Comparison of Zero-Inertia and Volume Balance Advance-Infiltration Models

Results of the advance-infiltration phase from a zero-inertia model and a volume balance model in level basins are analyzed and compared. Level basin irrigation systems are traditionally more efficient than other surface irrigation systems (e.g., furrows, borders). An important factor in the design and operation of level basins is the time of advance, which is primarily a function of the inflow rate, soil infiltration parameters, and roughness coefficient. The advance-infiltration phase is determined by two well-known and also very distinct mathematical approaches. The first approach is known as the zero-inertia model, which is categorized as “simplified hydrodynamics.” The simplification consists of ignoring some of the terms in the momentum equation. The second approach is based on the volume balance model and is considered to be “kinematics” because the momentum equation is ignored. The volume balance model, despite being less complex and less mathematically demanding than the zero-inertia model, provides satisfactory predictions of the advance-infiltration phase. The Lewis-Milne equation defines, in this case, the advance-infiltration phase with the modified Kostiakov infiltration function describing the infiltration process. The obtained solution is relatively simple to program. In spite of great advances in computers that facilitate the solution of complex mathematical schemes, hydrodynamic models, even simplified versions, are infrequently used in the daily practice of engineering because of their complexity. Time steps to be used in these simulations are extremely small to guarantee good accuracy and to avoid instability in the numerical scheme. Errors in the estimation of the time of advance between the zero-inertia and volume balance models range from 3.87 to 8.44% from unit inflows ranging from 2.0 to 7.0 L/s/m. The time of advance t_L from the zero-inertia model is larger than that from the volume balance model, meaning that the zero-inertia model yields smaller average flow velocity for the entire basin than for the volume balance model.