From HUP to MCP: Analogies and extended performances

Abstract

► This work compares two known Predictive Uncertainty (PU) approaches, HUP and MCP. ► Both processors imply same joint distribution of predictand-model-latest observation. ► Both processors provide same correct results if lag-1 Markov is not assumed in HUP. ► Lag-1 Markov assumption in HUP leads to under-predict uncertainty estimates. ► MCP correct estimator of PU and extendable to multi site, multi temporal applications. This paper discusses the analogies and the performances of two uncertainty post-processors, the Hydrologic Uncertainty Processor (HUP) introduced by Krzysztofowicz (1999) and the Model Conditional Processor (MCP), which was proposed by Todini (2008) for the assessment of predictive uncertainty, as an alternative to HUP. The paper shows analytically and through a numerical example that the two uncertainty processors are strongly related and explains why MPC results into improved performances with respect to the HUP, when used with the same level of information. The simplicity of its derivation, the extended capabilities of MCP at tackling multi-predictand, multi-site, multi-model, multi-time problems together with the possible use of Truncated Normal Distributions in order to overcome heteroscedasticity in the residuals make MCP more easily applicable than HUP to describe predictive uncertainty in real time flood forecasting applications.