Stand level or tree level models?

Transcription

1 Modelling paradigms Hybrid models to make mensurationists smile Euan Mason New Zealand School of Forestry University of Canterbury Christchurch, New Zealand Stand level or tree level models? Ricardo Methol & Euan Mason Outline Background Objectives Data & Methods Results Model components Comparisons of approaches Conclusions Background Tree level information is important Representing trees in models individual tree models dis-aggregative methods (e.g. Weibull distributions) Background (cont.) Main methodological objective Tree-level and stand-level estimates should be compatible Comparisons of individual-tree models vs.. stand-level models constructed with the same data are scarce To compare 3 approaches for predicting stand structure and dynamics with comparable output resolution, namely: diameter distribution model (reverse Weibull) relative-basal-area-based dis-aggregative approach individual tree model

2 Main practical objective To develop growth models providing increasing levels of resolution for increasing levels of detail in the input data TYPE OF INPUT DATA Stand-level variables only Compatibility whole-stand + diameter stats. (max, st. dev) diameter distribution Complete tree lists MODEL TYPE individual-tree Data E. E. grandis (Uruguay) Data supplied by Fletcher Forests Ltd. 334 plots; 97 measurements (gratefully acknowledged) - 6 years Douglas-fir (NZ) plots; 6 measurements years P. P. radiata (NZ) 973 plots; measurements.4-7 years Required model components (Stand Stand- level; Tree-level level) For calculating volumes: individual-tree height model; tree and stand volume equations Component DDM RBA ITM MEAN TOP HEIGHT X X * BASAL AREA X X * STOCKING X X * STANDARD DEVIATION of dbh's X MAXIMUM DIAMETER X RELATIVE BASAL AREA X PROBABILITY OF TREE MORTALITY X X DIAMETER INCREMENT X Methodology ( of ) Growth intervals stand-level models: all possible individual tree models: annual intervals Redundant data and autocorrelation were minimised by subsampling. Various equation forms and modelling techniques were examined for each component. * only required if the ITM is to be adjusted Methodology ( of ) Comparisons Basal area and stocking estimates: plots of residuals analysis of residual statistics (mean, std. dev., etc.) Diameter distributions error indices (Reynolds et al.. 988) Results () Main model components

3 Selected Mean Top Height equation for all species Altitude effect on MTH (P. radiata) H H = a a Mean Top Top Height Height (m) (m) Mean Chapman-Richards polymorphic: ln ( exp ( kt )) ln ( exp ( kt )) a=a+a*alt/ k=k+k*alt/ 3 3 Age (years) (years) Age (for NZ grown species) m Comparison of MTH projections (Independent validation plots; MTH>8m) m 7 m m (start 7 mas 7 m) Selected Basal Area equation for all species KGM3/PPM88 (left (left)) vs. vs. new model (right (right)) < Residual of MTH (m) > Schumacher Polymorphic: t b b G = G( t /t ) exp a t Predicted Value (m) Initial MTH (m) - parameters a & b modified by Altitude and Thinning Indices (for NZ grown species) Projection Interval (years) Altitude & Thinning effects on B.A. (P. radiata) (Limited) comparison of B.A. projections from PPM88 (left) and the new model (right) (Independent validation plots; MTH>8m) 8 Basal Area (m /ha) 7 join point of the models Basal area residuals Basal area residuals unthinned - m % of G thinned - m unthinned - 6 m % of G thinned - 6 m Age (years) interval (years) Statistic 3 interval (years) PPM88 New model PPM88 New model Mean Standard deviation Skewness...9. Minimum Maximum (MTH > m) 3

