Accounting for heteroscedasticity in rating curve estimates

The non-linear least squares (NLS) method has long been the standard technique used by hydrologists for constructing rating curves. The reasons for its adaptation are vague, and its appropriateness as a method of describing discharge measurement uncertainty has not been well investigated. It is shown in this paper that the classical method of NLS can model only a very limited class of variance heterogeneity. Furthermore, this lack of flexibility often leads to unaccounted heteroscedasticity, resulting in dubious values for the rating curve parameters and estimated discharge. By introducing a heteroscedastic maximum likelihood model, the variance heterogeneity is treated more generally. The maximum likelihood model stabilises the variance better than the NLS approach, and thus is a more robust and appropriate way to fit a rating curve to a set of discharge measurements. Finally, it is shown that an extreme value analysis of the discharge can be affected by the model used to construct the rating curve.