Online climate change projections report 3.2.3 Sampling uncertainties
Based on the assessment that surface and atmospheric feedbacks are likely to provide the largest source of uncertainty in regional changes during the coming century, we focus our resources on sampling the parameter space of these processes more comprehensively than those of the ocean, sulphur cycle or carbon cycle modules. The atmosphere module of HadCM3, which also includes land surface processes and surface-atmosphere exchanges, contains 100 or more parameters controlling the model parameterisations of small scale processes (which cannot be resolved explicitly on the model grid) in terms of grid box variables. It would not be computationally feasible to explore the combined effects of perturbing all these parameters, and in any case some parameters exert a much more significant influence than others on the simulated outputs of the model. Parameterisation experts were therefore asked to identify a subset of these which control the main processes most important for the simulation of (both global and regional) climate, and then to estimate plausible minimum, intermediate and maximum values (accepting that, in general, there would be insufficient evidence to provide a unique specification of the likely distribution of parameter values between the minimum and maximum values). This exercise resulted in a subset of 31 key parameters for perturbation. We assume that neglect of possible perturbations to additional parameters does not significantly affect the spread of model behaviour generated from our simulations.
Simulations of equilibrium climate changes in response to doubled CO2
A large ensemble of (at minimum) a few hundred members is required to provide a reasonable first order estimate of how the model behaviour varies within this 31-dimensional space, given that both the linear effects of each parameter (Murphy et al. 2004), and non-linear interactions between them (Stainforth et al. 2005), can have important influences on the model simulations. Resource limitations prevented us from undertaking ensembles of transient climate change simulations of this size, so the required large ensemble was run using a computationally less demanding model configuration (HadSM3) in which the atmosphere module is coupled to a simple thermodynamic model of the near-surface ocean, which warms or cools in response to surface heat exchanges with the atmosphere, and in which horizontal and vertical transport within the ocean is prescribed. Such a model configuration is widely accepted as a suitable set-up for the simulation of equilibrium climate changes, including the climate sensitivity, a standard benchmark of climate change defined as the global mean equilibrium response of surface temperature to doubled carbon dioxide. However, this simplified approach neglects climate change feedbacks involving changes in regional ocean heat transport (Boer and Yu, 2003), and implies the need for a method of converting simulated equilibrium changes into corresponding estimates of transient climate change. This conversion relies on the assumption that a reasonable relationship exists between patterns of time-dependent and equilibrium climate changes in response to increasing greenhouse gas concentrations. Harris et al. (2006) find a close relationship for multiyear averages of surface temperature changes, whereas for precipitation the degree of correspondence varies significantly with location, though it is quite good for the UK and Europe. Note, however, that our conversion method (described in Section 3.2.4) also accounts for random and systematic differences between simulated patterns of time-dependent and equilibrium changes.
An ensemble of 280 HadSM3 experiments was run, sampling the effects of perturbing these parameters relative to the settings used in the standard published variant of HadCM3 (Gordon et al. 2000). [These settings are referred to hereafter as the standard parameter values, though a number of these values actually correspond to extremes of the ranges identified by experts, due to the practice of tuning the model to improve its simulation of certain basic aspects of climate, such as the planetary radiation balance]. Each experiment consisted of a control simulation of recent climate, and a simulation of the response to a doubled carbon dioxide concentration, run for a sufficient length of time to allow the resulting climate change to reach equilibrium. Murphy et al. (2004) carried out an initial ensemble of 53 members in which one parameter was perturbed at a time. This was subsequently augmented by a second ensemble of 128 members containing multiple parameter perturbations chosen to sample a wide range of climate sensitivities, achieve skilful simulations of present climate and maximise coverage of parameter space (details in Webb et al. 2006). Further HadSM3 simulations were then run to achieve improved sampling of parts of parameter space influenced by key interactions between parameters (Rougier et al, 2008). Together, these ensembles provide the 280 simulations used in UKCP09.
Emulation of equilibrium climate changes in response to doubled CO2
This set of simulations is sufficient to sample the main effects of parameter variations within our 31-dimensional space, but not to cover it comprehensively. We therefore use a statistical tool called an emulator (e.g. Rougier et al. 2008), to help us estimate the values of the required set of climate variables at any given point in parameter space. The emulator is trained on the available GCM simulations to estimate the results of a set of historical and future climate variables required in the production of our probabilistic projections. Each climate variable is emulated using an equation which provides a best estimate value and associated errors for any combination of model parameter values. This is done by using the available GCM simulations to train multiple regression relationships which express the required climate variables as functions of the model parameters, where the set of regressors capture key interactions between the effects of different parameters, as well as the effects of each parameter in isolation. Emulation errors are guaranteed to be greater than or equal to internal climate variability, and are typically 20–50% larger.
Using the emulator, we are then in a position to integrate over the whole of our parameter space, estimating values of both historical climate variables (required to weight each location according to how well the GCM would simulate historical climate given that particular combination of parameter settings), and future climate changes. This integration allows us to estimate observationally-constrained probabilities for different changes, accounting for model uncertainties. It provides the bedrock of our approach to probabilistic projection, however a number of additional elements are required to convert the results into user-relevant estimates of climate change for specific 21st century periods, and to ensure that additional sources of uncertainty are included. These are described in sections 3.2.4–3.2.11. Several aspects of the methodology (in addition to the emulation stage described here) require the estimation of uncertainties from the residual errors of statistical regression or optimisation procedures. These statistical errors are assumed to be , and they are all included in the uncertainty expressed in the projections. In view of this, several of the UKCP variables are transformed prior to the calculation of projected changes, the inverse transformation being applied afterwards to recover projected changes in the original variables. These transformations are made either to reduce the risk of non-Gaussian error characteristics, or to ensure that absolute bounds in some of the projection variables cannot be exceeded by the addition of several sources of statistical error. In particular, this ensures that variables presented as percentage changes relative to the UKCP baseline period cannot go beyond –100%.