4 Relative Basal Area (R).8. R gi = R i g i =.6..6 gi G/N R projection equation selected for all species One-parameter model proposed by Clutter & Allison (974): R = R (T β /T ) Validation of RBA model P. radiata (up to -yr projections) Individual-Tree Mortality.8 Residuals (cm) Mean residual Frequency Frequency Logistic model predicts probability of survival (~) from stand-density and tree-hierarchy variables >.3 Relative basal area class Annual Diameter Increment Validation of D model P. radiata (up to -yr projections) E. grandis dbh MTD D= a + a + a + a 3ln QMD t ( SDI) a 4 a + SDI SI + Mean Residual Frequency 3 3 Douglas-fir dbh N D= exp a + aln(chg_pd) + a + a 3 + a 4RS+ a RS QMD Residuals (cm) Frequency ( b ) P. radiata b bdbh bdbh/ D= x + exp x + xchg_pd+ + x 3 SDI+ x t 4 BAL dbh - - < >69 dbh class (cm) 4

5 Individual tree heights Twenty one -parameter models of the form h = f {dbh} were tried e.g. Petterson eq. h =.4 + α + β dbh. Results () Comparison of modelling approaches Basal Area Residuals (P. radiata; valid. plots) Individual tree model. Mean residual=.8 m /ha Stand model. Mean residual= -. m /ha Residuals of stocking (P. radiata; valid. plots) Individual tree model. Mean residual= 7. stems/ha Stand model. Mean residual= -.8 stems/ha Comparing diameter distribution depictions Error Index (Reynolds et al.. 988) EI ( obs_freq i pred_freq i ) = Wi where i indicates the i th diameter class, and W is a weighting factor (e.g. tree volume) Average Error Indices (P. radiata,, validation plots) Weighting factor Method Tree volume Tree b. area None (p=.64) (p=.367) (p=.3) ITM ITM_adj.6 8 RBA DDM

6 Trend of error index with projection interval Example: PSP 944 (P.( radiata) t=., t=., 9 stems/ha ITM adj 3 3 actual DDM ITM adj PSP=9 t=.6 t= DDM Frequency (stems/ha) Projection interval (years) Diameter class (cm) Conclusions ( of ) Conclusions ( of ) Including altitude improved models Use of long projection intervals: better performance of the new MTH model as compared to the MTH model of KGM3/PPM88 over long projections good performance of DDM over long projections Basal area estimates from unadjusted ITM were unbiased, whereas stocking estimates were biased. Diameter distribution depiction. Ranking of methods by decreasing error index: ITM adj - ITM - RBA - DDM ITM adj was the best approach overall (also compatible with stand level models). DDM also useful: when there are no tree lists available long projections Modelling effects of weed competition on growth of Pseudotsuga menziesii: A hybrid approach Euan Mason Robin Rose Lee Rosner Outline Outline of Starker critical period study Results of study Modeling the results Conclusions Implications for hybrid modelling 6

7 Basic IGM equation Starker CPT study Y T Y + αt = Y=height, dbh or basal area, T=time, α & β = coefficients Fitted to a range of species Accounts for a decline in relative growth rate with tree size Allows for changes in allocation of carbon increased self shading Changes in leaf dimensions Mason & Whyte (997) Mason () Kirongo & Mason (3) β Layout Vegetation management schedules 4 species Douglas fir, western hemlock, western red cedar, grand fir 8 vegetation management schedules 4 replications Planting at 3.*3. m 64 trees/plot, 36 central trees measured T =treated, March-May May O =not treated OOOOO TOOOO TTTTO OOTTT TTOOO TTTTT OTTTT TTTOO Estimated weed cover within m diameter zones around trees 4 Climate by month rainfall Radiation meant 3 3 % Weed cover OOOOO OOTTT OTTTT TOOOO TTOOO TTTOO TTTTO TTTTT Rainfall/month (mm) 3 3 T (C), Radiation (MJ/day) Time (Years) Time (Years) 7

