Uncertainties due to transport-parameter sensitivity in an efficient 3-D ocean-climate model

Abstract

A simplified climate model is presented which includes a fully 3-D, frictional geostrophic (FG) ocean component but retains an integration efficiency considerably greater than extant climate models with 3-D, primitive-equation ocean representations (20 kyears of integration can be completed in about a day on a PC). The model also includes an Energy and Moisture Balance atmosphere and a dynamic and thermodynamic sea-ice model. Using a semi-random ensemble of 1,000 simulations, we address both the inverse problem of parameter estimation, and the direct problem of quantifying the uncertainty due to mixing and transport parameters. Our results represent a first attempt at tuning a 3-D climate model by a strictly defined procedure, which nevertheless considers the whole of the appropriate parameter space. Model estimates of meridional overturning and Atlantic heat transport are well reproduced, while errors are reduced only moderately by a doubling of resolution. Model parameters are only weakly constrained by data, while strong correlations between mean error and parameter values are mostly found to be an artefact of single-parameter studies, not indicative of global model behaviour. Single-parameter sensitivity studies can therefore be misleading. Given a single, illustrative scenario of CO 2 increase and fixing the polynomial coefficients governing the extremely simple radiation parameterisation, the spread of model predictions for global mean warming due solely to the transport parameters is around one degree after 100 years forcing, although in a typical 4,000-year ensemble-member simulation, the peak rate of warming in the deep Pacific occurs 400 years after the onset of the forcing. The corresponding uncertainty in Atlantic overturning after 100 years is around 5 Sv, with a small, but non-negligible, probability of a collapse in the long term.

Oracle-based optimization applied to climate model calibration

“…As a result of its efficient but relatively faithful representation of large-scale ocean dynamics, the model has proved useful for studies of glacial circulation states (Rohling et al, 2004), integrated assessments of climate change impacts (Drouet et al, 2005) and parametric investigations of the stability of the thermohaline circulation . The model is described more fully in (Edwards and Marsh, 2003). C-GOLDSTEIN forms a component of the Grid Enabled Integrated Earth System Model (GENIE) project (http://www.genie.ac.uk) in the context of which an Earth System Model with more detailed representations of atmosphere, land-ice, ocean biogeochemistry and land-surface processes is under development.…”

“…C-GOLDSTEIN contains a total of around 75 physical and model parameters, a subset of 12 or which were identified in (Edwards and Marsh, 2003) as the principal adjustable parameters governing transport and mixing, and thus the large-scale distributions of climatic variables (temperature, humidity etc). Even where these parameters correspond to well-defined physical processes which may, in principle, be measurable, the correct physical values remain hard to ascertain experimentally.…”

“…Thus in (Edwards and Marsh, 2003), an averaged error function is defined which measures the mean square departure of the model state from observations. Good estimates of the 12 parameters are found by minimizing the error, over an ensemble of 1000 randomly chosen parameter sets within a predefined range.…”

“…1-2) thus is clearly not a fully convex function. Similar, single-parameter bifurcation experiments were conducted by (Edwards and Marsh, 2003) for all 12 parameters. Most yielded convex graphs, but parameters controlling the global hydrological cycle in particular, such as atmospheric humidity transport, showed evidence of non-convexity associated with hysteresis and bifurcations between contrasting global ocean circulation states.…”

Optimal tuning of a GCM using modern and glacial constraints

“…The simplest methods consist of sampling the whole parameter space. This method usually requires a number of samples which increases exponentially with the number of parameters but the efficiency of the sampling can be improved by using a Latin Hypercube Sampling (LHS; Mckay 1992) which has been successfully used in uncertainty analysis studies (Schneider von Deimling et al 2006;Edwards and Marsh 2005). Efficient Heuristics methods, such as the Monte Carlo Markov Chain (Hargreaves and Annan 2002), genetic algorithms (Price et al 2006) and oracle based optimization (Beltran et al 2006), require a lower number of experiments.…”