ecolmas training course – introduction to climate modelling · ecolmas training course –...

ECOLMAS Training Course –Introduction to climate modelling

Bremen, 1-4 April 2008

Part 3: The Atmosphere

Ute Merkel

ECOLMAS Course Bremen 2008 – Part 3 Atmospheric mode lling

(British Weather Service, 2008)

Storm "Emma", March 2008

Weather versus Climate

time

Initial conditions at t=0(almost identical, not perfectly known)

Exponential growth of the error(i.e. the difference between the trajectories starting from almost identical initial conditions)

The weather prediction does not make sense beyond a certain time range (~ 15 days for the atmosphere) because the deviations between the trajectories are of the same order of magnitude as the change in X).

X

(adapted from V. Moron, 2003)

Atmospheric modelling - General atmospheric circulat ion

Weather versus climate

Climate is what we expect,weather is what we get.


Larry Riddle

Introduction to atmospheric circulation


λ = longitudeφ = latitudet = time

Averaging with respect to time

Averaging with respect to longitude (zonal mean)

zonal mean meridional circulation

zonally asymmetric circulation

time meancirculation

transientcirculation / eddies

stationary waves



(Univ. Wales, Bangor)

thermallydirect cells


Annual mean Hadley Cells (NCEP reanalysis 1948-2001)from the meridional stream function (1010 kg/s)

(Liu and Alexander, 2007)

latitude

pres

sure

(hP

a)

ECOLMAS Course Bremen 2008 – Part 3 Atmospheric mode lling



(Fig. 6.22, Hartmann, 1994)

Zonal Walker circulation along the equator

⇒ low-level convergence and associated upward motion (convection)


(The Dynamic Earth, Fig. 2.18)

Near surface wind fields and pressure systems -Position of the ITCZ

July, boreal summer

January, boreal winter

General circulation: Monsoons


(The Dynamic Earth,Fig. 2.19)

July, boreal summer

January, boreal winter



Tropics: large-scale overturning by mean meridional circulation

Extratropics: baroclinic eddies (cyclones and anticyclones with associated warm and cold fronts) and stationary waves

General circulation: Extratropics


Jetstream at 10 km height

• Meandering jet• wave-like

structure at a maximum

• polar air reaches lower latitudes and tropical air is advected to higher latitudes

General circulation: Zonally asymmetric circulation


⇒Jets show clear deviations from zonal symmetry

* separation of air masses

* definition of tropics ?

General circulation: Heat and momentum transports

• Atmospheric circulation provides import contributions to meridional heat and momentum transports to compensate for latitudinal gradients between tropics and polar regions.

• Atmospheric circulation imposes momentum forcing to the ocean.


General circulation: Summary

• Meridional gradients in solar insolation are the main driver for atmospheric circulation.

• Hadley, Ferrel and polar cells (zonal mean meridional structure)

• Important contribution to the structure of the atmosphere: Coriolis force (large-scale, trop. storms)

• Important role of the Earth's rotation and the land sea contrasts


Why modelling?

⇒ Provide hypotheses on how mechanisms in the climate system are operating

⇒ better understand large-scale relationships in the atmosphere (e.g. teleconnections ) and its interaction with other climate subsystems (ocean, land, ice sheets...)

⇒ better understand the different time and space scales , how they are interacting and superposedas shown by observations

Atmospheric modelling - Motivation

Time and spatial scales of the African monsoon

(AMMA)

Atmospheric modelling - Motivation

Hierarchy of models -From simple to comprehensive models

• Energy Balance Models

• Earth System Models of Intermediate Complexity (quasi-geostrophic approach, no humidity,...)

• Atmospheric General Circulation Model (full dynamics and physical processes represented)

• Coupled Atmosphere-Ocean Circulation Models

Atmospheric modelling - Complexity of models

From simple to comprehensive models

• Include all fundamental processes

• Resolve all spatial dimensions

(Ruddiman, 2001)


From simple to comprehensive

models:

Processesincluded in

ECHAM3 model

(DKRZ Report, 1993)


Which processes are taken into account? Example: Radiation


(UW Atmospheric Sciences)

Which processes are taken into account? Example: cloud feedbacks

Cloud-Albedo Feedback Cloud-Greenhouse Feedback

+–

(http://www.worc.ac.uk/LTMain/Rowland/mec/climate/Feedback/Cloud.html)

What are atmospheric models based on? - Primitive equations

• Conservation of energy (1st law of thermodynamics)– temperature

• Conservation of momentum– horizontal velocity (wind, circulation)

• Conservation of mass (continuity equation)– vertical velocity

• Equation of state– ideal gas law


Complex atmosphere models

• global general circulation model of the atmosphere

• based on the ECMWF model for medium-range weather forecast → modifications and improvements for applications in climate research

• prognostic variables: vorticity, divergence, temperature, logarithm of air pressure, specific humidity, mixing ratio of total water content in clouds

• 19 levels

• horizontal resolutions T21, T31,T42, T63, T106, T159,..

Example: The ECHAM model (MPI for Meteorology in Hamburg)


(McGuffie and Henderson-Sellers,1997)

Vertical coordinate system

(Hartmann, 1994)

• Assumption of hydrostatic balance (i.e., ∆p = -ρg∆z) � height (z) expressed in terms of pressure (p)

• Pressure normalized to surface pressure (σ;terrain-following)

• Troposphere and lower stratosphere (<20 km) usually represented

Atmospheric modelling - Spectral method and resoluti on

Spectral method

• Global atmospheric fields can be represented in terms of spherical basis functions

• Similar to the use of trigonometric functions such as sines or cosines

See Washington and Parkinson (1986), Chapter 4, pp. 18.


