1. Dynamical Models - Purposes and Limits
5-10 February Fourth Santa Fe Conference on Global & Regional Climate Change, Santa Fe
Dynamical Models - Purposes and Limits
Hans von Storch,
Helmholtz Centre Geesthacht, and
KlimaCampus „clisap“, University of Hamburg Germany
The concept of climate simulations with quasi-realistic climate models is discussed and illustrated with examples. The relevant problem of deriving regional and local specifications is considered as well.

2. Background information on this issue:
Müller, P., and H. von Storch, 2004: Computer Modelling in Atmospheric and Oceanic Sciences - Building Knowledge. Springer Verlag Berlin - Heidelberg - New York, 304pp, ISN X 2

3. Conceptual aspects of modelling

4. Conceptual aspects of modelling Hesse’s concept of models
Reality and a model have attributes, some of which are consistent and others are contradicting. Other attributes are unknown whether reality and model share them.
The consistent attributes are positive analogs.
The contradicting attributes are negative analogs.
The “unknown” attributes are neutral analogs.
Hesse, M.B., 1970: Models and analogies in science. University of Notre Dame Press, Notre Dame 184 pp.

5. The constructive part of a model is in its neutral analogs.
Conceptual aspects of modelling
Validating the model means to determine the positive and negative analogs.
Applying the model means to assume that specific neutral analogs are actually positive ones.
The constructive part of a model is in its neutral analogs.

6. Conceptual aspects of modelling

7. Conceptual aspects of modelling

8. Conceptual aspects of modelling

9. Parameter range limited
Conceptual aspects of modelling
Models represent only part of reality;
Subjective choice of the researcher; Certain processes are disregarded.
Only part of contributing spatial and temporal scales are selected.
Parameter range limited

10. reliably be reproduced.
Conceptual aspects of modelling
Models can be shown to be consistent with observations, e.g. the known part of the phase space may
reliably be reproduced.

11. Models can not be verified because reality is open.
Conceptual aspects of modelling
Models can not be verified because reality is open.
Coincidence of modelled and observed state may happen because of model´s skill or because of fortuitous (unknown) external influences, not accounted for by the model.

12. The purpose of building and using a model is to generate „added value“, i.e., additional knowledge about reality over what is known before.
The added value resides with the neutral analogs; if real added value is generated or not needs further independent confirmation (theoretical, observational).
A model may serve its purpose of returning the requested added value, when suitable positive analogs prevail.

13. Main purposes of modelling
Conceptual aspects of modelling
Main purposes of modelling
Reducing complexity to simple, dominant, low-dimensional subsystems  representing „understanding“, „knowledge“, „theory“
Detailed „surrogate reality“ description of considered system in a high-dimensional phase space, including many complexities  representing an „experimental tool“, „simulation“, „analysis“

14. Conceptual models for the reduction of complex systems

15. Models for reduction of complex systems
identification of significant, small subsystems and key processes
often derived through scale analysis
(Taylor expansion with some characteristic numbers)
often derived semi–empirically
constitutes “understanding”, i.e. theory
construction of hypotheses
characteristics: simplicity idealisation conceptualisation
fundamental science approach

16. Models for reduction of complex systems
Idealized energy balance

17. Noise or deterministic chaos?
Mathematical construct of randomness adequate concept for description of features resulting from the presence of many chaotic processes.

18. Quasi-realistic modelling

19. Models as surrogate reality Purposes
dynamical, process-based models,
Purposes
experimentation tool (test of hypotheses)
design of scenario
deconstruction of observational record (detection and attribution)
sensitivity analysis
dynamically consistent interpretation and extrapolation of observations in space and time (“data assimilation”)
forecast of detailed development (e.g. weather forecast)
characteristics:
complexity
quasi-realistic
mathematical/mechanistic
engineering approach

20. Quasi-realistic climate models …
… are dynamical models, featuring discretized equations of the type
with state variables Ψk and processes Pi,k.
The state variables are typically temperature of the air or the ocean, salinity and humidity, wind and current.
… because of the limited resolution, the equations are not closed but must be closed by “parameterizations”, which represent educated estimates of the expected effect of non-described processes on the resolved dynamics, conditioned by the resolved state.

21. Dynamical processes in the atmosphere

22. Dynamical processes in a global atmospheric general circulation model

23. Laboratory to test conceptual models

24. Laboratory to test conceptual models
Stommel‘s theory
Rahmstorf‘s model
Rahmstorf, 1995

25. Deconstruction of recent climatic development
simulation without anthropogenic drivers
simulation with anthropogenic drivers
vs. „observation“ (centered on mean) 25

26. Conclusions
“Model” is a term with very many different meaning in different scientific and societal quarters.
The constructive part of models is in their neutral analogs.
The design of models depends on its purpose, namely the expected added value generated by the model.
Validation of models means to check positive and negative analogs.
In climate science we have conceptual models – constituting understanding – and quasi-realistic models, allowing for numerical experimentation.
Quasi-realistic models may be used for testing hypothesis, for developing hypothesis, for the construction of a full and dynamically consistent 4-d state, forecasts and for scenarios but also for deconstructing events and past developments.

27. The purpose of building and using a model is to generate „added value“, i.e., additional knowledge about reality over what is known before.
The added value resides with the neutral analogs; if real added value is generated or not needs further independent confirmation (theoretical, observational).
A model may serve its purpose of returning the requested added value, when suitable positive analogs prevail.

28. Thinking and speaking about
models of something
makes no sense.
Instead, models should be presented as models for something. i.e., as tools for
describing some (specific) features of reality, which are needed to generate an added value in terms of hypotheses on past and future states and trajectories, sensitivity to certain drivers