UNIVERSITY OF CALIFORNIA
COLLEGE OF AGRICULTURE
AGRICULTURAL EXPERIMENT STATION
BERKELEY, CALIFORNIA
YIELD, STAND AND VOLUME TABLES
FOR DOUGLAS FIR IN CALIFORNIA
FRANCIS X. SCHUMACHER
BULLETIN 491
APRIL, 1930
UNIVERSITY OF CALIFORNIA PRINTING OFFICE
BERKELEY, CALIFORNIA
1930
YIELD, STAND AND VOLUME TABLES FOR
DOUGLAS FIR IN CALIFORNIA
FEANCIS X. SCHUMACHER!
INTRODUCTION
The United States Forest Service has reecntly completed a study of
the yields of Douglas fir (Pseudotsuga taxifolia Britt.) for even-aged
stands of Oregon and Washington. 2 The work was not extended to
stands south of the Willamette-Umqua divide in Oregon because from
observation it is believed that this line roughly divides the Douglas
fir forest into two types of decided difference in stand characteristics.
But the commercial range of the species on the Pacific slope extends
into California about as far south as Yosemite National Park in the
Sierra and about San Francisco Bay along the coast. To report the
yields of well-stocked, even-aged stands of the species in California is
the object of this bulletin.
That there are significant differences in certain stand character-
istics between the two general regions seems established from the work
presented herein.
GROWTH OF DOUGLAS FIR STANDS IN CALIFORNIA
The growth of the species is shown by tables which state the yield
of even-aged stands over a period of years. Age, timber productive
quality of the area, and stand density are the most important growth-
determining factors of a stand. As there is no satisfactory way of
expressing stand density in absolute terms, normal-yield tables based
on the ideal density which produces maximum volume are presented.
Basic Data
The normal-yield tables for Douglas fir are based on 159 sample
plots scattered through the geographical range of the species in
California.
i Assistant Professor of Forestry and Assistant Forester in the Experiment
Station.
2 McArdle, R. E. Rates of growth of Douglas fir forests. West Coast
Lumberman, 54:90-95, 1928. This article summarizes the results of the study.
The complete work is to be published soon as a bulletin of the United States
Department of Agriculture.
4 University of California — Experiment Station
Plot Selection. — Within even-aged stands plots were established so
as to enclose a comparatively complete crown canopy by excluding the
larger openings which follow failure of reproduction or accident and at
the same time to include within boundaries the area equivalent to that
which seemed to be used by the enclosed timber. Plots were surveyed
with staff compass and chain.
Age Determination. — The age of each plot was determined by
counting the annual rings on cores extracted (with Swedish increment
borers) from near the base of several trees. By the age of the tree is
understood the number of rings on the core plus the necessary cor-
rection for height growth to the point of boring. The age of the
oldest tree was taken as the plot age although the difference between
the ages of the youngest and oldest tree examined was seldom more
than two or three years.
Field Measurements. — Diameter breast high of every tree was
measured with diameter tape and tallied by species and crown class
(dominant, codominant, intermediate, or suppressed).
The heights of fifteen to twenty-five trees were measured with the
Forest Service hypsometer, from horizontal distances measured with
the Leitz Fardi Range Finder of 20-centimeter base. Heights were
plotted over diameter on cross-section paper in the field, the number
of measurements necessary being judged at the time by the range of
diameters present and their dispersion around the free-hand curve.
A short description of physiographic features completed the field
work on each plot.
Office Computations. — The computational work necessary for each
plot is evident from following paragraphs. The yield tables were
constructed by correlating dependent growth variables with age and
site quality by the method described by Bruce and Reineke, 3 and the
stand tables are based on CharlierV method of calculating theoretical
frequencies.
Normal Yield Tables
Tables 1 to 11 and figures 1 to 11 indicate the growth of Douglas fir
in fully-stocked stands in California, for age and site index. 5 Site
index is herein defined as the height that the average dominant
Douglas fir will attain, or has attained at 50 years of age. Average
'■> Druce, D., and L. H. Reineke. Multiple curvilinear correlation in forest
investigative work. Unpublished contribution of the United States Forest
Service. 1927.
< Charlier, C. V. L. Die Grundzuge der mathematischen Statistik. p. 3-125.
Lutke und Wulff, Hamburg. 1920.
: - Before constructing these tables the sample plot data were compared to
the yield tables for Douglas fir in Oregon and Washington. See p. 27.
Bul, 491] Yield, Stand, and Volume Tables for Douglas Fir
TABLE l
Height of the Average Dominant Tree*
Age,
Site index — height of average dominant at 50 years
years
60
80
100
120
140
30
feet
• 39
feet
54
feet
67
feet
81
feet
95
40
50
68
85
102
120
50
60
80
100
120
140
60
68
89
112
135
156
70
74
98
122
147
170
80
79
104
131
158
182
90
83
110
138
166
192
100
86
114
146
173
201
110
89
118
152
179
209
120
92
122
156
185
216
130
96
125
159
189
220
140
98
128
162
193
224
150
99
130
164
196
228
160
100
132
165
198
232
* The height from average ground level to tip of the dominant tree of average basal area for the
dominant class.
SO 60 70 80
^20 /JO /-90 /so Too
Fig. 1. — Height of the average dominant tree for age and site index. These
curves were used in site classification of the plots.
University of California — Experiment Station
TABLE 2
Height of Average Tree*
Age,
Site index — height of average dominant at 50 years
years
60
80
100
120
140
30
feet
feet
41
feet
58
feet
72 *
feet
85
40
58
77
94
110
50
47
71
92
110
131
60
57
81
104
127
148
70
65
89
114
140
163
80
70
96
123
152
176
90
75
102
132
160
187
100
78
107
139
168
196
110
82
112
145
176
120
85
117
149
180
130
88
121
154
184
140
90
124
157
188
150
91
126
159
192
160
92
127
161
194
The height from average ground level to tip of the tree of average basal area.
/30 /-K) /5Q
Age /r? c/ears
Fig- 2. — Height of the average tree for age and site index.
Bul. 491] Yield, Stand, and Volume Tables for Douglas Fir
TABLE 3
Number of Trees to the Acre*
Site index — height of average dominant at 50 years
Age,
60
80
100
120
140
years
Number of trees to the acre
30
1060
672
485
394
40
780
497
364
297
50
1033
601
386
278
230
60
790
475
302
220
182
70
643
382
241
176
147
80
530
313
200
148
121
90
445
260
168
125
100
100
378
225
143
104
85
110
324
193
122
91
120
282
170
107
80
130
254
152
95
70
140
230
138
87
62
150
212
124
79
58
160
198
113
75
54
The number of trees that have reached a height of at least 4.5 feet (breast height).
Fig. 3. — Number of trees to the acre for age and site index.
University of California — Experiment Station
TABLE 4
Basal, Area to the Acre*
Age,
Site index— height of average dominant at 50 years
years
60
80
100
120
140
30
sq.ft.
sq. ft.
198
sq. ft.
217
sq. ft.
230
sq.ft.
243
40
223
243
267
285
50
205
237
264
290
305
60
214
249
281
305
319
70
222
260
295
316
328
80
228
271
305
323
334
90
233
280
313
329
339
100
238
288
318
333
342
110
242
294
322
336
120
245
298
326
338
130
248
302
328
340
140
250
305
330
341
150
251
308
331
342
160
252
309
332
343
The sum of the cross-sectional areas at breast height, in square feet.
60 70 SO 90
Age /n years
Fig. 4. — Growth in basal area to the I
/20 J30 1<K)
for age and site index.
Bul. 491] Yield, Stand, and Volume Tables for Douglas Fir
TABLE 5
Average Diameter, Breast 1 High*
Age,
Site index — height of average dominant at 50 years
years
60
80
100
120
140
inches
inches
inches
inches
inches
30
5.9
7.7
9.3
10 6
40
7.2
9.5
11.6
13.3
50
6.0
8.5
11 2
13 8
15 6
60
7
1
9.8
13.1
15.9
17.9
70
8
11.2
15
18.1
20.3
80
8
9
12 6
16.7
20
22.5
90
9
8
14.0
18 5
22
25
100
10
7
15.3
20.2
24.2
27
110
11
7
16 7
22.0
26.0
120
12
6
17 9
23.6
27.2
130
13
4
19 1
25.2
29.8
140
14
1
20 2
26.3
31.8
150
14
7
21 3
27.7
32.9
160
15
3
22.4
28.5
34 1
The diameter in inches of the tree of average basal
Fig. 5. — Average diameter breast high for age and site index — the
diameter of the circle of average basal area.
10
University of California — Experiment Station
TABLE 6
Mean Diameter, Breast High*
Age,
Site index — height of average dominant at 50 years
years
60
80
100
120
140
inches
inches
inches
inches
inches
30
5
6 7
8.4
9 6
40
6 3
8.5
10
7
12 2
50
5 1
7.6
10 2
12
8
14 5
60
6.1
8.9
12
14
8
16.7
70
7.0
10.3
13.8
16
9
19.0
80
8.0
11.6
15.7
18
9
21.3
90
8.9
12 9
17.3
20
9
23.7
100
9.8
14 2
18
22
9
25 6
110
107
15.6
20.6
24
8
120
11.6
16.8
22
26
6
130
12 4
17.9
23.4
28
4
140
13.0
19.0
24.8
30
2
150
13 6
20.1
26.2
31
9
160
14 .2
21.2
27.6
33
5
* The mean of all diameters on an average acre.
s
£
v.
s
&
>
y y
1
/,
>
s
1"
A
^
«5j «?
s>
90' J ^
/O 20 30 <K> 50 CO 70 60 90 /OO //O /20 /30 tfO (SO /60
Age /n years
Fig. 6. — Mean diameter breast high for age and site index — the
average of all diameters in the stand.
