First of all there are some practical approaches that you can look for, for example Troy Baisden working with radiocarbon (the same field where I come) found a practical way to model 14C signatures of SOM along profiles, but as far as I understood you are looking to a more mechanicistic model.

My advice about this problem can be resumed as follows:

Basically you should model you profile as a sequence of discrete layers (I use to define it cascade box model).

In theory the best approach should be modeling you profile as an infinite sequence of infinitesimal layers, but later if you have to validate such a kind of model it will be more difficult finding appropriate datasets.

Each layer can be schematised as a box (the Jenny box model) whose C content is the result of inputs minus outputs balances.

For the first layer the inputs come from the litter while for the successive they come from the upper layer outputs (but this is something that will be better specified later on in the text). Regarding the outputs they are related to the k (decomposition constant of the OM) or to its inverse (i.e. Mean Residence Time) but please note that k and, hence MRT, takes into account for both C losses typologies form each layer: i) respired CO2; ii) trasferred C to successive layers. Please remember that the amount of C reaching the successive layer is only a fraction of C lost from the upper one.

I guess with this model you should be able to quite well describe SOC concentrations along your profile, but remember that i) with this approach you are neglecting DOC vertical exports; ii) k and MRT of layers changes along your profile.

For more math details you can have a look at

Bruun, S., Six, J., Jensen, L.S., and Paustian, K., 2005. Estimating turnover of soil organic carbon fractions based on radiocarbon measurements. Radiocarbon 47 (1), 167-173.

or you can ask me.

It is in my thought publishing a review about this issue as soon as possible.

Hope this helps

Fabio

Thanks for you answer. I also believe that using rate limited decomposition equations is probably the simplest way to deal with vertical transport of organic matter. I was hesitating with a dummy equations where at each time step a fraction of SOM in layer (n) is transported to layer (n+1). But this cannot be related to any real process so I'm giving the idea up!

I think I will stick with a decomposition equation with part of the decomposition flux becoming CO2, DOC and transport flux to layer below.

Thanks for your help

How will you treat inputs from roots and mycorrhiza via turnover? They contribute organic matter directly at different depths.

This is a good question... in my brief experience belowground inputs are no so big enough to influence the expected c saturation profile... but I guessbit may depend on sites... for example looking at 14c i have always seen ageing of som implying no sigbificant amounts of bomb c pumped directly belowground...

CIAO