outline of presentation
DESCRIPTION
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 [email protected] , 208-885-8017. - PowerPoint PPT PresentationTRANSCRIPT
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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 [email protected] , 208-885-8017
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Outline of Presentation• Introduction
• Background: Cooperative Site Type Initiative (IFTNC - STI)
• Maximum Stand Density-Size
Relationships in the Inland Northwest
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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
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IFTNC – Research Regions
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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
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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, soils and geology
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IFTNC - STI• Database is being use to identify the
drivers of site quality and define site-type classes throughout the Inland Northwest
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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-fir– Grand-fir
– Ponderosa pine– Western larch
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The Settings: Inland Northwest
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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
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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
qDN lnlnln
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Log
Den
sity
Log Diameter- (QMD)
Lines approach a maximum line = self-thinning line
self-thinning line
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qDN lnlnln
SDI = e α +β Ln(Dq)
Limiting Density-Size Relationship and Reineke’s Max Stand Density Index
Max SDI is the number of trees per unit area with a specified diameter (Dq = 10 in)
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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 frontiers
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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
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Fitting the Self-thinning line using Stochastic Frontier Regression
Fitting and data analysis performed using SAS 9.2 (proc qlim)
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Results: Species Limit Density-Size lines and Max SDI
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Results: Species Limit Density-Size lines
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Results: Limiting Species Density- Size Relationship by Rock Type
• Are the self-thinning lines (and the corresponding SDI Max) affected by soil parent material ?
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Results: Limiting Density-Size by Rock Type
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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
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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
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Comparing Max SDI: Bootstrap 95% Confidence Intervals
• The bootstrap distribution of each regression coefficient was compiled
• 2.5th and 97.5th percentiles of the empirical distribution formed the limits for the 95% bootstrap percentile confidence interval.
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Results: Bootstraps 95% Confidence Intervals for Max SDI
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Results: Bootstraps 95% Confidence Intervals for Max SDI
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Results: Bootstraps 95% Confidence Intervals for Max SDI
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Results: Bootstraps 95% Confidence Intervals for Max SDI
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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
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Effect of Climate Variables on the Limiting Density-Size relationship
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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 (proc varclus 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 – R2 ratio
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Results: Clusters of climate variables
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Clusters of climate variables5 Clusters
R-squared with 1-R**2 Cluster Variable Own Next Ratio
Cluster Closest
Cluster 1 d100 0.97 0.67 0.08 dd5_f 0.98 0.60 0.05 mat_f 0.97 0.80 0.13 mmax_f 0.90 0.62 0.27 mtwm_f 0.94 0.64 0.16 Cluster 2 fday 0.88 0.18 0.15 ffp 0.95 0.28 0.08 gsdd5 0.92 0.69 0.25 mmindd0 0.72 0.73 1.03 sday 0.93 0.41 0.12 Cluster 3 dd0 0.95 0.78 0.25 mmin 0.90 0.53 0.22 mtcm 0.96 0.56 0.08 Cluster 4 adi_sqroot 0.93 0.44 0.12 gsp_inches 0.90 0.34 0.15 map_inches 0.87 0.33 0.19 sdi 0.83 0.54 0.38 Cluster 5 pratio 0.26 0.08 0.80 smrpb 0.80 0.30 0.28 smrsprpb 0.97 0.26 0.05
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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
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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)
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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
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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
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Douglas-Fir: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship
(Response variable: Ln(Tres per acre))
Parameter
Estimate Standard Approx
Error Pr > |t|
Intercept
12.957 0.409 <.0001 Rock Type CaMetased -0.063 0.018 0.0007 Rock Type Extrusive 0.021 0.016 0.1765 Rock Type Glacial -0.051 0.017 0.0021 Rock Type Intrusive -0.132 0.016 <.0001 Rock Type Metasedimentary -0.081 0.016 <.0001 Rock Type Sedimentary
Baseline .
Ln(QMD)
-1.716 0.209 <.0001 Cos_Aspect
0.074 0.005 <.0001
Ln(ADI)
-0.398 0.012 <.0001 Ln(Elevation)
-0.524 0.050 <.0001
Ln(Prop.BA)
-1.080 0.039 <.0001 Ln(QMD)*Ln(Elev)
0.074 0.026 0.0043
Ln(QMD)*Ln(Prop BA) 0.281 0.021 <.0001
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)
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Grand-fir: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship
(Response variable: Ln(Tres per acre))
Parameter
Estimate Standard Approx
Error Pr > |t|
Intercept
9.132 0.046 <.0001 Rock Type CaMetased -0.144 0.035 <.0001 Rock Type Extrusive -0.190 0.032 <.0001 Rock Type Glacial -0.134 0.035 0.0002 Rock Type Intrusive -0.207 0.034 <.0001 Rock Type Metasedimentary -0.172 0.033 <.0001 Rock Type Sedimentary
Baseline
Ln(QMD)
-1.139 0.016 <.0001 Cos_Aspect
0.079 0.008 <.0001
Ln(ADI)
-0.280 0.017 <.0001 Ln(Prop.BA)
-0.828 0.055 <.0001
Ln(QMD)*Ln(Prop BA) 0.259 0.030 <.0001
Ln(TPA) = b0 + b1·Ln(QMD) + b·Ln(ADI) + b5· Ln(Prop. BA) + b6·Ln (Prop. BA) ·Ln(QMD)
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Ponderosa pine: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship
(Response variable: Ln(Tres per acre))
Parameter
Estimate Standard Approx
Error Pr > |t|
Intercept
7.579 0.202 <.0001 Rock Type CaMetased -0.216 0.037 <.0001 Rock Type Extrusive -0.011 0.019 0.5595 Rock Type Glacial -0.186 0.024 <.0001 Rock Type Intrusive -0.276 0.022 <.0001 Rock Type Metasedimentary -0.202 0.023 <.0001 Rock Type Sedimentary
Baseline
Ln(QMD)
-1.169 0.013 <.0001 Ln(ADI)
0.052 0.018 0.0047
Ln(Elevation)
0.081 0.023 0.0004 Ln(Prop.BA)
-1.056 0.061 <.0001
Ln(QMD)*Ln(Prop BA) 0.322 0.032 <.0001
Ln(TPA) = b0 + b1·Ln(QMD) + b·Ln(ADI) + b4· Ln(Elevation) + b5· Ln(Prop. BA) + b6·Ln (Prop. BA) ·Ln(QMD)
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Western larch: Parameter Estimates of the Multidimensional Limiting Density-Size Relationship
(Response variable: Ln(Tres per acre))
Parameter Estimate Standard Approx
Error Pr > |t|
Intercept 9.974 0.520 <.0001 Ln(QMD) -0.961 0.031 <.0001 Cos_Aspect 0.068 0.014 <.0001 Ln(ADI) -0.421 0.041 <.0001 Ln(Elevation) -0.189 0.061 0.0018 Ln(Prop.BA) -1.477 0.088 <.0001 Ln_QMD*LN(Prop.BA) 0.509 0.051 <.0001
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)
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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 Weiskittel 2010- Addressing climate change in the forest vegetation simulator to assess impacts on landscape forest dynamics.
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Douglas-fir: Regional Geospatial Map
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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