(a) From 1980 to 2010, atmospheric CO2 concentrations rose from 340 ppm to 390 ppm. Assuming a fixed Henry’s law constant for CO2 for the temperature in the North Atlantic of kH = 0.050 mol · kg−1 · bar−1 , calculate the increase in dissolved CO2 in the surface layer of North Atlantic water due only to the change in atmospheric concentrations. [2 marks] (b) Calculate the change in pH given the enhancement of dissolved CO2 calculated in part (a). Recall that dissolved CO2 will be in equilibrium with bicarbonate and carbonate according to the reactions: CO2(aq) + H2O ←−→ H
+ HCO3 − (1) HCO3 − ←−→ H
+ CO3 2−, (2) where the equilibrium constants for these reactions are K1 = 9.1 × 10−7 mol · kg−1 and K2 = 5.2 × 10−10 mol · kg−1 respectively. Assume that the carbonate concentration in the ocean, which is buffered by other reactions, remains constant over this time period, at [CO3 2−] = 2.4 × 10−4 mol · kg−1 . [2 marks]
(a) Assume an initial input of carbon dioxide to the atmosphere E. The temperature response without including any carbon cycle feedbacks is ∆CA = E (3) ∆T = α∆CA, (4) where CA denotes atmospheric concentration of CO2 and α is a constant proportional to the climate sensitivity. Let us examine the temperature response ∆T considering only β feedbacks in the carbon system (i.e. carbon cycle responses to increased CA only). In this case, ∆CA depends on additional carbon fluxes to the ocean (FAO) and land (FAL) caused by the initial atmospheric carbon perturbation. ∆CA = E − FAO − FAL (5) FAO = βO∆CA (6) FAL = βL∆CA, (7) where subscripts A, O, and L denote atmosphere, ocean, and land, respectively. Compare the temperature response with and without β feedbacks. [2 marks] (b) Now let us examine the temperature response considering the coupled β and γ feedbacks (i.e. carbon cycle responses to ∆CA and ∆T together). Here, the ocean and land fluxes are further dependent on changes in temperature. FAO = βO∆CA + γO∆T (8) FAL = βL∆CA + γL∆T. (9) 1 Compare the temperature response in the coupled system (with both β and γ feedbacks) to the temperature response with only carbon (β) feedbacks. [2 marks] (c) To which parameter (α, βX, γX) is the ratio of the temperature response in the coupled system (with β and γ feedbacks) to the temperature response in the uncoupled system (with β feedbacks only) most sensitive? Typical values of the parameters are α = 0.0060 K · ppm−1 , βX = 1.2 GtC · ppm−1 , and γX = −3 GtC · K−1 . Show your work. What does this tell you about carbon cycle feedbacks? [2 marks]