Presentation on theme: "Maximum Density-Size Relationships for Douglas-fir, Grand-fir, Ponderosa pine and Western larch in the Inland Northwest Roberto Volfovicz-Leon1, Mark."— Presentation transcript:
1 Maximum Density-Size Relationships for Douglas-fir, Grand-fir, Ponderosa pine and Western larch in the Inland Northwest Roberto Volfovicz-Leon1, Mark Kimsey, Terry Shaw, and Mark Coleman Intermountain Forest - Tree Nutrition Cooperative (IFTNC) 1 ,
2 Outline of Presentation IntroductionBackground: Cooperative Site Type Initiative (IFTNC - STI)Maximum Stand Density-Size Relationships in the Inland Northwest
3 Background: IFTNC Site Type Initiative (STI) Identify site factors driving carrying capacity and optimal productivityDevelop models to estimate site quality based on factors that control max density (max SDI) and optimal productivityCreate regional, geospatial tools that predict site quality
5 IFTNC – Site Type Initiative - Drivers of Forest Site Quality Principal factors:LightAspect, latitude, cloudiness, slopeMoisturePrecipitation, soil available water, aspectTemperatureSoil/air temperature, elevation, slope/aspect, latitudeNutrientsParent material elemental composition, rock weathering, organic matter, water availabilitySite quality is an expression of a complex interaction among these factors
6 IFTNC – Site Type Initiative: Past and current work Developed a database of IFTNC member forest stand cruise and permanent plot growth dataDatabase was merged with geospatial representation of physiography, climate, soils and geologypast and current work. Very recently we developed the databe
7 IFTNC - STIDatabase is being use to identify the drivers of site quality and define site-type classes throughout the Inland NorthwestPresent work
8 Objective of Present Study Identify the effects of Soil parent material (Rock type), Topography and Climate variables on Reineke’s Maximum Stand Density Index (SDI max) in the Inland NW for:Douglas-firGrand-firPonderosa pineWestern larch
9 The Settings: Inland Northwest Where each dot now represents a plot from a member of the coop
10 IFTNC- STI Dataset + 150,000 plot data ~ 4,000,000 individual tree data28 species~ 100 variables: stand and tree level variables, climate, topography, soil parent material characteristics
11 Background: Limiting Density-Size Relationship Reineke (1933) observed a limiting linear relationship (on the log-log scale) between number of trees N and quadratic mean diameter Dq in even-aged stands of full density
12 Log Density Log Diameter- (QMD) Lines approach a maximum line = self-thinning lineLog DensityLog Diameter- (QMD)self-thinning line
13 Limiting Density-Size Relationship and Reineke’s Max Stand Density Index SDI = e α +β Ln(Dq)Max SDI is the number of trees per unit area with a specified diameter (Dq = 10 in)
14 Fitting the Self-thinning line: SFR Fitting Method: Stochastic Frontier Regression SFR (Comeau et al. 2010, Weiskittel et al. 2009, Bi 2001)Econometrics fitting technique used to study production efficiency, cost and profit frontiersSince 1930 ‘s many methods have been proposed to fit the limiting relationship (manually locating the line, OLS, quantile regression) they give a ‘good’ average line curve but don’t describe the limithing beahviour. In this study we apply SFR, which has been shown to provide a true boundary to the data.
15 Fitting the Limiting Density-Size line: SFR SFR Model:Ln(TPA) = α + β*Ln(QMD) + v - uv = two-sided random erroru = non-negative random errorMaximum likelihood techniques are used to estimate the frontier
16 Fitting the Self-thinning line using Stochastic Frontier Regression Fitting and data analysis performed using SAS 9.2 (proc qlim)
17 Results: Species Limit Density-Size lines and Max SDI Lspecies limiting line through all sites in the inland NW. These are the 4 most popular and valueables species in the region.Parameter estiMATES AND CALCULATED max sdi.Some of these values for these species are somehow lower than those reported for these species (western larch)
18 Results: Species Limit Density-Size lines Graphically, scatterplots and fitted line , SFR line.You can see the huge amount if data.
22 Comparing Max SDI: Bootstrap 95% Confidence Intervals Stochastic frontier models introduce skewed error termsAssumption of normality of errors is not valid and traditional statistical tests cannot be appliedBootstrapping provides approximate Confidence Limits for estimation of Max SDI
23 Comparing Max SDI: Bootstrap 95% Confidence Intervals Nonparametric bootstrap percentile confidence intervals1,000 bootstrap replications with replacementSFR Intercept, Slope and corresponding Max SDI were obtained from each sample
24 Comparing Max SDI: Bootstrap 95% Confidence Intervals The bootstrap distribution of each regression coefficient was compiled2.5th and 97.5th percentiles of the empirical distribution formed the limits for the 95% bootstrap percentile confidence interval.
25 Results: Bootstraps 95% Confidence Intervals for Max SDI
26 Results: Bootstraps 95% Confidence Intervals for Max SDI
27 Results: Bootstraps 95% Confidence Intervals for Max SDI
28 Results: Bootstraps 95% Confidence Intervals for Max SDI
29 Effect of Climate Variables on the Limiting Density-Size relationship Climate variables from the US Forest Service Moscow-ID LaboratoryThirty-year averaged monthly values for maximum, minimum and mean daily temperatures and monthly precipitationDerived climatic variablesAfter rock type, we investigated the effect of Climate variables on the limitng relationship.
