1. ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)
+ b4 CCF + b5ln(CFF)
+ b7DBH
+ b8DBH2
+ b10HT + b11HT2 + b12PCT + b14ln(PCT)
+ b9ln(DBH)
Should tree crown ratio be measured to obtain reliable tree diameter growth predictions?
by Laura Leites,
Nicholas Crookston,
Andrew Robinson

2. ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)
+ b4 CCF + b5ln(CFF)
+ b7DBH
+ b8DBH2
+ b10HT + b11HT2 + b12PCT + b14ln(PCT)
+ b9ln(DBH)
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.

3. 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.

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

5. 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.

6. 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

7. 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.

8. FVS NI and SO Variants: CR predictions at a point in time.
NI variant: Hatch (1980) exponential model

9. SO variant:
Small trees use a logistic model:

10. 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

11. 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
CNF
WNF

12. Methods
Data
Sampling design: five ha subplots within 1 ha main plot. Different grid sizes.
The CNF comprised 2, ha subplots, used as our simulation units.
The WNF comprised 2, ha simulation units.

13. 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.

14. Colville National Forest

15. Winema National Forest

16. Methods Analysis Step 1. Evaluation of CR predictions.
By species and by CRm classes.

17. 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.

18. Methods The FVS DG at tree-level: DBH small trees large trees
dds prediction = DG
HT growth driven DG
dds prediction DG

19. SO variant incorporates other predictor variables.
Methods
FVS dds base model:
SO variant incorporates other predictor variables.

20. 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.

21. 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.

22. 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.

23. Results
Step 1. Evaluation of CR predictions.

24. Results
Step 1. Evaluation of CR predictions.

25. Results Step 2. DGmCR v.s.DGpCR ST = small trees LT = large trees
% of DGpCR
ST = small trees
LT = large trees

26. Results
Step 2. DGmCR v.s.DGpCR

27. Step 3. BAImCR v.s. BAIpCR

28. Step 3. BAImCR v.s. BAIpCR

29. 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.

30. 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.

31. Literature
Dixon, G.E 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 Modelling crown size using inventory data. Mitt.Forstl. Bundes- Versuchsanst. Wien, 130:
Robinson, A.P., Duursma, R.A., and Marshall, J.D A regression-based equivalence test for model validation: shifting the burden of proof. Tree Physiology. 25:
ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)
+ b4 CCF + b5ln(CFF)
+ b7DBH
+ b8DBH2
+ b10HT + b11HT2 + b12PCT + b14ln(PCT)
+ b9ln(DBH)

32. Acknowledgements: Gary E. Dixon Charles R. Hatch
ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)
+ b4 CCF + b5ln(CFF)
+ b7DBH
+ b8DBH2
+ b10HT + b11HT2 + b12PCT + b14ln(PCT)
+ b9ln(DBH)
Acknowledgements:
Gary E. Dixon
Charles R. Hatch
This study was funded by USFS Grant 04DG

33. Thank you Questions? + b7DBH + b4 CCF + b5ln(CFF) + b9ln(DBH)
ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)
+ b4 CCF + b5ln(CFF)
+ b7DBH
+ b8DBH2
+ b10HT + b11HT2 + b12PCT + b14ln(PCT)
+ b9ln(DBH)
Thank you
Questions?

34. Colville National Forest
Mean DGp  mean DGp for CRm class = 40-60%

35. Winema National Forest
ST: Mean DGp  mean DGp for CRm class = 40-60%
BT: LP mean CRm= 61, mean CRp= 68