- (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]
