Enrichment of leaf & leaf-transpired water – beyond Craig & Gordon –
Matthias CuntzResearch School of Biological Sciences (RSBS), ANU, Canberra, Australia
Jérôme Ogée, Philippe PeylinLaboratoire des Sciences du Climat et de l’Environnement (LSCE), Gif-sur-Yvette, France
Graham D. Farquhar, Lucas A. CernusakResearch School of Biological Sciences (RSBS), ANU, Canberra, Australia
Leaf water enrichment?
• Strong influence on atmospheric water vapour (18O, D)• Partition evaporation from transpiration• Dew uptake• Water redistribution in soils by trees• Water recycling
• Determines isotopic composition of plant organic matter (18O, D) • Determine physiological and genetic changes in stomatal conductance and crop yield• Resource utilisation of mistletoes• Paleo-climatic reconstructions (e.g. tree rings)
• Important determinant of 18O in O2 (Dole effect)• Paleo-reconstructions of terrestrial vs. marine productivity• Synchronisation tool between different paleo records
• Important determinent of 18O in CO2
• Partition net CO2 exchange in assimilation and respiration
Steady-state: Craig & Gordon
RE
xylem
stomaRe
Rs
RL=Re
RE Re or Re RE
Steady-state: RE=Rs
vsksse hRαRh-1αR
Rv
Two compartments:
s1sse1
ssL R)f1(RfR
sse1
ssL f
1R
R
R
RRΔ
ss
s
RL=f1Re+(1-f1)Rs
vEke hRαRh-1ααR Craig & Gordon equation:
Steady-state: Péclet effect
RE
xylem
stomaRe
Rs
R
x
LD
v
CD
EL
with
e1
f
eff
sse
ssL
1sse
ssL
The effective length: Leff
RE
xylem
stomaRe
Rs
x
LL Leff=k·LL
Leaf geometry à la Farquhar & Lloyd
v=vxk vx=E/C
Dx
D=Dx
LL
RE
xylem
stomaRe
Rs
Leff=kLL
CD
EL
CD
EkL
D
kLv
D
vL
eff
L
Lx
L
The effective length à la Farquhar & Lloyd: Leff
RE
xylem
stomaRe
Rs
LL
k1·LL
k2·LL
k3·LL
k4·LL
Leff LkL
The effective length à la Cuntz (or à la soil): Leff
RE
xylem
stomaRe
Rs
LL
k1·LL
k2·LL
k3·LL
k4·LL
Leff LkL
Leaf geometry à la Cuntz (or à la soil)
vxki
vx=E/C
D
LL
RE
xylem
stomaRe
Rs
CD
EL
kDC
EL
kD
Lv
D
Lv
eff
L
Lx
x
Lx
k
DDx
CD
ELCD
EkLD
kLvD
vL
eff
L
Lx
L
Cuntz Farquhar
Leaf geometry of dicotyledon leafTortuous path:
air space L
through aquaporinesor around mesophyllcells
k = L·
Leff(t) if L(t) or (t)
For example:leaf water volumeaquaporine stimulation
Experimental determination of Leff #1
CD
ELwith
e111
eff
sse
ssL
E
valid only if Leff = const
Experimental determination of Leff #2
up
down
L
downdown,L
upup,L
sse
sstot,L
V
e1V
e1V
11
downup
with Leff,up = constand Leff,down = const
CD
ELand
CD
ELwith
down,effdown
up,effup
Is one Leff enough to describe the problem? Can we take Leff=const?
One Leff? #1 (lupinus angustifolius - clover)
One Leff? #2
Take Leff=const?
The answer to this exciting questions is just a few slides away.
Isotopic leaf water balance
E·RE
xylem
stoma
Js·Rs
ELL
EssLL
sL
ΔEdt
ΔdV
RERJdt
RdV
EJdt
dV
Re, e
RL, L
VL
esse
k
isLL ΔΔαα
wg
dt
ΔdV
Gordon&Craigwith
Farquhar & Cernusak (in press)
E·RE
xylem
stoma
Js·Rs
LssLe1
k
isLL
1
Lsse
k
isLL
1
1
sse1
ssL
ΔΔ1
αα
wg
dt
ΔdV
f
ΔΔ
αα
wg
dt
ΔdV
stepstimeallatformthisinvalidf
:assumptionBrave
e1fwith
ΔfΔ:statesteadyin
Re, e
RL, L
VL
Advection-diffusion equation
Advection: v·RDiffusion: D·dR/dx
2
2
outin
dx
RdD
dx
dRv
dt
dR
dx
dRDvR
dx
d
dx
dRDvR
dx
dRDvR
dt
dR
indx
dRD
outdx
dRD
dt
dR
invR
outvR
Boundary conditions:at xylem: vRs
at stoma: vRE
Comparison of different descriptions
Is the brave assumption (f1 always valid) justified?Is taking VL=const, i.e. Leff=const justified?
Comparison of different descriptions (repeat)
Summary (up to now)
• Revise thinking about leaf geometry○ i.e., one cannot think about the leaf water isotope path as tortuous tubes because there is mixing between tubes.○ It is the reduced diffusion in x-direction that determines Leff not the enhanced advection speed.
• There are several Péclet effects inside one leaf (upper/lower). Measurements give the water volume weighted average.
• Leff is not constant in time anymore. But:○ Taking just one single Leff seems to be sufficient.○ Taking also Leff=const in time seems to be justifiable.○ The assumption that f1 of the Péclet effect holds for non-steady-state is valid during most of the time, except for for late afternoon/early evening. This leads to an under- estimation of leaf water enrichment during afternoon and night.
Saving private Dongmann
LssL
1k
isLL
LssL
k
isLL
LssL
k
isLL
ΔΔf
1
αα
wg
dt
ΔdV
ΔΔαα
wg
dt
ΔdV
ΔΔαα
wg
dt
ΔdV
Dongmann et al. (1974), Bariac et al. (1994):
Cernusak et al. (2002):
Farquhar & Cernusak (in press):
Difference between Dongmann and Farquhar
dt
dVf
wg
αα1ΔΔ
f
1
αα
wg
dt
ΔdV
ΔΔf
1
αα
wg
dt
ΔdV
dt
dVΔ
ΔΔf
1
αα
wg
dt
ΔdV
L1
is
kL
ssL
1k
isLL
LssL
1k
isLL
LL
LssL
1k
isLL
Farquhar & Cernusak (in press):
LssL
k
isLL
wg
dt
dV
Dongmann et al. (1974):
1c
1
Dongmann-style solving
dtcV
E
sse1L
sse1L
dtcV
wg
sse1L
sse1L
1L
1Lk
is
e))1(c)0(()1(c)1(
e))dtt(c)t(()dtt(c)dtt(
Approach name
VL f1 c1
Dongmann constant 1 1
Cernusak varying 1
This study constant f1
Farquhar varying
e1
e1
dt
dV
E1
1
L
dt
dV
Ef
11
L
1
Dongmann-style solutions
Evaporating site ≡ evaporated water
Isoflux
Summary (for second part)
• Leaf water volume change seems to be negligible for L
• Gradient in leaf is important for L (Péclet effect, f1)
• The error done in the afternoon when using Farquhar & Cernusak’s equation for L is passed on to evening and night
• For water at the evaporating site e: Dongmann and Farquhar give
essentially the same results and both compare well with observations
• For the isoflux EE: even steady-state Craig & Gordon appropriate
Beware of high night-time stomatal conductance
FIN