Review status: this discussion paper is a preprint. It has been under review for the journal Hydrology and Earth System Sciences (HESS). The manuscript was not accepted for further review after discussion.
Hydrological model parameter dimensionality is a weak measure of prediction uncertainty
S. Pande1,L. Arkesteijn1,H. H. G. Savenije1,and L. A. Bastidas2S. Pande et al.S. Pande1,L. Arkesteijn1,H. H. G. Savenije1,and L. A. Bastidas2
Received: 03 Feb 2014 – Accepted for review: 21 Feb 2014 – Discussion started: 03 Mar 2014
Abstract. This paper presents evidence that model prediction uncertainty does not necessarily rise with parameter dimensionality (the number of parameters). Here by prediction we mean future simulation of a variable of interest conditioned on certain future values of input variables. We utilize a relationship between prediction uncertainty, sample size and model complexity based on Vapnik–Chervonenkis (VC) generalization theory. It suggests that models with higher complexity tend to have higher prediction uncertainty for limited sample size. However, model complexity is not necessarily related to the number of parameters. Here by limited sample size we mean a sample size that is limited in representing the dynamics of the underlying processes. Based on VC theory, we demonstrate that model complexity crucially depends on the magnitude of model parameters. We do this by using two model structures, SAC-SMA and its simplification, SIXPAR, and 5 MOPEX basin data sets across the United States. We conclude that parsimonious model selection based on parameter dimensionality may lead to a less informed model choice.
How to cite. Pande, S., Arkesteijn, L., Savenije, H. H. G., and Bastidas, L. A.: Hydrological model parameter dimensionality is a weak measure of prediction uncertainty, Hydrol. Earth Syst. Sci. Discuss., 11, 2555–2582, https://doi.org/10.5194/hessd-11-2555-2014, 2014.