Transcript Document

ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)
Should tree crown ratio be
measured to obtain reliable tree
diameter growth predictions?
by
Laura Leites,
Nicholas Crookston,
Andrew Robinson
An evaluation of the utility of crown ratio
ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)
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
1. 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).
2. We evaluate the effect of using CRm against
using CRp on the diameter growth (DG)
predictions at the tree level.
Objectives
3. We evaluate the effect of using CRm against
using CRp at the plot level through
predictions of basal area increment (BAI).
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.
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
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.
• FVS NI and SO Variants: CR predictions at a
point in time.
NI variant: Hatch (1980) exponential model
ln(CR)  HAB  b1BA  b2 BA  b3 ln( BA)  b4CCF
2
 b6 ln(CCF )  b7 DBH  b8 DBH  b9 ln( DBH )
2
 b10 HT  b11HT  b12 ln( HT )  b13 PCT  b14 ln( PCT )
2
SO variant:
• Small trees use a logistic model:
1
CR 
k
1 e
k  FCR  b0  b1 DBH  b2 Ht  b3 BA  b4 PCCF
 b5 ( HT 40 / Ht )  b6 HT 40  b7 ( BA * PCCF )
 b8 MAI
Large trees use Dixon’s (1985) Weibull based model.
Specify Stand CR distribution:
c  x a 
f ( X ) 
b  b 
( c 1)
e
 ( xa)  c


 b 
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
Data
1. Acquired from the USDA Forest Service,
Pacific Northwest Region's Current Vegetation
Survey (CVS) project.
2. Data collected at the Winema National Forest
(WNF) and the Colville National Forest (CNF)
in 1993-1996.
CNF
WNF
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.
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.
Colville National Forest
Proportion
Species in sample
(%)
WRC
DF
LP
Other
PP
WH
WP
15
29
16
32
2
6
<1
DBH (cm)
Mean
16
23
16
20
39
13
18
SD
(16)
(17)
(8)
(15)
(24)
(11)
(19)
Total Height
(mt)
Mean
11
16
15
17
21
9
13
SD
(8)
(9)
(5)
(10)
(10)
(6)
(12)
CR
Mean
45
45
28
41
43
46
53
SD
(21)
(21)
(17)
(21)
(19)
(22)
(23)
Winema National Forest
Proportion
Species in sample
(%)
DF
2
LP
37
MH
3
Other
24
PP
30
SP
2
WP
<1
DBH (cm)
Mean
41
15
30
28
28
24
21
SD
(34)
(11)
(21)
(24)
(24)
(25)
(22)
Total Height
(mt)
Mean
22
10
15
15
14
13
13
SD
(13)
(6)
(9)
(11)
(10)
(10)
(10)
CR
Mean
47
42
51
44
47
53
46
SD
(22)
(21)
(20)
(21)
(18)
(19)
(20)
Methods
Analysis
Step 1. Evaluation of CR predictions.
RMSE 
 ( xCR p  xCRm )2
n
1
MAD  x CR p  x CRm
n
By species and by CRm classes.
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.
Methods
• The FVS DG at tree-level:
HT growth driven DG
small trees
(ST)
DG
dds prediction
DBH
large trees
(LT)
dds prediction = DG
Methods
FVS dds base model:
ln(dds)  HAB  LOC  b1 cos( ASP) SL 
b2 sin( ASP) SL  b3SL  b4 SL2  b5 EL
2
 b6 EL  b7 (CCF / 100)  b8 ln( DBH )
2
 b9 CR  b10CR  b11 ( BAL / 100)  b12 DBH
2
SO variant incorporates other predictor variables.
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.
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 30year-period.
• All the rest of the variables were the same in both runs.
• FVS was ran using default mode.
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
Step 1. Evaluation of CR predictions.
