# Publications

## Generation of pareto optimal ensembles of calibrated parameter sets for climate models

Climate models have a large number of inputs and outputs. In addition, diverse parameters sets can match observations similarly well. These factors make calibrating the models difficult. But as the Earth enters a new climate regime, parameters sets may cease to match observations. History matching is necessary but not sufficient for good predictions. We seek a 'Pareto optimal' ensemble of calibrated parameter sets for the CCSM climate model, in which no individual criteria can be improved without worsening another. One Multi Objective Genetic Algorithm (MOGA) optimization typically requires thousands of simulations but produces an ensemble of Pareto optimal solutions. Our simulation budget of 500-1000 runs allows us to perform the MOGA optimization once, but with far fewer evaluations than normal. We devised an analytic test problem to aid in the selection MOGA settings. The test problem's Pareto set is the surface of a 6 dimensional hypersphere with radius 1 centered at the origin, or rather the portion of it in the [0,1] octant. We also explore starting MOGA from a space-filling Latin Hypercube sample design, specifically Binning Optimal Symmetric Latin Hypercube Sampling (BOSLHS), instead of Monte Carlo (MC). We compare the Pareto sets based on: their number of points, N, larger is better; their RMS distance, d, to the ensemble's center, 0.5553 is optimal; their average radius, {mu}(r), 1 is optimal; their radius standard deviation, {sigma}(r), 0 is optimal. The estimated distributions for these metrics when starting from MC and BOSLHS are shown in Figs. 1 and 2.