PHOTO BY S. MANZONI

Eco-hydrological optimality to link Eco-hydrological optimality to link water use and carbon gains by plants water use and carbon gains by plants

Manzoni S.1,2, G. Vico2, S. Palmroth3, G. Katul3,4, and A. Porporato3,4

1Physical Geography and Quaternary Geology, Stockholm Univ.2Crop Production Ecology and Ecology Dept., SLU, Uppsala3Nicholas School of the Environment, Duke Univ., USA4Civil and Environmental Engineering, Duke Univ., USA

PHOTO BY S. MANZONI

Carbon uptake

Soil carbon

Respiration

Food, fiber, biofuels… Respiration

Soil moisturePHOTO BY S. MANZONI

EA

TranspirationCarbon uptake

Rainfall

Stomatal conductance as a “compromise between the need to provide a passage for assimilation and the prevention of excessive transpiration” (Cowan and Troughton, 1971, Planta)

How do plants respond to altered climatic conditions?

Can we optimize agro-ecosystem management to balance productivity and resource use?

Can we breed crops towards more efficient resource use?

Regulation of water transportStomatal closure limits

evaporation from the leaves

Lens (2011), New Phytologist

Plant xylem limits transport of liquid water to the leavesManzoni et al. (2013) Adv. Water Res.

-ψP

g c

-ψP

g P

E

LAI gc(P)

Water use strategies involve tradeoffs

1) High transpiration allows plants to grow faster → competitive advantage

(Eagleson, 2002, Rodriguez-Iturbe and Porporato 2004)

BUT: high transpiration lowers soil moisture faster → earlier water stress?

2) Stomatal closure reduces desiccation risk (Cowan, 1982)

BUT: lower stomatal conductance decreases C uptake → carbon starvation?

Tradeoffs require ‘balanced’ solutions

Hypothesis:Water use strategies are optimal in a given

environment(idea pioneered by Givnish, Cowan and Farquhar)

Process-based optimal control problem

1) Objective: maximize photosynthesis (A)

2) Control: stomatal conductance to CO2 (gC)

3) Constraint: soil water is limited

Optimality at different time scales

1) Sub-daily, at ~constant soil

moisture2) One dry-down

(days-weeks)

3) Several years and longer: stochastic soil moisture

Water use strategies vary with the temporal scale of interest, because environmental drivers fluctuate at different scales

Data from Fazenda Tamandua, Brazil R

iiaC cQkccgA

The water flux is driven by the atmospheric evaporative demand

The CO2 flux is driven by the gradient between atmospheric and internal CO2 concentrations

DagwwagE CaiC

Stomatal controls on transpiration and photosynthesis

Biochemical C fixation

waca

wi ci

gc

E A

C fixationFrom the xylem

Stomatal cavity

Guard cells

iiaC cQkccgA

The water flux is driven by the atmospheric evaporative demand

The CO2 flux is driven by the gradient between atmospheric and internal CO2 concentrations

Stomatal controls on transpiration and photosynthesis

Biochemical C fixation

A(gc)

gc

Downward concavity!

E(gc)

DagwwagE CaiC

C

aCC gk

kcggA

1) Sub-daily time scale

T

c dtgA0

Objective: maximize

Soil moisture changes slowly compared to light and VPD Soil moisture is assumed constant

Marginal water use efficiencyOptimal stomatal conductance

1

aD

ckg a

C

λ is constant, but undetermined!(classical solution by Cowan and Farquhar; Hari and Mäkelä)

0

E

At

λ = constant at given soil moisture

Correct scaling gc and E vs. vapor pressure deficit D

Katul et al., 2009, PCE

Proportionality of gc and A(see also Hari et al., 2000, Aus. J. Plant Phys.)

Pal

mro

th e

t a

l., 1

999,

Oec

olog

ia

2) Dry-down time scale (days to weeks)

T

c dtgA0

Objective: maximize

s

R E

QLgERdt

dsnZ cr Subject to the

constraint

L

Zr

Q

Marginal water use efficiency

t

Optimal stomatal conductance

λ is defined by the boundary conditions of the optimization (Manzoni et al. 2013, AWR)

1

aD

ckg a

C with time

λ increases with decreasing water availability

λ increases as drought progresses across species, ecosystems, and climates

(Man

zoni

et

al.,

201

1, F

unc

tion

al E

col)

Water stress

Wat

er u

se e

ffici

ency

Ψ

λ/λ w

w eww

-ψ

λ

λww

-ψ

gc

Time

Tim

e

Time

3) Optimal water use in stochastic environments

Ψ90,s

-ψP

g c

-ψP

g Pψ50

s

E

Transpiration – moisture curve depends on plant hydraulic traits

Constraint:

Stochastic rainfall

QLERdt

dsnZ r

→ p(s) depends on the E(s) curve and hence also on plant hydraulic traits

LAI gc

SPAC model

Objective: maximize

Constraint:

3) Optimal water use in stochastic environments

QLERdt

dsnZ r

0

dsspsAA

→ Focus on stomatal and xylem conductances:

What is the optimal shape of gc(P) and gP(P)?

→ p(s) depends on the E(s) curve and hence also on plant hydraulic traits

→ Plant strategies optimize the long-term mean C uptake

Optimal water use explains plant trait coordination

Observations are consistent with prediction of coordinated stomatal closure and cavitation occurrence

-ψPg c

Ψ90,s

-ψPg P

ψ50

A

<A>

LAI gc

Conclusions

1. Sub-daily time scale: optimization explains stomatal responses to air humidity and photosynthesis-transpiration relations

2. Dry-down time scale: plants optimally down-regulate water losses as soils dry

3. Long term: coordination among plant hydraulic traits emerges as an optimal evolutionary strategy