In an earlier treatment, we used the concept of coupling between vegetation and the atmosphere to demonstrate how the sensitivity of transpiration to a change in stomatal conductance decreases as the spatial scale increases from leaf to region.
We introduced the omega coefficient to define the degree of coupling quantitatively and showed the increasing dependence of transpiration on radiation and decreasing dependence on saturation deficit with the increase in scale.
Whilst this approach was effective for this limited purpose, it was not capable of easy extension to include other variables and it does not clearly demonstrate the reasons for the changes in sensitivity of transpiration to the stomata and the changes in emphasis on environmental driving variables as the scale increases.
In the present treatment, we develop the thesis that increasing scale leads to an increase in number of negative feedback paths that stabilise the system and diminish the sensitivity of transpiration to change in stomatal conductance.
We show that a consequence of negative feedback at the leaf and canopy scales is that we need only crude models of stomatal response to environmental variables so long as the ratio of stomatal conductance to the boundary-layer conductances is large, but we need rather better models where this ratio is small.
At the regional scale, the effects of the negative feedbacks acting through the planetary boundary layer are even stronger, so that the boundary-layer conductances are of little effect, and we have no need for complex multi-layer models over a wide range of large canopy conductances.
When water stress causes stomatal closure, however, the importance of the stomatal and canopy conductances increases so that we need more reliable estimates of them, but there is still no benefit to be gained from multi-layer models. When the supply of water completely dominates transpiration and canopy conductance is very small, crude models again suffice.