# bT=R - UW Program on Climate Change

```Simple climate model lab
Worksheet
Part I: Equilibrium temperature:
Equation (1) tells us that in steady state (no variations in temperature) and in
the absence of weather forcing, the temperature can be found by
= − +
or
bT=R
and then an extra heat is applied a constant rate and the temperature reaches a
new value, then
T=R/b
This is the case when the heat balances the radiative cooling.
If  is 2, calculate the equilibrium temperature change for R=3, R=4.5, R=6,
and R=8.5. This is how much the planet would warm if we bring the radiative
forcing up to the above values, and then leave it at that value for 1000 years or
so.
The values are given by the following table
3 Watts m-2
4.5 Watts m-2
6 Watts m-2
8 Watts m-2
Equilibrium Temperature change
1.5oC
2.25 oC
3 oC
4 oC
Part I: Forcing of the climate system.
1. Go to see sheet 1 and set the weather amplitude to 0.
1. Plot the different components of forcing as a function of year (Column D,
E, F) and the Total forcing (Column G). What year does manmade
forcing surpass the natural forcing (solar + volcano). The students
should note that the manmade forcing starts to dominate around 1920.
Simple climate model lab
2.500
2.000
1.500
1.000
Volcano
0.500
0.000
1850
-0.500
Solar
1900
1950
2000
2050
-1.000
-1.500
-2.000
Plot the total forcing
+weather)
2.500
2.000
1.500
1.000
Total =
volcano +weather)
0.500
0.000
1850
-0.500
1900
1950
2000
2050
-1.000
-1.500
2. Make a plot of the carbon dioxide concentration as a function of time
(note change the axis to start at 280 ppm). Comment on the relationship
between the manmade forcing and the carbon dioxide concentration.
The students should say that the curves look very similar.
Simple climate model lab
Carbon dioxide concentration (ppm)
4.00E+02
3.80E+02
3.60E+02
3.40E+02
Carbon dioxide
concentration (ppm)
3.20E+02
3.00E+02
2.80E+02
1850
1900
1950
2000
2050
3. Now go to the other sheets RCP3, RCP45, RCP6 and RCP85 and make a
plot of the total forcing on the same graph. What are the values at 2100?
What are the wiggles in each of the lines?
9.000
8.000
7.000
6.000
5.000
4.000
3.000
2.000
1.000
0.000
2000
2020
2040
2060
2080
2100
2120
The students can note that the RCP name is related to the radiative
forcing at the end of the century.
Simple climate model lab
The wiggles are the 11 year solar cycle that we assume continues
without change into the 21st century.
Part II: Controls of surface temperature
1. The first thing to explore is how the ocean controls temperature changes
on the earth.
Before we begin, determine much energy it would take to warm up the
atmosphere by 1°C.
To do this calculation you need
The mass of the atmosphere per square meter: Ma=10,000 kg/m2
Specific heat of air cp air = 1006 Joules/kg/K
Energy needed E= Ma X cp air X 1K
E=10,000,006 Joules/m2
Next, determine the depth of the ocean that could be heated 1K using the
amount of energy that you calculated above
The density of sea water is ρ=1025 kg/m3
The specific heat of sea water is cp ocean= 3985 Joules/kg/K
10,000,006=ρ X cp ocean X H X 1K
where H is the thickness of ocean
Joules/m2= kg/m3 X Joules/kg/K X m X K
Joules/m2= Joules/m2
Solve for H to get
H=10,000,006/(ρ X cp oceanX 1)=2.5 m (!)
2. Go to sheet 1 (1880-2006). Set the weather forcing to 0 and the
sensitivity parameter to 2 and the depth of the ocean to 300 m. Save the
Simple climate model lab
results in column H in another workbook or sheet (use paste special to
paste the values without the formula)
Change the sensitivity parameter to 0.5 and save the results in column H
Change the sensitivity parameter to 4.0 and save the results in column H
Plot the three temperatures on the same plot.
How does the surface temperature in 2005 depend on the sensitivity
parameter?
