Math 5421 Spring 2025
Introduction to Climate Models
Assignment 11
due April 8, 2025
Planetary Heat Storage
Exercise 1
Asuming an energy imbalance of 1.2 W/m2, how long would it take to raise the temperature of the entire ocean by 5°C? (Assume that the average ocean depth is 4300 meters.) How long would it take to melt enough ice to raise the ocean depth by 70 meters?
Exercise 2
By some estimates, it took 20,000 years to raise the temperature of the entire ocean 5°C during the PETM (Paleoeocene-Eocene Thermal Maximum, occuring about 56 million years ago). What energy imbalance would account for that rise. Assume all other temperatures were unchanged and that the ocean depth was 4400 meters.
Exercise 3
What energy imbalance would be required to melt enough ice to raise the ocean depth by 70 meters in 1000 years, assuming all atmosphere, land, and ocean temperatures remained constant? What energy imbalance would accomplish the same rise in 100 years?
Exercise 4
Assume that, over the course of 100,000 years, the air temperature fell by 5°C, as did the top kilometer of the ocean, and ice sheets formed to lower the sea level by 125 meters. What average energy imbalance would be required?
Exercise 5
(The Day After Tomorrow scenario) Assume that, over the course of 6 weeks, the air temperature dropped by 13°C, as did the top 100 meters of the ocean, and enough snow accumulated on land to lower the sea level by 2 meters. What energy imbalance would be required? Compare your number to the current insolation and compute the heat imbalance necessary for the scenario.