Simulation of the Last Glacial Maximum using a two-

dimensional energy balance model

Modeling Past and Future Climate ChangesA. Paul and M. Schulz

Reading

• 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

outgoing longwave radiation

incoming solar radiation

removal of energy by horizontal transport in the atmosphere and ocean

=

-

-

Parameterizations

• 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.

Discretization

• The horizontal resolution x y is

10°10°

– 3618 grid cells

• The time step t 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

concentration

– co2ccn=180, ice_yr=-21000.0

• Go to the website:

http://www.palmod.uni-bremen.de/~apa

u/models/ebm_2d/

• Downlowd the zip-file ebm_2d_1.1.zip (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 ebm.in

• 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

averaged).

• 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.

E1/E3

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.

E2/E4

Exercise

• 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 hemispheres?

Experimental procedure

• To run the model, first double-click on start_cygwin

• To check and change the model parameters, type notepad ebm.in & on the cygwin commandline and press <enter>.– For your first experiment “E1”, set ice_yr to 0.0 and co2ccn to 280.0.

• 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 snapshot_ebm.nc to

snapshot_ebm_E1.nc

• 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 ebm.in accordingly

– For example, change ice_yr from 0.0 to -21000.0

Sample MATLAB session

• Start MATLAB.

• Point “Current Directory” to output (the full path name is probably: C:\Documents and Settings\geo\My Documents\ebm_2d_1.1\output)

• 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: plot_data.

– 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

lfrac land fraction of a grid cell

aicel land-ice fraction of a grid cell

slat sea-level air temperature

ta_attime-averaged sea-level air

temperature

apln planetary albedo

netswpln net shortwave planetary radiation

netlwpln net longwave planetary radiation

tmax annual maximum temperature

• To plot the temperature difference

between two experiments, inspect the M-

file script: plot_diff.m

• To compute the area-weighted global

mean of a latitude-longitude field like

ta_at, use

global_mean(xt,yt,ta_at)

Sample ferret session

• Double_click start_ferret in output folder

• Type ferret and press <enter>

• Type use snapshot_ebm (and press <enter>)

• To shade sea-level air temperature: type shade ta_at

• To compute global-mean temperature: type list ta_at[x=@ave,y=@ave]

Sym-

bol

Fortran name Description Unit

runlen length of run years

t dt time step days

h ice_yr ice-sheet forcing

year (-/+ = BC/AD)

yr

tinit initial temperature °Cice_albedo_feedback flag for ice-albedo

feedback

Input parameters in file “ebm.in”:

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.