Models Quantify the Total Maximum Daily Load Process

Mathematical models have been used for many years to assist in the management of water quality. The total maximum daily load ~TMDL! process is no exception; models represent the means by which the assimilative capacity of a water body can be quantified and a waste load allocation can be determined such that the assimilative capacity is not exceeded. Unfortunately, in many TMDLs, the use of models has not always adhered to the best modeling practices that have been developed over the past half-century. This paper presents what are felt to be the most important principles of good modeling practice relative to all of the steps in developing and applying a model for computing a TMDL. These steps include: Problem definition and setting management objectives; data synthesis for use in modeling; model selection; model calibration and, if possible confirmation; model application; iterative modeling; and model postaudit. Since mathematical modeling of aquatic systems is not an exact science, it is essential that these steps be fully transparent to all TMDL stakeholders through comprehensive documentation of the entire process, including specification of all inputs and assumptions. The overriding consideration is that data richness and quality govern the level of model complexity that can be applied to a given system. The model should never be more complex than the data allow. Also, in applying a model, one should always attempt to quantify the uncertainty in predictions. In general, quantifying uncertainty is easier with simple models, which is another reason to begin with a simple framework.