Download Atmospheric circulation and atmospheric modeling

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 modelling
Storm "Emma", March 2008
(British Weather Service, 2008)
Storm "Emma", March 2008
(British Weather Service, 2008)
Weather versus Climate
X
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
time
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).
(adapted from V. Moron, 2003)
Atmospheric modelling - General atmospheric circulation
Weather versus climate
Climate is what we expect,
weather is what we get.
Larry Riddle
Atmospheric modelling - General atmospheric circulation
Introduction to atmospheric
circulation
Averaging with respect to longitude (zonal mean)
zonal mean meridional
circulation
zonally asymmetric
circulation
stationary waves
Averaging with respect to time
time mean
circulation
transient
circulation / eddies
λ = longitude
φ = latitude
t = time
Atmospheric modelling - General atmospheric circulation
Introduction to atmospheric
circulation
thermally
direct cells
(Univ. Wales, Bangor)
Atmospheric modelling - General atmospheric circulation
Introduction to atmospheric
circulation
pressure (hPa)
Annual mean Hadley Cells (NCEP reanalysis 1948-2001)
from the meridional stream function (1010 kg/s)
latitude
(Liu and Alexander, 2007)
ECOLMAS Course Bremen 2008 – Part 3 Atmospheric modelling
Introduction to atmospheric
circulation
Zonal Walker circulation along the equator
⇒ low-level convergence and associated upward motion (convection)
(Fig. 6.22, Hartmann, 1994)
Atmospheric modelling - General atmospheric circulation
July, boreal summer
Introduction to atmospheric
circulation
Near surface wind fields
and pressure systems Position of the ITCZ
January, boreal winter
(The Dynamic Earth, Fig. 2.18)
General circulation: Monsoons
January,
boreal winter
July,
boreal summer
(The Dynamic Earth,
Fig. 2.19)
Atmospheric modelling - General atmospheric circulation
Introduction to atmospheric
circulation
Tropics: large-scale
overturning by
mean meridional
circulation
Extratropics:
baroclinic eddies
(cyclones and
anticyclones with
associated warm
and cold fronts)
and stationary
waves
Atmospheric modelling - General atmospheric circulation
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
Atmospheric modelling - General atmospheric circulation
General circulation: Zonally
asymmetric circulation
⇒ Jets show clear
deviations from
zonal symmetry
* separation of air masses
* definition of tropics ?
Atmospheric modelling - General atmospheric circulation
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.
Atmospheric modelling - General atmospheric circulation
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
Atmospheric modelling - General atmospheric circulation
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 superposed
as 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)
Atmospheric modelling - Complexity of models
From simple to
comprehensive
models:
Processes
included in
ECHAM3 model
(DKRZ Report, 1993)
Atmospheric modelling - Complexity of models
Which processes are taken into
account? Example: Radiation
(UW Atmospheric Sciences)
Atmospheric modelling - Complexity of models
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
Atmospheric modelling - Complexity of models
Complex atmosphere models
Example: The ECHAM model (MPI for Meteorology in Hamburg)
• 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,..
Atmospheric modelling - Complexity of models
(McGuffie and
Henderson-Sellers,
1997)
Vertical coordinate system
• 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
(Hartmann, 1994)
Atmospheric modelling - Spectral method and resolution
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.
Atmospheric modelling - Spectral method and resolution
Spectral method and model resolution
●
X : divergence, temperature, vorticity,...:
represented in the model by a truncated series of
spherical harmonics
m = zonal wave number
n = 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,...)
Atmospheric modelling - Spectral method and resolution
Spectral representation
ADVANTAGES
• Easy and exact spatial differentiation
• Natural description of planetary waves in unbounded domain
• 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
Atmospheric modelling - Spectral method and resolution
Fourier theorem
• The actual shape of a vibrating string can
always be represented as an infinite series
of eigenvector basis functions:
∞
f ( x) = ∑ Ψ n ( x ) ,
n =!
where
2
nπ x
Ψn =
sin
.
l
l
Atmospheric modelling - Spectral method and resolution
Spectral
representation:
Gibbs
phenomenon
4
1
1