Bul, 491] Yield, Stand, and Volume Tables for Douglas Fir 11
TABLE 7
Cubic Volume to the Acre*
Age,
Site index — height of average dominant at 50 years
years
60
80
100
120
140
cu. ft.
cu.ft.
cu. ft.
cu.ft.
cu. ft.
30
3,300
4,900
6,500
7,700
40
2,300
5,000
7,200
9,350
10,900
50
3,650
6,400
9,000
11,700
13,100
60
4,800
7,600
10,500
13,200
14,800
70
5,700
8,550
11,750
14,500
16,200
80
6,400
9,350
12,750
15,500
17,400
90
6,950
10,000
13,550
16,400
18,400
100
7,400
10,500
14,300
17,200
19,200
110
7,700
11,000
14,900
17,950
120
7,950
8,150
11,400
11,700
15,400
15,950
18,600
19,200
130
140
8,350
8,500
12,000
12,300
16,400
16,800
19,800
20,300
150
160
8,600
12,500
17,200
20,800
* The cubic volume of the entire stem of all trees from ground to tip but without limbs or bark.
The volume table used is given following p. 22.
Fig. 7. — Growth in cubic volume to the acre for age and site index.
12
University of California — Experiment Station
TABLE 8
Mean Annual. Growth in Cubic Volume to the Acre*
Age,
Site index — height of average dominant at 50 years
years
60
80
100
120
140
30
cu. ft.
cu. ft.
110
cu. ft.
163
cu.ft.
217
cu.ft.
257
40
58
125
180
234
270
50
73
128
180
234
262
60
80
127
175
220
247
70
82
122
168
207
232
80
80
117
159
194
218
90
77
110
151
182
205
100
74
105
143
172
192
110
70
100
135
163
120
66
95
128
155
130
63
90
123
m
140
60
86
117
141
150
57
82
112
135
160
54
78
107
130
The cubic volume on the acre divided by the age
60 70 80 90
Age tn years
/OO //O /20 /30 MO /SO /GO
Fig. 8. — Mean annual growth in cubic volume to the acre for age and site index.
Bui* 491] Yield, Stand, and Volume Tables for Douglas Fir 13
TABLE 9
Number of Trees Eight Inches and Over,, to the Acre
Site index — height of average dominant at 50 years
Age,
60
80
100
120
140
years
Number of trees eight inches and over
30
185
265
258
252
40
252
278
251
230
50
191
279
258
221
198
60
250
277
230
190
170
70
266
260
203
165
143
80
269
234
179
144
118
90
260
210
158
124
98
100
243
190
139
195
85
110
225
174
122
SI
120
210
159
106
80
130
199
146
94
70
140
187
135
85
63
150
178
124
79
58
160
167
114
75
54
O JO 20 30 <K> 50 CO 70 80 90 /OO //O /20 /30 /fO /SO /60
Age /n c/eors
Fig. 9. — Number of merchantable trees to the acre for age and site index.
14
University of California — Experiment Station
TABLE 10
Volume Board Measure to the Acre*
Site index — height of average dominant at 50 years
Age,
years
60
80
100
120
140
bd. ft.
bd. ft.
bd. ft.
bd. ft.
bd. ft.
30
7,760
17,050
27,900
37,000
40
16,000
31,700
47,700
59,400
50
8,940
25,200
45,000
64,800
76,200
60
15,060
34,300
56,900
77,400
90,600
70
21,000
42,700
67,300
89,000
103,500
80
26,500
49,650
76,200
98,400
114,800
90
31,400
55,700
83,800
107,400
124,100
100
35,900
60,600
91,000
115,300
131,500
110
39,400
42,200
65,650
68,200
73,200
76,400
97,600
102,700
122,200
120
127,600
130
44,600
46,750
107,800
133 , 700
140
111,800
139,000
150
48,300
79,700
115,700
142,900
160
49,600
82,400
119,000
146,600
* The board foot contents of the trees by the International log rule of J^-inch kerf between a stump
of one foot and a top diameter inside bark of 5 inches scaled in 16-foot logs with 0.3-foot trimming allot-
ment to each. Gross volumes are presented, no account being taken of cull factors. The volume table
used is given following p. 22.
MQ/QOL
S
HO'
I30.0OG
/
/20,OOC
,/
/
/
/OQOOO
/
9QOO0
80.000
70,00C
/
/
eopoo
//
/
/
5O.0OC
/
It
■9O.000
30.000
20,000
/QOOO
O
LL
' .
f /
/
'
r
/
■20<Q
•oo- §
!
C 10 20 30 fO 30 00^ 70 80 90 /OO I/O 120 130 1*0 ISO 160
Age. //? years
Fig. 10. — Growth in volume board measure to the acre for age and site index.
Bul. 491] Yield, Stand, and Volume Tables for Douglas Fir 15
TABLE ll
Mean Annual Growth m Board Feet to the Acre*
Age,
Site index— height of average dominant at 50 years
years
60
80
100
120
140
30
bd. ft.
bd. ft.
259
bd. ft.
568
bd. ft.
930
bd. ft.
1,234
40
400
793
1,193
1,485
50
179
504
900
1,296
1,525
60
251
565
948
1,290
1,510
70
297
610
962
1,270
1,480
80
331
620
952
1,230
1,436
90
349
619
931
1,193
1,380
100
359
606
910
1,153
1,315
110
359
597
888
1,112
120
352
568
859
1,065
130
343
553
830
1,028
140
334
546
799
993
150
325
531
771
953
160
310
515
744
916
The board foot volume on the acre divided by the age.
Fig. 11. — Mean annual growth in volume board measure to the acre
for age and site index.
16
University of California — Experiment Station
height of the dominant, or of the dominant and codominant stand is
generally accepted as the most accurate and readily measurable factor
of timber-productive quality of an area, because it bears a very close
relationship to volume production within the limits of normal stocking.
Although the yield tables for Douglas fir in Oregon and Washing-
ton define site index as the height of the average dominant and
codominant at 100 years, the height of the average dominant at 50
years is used here in order to conform with site index as defined in
other California yield studies. 6 ' 7 Height curves used in determining
the site-index of each plot are shown in figure 1.
Check of Basic Data Against the Yield Tables
Table 12 shows the check of the values of the 159 sample plots
against the yield tables interpolated to nearest year of age and nearest
foot of site index.
TABLE 12
Check of Basic Data Against 1 Yield Tables
Basal area
All trees per acre
Average d. b. h
Volume in cubic feet
Volume in board measure.
Aggregate
difference,
per cent*
-0.0
-0.2
+0 9
-0.0
+0.8
Mean
difference,
per cent**
Standard
error of
estimate,
per centf
16 4
27.0
15 .7
16 3
20 4
Standard
error of yield
table value,
per centj
±1 30
±2 14
±1.24
±1.29
±1.67
* The aggregate difference is the sum of the plot values expressed as a percentage difference from
the sum of corresponding tabular values.
** The mean difference is the mean of the per cent deviations of the plot values from corresponding
tabular values.
t Standard error of estimate (<r es <) = — in which x = deviation of each plot from its tabular value
N
in per cent, 2=the sum, and N = number of plots.
% Standard error of yield table value is the same as that ordinarily understood as standard error
of the mean, the mean here being tabular value for age and site index. It is expressed thus: a™ =— % =L .
Stand Tables
Although yield tables are basic to the solution of many forest
management problems, they are not complete without stand tables as
problems of valuation and utilization require knowledge of such stem
distribution.
Stand ta bles for Douglas fir are given in table 13. 8
6 Schumacher, Francis X. Yield, stand and volume tables for white fir in the
California pine region. California Agr. Exp. Sta. Bui. 407:1-26. 1926.
7 Schumacher, Francis X. Yield, stand and volume tables for red fir in Cali-
fornia. California Agr. Exp. Sta. Bui. 456:1-32, 1928.
8 The analysis of stem distribution and construction of stand tables is
explained on pp. 32.
Buu 491] Yield, Stand, and Volume Tables for Douglas Fir 17
TABLE 13
Normal Stand Table, for Douglas Fir Including all Trees
Age of stand in years
D. b. h. class,
inches
30
40
50
60
70
80
90
100
110
120
130
140
150
160
Number of trees by diameter classes
Site index 60 feet at 5C
years
0.0- 2.0
2 0-40
173
233
251
184
107
52
22
8
97
135
177
159
110
65
32
11
2
58
90
127
132
105
72
36
16
6
28
60
89
102
91
70
46
27
16
1
15
36
62
79
80
67
49
31
24
2
13
22
44
59
65
60
45
33
32
5
8
14
31
43
52
51
45
36
36
9
7
9
21
33
41
43
40
34
40
12
2
2
7
16
26
33
37
36
32
42
16
4
2
5
12
21
27
32
33
30
44
19
5
2
4
9
17
23
28
29
27
43
21
6
1
3
4.0- 6.0
8
6.0- 8.0
15
8.0-10.0
21
10.0-12.0
12.0-14.0
25
27
14.0-16.0
26
16.0-20
42
20.0-24.0
24 0-28 . .
