• channel flow routing;
  • hydrologic modelling;
  • infiltration;
  • overland runoff routing;
  • rainfall excess;
  • subsurface flow


Currently, many watershed models are available that have various complexities, strengths, and weaknesses. The basic mathematical foundations of these mathematical models are often overlooked due to high demands on convenient applications with graphical user interfaces. Although this and other factors are important while selecting a model, the mathematical foundation should also be taken into account, as performance or efficiency and accuracy of a model depend on its simplicity or complexity. A comprehensive review of 14 storm event watershed models was conducted. Hydrologic procedures (rainfall excess, flow routing, and subsurface flow) of the models are presented and compiled. Among the procedures, flow routing has the most influence on model performances (speed and accuracy). Overland and channel flow routing procedures using different flow-governing equations, having various approximations and solved by different methods, are compared based on their relative levels of physical bases, complexities, and expected accuracies in simulating the dynamics of water flow. Models using more mathematical terms in the flow-governing equations are more physically based and expected to be more accurate than models using approximations, however, are more complex due to more intensive but approximate numerical schemes (inefficient). Models using approximate equations with analytical solutions may provide a balance between complexity and accuracy. The review and comparisons are useful to modellers, water resources managers, and researchers in understanding the basic foundations of the models and making informed selections for practical applications or further developments. Other factors such as data intensiveness, user friendliness, and resource requirements are also important considerations. Copyright © 2011 John Wiley & Sons, Ltd.