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