Well, you mean studies that show a decrease of biomass due to global warming? You wouldn't find any. Global warming would have the opposite effect. This happens due to the increase of kinetic energy in the system, which leads to an increase of evaporation, and thus rainfall. And of course it also leads to a more tolerable climate in the hemispheres, with less restrictive winters.
Practical consequences of this could be the greening of deserts or parts of deserts such as the Sahara. There's an article about that in the journal Science:
Sahara dried out slowly, not abruptly: study | Environment | Reuters.
Consider different global temperatures. A very cold temperature, such as would be the case in a snowball phenomena, wouldn't allow much life on Earth. On the other hand, warmer temperature from this snowball point would see the biomass density increasing, until a point where it gets to warm and this measure start decreasing. So there is a peak for the biomass density, which relate to an optimal temperature. We can evaluate the biomass density and correlate it to the global temperature in archaeological data. During the reign of the Dinosaurs, some 230 millions to 65 millions years ago, ecosystems underwent a phenomena of gigantism, which was only possible due to an increase of available energy. In fact, the global temperature was at these times a few degrees higher then currently, by a magnitude of about 3.
Biomass changes and Global Warming
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Linear Mode
