Earth-system models

Simulation of the Last Glacial
Maximum using a twodimensional energy balance
Modeling Past and Future Climate Changes
A. Paul and M. Schulz
• Hartmann, D. L., 1994: Global physical
climatology, Academic Press.
– Section 11.6: Modeling of Ice Age Climates
– Section 9.4: Ice-albedo feedback
• North, G. R., Mengel, J. G. and Short, D. A.:
Simple energy balance model resolving the
seasons and the continents: Application to the
astronomical theory of the ice ages. Journal of
Geophysical Research 88, 6576-6586, 1983.
Fundamental equation
• Basic assumption: everything about climate can
be characterized by surface temperature
• Conservation of energy in terms of
– Absorbed solar energy
– Emitted terrestrial energy
– Energy removed by horizontal energy transport
time rate of change of the energy content of an atmosphere-ocean
column of unit horizontal area
incoming solar radiation
outgoing longwave radiation
removal of energy by horizontal transport in the atmosphere and ocean
• Horizontal energy transport is assumed to
be diffusive
• Outgoing longwave radiation is assumed
to be a linear function of surface
temperature and a logarithmic function of
the atmospheric CO2 concentration.
• The horizontal resolution Dx  Dy is
– 3618 grid cells
• The time step Dt is about one day.
Numerical experiments
• Experiment E1: control experiment, present-day land
fraction, land-ice cover and CO2
• Experiment E2: glacial land-ice distribution (but still
present-day land fraction)
– co2ccn=280, ice_yr=-21000.0
• Experiment E3: glacial CO2 concentration
– co2ccn=180, ice_yr=0.0
• Experiment E4: glacial land-ice distribution and CO2
– co2ccn=180, ice_yr=-21000.0
• Go to the website:
• Downlowd the zip-file (1.8
MB) to your “My Documents” directory
• Click on right-hand mouse button to „Extract
All…“ files to a directory called: ebm_2d_1.1
• Directory structure:
– doc: contains the ppt file of the exercise
– output: contains example MATLAB M-files (adapt to
your needs)
• import_data: to import model output in netCDF format
• plot_data: to plot a specific variable from the model output
• plot_diff: to import the model output of two experiments
to plot the difference in one specific variable
• global_mean: to compute the area-weighted global mean
of a latitude-longitude field
• work:
– contains the executable program
ebm_2d.exe for Windows, as well as compile
scripts and a makefile if you want to build the
model from the sources.
– contains the parameter input file
• For all experiments, the run length runlen is
taken to be 50 years (which is roughly the
equilibrium timescale of the ocean mixed layer),
and the time step dt is set to 1 day.
• The total CPU time required for one experiment :
about 13 s (for Intel Pentium 4 1.7 GHz)
Boundary conditions
• Land fraction and land-ice fraction are
read from file.
• Surface albedo is read from file (data from
McGuffie and Henderson-Sellers, zonally
• Atmospheric CO2 concentration can be
changed through namelist.
Land fraction - fraction of 10°10° grid cell covered by land:
1.0  grid cell is completely land-covered,
0.0  grid cell is completely ocean-covered.
Present-day land-ice fraction - fraction of 10°10° grid cell covered by land ice:
1.0  grid cell is completely land ice-covered,
0.0  grid cell is completely land ice-free.
LGM land-ice fraction - fraction of 10°10° grid cell covered by land ice:
1.0  grid cell is completely land ice-covered,
0.0  grid cell is completely land ice-free.
• Carry out experiments E1 to E4, one after the other.
• Prepare a table that lists the global-mean temperature
for each experiment.
• Plot the time-averaged sea-level air temperature for
each experiment, as well as the change from one
experiment to the next.
– Describe characteristic features (maximum changes, patterns) of
the temperature anomalies.
• Key question: From your series of experiments, which
mechanism makes ice ages simultaneous in both
Experimental procedure
• To run the model, first double-click on start_cygwin
• To check and change the model parameters, type
notepad & on the cygwin commandline and
press <enter>.
– For your first experiment “E1”, set ice_yr to 0.0 and co2ccn to
• To start the model, type ebm_2d on the cygwin
command line and press <enter>.
• Upon completion of the run, the model outputs the total
number of time steps performed ittmax, the number of
time steps per year ntyear and the area-weighted
global mean temperature at the end of the experiment in
°C tgmean.
• After running the model, rename the output file.
– For example, from to
• Visualize the output using MATLAB.
– Alternatively, you could use ferret or Panoply.
• To prepare the next experiment, change the
input parameter(s) in the file accordingly
– For example, change ice_yr from 0.0 to -21000.0
Sample MATLAB session
Point “Current Directory” to output (the full path name is probably:
C:\Documents and Settings\geo\My
Take the time to inspect the M-files provided in the MATLAB editor (you can
open them using File > Open).
Initialize all MATLAB paths by typing start in the “Command Window”.
Import the model output using: import_data
– This M-file script lists the variables contained in the model output file (see table).
To plot, e.g. the time-averaged sea-level air temperature ta_at, try:
– If you want to plot a different variable, edit the M-file script plot_data.m
accordingly, or use the MATALAB Command Window.
Variables contained in model output file
land fraction of a grid cell
land-ice fraction of a grid cell
sea-level air temperature
time-averaged sea-level air
planetary albedo
net shortwave planetary radiation
net longwave planetary radiation
annual maximum temperature
• To plot the temperature difference between
two experiments, inspect the M-file script:
• To compute the area-weighted global
mean of a latitude-longitude field like
ta_at, use
Sample ferret session
• Double_click start_ferret in output folder
• Type ferret and press <enter>
• Type use snapshot_ebm (and press
• To shade sea-level air temperature: type shade
• To compute global-mean temperature: type
list ta_at[[email protected],[email protected]]
Input parameters in file “”:
Sym- Fortran name
length of run
time step
ice-sheet forcing
year (-/+ = BC/AD)
initial temperature
flag for ice-albedo
Differences to text book example
• Experiment missing with respect to Section 11.6
by Hartmann (1994): Change in snow-free
surface albedo that would correspond to the
land conditions for the last glacial age
– associated with changes in the vegetation and soil
• Furthemore, 2D EBM does not contain explicit
„50-m-deep mixed-layer ocean“, which would
allow the prediction of SST.
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