Carbon dynamics is related to temporal change of C state in a given pool or to fluxes among pools. It can be studied by measuring changes of C or it specific forms in defined pool, measuring fluxes or processes related to C transformation.
Changes among C pools can described by turnover rate and residence time. Example: if global soil organic carbon (SOC) stock is 1500 Pg and annual C soil respiration flux 60 Pg then turnover rate of SOC will be 4% per year (60/1500*100) and mean residence time 25 years (1500/60). C turnover rate and mean residence time varies in large extent across specific pool (or sub-fraction of it) and is affected by climate, soil, management etc factors.
Direct measurement of all C fluxes is complicated and thus often models are used for predicting C dynamics. There are huge number simulation models developed for predicting C behavior in soil-plant-(atmosphere) system. See exemplary list of respective soil/plant models here.