Keywords
lake water quality modelling, multi objective calibration, bias, uncertainty
Start Date
1-7-2010 12:00 AM
Abstract
Models of environmental systems are simplified representations of reality. For this reason, their results are affected by systematic errors. This bias makes it difficult to get reliable uncertainty estimates of model parameters and predictions. We were faced with that difficulty when applying the lake model BELAMO to data from three Swiss lakes. This model combines the description of biogeochemical and ecological processes in lakes. Considering bias in the model output, lead to a description of system observations as the sum of the output of the deterministic model, bias and observation error. The identifiability problem between model output and bias was addressed by specifying informative priors for the standard deviations of the observation errors and choosing means of zero for the observation error and the bias. The resulting multi-objective calibration problem was solved by using the prior of the bias to specify how much model error we are willing to accept for which output variable. To avoid the very high computational demand of conventional Bayesian numerical techniques, the maximum of the posterior was calculated and a local Gaussian approximation was used to estimate parameter and model prediction uncertainty. Parameter estimations for 9 to 20 years until 1995 were conducted. The remaining 10 years of data were used for model validation and to compare with estimated prediction uncertainty. The results show the large influence of the bias for the model output. The results for the validation period indicate the large uncertainty in model prediction, but also the ability to estimate the role of model bias with the suggested technique.
Using Statistical Bias Description for Multiobjective Calibration of a Lake Water Quality Model
Models of environmental systems are simplified representations of reality. For this reason, their results are affected by systematic errors. This bias makes it difficult to get reliable uncertainty estimates of model parameters and predictions. We were faced with that difficulty when applying the lake model BELAMO to data from three Swiss lakes. This model combines the description of biogeochemical and ecological processes in lakes. Considering bias in the model output, lead to a description of system observations as the sum of the output of the deterministic model, bias and observation error. The identifiability problem between model output and bias was addressed by specifying informative priors for the standard deviations of the observation errors and choosing means of zero for the observation error and the bias. The resulting multi-objective calibration problem was solved by using the prior of the bias to specify how much model error we are willing to accept for which output variable. To avoid the very high computational demand of conventional Bayesian numerical techniques, the maximum of the posterior was calculated and a local Gaussian approximation was used to estimate parameter and model prediction uncertainty. Parameter estimations for 9 to 20 years until 1995 were conducted. The remaining 10 years of data were used for model validation and to compare with estimated prediction uncertainty. The results show the large influence of the bias for the model output. The results for the validation period indicate the large uncertainty in model prediction, but also the ability to estimate the role of model bias with the suggested technique.
