Aggregate models of climate change


Cost-efficient and accurate computation of regionalized climate change scenarios

Climatological context and concept

Integrated assessment studies typically evaluate many greenhouse-policy scenarios with their respective time-dependent greenhouse gas emissions, the corresponding changes in climate and global environment, and the resulting impact on human society and economy. A climate module designed for this purpose must, on the one hand, provide the required climate-change information for hundreds to thousands of scenarios without prohibitive computational effort. On the other hand, it should desirably approach the reliability of sophisticated circulation models.

Coupled general circulation models (GCMs) are the most reliable instruments currently available for the estimation of anthropogenic climate change. They are, though, extensive in computation time and difficult to handle. For typical climate scenarios of a few hundred to one thousand simulated years, they need roughly half a year of real time even in coarse-resolution experiments. Of the enormous amount of data in GCM simulations, only a few climate variables, such as global-mean temperature or sea-level rise, are typcially required for assessments of economic impacts of anthropogenic climate change.

The therory of impulse-response functions (IRFs) allows to construct simple models that reproduce the greenhouse response of any given GCM in appropriately selected variables to arbitrary perturbations, consuming cpu time in the order of seconds on a workstation. Once calibrated against the outcome of a single GCM simulation, an IRF model works without further reference to the GCM, and may serve as an accurate substitute for the GCM, as long as the forcing is so small that the system responds linearily.

For a choice of policy-relevant climate variables, the time-dependent response of the climate system to small perturbations can be computed to good accuracy through a collection of impulse-response function (IRF) modules. The greenhouse perturbation is represented as a time series of emission impulses, and the total response is computed as linear superposition of the responses to these single impulse (K.Hasselmann et al. 1997).

Because of the general nonlinear nature of the climate system, the use of such linearized IRF models is confined to, approximately, a doubling of the atmospheric CO2 concentration with respect to the preindustrial value of 280 ppm, or to a corresponding equilibrium warming of 2.5 degrees C. In order to extend the range of applicability to larger CO2 concentrations and temperatures, a model has been designed that is still based on the IRF approach but is able to treat the most important nonlinear processes:

Nonlinear Impulse-response representation of the coupled Carbon cycle-Climate System (NICCS)

The most critical processes limiting linear response are the following:

  1. IR absorption by atmospheric CO2 is already close to saturation in the strongest spectral bands. Thus the greenhouse warming varies approximately logarithmic rather than linearily with the concentration. 
  2. The oceanic uptake of CO2 is governed by the nonlinear carbon chemistry of seawater; the higher the background concentration the slower the downward transport of additional carbon through the surface layer (see e.g. Maier-Reimer & Hasselmann 1987, or Maier-Reimer 1993). 
  3. The model carbon cycle further includes a simple logarithmic fertilization of the land vegetation, which is a differential analogue to a modified version of the Joos vegetation IRF model (F.Joos et al. 1996).

To perturbations beyond doubled preindustrial carbon dioxide concentrations, the problem of nonlinear deformations of the climate response has been overcome through the basic mathematical concept of a differential analogue that can be tuned to a GCM-calibrated IRF in the linear limit of small CO2 emissions. Although only a mathematical tool to reproduce the desired impulse-response, the differential equations of the analogue are physically interpretable sufficient for treatment of critical nonliear processes. Thus the model's validity is extended into the nonlinear domain, up to the uncertain thresholds of abrupt state transitions in the dynamics of the climate system.

In a further extension, the greenhouse warming module now computes not only the global annual mean of the surface temperature, but also, as a first attempt to include spatial information, the first principal components of the annual-mean change in surface temperature, precipitation, cloudiness, and sea level rise (Hooss & al. 2001). The corresponding EOF patterns and the IRFs for the EOF coefficients have been calibrated against a transient 850 year simulation with the periodically-synchronously coupled ECHAM3-LSG (Voss & al. 1998; Voss & Mikolajewicz 2001).

Limits to Knowledge: Abrupt Climate Change

A common problem of climate impact assessments is the determination of probabilities and thresholds for abrupt shifts in the Earth System's workings. Candidates in the current debate are:

  1. Breakdown of the North-Atlantic thermohaline circulation could lead to a severe cooling of the Northern midlatitudes, especially Northern and Central Europe to the western part of Russia;
  2. Destabilization of the West-Antarctic Ice shield could rise the global sea level by up to additional 6 meters;
  3. Large-scale ecosystem disruptions with significant climatic feedbacks, e.g. a climate-accelerated desertification of large parts of the Amazon or African rain forest;
  4. Ecological foodchain disruptions through unforeseen species interactions at changed climatic conditions, in combination with the ever growing transport of all kinds of biological species across the world's trading system.
Abrupt climate changes of this kind and magnitude have been reconstructed from the geological records; despite the astonishing relative stability of the climate system throughout the past 10,000 years (after the end of the last glaciation), the system might turn out to be not so stable at all if sufficiently perturbed.However it must be stressed that this severe limitation of the validity is necessarily common among all existing models for assessment of climate change.


The NICCS model is available in FORTRAN 77.

A version with additional modules describing the atmospheric life times and radiative contributions of non-CO2 greenhouse gases has been implemented in GAMS (Bruckner & al. 2003). The linear, box-type modules are adopted from the Model for the Assessment of Greenhouse-gas Induced Climate Change (MAGICC; see Wigley 1988, Wigley & Raper 1992, Wigley 1994, Osborn & Wigley 1994, Wigley & al 1996). These components are similar, or identical to, the "simple models" (Harvey & al 1997) used by the IPCC for scenario analyses (IPCC 1996).