Accounting for heteroscedasticity in rating curve estimates

摘要

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. (C) 2004 Elsevier B.V. All rights reserved.