OC450 HW #4 Winter 2010 (due Friday Feb 19)
A simple model of ice sheet growth and retreat is formulated using Excel. The model
uses input of a sinusoidal oscillating temperature as the forcing function and then
calculates the ice accumulation and ablation rates for that temperature based on the
temperature dependence shown graphically in Fig 10-1 of the text and the change in Ice
Sheet Height.
The purpose of this exercise is to learn about the effects of feedbacks between forcing
and response of a reservoir. In the case of ice sheet growth, accumulation increases ice
sheet height and ablation decreases ice sheet height, however these two processes have
very different sensitivities to temperature (see Fig 10-1). If the net change in ice
(accumulation-ablation) is positive the ice grows higher, whereas if the change is
negative then the ice sheet shrinks in height.
The calculations are done using Excel and make use of an iterative approach. Using this
approach, the net change in ice sheet height (ΔHeight) is calculated over a time step
(Δtime) and then added to the previous ice sheet height. This process is repeated over
lots of time steps (iterating) in order to calculate the increase and decrease of ice sheet
height over time. The change in ice height is calculated from the following expression.
ΔHeight (m) /Δtime (yr) = Accumulation (m/yr) – Ablation (m/yr)
Thus: ΔHeight (m) = [Accumulation (m/yr) – Ablation (m/yr)] * time step (yr)
[*This iterative approach will be used for a future problem set in class in order to
calculate the effect of increasing atmospheric CO2 levels on the earth’s temperature. For
that problem I’ll expect you to be able to set up a similar iterative calculation in Excel on
your own. So, it would be wise to make sure you understand the calculation procedure
used in the current problem.]
You will calculate the change in ice sheet growth over a total time interval of 200,000
years during which the temperature is oscillating and the ice sheet height oscillates in
response to temperature changes.
For this problem set, I’d like you to learn about the sensitivity of ice sheet response to the
characteristics of the forcing. This will require performing the calculations for several
different model scenarios.
Here are some of the characteristics of the ISH model.
a. The temperature dependences of Accumulation = 0.017*Temp (ºC) +0.5 (cells F4 and
G4) and for Ablation = 0.300*Temp (ºC) +3.3, (cells F5 and G5), respectively.
b. The time step (Δtime) = 1000 years. At the starting time, the ISH = 0.
c. You select the mean temperature (cell B7) and period of the temperature oscillation
(cell B3). The temperature range of 10ºC (cell B8) is fixed for all scenarios.
d. Once you selected the oscillation period, mean temperature then calculate the changes
in Ice Sheet Height (ISH) over a time interval of 200,000 year.
Calculations
1. Determine the dependency of the maximum ice sheet height (ISH) to the period of the
temperature forcing over a range from 20000 to 100000 years at 20000 yr intervals.
(This is done by changing the value in cell “B3” in worksheet in accompanying Excel
file.). Fix the mean temperature at -10ºC. Plot ISH versus period of forcing
2. Calculate the lag (yrs) between ISH growth and forcing. Determine the dependence of
the lag on the period of the temperature forcing over a range from 20000 to 100000 years
at 20000 intervals. Fix the mean temperature at -10ºC. Plot lag versus period of forcing.
3. Determine the dependence of the maximum ISH to the mean annual temperature over a
range from 5 ºC to –20ºC at 5ºC intervals. (This is done by changing the value in cell
“B7” in worksheet in accompanying Excel file.). Fix the period at 20,000 yrs.
Plot ISH versus mean annual temperature.
Questions
1. Explain the trend you calculated for ISF versus period of forcing.
2. Explain the trend you calculated for lag versus period of forcing
3. Explain the trend you calculated for ISF versus mean annual temperature.
4. Explain why the model predicts a sawtooth (asymmetric) pattern of ice sheet growth
and retreat.
5. Explain the climatic importance of the predicted sawtooth pattern of ice sheet growth.
Give one example of a climate record discussed in class that has a similar sawtooth
shape.
6. Explain how this illustrative exercise is relevant to using climate records to test
Milankovitch’s theory.
7. Identify a process that isn’t included in this simple ice sheet model but would constrain
the maximum ISHs?
Turn in an Excel file with your initials in the title (HW#4 XX.xls) by next Friday.
Include the figures and answers to the questions in a separate worksheet in the file (or an
accompanying Word doc if you prefer).