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Maximum Density-Size Relationships for Douglas-fir, Grand-fir, Ponderosa pine and Western larch in the Inland Northwest Roberto Volfovicz-Leon 1 , Mark Kimsey, Terry Shaw, and Mark Coleman Intermountain Forest - Tree Nutrition Cooperative (IFTNC ) 1 robertov@uidaho.edu , 208-885-8017.

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  1. Maximum Density-Size Relationships for Douglas-fir, Grand-fir, Ponderosa pine and Western larch in the Inland NorthwestRoberto Volfovicz-Leon1, Mark Kimsey, Terry Shaw, and Mark ColemanIntermountain Forest - Tree Nutrition Cooperative (IFTNC)1robertov@uidaho.edu , 208-885-8017

  2. Outline of Presentation Introduction Background: 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 productivity Develop models to estimate site quality based on factors that control max density (max SDI) and optimal productivity Create regional, geospatial tools that predict site quality

  4. IFTNC – Research Regions

  5. IFTNC – Site Type Initiative - Drivers of Forest Site Quality • Principal factors: • Light • Aspect, latitude, cloudiness, slope • Moisture • Precipitation, soil available water, aspect • Temperature • Soil/air temperature, elevation, slope/aspect, latitude • Nutrients • Parent material elemental composition, rock weathering, organic matter, water availability • Site 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 data Database was merged with geospatial representation of physiography, climate, soilsand geology

  7. IFTNC - STI Database is being use to identify the drivers of site quality and define site-type classes throughout the Inland Northwest

  8. Objective of Present Study • Identify the effects of Soil parent material (Rock type), Topographyand Climate variables on Reineke’s Maximum Stand Density Index (SDI max) in the Inland NW for: • Douglas-fir • Grand-fir • Ponderosa pine • Western larch

  9. The Settings: Inland Northwest

  10. IFTNC- STI Dataset + 150,000 plot data ~ 4,000,000 individual tree data 28 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 Dqin even-aged stands of full density

  12. Log Density Log Diameter- (QMD) Lines approach a maximum line = self-thinning line 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 (Comeauet al. 2010, Weiskittel et al. 2009, Bi 2001) • Econometrics fitting technique used to study production efficiency, cost and profit frontiers

  15. Fitting the Limiting Density-Size line: SFR SFR Model: • Ln(TPA) = α + β*Ln(QMD) + v - u • v = two-sided random error • u = non-negative random error • Maximum 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 (procqlim)

  17. Results: Species Limit Density-Size lines and Max SDI

  18. Results: Species Limit Density-Size lines

  19. Results: Limiting Species Density- Size Relationship by Rock Type Are the self-thinning lines (and the corresponding SDI Max) affected by soil parent material ?

  20. Results:Limiting Density-Size by Rock Type

  21. Comparing Max SDI: Bootstrap 95% Confidence Intervals Stochastic frontier models introduce skewed error terms Assumption of normality of errors is not valid and traditional statistical tests cannot be applied Bootstrapping provides approximate Confidence Limits for estimation of Max SDI

  22. Comparing Max SDI: Bootstrap 95% Confidence Intervals Nonparametric bootstrap percentile confidence intervals 1,000 bootstrap replications with replacement SFR Intercept, Slope and corresponding Max SDI were obtained from each sample

  23. Comparing Max SDI: Bootstrap 95% Confidence Intervals The bootstrap distribution of each regression coefficient was compiled 2.5thand 97.5thpercentiles of the empirical distribution formed the limits for the 95% bootstrap percentile confidence interval.

  24. Results: Bootstraps 95% Confidence Intervals for Max SDI

  25. Results: Bootstraps 95% Confidence Intervals for Max SDI

  26. Results: Bootstraps 95% ConfidenceIntervals for Max SDI

  27. Results: Bootstraps 95% ConfidenceIntervals for Max SDI

  28. Effect of Climate Variables on the Limiting Density-Size relationship Climate variables from the US Forest Service Moscow-ID Laboratory Thirty-year averaged monthly values for maximum, minimum and mean daily temperatures and monthly precipitation Derived climatic variables

  29. Effect of Climate Variables on the Limiting Density-Size relationship

  30. Climate Variable Reduction for Modeling using Clustering In high dimensional data sets, identifying irrelevant inputs is usually more difficult than identifying redundant (highly correlated) inputs Our strategy was to first reduce redundancy and then tackle irrelevancy in a lower dimensional space Variable clustering (procvarclus SAS 9.2) was used to reduce the number of redundant climate variables to use as input in the self-thinning model Cluster representatives for each group were selected using 1 – R2ratio

  31. Results: Clusters of climate variables

  32. Clusters of climate variables

  33. 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: dd5 Length of the frost-free period: ffp Mean temperature in the coldest month: mtcm Annual Dryness Index: ADI (temperature/precipitation) Summer/Spring precipitation balance (jul+aug)/(apr+may): smrsprpb

  34. Effect of Topographic variables on the Density-Size Relationship Elevation (ft) Slope Aspect The joint effect of Slope and Aspect was modeled using the cosine and sine transformation (Stage ,1976)

  35. Testing the Significance of Climate, Topographic, Soil Parental Material and Stand Variables on the Density-Size Relationship • Self-thinning relationship as a multidimensional surface (Weiskittel et al . 2009) • 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 function • Significance of final covariates was tested using log-likelihood ratio test

  36. Results: Multidimensional Limiting Density-Size Relationship • Douglas-fir final model: Ln(TPA) = b0 + b1·Ln(QMD)+ b·Ln(ADI) + b5·Ln(Elevation) + b5· Ln(Prop. BA) + b6·Ln(Elevation)·Ln(QMD) + b7·Ln(Prop. BA) ·Ln(QMD) where Rock 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 species All other variables defined as before

  37. Douglas-Fir: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship (Response variable: Ln(Tres per acre)) Ln(TPA) = b0 + b1·Ln(QMD)+ b·Ln(ADI) + b5·Ln(Elevation) + b5· Ln(Prop. BA) + b6·Ln(Elevation)·Ln(QMD) + b7·Ln(Prop. BA) ·Ln(QMD)

  38. Grand-fir: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship (Response variable: Ln(Tres per acre)) Ln(TPA) = b0 + b1·Ln(QMD)+ b·Ln(ADI)+ b5· Ln(Prop. BA) + b6·Ln(Prop. BA) ·Ln(QMD)

  39. Ponderosa pine: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship (Response variable: Ln(Tres per acre)) Ln(TPA) = b0 + b1·Ln(QMD)+ b·Ln(ADI) + b4· Ln(Elevation) + b5· Ln(Prop. BA)+ b6·Ln(Prop. BA) ·Ln(QMD)

  40. Western larch: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship (Response variable: Ln(Tres per acre)) Ln(TPA) = b0 + b1·Ln(QMD)+ b·Cos_Aspect +b·Ln(ADI) + b4· Ln(Elevation) + b5·Ln(Prop. BA) + b6·Ln(Prop. BA) ·Ln(QMD)

  41. Predicting Max SDI: Geospatial Maps • Datum: NAD 1983 • Climate ~ 600 meters • Topographic ~ 20 meters • Parent 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 Weiskittel2010- Addressing climate change in the forest vegetation simulator to assess impacts on landscape forest dynamics.

  42. Douglas-fir: Regional Geospatial Map

  43. Next Steps Developing models to estimate site quality and productivity based on these identified factors Develop regional geospatial tools that predict site quality for Grand-fir, Ponderosa pine, and Western larch

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