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#OREST RESEARCH NOTES 

NORTHEASTERN FOREST EXPERIMENT STATION 

Upper Darby, Pennsylvania 

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7 - ,ao, ~$5 : 

2. ' ~1955 ,+ . * - -- 

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For Yellow Birch In The Northeast 

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This is the fourth report on a series 0% studies to 

show the relationship of stump diameter to diam&er breast 

high (d.b,@.) for com~e~~ially important tree species in the 

Northeast. ~' This report is for yellow birch (~etula alleghaniensis) . 

In this study 463 stump-diameter measurements were 

used, ranging from 4 inches to 38 inches. Both stump diameter and d.b.h. were measured to the nearest l/l0-inch with a 

diameter tape, To obtain diameter inside bark, bark 

thickness was measured with a Swedish bark gage. Stump 

heights were measured on the uphill side to the nearest 

l/l0-f oot . 

It was found that 77 percent of the stumps left on 

logging operations were between 0.6 and 1.8 feet high; 20 

percent were higher than 1.8 feet; and only 3 percent were 

lower than 0.6 foot. 

In the computations, inside--bark stump diameters were 

used, to avoid inaccuracies due to unequal bark thickness, 

logging damage to bark, and bark peeling off. Stump diameters were sorted into 2-inch classes. Stump-height measurements were sorted into 0.6-foot classes mithin each stumpdiameter classo 

To develop an equation expressing the stimp diameter--debah. relationship for yellow birch, the method described by ~emmingi"( was used. The following equation was 

obtained: 

D.b.h. = 0.776 (stump d.i.b.) + 2.108 (stump height) - 1.579 

The relationships developed from this equation were worked 

out as a graph (fig. l), 
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To determine the 2-inch deboh. class of a yellow 

birch stump from this graph, you merely plot the inter- 

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section of the vertical ordinate (stump height) with the 

horizontal ordinate (stump diameter). For example, for a 

stump 19.1 inches in diameter and 1.4 feet high, the two 

lines intersect about halfway between the two limits of the 

16-inch debah. class. 

Comparison of actual d.b.h,'s and those calculated 

with the equation showed an average weighted difference of 

less than 0.3 inch. The standard error of estimate for all 

data was 0.737 inch. At the mean of stump diameters, you 

can expect 82 percent of the estimates of d.b.h. to fall in 

the correct 2-inch d.b.h. class. Another 17 percent can be 

expected t o f a l l one class above or below the correct one; 

and 1 percent will fall outside this range. These errors 

are compensating. As the stump diameters increase beyond 

the mean of these data, the error will also increase. 

(1f you use the graph by 1-inch d.b.h. classes, this 

is what you can expect: 50 percent of the estimates should 

fall in the correct 1-inch d. b.h. class; 46 percent should 

fall one class above or below it; and 4 percent should fall 

outside this range. ) 

For all practical purposes this graph is expected to 

give reliable deb, h. estimates for yellow birch anywhere in 

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the Northeast, 

--FREDERICK E. HAMPF 

Forest Economist 

Division of Forest Economics 

Northeastern Forest Experiment Station 

Forest Service, U.S Dept. Agriculture 

35 

For earlier reports on these studies see Forest Research Note No. 38 (white ~ine), No. 42 (sugar maple), and 

No. 43 (American beech). 

3<+ 

Deming, W. Edwards. Statistical adjustment of data. 

261 pp., illus. Wiley & Sons, New York. 1938. 

Agriculture-Forest Service-Upper Darby 

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STUMP DIAMETER- D. B.H. RELATIONSHIP FOR 

YELLOW BIRCH 

IN THE NORTHEAST 

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 

STUMP HEIGHT, IN INCHES 

Figure