Climate Model Investigation
Objectives
Use a climate model to:
 Determine the role of climate sensitivity in controlling the globally
averaged temperature of the earth’s surface
 Determine the role of the oceans in regulating the climate
 Determine the role of the natural and anthropogenic forcing in climate
change in the last century
 Determine how far the climate system is out of equilibrium
 Predict the temperature for the next several centuries
Textbook references: Chapter 15, Pages 309-315 (Kump, Earth System)
See also FAQ on climate models
http://www.realclimate.org/index.php/archives/2008/11/faq-on-climate-models/
and Box TS.7 of the IPCC
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/tssts-4-1.html
A simple climate model is contained in the excel spreadsheet that can be
downloaded from the coursesite. This climate model simulates the globally
averaged surface temperature anomaly from the long-term mean using the very
simple balance
Heat storage rate =longwave cooling + radiative forcing +weather noise
There are three parameters that you can change (see the green box on the first
sheet), the climate sensitivity, the depth of the upper ocean, and the size of the
weather (year to year) variability. The temperature is determined by the
accumulation of heat in the climate system, the sensitivity of the climate system
(related to longwave cooling), the heat capacity of the climate system, and
external forcing.
For each plot use “scatter plot” to plot the data.
rc p H
dT (t)
= -bT (t) + R(t) + W (t)
dt
Here
r is the density of sea water (1025 kg m-3),
cp is the specific heat of sea water (3985 Joules kg-1 oC-1)
H is the depth of the upper ocean where heat is absorbed ( m)
T is the temperature change from preindustrial conditions (oC)
t is time (seconds)
b is the climate sensitivity (Watts m-2 oC—1)
R is the radiative forcing from natural and anthropogenic effects (Watts m-2)
W is the year to year random weather forcing (Watts m-2)
Here you can change b the size of W and H the depth of the ocean that is
absorbing the heat.
We can write equation (1) in finite difference form
rc p H
T n+1 - T n
= -bT n + Rn+1 + W n+1
Dt
Here the n superscript is the value at time n where n goes from 1880 through
2006 in the first sheet. We can rearrange (2) to get
T n+1 = T n +
(-bT n + Rn+1 + W n+1 )
Dt
rc p H
This is the equation that is in the spread sheet.
Column definitions for each sheet
Sheet: 1880-2006
Column A: Year
Column B: Weather forcing, given by a random number times the size
parameter in the orange box
Column C: Forcing from volcanos. This forcing mostly comes from the small
particles that are released from the atmosphere during an eruption. These
particles reflect incoming sunlight, and you can see that volcanos mostly act as
a negative (cooling forcing)
Column D: Forcing from changes in incoming sunlight. This comes about
because of variations in the sun’s luminolosity, and is related to solar cycles
Column E: Manmade forcing (see below for details)
Column F: The sum of solar plus volcano plus manmade forcing
Column G: The total forcing, solar plus volcanic plus manmade plus weather
Column H: Temperature that results from the total forcing (solar plus volcanic
plus manmade plus weather) using equation (3)
Column I: Temperature from natural forcing only (solar plus volcano plus
weather) using equation (3)
Column J: Observed temperature
Column K: Carbon dioxide concentration
For Sheets RCP3, RCP45, RCP6, and RCP85
Column A: Year
Column B: Weather forcing, given by a random number times the size
parameter in the orange box
Column C: Manmade forcing plus solar variability
Column D: The total forcing, solar plus manmade plus weather
Column E: Temperature that results from the total forcing (solar plus manmade
plus weather) using equation (3)
Column F: Carbon dioxide concentration
Information about the scenarios can be found at
http://www.iiasa.ac.at/webapps/tnt/RcpDb/dsd?Action=htmlpage&page=welcome#descript
Also see the Nature paper for more details. This paper should be accessible to
the high school students.