23
7
28.0-32.0
Total
1030
788
642
530
445
378
325
282
251
230
210
198
Site index 80 feet at 5C
years
0.0- 2.0
189
240
259
183
105
53
21
5
72
134
175
157
122
69
36
14
4
42
71
104
119
101
77
48
26
12
19
39
67
85
85
70
52
33
23
2
10
21
40
55
65
60
50
37
37
7
6
13
26
37
46
48
43
37
43
13
2
4
6
15
25
32
36
37
32
47
22
5
4
5
9
16
23
28
31
29
46
25
8
1
2.0- 4.0
3
6
11
17
21
24
25
43
28
13
3
2
4
7
13
16
19
21
39
29
15
6
1
1
3
5
9
12
15
17
35
28
18
8
1
1
2
4
6
10
12
14
30
27
19
10
3
4.0- 6.0
6 0-80
1
3
5
7
9
11
26
25
19
12
5
1
2
8.0-10.0
10.0-12.0
4
6
12 0-14
g
14.0-16.0
9
16.0-20.0
23
20 0-24
23
24 0-28
19
28 0-32
12
32 0-36
6
36 0-40
1
Total
1055
783
600
475
382
314
261
225
194
172
152
138
123
114
Site index 100 feet at 50 years
0.0- 2.0
65
101
139
136
106
65
36
17
5
18
47
73
92
88
75
51
30
19
2
10
20
41
56
64
61
51
37
37
7
3
10
22
33
41
45
43
37
49
16
3
2
5
11
20
27
32
34
31
49
26
7
1
1
3
6
11
17
21
25
26
45
30
14
3
2.0- 4.0
1
3
6
11
14
18
20
39
31
18
6
1
1
2
4
7
10
12
14
32
28
20
10
3
1
1
2
4
7
9
10
26
25
20
12
5
1
4.0- 6.0
1
2
3
4
6
8
19
20
19
14
8
3
6.0- 8.0
1
2
3
5
6
15
18
17
13
9
5
1
2
2
3
5
12
15
15
13
10
5
3
8 0-10.0
1
2
3
4
10
13
14
12
9
7
3
1
1
10.0-12.0
2
12.0-14.0
2
14.0-16.0
3
16 0-20.0
9
20 0-24.0
11
24.0-28.0
28 0-32
12
12
32 0-36
10
7
4
2
36 0-40
40 0-44
44.0-48.0
48 0-52.0
Total
670
495
384
302
245
202
168
143
123
107
95
86
79
75
18 University of California — Experiment Station
Table 13 — (Concluded)
Age of stand in years
D. b. h. class,
inches
30
40
50
60
70
80
90
100
110
120
130
140
150
160
Number of trees by diameter classes
Site index 1W feet at 50 years
0-20
26
51
77
92
86
67
45
26
16
14
20
39
52
60
56
47
35
33
7
2
8
19
29
37
41
40
35
48
18
3
1
4
8
16
21
26
29
28
48
28
10
1
2 0-40
1
4
8
13
17
20
21
40
31
16
5
1
2
4
7
10
13
15
32
28
21
10
3
1
1
2
4
6
8
10
24
24
20
14
6
2
4 0- 6.0
1
1
2
4
6
7
17
20
19
14
9
4
1
1
2
3
4
5
13
16
16
14
10
5
3
1
1
2
3
3
9
13
14
13
11
7
3
1
6 0- 8.0
8 0-10
10 0-12.0
1
2
3
7
10
12
12
10
8
5
2
1
2
6
8
10
10
10
8
5
3
1
1
1
1
5
6
8
8
8
8
6
4
2
1
12.0-14.0
14.0-16.0
1
1
16.0-20.0
4
20 0-24
5
24 0-28
7
28.0-32.0
32 0-36
8
g
36.0-40.0
40 0-44
7
6
44.0-18.0
48 0-52
4
2
52 0-56
1
105
72
Total
486
363
280
220
177
146
122
92
81
65
59
54
Site index 140 feet at 50 years
0.0- 2.0
12
26
48
63
69
62
49
34
29
3
10
10
22
33
42
45
43
37
44
13
1
2
3
8
16
22
28
31
30
49
29
10
1
2.0- 4.0
1
4
7
13
17
20
23
44
31
18
6
1
2
4
7
10
12
14
32
29
21
11
3
1
4.0- 6.0
6.0- 8.0
1
2
3
6
8
9
23
24
21
14
7
3
1
1
2
3
5
6
16
18
18
15
10
5
1
1
1
2
3
4
11
14
15
13
11
7
3
1
8.0-10.0
,
10.0-12.0
12.0-14.0
14.0-16.0
16.0-20.0
20.0-24.0
24.0-28.0
28.0-32.0
32.0-36.0
36.0-40.0
40.0-44.0
44.0-48.0
48.0-52.0
Total
395
300
229
183
147
121
101
86
Bul, 491] Yield, Stand, and Volume Tables for Douglas Fir
19
VOLUME TABLES
Preliminary to the study of yields in cubic and board feet, volume
tables in these units were prepared. 9 The basic tree data of the tables
presented are from measurements taken by the Division of Forestry
from eight, previously measured, even-aged sample plots in Mendo-
cino and Trinity counties. The ages of the trees measured were from
33 to 111 years.
Table 14 is the volume in cubic feet, and states the entire volume
of the stem, including stump and top, but without bark. It was pre-
pared by correlating cylindrical form factor with diameter, height
and site index. As no significant relationship was discovered with site
index, the table may be used for any site class.
TABLE 16
Check of Basic Tree Data Against Volume Tables
Aggregate
difference,
per cent
Mean
difference,
per cent
Standard
error of
estimate,
per cent
Standard
error of volume
table value,
per cent
Cubic foot volume
-0
-0.7
-0.7
-0.4
11.7
12.1
±0.71
±0.81
Table 15 is the volume in board measure. It includes the board-
foot contents of the trees between a one-foot stump and top diameter
inside bark of five inches. It was prepared by correlating the number
of board feet to a cubic foot with the diameter and height of the trees.
Table 16 shows the check of the basic tree data with the volume
tables.
DISCUSSION
The generic name of Douglas fir, Pseudotsuga, implies that its
common name is a misnomer in that the tree is not a true fir of the
Abies genus, such as red and white fir.
One of the outstanding differences in characteristic growth between
Douglas fir and the California true firs already studied 10 is the fact
that the crown of the former becomes rather widespread when not
confined by neighboring trees. Now diameter breast high bears a
9 The check of the volumes of the basic tree data against the volume tables
for immature Douglas fir in Oregon and Washington is explained on pp. 35,
io See Bul. 407 and Bul. 456 previously referred to.
20
University of California — Experiment Station
noticeably constant ratio to crown width in any one timber species;
hence the net result of widespread Douglas fir crowns with their asso-
ciated greater trunk diameters at breast-height — when the stand is
deficient in number of trees — is the tendency to form complete crown
canopies and therefore to approach normal stocking by basal area.
Figure 12 indicates this within the limits of the data presented. The
regression of average diameter breast high on number of tree is
Average d.b.h. in per cent of the tabular value
^
1,000,000
Number of trees in per cent
of the tabular value
Now basal area in square feet is .00545 times the number of trees
times the square of average diameter breast high in inches. But
30 -90 SO 60 70 GO 90 JOO //O /SO /30 tfO /50 /CO /70 /80 /SO 200
A/umber of trees on p/ofs /n per cenf of c//e/d tob/e.
Fig. 12. — Relation between average diameter and number of trees.
within a given site-age class by the above equation, the number of trees
times the square of the average diameter is constant ; that is, basal area
tends to be independent of the number of trees as long as there are at
least sufficient trees to allow a complete crown canopy.
The true firs, on the other hand, have characteristically narrow
crowns even when growing in the open; hence they have not the
ability to form complete crown canopies when deficient in number of
trees. Deficiency in number of trees within a site-age class results
in deficiency in basal area, because of the narrower crowns and the
crown diameter— diameter breast high ratio. Therefore, average
diameter is proportional to the number of trees and not to the square
Bul. 491] Yield, Stand, and Volume Tables for Douglas Fir
21
L
•^Z5C
t
§ 20C
Si
Co//fom/a -x
/^Oregon drd
Wos/i/ng/on
^/ou
^6
<^0 ^0 6<? ao /tfO /.a? /w /<^?
Age /n years
/ZOO
/ooc
a)
S 60C
^ 50C
^300
\
\^rOreana nns/
hSas/7/rafnr,
Co/zforn/'o
^
^ ao
\ 6C
I
20 40 60 80 /0O
Age //? yeans
/20 W /60
Fig. 13. — Comparison of California stands by basal area and by number of
trees with those of Oregon and Washington for site index 140' feet — height of
the average dominant and codominant tree at 100 years.
