Simultaneously Determining Global Sensitivities of Model Parameters and Model Structure

Abstract

<jats:p>Abstract. Model structure uncertainty is known to be one of the three main sources of hydrologic model uncertainty along with input and parameter uncertainty. Some recent hydrological modeling frameworks address model structure uncertainty by supporting multiple options for representing hydrological processes. It is, however, still unclear how best to analyze structural sensitivity using these frameworks. In this work, we apply an Extended Sobol' Sensitivity Analysis (xSSA) method that operates on grouped parameters rather than individual parameters. The method can estimate not only traditional model parameter sensitivities but is also able to provide measures of the sensitivities of process options (e.g., linear vs. non-linear storage) and sensitivities of model processes (e.g., infiltration vs. baseflow) with respect to a model output. Key to the xSSA method's applicability to process option and process sensitivity is the novel introduction of process option weights in the Raven hydrological modeling framework. The method is applied to both artificial benchmark models and a watershed model built with the Raven framework. The results show that: (1) The xSSA method provides sensitivity estimates consistent with those derived analytically for individual as well as grouped parameters linked to model structure. (2) The xSSA method with process weighting is computationally less expensive than the alternative aggregate sensitivity analysis approach performed for the exhaustive set of structural model configurations, with savings of 81.9 % for the benchmark model and 98.6 % for the watershed case study. (3) The xSSA method applied to the hydrologic case study analyzing simulated streamflow showed that model parameters adjusting forcing functions were responsible for 42.1 % of the overall model variability while surface processes cause 38.5 % of the overall model variability in a mountainous catchment; such information may readily inform model calibration. (4) The analysis of time dependent process sensitivities regarding simulated streamflow is a helpful tool to understand model internal dynamics over the course of the year. </jats:p>

Simultaneous Calibration of Hydrologic Model Structure and Parameters Using a Blended Model

“…J. Mai et al. (2020) calculates that approximately 8 × 10 12 hydrologic model configurations may be setup using Raven. For this study, the benefits of using Raven include (1) the large number of available model structures, (2) the computational efficiency of the software, and (3) the unique support for blended model structures, which is necessary to support the proposed calibration approach.…”

“…The approach of blended model structures used here was introduced by J. Mai et al. (2020), and uses the exact same set of blended process groups. In this setup, Raven is applied as a lumped model with two options for P i for the baseflow process, two options O i for evapotranspiration, three options M i for infiltration, three options N i for quickflow, and three options Q i for snow balance.…”

“…(2011) and is provided in detail in Appendix A of J. Mai et al. (2020). The blended model weights therefore add a total of eight additional model parameters (weight‐generating parameters) with this approach, which are used to generate 13 weights internally in Raven.…”

“…This idea was introduced by J. Mai et al. (2020) for simultaneous model structure and parameter sensitivity analysis. For instance, rather than choosing between two discrete process algorithms for baseflow, the baseflow flux may be calculated as the weighted average of that generated from two available baseflow algorithms.…”

“…This study uses the concept of blended model structures proposed by J. Mai et al. (2020) directly within a calibration framework, enabling efficient simultaneous calibration of structure and parameters. The objectives of the study are to (1) assess the efficacy of this blended model structure calibration (BMSC) approach on a number of MOPEX catchments and (2) compare the computational efficiency of the BMSC approach to independently calibrating a finite sample of different model structures.…”