Abstract
We tested four likelihood measures including two limits of acceptability and two absolute model residual methods within the generalized likelihood uncertainty estimation (GLUE) framework using the topography model (TOPMODEL). All these methods take the worst performance of all time steps as the likelihood of a model and none of these methods were successful in finding any behavioral models. We believe that reporting this failure is important because it shifted our attention from which likelihood measure to choose to why these four methods failed and how to improve these methods. We also observed how large parameter samples impact the performance of a hybrid uncertainty estimation method, isolated-speciation-based particle swarm optimization (ISPSO)-GLUE using the Nash–Sutcliffe (NS) coefficient. Unlike GLUE with random sampling, ISPSO-GLUE provides traditional calibrated parameters as well as uncertainty analysis, so over-conditioning the model parameters on the calibration data can affect its uncertainty analysis results. ISPSO-GLUE showed similar performance to GLUE with a lot less model runs, but its uncertainty bounds enclosed less observed flows. However, both methods failed in validation. These findings suggest that ISPSO-GLUE can be affected by over-calibration after a long evolution of samples and imply that there is a need for a likelihood measure that can better explain uncertainties from different sources without making statistical assumptions.
Highlights
It is important to assess how much uncertainties are involved in hydrologic modeling because there are many different sources of uncertainty including model structures, parameters, and input and output data [1,2,3,4]
NS coefficients of forparticles the validation periods between the validation two methods, we found weak evidence of over-conditioning to the periods between the two methods, we found weak evidence of over-conditioning of particles to the calibration data because isolated-speciation-based particle swarm optimization (ISPSO)-generalized likelihood uncertainty estimation (GLUE) performed marginally worse than GLUE for all validation calibration data because performed marginally worse than for all validation periods
Half a million random samples were used to evaluate the four likelihood approaches. All these methods did not produce any behavioral models because it was very challenging for any models to make predictions within the acceptable effective observational error for all time steps. This failure highlighted the challenge of the limits of acceptability approach, especially in long simulations, and moved our attention to how we can better take into account different sources of uncertainty in model evaluation without strong statistical assumptions
Summary
It is important to assess how much uncertainties are involved in hydrologic modeling because there are many different sources of uncertainty including model structures, parameters, and input and output data [1,2,3,4]. Epistemic uncertainty results from a lack of our knowledge while aleatory uncertainty arises from random variability. The former can sometimes be reduced by gathering more data and improving our knowledge while the latter cannot. A typical modeling process involves comparing the observed data with unknown errors (aleatory or epistemic) and model output that is simulated by an imperfect model with its own structural (epistemic), parameter (epistemic, aleatory, or both), and measurement (aleatory or epistemic) uncertainties.
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