I'm going to venture a prediction that his calculations won't match up to reality because there will be a load of factors that he won't have taken into account. It's so neat and simple feeding numbers into computer models...
I tracked down the paper. Seems the big idea is that extra mammals will trample down the snow and lessen its insulative properties, thus allowing the ground underneath to get colder over the winter months:
'One particular possible mitigation strategy is the additional introduction and management of herbivores, such as reindeer, horses, bison, etc. in contemporary northern high-latitude ecosystems. In the late Pleistocene the mammoth steppe ecosystem consisted of numerous herbivores of about 10 ton per km2 biomass15 and occupied most of Northern Eurasia. Since the beginning of the Holocene, big mammals disappeared and the mammoth steppe vanished. Today, only reindeer is found16 with a density below 10 individuals per km2 in most of the Arctic17. This can, however, be changed since most populations of large herbivores like reindeer and muskoxen are directly managed by humans, either by hunting or management18. The herbivore community can also be manipulated even more by reintroducing lost components of the Arctic herbivore assembly. In a huge and long-term experiment called Pleistocene Park, a 2000 hectare area in the Kolyma river lowland, Russian Far East has been fenced in 199619. Then, different herbivores have been introduced into this park in order to study their effect on plant biodiversity, vegetation productivity, and soil temperature regime. Winter grazing and movements by the animals compact snow, thereby substantially decreasing the thermal insulation efficiency of snow. This allows much colder freezing of soil in winter, hence colder overall mean annual soil temperature. The hypothesis is that this cooling effect may prevent permafrost from thawing or at least postpone the degradation15. However, to test this hypothesis, a quantitative assessment is needed on the long-term effect of increasing snow compaction until 2100 under climate change. Would a high potential increase in the population density of large herbivores preserve permafrost temperature and gelisol extent until the end of the century? Or, would the increasing air temperature forcing anyhow dominate over the reduced soil insulation effect, and thus lead to a positive permafrost carbon-climate feedback mechanism?' - https://www.nature.com/articles/s41598-020-60938-y
Later they at least note some of the possible counter-effects:
'Introducing a large amount of big mammals into tundra and forest tundra ecosystems will also have other consequences for ecosystem functions, such as enhancing of primary productivity or nutrient cycling while at the same time reducing shrub and tree cover15. The resulting enhancement of both carbon dioxide uptake and surface albedo led to an additional negative feedback to global warming. However, higher grazing activities may also disturb near-surface vegetation such as lichens andsuch first model experiments do not take into consideration all interactions between ecological and physical processes. For instance, changing veget bryophytes, thereby reducing their insulation efficiency in summer and leading to soil warming. Since our land surface model version includes a process-based representation of lichens and bryophytes21, we could explicitly account for such effects on soil temperature by doubling the turnover rate constant of mosses. The sensitivity study results suggest an overall negligible effect of moss turnover rate on permafrost temperature and illustrate the importance of snow properties (Table 2). However, such first model experiments do not take into consideration all interactions between ecological and physical processes. For instance, changing vegetation type and cover by herbivores will impact surface albedo and evapotranspiration. Therefore, our results demonstrate the need for further research on the effects of big herbivores on land-atmosphere interactions and on integrating fauna dynamics into complex Earth System Models.'
'such first model experiments do not take into consideration all interactions between ecological and physical processes' - you don't say! Also not covered is what all these extra animals are going to be eating - presumably there's a reason reindeer herds are so low nowadays, a question generally having to do with the amount of forage available to them, especially during winter. They say the numbers can be 'managed by humans' - well, that's that problem sorted then, where there's a will there's a way! They'll be dropping hay bales off by helicopter before you know it, with funding from BP, joyously announced in full-page advertorials in the graun... Why not just send in a bunch of steamrollers?
Forgive my cynicism...
I
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