Torben Königk

Rossby Centre/ SMHI

Fundamentals of Climate Modelling

Outline

IntroductionWhy do we need models?

Basic processesRadiationAtmospheric/Oceanic circulation

Model basicsResolutionParameterizationsLimitations

Why do we need models?

Weather forecastWhat will the weather be in Norrköping tomorrow?

What activities shall we plan for the weekend?

Why do we need models?

Climate analysisHow large is the natural variability? Mechanisms of climate processes?

Why do we need models?

Climate scenariosHow will the climate be in Norrköping in 30 years?Do we will have more extremes?How is sea level changing?

Simulated temperaturechange until 2090-2099

The Climate System : What do we need to include ?

Radiation: Black body radiation

� A black body absorbs all incident radiation

� A blackbody emits radiationaccording to Planck’s law(shape of curves)

� Wien’s displacement law givethe temperature of a radiationsource (maximum of curves)

� Total flux given by the Stefan-Boltzmann law(integration over the curve)

wavelength [µm]

Longwave radiation of the Earth

Emitted radiation at the Earth’s surface 4-100µm (maximum at around10µm)

CO2 and O3 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.

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 ratiobetween reflected and incoming radiation

� Cloud albedo varies (30-90%)� Global average ca 30%

(including clouds)

10-100Water (Sun close to horizon)

3-10Water

5-20Forest

10-20Grass

20-40Sand

50-80Ice

50-70Old snow

75-95Snow

Albedo (%)Properties of the ground

� Assume balance betweenoutgoing and incoming radiationon long term basis

Radiation balance of the Earth

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)

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

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 forcethat 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 towardsthe poles)

Atmospheric Circulation

Conservation of absolute angular momemtum and the stability of fluid flows leads to the break up of a thermally direct circulation around 30°poleward ofthe equator. Here the atmosphere develops instabilities (extra-tropical cyclones)that efficiently transport energy and momentum poleward.

heating

cooling

cooing

No rotation of the Earth

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.

Large scale ocean circulation

Equations describing the atmosphere

XFx

fvp

uuV

t

u =∂∂+−

∂∂+∇⋅+

∂∂ φω

r

yFy

fup

vvV

t

v =∂∂++

∂∂+∇⋅+

∂∂ φω

r

αφ −=∂∂

p

CpQCpp

TTV

t

T// =−

∂∂+∇⋅+

∂∂ αωω

r

0=∂∂+⋅∇

pV

ωr

RTp =α

qSp

qqV

t

q =∂∂+⋅∇⋅+

∂∂ ω

r

• 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 toprovide approximate solutions.

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 100-200 km in the horizontal

� 40-60 Iayers in the vertical both in atmosphere and ocean

� Typical time step can be 30 min

Climate Model

� The information needed to run a GCM (atmosphere and ocean) is:Initial state of all the variables in all boxesA description of the land surface (topography and land use)Solar radiationGas 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

Space and time scalesSpace and time scalesSpace and time scalesSpace 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)

ParametrizedParametrizedParametrizedParametrized processes in a climate processes in a climate processes in a climate processes in a climate

modelmodelmodelmodel

MixingDeepConvection Eddies

Sea iceprocesses

The Development of Climate models

Source: IPCC, TAR, 2001

Mid-1970s Mid-1980s Early 1990s Late 1990s Early 2000s Late 2000s

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)!

Summary

� Climate models are an important tool to investigate past, present and future climates.

� Differential heating of the Earth causes atmospheric and oceaniccirculation.

� 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.