8 Observed Ground Line Diameter Modeled Ground line diameter 6 6 GLD (mm) 4 3 OOOOO OOTTT OTTTT TOOOO TTOOO TTTOO TTTTO TTTTT GLD (mm) 4 3 OOOOO OOTTT OTTTT TOOOO TTOOO TTTOO TTTTO TTTTT Time (Years) Time (Years) N.B.: Analysis of Douglas fir only N.B.: Analysis of Douglas fir only An example hybrid model How do we know this? 3-PG Model (Landsberg & Waring 997) NPP = ε t t= APAR t min [ fθ f D ] ft f F fs Allocation varies with fertility Potential issues with 3-PG3 Allocation of C is derived from allometry Recursiveness,, compounded errors Over parametarisation Fertility is inadequately represented Stand and stem geometry are not modelled Circularity DBH->Carbon, Carbon->DBH Measurement of LAI may partially solve this Solution Blend mensurationist s methods with 3-PG3 Substitute potentially useable light sum for time in equation Y T Y + αr = R=Modified light sum from time of planting to time T Modified by the capacity for plants to use light, given Temperature, VPD, Soil water β 8

9 GLD versus time GLD versus PULSE Ground line diameter (mm) Year Ground line diameter (mm) Potentially useable light sum (Megajoules) Temperature modifier Douglas fir Calculate temperature modifier for each month in each plot (3PG modifier) Ta T min Tmax T a ft( Ta) = Topt T min Tmax T opt ( Tmax Topt ) ( Topt Tmin ) Temp modiier Mean temprature Values from Lewis et al. 999 Temperature modifier VPD Modifier Modifier VPD Modifier Time (years) VPD Landsberg & Waring 997 9

10 VPD modifier Soil water balance model VPD modifier Time (years) Soil characteristics Clay Depth of roots = 4 cm Gravimetric water content at field capacity =.4 Max Available Soil Water = 8 Gravimetric water content at minimum ASW =. Min ASW = 9 Interception by weeds Rainfall Interception by trees Available Soil Water Drainage Evapotranspiration Penman Monteith equation Critical values for trees and weeds: Leaf area indices Maximum stomatal conductances Boundary layer conductance Physiological activity levels ASW deficit (mm) Available soil water deficit 3 4 Time (years) OOOOO OOTTT OTTTT TOOOO TTOOO TTTOO TTTTO TTTTT R T = T Model form Y Y + t t= = R t f T β αr T min Summed across months [ f D fθ ] f LC

11 GLD is represented by only one overall equation GLD (mm) Time (Years) OOOOO OOTTT OTTTT TOOOO TTOOO TTTOO TTTTO TTTTT Hybrid modeling of growth and yield Euan Mason, Helge Dzierzon and Joe Landsberg Potential for hybrid models Potential for representing rotation-length impacts of regeneration practices Geographic Information Systems More known about each site and stand Variation in growth pattern from site to site Less need for regional models Variation in weather from year to year Predicting the past Variation in monthly climate offers monthly predictions Climate change may affect growth patterns Kyoto protocol Carbon storage explicit in some models Potentially useable light sum equation (PULSE) modelling Time = accumulated light Use 3-PG 3 type quantum efficiency modifiers to accumulate potentially used light Use sigmoidal difference equations as usual, fitted to PSP data Avoids some of 3-PG3 PG s s problems Compounded errors Allocation of C Overparametarisation Lack of stand geometry ln( exp( k RAD )) MTH ln( exp( k RAD )) MTH = a a PULSE modelling Estimate genetic components of seasonal variations in primary and secondary growth Different radiation sums for primary and secondary growth PULSE modelling Climatic variables as well as stocking and radiation sum estimates in mortality model NB: Fertility of soils is not well sorted To what extent can temporal variation in climatic influences inform us about influences on crop growth and mortality of spatial variation in climate?

12 PULSE modelling Compatible stand, distribution & individual tree projection systems Models that represent height vs basal area growth as functions of site variables Models that respond to climatic and local weather variation Models specific to each site Models that naturally provide growth estimates within years Preliminary Example P. radiata in Central North Island Residual SS Time Radiation Radiation, temp, VPD Rad, temp, VPD, H Schumacher difference equation, basal area/ha Conclusions Compatible stand and tree-level growth and yield models were complementary Diameter distribution for longer projections Potentially useable light sum equations (PULSE) fitted experimental and PSP data better than models based on time Link G & Y with ecophysiology Within year estimates Sensitive to site variation in space and time May facilitate modelling effects of silvicultural treatments