In addition to the important academic / scientific details and answers I wish to give these orientations from observations in various countries: 1) Organic matter OM, leading to stable humus-compounds / complexes should be appreciated and promoted to whatever level, provided that there is no N-blockage developping; 2) The very diverse advantages of OM are well established and should never be neglected. 3) The most dramatic agro-ecological catastrophes in many countries were mostly related to loss of OM due to poor agronomical practices; 4) A major benefit of OM in agricultural and land-use-planning-contexts is its capacity to buffer the soil against almost all human mistakes in land-use.  5) All farmers and researchers have ample opportunities to increase gradually the OM-content in soils as a matter of allmost costfree routine. 6) All countries / regions (USA, Europe) with a strong Agro-Chem-Mech-Tech-GMO-Lobby are invited to look carefully into the matter.

As you indicated the amount of crop residue inputs that are needed to maintain soil organic matter is variable depending on the climate and management. I think climate has more weight.  In cool western Canada for instance Shrestha et al (2013) found that the C inputs required to maintain SOC range from about 1 to 2.5 Mg C/ha/year, across tilled and no-till systems with greater C inputs required in wetter periods:

Shrestha et al. 2013. Effects of crop rotation, crop type and tillage on soil organic carbon in a semiarid climate. Can. J. Soil Sci. 93, 137-146. DOI:10.4141/cjss2012-078

The amount of C inputs required to maintain SOC in more humid and warmer areas would generally be considerably higher.

As Olivier said, it's hazardous to throw a number of Mg/ha/year. In Southwetern of Morocco which has a sandy soil in arid condition, I've added more than 6.2 Mg C/ha/year and still have a loss of 2.3% of TOM annually under organic greenhouse vegetables production. The annual balance of soil TOM can give you an idea about how you can add of OM or leave it as plant residues. Warmer temperature and high moisture and OM content of the soil, in addition to plant exudate and microorganisms degradation are major concern of OM mineralization and stabilization. Those factors are summarized in two coefficient: K1 (Isohumic coefficient) and K2 (coeff. of mineralization), and for those you have to go back to literature and find the values for the soil you are testing, and apply then the fomula of Hénin-Dupuis (Hénin S., Dupuis M., Essai de bilan de la matière organique du sol, Ann. Agron.11 (1945)17-29.).

Please see attached link (old paper but consistent finding)

http://link.springer.com/article/10.1007%2FBF02205588#page-1

Thanks Eric for asking this crucial and deceptively simple question.

A colleague of mine, Jane Mt. Pleasant, did an interesting study to address that question, taking a hisotrical approach that plant physiologists might miss.

The  Iroquois in New York practiced no-till agriculture continuously for centuries without depleting SOM. That practice provides an opportunity to estimate the steady-state carbon input needed to maintain SOM at ~4%. The answer, calculated from stover estimates, is 4-5 Mg/ha/year.

However, when tillage was introduced, the SOM was quickly depleted to around 2% and the OM input declined with declining yield. Today, with high-yielding field corn, farmers on the same land  maintain a steady state SOM with difficulty despite much higher OM input. It is only with reduced tillage that SOM has begun to climb. Thus, the tilled system requires a much higher SOM input.

Here is the reference, in a journal that may otherwise escape the notice of people asking your question for practical reasons.

http://www.jstor.org/stable/10.3098/ah.2011.85.4.460

Mt. Pleasant, J. 2011. Paradox of Plows and Productivity: An Agronomic Comparison of Cereal Grain Production under Iroquois Hoe Culture and European Plow Culture in the Seventeenth and Eighteenth Centuries. Agricultural History 85:460-492

Hi everybody that has added input to my question.   I appreciate the ideas and citations.  As many of you have pointed out it is quite complex.  take care, Eric

It will also depend on the current organic matter status of the intended soil.

Eric,

I have uploaded on my RG page a few graphs we used in an Extension bulletin a few years back that we used (with permission) to make the point that the amount needed varies with climate and form of crop residue.  The graphs provide a nice quantification of the effect of both climate and crop residue on change in SOM.  The graphs are available if you click on the Michigan Field Crop Ecology publication from 1998. I have added the full Extension bulletin on my list of pubs. 

The graphs are from a chapter called Carbon.  I relied heavily on an excellent chapter by Keith Paustian et al. called Management Controls on Soil Carbon that was in the book, Organic Matter in Temperate Agroecosystems (Paul et al., eds), 1997, CRC Press, Boca Raton, FL. 

The Extension bulletin is not readily available as a pdf but is available from the MSU Extension bookstore:

http://web2.msue.msu.edu/bulletins2/product/michigan-field-crop-ecology-503.cfm.