Toward diagnostic model calibration and evaluation: Approximate Bayesian computation

TLDR

The rapid growth of computational power and measurement technologies has driven the creation of increasingly complex hydrologic models, yet reconciling these models with expanding field data remains difficult because classical likelihood‑based fitting cannot detect structural deficiencies. This paper introduces approximate Bayesian computation (ABC) as a tool for diagnostic model evaluation. ABC replaces explicit likelihood functions with multiple hydrologically grounded summary statistics, using signature behaviors and patterns in input–output data to provide clearer diagnostic insight. Case studies show that ABC is straightforward to implement and effectively uses signature‑based indices to identify and localize model malfunctions. Gupta et al.

Abstract

The ever increasing pace of computational power, along with continued advances in measurement technologies and improvements in process understanding has stimulated the development of increasingly complex hydrologic models that simulate soil moisture flow, groundwater recharge, surface runoff, root water uptake, and river discharge at different spatial and temporal scales. Reconciling these high‐order system models with perpetually larger volumes of field data is becoming more and more difficult, particularly because classical likelihood‐based fitting methods lack the power to detect and pinpoint deficiencies in the model structure. Gupta et al. (2008) has recently proposed steps (amongst others) toward the development of a more robust and powerful method of model evaluation. Their diagnostic approach uses signature behaviors and patterns observed in the input‐output data to illuminate to what degree a representation of the real world has been adequately achieved and how the model should be improved for the purpose of learning and scientific discovery. In this paper, we introduce approximate Bayesian computation (ABC) as a vehicle for diagnostic model evaluation. This statistical methodology relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics rooted in hydrologic theory that together have a clearer and more compelling diagnostic power than some average measure of the size of the error residuals. Two illustrative case studies are used to demonstrate that ABC is relatively easy to implement, and readily employs signature based indices to analyze and pinpoint which part of the model is malfunctioning and in need of further improvement.