Coupled Modelling and Uncertainty in Climate System Models

Principal Investigator

Jerzy A. Filar

CIAM, School of Mathematics, University

of South Australia

In the project we investigate the problem of the balance between computational efficiency and the complexity of coupling between different components of climate system models such as the atmosphere and oceans. The main features of such models are captured in the Community Climate Model (CCM3) which was used in this research.

The principal challenge that we have addressed in the project stems from the fact that many dynamical systems such as climate may only be observable in transient states. Consequently, climate data sets can never completely validate simulations. In addition, computational experiments are too costly to permit investigation of all relevant factors. However, although we cannot carry out controlled experiments on the climate, we can construct models of "proxy climate" on which such experiments can be conducted. The CCM3 model plays the role of such "proxy system", in this project. The problem of a trade-off between the degree of coupling between system components and the associated model uncertainty is also addressed in this project.


Paul S. Gaertner

V. Nick Melnik

Environmental Modelling Research Group, CIAM

School of Mathematics

University of South Australia;

John A. Taylor

Centre for Resources and Environmental Studies


g55 - VPP

What are the results to date and the future of the work?

Once a physical parameterization of climate processes is chosen, and hence, the mathematical model is "frozen", an examination of model sensitivity and related uncertainties can be effectively performed using tools of mathematical modelling and computational experiment (Melnik, 1997). We performed a series of computational experiments with the CCM3 on both a SUN station and the VPP-300 supercomputer. Typical outputs obtained as a result of climate simulation are presented on Fig. 1 (zonal component of the wind at vertical level 15) and 2 (water vapour field at vertical level 15).

- Appendix B

The error of the resulting simulations consists of three parts:

(a) the error of initial data at the start of computer simulation;

(b) error of the finite set of differential equations in the description of climate, and

(c) the error of the numerical algorithm that is used.

For models such as the CCM3, the estimation of the total error obtained from the contributions from all three sources is still practically infeasible. Instead, we are currently developing a technique for the evaluation of such an error for a simplified model.

In future phases of this project we plan to conduct experiments with the Climate System Model and random error growth to analyse the interconnection with the degree of coupling in the model. This requires numerical analysis of coupled models of the atmosphere-and-active-layers system by simulation of interactions between components of climate using the Flux Coupler code. A theoretical justification of the Climate System Model requires the relaxation of a priori too stringent assumptions on the solution smoothness. The implied mathematical challenge stems from the fact that the standard energy norms may not provide an appropriate choice for the error control in mathematical models of such systems. Under a fixed degree of coupling and a given physical parameterization we need a scale of a-priori and a-posteriori estimates in a spectrum of norms to ensure the stability of the model. Further computational experiments are required to support theoretical results along this direction.

What computational techniques are used?

We used both the standard mode of the CCM3 package (in which climatological sea surface temperatures are input of the model) and the slab-ocean mode. In the latter case we used a special initial data set as well as a special time-varying boundary data set instead of the prescribed sea-surface data set as in the standard option.

The core atmospheric modelling of CCM3 is the solution of a system of so-called primitive equations which include prognostic and diagnostic equations. For the resulting system of partial differential equations time-discretization involves semi-implicit formulations whereas horizontal aspects of dynamics are treated using spectral transform.

For the ocean part of the model we used a simple ocean model for coupling with the atmospheric modelling core of CCM3. We also used a vectorised slab-ocean version of the model which was tuned by Dr Murray Dow from the ANUSF whose help is, hereby, gratefully acknoledged.

From the computational point of view, the future development of this work requires the implementation of the message passing using the PVM facility for a parallelized code. The multicomponent climate model, which requires an effective comparison of the results obtained from spectral and semi-Lagrangian modes, will be run as the next step of the project. Computational experiments and theoretical investigations are currently under way for a simplified mathematical model.


Filar, J.A. and Zapert, R. Uncertainty Analysis of a Greenhouse Model. C. Carraro and A. Haurie (eds), Operations Research and Environmental Management Kluwer, Dodrecht, 1996.

Melnik, V. N., Error Dynamics and Coupling Procedures Mathematical Climate System Models, Proceedings of the 15th World Congress on Scientific Computation, Modelling and Applied Mathematics, Germany, 1997 (accepted, see

Melnik, V.N., Mathematical Models for Climate as a Link Between Coupled Physical Processes and Computational Decoupling, TR 1/1997, CIAM, School of Mathematics, University of South Australia, 42 pages

Melnik, V.N., Nonconservation law equation in mathematical modelling: aspects of approximation, Proc. of the International Conf. AEMC'96, Sydney, 1996, 423430.

- Appendix B