SDI-Flex: A new technique for
Developing Treatment
Prescriptions in Uneven-aged
Forests
Wayne D. Shepperd, Ph.D.
U.S. Forest Service
Rocky Mountain Research Station
Some Observations:
z
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Silviculture on federal lands now emphasizes
maintaining desired conditions through time
If the desired condition is to maintain a structurally
diverse forest, then UEA management is required
Current underthinning to reduce fire risk places
forests on an even-aged trajectory
Many silviculturists view UEA as being too
complex
BDQ stocking is not well understood and detailed
guides are not available for all regions or forest
types
Stand Density Index provides an alternative
stocking guide suitable for either even, or unevenaged management
What is SDI?
(A brief review)
Ducey and Larson (2003, WJAF) presented
an excellent technical review of SDI
z Developed by Reineke (1933, J. AG. Res.)
z Long and Daniel (1990, WJAF) presented a
method of assessing growing stock in UEA
stands
z SDI is related to other stocking guides (e.g.
Gingrich curves)
z
SDI is based on Size/Density Relationships
SDI = TPA * (DQ/10)^1.605
Ponderosa Pine
45
4
40
3.5
35
3
30
2.5
LN(QMD)
QMD
Ponderosa Pine
25
20
Max
2
1.5
15
1
10
0.5
5
0
0
0
0
1000
2000
3000
4000
5000
TPA
Data courtesy of Pat Miles, NCRS
2
4
LN(TPA)
6
8
10
Stand Density Index
SDI = TPA * (DQ/10)1.605
When DQ = 10.0 inches
SDI = TPA
Mgmt. Zone = 30-50% of SDIMAX
SDIMAX = MAXBA/0.54542
Relationship of SDI to Gringrich Curves
300
Quadratic
20
18 mean
16
diameter (inches)
14
12 Max SDI = 400
10
9
8
Basal area (sq. ft. per acre)
250
200
Ponderosa Pine
7
6
Average
maximum
density
90%
150
0.6 * 400 = 240
5
80%
70%
60%
Manag
ement
zone
100
50
4
50%
40%
3
30%
0.2*400 = 80
20%
Relative stand density
Relative density = %SDImax
0
0
200
400
600
Trees per acre
800
1000
1200
Even-aged SDI Prescription
z Calculate
existing SDI using:
SDI = TPA * (DQ/10)1.605
z Thin from below until desired %MaxSDI
stocking goal is reached
(e.g. Residual SDI/MaxSDI = .3, .2, etc.)
Calculating SDI in Uneven-aged
Stands
Pipo
BA = 80
SDIMAX = 450
SDIi = TPAi * (DBHi /10)1.605
where i = DBH class
(Long and Daniel, 1990)
13.99 = 4.6*(20/10)1.605
DBH
TPA
SDI
2
4
6
8
10
12
14
16
18
20
49.0
3.70
37.7
8.66
29.0
12.77
22.3
15.59
17.2
17.20
13.2
17.69
10.2
17.50
7.8
16.58
6.0
15.41
4.6
13.99
Total=
139.11
%Max=
31.00
1 – (7.5/24.7) = 0.7
327 * 0.7 = 227.7
20% SDIMax UEA Prescription
(Evenly distributed across dbh classes)
%SDIMAX=
Colorado, State and Private
DBH
TPA
2
327.0
4
82.9
6
35.8
8
26.8
10
15.6
12
12.6
14
8.8
16
4.7
18
2.2
20
0.7
25
0.7
30
0.1
Total =
518.0
20 % of 450 = 90
SDI
24.70
19.05
15.76
18.75
15.60
16.87
15.08
10.02
5.69
2.16
3.17
0.80
147.64
0.20
Target %TPAcut
7.50
0.70
7.50
0.61
7.50
0.52
7.50
0.60
7.50
0.52
7.50
0.56
7.50
0.50
7.50
0.26
7.50
0.00
7.50
0.00
7.50
0.00
7.50
0.00
90
Data courtesy NCRS RPA/FIA TableMaker Program
TPAcut Residual
227.70
99.3
50.26
32.6
18.75
17.0
16.09
10.7
8.10
7.5
7.00
5.6
4.42
4.4
1.23
3.5
0.00
2.2
0.00
0.7
0.00
0.7
0.00
0.1
333.54
184.43
90/12 = 7.50
(Long and Daniel WJAF, 1990)
SDI Guide Curve
(evenly distributed across dbh classes)
PipoTPA by Diameter Class
CO, State and Private
Increasing
%SDImax
changes
Height of line
But not slope
350
300
250
200
150
100
50
0
1.02.9
5.06.9
9.010.9
13.014.9
Courtesy Wayne Shepperd, RMRS
17.018.9
21.028.9
Evenly distributed SDI removal
Too many little trees!