22 University of California — Experiment Station
root of the number; while the effect on basal area of increasing the
number of trees through normality to an overstocked condition is that
it rises to a maximum and then falls off. 11
The differences in growth of Douglas fir between the central and
southern parts of its range are evident from figure 13 which shows
the comparison of yield values in basal area and in number of trees
with age for average site class. One must infer that the stand in
California breaks up earlier in life than it does farther north for the
following reasons :
(1) It has fewer trees to the acre throughout and these decrease
at a greater rate.
(2) It grows faster in basal area when young, but after about 100
years this growth practically stops though in the north it is still
vigorous.
Such differences are not unknown in other species which have a
wide latitudinal range. In taking part in a recent discussion as to
the relative merits of timber producing regions in the United States,
Zon 12 compares the yield of two Russian species — Scotch pine and
birch — in northern and southern provinces of that country and notes
the same tendencies.
11 See figures 6 and 7, Bui. 456.
12 Zon, E, Forestry versus climate. Jour. Forestry. 26:711-713. 1928.
Douglas I
Diameter
breast
height,
inches
Basis, No
of trees...
Th<
Diameter
breast height,
inches
6
7
8
9 :
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39 ,
40
41
42
43
44 1
Basis, number of trees
70
80
10
20
30
40
49
59
70
84
97
111
126
140
157
174
190
206
224
240
261
277
296
316
335
355
374
396
415
437
457
480
502
525
546
570
593
617
640
680
87
107
124
142
160
182
203
226
250
273
299
323
350
378
405
334
463
492
526
553
583
613
642
684
707
738
770
810
836
872
910
945
985
20
115
140
162
189
214
240
268
298
320
348
375
420
454
480
523
560
598
634
670
715
754
792
830
878
912
955
997
1030
1080
1120
1180
1210
1270
29
33
50
73
97
120
144
170
198
225
254
285
317
350
384
418
452
490
530
573
617
666
700
741
792
833
880
928
975
1020
1070
1110
1180
1220
1280
1340
1390
1450
1500
50
100
60
84
112
138
165
193
223
256
291
328
365
403
445
482
525
573
617
664
705
760
815
910
967
1020
1080
1130
1190
1250
1300
1380
1420
1490
1550
1600
1680
1720
36
Ag(
tr_.
Stump height, 1 foot.
Trees scaled in 16-foot logs with 0.3-foot trimming allowance to 5 i
Basis, 215 trees, measured by the Division of Forestry, 1927, in ev
Heavy lines in the tables show limits of basic data.
22 University of California — Experiment Station
root of the number; while the effect on basal area of increasing the
number of trees through normality to an overstocked condition is that
it rises to a maximum and then falls off. 11
The differences in growth of Douglas fir between the central and
southern parts of its range are evident from figure 13 which shows
the comparison of yield values in basal area and in number of trees
with age for average site class. One must infer that the stand in
California breaks up earlier in life than it does farther north for the
following reasons :
(1) It has fewer trees to the acre throughout and these decrease
at a greater rate.
(2) It grows faster in basal area when young, but after about 100
years this growth practically stops though in the north it is still
vigorous.
Such differences are not unknown in other species which have a
wide latitudinal range. In taking part in a recent discussion as to
the relative merits of timber producing regions in the United States,
Zon 12 compares the yield of two Russian species — Scotch pine and
birch — in northern and southern provinces of that country and notes
the same tendencies.
ii See figures 6 and 7, Bui. 456.
12 Zon, R. Forestry versus climate. Jour. Forestry. 26:711-713. 1928.
TABLE 14— Douolas Pra— Volume in Cubic Feet
Tola, hri.ht i„ ,..t
s
-l-l-l-l "
80
90
- | 1, | ,29
,80
,40 | ,60 | ,80 | 170 | ,80 | ,90
200
n"m-
.'»"
15 9
63.2
81.8
8 09
30.0
69 5
76 3
83.1
900
108
123
21
30 3
68.7
75.8
128
6S.7
148
158
88.3
98.1
,08
118
127
,70
26 1
10
27.9
55.5
m
180
13 9
68
108
130
101
81 5
138
150
202
2,9
231
247
,86
29,
90 8
,97
21,
326
36,
510
580
35
8.66
10.7
180
36.1
\Z
1 29
2
-
:;;
11
11 30
22
29 1
553
69.1
66 8
81 6
86.7
90 8
17 4
200
29 6
24
30.9
161
169
171
179
187
200
, 4
31.9
36.10
160
168
176
182
200
208
214
223
,3
I
62
66
61
65
70
79
84
89
3
3
2
3
6
160
,70
\
26
197
205
213
221
232
242
2M
261
I
»
239
260
271
160
186
218
230
240
324
338
318
179
236
246
260
270
283
349
361
202
267
320
333
319
361
32
91 8
104
109
120
-.:
Jlu
343
300
377
1
38
328
346
359
375
390
200
349
385
380
307
413
3O0
310
370
390
424
Unsis, No.
2
.7
19
20
„
50
36
,3
.6
u
•
„
4
9
267
TABLE 15
DovauiS Fir-Volume in Board Feet
Total hoight in Tort
br ^B"'
00
70
.
J»oJj»J_™Jjlo| "0 I ,40 1 ,50 1 160 1 170 1 ,80 | ,90 1 200
Ba«i«,
Volume in board feet
;
4 :
17
"
Jl_
47
34
62
::
■
■
:
107
»
126
,:
8
32
42
50
60
— !il_
79
91
100
113
,24
139
160
161
175
10
»
30
44
01
73
95
no
125
140
152
,67
185
200
216
230
19
10
40
58
81
07
1,2
128
143
162
,8,
198
2,5
' 238
254
271
295
21
59
115
M
!«
187
m
200
220
287
260
2
' 332
391
m
12
87
u
13
Si"
162
,98
223
259
290
Hir
306
Z
366
427
Z
600
570
"
15
97
142
189
225
258
294
330
367
106
118
483
526
570
602
626
16
111
160
214
254
29,
332
370
415
410
500
543
595
642
692
735
7
17
140
103
268
285
"
«6
m
483
515
604
680
708
z
z
5
10
157
128
291
350
403
458
617
572
634
605
751
8,7
883
950
,000
8
20
171
250
320
384
445
805
559
628
700
788
827
900
075
1010
1110
21
190
273
348
418
482
550
613
690
764
817
900
080
1070
1140
1210
,
22
209
299
375
452
526
600
662
750
836
007
978
,070
1150
1230
1300
s
23
224
323
420
i-iii
573
656
718
812
900
985
1080
1210
1320
1410
5
21
240
350
454
_530_
617
705
774
880
075
,060
1140
,240
1310
1420
1510
8
25
261
>78
480
573
664
735
837
950
,060
1,10
,230
,320
1150
1530
1610
Z
2
2
666
70S
1210
1400
1510
1510
1630
!™
;™
27
■...7
051
inv,
ILW
2
28
310
463
598
700
815
918
1010
1150
1270
1390
1500
1620
1870
2000
„
29
335
482
634
741
860
078
1070
1210
1340
1470
1800
1720
1880
1000
2100
30
355
626
670
702
010
1040
1140
1300
1430
1560
1700
1830
1990
2,00
2200
31
374
553
715
833
967
1090
1200
1380
1510
1650
1800
1030
2000
3230
2380
„
32
415
613
792
2
z
un
1350
1M0
1590
irni
,<«]
2300
16 3 »
2»
,
31
437
642
830
975
1130
1280
1100
1000
1760
1910
2100
2160
2130
26,0
2780
36
457
684
878
1020
1,90
1340
1500
1690
1850
2040
2200
2380
2680
2740
2900
„
,070
37
502
738
955
1110
,300
1480
1620
1830
2000
2230
MOO
2600
2800
3000
3200
„
38
525
770
097
,180
,380
1530
1700
1910
2100
2320
2530
2710
2930
3160
3310
39
546
810
1939
1220
,420
1600
1760
2000
2200
2430
2640
2830
3060
3190
3400
o
40
570
836
1080
,280
,490
1680
1890
2090
2300
2550
1730
2020
3200
3420
3630
n
11
593
872
1120
1340
,550
1730
1920
2180
2390
2640
2880
3080
3330
3850
3760
42
617
910
1180
1390
1600
1800
2000
2240
2490
1710
<
3200
3180
j;i«i
3920
"
640
945
1210
1450
1680
1890
2090
2310
1580
2830
310O
3340
3600
3810
4050
14
m
,,:,
1170
1500
1720
1950
2170
2440
2680
2950
3830
3180
3760
3980
1
B„i.. number ol tree,
1
20
19
50
36 j 33 ,6
"
1
11 4
•
■1 •
o
215
■ [i.trri,,,!,.,,,!,! rulf i»,-mrli k
TABLE 15
22 i IB — Volume in Board Feet
rot
Total height
in feet
nu
110
120
130
140
150
160
170
180
190
200
Basis,
Number
it ]
1
of trees
Volume in board feet
sou
30
34
39
45
52
58
66
73
79
87
5
the
47
53
62
69
77
86
96
107
117
126
16
wit
68
79
110
91
125
100
140
113
152
124
167
139
185
150
200
161
216
175
230
10
CaJ
95
19
fol]
128
143
162
181
198
215
* 238
254
274
295
24
155
177
200
220
240
260
286
309
332
353
24
at i
187
220
259
294
212
238
279
261
306
354
287
338
390
448
312
366
427
483
340
400
460
526
368
430
500
570
394
454
535
602
421
493
570
626
14
250
290
330
14
320
367
13
yea
406
11
vigi
332
370
415
460
500
543
595
642
692
735
7
373
415
415
461
463
518
515
575
564
613
680
665
740
718
798
778
860
824
915
5
wid
627
10
458
517
572
634
695
751
817
883
950
1000
8
the
Zon
birc
505
559
628
700
768
827
900
975
1040
1110
3
550
613
690
764
817
900
980
1070
1140
1210
6
600
662
750
836
907
978
1070
1150
1230
1300
5
the
656
705
718
774
812
880
900
975
985
1060
1080
1150
1240
1240
1340
1320
1420
1410
1520
5
i
1140
8
l:
735
837
950
1060
1140
1230
1320
1450
1530
1640
807
890
1010
1120
1210
1300
1310
1400
1410
1510
1540
1630
1640
1770
1750
1880
3
867
951
1080
1200
2
918
1010
1150
1270
1390
1500
1620
1760
1870
2000
976
1070
1210
1340
1470
1600
1720
1880
2000
2100
1040
1140
1300
1430
1560
1700
1830
1990
2100
2200
1090
1160
1210
1200
1270
1350
1380
1440
1510
1510
1590
1690
1650
1740
1800
1900
1930
2090
2220
2380
2500
2380
2500
2620
2030
2200
2300
1
1850
2000
2150
1280
1400
1600
1750
1920
2100
2260
2430
2610
2780
1340
1500
1690
1850
2040
2200
2380
2580
2740
2900
1400
1560
1760
1920
2130
2300
2500
2680
2890
3040
1
1480
1620
1830
2000
2230
2400
2600
2800
3000
3200
1530
1700
1910
2100
2320
2530
2720
2930
3160
3340
'
1600
1790
2000
2200
2430
2640
2830
3060
3290
3490
,
1680
1890
2090
2300
2550
2730
2920
3200
3420
3630
1730
1920
2180
2390
2640
2880
3080
3330
3850
3760
1800
2000
2240
2490
2720
3000
3200
3480
3700
3920
1890
2090
2310
2580
2830
3100
3340
3600
3810
4050
i
1950
2170
2440
2690
2950
3330
3480
3750
3980
4200
1
i 33
16
11
9
11
4
2
215
ach< i d. i. b. in top by International rule (H-inch kerf).
