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+ b 7 DBH. + b 8 DBH 2. + b 4 CCF + b 5 ln(CFF). + b 9 ln(DBH). + b 10 HT + b 11 HT 2 + b 12 PCT + b 14 ln(PCT). ln(CR) = HAB + b 1 BA + b 2 BA 2 + b 3 ln(BA). Should tree crown ratio be measured to obtain reliable tree diameter growth predictions?. by Laura Leites ,

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slide1

+ b7DBH

+ b8DBH2

+ b4 CCF + b5ln(CFF)

+ b9ln(DBH)

+ b10HT + b11HT2 + b12PCT + b14ln(PCT)

ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)

Should tree crown ratio be measured to obtain reliable tree diameter growth predictions?

byLaura Leites,

Nicholas Crookston,

Andrew Robinson

slide2

+ b7DBH

+ b8DBH2

+ b4 CCF + b5ln(CFF)

+ b9ln(DBH)

+ b10HT + b11HT2 + b12PCT + b14ln(PCT)

ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)

An evaluation of the utility of crown ratio estimations on the predictions of diameter growth and stand basal area increment for the Forest Vegetation Simulator, North Idaho (NI) and South Central Oregon/North Eastern California(SO) variants.

objectives
Objectives
  • We evaluate the CR models used in two major variants of FVS: NI and SO, and quantify the differences between measured (CRm) and FVS predicted CR (CRp).
  • We evaluate the effect of using CRm against using CRp on the diameter growth (DG) predictions at the tree level.
objectives4
Objectives

3. We evaluate the effect of using CRm against using CRp at the plot level through predictions of basal area increment (BAI).

introduction
Introduction
  • CR and diameter growth (DG) predictions:
  • Indirect measure of the tree’s photosynthetic capacity & a measure of stand density.
  • As the CR increases so does the DG rate.
introduction6
Introduction
  • CR and diameter growth (DG) predictions:
  • FGYM DG models: CR as a predictor variable.
  • The FVS 10-year squared basal diameter increment model (dds).
  • CR: measured and predicted
introduction7
Introduction

On CR models:

  • CR at a point in time vs. change in CR.
  • Mathematical forms for allometric CR models:
  • exponential, logistic, Weibull distribution based models, Richards.
  • Predictor variables - 3 groups:
  • Tree size, competition level, stand productivity.
slide8

FVS NI and SO Variants: CR predictions at a point in time.

NI variant: Hatch (1980) exponential model

slide9

SO variant:

  • Small trees use a logistic model:
slide10

Large trees use Dixon’s (1985) Weibull based model.

Specify Stand CR distribution:

a & c: species-specific constants

b for a given species:

Calculate mean stand CR (MCR) from relative stand density index (RSDI):

MCR = d0 + d1*RSDI (d0 and d1 are species-specific)

Use MCR to calculate b:

b = j0 + j1*MCR ( j0 and j1 are species-specific)

Assign CR values based on tree’s DBH ranking

methods

CNF

WNF

Methods

Data

  • Acquired from the USDA Forest Service, Pacific Northwest Region's Current Vegetation Survey (CVS) project.
  • Data collected at the Winema National Forest (WNF) and the Colville National Forest (CNF) in 1993-1996.
methods12
Methods

Data

  • Sampling design: five 0.076 ha subplots within 1 ha main plot. Different grid sizes.
  • The CNF comprised 2,611 0.076 ha subplots, used as our simulation units.
  • The WNF comprised 2,426 0.076 ha simulation units.
slide13

Measurements in each simulation unit:

  • Species
  • DBH (in)
  • Total tree height (HT, ft )
  • 10-yr radial growth (cores)
  • CR (measured in 10%-wide classes)
  • Crown width (ft)
  • Age (rings count), crown class, damages/injuries, and defects.
  • Variables used to FVS runs were in English units.
  • Simulations results were converted to Metric units.
methods16
Methods

Analysis

Step 1. Evaluation of CR predictions.

