) of approximately 0.7 over the
upper 30 cm.
Some helpful references for this problem set:
1.) Doing the Abyssal Radiocarbon Thing: Redo the abyssal radiocarbon thing using non-linear least squares fitting to the advection diffusion equations. The hydrographic data are contained in hydro.mat and the radiocarbon data are contained in c14.mat. The data names in the files are self explanatory. The reason for the two files is that the radiocarbon data is from a different cruise, and therefore at different depths. Start with the T,S profiles and compute (using regression techniques) K/w and its uncertainty. Then do the same thing for J/w and its uncertainty, and finally do the radiocarbon. Because the propagation of errors in coming to the final estimate of w, K and J are so gnarly, estimate the uncertainty in w by simple substitution of the extreme values of K/w (add/subtract uncertainties given from the non-linear least squares fit) and J/w. For your reference, this link is to a PDF version of Craig (1969) for your reading pleasure.
2.) Use the tridiagonal algorithm to solve a boundary value problem involving the distribution of 222Rn in the sediments of the Bering Sea. This problem has similarities to the CH4 profile problem of Martens and Berner that was reviewed in class (download the ch4_prof.m m-file and ch4.dat data file to see how it works and to use as an example only). We've also scanned in the 1976 version of Roache's Appendix A, which you may wish to read over while doing this problem.
When the activity of 222Rn is equal to the activity of
226Ra (its parent), it is said to be in secular equilibrium.
The sediment profiles of the southeastern Bering Sea are mostly sandy
sediment with little or no compaction and a porosity () of approximately 0.7 over the
upper 30 cm.
a). If the 226Ra concentration can be considered constant over this depth at 9.614x107 atoms cm-3 whole sediment, the sediment diffusion coefficient is also constant at 2.66x10-6 cm2 sec-1, and 222Rn concentration at the seawater-sediment interface is 283.1 atoms cm-3 whole sediment, use the diagenetic equation and the tridiagonal algorithm (tridiag.m) to produce a profile of 222Rn and 226Ra down to 30 cm. The diagenetic equation in this case would look like:
Where 
represents the
222Rn concentration in atoms cm-3 whole sediment
and 
s-1 and 
s-1. Use the above
value for the sediment diffusivity, already corrected for temperature
and tortuosity. From 210Pb profiles the burial rate has been
estimated to be 
cm
s-1. Produce a figure with the radon and radium plot together
in terms of their activity vs. depth..
b). Correctly modeled, the above diagenetic equation does not do two, interrelated, things: the depth of the deficit is not deep enough and the size of the implied radon flux is too low. The deficit in actual sediment cores is observed to extend 25 to 30 cm below the seawater-sediment interface. In steady state, the size of the radon deficit is presumed to be maintained by a balance between the flux out of the sediment and radioactive decay. Integrating the 222Rn deficit with a quadrature such as "trapz" will allow you to compare the size of the radon flux obtained in part (a) with independent estimates from actual sediment cores taken from the southeastern Bering Sea shelf, which yielded 3.5x10-3 atoms cm-2 s-1, what was the size of the deficit in part (a)? If the 210Pb profiles tell you that there could not be enough bioturbation to homogenize the upper centimeters of the core and the biologists tell you that there are large colonies of tube dwelling worms living on the shelf, can the process of bio-irrigation account for the extra 222Rn deficit? Model a radon/radium profile as above but with an additional term representing bio-irrigation in the form of:
How much bio-irrigation (VBI) is necessary to account for the above radon flux? How well does it compare to estimates from the Washington continental shelf of approximately 2 cm d-1? Why is VBI divided by porosity?