The Use of Mathematical Models to Predict Beach Behavior for U.S. Coastal Engineering: A Critical Review


  • E. Robert Thieler
  • Orrin H. Pilkey, Jr.
  • Robert S. Young
  • David M. Bush
  • Fei Chai


Analytical model, Bruun Rule, coastal processes, equilibrium profile, GENESIS, numerical model, SBEACH, sediment transport, shoreline change


A number of assumed empirical relationships (e.g., the Bruun Rule, the equilibrium shoreface profile, longshore transport rate equation, beach length: durability relationship, and the renourishment factor) and deterministic numerical models (e.g., GENESIS, SBEACH) have become important tools for investigating coastal processes and for coastal engineering design in the U.S. They are also used as the basis for making public policy decisions, such as the feasibility of nourishing recreational beaches. A review of the foundations of these relationships and models, however, suggests that they are inadequate for the tasks for which they are used. Many of the assumptions used in analytical and numerical models are not valid in the context of modern oceanographic and geologic principles. We believe the models are oversimplifications of complex systems that are poorly understood. There are several reasons for this, including: (1) poor assumptions and important omissions in model formulation; (2) the use of relationships of questionable validity to predict the morphologic response to physical forcing; (3) the lack of hindsighting and objective evaluation of beach behavior predictions for engineering projects; (4) the incorrect use of model calibration and verification as assertions of model veracity; and (5) the fundamental inability to predict coastal evolution quantitatively at the engineering and planning time and space scales our society assumes and demands.

It is essential that coastal geologists, beach designers and coastal modelers understand these model limitations. Each important model assumption must be examined in isolation; incorporating them into a model does not improve their validity. It is our belief that the models reviewed here should not be relied on as a design tool until they have been substantially modified and proven in real-world situations. The "solution," however, is not to increase the complexity of a model by increasing the number of variables. What is needed is a thoughtful review of what beach behavior questions should or could be answered by modeling. Viable alternatives to the use of models do exist to predict the behavior of beaches. Three such alternatives to models are discussed for nourished beach design.