m-aged stands in Mendocino and Trinity Counties.
APPENDIX
Bul. 491] Yield, Stand, and Volume Tables for Douglas Fir
25
YIELD AND STAND TABLES
Basic Data
The sample plots on which the yield and stand tables are based
were measured by the Division of Forestry in 1927. Out of the 175
plots originally measured, 16 were discarded (see table 20). The 159
actually used are from the following- watersheds given in table 17.
TABLE 17
Distribution of Plots by Principal, Watersheds
Region and watershed
Number
of plots
Coast Range:
3
3
2
5
Big River
Eel River
Van Duzen River
3
38
6
Mad River
12
23
Trinity River
38
Klamath River
Sierra Nevada Mountains:
5
14
Yuba River
Feather River
5
2
Total
159
The composition of the plots by basal areas of the various species
included is shown in table 18.
TABLE 18
Composition op Basal Area of the Plots Used
Species
Douglas fir
Western yellow pine
Oak, laurel and madrone
Redwood
White fir
Sugar pine
Incense cedar
Grand fir
Total
Basal
area in
percentage
of total
94.99
1.48
1 04
98
57
45
37
12
100.00
26
University of California — Experiment Station
The distribution of the plots by site and age classes is given in
table 19. In this table, site index is defined as the height of the
average dominant and codominant at 100 years, as the tables were
first constructed on site index so denned for purposes of comparison
with yields of Douglas fir in Oregon and Washington.
TABLE 19
Distribution of Plots by Site and Age Classes
Age in
Site index
—height in
feet of the average dominant and codominant tree at 100
years
years
75-84
85-94
95-
104
105-
114
115-
124
125-
134
135-
144
145-
154
155-
161
165-
174
175-
184
185-
194
195-
204
205-
214
Total
25- 34
35- 44
1
1
3
10
5
1
2
8
2
1
4
2
10
2
1
5
6
7
2
2
1
8
8
45- 54
1
1
4
12
55- 64 .
4
1
5
1
7
2
5
2
7
4
5
2
2
59
65- 74
39
75- 84 .
2
85- 94
95-104
1
3
105-114
1
5
6
1
12
115-124
125-134
7
3
1
11
1
135-144
145-154
2
2
155-164
165-174
11
1
1
12
9
4
1
Total 5
6
6
8
24
24
25
24
159
20 30
/OO //O 720 /JO /<?0 /50 /60 /70
JO 60 70 60 90
Age /n c/eors
Fig. 14. — Comparison of heights of average dominant and codominant tree
in the California plots with the height curve for Oregon and Washington stands
of the same average site index.
Bul, 491] Yield, Stand, and Volume Tables for Douglas Fir
27
Comparison of the California Sample Plots with Yield Tables
for Douglas Fir in Oregon and Washington
Yield tables for Douglas fir in Oregon and Washington define site
index as the height of the average dominant and codominant tree at
100 years. In order, therefore, to compare the values of the California
sample plots with the Oregon- Washington tables, each California plot
was assigned a site index number as defined for the tables of the
northern material. That the latter 's height growth curve for the
average dominant and codominant, on which site index is based, fits
the California data is shown in figure 14. Then the values of each
California plot were compared with the Oregon-Washington yield
tables and the percentages of the former to the latter were arranged
O 20 'fO 60 80 /OO /20 /<K) /60 /60 200 220 ' 210 260 280 300
Qosot ere& //? per cent of Oregon- IVosn/ngton g/e/ct tables
20 10 60 60 /OO /20 /1V /60 Z&O 20O 220 210 260 260 300
Number of trees /n p?r cent of Oregon -IVosh/hgton g/e/ct tob/es
Fig. 15. — Frequency distribution of the California sample plots in per cent
of the Oregon-Washington yield tables by basal area and by number of trees.
28
University of California — Experiment Station
in a frequency array by basal areas and by numbers of trees. Figure
15 shows these dispersions graphically. The comparison of the means
for the original 175 plots are as follows :
By basal area, + 33.2% ± 2.65%
By number of trees to the acre, — 4.3% ± 2.49%
Were the means of the California plots by both basal area and
number of trees either higher or lower than the Oregon-Washington
tables by about the same amount, one might doubt the validity of the
comparison, as the differences might be due to different conceptions
as to what constitutes normal stocking, on the part of those who
originally laid out and measured the plots in the two regions. But
as the basal area of the California material is 33 per cent higher, and
the number of trees 4 per cent lower, this can hardly be the case.
Rejection of Abnormal Plots
The rejection of abnormal plots is based on the above comparison.
Those which deviated by about two standard deviations from the mean
difference of the California plots were checked over for explanation
of their abnormal values. As the explanation was seldom evident
from the measurements taken or from the plot description, nearly all
were rejected. Table 20 summarizes the rejected plots.
TABLE 20
California Plots Rejected as Abnormal
Age,
years
Site
index
Per cent of difference from
corresponding values in
Oregon- Washington
yield tables
Basis for rejection
By basal
area
By number
of trees
63
71
+ 55
+ 62
Too many incense cedar trees
67
98
+ 45
+ 61
Too many incense cedar trees
72
109
+ 84
+107
Basal area and number of trees too high
67
122
+ 95
+ 80
Basal area and number of trees too high
111
125
+147
+ 76
Basal area and number of trees too high
27
130
+126
- 8
Basal area too high
27
132
+152
+ 9
Basal area too high
168
146
+ 44
- 26
Basal area too high
91
148
+ 74
+ 24
Basal area too high
27
151
+125
- 20
Basal area too high
45
158
+173
+ 53
Basal area and number trees too high
45
156
+139
+ 45
Basal area and number trees too high
168
150
+ 80
+ 11
Basal area too high
45
171
+ 83
+ 88
Too many redwood sprouts and tan oak trees
45
178
+ 53
+ 139
Basal area and number trees too high
33
200
+ 99
+125
Too many redwood sprouts
Bul. 491] Yield, Stand, and Volume Tables for Douglas Fir 29
The means of the remaining 159 plots are as follows :
Basal area: + 25.9 ± 1.97%
Number of trees: — 9.6 ± 1.97%
Obviously these figures cannot be accepted as due to chance fluctua-
tion. There must be differences in Douglas fir stand characteristics
between the southern and central part of its range on the Pacific slope.
Construction of the Yield Tables on the 100- Year Site Index
Rather than correlate the percentage deviations of basal area, num-
ber of trees, and of other growth units with age and site, the original
units are correlated directly with age and site on the 100-year site
index and later transferred to the 50-year site index to conform with
site as defined for other California species.
