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. Global sensitivity analysis (GSA) is a powerful approach in identifying whichinputs or parameters most affect a model's output. This determineswhich inputs to include when performing model calibration or uncertaintyanalysis. GSA allows quantification of the sensitivity index (SI) of aparticular input – the percentage of the total variability in the outputattributed to the changes in that input – by averaging over the other inputsrather than fixing them at specific values. Traditional methods of computingthe SIs using the Sobol and extended Fourier AmplitudeSensitivity Test (eFAST) methods involve running amodel thousands of times, but this may not be feasible for computationallyexpensive Earth system models. GSA methods that use a statistical emulator inplace of the expensive model are popular, as they require far fewer modelruns. We performed an eight-input GSA, using the Sobol and eFAST methods, ontwo computationally expensive atmospheric chemical transport models usingemulators that were trained with 80 runs of the models. We considered twomethods to further reduce the computational cost of GSA: (1) adimension reduction approach and (2) an emulator-free approach. Whenthe output of a model is multi-dimensional, it is common practice to build aseparate emulator for each dimension of the output space. Here, we usedprincipal component analysis (PCA) to reduce the output dimension, built anemulator for each of the transformed outputs, and then computed SIs of thereconstructed output using the Sobol method. We considered the globaldistribution of the annual column mean lifetime of atmospheric methane, whichrequires ∼  2000 emulators without PCA but only 5–40 emulatorswith PCA. We also applied an emulator-free method using a generalisedadditive model (GAM) to estimate the SIs using only the training runs.Compared to the emulator-only methods, the emulator–PCA and GAM methodsaccurately estimated the SIs of the ∼  2000 methane lifetimeoutputs but were on average 24 and 37 times faster, respectively.

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