Future climate emulations using quantile regressions on large ensembles

The study of climate change and its impacts depends on generating projections of future temperature and other climate variables. For detailed studies, these projections usually require some combination of numerical simulation and observations, given that simulations of even the current climate do not perfectly reproduce local conditions. We present a methodology for generating future climate projections that takes advantage of the emergence of climate model ensembles, whose large amounts of data allow for detailed modeling of the probability distribution of temperature or other climate variables. The procedure gives us estimated changes in model distributions that are then applied to observations to yield projections that preserve the spatiotemporal dependence in the observations. We use quantile regression to estimate a discrete set of quantiles of daily temperature as a function of seasonality and long-term change, with smooth spline functions of season, long-term trends, and their interactions used as basis functions for the quantile regression. A particular innovation is that more extreme quantiles are modeled as exceedances above less extreme quantiles in a nested fashion, so that the complexity of the model for exceedances decreases the further out into the tail of the distribution one goes. We apply this method to two large ensembles of model runs using the same forcing scenario, both based on versions of the Community Earth System Model (CESM), run at different resolutions. The approach generates observation-based future simulations with no processing or modeling of the observed climate needed other than a simple linear rescaling. The resulting quantile maps illuminate substantial differences between the climate model ensembles, including differences in warming in the Pacific Northwest that are particularly large in the lower quantiles during winter. We show how the availability of two ensembles allows the efficacy of the method to be tested with a “perfect model” approach, in which we estimate transformations using the lower-resolution ensemble and then apply the estimated transformations to single runs from the high-resolution ensemble. Finally, we describe and implement a simple method for adjusting a transformation estimated from a large ensemble of one climate model using only a single run of a second, but hopefully more realistic, climate model.</p

Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion

<p>Computer experiments based on mathematical models are powerful tools for understanding physical processes. This article addresses the problem of kriging-based optimization for deterministic computer experiments with tunable accuracy. Our approach is to use multi-fidelity computer experiments with increasing accuracy levels and a nonstationary Gaussian process model. We propose an optimization scheme that sequentially adds new computer runs by following two criteria. The first criterion, called EQI, scores candidate inputs with given level of accuracy, and the second criterion, called EQIE, scores candidate combinations of inputs and accuracy. From simulation results and a real example using finite element analysis, our method outperforms the expected improvement (EI) criterion that works for single-accuracy experiments. Supplementary materials for this article are available online.</p