Observed CR class
< 40%
40% < CR < 60%
> 60%
NI Variant
Hatch (1980)
SO Variant
logistic
SO Variant
Dixon (1985)
MAD
21
10
22
MAD
25
10
18
MAD
42
26
14
RMSE
25
13
26
RMSE
28
13
22
RMSE
44
29
17
Results
Step 1. Evaluation of CR predictions.
NI Variant Hatch
Species (1980) exponential SO Variant logistic
SO Variant Dixon
(1985) Weibull
MAD
RMSE
MAD
RMSE
MAD
RMSE
WRC
19
24
--
--
--
--
DF
16
21
18
21
23
27
LP
14
18
18
22
30
34
MH
--
--
16
18
30
35
Other
23
28
21
25
37
41
PP
16
20
20
23
27
31
SP
--
--
20
24
24
29
WH
19
25
--
--
--
--
WP
18
24
26
28
30
35
Results
Step 2. DGmCR v.s.DGpCR
RMSE ( % of DGpCR )
CR class
NI Variant
SO Variant
ST subset
LT subset
ST subset
0.53 (27%)
0.42 (21%)
1.05 (46%) 1.05 (54%)
40% < CR < 60% 0.50 (21%)
0.43 (19%)
0.77 (24%)
1.26 (45%)
0.82 (29%)
1.14 (28%)
1.41 (37%)
< 40%
> 60%
1.05 (33%)
ST = small trees
LT = large trees
LT subset
Results
Step 2. DGmCR v.s.DGpCR
NI Variant
Species
WRC
WH
DF
LP
Other
PP
WP
MH
SP
ST Subset
N
b0
b1
5174
s
ds
2274
s
s
8731
s
s
3825
s
ds
12222 s
s
293
ds
ds
145
s
ds
LT Subset
N
b0
1687
s
379
ds
6883
s
5699
s
5715
s
812
s
130
s
b1
s
s
s
ds
s
s
ds
SO Variant
ST Subset
LT Subset
N
b0
b1
N
b0
b1
46
3523
2107
3709
8
33
269
s
ds
s
s
ds
s
s
ds
s
ds
s
ds
s
ds
622
8436
7093
7994
214
1182
432
s
s
ds
s
ds
s
ds
ds
ds
ds
ds
ds
ds
ds
Step 3. BAImCR v.s. BAIpCR
Step 3. BAImCR v.s. BAIpCR
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.
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.
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. BundesVersuchsanst. 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.
ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)
Acknowledgements:
• Gary E. Dixon
• Charles R. Hatch
• This study was funded by USFS Grant
04DG11010000037
ln(CR) = HAB + b1BA + b2BA2 + b3ln(BA)
Thank you
Questions?
Colville National Forest
Proportion
Species in sample
(%)
WRC
DF
LP
Other
PP
WH
WP
15
29
16
32
2
6
<1
DBH (cm)
Mean
16
23
16
20
39
13
18
SD
(16)
(17)
(8)
(15)
(24)
(11)
(19)
Total Height
(mt)
Mean
11
16
15
17
21
9
13
SD
(8)
(9)
(5)
(10)
(10)
(6)
(12)
CR
Mean
45
45
28
41
43
46
53
Mean DGp  mean DGp for CRm class = 40-60%
SD
(21)
(21)
(17)
(21)
(19)
(22)
(23)
Winema National Forest
Proportion
Species in sample
(%)
DF
2
LP
37
MH
3
Other
24
PP
30
SP
2
WP
<1
DBH (cm)
Mean
41
15
30
28
28
24
21
SD
(34)
(11)
(21)
(24)
(24)
(25)
(22)
Total Height
(mt)
Mean
22
10
15
15
14
13
13
SD
(13)
(6)
(9)
(11)
(10)
(10)
(10)
CR
Mean
47
42
51
44
47
53
46
SD
(22)
(21)
(20)
(21)
(18)
(19)
(20)
ST: Mean DGp  mean DGp for CRm class = 40-60%
BT: LP mean CRm= 61, mean CRp= 68