I am trying to calculate carbon content incorporated into soil every year through root, rhizodeposition and stubble biomass. How can I calculate these from above-ground biomass for the crops sunflower, sorghum, lentil and groundnut?
Each of these crop plants will have a relationship of their above ground biomass which will be proportional to their below ground biomass.
Ideally through experimentation this can be determined with increased precision.
Use experimentation with sample plants can be taken into phonological full cycle development with a measurement of respective above ground and below ground dry weights.
This will give a good estimation of the ratio at the different stages. Then you can use the appropriate ratio to determine with accuracy the amount underground from taking quad samples of the aboveground foliage component. While this will give an estimate we need to remember that practices of tillage and fertilization as example could alter this 'normal' ratio.
Because doing this type of root harvest in labor intensive it is much avoided yet the information can be very valuable. Root biomass is very important for crop avoidance of drought and contributes more to Carbon and Nitrogen retention as the below ground parts are greater in their resistance to rapid decay.
Paul’s answer above perfectly explains how you can derive experimental data for calculating Carbon inputs to soil from crops you mentioned. Here is an example (paper by Bolinder et al 2007 in the link below) explaining the approach. Data in this paper have been derived from several years of research (as Paul explained) and mostly applicable to agricultural crops in Canada and Northern USA.
This same approach or a very similar approach can be found in IPCC 2006 Guidelines for National Greenhouse Gas Inventories. The link for that document is also below (please see in Chapter 4, Table 11.2 in page 11.17). The data in the Table 11.2 of IPCC (2006) document is for calculating N inputs, but can be used to calculate C inputs if you can find average C concentration in these crops in your region. IPCC also has several other documents in the same site explaining C inputs in crops lands. I am sure you can find the parameters applicable to your region in these documents. I hope these are useful for your purpose.
Bolinder et al. (2007) An approach for estimating net primary productivity and annual carbon inputs to soil for common agricultural crops in Canada. Agriculture, Ecosystems & Environment. 118: Pages 29–42.