Homework #6 Glaciology, GEOL 4888,  Spring 2022 Humphrey

1. This homework is mainly to force you to make some progress on your term paper. For this question, you need to answer a series of questions about your topic;

· What is your title? (not just the subject area, but what would be a good title of your paper)

· Why is your subject important or interesting in terms of the cryosphere?

· What is the main focus of your paper? No matter how tiny or big your subject area, you will have to define limits. What are they?

· Is your paper a literature review? Or are you going to synthesize outside information with information from this course? Or are you taking a completely different approach? What approach are you taking?

· What are your information sources?

2. We are talking in class about all sorts of time scales for glacial behavior. One of the most fundamental scales is based on heat conduction. It calculates how quickly the temperature of ice can respond to climate change or other forcings, due to heat conduction through the ice. A very useful scale (it can be used as a rough guide in a host of thermal situations) is the exponential decay equation given below. It is used to estimate the temperature change at some point inside the ice away from the ice surface, as a function of time since the temperature at the surface changed. We will also use it when we talk about permafrost.

This expression gives a dimensionless number between 1 and 0. You interpret this as the fraction of temperature change that has yet to happen at that point. (a 1 means nothing has happened, while 0 means the ice has responded completely to the temperature change)

K – thermal conductivity of ice (remember to use consistent units) ~6.6x10⁷ J/(m yr C)

t – time since temperature changed at the surface. (use years since K is in yrs)

r (should be rho ice) – density of ice (or whatever material)

C – heat capacity of ice, per kilogram. For ice and snow this is approximately a constant. ~ 2090 J / (kg C)

L – thickness of ice for the heat to flow through, or distance from surface to point of interest

a. Using this, calculate the approximate time it takes for a climate change signal to reach the bed of an ice-sheet that is 3000m deep. To be more specific; the time for the ice to respond by about 80-90% of the surface change. (hint, it should be many thousands of years)

b. (harder) Try using this to calculate the approximate depth in the firn (density about 600kg/m^3) at which the yearly temperature signal mostly dies away, only a few percent of change left. (hint, it should be a few tens of meters)