1.800
1.600
1.400
1.200
1.000
Climate sensitivity 2
0.800
Climate sensitivity 0.5
0.600
Climate sensitivity 4
0.400
0.200
0.000
1850
-0.200
1900
1950
2000
2050
The students should see that the temperature at the end of the century is
be proportional to the inverse of the climate sensitivity parameter as we
also found in the equilibrium solution
1. Set the sensitivity parameter to 2, and change the depth of the upper
ocean to 1000 m, and record the surface temperature in 2005. Do the
same for depth of the upper ocean to 50m and record the surface
temperature.
How does the surface temperature depend on the depth of the ocean?
Simple climate model lab
1.2
1
0.8
0.6
Depth 300 m
0.4
Depth 50 m
Depth 1000 m
0.2
0
1860
-0.2
1880
1900
1920
1940
1960
1980
2000
2020
-0.4
There are two things to notice, the temperature at the end of the century is
larger for shallower oceans, and second that the shallower ocean adjusts more
quickly to changes in forcing and tracks the forcing curve more closely.
Part III: Simulation of 20th century temperature, natural vs. anthropogenic
forcing
3. Set the sensitivity parameter to 2, the depth of the upper ocean to 300
and the weather forcing to zero. Plot the observed surface temperature
(column K) and the temperature from natural (column I) and total
forcing (column H) on the same graph. Which curve compares better
with the observed temperature. What is missing? The students should
note that there is interannual variability (or wigglyness) in the observed
temperature. That is missing from the modeled temperature records.
Simple climate model lab
1.000
0.800
Temperature from
+weather
0.600
Temperature from solar
+volcano +weather
0.400
Observed Temperature
0.200
0.000
1850
1900
1950
2000
2050
-0.200
4. Now add weather forcing. Change the weather forcing parameter to 2.
Do the curves look more similar? How?
5. Now add weather forcing. Change the weather forcing parameter to 2.
Do the curves look more similar? How?
Simple climate model lab
Part IV: Predicting the surface temperature for the next 300 years.
The predicted radiative forcing is given by the amount of anthropogenic
greenhouse gases in the atmosphere and how the atmosphere radiates and
absorbes that radiation, how cloud react to warming and other feedbacks in the
climate system. We are taking the radiative forcing from the web site
http://www.pik-potsdam.de/~mmalte/rcps/.
representation of the 20th century as you can. Use the 300 for the depth
of the upper ocean. Plot your best simulation for globally averaged
temperature for total forcing and for natural forcing only. Compare
against the plot found at
http://www.climatechange2013.org/images/figures/WGI_AR5_FigFAQ1
0.1-1.jpg
(note: figure caption in WG1AR5_Chapter10.pdf)
I used b=1.8 and weather =2.1
Also, the students can note that every time a new run is done, the random
forcing changes.
2. Using the weather parameter and the sensitivity parameter that you chose
for the 20th century, predict the temperature for the next 100 years. Plot
your predictions for each of the “scenarios” in sheets 2-5. Compare
against the 2007 projections at 2100
http://www.climatechange2013.org/images/figures/WGI_AR5_FigTS15.jpg
Simple climate model lab
(note: figure caption in WG1AR5_TS_FINAL 57.pdf)
4
3.5
3
Temperature from
RCP3
2.5
2
Temperature from
RCP45
1.5
Temperature from
RCP6
Temperature from
RCP8
1
0.5
0
2000
2050
2100
2150
3. Next determine how close to equilibrium the climate system is.
Set the weather noise to 0 and use the value for b that you chose for 1
above. Record the temperature for each of the cases listed in the Table
below then answer the following questions:
How far out of equilibrium (in degrees C) is the climate system out of
equilibrium in 2005? How far will it be out of equilibrium in 2100?
The students can note that the more rapidly we introduce carbon dioxide
into the atmosphere, the more out of equilibrium the climate system is.
Simple climate model lab
Value of b
1.8
Date
Transient total
forcing
Equilibrium total
forcing
RCP3 Transient
RCP3
Equilibrium
RCP 45
Transient
RCP 6 Transient
RCP 6
Equilbrium
RCP 6 Transient
RCP 8.5
Equilibrium
RCP 8.5
Transient
Simple climate model lab
Temperature
2005
forcing
Parameter
1.994
2005
1.994
1.11
2100
2100
2.6
2.6
1.473
1.44
2100
4.281
2.033
2100
2100
4.281
5.552
2.378
2.424
2100
2100
5.552
8.34
3.084
3.497
2100
8.34
4.633
0.737
```

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