Spectral method and model resolution● X : divergence, temperature, vorticity,...:

represented in the model by a truncated series of spherical harmonicsm = zonal wave numbern = meridional index

● in ECHAM5 only triangular truncation can be done (implied by the parallelization of the model's spectral part)

● truncation done at a certain wave number(typically T21, 31, 42, 63, 85, 106, 159,...)


Spectral representationADVANTAGES• Easy and exact spatial differentiation• Natural description of planetary waves in unbounded d omain• Homogenous resolution on a sphere

DISADVANTAGES

• Transformations become computationally inefficient at high resolution

• For any truncated basis function expansion, there is overshooting and undershooting (Gibbs phenomenon )

• Gibbs phenomenon occurs near steep gradients

– yields negative values of mass and humidity

– makes representation of mountain ranges or ice sheets difficult


Fourier theorem

• The actual shape of a vibrating string can always be represented as an infinite series of eigenvector basis functions:

2sin .n

n x

l l

πΨ =

( )!

( ) ,nn

f x x∞

=

= Ψ∑where


Spectral representation:

Gibbs phenomenon

Example of the Gibbs phenomenon (overshooting and undershooting) for a step function

(Figure 4.6 from Washington and Parkinson,1986)

( ) 4 1 1sin sin 3 sin 5

3 5f x x x x

π = + + +

K


Land sea masks for the ECHAM model


~ 600 km

~ 200 km ~ 120 km

~ 300 km

T31 simulations about 25 times faster than T106

Horizontal model resolution

ECHAM4 model topography over Europe [m]

T42 T106


(Merkel, 2003)

Model resolution• Grid representation leads to the fact that

some sub-grid scale processes cannot be fully simulatedin their overall complexity=> transfer of radiation=> phase changes of water vapour=> turbulent transports

• Parameterizations (based on theoretical and observational considerations) take into account the impact of these processes onto model variables (via simplified functions of fully resolved model variables).


Role of model resolution: Stormtrack activity

T42 control simulation [gpm]

T106 control simulation [gpm]

Root-mean-square (RMS)of bandpass-filtered(2.5-6 d) 500 hPageopotential height data

⇒ Role ofhorizontal resolution

(Merkel, 2003)

Role of vertical model resolution Normalized RMS errors relative to T21 error

(Ratio of RMS error of Txx to RMS error of T21)

(Roeckner et al., 2006)

ERA40 w.r.t.ERA15

19 vertical levels 31 vertical levels


Computational scheme of a

spectral AGCM

(McGuffie and Henderson-Sellers, 2005)

Vertical exchange in grid space

Each surface fieldheld in grid space

Each atmospheric field held and moved

in spectral space (“wave functions”)

Transformation to grid space samples field around zones of latitude and longitude

Spectral truncation restricts information

Surface fields are computed in grid

space

(McGuffie and Henderson-Sellers,1997)

Initialization

• climatological values• previous model runs (restart run)

• Spin-up: How long does it take for the atmosphere model to reach equilibrium? Typical climatological model runs with AGCM have a length of ~ 30-50 years- analysis of the last decades only

Atmospheric modelling - Running the model

Boundary conditions and forcings for an AGCM

Atmospheregeneral circulation

model

Source: M

ontana State U

niv.

Continental ice sheets and albedo

Orbital parameters

Source: S

cott Rutherford

N2O

CH4

CO2

Greenhouse gas concentrations

Sou

rce:

SO

ES

T, H

awai

i

Sea level changes

SST, Sea ice

Aerosols

Coupling to models ofocean and/orvegetation and/orsea ice....

Computing requirements

(TerraFlops, 2002)


Output of an AGCM• 2-d or 3-d distributions of state (“prognostic”) variables:

– temperature– vorticity– divergence – ....

• Many diagnostic variables, e.g.:– vertical velocity– clouds – SW radiation at top of atmosphere– LW radiation– snow depth– ...


Output of an AGCM

CCSM2 (~3.7°, 26 L)

(M. Prange)

Annual mean precipitation [cm/yr]


Model performance -How good are the models?

Model results have to be compared to observationsand paleo data

⇒ evaluate the model performance in reproducing

- mean climate- climate variability

Atmospheric modelling - Model performance

Model performance -Output of an AGCM as part of a CGCM

CCSM2 (~3.7°, 26 L) Modern obs.

(M. Prange)

Annual mean precipitation [cm/yr]


Model performance -Surface air temperature [K]

(IPCC TAR, ch. 8)


Model performance -Precipitation [mm/day]

(IPCC TAR, ch. 8)


(IPCC TAR, ch. 8)


Model performance -Precipitation [mm/day]

Model performance -Temperature of troposphere and

stratosphere [K]

(IPCC TAR, ch. 8)


Model performance -Temperature of stratosphere [K]

(IPCC TAR, ch. 8)


Model performance - Sea ice

(IPCC TAR, ch. 8)


North. hemisphere DJF extent South. hemisphere JJA extent

Model performance -Tropics vs. extratropics

(Bengtsson et al., 1996)


Eastern tropical Pacific precipitation DJF (1979-1992)

individ. experiments

observations

Model performance -Tropics vs. extratropics

(Bengtsson et al., 1996)


Western Canada surface temperature DJF (1979-1992)

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