Assignment_4_iso_2023_Student (1)

Assignment 4: What was the last ice age like? Mar 2023 In this assignment, you will use the skills learned in class (Day 12 and 13), and apply them to investigate the climate of the last ice age. How cold was it? Was the temperature change the same at the equator and in polar regions? Learning objectives: - Use the Rayleigh distillation model to understand potential biases in temperature reconstruction from precipitation d 18 O. - Interpret quantitatively ice core d 18 O over the last glacial cycle. - Interpret benthic foraminifera d 18 O in terms of biological fractionation, sea water temperature and sea level. - Investigate the climate of the last ice age. Work on the questions here, and then, enter your answers in Gradescope. Note that Part 1 is moved to the end (Part 4) on Gradescope. https://www.gradescope.ca/courses/9745/assignments/42474 Part 1. Water isotopes in precipitation. (21 points) In this question, we will use the Rayleigh distillation model to investigate various factors influencing the d 18 O composition of precipitation. The equation for the saturation vapor pressure , that determines the fraction of vapor remaining is: ࠵? !"# (࠵?) = 6.1094 exp / 17.625 ࠵? 243.04 + ࠵? 6 ࠵?࠵?࠵?ℎ ࠵? ࠵?࠵? °࠵? ࠵?࠵?࠵? ࠵? ࠵?࠵? ℎ࠵?࠵? The Rayleigh distillation equation is: ࠵? = ࠵? $ ࠵? (&’() 1.1. Control situation: Take an initial temperature of 25°C, and an end temperature of -10°C. a. Calculate the saturation vapor pressure at the starting temperature: P 0 (25°C) = ___ hPa b. Calculate the isotopic ratio of the water vapor, at equilibrium with the ocean, (R l = 1) using a = 1.0115 (at 25°C) R v (25°C) = ____ c. Calculate the saturation vapor pressure at the end temperature: P 1 (-10°C) = ____ hPa d. Calculate the fraction of vapor remaining at -10°C: f = ____ If you don’t remember what this means, check the in-class worksheet of Day 12.

e. Calculate the isotopic ratio of the water vapor at -10°C, using the Rayleigh distillation equation: R v = ____ f. Calculate the isotopic ratio of the precipitation at -10°C, using the fractionation factor a : R l = ____ g. Calculate the isotopic composition of the precipitation d 18 O l1 = ____ ‰ 1.2. Colder precipitation temperature: Reproduce the steps above to find the d 18 O l of the precipitation falling at -20°C: a. P 2 (-20°C) = ____ hPa b. f = ____ c. R v = ____ d. R p =____ e. d 18 O l2 = ____ ‰ f. Calculate the difference between this answer and the control: d 18 O l (-20°C) - d 18 O l (-10°C) = ____ ‰ 1.3. Colder source temperature: Imagine now, that the origin of the vapor in the air has changed, and cooled to +15°C . Using the updated a corresponding to this temperature a = 1.013 , reproduce the steps above to find the isotopic composition of the precipitation at -10°C: a. P 0 (15°C) = ____ hPa b. R v (15°C) = ____ c. f(-10°C) = ____ d. Rl(-10°C) = ____ e. d 18 O l = ____ ‰ f. Calculate the difference between this result and the first result: d 18 O l3 - d 18 O l1 = ____ ‰ 1.4. Interpret the result: According to this calculation, which parameter is more important in controlling the d 18 O of precipitation: a) the precipitation temperature b) the source temperature