Non-linear interactions between $\hbox {CO}_2$ radiative and physiological effects on Amazonian evapotranspiration in an Earth system model

Abstract

We present a detailed analysis of mechanisms underlying the evapotranspiration response to increased $\hbox {CO}_2$ in HadGEM2-ES, focussed on western Amazonia. We use three simulations from CMIP5 in which atmospheric $\hbox {CO}_2$ increases at 1% per year reaching approximately four times pre-industrial levels after 140 years. Using 3-hourly data, we found that evapotranspiration (ET) change was dominated by decreased stomatal conductance ($g_s$), and to a lesser extent by decreased canopy water and increased moisture gradient (specific humidity difference between surface and near-surface). There were large, non-linear decreases in ET in the simulation in which radiative and physiological forcings could interact. This non-linearity arises from non-linearity in the conductance term (includes aerodynamic and stomatal resistance and partitioning between the two, which is determined by canopy water availability), the moisture gradient, and negative correlation between these two terms. The conductance term is non-linear because GPP responds non-linearly to temperature and GPP is the dominant control on $g_s$ in HadGEM2-ES. In addition, canopy water declines, mainly due to increases in potential evaporation, which further decrease the conductance term. The moisture gradient responds non-linearly owing to the non-linear response of temperature to $\hbox {CO}_2$ increases, which increases the Bowen ratio. Moisture gradient increases resulting from ET decline increase ET and thus constitute a negative feedback. This analysis highlights the importance of the $g_s$ parametrisation in determining the ET response and the potential differences between offline and online simulations owing to feedbacks on ET via the atmosphere, some of which would not occur in an offline simulation.

Appendix: Correlation effect

$$\begin{aligned} ET = x * y \end{aligned}$$

Writing as mean and anomalies:

$$\begin{aligned} x&=\, \bar{x} + dx\\ y&=\, \bar{y} + dy \end{aligned}$$

where dx is anomaly w.r.t time mean $\bar{x}$ and dy is anomaly w.r.t time mean $\bar{y}$.

So

$$\begin{aligned} ET&=\, (\bar{x}+dx)*(\bar{y}+dy)\\ &=\, \bar{x}*\bar{y} + \bar{x}*dy + \bar{y}*dx + dx*dy \end{aligned}$$

Taking the time mean:

$$\begin{aligned} \overline{ET} = \overline{x}*\overline{y} + \overline{dx*dy} \end{aligned}$$

(as time means of dx and dy are zero by definition).

If $corr(x,y) > 0$ then $\overline{dx*dy} > 0$ and $\overline{ET} > \bar{x}*\bar{y}$.

If $corr(x,y) < 0$ then $\overline{dx*dy} < 0$ and $\overline{ET} < \bar{x}*\bar{y}$.