On the practical usefulness of least squares for assessing uncertainty in hydrologic and water quality predictions

D. Del Giudice, R.L. Muenich, M.M. Kalcic, N.S. Bosch, D. Scavia and A.M. Michalak


SUMMARY

The predictive ability of hydrological and water quality models can be influenced by the statistical method chosen for model calibration and uncertainty quantification (UQ). In the current modeling landscape, both simple and complex UQ methods coexist without clear guidance on which methods perform best under what circumstances. In this study we explore conditions under which a simple statistical method (i.e., least squares) generates predictions as accurate and reliable as a more sophisticated approach (i.e., the Bayesian autoregressive error model). We do so using two case studies of a small sewer catchment with limited calibration discharge data, and one case study of an agricultural river basin with rich calibration data. Surprisingly, we find that simple approaches match the performance of more complex UQ approaches when calibration periods are long or when the input data and model have minimal bias.

Figure: Discharge (A, B) and nutrient load (C, D) predictions for the River Raisin watershed using least squares (A, C) and an autoregressive error model (B, D). Validation data are shown. Parameter uncertainty for AREM is too small to be visible on panels B and D.


ABSTRACT

Sophisticated methods for uncertainty quantification have been proposed for overcoming the pitfalls of simple statistical inference in hydrology. The implementation of such methods is conceptually and computationally challenging, however, especially for large-scale models. Here, we explore whether there are circumstances in which simple approaches, such as least squares, produce comparably accurate and reliable predictions. We do so using three case studies, with two involving a small sewer catchment with limited calibration data, and one an agricultural river basin with rich calibration data. We also review additional published case studies. We find that least squares performs similarly to more sophisticated approaches such as a Bayesian autoregressive error model in terms of both accuracy and reliability if calibration periods are long or if the input data and the model have minimal bias. Overall, we find that, when mindfully applied, simple statistical methods such as least squares can still be useful for uncertainty quantification.

Del Giudice, D., R.L. Muenich, M.M. Kalcic, N.S. Bosch, D. Scavia, A.M. Michalak (2018) "On the practical usefulness of least squares for assessing uncertainty in hydrologic and water quality predictions," Environmental Modelling & Software, 105, 286-295, doi:10.1016/j.envsoft.2018.03.009.