Derivative-free Calibration of a Computationally Expensive Watershed Model

Stefan Wild, Cornell University

Advances in computer hardware have allowed researchers in a multitude of scientific and engineering disciplines to pursue ever more realistic and complex numerical models. In order for these models to effectively reflect nature, model parameters must be calibrated to observed data. Here we address calibration of computationally expensive models whose analytic derivatives are unavailable. Traditional derivative-free optimization methods for such problems require evaluation of the model at many different sets of parameter values, a computationally intractable approach in our setting, driving the need for new algorithms.

In this investigation we consider the Town Brook watershed in upstate New York which contributes to the drinking water supply of New York City. If phosphorous loads from the watershed become too high, New York City would either have to abandon the water supply or build a filtration plant costing around $8 billion. In order to control the phosphorous at the watershed level, we require an accurate model to assess the impact of changes in management practices on phosphorous loads.

The goal of calibration here is to determine values for 14 model parameters so that an existing model most closely approximates measured data recorded over a three year period. We develop a new optimization algorithm which relies on computationally attractive approximations of the model. Our particular approach allows us to return a set of near-optimal parameters in many fewer model evaluations than current alternatives.

Abstract Author(s): Stefan M Wild<br />Jorge J Mor&eacute;<br />Christine A Shoemaker