1. Alain Perrier, Professor National Agronomic Institute “Paris-Grignon” University Pierre and Marie Curie, UPMC Paris VI A.Tuzet, Senior Scientist National Agronomic research Institute (Laboratory EGC “Grignon”) « BILHYNA » MODEL Energy and water balance biophysical model for regional approaches

2. « BILHYNA » MODEL Main objectives : Integrative system  To approach regional Water Durability : - Adapted to any time-space situations ¤ Continuous multi annual analyses ¤ Any vegetations or crop rotations ¤ taking into account any practices (either given or forecasted) Irrigation ? Soil water balance Deep drainage Potential Runoff Effective rain Soil Evaporation Soil surface Dich-river Evaporation Transpiration Rains Interception Vegetation Direct rain -Adapted to any system conditions ¤ Meteorological climatic forcing ¤ Physico-chemical soil properties ¤ Specific crop characteristics  An Agro-Pedo-Climatic model has been built

3. « BILHYNA » MODEL Integrative system description  Climatic data restored at level : Z R (Z h )  Plant and Soil aerodynamic resistances : ra p (Z h,LAI), ra s (z os )  Rain intensity (over rain duration) : I(t) (100 steps)  Captation model : C{I(t),C(0), LAI}  Plant water exchange model : ET p (EP p,r st,LAI) Ploughing depth Zh(t) ve ZR(t) Z ZR Zh 0 Zp Z pl Boundary layer (t) (conservative flux) Deep Soil n S oi l L a y e r s Mulch(t) Z r max Z(t) root Root water uptake zone Vegetation (t)  Infiltration, run off (Green-Ampt): according to soil layer properties  Soil surface water exchange model : ET s (EP s ),r mulch )  Water diffusion model (Richard eq, 24h) water flux between layers, drainage  Daily calculation  Night calculation (virtual time s to mn )

4. z ET sv, ET pv calculated from EP sv and EP pv From bare soil evaporation model  ET sv From Vegetation transpiration model  ET pv « Bilhyna » MODEL Model Agro-Pedo-Climatic, schematic two layers canopy z EP sv and EP pv given by: Ra s,p = f[z h, LAI, z 0 (z h,z 0 ), D(z h,z 0 )] z ET a, soil-vegetation-atmosphere system :

5. ET/EP R ma x R cap a0a0 R min Model « Bilhyna » Cumulative solution for soil and vegetation evaporation models z Vegetation transpiration H R>R max H R<R max z Bare soil evaporation : H resistance to water vapour diffusion  H mass conservation equation  HRelation to EP s : 

6. z LAI growth for corn (maïs) Measurements (*) and simulations z Growth rate equation, F(T) F(T) = F M. Exp [ .x+  /4].{ 1 – Exp [ .x.(x-1)]} z Logistic growth function depending on F(T) « Bilhyna » Model Growth rate and growth logistic model (LAI, Z h, RAI) Water stress applied F(T) / F M X= 100.(T-T m )/(T f -T m )

7. k with constraint: z (1) Constraint due to PAR : Photosynthetic active radiation z (2) Constraint due to water content : Rmin < R < Rmax « Bilhyna » Model Growth constraints induced by radiation and water (LAI, Z h, RAI) Plant sensibility parameter to water stress,  :  1more and more sensible

8. « Bilhyna » MODEL Rain intensity, water intercepted, infiltration and run off  Green and Ampt approach for infiltration and potential run off : Calculation in the successive layers (including a surface crust)  Calculation of rain duration and intensity using a gaussian distribution of rain amount  From rain intensity and its cumulative value (blue line) : - direct rain arriving at soil (rain with kinetic energy) (green) - Water intercepted by canopy is divided in : * indirect rain dripping from the canopy (rain without kinetic energy)(red) ; *accumulated water on leaves (grey-blue) - evaporation during rain (purple) plus water on leaves (dark green) - time of continuous watered plant is cumulated over days (epidemiology)

9. « Bilhyna » MODEL Soil water budget :rainfall, soil storage water and drainage Time course of soil water budget terms Daily calculation during four years Months of years Drainage at 1 m depth

10. « Bilhyna » MODEL Annual course of predicted (curve) and measured (point) soil water content on three experimental fields with different crops followed by new growth (n.g.) years Soil water content, mm

11. « Bilhyna » MODEL Cumulative terms of water balance : precipitation and rain reaching the soil surface, evapotranspiration, irrigation,drainage and run off (a) Corn crop evapotranspiration and drainage without irrigation (Irg.=0 and run off 67 mm (b) Corn crop evapotranspiration and drainage with irrigation (Irg.=4800 and run off 96 mm

12. « Bilhyna » MODEL Daily variation of LAI for wheat crop over 41 years Variability of LAI growth and new growth according to climatic variables (a) without irrigation (b) with irrigation

13. « Bilhyna » MODEL (a) Results of additional transpiration according to cumulative irrigation (b) Mean annual irrigation amount according to LAI(max)

14. « BILHYNA » MODEL Main conclusions on an integrative system  To use the model at regional scale, it must be driven by GIS including : - Ground numerical model : slope calculation - Meteorological forcing distribution - Spatial distribution of fields and boundaries (streams, ditches, hedges…) - Soil spatial distribution - Annual agricultural calendar for crops  How to modify potential net water availability at regional scale,  (Rf+Ir-ET) : - Using different and new crops with different rotations - Using better management of landscape (reducing ET) - Using model (such as Bilhyna) to adjust irrigation with net water availability  How to reduce irrigation with minimum impact on yield : - How to reduce effectively irrigation for a crop ? - What are the best moment to allocate available irrigation?

15. z Demande climatique EP H Energie radiative H Déficit hydrique de l’air HVitesse du vent  r as et r av r = f (U, D,z o ) D/h = f (LAI) z o /h = f (LAI, z os ) Modèle Bilhyna : Modèle agro-pédo-climatique Culture bi-strates : modèle d’analyse de la demande climatique

16. What sustainable management for water resources, Under climatic constraints ? AN Net availability water for irrigations :  P+  Ir -  ETM =  (D+r) Ir = AN Ir  AN Ir =  Ir +AN m (ou [  P -  ETM]) Local sustainability for irrigation? ¤ No climatic constraint :  P >  ETM  sustainable ¤ Climatic constraint :  P <  ETM  partial sustainability -   ET >  Ir low sustainability (AN Ir =  Ir  90 mm)   -   ET <  Ir higher sustainability (AN Ir =  Ir (  290) [sustainable limit  (D+r) =  ET] Increasing sustainability by transfer from positive zone of Net availability water (AN)

17. « BILHYNA » MODEL Main conclusions on an integrative system