By species and by CRm classes.

methods17
Methods
  • Step 2. Assessment of the effect of using CRm against using CRp on the DG predictions at the tree level.
  • We ran FVS NI and SO variants twice, once using CRm and once using CRp.
  • All the rest of the variables were the same in both runs.
  • FVS was ran using default mode.
methods18

HT growth driven DG

small trees

(ST)

DG

dds prediction

DBH

large trees

(LT)

dds prediction = DG

Methods
  • The FVS DG at tree-level:
methods19
Methods

FVS dds base model:

SO variant incorporates other predictor variables.

methods20
Methods

Predicted 10-year-period tree-level DG:

with CRm (DGmCR) & with CRp (DGpCR)

  • RMSE by CRm classes and species.
  • Equivalence tests:
    • non-parametric bootstrap procedure by Robinson et al. (2005).
    •  = 0.05, region of similarity for slope and intercept were set equal to  10% of the mean.
methods21
Methods
  • Step 3. Assessment of the effect of using CRm against using CRp on the BAI at the simulation unit (SU) level
  • We ran FVS NI and SO variant models twice for a 30-year-period.
  • All the rest of the variables were the same in both runs.
  • FVS was ran using default mode.
methods22
Methods

BAImCR v.s. BAIpCR

  • Equivalence tests:
    • non-parametric bootstrap procedure by Robinson et al. (2005).
    •  = 0.05, region of similarity for slope and intercept were set equal to  10% of the mean.
results
Results

Step 1. Evaluation of CR predictions.

results24
Results

Step 1. Evaluation of CR predictions.

results25

% of DGpCR

Results

Step 2. DGmCR v.s.DGpCR

ST = small trees

LT = large trees

results26
Results

Step 2. DGmCR v.s.DGpCR

conclusions
Conclusions
  • The three CR equations were biased.
  • The larger the difference between RMSE of CRm and CRp, the larger the difference between RMSE of DGpCR and DGmCR.
  • Overall RMSE values for the NI variant were lower than those for the SO variant.
conclusions30
Conclusions
  • Equivalence tests resulted in similarity for more species in the NI variant than in the SO variant.
  • Equivalence tests of BAImCR v.s. BAIpCR resulted in similarity for intercept and slope for both variants.
slide31

+ b7DBH

+ b8DBH2

+ b4 CCF + b5ln(CFF)

+ b9ln(DBH)

+ b10HT + b11HT2 + b12PCT + b14ln(PCT)

ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)

Literature

Dixon, G.E. 1985. Crown ratio modeling using stand density index and the Weibull distribution. Internal Report. Fort Collins, CO: USDA Forest Service. Forest Management Service Center. 13p.

Hatch, C.R. 1980. Modelling crown size using inventory data. Mitt.Forstl. Bundes- Versuchsanst. Wien, 130: 93-97.

Robinson, A.P., Duursma, R.A., and Marshall, J.D. 2005. A regression-based equivalence test for model validation: shifting the burden of proof. Tree Physiology. 25:903-913.

slide32

+ b7DBH

+ b8DBH2

+ b4 CCF + b5ln(CFF)

+ b9ln(DBH)

+ b10HT + b11HT2 + b12PCT + b14ln(PCT)

ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)

  • Acknowledgements:
  • Gary E. Dixon
  • Charles R. Hatch
  • This study was funded by USFS Grant 04DG11010000037
slide33

+ b7DBH

+ b8DBH2

+ b4 CCF + b5ln(CFF)

+ b9ln(DBH)

+ b10HT + b11HT2 + b12PCT + b14ln(PCT)

ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)

Thank you

Questions?

colville national forest34
Colville National Forest

Mean DGp mean DGp for CRm class = 40-60%

winema national forest35
Winema National Forest

ST: Mean DGp mean DGp for CRm class = 40-60%

BT: LP mean CRm= 61, mean CRp= 68