Climate Modeling OCN760

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Climate ModelingOCN-760

• Axel Timmermann

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Prolegomena
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Main goals of the class

• to develop the mathematical-physical basis of the
  climate components and their interactions
• to provide a practical introduction into
  numerical techniques used in climate research
• to develop skills that help you to solve
  complicated climate problems with publicly
  available tools

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Concept of climate modeling
Dynamical equations
Mechanisms
Climate model numerical solution
Thermodynamical equations
Model output
unresolved processes
Observations
climate forcing
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Hierarchy of climate models

• simplified models understanding basic processes
  and prediction
• intermediate complexity models understanding
  interactions between components, paleo-modeling
• comprehensive models comparison with
  observations, diagnosing mechanism, prediction

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Climate models versus reality
climate processes
climate archives
climate data
climate model data
climate models
process studies
Synthesis
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Limitations of climate models

• a climate model is always a simplification of
  mother nature
• complexity has different aspects number of
  unresolved processes and model resolution
• both are limited
• it is important to use a hierarchy of models to
  understand and to simulate nature, to
  flasify/verify hypotheses

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Historical development

• Vilhelm Bjerknes (1862-1951) suggests weather
  forecasting is a matter of mathematics and
  physics (deterministic, nonchaotic approach)
• Lewis Fry Richardson (1881-1953) first numerical
  weather forecast 3x1.8 degree, 5 vertical layers
  over Europe, 12 (p,T) profiles over Europe as
  initial conditions, 24 hour forecast took 3
  months, primitive equations, unstable numerical
  technique

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Historical development

• N. Philipps 1955 first Atmospheric General
  Circulation Model run on ENIAC
• Syukuro Manabe and Smagorinsky 1963-1969, fisrt
  coupled atmosphere-ocean model using flux
  corrections
• since 1990s climate models include chemistry,
  carbon cycle, biosphere, vegetation etc -gt
  climate modeling becomes multidisciplinary

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Climate goes engineering

• 1969 Budyko disperse ashes over Siberia -gt
  reduce snow-covered area -gt more area for
  agriculture
• iron ferilization of the oceans iron in Southern
  ocean -gt more biological productivity -gt drawback
  of atmospheric CO2
• Bering strait closure preventing THC collapse

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Term projects

• Hasselmann's socio-economic climate model
• Socio-economic-physical modeling using Gildors
  model
• 1.5 layer equatorial beta plane model
• Stationary Gill-type model
• Simple ice-sheetsimple ocean model
• barotropic vorticity equation and jets
• Diagnostics of 4th AR models thermostats vs.
  runnaway-greenhouse effects
• Patterns of sea-level rise and climate change for
  west-Antarctic ice sheet collapse (Thomas)
• Exploration of JEBAR term in BARBIEy

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Term projects

• ENSO forecasting using nonlinear ENSO model
• Paleo-ocean circulation with BARBIE
• bifurcation analysis of hydrodynamical equations
• geothermal processes and THC stability
• POSTER of term projects

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Components of the climate system and Earth system
history
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Radiation and its influences on global climate
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Energy balance of the earth

• 4pR2 h?C dT/dtp R2 (1-a)S -4pR2 esT4
• a Reflectivity 0.3
• e Emissivity 0.6 (Erde, 1 black body)
• C Specifiic heat of air 1000 J/kg/K
• S Solarconstant 1367 W/m2
• s5.67 10-8 Wm-2K-4
• T(1-a)S/4/e/s)0.25

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Energy Balance of the Earth

• T black body -18.3 C
• T for emissivity 0.6 15 C
• Natural Greenhouse effect 33 Cdue to water vapor
• However Problem is true emissivity is 0.8

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Energy Balance of the earth

• Introduce cirrus clouds that cover fraction c and
  have temperature T2, whereas ground temperature
  is T1
• p R2 (1-a)S c4pR2 esT244pR2 esT14
• with further geometrical considerations
• using true e0.886
• T2-38.8 C
• T114 C
• infrared radiation is emitted from each
  atmospheric level

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Climate Sensitivity

• ? response of climate system to 1W/m2 radiation
  change
• Albedo-Backscattered LW radiation climate
  feedbacks (clouds, CO2) Forcing 0
• A(T)-B(T)W(T)Q'0
• TTT'
• A(T)-B(T)W(T)ATT'-BTT'WTT'Q'0
• T'-Q'/(AT -BTWT)

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Climate sensitivity

• Climate sensitivity ?T'/Q'
• -?-1?A-1-?B-1?W-1
• EBM with clouds (1-a)S/4 -esT4 c/2 esT40
• ?A-1-S/4 da/dT
• ?B-14esT3
• ?W-12c esT3esT4/2 dc/dT
• let us assume only longwave feedback, no cloud
  and albedo effect
• ?0.3 K/W/m2