I am tracking the importance of carbon originating from forest upper reaches (C3 dominated) to downstream river sections where C4 grasses dominate the landscape. Which statistical approaches should I use and what are the expected changes in carbon signatures arising from in stream processes?
C3 and C4 plants have distinct stable isotope values (C3: around -28 delta13C and C4: around -12 delta13C) thus these can be distinguished from each other. In-stream processes may slightly increase delta13C values but the increase is small. Therefore, delta13C values are usually used to assess the source not the processing of the target pool (e.g. consumers, or in your case stream carbon).
Mixing models are a good approach to assess the change of the stable isotope signature due to change in plant source. I prefer SIAR which can deal with more than two sources, however it makes use of two or more elements. I am not sure if this approach only works with one element (eg carbon). There are simpler approaches which also work with one element but cannot mix more than two sources. See this link for an extensive introdduction (its about mammal food webs but the principles are the same everywhere):
http://www.mammalsociety.org/uploads/Phillips%202012%20-%20JM%2093(2),%20342-352.pdf
It would be good to have a look at the very interesting paper by Tom Battin's group in Vienna, Austria on this interesting question. It's a conceptual model in Nature Geoscience 2008 entitled 'Biophysical controls on organic carbon fluxes in fluvial networks'. Nature Geoscience 1: 95-100. (But watch out for the correction to the tabulated data in the 2008 papers that they published in July 2009.)
They hypothesise some downstream trends in carbon etc. Indeed, some of their carbon trend speculations link in quite well with work we have done on the basin-scale downstream trends in stream power for a number of UK upland and montane river systems. Our results were reported in the 2009 paper in Earth Surface Processes and Landforms vol 34, pp. 280–290 (it's on my Research Gate profile). We reasoned that, if microbial communities are adapted to changing stream hydraulics and associated bed stability, sediment load, carbon quality and fluxes, then stream power may be a good index of these drivers. Back in 1992 and 1995, I published papers which predicted that peak stream power can often occur in mid-basin positions, rather than in catchment headwaters or in lower reaches. The model is now (since the ESPL 2009 paper) called the CASSP (CAtchment-Scale Stream Power) model.
The ESPL 2009 paper also uses a new high spatial resolution (60m downstream spacing) approach we called the CAFES system. The CAFES system is based on welding hydrological estimates of (a) bankfull discharges to (b) channel slopes derived from DEMs, to estimate (c) stream power along complete river mainstems. This power trend could then function as one index of 'geophysical opportunity'. Power trends can relate well to river bank erosion rates too (our 1999 paper in Hydrological Processes).
P.S. The Battin et al 2008 paper also cites 50 references relevant to this question, so it's well worth getting hold of for that reason too! Here are the first 10:
1. Cauwet, G. in Biogeochemistry of Marine Dissolved Organic Matter (eds Hansell, D. A. & Carlson, C. A.) 579–602 (Academic Press, New York, 2002).
2. del Giorgio, P. A. & Williams, P. J. B. Respiration in Aquatic Ecosystems (Oxford Univ. Press, USA, 2005).
3. Cole, J. J. et al. Plumbing the global carbon cycle: Integrating inland waters into the terrestrial carbon budget. Ecosystems 10, 172–185 (2007).
4. Richey, J. E. in Encyclopedia of Hydrological Sciences Vol. 5 (ed. Anderson, M. & McDonnell, J. J.) 184 (Wiley, New Jersey, 2005).
5. Trumbore, S. E. Potential responses of soil organic carbon to global environmental change. Proc. Natl Acad. Sci. USA 94, 8284–8291 (1997).
6. Cole, J. J. & Caraco, N. F. Carbon in catchments: connecting terrestrial carbon losses with aquatic metabolism. Mar. Freshwater Res. 52, 101–110 (2001).
7. Richey, J. E., Melack, J. M., Aufdenkampe, A. K., Ballester, V. M. & Hess, L. L. Outgassing from Amazonian rivers and wetlands as a large tropical source of atmospheric CO2. Nature 416, 617–620 (2002).
8. Mayorga, E. et al. Young organic matter as a source of carbon dioxide outgassing from Amazonian rivers. Nature 436, 538–541(2005).
9. Paola, C. et al. Toward a unified science of the Earth’s surface: Opportunities for synthesis among hydrology, geomorphology, geochemistry, and ecology. Wat. Resour. Res. 42, doi:10.1029/2005WR004336 (2006).
10. Battin, T. J., Kaplan, L. A., Newbold, J. D. & Hansen, C. Contributions of microbial biofilms to ecosystem processes in stream mesocosms. Nature 426, 439–442 (2003).