1. Enrichment of leaf & leaf-transpired water – beyond Craig & Gordon – Matthias Cuntz Research School of Biological Sciences (RSBS), ANU, Canberra, Australia Jérôme Ogée, Philippe Peylin Laboratoire des Sciences du Climat et de l’Environnement (LSCE), Gif-sur- Yvette, France Graham D. Farquhar, Lucas A. Cernusak Research School of Biological Sciences (RSBS), ANU, Canberra, Australia

2. Leaf water enrichment? Strong influence on atmospheric water vapour ( 18 O, D) Partition evaporation from transpiration Dew uptake Water redistribution in soils by trees Water recycling Determines isotopic composition of plant organic matter ( 18 O, 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 18 O in O 2 (Dole effect) Paleo-reconstructions of terrestrial vs. marine productivity Synchronisation tool between different paleo records Important determinent of 18 O in CO 2 Partition net CO 2 exchange in assimilation and respiration

3. Steady-state: Craig & Gordon RERE xylem stoma ReRe RsRs R L =R e R E  R e or R e  R E Steady-state: R E =R s RvRv Two compartments: R L =f 1 R e +(1-f 1 )R s Craig & Gordon equation:

4. Steady-state: Péclet effect RERE xylem stoma ReRe RsRs R x

5. The effective length: L eff RERE xylem stoma ReRe RsRs x L L eff =k·L L

6. Leaf geometry à la Farquhar & Lloyd v=v x kv x =E/C DxDx D=D x L RERE xylem stoma ReRe RsRs L eff =kL L

7. The effective length à la Farquhar & Lloyd: L eff RERE xylem stoma ReRe RsRs L k1·LLk1·LL k2·LLk2·LL k3·LLk3·LL k4·LLk4·LL

8. The effective length à la Cuntz (or à la soil): L eff RERE xylem stoma ReRe RsRs L k1·LLk1·LL k2·LLk2·LL k3·LLk3·LL k4·LLk4·LL

9. Leaf geometry à la Cuntz (or à la soil) vxkivxki v x =E/C D L RERE xylem stoma ReRe RsRs CuntzFarquhar

10. Leaf geometry of dicotyledon leaf Tortuous path: air space   L through aquaporines or around mesophyll cells    k =  L ·   L eff (t) if  L (t) or  (t) For example: leaf water volume aquaporine stimulation

11. Experimental determination of L eff #1  E valid only if L eff = const

12. Experimental determination of L eff #2 up down with L eff,up = const and L eff,down = const  Is one L eff enough to describe the problem?  Can we take L eff =const?

13. One L eff ? #1 (lupinus angustifolius - clover)

14. One L eff ? #2

15. Take L eff =const? The answer to this exciting questions is just a few slides away.

16. Isotopic leaf water balance E·REE·RE xylem stoma Js·RsJs·Rs R e,  e R L,  L VLVL

17. Farquhar & Cernusak (in press) E·REE·RE xylem stoma Js·RsJs·Rs R e,  e R L,  L VLVL

18. Advection-diffusion equation Advection: v·R Diffusion: D·dR/dx Boundary conditions: at xylem: vR s at stoma: vR E

19. Comparison of different descriptions

20. Is the brave assumption (f 1 always valid) justified? Is taking V L =const, i.e. L eff =const justified?

21. Comparison of different descriptions (repeat)

22. 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 L eff not the enhanced advection speed. There are several Péclet effects inside one leaf (upper/lower). Measurements give the water volume weighted average. L eff is not constant in time anymore. But: ○ Taking just one single L eff seems to be sufficient. ○ Taking also L eff =const in time seems to be justifiable. ○ The assumption that f 1 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.

23. Saving private Dongmann Dongmann et al. (1974), Bariac et al. (1994): Cernusak et al. (2002): Farquhar & Cernusak (in press):

24. Difference between Dongmann and Farquhar Farquhar & Cernusak (in press): Dongmann et al. (1974):

25. Dongmann-style solving Approach name V L f1f1 c1c1 Dongmann constant11 Cernusak varying1 This study constantf1f1 Farquhar varying

26. Dongmann-style solutions

27. Evaporating site ≡ evaporated water

28. Isoflux

29. Summary (for second part) Leaf water volume change seems to be negligible for  L Gradient in leaf is important for  L (Péclet effect, f 1 ) 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 E  E : even steady-state Craig & Gordon appropriate Beware of high night-time stomatal conductance

30. FIN