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Modellierung

- insbesondere in der Umwelforschung

Hans von Storch

Geesthacht, 6.12.2001

( 20. Auflage Leipzig, Mannheim 1998)

Modell ...

.... Naturwissenschaften: ein Abbild der Natur unter Hervorhebung für wesentlich erachteter Eigenschaften und unter Außerachtlassen als nebensächlich angesehener Aspekte. Das Modell ... ist umso realistischer oder wirklichkeitsnäher, je konsistenter es den von ihm umfassten Erfahrungsbereich zu deuten gestattet und je genauer seine Vorhersagen zutreffen; es ist umso tragender, je größer der von ihm beschriebene Erfahrungsbereich ist.

Modelle entstehen aus der Wechselwirkung zwischen Hypothesenbildung und Beobachtung: Die Hypothese lenkt die Beobachtung, und deren Resultate geben ihrerseits Anlass zur Verifizierung der Hypothese. Damit sind Modelle grundsätzlich nicht endgültig: sie müssen immer wieder der Erfahrung angepasst und, sofern das in einer konsistenten Weise nicht möglich ist, verworfen und durch neue Modelle ersetzt werden.

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Hydraulisches Modell

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Sündermann und Vollmers (1972)

Surface currents

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ollm

ers

(197

2)

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TIDAL CURRENTS & SEA LEVELState variables

• vertically averaged components of current (u, v) • sea level (relative to undisturbed level h) ()

du

dt Pi

u

i Pr ocesses Pi

u , Piv

dv

dt Pi

v

i

t

net divergence effect

geometry

boundary conditions (x o, y,t) sin2T

t

T ~ 12.5 hrs.

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process u v P1: Coriolis effect -fv fu

P2: pressure gradient

P3: bottom friction can not be expressed in terms of state variables

P4: diffusion needs parameterization

net divergence

g x

g y

x

h u y

h v Parameterizations

P3u ~

r

hu2 v2 u

P3v ~

r

h u2 v2 v

P4u ~ AH u

P4v ~ AH v

model equations complete already severely simplified system compared to the real system (e.g. vertical homogeneity)

bottom friction

diffusion

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NUMERICAL FORMULATION

Finite differences

Replace differential operators by difference operators

x

x x x x

2x

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APPLICATION

• replicate hydraulical model

• derive numerical values in high spatial and temporal resolution

• no problem to “measure” state variables

• examine sensitivity to

— boundary conditions

— formulation of parameterizations

— relevance of processes

Example: Coriolis force

Surface currents

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Surface currentSündermann und Vollmers (1972)

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Result with CORIOLIS Force

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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.

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.

Hesse, M.B., 1970: Models and analogies in science. University of Notre Dame Press, Notre Dame 184 pp.

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Purpose of models

• surrogate reality

realism

• reduction of complex systems

understanding

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Models as surrogate reality• dynamical, process-based models, • experimentation tool (test of hypotheses) • design of scenarios • 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/mechanisticengineering approach

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Models are• • • smaller than reality (finite number of processes, reduced size of phase space)

• • • simpler than reality   (description of processes is idealized)

• • • closed, whereas reality is open   (infinite number of external, unpredictable (or unspecifiable) forcing factors is reduced to a few specified factors)

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– Models in environmental sciences representonly part of reality;

– Subjective choice of the researcher.– Usually only part of all contributing spatial and

temporal scales are selected.– Certain processes are disregarded.

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I f KDynamical processes in the atmosphere

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I f KDynamical processes in a global atmospheric model

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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.

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Models can be shown to be consistent with observations, e.g. the know part of the phase space may reliably be reproduced.

However the technically possible representation of the unknown part of the phase space (e.g. 2xCO2) is in principle questionable (but perhaps plausible)

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1973–1993

ERA ECMWF

1880–2049

ECHAM3/LSG

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A new Set of IPCC Emissions Scenarios (SRES Scenarios )

A world of rapid economic growth and rapidintroduction of new and more efficient technology.

A very heterogeneous world with an emphasis onfamily values and local traditions.

A world of “dematerialization” and introduction of clean technologies.

A world with an emphasis on local solutions toEconomic and environmental sustainability.

“ business as usual ” scenario (1992).

A1

A2

B1

B2

IS92a

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Scenario A2

Scenario B2

Danmarks Meteorologiske Institut

Annual temperature changes [°C]

(2071–2100) –(1961–1990)

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Modelle dienen einem Zweck. Modelle “per se” gibt es nicht: Nicht “Modelle von X” sondern “Modelle für A”. “Modelle” können nicht verifiziert werden, sondern nur validiert (d.h. zegen, daß sie nicht im Widerspruch zu bekannten Tatsachen stehen)

“Quasirealistische Modelle” schaffen eine Ersatzrealität, in der ansonsten unmögliche Experimente realisiert werden können und in denen Szenarios plausibler Änderungen als Reaktion menschlicher Einwirkung dargestellt werden können.

von Storch, H., and G. Flöser (Eds.), 2001: Models in Environmental Research. Proceedings of the Second GKSS School on Environmental Research, Springer-Verlag, ISBN 3-540-67862, 254 pp.

Zusammenfassung