Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation

TLDR

Hydrologic models simplify complex, spatially distributed water, energy, and vegetation processes, and because model parameters are not directly measurable, calibration must adjust them to match observed system responses, but structural and data errors make this difficult and generate substantial prediction uncertainty. This paper surveys the shortcomings of existing calibration approaches that attribute input–output uncertainty mainly to parameter uncertainty and proposes a simultaneous optimization and data‑assimilation (SODA) method to better handle uncertainty in hydrologic modeling. SODA integrates global optimization with data assimilation to jointly estimate parameters and state variables, and its implementation is illustrated in a pilot study of the Leaf River watershed using a simple conceptual hydrologic model. The pilot study demonstrates that SODA improves model performance and uncertainty quantification, showing its usefulness and applicability for hydrologic modeling.

Abstract

Hydrologic models use relatively simple mathematical equations to conceptualize and aggregate the complex, spatially distributed, and highly interrelated water, energy, and vegetation processes in a watershed. A consequence of process aggregation is that the model parameters often do not represent directly measurable entities and must therefore be estimated using measurements of the system inputs and outputs. During this process, known as model calibration, the parameters are adjusted so that the behavior of the model approximates, as closely and consistently as possible, the observed response of the hydrologic system over some historical period of time. In practice, however, because of errors in the model structure and the input (forcing) and output data, this has proven to be difficult, leading to considerable uncertainty in the model predictions. This paper surveys the limitations of current model calibration methodologies, which treat the uncertainty in the input‐output relationship as being primarily attributable to uncertainty in the parameters and presents a simultaneous optimization and data assimilation (SODA) method, which improves the treatment of uncertainty in hydrologic modeling. The usefulness and applicability of SODA is demonstrated by means of a pilot study using data from the Leaf River watershed in Mississippi and a simple hydrologic model with typical conceptual components.