Abial a growth simulator for pure even-aged stands of silver fir (Abies alba Mill.) in Vosges and Jura

Transcription

1 Abial a growth simulator for pure even-aged stands of silver fir (Abies alba Mill.) in Vosges and Jura Frédéric Mothe (1), Jean-Daniel Bontemps (1), Fleur Longuetaud (1), Vincent Perez (1), Daniel Rittié (1), Laurent Saint-André (2), Ingrid Seynave (1) (1) INRA-AgroParisTech Lerfob, Nancy (2) Cirad, Nancy Journée Capsis, 21 juin 2010, Montpellier

2 Objective Reply to a demand by Office National des Forêts a model able to predict future growth of silver fir stands in NE France mainly : pure and even aged natural stands in Vosges + Jura / Morvan model for mixed forests & Alpes in construction at Cemagref at low cost using yet available data (INRA, ONF, IFN) based on the Fagacées model for oak and beech (by Jean-François Dhôte, Gilles Le Moguédec, Patrick Vallet) implemented in the open Capsis platform ( short development time (~ 2 months + data preparation) 2

3 Model overview Distance-independent individual tree model initial data stand data (fertility + location) age, G, N (or inventory list of diameters) management scenario results (at each step) tree heights, diameters, volumes Based on 5 core equations + volume self-thinning stand level tree level dominant height ln (N) <= a + b ln (Dg) Ho = f (age, fertility) basal area increment dg = f' (Ho, silv). dho tree radial increment tree height dgi = f (gi,a-1, dg,...) hi = f (di) tree volume vi = f (hi, di) 3

4 Available data permanent plots temporary plots height increments IFN inventory data Vosges Jura Vosges Jura Vosges Vosges + Jura # plots good sampling for Vosges few data in Jura + Morvan data encoding (Daniel Rittié et al) automatic verification & corrections (Ingrid Seynave) altitude from GIS + digital terrain model (Vincent Perez) 4

5 Data structure large ranges: - elevation 350 to 1000 m - age 50 to 160 years - fertility 20 to 35 m at 100 years - RDI 0.1 to 1 ~ good sampling for elevation, fertility, age lack of young stands with low density (RDI < 0.6) 5

6 self thinning Self-thinning model ln (N) <= a + b ln (Dg) F. Longuetaud, F. Mothe data IFN points + permanent plots method Stochastic frontier analysis (SFA) (Zhang et al 2005) using R package "Frontier" Nmax N Y = α + X β + (V U) V = normal distribution U = half-normal distribution RDI = N / Nmax plots with Dg < 15 cm or Dg > 45 cm were removed allows to compute the RDI (Reineke Relative Density Index) Zhang L., Bi H., Gove J.H., Heath L.S., A comparison of alternative methods for estimating the self-thinning boundary line. Canadian Journal of Forest Research 35:

7 dominant height curve Dominant height curve Ho = f (age, fertility) J.D. Bontemps data 29 permanent plots + height increments for Vosges 7 permanent plots for Jura method Vosges : Lundqvist-Matern model (Zeide 1993) [ R m C m K H 0 t = K exp t t 0 ln K H 0 t 0 with: 1/m m ] C m=exp 1 m 1 ln 1 m t 0 = 15 years H 0 t 0 = 1.30 m R = fertility index m, K = constants Zeide, B. (1993). Analysis of growth equations. Forest Science 39: Jura : existing Duplat (1980) model Duplat P. (1980). Tables de production de référence pour le sapin du Jura. Bulletin Technique de l'onf, 11:

8 basal area increment Stand basal area increment dg = f' (Ho, silv). dho J.D. Bontemps data 15 permanent plots for Vosges 7 permanent plots for Jura exploratory analysis using IFN data method Eichorn relation: G = f (Ho, silv.) Differential form: G / t = f' (Ho, silv.). Ho / t In practical: silviculture effect = RDI elevation and region effect 2 ΔG σ ΔH 0 a t = RDI exp [ b ALT c 0 cma d ma H 0 t ] exp t Δt 2 Δt with: a, b, c0, σ = constants c ma,d ma = region dependant constants 8

9 tree diameter increments Tree radial increment dgi = f (gi,a-1, dg,...) dg/dho L. Saint-André data 15 permanent plots for Vosges 7 permanent plots for Jura + remeasured temporary plots method Deleuze et al 2004 model 2 Δg t = p ΔG t c t m A m A c t 4 A c t with: 1/2 c t = circumference p= p 0 [ RDI t p 2 ln Δ RDI t ] p1 p 0, p1, p 2, m, A = constants Deleuze C., Pain O., Dhôte J.-F., Hervé J.-C. (2004). A flexible increment model for individual trees in pure and even-aged stands. Annals of Forest Science, 61:327:335. 9

10 Tree height F. Longuetaud, F. Mothe tree heights hi = f (di) data 84 permanent + temp plots for Vosges 19 permanent + temp plots for Jura method Height vs diameter relation: h t =1.30 m1 1 exp b0 b1 m1 ct with: c t = circumference m1 =a 0 a 1 H 0 a 2 FI a 3 Age a 4 ALT a i, bi = constants 10

11 tree volume Tree volume vi = f (di, hi) literature models total aboveground volume 2 [ c h t c c t vt= a b c t π ht commercial volume > 7 cm ] with: c t = circumference h t = height a,b,c = constants Vallet P., Dhôte J.-F., Le Moguedec G., Ravart M., Pignard G. (2006). Development of total aboveground volume equations for seven important forest tree species in France. Forest Ecology and Management. 229: v t =a b d 2t ht c h t d d 3t ht e d t with: c t = circumference h t = height a, b, c, d, e = constants Duplat P. (1980). Tables de production de référence pour le sapin du Jura. Bulletin Technique de l'onf, 11:

12 General work-flow dh0 inventory age ++ dominant height curve a0 a1 stand Ho = f (age, fertility) age, N, di, fertility, area basal area increment dg thinning dg = f' (Ho, silv). dho outputs tree radial increments hi, di, vi = f (hi, di) dh0 interv.? dgi = f (gi,a-1, dg,...) dgi gi,a-1 + dgi = gi,a death of the smallest trees Σdgi = dg tree heights hi hi = f (di) di hg = f (dg) self thinning N ln (N) <= a + b ln (Dg) Dg 12

13 General work-flow inventory age ++ dominant height curve stand Ho = f (age, fertility) age, N, di, fertility, area initial stand age, N, G, fertility, area tree diameters generation di ~ N(µ, σ²) basal area increment thinning dg = f' (Ho, silv). dho outputs tree radial increments hi, di, vi = f (hi, di) interv.? dgi = f (gi,a-1, dg,...) tree heights hi = f (di) death of the smallest trees self thinning ln (N) <= a + b ln (Dg) 13

14 AbiAl 2.0 software 14

15 Conclusions the model seems to satisfy ONF request but there are strong limitations: * pure and even aged stands * not accurate for the juvenile phasis * understory not considered * mortality only due to competition and concerning smallest trees * outputs limited to yield (no stem profile, no wood quality...) * restricted to the validity domain: - Vosges and Jura mountains - elevation 350 to 1000 m - age 50 to 160 years - fertility 20 to 35 m at 100 years - RDI 0.6 to 1 15

16 Photo Pierre Gelhaye 2007 Le Donon, Vosges