Basal Area, Number of Trees, and Cubic Volume. — Plot values on
the acre basis for these variables were correlated with age and site by
comparing them with the multiple linear regression equation, and,
by a series of successive estimates, converting the net regression lines
for age and for site index as well as the relationship between actual
and estimated values, to curvilinear forms where necessary. The
calculation of the correlation, measured by the correlation index, is
analogous to the Pearsonian correlation ratio :
CI
^m
in which CI = correlation index
<j est = the standard error of estimate; the standard deviation of the de-
pendent (y) variable measured from the regression line or curve.
o- J/ = the standard deviation of the dependent variable.
The term-^ measures the percentage dispersion of the dependent
ffy
variable due to factors other than the independent variables — in this
case, age and site index — considered ; that is, it measures the extent
of the independence of the relationship.
The numerical value of the correlation index and of the standard
error of estimate give the best idea of the association of a particular
dependent variable with age and site index. These are :
For basal area : <j est = 34.8 sq. ft. ; CI = .845
For no. of trees: cr es< = .116 log trees; CI = .909
For cu. volume : <r e8t = 1930 cu. ft. ; CI = .880
30
University of California — Experiment Station
Average Diameter Breast High. — This is the diameter in inches of
the tree of average basal area. It varies as the square root of the total
basal area divided by the number of trees. If the curves for these
variables are accurate, it may be calculated directly from them. This
was accordingly tried, giving the average diameter breast high of the
yield tables.
A check on the work is afforded by the relationship,
»(l-:)=™[f; ■(§-:)']
in which BA =■ the total basal area,
T = the number of trees,
D s= average diameter breast high,
and subscripts a and t refer to actual and tabular values respectively.
The basal area of each plot in per cent of its tabular basal area
was subjected to this equation with the following results:
Mean = 100.38% ; standard deviation = 1.72% showing a
satisfactory check.
Height of Average Tree. — This was arrived at through the relation-
ship of the ratio of height of average tree to height of average
dominant and codominant with average diameter (fig. 16).
•k
£- too
•^ 90
/s
3'
12
"t%
14
-*®
^r
\'
-3 1
tl—
/H
i — H
ioy
? +
^0 X4C
fi:
O 2 4 6 8 10 /2 /4 /& t8 20 22 24 26 28 30 32 34 36 Z
Aver&oe- cf /a meter breosf high
Fig. 16. — Ratio of height of average tree to height of average dominant and
codominant tree for average diameter.
Volume in Board Feet. — This is based on the correlation of the
ratio of board feet to a cubic foot, with the average diameter (fig. 17).
The curved ratio applied to cubic volume gives board foot volume.
Bul. 491] Yield, Stand, and Volume Tables for Douglas Fir 31
-0 *
/
MS
^JZ
,
15 '
\
20
"T'r
^^T
'zZ-
^ s ** ><
**»
^ 1
®Jf
/^3I
//
t
V
7
/' 10
i
aa a<? ad ae jo
3a 3<? 36
Average diameter breasf high
Fig. 17. — Relation of the number of board feet per cubic foot to
average diameter.
Site Index Translated to Height of Average Dominant at
50 Years
In order to change the basis of the yield tables from height of
average dominant and codominant at 100 years to height of average
dominant at 50 years, the latter site index was plotted over the former
(fig. 18) and the final tables re-read accordingly.
ML
**f
GjS
4f-
-I
S /2 °
ft Co
S*Z9
£
£
p?
6x/
-7
+,
4
O 20 <?0 60 SO /OO /20 i<90 /60 /80 200 22.0 2<90
Site index ~ height of average c/om/nanf ond
codom/nonh of /oo years
Fig. 18. — Relation of site index based on the height of the average dominant
tree at 50 years to site index based on the height of the average dominant and
codominant tree at 100 years.
32
University of California — Experiment Station
Construction of the Stand Tables
The distribution of trees by diameter class in a stand forms a fre-
quency series which may be analyzed and graduated into a frequency
curve when four constants are known — (1) the mean diameter, (2) the
standard deviation, (3) the coefficient of asymmetry, (4) the coeffi-
cient of excess. These were computed for each of the 159 sample plots.
Average Diameter, Mean Diameter and Standard Deviation. —
Average diameter, mean diameter and standard deviation are tied
together in any one stand by the relationship,
o* = A dhl ?-M dbh *
in which o- = the standard deviation of diameter distribution,
Adbh = the diameter of average basal area,
Mdbh = the mean of the diameters breast high.
As these three constants were computed independently for each
plot, their relationship was checked as follows:
/
*
/
/
<0
■£ V
/
r>
■§
.^
J
/
r
A-
?
ome
fer
A
y>+s
F a
/
J™
/
<
<
\ r
-/
^az
°- 5j r
o 8
°°u
lo
^Stor
ic/aro
' ' c/ev
iaf/o/
7
sy
&+
p&
p-r*
■O/O
06
""^5
~~**35
p <
j
1
/
i
5
z
J
2
f
3
-<
j
r— J
tf
o '
<*5
Averoqe dto meter- breast high
Fig*. 19. — Relation of mean diameter and standard deviation to average diameter.
Bul,. 491] Yield, Stand, and Volume Tables for Douglas Fir 33
1. The plots were sorted into classes according to the squares of
their average diameters using class intervals of 50 square inches.
2. For each plot within the respective classes, were tallied the
squares of its average diameter, of its mean diameter, and of its
standard deviation. Adding the sums of the squares of mean diameter
and of standard deviation, and subtracting this total from the sums
of squares of average diameter left an aggregate difference of 15
hundredths of one per cent.
•hlU
r
§
y
2
,17.
i, •
t3+^
-rj>*
">A3
-"
*fc*
**<&
/
-+'//
>
A
**?26
Vj^
,
4s
2 ? 6 8/0/2/^/6 /6 20 22 2f- 26 28 30 32 3* 36 36
Fig. 20. — Relation of the coefficient of asymmetry to mean diameter.
3. Within each class interval were plotted the square root of the
average of the mean diameters squared, and of the average of the
standard deviations squared, over the square root of the average of
the average diameters squared (fig. 19). Straight lines were fitted to
these points so that
M dbt ?+o* = A dbt ?
Asymmetry and Excess. — The coefficient of asymmetry (/?..) and
the coefficient of excess (/? 4 ) of the plots were correlated with mean
diameter (figs. 20 and 21).
Starting with average diameter of a site-age class from table 5,
its mean diameter and standard deviation were read from figure 19,
and, for the indicated mean diameter, its coefficient of asymmetry and
34
University of California — Experiment Station
5"
\
y \
—01
\ \
2
3
^ 02
/6 ~
^
1 \
1 1
/ N
/ '
.
if
/
V
1
'
1
//V"
■-la
_ +'„
\
1
1
\
1
\J
v
N
1
1
•s
/
o a -f 6 e to /2 ./# /6 /e ao 22 a<f ^<5 ae jo sa 1 j-? jc js
ffeon d/'ornef-er- breosf /?/gh
Fig. 21. — Relation of the coefficient of excess to mean diameter.
of excess taken from figures 20 and 21 ; from these parameters, with
the aid of Charlier's Tables, 13 the theoretical frequencies were
calculated.
13 Charlier's "Type A" frequency curve has the form
AT r
in which
F(x) = frequency of x (in this case frequency per unit of one-half standard
deviation measured from mean diameter).
N = total frequency.
<r = standard deviation.
1 -x 2
<Mz)=-
03 (x)
V2T 2
<* 3 0o
dx*
4 (z)=^0o
dx*
These are tabulated for unit frequency with x in terms of
standard deviation in Charlier.
Coefficient of asymmetry, &= -— 3 („ 3 = the 3rd moment measured from the mean).
Coefficient of excess, fo^f ~ 4 - 3 ) ("4 = the 4th moment measured from the
mean,
Bul. 491] Yield, Stand, and Volume Tables for Douglas Fir
35
VOLUME TABLES
Basic Data
From 10 to 50 taper measurements were taken on each of eight
of the yield study sample plots, two of the plots on cut-over lands of
the Union Lumber Company, Mendocino County, two on holdings of
the Casper Lumber Company, Mendocino County, and four on the
Trinity National Forest in Trinity County.
Diameters were measured along the stem of each felled tree out-
side and inside bark at breast-height, at each tenth of length above
breast-height, at each fifth of length from the lowest tenth downwards
and at 1 per cent of total height from the ground.
TABLE 21
Basic Data op the Volume Tables
Plot
County
Trees
measured
Plot
age
Site
index*
Ft. Bragg No. 1
42
10
25
42
25
25
48
50
33
33
45
45
68
68
72
111
200
Ft. Bragg No. 2
210
Casper No. 2
178
Casper No. 3
171
Minersville No. 3
Trinity
93
Trinity
90
Minersville No. 14
Trinity
109
South Fork Trinity River No. 16
Trinity
143
* Height of average dominant and codominant at 100 years.
Table 21 shows the number of trees by plots and the range in age
and site of the data.
Each tree was plotted on cross-section paper and its cubic volume
computed as the sum of the sectional volumes, each by the Smalian
formula. The section lengths were in per cent of total height starting
with the stump of 1 per cent, the second section of 3 per cent, the third
of 6 per cent, and the remaining nine sections each having length of
10 per cent of tree 's total height.
