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Volume 11, issue 8 | Copyright
Geosci. Model Dev., 11, 3131-3146, 2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Methods for assessment of models 03 Aug 2018

Methods for assessment of models | 03 Aug 2018

Fast sensitivity analysis methods for computationally expensive models with multi-dimensional output

Edmund Ryan1, Oliver Wild1, Apostolos Voulgarakis2, and Lindsay Lee3 Edmund Ryan et al.
  • 1Lancaster Environment Centre, Lancaster University, Lancaster, UK
  • 2Department of Physics, Imperial College London, London, UK
  • 3School of Earth and Environment, University of Leeds, Leeds, UK

Abstract. Global sensitivity analysis (GSA) is a powerful approach in identifying which inputs or parameters most affect a model's output. This determines which inputs to include when performing model calibration or uncertainty analysis. GSA allows quantification of the sensitivity index (SI) of a particular input – the percentage of the total variability in the output attributed to the changes in that input – by averaging over the other inputs rather than fixing them at specific values. Traditional methods of computing the SIs using the Sobol and extended Fourier Amplitude Sensitivity Test (eFAST) methods involve running a model thousands of times, but this may not be feasible for computationally expensive Earth system models. GSA methods that use a statistical emulator in place of the expensive model are popular, as they require far fewer model runs. We performed an eight-input GSA, using the Sobol and eFAST methods, on two computationally expensive atmospheric chemical transport models using emulators that were trained with 80 runs of the models. We considered two methods to further reduce the computational cost of GSA: (1) a dimension reduction approach and (2) an emulator-free approach. When the output of a model is multi-dimensional, it is common practice to build a separate emulator for each dimension of the output space. Here, we used principal component analysis (PCA) to reduce the output dimension, built an emulator for each of the transformed outputs, and then computed SIs of the reconstructed output using the Sobol method. We considered the global distribution of the annual column mean lifetime of atmospheric methane, which requires  ∼ 2000 emulators without PCA but only 5–40 emulators with PCA. We also applied an emulator-free method using a generalised additive model (GAM) to estimate the SIs using only the training runs. Compared to the emulator-only methods, the emulator–PCA and GAM methods accurately estimated the SIs of the  ∼ 2000 methane lifetime outputs but were on average 24 and 37 times faster, respectively.

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Short summary
Global sensitivity analysis (GSA) identifies which parameters of a model most affect its output. We performed GSA using statistical emulators as surrogates of two slow-running atmospheric chemistry transport models. Due to the high dimension of the model outputs, we considered two alternative methods: one that reduced the output dimension and one that did not require an emulator. The alternative methods accurately performed the GSA but were significantly faster than the emulator-only method.
Global sensitivity analysis (GSA) identifies which parameters of a model most affect its output....