We describe the method of history matching, a method currently used to help quantify parametric uncertainty in climate models, and argue for its use in identifying and removing structural biases in climate models at the model development stage. We illustrate the method using an investigation of the potential to improve upon known ocean circulation biases in a coupled non-flux-adjusted climate model (the third Hadley Centre Climate Model; HadCM3). In particular, we use history matching to investigate whether or not the behaviour of the Antarctic Circumpolar Current (ACC), which is known to be too strong in HadCM3, represents a structural bias that could be corrected using the model parameters. We find that it is possible to improve the ACC strength using the parameters and observe that doing this leads to more realistic representations of the sub-polar and sub-tropical gyres, sea surface salinities (both globally and in the North Atlantic), sea surface temperatures in the sinking regions in the North Atlantic and in the Southern Ocean, North Atlantic Deep Water flows, global precipitation, wind fields and sea level pressure. We then use history matching to locate a region of parameter space predicted not to contain structural biases for ACC and SSTs that is around 1% of the original parameter space. We explore qualitative features of this space and show that certain key ocean and atmosphere parameters must be tuned carefully together in order to locate climates that satisfy our chosen metrics. Our study shows that attempts to tune climate model parameters that vary only a handful of parameters relevant to a given process at a time will not be as successful or as efficient as history matching.

The calibration of complex computer codes using uncertainty quantification (UQ) methods is a rich area of statistical methodological development. When applying these techniques to simulators with spatial output, it is now standard to use principal component decomposition to reduce the dimensions of the outputs in order to allow Gaussian process emulators to predict the output for calibration. We introduce the 'terminal case', in which the model cannot reproduce observations to within model discrepancy, and for which standard calibration methods in UQ fail to give sensible results. We show that even when there is no such issue with the model, the standard decomposition on the outputs can and usually does lead to a terminal case analysis. We present a simple test to allow a practitioner to establish whether their experiment will result in a terminal case analysis, and a methodology for defining calibration-optimal bases that avoid this whenever it is not inevitable. We present the optimal rotation algorithm for doing this, and demonstrate its efficacy for an idealised example for which the usual principal component methods fail. We apply these ideas to the CanAM4 model to demonstrate the terminal case issue arising for climate models. We discuss climate model tuning and the estimation of model discrepancy within this context, and show how the optimal rotation algorithm can be used in developing practical climate model tuning tools. * The authors gratefully acknowledge support from EPSRC fellowship No. EP/K019112/1 and support from the NSERC funded Canadian Network for Regional Climate and Weather Processes (CNRCWP). We would also like to thank Yanjun Jiao for managing our ensembles of CanAM4.

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Atmospheric global or regional circulation models used either for numerical weather prediction (NWP) or climate studies encompass a dynamical core and a physical component. The dynamical core computes the spatio-temporal evolution of atmospheric state variables by solving a discrete version of the fluid dynamic equations. The physical component quantifies the impact on the resolved variables of radiative, thermodynamical, and chemical processes, as well as dynamical processes that occur at scales smaller than the computational grid. These processes are handled by a suite of sub-models, most often referred to as parameterizations, which provide source terms in the resolved-scale equations. Parameterizations (e.g., turbulence, convection, radiation, microphysics) are often based on a mixture of physical principles and heuristic description of the involved processes, of their interactions and of their impact on the larger resolved scales. Although it is difficult to trace back the origin of the term "parameterization" in climate modeling, it semantically points to the fact that the sub-models summarize the processes as functions of the model state vector x (typically the value of zonal and meridional wind, temperature, and water phases at each point of the three-dimensional [3D] model grid) that depends on some free parameters. These free parameters arise from the simplification of the complex nature of the subgrid processes (e.g., assuming a bulk thermal plume instead of a population of plumes, stationarity). The atmospheric model can be summarized as      () (,)