Combined analysis of time-varying sensitivity and identifiability indices to diagnose the response of complex environmental models
Eawag: Swiss Federal Institute of Aquatic Science and Technology
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The problem of parameter non-uniqueness in complex hydrological models limits their potential applications for decision making. While it takes a long time to estimate the values of a larger number of unknown parameters, their predictive capabilities may be reduced due to non-identifiability. Sensitivity and identifiability analyses are common diagnostic tools to address these limitations, although combined application of the two methods is rarely reported and discussed in the literature. In this study, we employed an integrated and physically-based hydrologic model to: i) perform a temporal sensitivity analysis (TSA) using the global and variance-based method of Sobol (2001), to study how the uncertainty in the model output can be apportioned to different inputs, ii) perform a temporal identifiability analysis (TIA) of model parameters, using the dynamic identifiability method of DYNIA (dynamic identifiability analysis) to extract the maximum information content from available observations, and iii) discuss the relationship between TSA and TIA results. The study was performed in the framework of a weighing lysimeter where HydroGeoSphere was used to build a hydrologic model to simulate daily actual evapotranspiration, water content, and discharge from the bottom of the lysimeter. We then performed a TSA of model parameters for each individual output to highlight: 1) the most contributing parameters to the uncertainty of the model outputs based on their individual effects (main effect) 2) the parameters affecting model output through their interactions with other parameters (interaction effect) and 3) the dominant processes based on the contribution of relevant parameters to the output uncertainty over the course of the simulation. Consequently, we performed a TIA to find out time periods that gave the maximum information about model parameters for each output. Contrary to the TSA which showed that sensitivity of parameters to different outputs of the model was not the same, TIA indicated a consistent response to different outputs, meaning that the most identifiable parameters remained the same, independent of the output. Exploring the relation between the two analyses revealed that both Sobol indices (main and interaction effects) are required to be considered in addition to the identifiability for a proper evaluation of uncertainty reduction in the model output. We also found that identifiability is a necessary but not sufficient condition for a parameter to reduce the uncertainty in the model output. Furthermore, we underlined how hydrologic conditions, represented by average water content in our study, can affect the two requirements for uncertainty reduction. Overall, the study highlights the problem of model over-parameterization as many of the parameters did not meet the two requirements, considering the available observations.