f ( x ) =  sin x + sin 3 x + sin 5 x + K 
3
5
π

Example of the Gibbs phenomenon (overshooting and
undershooting) for a step function
(Figure 4.6 from Washington and Parkinson,1986)
Atmospheric modelling - Spectral method and resolution
Land sea masks for the ECHAM
model
~ 600 km
~ 300 km
~ 200 km
~ 120 km
T31 simulations about 25 times faster than T106
Atmospheric modelling - Spectral method and resolution
Horizontal model resolution
ECHAM4 model topography over Europe [m]
T42
T106
(Merkel, 2003)
Atmospheric modelling - Spectral method and resolution
Model resolution
• Grid representation leads to the fact that
some sub-grid scale processes cannot be fully simulated
in 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).
Atmospheric modelling - Spectral method and resolution
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 hPa
geopotential height data
⇒ Role of
horizontal 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)
ERA40 w.r.t.
ERA15
19 vertical levels
31 vertical levels
Atmospheric modelling - Spectral method and resolution
(Roeckner et al., 2006)
Computational
scheme of a
spectral AGCM
(McGuffie and Henderson-Sellers, 2005)
Transformation to grid space samples field
around zones of latitude and longitude
Each atmospheric
field held and moved
in spectral space
(“wave functions”)
Spectral truncation
restricts information
Vertical exchange in
grid space
Each surface field
held in grid space
Surface fields are
computed in grid (McGuffie and
Henderson-Sellers,
space
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
Orbital parameters
Aerosols
Greenhouse gas
concentrations
CH4
CO2 N2O
Coupling to models of
ocean and/or
vegetation and/or
sea ice....
Source: Montana State Univ.
Sea level changes
Continental ice sheets
and albedo
SST, Sea ice
Source: SOEST, Hawaii
Source: Scott Rutherford
Atmosphere
general circulation
model
Computing requirements
(TerraFlops, 2002)
Atmospheric modelling - Running the model
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
– ...
Atmospheric modelling - Running the model
Output of an AGCM
Annual mean precipitation [cm/yr]
CCSM2 (~3.7°, 26 L)
(M. Prange)
Atmospheric modelling - Running the model
Model performance How good are the models?
Model results have to be compared to observations
and 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
Annual mean precipitation [cm/yr]
CCSM2 (~3.7°, 26 L)
Modern obs.
(M. Prange)
Atmospheric modelling - Model performance
Model performance Surface air temperature [K]
(IPCC TAR, ch. 8)
Atmospheric modelling - Model performance
Model performance Surface air temperature [K]
(IPCC TAR, ch. 8)
Atmospheric modelling - Model performance
Model performance Precipitation [mm/day]
(IPCC TAR, ch. 8)
Atmospheric modelling - Model performance
Model performance Precipitation [mm/day]
(IPCC TAR, ch. 8)
Atmospheric modelling - Model performance
Model performance Temperature of troposphere and
stratosphere [K]
(IPCC TAR, ch. 8)
Atmospheric modelling - Model performance
Model performance Temperature of stratosphere [K]
(IPCC TAR, ch. 8)
Atmospheric modelling - Model performance
Model performance - Sea ice
North. hemisphere DJF extent
South. hemisphere JJA extent
(IPCC TAR, ch. 8)
Atmospheric modelling - Model performance
Model performance Tropics vs. extratropics
Eastern tropical Pacific precipitation DJF (1979-1992)
individ. experiments
observations
(Bengtsson et al., 1996)
Atmospheric modelling - Model performance
Model performance Tropics vs. extratropics
Western Canada surface temperature DJF (1979-1992)
(Bengtsson et al., 1996)
Atmospheric modelling - Model performance