Relative stability of Earth’s climate system is considered an emergent property of coupled ecosystems. We apply a spatio-temporal scaling relation for root growth to couple bacterial/fungal/vegetational response to climate crises triggered by land plant invasion and predict an absolute time scale to reach homeostasis. The predicted time is 33 % larger than required for the biosphere to emerge from associated Paleozoic ice ages. We propose a basis for understanding the biosphere and critical zone.

The same power law we previously used to quantify growth of tree roots in time describes equally the assemblage of river networks in time. Even the basic length scale of both networks is the same. The one difference is that the basic time scale is ca. 10 times shorter for drainage networks than for tree roots, since the relevant flow rate is 10 times faster. This result overturns the understanding of drainage networks and forms a basis to organize thoughts about surface and subsurface hydrology.