ESE 148c Problem Set #1 - Due April 12 (in class or to Ashley by 5 PM)
1) Isotopic Constraints on the Geologic Carbon Cycle.
a) Typical average modern values of C for organic carbon and marine carbonates are
-25‰ and -1‰ respectively. It has also been estimated that 30% of the carbon buried in
sediments is in organic form. What is the average isotopic composition of carbon entering
the surface carbon cycle through volcanic degassing?
b) Marine sediments record an event about 55 Ma termed the Late Paleocene Thermal
Maximum. This event is characterized by rapid warming on a global scale, but the trigger
mechanism of such anomalous rapid warming remains unknown. Carbonates from this
same time period have anomalous 13C values as high as +2‰. Assuming no other
changes in the carbon cycle (ie – Paleocene values for i and o are the same as modern),
what fraction of organic carbon burial do you predict for the Late Paleocene? Now
assume that Paleocene values for i and p (the fractionation between a and o) were the
same as today and redo the calculation. Which set of assumptions seems more
reasonable?
c) You should have just shown that the fraction of carbon buried as organic carbon is
related to a change in global mean temperature. Propose a mechanism to explain this
hypothesized link.
2) Carbonate Equilibrium. Carbonate equilibrium is one of the most important chemical
concepts in studying natural systems, because essentially all natural waters (and
especially the oceans) are buffered by the carbonate system. You will find the following
values for the carbonate equilibrium constants (in seawater) helpful.
Temperature (ºC) pK1
pK2
2
6.10
9.39
15
5.95
9.10
Concentrations are mol/kg and Kw has units of mol/kg atm
pKH
1.42
a) The global ocean has an average pH of 8.1 and an average temperature of 2ºC. The
average bicarbonate (HCO3-) concentration is 2000 mol/kg. Considering all dissolved
forms, what mass of inorganic carbon is stored in the oceans (the ocean has a mass of 1.4
x 1021 kg)? The pre-industrial atmosphere had an average CO2 concentration of 280 ppm.
The mass of the atmosphere is 5.3 x 1018 kg. What mass of carbon is stored in the
atmosphere? Which carbon reservoir is bigger?
b) Consider the pre-industrial atmosphere to be in equilibrium with the surface ocean
which has an average temperature of 15ºC and an average HCO3- concentration of 1600
mol/kg. What is the pH of the pre-industrial surface ocean? What is the pH of the
modern surface ocean in equilibrium with today’s atmosphere which has 380 ppm CO2?
What about a potential future ocean in equilibrium with an atmosphere with 500 ppm
CO2?
c) The concentration of carbonate ion (CO32-) is a critical environmental parameter for
many marine organisms that build skeletons of calcium carbonate (for example corals).
How much does the carbonate concentration decrease from the pre-industrial 280ppm to
the near-future 500ppm atmospheric CO2 values?
3) Studying the Hydrologic Cycle through Isotopes.
The small Mexican community of Popocatepetyl relies on a nearby lake for fishing. A
large manufacturing facility that is being planned has proposed to drill a deep well in the
town to extract groundwater for industrial uses. The locals are worried that this will
ultimately divert groundwater from their lake and threaten that resource. The critical
question is the relative contributions of precipitation versus groundwater in supplying
water to the lake. The manufacturer has claimed that it will cost millions of pesos for a
detailed hydrologic study to answer this question, and shouldn’t be necessary. The
townsfolk have asked you to give them some advice based on your knowledge of stable
isotopes. Answer the question quantitatively using the following data: The water in the
lake is completely replenished each year by precipitation and groundwater recharge. The
D of the lake water has a yearly average value of -70‰. Precipitation in the region is
supplied by a nearly constant weather pattern that picks up water vapor over the Pacific
Ocean (mean annual temperature of 14.5ºC) and carries it eastward. As these clouds pass
over the town, 25% of the vapor condenses into liquid water at a temperature of 10ºC and
falls on the lake as precipitation. As the clouds continue to move over the nearby
mountains, 95% of the remaining vapor condenses out as snow at a temperature of -10ºC.
This snow ultimately melts and provides the source of water to recharge regional
groundwater. (Note that l-v is temperature dependent. At 15ºC it is 1.08, at 10ºC it is
1.095, and at -10ºC it is 1.155).
4) Oxygen in the Deep Ocean.
a) The oxygen concentration of the deep ocean is initially set by equilibrium gas
exchange occurring at high latitudes (recall that this is where deep water is formed). At
equilibrium, the high latitude surface ocean holds about 350 mol O2/kg seawater.
Oxygen is then consumed through deep heterotrophic consumption of organic matter
raining from the surface (this flux is roughly 0.6 mol C/m2 yr). Assume that deep
heterotrophs utilize 90% of the organic matter raining into the deep ocean (the remaining
10% gets buried in sediments). What would you predict is the concentration of oxygen in
the deep Atlantic Ocean? In the deep Pacific Ocean?
b)_In the year 2020, the sudden collapse of the Greenland ice sheet introduces enough
meltwater to the North Atlantic to completely stop thermohaline circulation. Assuming
that surface primary production continues as today, how long would it take for the deep
Atlantic to become anoxic? (You can assume that respiration continues at the same rate
despite decreasing oxygen concentrations)