Modeling water availability for trees in tropical forests

Transcription

1 Modeling water availability for trees in tropical forests Fabien Wagner 1, Bruno Herault 1, Clement Stahl 2, Damien Bonal 3 Vivien Rossi 4 1 Université Antilles-Guyane, UMR Ecologie des Forêts de Guyane, French Guiana; 2 INRA, UMR Ecologie des Forêts de Guyane,French Guiana 3 INRA, UMR INRA-UHP 1137 Ecologie et Ecophysiologie Forestière, France; 4 CIRAD, UMR Ecologie des Forêts de Guyane, French Guiana IBC 2010: Florianopolis, SC, Brazil, December 5-10, 2010

2 outline 1 background 2 the model 3 results 4 summary/future works

3 why modelling water availability in tropical forest? tropical forests are subject to a dry season, incl. Amazon Basin climate modeling scenarios, Hadley center, change in annual soil water content for the late XXIth need for developping soil water availability model for tropical forests

4 soil water cycle model plant extraction dry soil field capacity saturation θ FC permanent wiltingpoint θ PWP deep drainage extractable water, EW Relative Extractable Water: REW = EW EW MAX, [0, 1]

5 soil water balance model EW = P In Tr Eu Dr

6 water infiltration soil layers soil = succession of 1cm layers each layer has a θ PWP a θ FC and a % of roots estimates of θ PWP and θ FC in the calibration water dynamics water > field capacity in a layer = water fills the next layers water remains after the last layer = lost by deep drainage REW REW d = N layer l=1 ( (ÊW l,d θ PWP,l ) (θ FC,l θ PWP,l ) ) Rfd l / }{{} REW layer N layer l=1 Rfd l } {{ } layer roots %

7 tree transpiration computation ρ = Tr PET REW tree transpiration extraction fine root density (Rfd) = exponential function Rfd(depth) = λ Rfd exp( λ Rfd depth) depthl Rfd l = Rfd(depth)ddepth depth l 1 Tr l,d = ρ l PET (1 exp( λ Rfd N layer )) Rfd l

8 calibration data site : Paracou experimental site, French Guiana meteorological data : Guyaflux, flux tower, since 2003

9 calibration data altitude (m) a 4 5 Flux Tower SW NE 5 7 W creek creek creek E TDR measurements distance (m) soil moisture measurment : 10 tubes on 4 soil types, TDR probe measurements from 20 to 260 cm by 20, since 2004 automatic stem growth measurements: 6 dominant trees

10 model parameters and inference nested structure of the model Forest Paracou Soil Alt SLD DhS UhS Tube tube 1 tube 2 tube 4 tube 13 tube 5 tube 9 tube 18 tube 7 tube1 9 tube 16 Parameters

11 model parameters and inference stochasticity of the model : normal error of the probe likelihood of the model L(Data Θ m) = = N tube p=1 N tube L(Data p Θ m) N day N layer p=1 d=1 l=1 [ exp (ÊW p l,d EW p l,d )2 2(0.2 EW p 2π(0.2 EW p l,d ) l,d )2 ] ÊW p l,d are the predicted extractable water values

12 Metropolis-Hastings within a Gibbs algorithm generation of a candidate θ k and the new vector of parameters Θ : θk π prop θ (θ n 1 k ) { } Θ = θ n 1 1,..., θ n 1 k 1, θ k, θ n 1 k+1,..., θn 1 Npar acceptation or rejection of the new candidate θk by computing the ratio of the likelihood : γ = the candidate θ k L(Data Θ ) L(Data Θ n 1 ) }{{} likelihood π 0(θk ) π 0 (θ n 1 k ) }{{} prior πprop θ (θ n 1 k θk ) π prop θ is accepted or rejected as follows : (θ k θn 1 k ) } {{ } proposal 1 u t U [0,1], θ n k { θ k if γ u t θ n 1 k if γ < u t

13 model predictions: soil water content m Soil Water Content (%) m 1.8 m m 1Jan2007 2Jul2007 1Jan2008 1Jul2008 1Jan2009 2Jul2009 1Jan2010 Time (days)

14 model predictions: REW, relative extractable water REW (%) validation optimisation 1Jan2006 1Jan2007 1Jan2008 1Jan2009 1Jan2010 Time (days)

15 REW and tree growth absolute values (mm) Dg Oa Sg Va Gg (a) Diameter growth derivative values ( mm.month 1 ) (b) 1Mar2008 1Jun2008 1Sep2008 1Dec2008 Time (days)

16 summary 1 the method achieve to reproduce the daily extractable water 2 new method to estimate field capacity and permanent wilting point 3 new method to model roots functionning in soil water balance model perspectives 1 history of the soil water availability 2 linking REW to long-term follow up of tropical forest dynamics 3 REW 0.4 threshold for tropical forest species