1. Concepts of downscaling Modelling Noise
24 January 2019 Lecture "Advanced conceptual issues in climate science"
Concepts of downscaling
Modelling
Noise
Hans von Storch

2. Background information on this issue:
von Storch, H., S. Güss und M. Heimann, 1999: Das Klimasystem und seine Modellierung. Eine Einführung. Springer Verlag ISBN , 255 pp
von Storch, H., and G. Flöser (Eds.), 2001: Models in Environmental Research. Proceedings of the Second GKSS School on Environmental Research, Springer Verlag ISBN , 254 pp.
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. “Models” and “Modelling”
Modelling is a basic concept in natural sciences, but the term is used for a large variety of objects.
In particular physicists and geographers use the term with different meanings.
In climate sciences we have two main groups, namely minimum and maximum complexity models (more on that later).
Models in climate science serve different purposes. They are used to construct knowledge, which is not yet available.
Sometimes, people equate modelling with the numerical treatment of certain differential equations. While the numerics are an important aspect of some parts of modelling, it is a mere technical issue.
The concept of “parameterizations” is deeply intertwined with the modelling concept in climate sciences (see below). 3

4. Overview:
Hesse’s concept of positive, negative, and neutral analogs: the added value resides with the neutral analogs.
Models describe a reduced, incomplete image of reality. Almost all models contain choices made by modelers. In particular parameterizations.
Purpose of models – what do we learn about the “real” world? – Understanding, simulation, analysis of data, experimentation.
We deal in this lecture only with mathematical models, not with physical models.

5. 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.

6. Conceptual aspects of modelling

7. Conceptual aspects of modelling

8. Conceptual aspects of modelling

9. Parameter range limited
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. Models can be shown to be consistent with observations, e. g
Models can be shown to be consistent with observations, e.g. the known part of the phase space may reliably be reproduced.
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.

11. Added value of modelling
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.
Designing models is conditioned by the expected added value.
There is hardly a model „of something“ but mostly a model „for studying / simulating something“.
Thus, models are conditioned upon the purpose of the model.

12. Main purposes of mathematical 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 „experimentation“, „simulation“, „analysis“

13. Models for reduction of complex systems
Minimum complexity models
identification of significant, small subsystems and key processes (cf. Hasselmann’s concepts of PIPs and POPs (1988))
often derived through scale analysis
often derived semi–empirically
constitutes “understanding”, i.e. theory
construction of hypotheses
characteristics: simplicity idealisation conceptualisation
fundamental science approach
Examples:
Energy balance model
Identifying stochastic climate model in action

14. Models for reduction of complex systems
E =  E +  A
with  = albedo
 = transmissivity
E = short wave solar radiation
A = long wave thermal radiation = sT4
without atmosphere =1,  = 0 : Teq = - 4°C
with present atmosphere =0.64,  = 0.30 : Teq = +15°C
Idealized energy balance

15. Integration of a zero–dimensional energy balance model
with constant transmissivity and temperature dependent albedo
no noise
evolution from different initial values
with noise
Temperature dependent albedo (reflectivity)
evolution with slightly randomized transmissivity
Presence of noise changes the dynamics of the system

16. Models for reduction of complex systems
Numerical experiment with ocean model: standard simulation with steady forcing (wind, heat and fresh water fluxes) plus random zero-mean precipitation overlaid.
forcing
Mikolajewicz, U. and E. Maier-Reimer, 1990
Stochastic Climate model at work: identification of a low-dimensional oscillatory mode in a high-dimensional oceanic environment
response

17. Models as surrogate reality
Maximum complexity models
dynamical, process-based models,
experimentation tool (test of hypotheses)
sensitivity analysis; including scenarios
dynamically consistent interpretation and extrapolation of observations in space and time (“data assimilation”; “analysis”)
forecast of detailed development (e.g. weather forecast)
characteristics: quasi-realistic complexity mathematical/mechanistic engineering approach

18. Components of the climate system. (Hasselmann, 1995)

19. 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.