Comparison with Douglas Fir Volume Tables for Oregon and
Washington
It would only make for confusion to construct volume tables for a
particular region when tables for the same species based on data of
another region may apply. As there is no readily observable difference
36 University of California — Experiment Station
between the forms of Douglas fir in California as against Oregon and
Washington, the volumes of the California data were checked against
the cubic volume table for immature Douglas fir in Oregon and
Washington. 14
The volumes of the tree data basic to the latter table were, how-
ever, computed as of different sectional lengths than those noted above
for the California trees. Stumps of 1% feet were used and all other
sections, regardless of tree's size, were cubed in 10-foot lengths.
In order to ascertain what differences in volume result from the
two methods of calculation, the trees of Minersville Plot No. 14 were
cubed by both methods. It was found that for constant height, both
methods gave the same results independent of diameter; but for con-
stant diameter, volume of trees less than about 50 feet in total height
averaged 6 per cent higher when cubed by the method used for the
California data, though the calculated volumes of taller trees were
independent of the method of computation. However, only 19 out of
the 267, or 7 per cent of the trees of all the plots are less than 55 feet
tall ; so that the difference in method should carry little weight in
explaining any difference between the actual volumes and those
tabulated for the species in Oregon and Washington.
Following are the results of the check of the California trees
against the Oregon-Washington volume tables :
Number of trees 267
Aggregate difference — 2.4 per cent
Mean difference — 6.2 per cent
Standard error of estimate 13.4 per cent
Now if the California trees of all sizes have consistently greater or
less taper than the Oregon-Washington trees, there should be no cor-
relation between the per cent deviation and tree size. In other words,
a blanket correction factor might be applied to the table to arrive at
true average volume.
This, however, is not the case. The multiple correlation coefficient
between per cent deviation and diameter and height was found to be
r 123 = .485 ± .034
in which subscript , = per cent deviation of the California volumes,
2 = diameter at breast-height,
„ = Total height.
] 4McArdle, R. E. A set of volume tables for second-growth Douglas fir in
western Oregon and Washington. Issued in mimeographed form by the Pacific
Northwest Forest Experiment Station, June 10, 1926.
Bul,. 491] Yield, Stand, and Volume Tables for Douglas Fir 37
/05
-
■2o
+40
+/
+40
-
-28
yJ1
^
II
IS'
Si"
23* '
+2
+3
^+<
4 3/^/6 20 24 28 32 36 40 44 48
D/a/7?efer breosf /?/gn /r? //7cf?es
/30
\ %)/20
ki
+2-
¥
&
1
»+/7
+/S
27
^4
^c
*2
Cr
<V
7
+<=
20
40 60 80 /OO /20 /40 /60 /80 200
Tofo/ fre/Qhf /n feef
Fig. 22. — Comparison of the California tree volumes with the Oregon-Washington
cubic foot volume table by diameter and by height.
38 University of California — Experiment Station
Site index was also included as an independent variable in the
trial correlation, but the coefficient was not materially increased
thereby. It seems likely that site quality does not affect taper in
comparatively young timber. Differences in taper due to site prob-
ably become significant in mature timber only, for several volume
tables for mature timber in which site quality is one of the important
variables are now in use.
The volumes of California immature Douglas fir compared to the
cubic volume table for Oregon and Washington vary with diameter
and with height, as shown in figure 22, in which the deviations of the
data from the multiple regression equation are compared with the net
regression lines for diameter with average height and for height with
average diameter. The differences must be due to one or more of the
following mensurational factors which make for systematic differences
in volume when the latter is based on diameter at breast-height out-
side bark and on total height of tree :
a Differences in bark thickness.
b Differences in taper near the base of the tree.
c Differences in taper in the upper part of the bole.
In order to compare taper of the species between the two regions,
it is necessary that the basic data be analyzed and compared. For this
purpose, the original field data from Oregon and Washington were
loaned by the United States Forest Service. 15
Lower Taper and Bark Thickness. — These factors were analyzed in
one operation rather than separately because their effect on volume is
dependent upon their sums.
The taper of a typical timber tree is concave towards its axis from
the tip downward until a point is reached, usually within the first
tenth of its length from the ground, below which it becomes convex
toward its axis. The importance of the lower taper from a volume-
determining standpoint lies in the fact that the diameter of the tree
is nearly always taken at 4% feet from the ground (breast-height),
which may or may not be above the point of taper inflection, depend-
ing partly upon the size of the tree and partly upon many other
factors difficult of measurement and analysis, and too involved for
ready application. It thus happens that the diameter at breast-height
is The writer is deeply indebted to Director T. T. Munger of the Pacific
Northwest Forest Experiment Station, United States Department of Agricul-
ture, for the use of 1600 taper measurements — over 80 per cent of the basic
data of the Oregon-Washington volume tables.
Bul. 491] Yield, Stand, and Volume Tables for Douglas Fir 39
is not satisfactory for accurate volume determination in conjunction
with a volume table. But as it comes at such a handy point, prac-
tically all volume tables are based upon it.
If the taper inside bark of Douglas fir were the same throughout
the upper nine-tenths of its length in its entire range on the Pacific
slope, it is evident that trees of the same total height and diameter
inside bark at one-tenth height would have the same volume. But if the
lower taper and bark thickness differ with latitude, while the upper
taper remains the same, their volumes may differ significantly if based
on a diameter, outside bark, below the point of inflection, because in
one case the diameter measured will be greater than in the other.
The following method was used to analyze the effect of bark thick-
ness and lower taper of the California Douglas fir on cubic volume as
tabulated in the Oregon-Washington volume table :
(1) Using the northern tree data, diameter breast high outside bark
was correlated with total height, site index and diameter inside bark
at one-tenth of total height. The effect of site index was found to be
negligible, and was dropped as a variable.
(2) The regression which was found to be linear, was put up in
the form of an alignment chart, and a new diameter outside bark at
breast-height read for the 267 California trees according to their total
height and diameters inside bark at one-tenth height, by referring
these measurements to the chart.
(3) Having assigned to each California tree the diameter at
breast-height outside bark which it would have had, had bark thickness
and lower taper been the same as that of the northern data, its cubic
volume was again checked against the volume table, on the new
diameter and total height.
The multiple correlation coefficient between per cent deviation of
the tree volumes from the tabular for diameter breast high and height
was computed to be
r 123 = .173 ± .060
a much less significant figure than the correlation based on the original
check; but the mean of the per cent deviation = + 4.3% ±0.8%,
which is approximately 10 per cent higher than the original check.
This indicates that in the lowest tenth of length, the California
trees have greater taper, greater bark thickness, or both, than the
northern trees, for the greater the ratio of diameter at breast-height
outside bark to an upper diameter inside bark, the less becomes volume
for a given diameter at breast-height, other factors remaining constant.
40
University of California — Experiment Station
4- 8/2/6 20 2<? 26 32 36 <?0 -?"?
Diameter /r?3/o / e horfc of //o heiohf in inches
90
(
1o//fi
or/7/t
7~^
85
ySVrego
^ Was/?//
no/7
?q/o/
7
. 60
/D
>T0
J> /o
Fc
>r A\
f era
ge L
hamt
sfer
->C
20 <K) CO SO /OO /20 fi?Q
Tbfo/ he/ghf /n feef
/60 /SO 200 220
Fig. 23. — Comparison of form quotations of the California trees with the
form quotients of the Oregon- Washington trees by diameter inside bark at
one-tenth height and by total height.
Bui,. 491] Yield, Stand, and Volume Tables for Douglas Fir 41
Upper Taper. — The upper taper of the Douglas fir material was
analyzed by comparing form quotients of the trees from the two
regions. For this purpose form quotient is defined as the diameter
inside bark at one-half total height divided by diameter inside bark
at one-tenth total height. It is evident that the higher the form
quotient the closer does the bole approach a cylinder in form except
near the tip.
Figure 23 shows the effect of tree size on form quotient for both the
northern and the California trees.
It must be concluded that the volume tables for immature Douglas
fir in Oregon and Washington — in which the northern foresters have
full confidence, as they are based on nearly 2000 trees — do not apply
to immature trees of the same species in California, because
(1) The California trees have greater basal flare, the tendency of
which is less volume for a given diameter at breast-height,
(2) The California trees have higher average form quotients with
consequent tendency to greater volume. This is in general, however,
more than offset by the loss in volume due to basal flare.
Therefore, since the average taper of immature Douglas fir in
California differs from that of the northern states, tables 14 and 15
were prepared.
STATION PUBLICATIONS AVAILABLE FOE FKEE DISTRIBUTION
BULLETINS
No.
253.
263.
277.
279.
283.
304.
310.
313.
331.
335.
343.
344.
346.
347.
348.
349.
353.
354.
357.
361.
362.
363.
364.
366.
367.
368.
369.
370.
371.
373.
374.
380.
385.
386.
388.
389.
390.
391.
392.
393.
394.
395.
396.
397.
400.
405.
406.
407.
Irrigation and Soil Conditions in the
Sierra Nevada Foothills, California.
Size Grades for Ripe Olives.
Sudan Grass.
Irrigation of Rice in California.
The Olive Insects of California.
A Study of the Effects of Freezes on
Citrus in California.
Plum Pollination.
Pruning Young Deciduous Fruit Trees.
