# ESE/Ge 148C Problem Set #3 (Tentative) ESE/Ge 148c Problem Set #3 – Due June 2, 2006

1) Robin Hood Plots.

Estimate the net flux of CO2 into (or out of) the biosphere and ocean using the two double deconvolution methods we discussed in class: carbon isotopic fluxes, and CO2 vs O2 fluxes. You will find the following data helpful.

Mass of CO2 in the atmosphere = 800 Pg

Observed rate of change of atmospheric CO2 = 3 Pg/yr

Observed 13C of atmospheric CO2 = -7.8 ‰

Observed rate of change of 13C of atmospheric CO2 = -0.02 ‰/yr

CO2 flux from fossil fuel burning = 6 Pg/yr

13C of CO2 emitted from fossil fuel burning = -28 ‰

Fractionation between atmospheric CO2 and biomass = -19 ‰

Fractionation between atmospheric CO2 and ocean DIC = -1.8 ‰

Gross CO2 flux from biosphere to atmosphere = 125 Pg/yr

Isotopic disequilibrium between atmosphere and biosphere = 0.33 ‰

Gross CO2 flux from oceans to atmosphere = 90 Pg/yr

Isotopic disequilibrium between atmosphere and oceans = 0.6 ‰

Observed rate of change of O2 in the atmosphere = -5 Pg/yr

2) Fun with Photosynthesis.

(a) The flux of CO2 into a leaf, and flux of H2O out of a leaf, areboth controlled by diffusion. Applying Fick’s First Law to the process of evaporation in a leaf, one finds the relationship

F = g(ca – ci)

where F is the diffusive flux of water out of the leaf, g is the stomatal conductance (a term that incorporates both the diffusivity constant and the cross-sectional area of the stomata), and (ca – ci) is the CO2 gradient between the atmosphere and the inside of the leaf in units of mole fractions. The same equation can be used to calculate the flux of carbon dioxide into the leaf, but g must be divided by a factor of 1.6 to account for the greater diffusivity of water vapor (because of its smaller size). If the average value of g for plants had remained constant over the past ~200 years, how much would water loss have changed between leaves in a pre-industrial and a modern atmosphere? How much would the carbon dioxide flux have changed? What does this imply about the change in growth rates of plants over this time interval? Now suppose that growth rate has remained the same in both pre-industrial and modern environments (possibly because of other limitations on growth like nutrient availability). How much has stomatal conductance (g) changed over this period? How much has water-loss changed?

(b) The Water Use Efficiency (WUE) of plants is defined as the ratio of the rate of photosynthesis (A) to the rate of transpiration (E). Derive an equation relating relative humidity (RH) and the isotopic discrimination of plants () to WUE (assume that the water vapor pressure of the intercellular space of a plant is 100%).

(c) Anomalies in the rate of change of 13C of atmospheric CO2 have been observed at several monitoring stations across the globe. One proposed explanation is that changes in global precipitation caused by El Nino events change the relative strength of the ocean and biosphere fluxes. Calculate the ocean and biosphere fluxes using the double deconvolution method for the years 1987-1988 which saw a change in13C of atmospheric CO2 of -0.1‰/yr. Describe qualitatively how your answer would change if you included changes in the relative distribution of C3 and C4 plants caused by increased drought stress during El Nino years (using some average values for the isotopic composition of C3 and C4 plants).