20. atmosphere

21. Dynamical processes in the atmosphere

22. Dynamical processes in a global atmospheric general circulation model

23. Dynamical processes in the ocean

24. Dynamical processes in a global ocean model

25. Reproduction of known properties of climate dynamics
validation
Reproduction of known properties of climate dynamics
Radiative balance
Climatic Zones
Storm track

26. Modell Observed Climatic Zones Classification following Koeppen
Erich Roeckner, pers. communication 26

27. Density of stromtracks
Observed
Simulated
Winter
(DJF)
Cyclogenesis
Density of stromtracks
Erich Roeckner, pers. Comm. 27

28. “Grid resolution” > “resolution”
variance
Insufficiently resolved
Well resolved
Spatial scales
Typical different atmospheric model grid resolutions with corresponding land masks. T42 used in global models. (courtesy: Ole Bøssing-Christensen)
“Grid resolution” > “resolution”

29. Free Simulation: 1000 years
Temperature (at 2m) deviations from 1000 year average [K]
Free Simulation: 1000 years
no solar variability, no changes in greenhouse gas concentrations or volcanic aerosol load
Zorita, 2001

30. Forced simulation: 1000 years
with estimated solar variability, volcanic activity, and changes in greenhouse gas concentrations,

31. Validation: Late Maunder Minimumvs
Reconstruction from historical evidence, from Luterbacher et al.
Model-based reconstuction

32. Added value – unobserved global air temperature anomaly
(or model artifact?)

33. Ft, Ht freshwater and heat flux Fp, Hp
Testing the : Stommel model of the North Atlantic overturning
Ft, Ht freshwater and heat flux Fp, Hp
Subtropical Atlantic Tt,St
Subpolar Atlantic Tp, Sp
Transport

34. Rahmstorf‘s model Ocean GCM without high-frequency atmospheric variability
Stommel‘s theory
Rahmstorf, 1995

35. Numerical experimentation
detailed parameterization
Numerical experimentation
Latitude-height distribution of temperature (deg C)
Roeckner & Lohmann, 1993
Effect of black cirrus
Difference “black cirrus” - detailed parameterization
No cirrus
Difference “no cirrus” - detailed parameterization

36. Deconstruction of recent climatic development
simulation without anthropogenic drivers
simulation with anthropogenic drivers
vs. „observation“ (centered on mean) 38

37. Climate Change simulations

38. Scenario building / traditional
Sequentieller Aufbau
Construction of scenarios of emissions.
Construction of scenarios of concentrations of radiatively active substances in the atmosphere.
(imulation of climate as constrained by presence of radiatively active substances in the atmosphere (“prediction” of conditional statistics).

39. “SRES” Scenarios SRES = IPCC Special Report on Emission Scenarios
A world of rapid economic growth and rapid
introduction of new and more efficient technology.
A very heterogeneous world with an emphasis on
family values and local traditions.
A world of “dematerialization” and introduction of
clean technologies.
A world with an emphasis on local solutions to
economic and environmental sustainability.
“ business as usual ” scenario (1992). A1 A2 B1 B2
IS92a

40. Annual temperature changes [°C]
Scenario A2
Annual temperature changes [°C]
(2071–2100) –(1961–1990)
Scenario B2
Danmarks Meteorologiske Institut

41. TAR (2001) „sub-continental development“ scenarios A2 and B2.
precipitation
Giorgi et al., 2001
Agreement among 7 out of a total of 9 simulations

42. Not dealt with Quasirealistic models for analysis of synoptic state
forcasting

43. Conclusions: mathematical models in climate science
“Model” is a term with very many different meaning in different scientific and societal quarters.
Validation of models means to check positive and negative analogs. Validation does not teach about functioning of the considered system but about the considered model.
The constructive part of models is in their neutral analogs with “reality”. They represent possible “added value”, or “added understanding”.
In climate science we have “minimum complexity” conceptual models – constituting understanding – and “maximum complexity” quasi-realistic models, allowing for simulation, numerical experimentation and data analysis.
The design of a model depends on the intended purpose/added value of the model. Such purposes may be framing basic dynamics of developments of phenomena as theory, the test of theories, the quasi-realistic simulation of interactions and developments, the dynamical analysis of limited empirical evidence , numerical experimentation for examining the effect of modifications impossible in the real world.
An identified neutral analog may be a property of the real world, representing added understanding, but it also may be a model artifact.