# 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 in13C 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).

3) You will need to download free software for analyzing the CTD (conductivity, temperature, depth) data from our cruise. You can find it at Follow the instructions on the site for downloading (note: this is for Windows. If you Mac people don’t have access to a PC, please come see me. ) Once you have the software installed, open SBEDataProcessing. Under the Run tab, open the Sea Plot module (#19). Input the CTD data files that are posted on the class webpage. Plot T (C) and O2 (ml/l) vs depth (sea water m – use the 1st setting). Include these plots in your solutions. Now you’re set to answer some questions. (Note: the instrument collects data as it is descending AND as it is ascending. Data from the descending profile are typically used.).

(a) The heat flux to the surface of the ocean (Q = 50 W/m2 for this site) is balanced by eddy diffusivity of heat across the thermocline. Model this as simple diffusion (Fick’s First Law) where you’ll need to use the density and heat capacity of seawater to make your units work out. Calculate the eddy diffusivity constant based on our temperature observations.

(b) To first order, the Santa Monica Bay is in steady state with respect to heat. The flux from solar radiation is matched by transfer of heat from the deep to the surface due to upwelling. The velocity of this upwelling, w, is defined by the equation

w = (D/Tdeep)(dT/dz)

where D is the eddy diffusivity constant, Tdeep is the temperature of water below the thermocline, and dT/dz is the temperature gradient across the thermocline. Calculate the upwelling velocity for our site.

(c) Assume that oxygen is a conservative tracer in the ocean and is mixed along with heat. What is the predicted oxygen concentration gradient (in (mL/L)/m) across the thermocline based on our data?

(d) Actually, thanks to the workings of biota, oxygen is not a conservative tracer in the ocean. Calculate the consumption of O2 due to respiration in the Santa Monica Bay by comparing the prediction you made above with the observed data.