Phylloxera-resistant stocks.
Cocoanut Meal as a Feed for Dairy
Cows and Other Livestock.
Cheese Pests and Their Control.
Cold Storage as an Aid to the Market-
ing of Plums, a Progress Report.
Almond Pollination.
The Control of Red Spiders in Decid-
uous Orchards
Pruning Young Olive Trees.
A Studv of Sidedraft and Tractor
Hitches.
Bovine Infectious Abortion, and Asso-
ciated Diseases of Cattle and New-
born Calves.
Results of Rice Experiments in 1922.
A Self-Mixing Dusting Machine for
Applying Dry Insecticides and Fun-
gicides.
Preliminary Yield Tables for Second
Growth Redwood.
Dust and the Tractor Engine.
The Pruning of Citrus Trees in Cali-
fornia.
Fungicidal Dusts for the Control of
Bunt.
Turkish Tobacco Culture, Curing, and
Marketing.
Methods of Harvesting and Irrigation
in Relation to Moldy Walnuts.
Bacterial Decomposition of Olives
During Pickling.
Comparison of Woods for Butter Boxes.
Factors Influencing the Development
of Internal Browning of the Yellow
Newtown. Apple.
The Relative Cost of Yarding Small
and Large Timber.
Pear Pollination.
A Survey of Orchard Practices in the
Citrus Industry of Southern Cali-
fornia.
Growth of Eucalyptus in California
Plantations.
Pollination of the Sweet Cherry.
Pruning Bearing Deciduous Fruit
Trees.
The Principles and Practice of Sun-
Drying Fruit.
Berseem or Egyptian Clover.
Harvesting and PaGking Grapes in
California.
Machines for Coating Seed Wheat with
Copper Carbonate Dust.
Fruit Juice Concentrates.
Crop Sequences at Davis.
I. Cereal Hay Production in California.
II. Feeding Trials with Cereal Hays.
Bark Diseases of Citrus Trees in Cali-
fornia.
The Mat Bean, Phaseolus Aconitifolius.
Manufacture of Roquefort Type Cheese
from Goat's Milk.
The Utilization of Surplus Plums.
Citrus Culture in Central California.
Stationary Spray Plants in California.
Yield, Stand, and Volume Tables for
White Fir in the California Pine
Region.
No.
408.
409.
410.
412.
414.
415.
416.
418.
419.
420.
421.
423.
425.
426.
427.
428.
430.
431.
432.
433.
434.
435.
436.
438.
439.
440.
444.
445.
446.
447.
448.
449.
450.
451.
452.
453.
454.
Alternaria Rot of Lemons.
The Digestibility of Certain Fruit By-
products as Determined for Rumi-
nants. Part I. Dried Orange Pulp
and Raisin Pulp.
Factors Influencing the Quality of Fresh
Asparagus After it is Harvested.
A Study of the Relative Value of Cer-
tain Root Crops and Salmon Oil as
Sources of Vitamin A for Poultry.
Planting and Thinning Distances for
Deciduous Fruit Trees.
The Tractor on California Farms.
Culture of the Oriental Persimmon in
California.
A Study of Various Rations for Fin-
ishing Range Calves as Baby Beeves.
Economic Aspects of the Cantaloupe
Industry.
Rice and Rice By-Products as Feeds
for Fattening Swine.
Beef Cattle Feeding Trials, 1921-24.
Apricots (Series on California Crops
and Prices).
Apnle Growing in California.
Apple Pollination Studies in California.
The Value of Orange Pulp for Milk
Production.
The Relation of Maturity of California
Plums to Shipping and Dessert
Quality.
Range Grasses in California.
Raisin By-Products and Bean Screen-
ings as Feeds for Fattening Lambs.
Some Economic Problems Involved in
the Pooling of Fruit.
Power Requirements of Electrically
Driven Dairy Manufacturing Equip-
ment.
Investigations on the Use of Fruits in
Ice Cream and Ices.
The Problem of Securing Closer Rela-
tionship between Agricultural Devel-
opment and Irrigation Construction.
I. The Kadota Fig. II. The Kadota
Fig Products'.
Grafting Affinities with Special Refer-
ence to Plums.
The Digestibility of Certain Fruit By-
Products as Determined for Rumi-
nants. II. Dried Pineapple Pulp,
Dried Lemon Pulp, and Dried Olive
Pulp.
The Feeding Value of Raisins and
Dairy By-Products for Growing and
Fattening Swine.
Series on California Crops and Prices:
Beans.
Economic Aspects of the Apple In-
dustry.
The Asparagus Industry in California.
A Method of Determining the Clean
Weights of Individual Fleeces of Wool.
Farmers' Purchase Agreement for Deep
Well Pumps.
Economic Aspects of the Watermelon
Industry.
Irrigation Investigations with Field
Crops at Davis, and at Delhi, Cali-
fornia, 1909-1925.
Studies Preliminary to the Establish-
ment of a Series of Fertilizer Trials
in a Bearing Citrus Grove.
Economic Aspects of the Pear Industry.
Series on California Crops and Prices:
Almonds.
Rice Experiments in Sacramento Val-
ley, 1922-1927.
BULLETINS— (Continued)
No.
455.
Reclamation of the Fresno Type of
Black-Alkali Soil.
456. Yield, Stand and Volume Tables for
Red Fir in California.
458. Factors Influencing Percentage Calf
Crop in Range Herds.
Economic Aspects of the Fresh Plum
Industry.
Series on California Crops and Prices :
Lemons.
461. Series on California Crops and Prices:
Economic Aspects of the Beef Cattle
Industry.
Prune Supply and Price Situation.
Drainage in the Sacramento Valley
Rice Fields.
459.
460.
462.
464.
No.
465.
466.
Curly Top Symptoms of the Sugar Beet.
The Continuous Can Washer for Dairy
Plants.
467. Oat Varieties in California.
468. Sterilization of Dairy Utensils with
Humidified Hot Air.
469. The Solar Heater.
470. Maturity Standards for Harvesting
Bartlett Pears for Eastern Shipment.
471. The Use of Sulfur Dioxide in Shipping
Grapes.
474. Factors Affecting the Cost of Tractor
Logging in the California Pine
Region.
475. Walnut Supply and Price Situation.
CIRCULARS
No.
115. Grafting Vinifera Vineyards.
117. The Selection and Cost of a Small
Pumping Plant.
127. House Fumigation.
129. The Control of Citrus Insects.
164. Small Fruit Culture in California.
166. The County Farm Bureau.
178. The Packing of Apples in California.
203. Peat as a Manure Substitute.
212. Salvaging Rain-Damaged Prunes.
230. Testing Milk, Cream, and Skim Milk
for Butterfat.
232. Harvesting and Handling California
Cherries for Eastern Shipment.
239. Harvesting and Handling Apricots and
Plums for Eastern Shipment.
240. Harvesting and Handling California
Pears for Eastern Shipment.
241. Harvesting and Handling California
Peaches for Eastern Shipment.
243. Marmalade Juice and Jelly Juice from
Citrus Fruits.
244. Central Wire Bracing for Fruit Trees.
245. Vine Pruning Systems.
248. Some Common Errors in Vine Pruning
and Their Remedies.
249. Replacing Missing Vines.
250. Measurement of Irrigation Water on
the Farm.
253. Vineyard Plans.
255. Leguminous Plants as Organic Ferti-
lizers in California Agriculture.
257. The Small-Seeded Horse Bean (Vicia
faba var. minor).
258. Thinning Deciduous Fruits.
259. Pear By-Products.
261. Sewing Grain Sacks.
262. Cabbage Production in California.
263. Tomato Production in California.
265. Plant Disease and Pest Control.
266. Analyzing the Citrus Orchard by Means
of Simple Tree Records.
No.
269.
270.
276.
277.
278.
279
282.
284.
287.
288.
289.
290.
292.
294.
295.
296.
298.
300.
301.
302.
304.
305.
307.
308.
309.
310.
311.
312.
313.
314.
315.
An Orchard Brush Burner.
A Farm Septic Tank.
Home Canning.
Head, Cane, and Cordon Pruning of
Vines.
Olive Pickling in Mediterranean
Countries.
The Preparation and Refining of Olive
Oil in Southern Europe.
Prevention of Insect Attack on Stored
Grain.
The Almond in California.
Potato Production in California.
Phylloxera Resistant Vineyards.
Oak Fungus in Orchard Trees.
The Tangier Pea.
Alkali Soils.
Propagation of Deciduous Fruits.
Growing Head Lettuce in California.
Control of the California Ground
Squirrel.
Possibilities and Limitations of Coop-
erative Marketing.
Coccidiosis of Chickens.
Buckeye Poisoning of the Honey Bee.
The Sugar Beet in California.
Drainage on the Farm.
Liming the Soil.
American Foulbrood and Its Control.
Cantaloupe Production in California.
Fruit Tree and Orchard Judging.
The Operation of the Bacteriological
Laboratory for Dairy Plants.
The Improvement of Quality in Figs.
Principles Governing the Choice. Oper-
ation and Care of Small Irrigation
Pumping Plants.
Fruit Juices and Fruit Juice Beverages.
Termites and Termite Damage.
The Mediterranean and Other Fruit
Flies.
8m-4,'30