The Cretaceous period was over ten degrees warmer than our current period [3,4,5]. It supported a lot (though much different) biodiversity. How long would it take us to push into these temperature ranges? And how long to exceed them?
How much species diversity will we lose at each half degree increment from this point forward? Will we see some species better equipped (increased as opposed to decreased fitness) by temperature increases? Will we see any quick evolution to support climage changes?
When will temperatures be incompatible with ranges necessary to sustain society? When will they be incompatible with human life? And all terrestrial and aquatic animal life? Will runaway heating (clatrate gun [6], etc.) be capable of achieving any of these?
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[1] https://en.wikipedia.org/wiki/Ice_age "Earth is currently in the ice age called Quaternary glaciation."
[2] https://en.wikipedia.org/wiki/Quaternary_glaciation "To geologists, an ice age is defined by the presence of large amounts of land-based ice." (So my question in terms of heating and time - how long until we exit the ice age?)
[3] https://en.wikipedia.org/wiki/Cretaceous "Mean annual temperatures at the poles during the MKH exceeded 14 °C.", "deep ocean temperatures were as much as 15 to 20 °C (27 to 36 °F) warmer than today's"
[4] https://en.wikipedia.org/wiki/Cretaceous_Thermal_Maximum "Late Cenomanian sea surface temperatures (SSTs) in the equatorial Atlantic Ocean were substantially warmer than today (~27-29°C). Turonian equatorial SSTs are conservatively estimated based on δ18O and high pCO2 estimates to have been ~32°C, but may have been as high as 36°C."
[5] https://www.nature.com/articles/ngeo1081 "During this period, we find sea-surface temperatures exceeding 32 °C at 15°–20° N and averaging 26 °C at ∼53° S. These temperatures substantially exceed modern temperatures at equivalent latitudes,"
[6] https://en.wikipedia.org/wiki/Clathrate_gun_hypothesis (truly horrifying)