saint-Venant equations, the volume-balance solution method, and the implementation of new algorithms to avoid numerical instability and solution divergence. The model has the capability of successfully simulating all surface irrigation phases in blocked-end borders for a range of inflow rates (0.01 - 0.05 m3/s per m), longitudinal slopes (up to 1.00%), and border lengths (100 - 500 m). To achieve numerical stability over the specified parameter ranges, the model was divided into three parts: (1) advance-phase simulation which uses the four-point implicit solution method of the Saint-Venant equations, with an algorithm that changes the spatial and temporal weighting, in addition to an algorithm that handles the water depth profile at the blocked-end downstream boundary upon completion of the advance phase; (2) simultaneous advance-recession-phase calculations using a hybrid algorithm to solve the governing equations; and (3) recession-phase simulation using the four-point implicit method until (and if) divergence occurs, then the volume-method is applied to complete the simulation. The three parts also involve the use of computational grid management algorithms and a parabolic equation which defines the Chezy coefficient as a function of water depth. The model incorporates the downhill simplex optimization method to determine the recommended inflow rate and irrigation cutoff time, maximizing a composite irrigation efficiency (water requirement efficiency and application efficiency). Different optimum values of inflow rate and irrigation cutoff time for a range of longitudinal slopes, border lengths, and soil types were generated. Most of the optimum values are for relatively high inflow rate and rapid cutoff time. In addition, exponential relations were developed, based on the simulation results, to determine the best irrigation time for maximization of the composite irrigation efficiency for specified, non-optimal inflow rates. The exponential relations are particularly useful in practice when it is not feasible to use the optimum inflow rate due to constraints at the water source, or because of irrigation scheduling issues.

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