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1 Fundamentals of Climate Modelling Torben Königk Rossby Centre/ SMHI

2 Outline Introduction Why do we need models? Basic processes Radiation Atmospheric/Oceanic circulation Model basics Resolution Parameterizations Limitations

3 Why do we need models? Weather forecast What will the weather be in Norrköping tomorrow? What activities shall we plan for the weekend?

4 Why do we need models? Climate analysis How large is the natural variability? Mechanisms of climate processes?

5 Why do we need models? Climate scenarios How will the climate be in Norrköping in 30 years? Do we will have more extremes? How is sea level changing? Simulated temperature change until

6 The Climate System : What do we need to include?

7 Radiation: Black body radiation A black body absorbs all incident radiation A blackbody emits radiation according to Planck s law (shape of curves) Wien s displacement law give the temperature of a radiation source (maximum of curves) Total flux given by the Stefan-Boltzmann law (integration over the curve) wavelength [µm]

8 Longwave radiation of the Earth Emitted radiation at the Earth s surface 4-100µm (maximum at around 10µm) CO 2 and O 3 absorb at wavelengths within the Earth s emission spectrum. Increases in their concentration will increase the natural greenhouse effect and warm the planet. Water Vapour is the most active abosrbing gas in the IR spectrum.

9 Solar radiation Absorption of incoming solar radiation small Incoming radiation may be reflected by clouds, particles or by the ground The albedo (A) is the ratio between reflected and incoming radiation Cloud albedo varies (30-90%) Global average ca 30% (including clouds) Properties of the ground Snow Old snow Ice Sand Grass Forest Water Water (Sun close to horizon) Albedo (%)

10 Radiation balance of the Earth Assume balance between outgoing and incoming radiation on long term basis Solar constant 1368 W m -2 planetary albedo 30% Outgoing terrestrial radiation (longwave) is absorbed and reemitted in the atmosphere. The net effect is a warming of the surface (Te = 288 K)

11 Radiation Balance, Differential Heating Imbalances leads to temperature differences and thereby pressure gradients generating the general circulation of the atmosphere (and the oceans) Long term imbalance leads to climate change

12 Atmospheric motion Air is under influence of a number of forces resulting in movements (winds and turbulence) The forces are; the pressure gradient force, gravity, friction, centrifugal forces and the Coriolis force, The Coriolis force is an apparent force that leads to a deflection to the right (left) of all motion in the northern (southern) hemisphere It is proportional to the speed and depends on latitude (increasing towards the poles)

13 Atmospheric Circulation No rotation of the Earth cooling heating cooing Conservation of absolute angular momemtum and the stability of fluid flows leads to the break up of a thermally direct circulation around 30 poleward of the equator. Here the atmosphere develops instabilities (extra-tropical cyclones) that efficiently transport energy and momentum poleward.

14 Large scale ocean circulation The ocean circulation is driven by density contrasts in the ocean. Regions of intense heat loss from the ocean, surface winds and salinity of the ocean (sea ice melt, runoff, precipitation) govern the circulation. The continents play an important role.

15 Equations describing the atmosphere u t r u + V u + ω p fv + φ = x v r v φ + V v + ω + fu + = t p y φ = α p T r T + V T + ω αω / Cp = t p F X F y Q / Cp r V q t + p α = RT r + V ω = 0 p q q + ω p The atmosphere is governed by a set of physical laws expressing how the air moves, heating and cooling, moisture, and so on. Although the equations describing atmospheric behaviour can be formulated, they cannot be solved analytically. Instead, numerical methods are needed to provide approximate solutions. = S q

16 A global climate model (model describing the general circulation - GCM) In a GCM grid boxes cover the entire planet (ocean and atmosphere) Typical size is km in the horizontal Iayers in the vertical both in atmosphere and ocean Typical time step can be 30 min

17 Climate Model The information needed to run a GCM (atmosphere and ocean) is: Initial state of all the variables in all boxes A description of the land surface (topography and land use) Solar radiation Gas and aerosol composition of the atmosphere The resources needed to run a GCM (atmosphere and ocean) are: Super computer (many processors & 100 TB disk) Takes 2 weeks for 100 years simulation

18 Space and time scales Typical timescales of variation in the climate system. Atmosphere (seconds to weeks) Surface vegetation (weeks to years) Surface snow and sea-ice (days to years) Upper Ocean (days to years) Deep Ocean (months to multi-century) Glaciers (years to multi-century) Continental distribution and mountain building (100s to 1000s of thousand years)

19 Parametrized processes in a climate model Sea ice processes Mixing Deep Convection Eddies

20 The Development of Climate models Mid-1970s Mid-1980s Early 1990s Late 1990s Early 2000s Late 2000s Source: IPCC, TAR, 2001

21 Initialization/ chaotic behaviour NWP integrations started from very similar initial conditions may result in quite different forecasts Simulations with climate models can never be directly compared to observations: Never compare a single month or year from a model simulations to the corresponding year in reality! Compare statistics of a longer period (decades or more)!

22 Summary Climate models are an important tool to investigate past, present and future climates. Differential heating of the Earth causes atmospheric and oceanic circulation. Clouds, gases and particles are important for radiation balance. Main uncertainties of climate models are connected to low resolution and the need to parametrize small-scale processes. Climate is the statistics of weather.

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