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