30 Effect of Climate Variables on the Limiting Density-Size relationship
31 Climate Variable Reduction for Modeling using Clustering In high dimensional data sets, identifying irrelevant inputs is usually more difficult than identifying redundant (highly correlated) inputsOur strategy was to first reduce redundancy and then tackle irrelevancy in a lower dimensional spaceVariable clustering (proc varclus SAS 9.2) was used to reduce the number of redundant climate variables to use as input in the self-thinning modelCluster representatives for each group were selected using 1 – R2 ratio
32 Results: Clusters of climate variables 5-clusters provided by proc varclust
33 Clusters of climate variables High correlations within a cluster, low between
34 Effects of Climate Variables on the Density-Size relationship We select one representative from each cluster, reducing the number of climate variable to include in the self-thinning model from 20 to 5:Annual degree-days >5 °C (based on monthly mean temperatures: dd5Length of the frost-free period: ffpMean temperature in the coldest month: mtcmAnnual Dryness Index: ADI (temperature/precipitation)Summer/Spring precipitation balance (jul+aug)/(apr+may): smrsprpb5 climate variables to test in the limiting density – size model
35 Effect of Topographic variables on the Density-Size Relationship Elevation (ft)SlopeAspectThe joint effect of Slope and Aspect was modeled using the cosine and sine transformation (Stage ,1976)
36 Testing the Significance of Climate, Topographic, Soil Parental Material and Stand Variables on the Density-Size RelationshipSelf-thinning relationship as a multidimensional surface (Weiskittel et al )The selected climatic, topographic and stand factors (Skewness of DBH^1.5 distribution, proportion of basal area in the primary species, PBA) were tested for relevance in the limiting functionSignificance of final covariates was tested using log-likelihood ratio test
37 Results: Multidimensional Limiting Density-Size Relationship Douglas-fir final model:Ln(TPA) = b0 + b1·Ln(QMD) b 2𝑖 ∙ 𝑅𝑜𝑐𝑘𝑇𝑦𝑝𝑒 𝑖 + b3·CosAspect + b4·Ln(ADI) b5·Ln (Elevation) + b5· Ln(Prop. BA)+ b6·Ln (Elevation)·Ln(QMD)+ b7·Ln (Prop. BA) ·Ln(QMD)whereRock typei : represents a set of 6 indicator variables taking values 0 and 1 for rock types (baseline sedimentary)Prop.BA: proportion of basal area in the primary speciesAll other variables defined as before
38 Douglas-Fir: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship (Response variable: Ln(Tres per acre))Ln(TPA) = b0 + b1·Ln(QMD) b 2𝑖 ∙ 𝑅𝑜𝑐𝑘𝑇𝑦𝑝𝑒 𝑖 + b3·CosAspect + b4·Ln(ADI) b5·Ln (Elevation) + b5· Ln(Prop. BA)+ b6·Ln (Elevation)·Ln(QMD)+ b7·Ln (Prop. BA) ·Ln(QMD)
39 Grand-fir: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship (Response variable: Ln(Tres per acre))Ln(TPA) = b0 + b1·Ln(QMD) b 2𝑖 ∙ 𝑅𝑜𝑐𝑘𝑇𝑦𝑝𝑒 𝑖 + b3·CosAspect + b4·Ln(ADI) b5· Ln(Prop. BA) + b6·Ln (Prop. BA) ·Ln(QMD)
40 Ponderosa pine: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship (Response variable: Ln(Tres per acre))Ln(TPA) = b0 + b1·Ln(QMD) b 2𝑖 ∙ 𝑅𝑜𝑐𝑘𝑇𝑦𝑝𝑒 𝑖 + b3·Ln(ADI) + b4· Ln(Elevation)+ b5· Ln(Prop. BA) + b6·Ln (Prop. BA) ·Ln(QMD)Rock type, elevation, ADI and prop BA
41 Western larch: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship (Response variable: Ln(Tres per acre))Ln(TPA) = b0 + b1·Ln(QMD) + b2·Cos_Aspect + b3·Ln(ADI) + b4· Ln(Elevation)+ b5·Ln (Prop. BA) + b6·Ln (Prop. BA) ·Ln(QMD)
42 Predicting Max SDI: Geospatial Maps Datum: NAD 1983Climate ~ 600 metersTopographic ~ 20 metersParent Material: Feature Class geology polygons at scales of 1:100,000 or 1:250,000 scale were rasterized. Raster pixel size was set to equal topographic layer resolution.Geospatial predictions are bounded by geology limits and are restricted to geographical zones where the species is estimated to have >25% viability per Crookston, NL, GE Rehfeldt, GE Dixon, and AR Weiskittel Addressing climate change in the forest vegetation simulator to assess impacts on landscape forest dynamics.
44 Next StepsDeveloping models to estimate site quality and productivity based on these identified factorsDevelop regional geospatial tools that predict site quality for Grand-fir, Ponderosa pine, and Western larch