A Solution: SDI-flex!
PipoTPA by Diameter Class
CO, State and Private
Change
the slope
of the
curve as
well as its
height
350
300
250
200
150
100
50
0
1.02.9
5.06.9
9.010.9
13.014.9
17.018.9
21.028.9
Parameters controlling SDI-flex
z Target
SDI = %SDImax desired for
residual stand
z Flex factor = a multiplier that controls the
shape of the target stocking curve by
sequentially reducing the portion of target
SDI assigned to each dbh class
z Seed = a multiplier that increases or
decreases the height of the target curve
without changing it’s shape
SDI-Flex Calculations
SDIFLEX PRESCRIPTION SPREADSHEET - PONDEROSA PINE, COLORADO FRONT RANGE
A
B
MaxSDI =
DBH
C
D
E
F
G
H
I
J
K
L
M
450
Existing
dbhi
Target
Target
Target
Cut
Residual
Residual
Residual
Residual
SDI
FACTOR
SDI
TPA
BAac-1
TPA
TPA
BAac-1
SDI
Cut%
BAac-1
TPA
2
200
4.36
15.11
0.35
7.13
94.42
2.06
105.58
94.42
2.06
7.13
0.53
4
100
8.73
22.98
0.39
7.92
34.49
3.01
65.51
34.49
3.01
7.92
0.66
0.43
8.81
19.99
3.92
40.01
19.99
3.92
8.81
0.67
0.35
=600.39*0.9
6
11.78
26.43
8
40
13.96
27.96
0.48
9.78
14.00
4.89
26.00
14.00
4.89
9.78
0.65
10
20
10.91
20.00
0.53
10.87
10.87
5.93
9.13
10.87
5.93
10.87
0.46
12
30
23.56
40.20
0.59
12.08
9.01
14
40
42.76
68.64
0.66
13.42
7.82
8.36
32.18
7.82
8.36
13.42
0.80
16
30
41.89
63.79
0.73
14.91
7.01
9.79
22.99
7.01
9.79
14.91
0.77
18
4
7.07
10.27
0.81
16.57
4.00
7.07
10.27
0.00
20
2
4.36
6.08
0.90
18.41
6.05
13.20
0.00
2.00
4.36
6.08
0.00
22
1
2.64
3.54
1.00
20.45
5.77
15.23
0.00
1.00
2.64
3.54
0.00
527
172.03
305.00
140.36
215.88
84.88
322.39
204.61
59.11
104.83
Classes
11
0.68
FlexFac
0.9
SDI seed
0.5
10.877.08= (450/11*0.5)*0.53
20.99
9.01
7.08
12.08
0.90
6.45= 1.00*0.9
11.40
0.00
31
0.23
Col L = Min of Cols. D, or F
0.70
Advantages of SDI-flex
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Science based - uses an established stocking
guide and can be crosswalked to EA guides
Can be adjusted to specific tree species and local
growing conditions
Allows total control of the stocking guide curve
A simple spreadsheet program can evaluate a
wide variety of UEA prescriptions to meet today’s
diverse management needs
Can UEA Fuels
Treatments
Work?
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Hayman Fire - Manitou
Exp. Forest
Middle portion of
photos reduced to
60BA with UEA entry,
whole-tree harvest,
slash piled
Fire burned through
1000 acres, did not
crown
For further information:
SDI-flex example spreadsheets are available at:
http://www.fs.fed.us/rm/landscapes/solutions/
or, email:
wshepperd@fs.fed.us
So How’s it work?
Open SDIflex Example.xls