crop simulation tools as DSSAT, INFOCROP, WOFOST, APSIM simulates the biomass and yield as related to climatic conditions and other biotic and abiotic factors.  The models take care of photosynthesis, respiration, net assimilate availability, biomass production, partitioning into various plant parts (potential growth, water and nitrogen limited growth).  MODIS,platform provides NPP directly for specified interval at regular interval, which you can reach through the platform. 

regards

You might be interested in "ecophysiological model BIOME-BGC’s‘soil water’and‘labile litter carbon’variable" in: 

C.S. Eastaugh, H. Hasenauer, Deriving forest fire ignition risk with biogeochemical process modelling, Environmental Modelling & Software, Volume 55, May 2014, Pages 132-142, ISSN 1364-8152, http://dx.doi.org/10.1016/j.envsoft.2014.01.018.

(http://www.sciencedirect.com/science/article/pii/S1364815214000280)

Abstract: Abstract

Climate impacts the growth of trees and also affects disturbance regimes such as wildfire frequency. The European Alps have warmed considerably over the past half-century, but incomplete records make it difficult to definitively link alpine wildfire to climate change. Complicating this is the influence of forest composition and fuel loading on fire ignition risk, which is not considered by purely meteorological risk indices. Biogeochemical forest growth models track several variables that may be used as proxies for fire ignition risk. This study assesses the usefulness of the ecophysiological model BIOME-BGC's ‘soil water’ and ‘labile litter carbon’ variables in predicting fire ignition. A brief application case examines historic fire occurrence trends over pre-defined regions of Austria from 1960 to 2008. Results show that summer fire ignition risk is largely a function of low soil moisture, while winter fire ignitions are linked to the mass of volatile litter and atmospheric dryness.

Keywords: Wildfire; Fire risk; BIOME-BGC; Fire index; Climate change regions; Risk indices; Ignition

https://www.researchgate.net/publication/260110834_Deriving_forest_fire_ignition_risk_with_biogeochemical_process_modelling 

All the best,

Eva

Article Deriving forest fire ignition risk with biogeochemical proce...

Although not a direct answer to your question, I would have a look at:

Beer, C., Reichstein, M., Tomelleri, E., Ciais, P., Jung, M., Carvalhais, N., ... & Bondeau, A. (2010). Terrestrial gross carbon dioxide uptake: global distribution and covariation with climate. Science, 329(5993), 834-838.

Attemps to model GPP and NPP by climatic variables (on a global scale) still show very large discrepancies between modeled and field data, i.e. the global NPP/GPP values are similar between models, but the distribution differs alot among models. It can be useful to narrow down your question to a specific climate. Also have a look at the bigfoot project, where they compare field with modeled data over a large number of field sites with different climates:

Pisek, J., & Chen, J. M. (2007). Comparison and validation of MODIS and VEGETATION global LAI products over four BigFoot sites in North America. Remote Sensing of Environment, 109(1), 81-94.

 thanks Eva and Richard for nice papers, really LAI estimates through MODIS /LANDSAT are really effective, but needs validation, even NPP NDVI are available and we have to make use of these imp info for regional estimates of production

regards

Thank you all for the comments and sources of information!