United States 

1 Department of 

Agriculture 

Forest Service 

Northeastern Fores 

Experiment Station 

Research Paper NE. 

Stand Basal-Area and 

Tree-Diameter Growth 

in Red Spruce-Fir Forests 

in Maine, 1960-80 
Abstract 

Stand basalarea change and individual surviving red spruce d.b.h. growth from 

1960 to 1980 were analyzed for red spruce-fir stands in Maine. Regression 

modeling was used to relate these measures of growth to stand and tree 

conditions and to compare growth throughout the period. Results indicate a 

decline in growth. The regression models helped identify trends and relationships 

but were not useful for predicting growth due to the tremendous amount of 

variability in the growth of red spruce-fir stands. 

The Authors 

STANLEY J. ZARNOCH is a mathematical statistician, Southeastern Forest 

Experiment Station, US. Department of Agriculture, Forest Service, Athens, 

Georgia. 

DAVID A. GANSNER is a resource analyst, Northeastern Forest Experiment 

Station, US. Department of Agriculture, Forest Service, Radnor, Pennsylvania. 

DOUGLAS S. POWELL is a resource analyst, Northeastern Forest Experiment 

Station, US. Department of Agriculture, Forest Service, Radnor, Pennsylvania. 

THOMAS W. BIRCH is a resource analyst, Northeastern Forest Experiment 

Station, U.S. Department of Agriculture, Forest Service, Radnor, Pennsylvania. 

Manuscript received for publication 25 July 1989 

Northeastern Forest Experiment Station 

100 Matsonford Road, Radnor, PA 19087 

February 1990 
Introduction 

Recent interest in the effect of pollution, particularly acid 

rain, on the growth of forests around the world and 

specifically on red spruce decline in the northeastern United 

States (Siccama et. al 1982, Scott et. al 1984, Vogelmann 

et. al 1985) has been emphasized by the initiation of the 

National Acid Precipitation Assessment Program (NAPAP). 

The Forest Response Program (FRP), a jointly funded and 

co-administered initiative by the Environmental Protection 

Agency and USDA Forest Service, is part of NAPAP and is 

responsible for addressing the following three policy questions: 

1. Is there a significant problem of forest damage in North 

America that could be caused by acidic deposition alone 

or in combination with other pollutants? 

2. If so, what is the causal relationship between acidic 

deposition alone or in combination with other pollutants, 

and forest damage in North America? 

3. If there is a causal relationship, what is the doseresponse relationship between acidic deposition alone or 

in combination with other pollutants, and forest damage 

in North America? 

This paper is related directly to policy question 1 and 

indirectly to policy question 3 for the red spruce-fir forests of 

Maine which are primarily of low elevation and used for 

commercial timber products. 

For policy question 1, we assessed growth in two periods, 

the 1960's and the 1970's. First, we defined what is meant 

by "growth". Since red spruce-fir forests consist of all-age, 

multi-species communities of trees, we had to decide what 

to measure. One can measure growth at the tree level and 

stand level. At the tree level, growth may be analyzed as 

diameter growth, basal-area growth, volume growth, or 

height growth on a species basis. At the stand level, one 

may use basal-area growth, quadratic-mean stand diameter 

growth or volume growth for the entire stand, or any one of 

these measures for a specific species. In this research, we 

analyzed surviving red spruce-tree diameter breast height 

(d.b.h.) growth and net change in total stand basal area. No 

attempt was made to relate growth changes to pollution, but 

the analysis does give an indication of the temporal and 

spatial variability that may be expected under the stand 

conditions and natural factors operating at the time. The 

analysis which included individual tree d.b.h. growth was 

only for red spruce trees that survived. It did not consider 

other species in the stand, or ingrowth, or trees that died. It 

was hoped that this measure would be related usefully to 

the numerous tree-core analyses that have been conducted 

recently (Hornbeck and Smith 1985, Van Deusen 1987). 

For policy question 3, the potential of modeling tree d.b.h. 

growth and net change in total stand basal-area was 

analyzed as a function of stand attributes. Typical 

regression techniques were used, and simplicity of models 

was an important criterion. The objective was to define 

structural correlation patterns between growth and stand 

variables, and to evaluate the potential for predicting growth 

in these very heterogeneous stands. If successful, it could 

help lay the groundwork for the development of doseresponse models for the effect of acidic deposition on red 

spruce-fir forests. 

Thus, three specific objectives were to: 

1. Estimate stand basal-area change and variability during the 

1960's and 1970's by geographic units of Maine (Fig. 1). 

2. Estimate individual surviving-tree d.b.h. growth and 

variability of red spruce by geographic units of Maine 

during the 1960's and 1970's. 

3. Develop empirical models by using correlation and 

regression methodology to isolateimportant variables 

and formulate pertinent models for stand basal-area 

change and individual surviving-tree d.b.h. growth. 

Figure 1 .-Geographic units used in the Maine FIA inventory. 
example, only 5 percent of the stands grew more than 4.5 

square feetlacre per year during growth period 1. 

The data consist of a subset of a larger data base developed 

by the Forest Inventory and Analysis (FIA) work unit of the 

Northeastern Forest Experiment Station for inventories of 

Maine's forest resources for 1960 (Ferguson and Longwood 

1960), 1970 (Ferguson and Kingsley 1972), and 1980 

(Powell and Dickson 1984). The exact dates of the field 

measurements span several years for inventory 1 (1954-58), 

inventory 2 (1968-70), and inventory 3 (1980-82). Hence, for 

analysis, two growth periods were available with interval 

lengths averaging 11.3 and 11.6 years, respectively. The 

data base originally consisted of 835 plots that contained 

0.10 and 0.20 acres and, based on cubic-foot volume 

classes, represented a stratified random sample of Maine. 

The focus of the present study was specifically on typical 

red spruce-fir stands unthinned during this period; thus, 

restrictions similar to those of Solomon and others (in 

preparation) were used as criteria in selecting plots for 

study. First, the percentage of softwood species' basal area 

at inventory 1 would be at least 65 percent (note that no 

restriction was imposed for the other inventories). Second, 

the plot had to show no human disturbances throughout 

both growth periods. Also, plots that were thinned with only 

a few trees left standing were deleted from the analysis if at 

inventory 1 their basal area was less than 75 square feet 

per acre and their quadratic-mean stand diameter was 

greater than 8.0 inches or their basal area was less than 75 

square feet per acre and the number of trees was less than 

75 per acre. Last, the percentage of the red spruce basal 

area on a plot at inventory 1 had to be at least 10 percent. 

The results of these restrictions yielded 87 plots that were 

measured at all three inventories. The distribution of the 

plots by basal area, quadratic-mean stand diameter, 

proportion of softwood per basal area, trees per acre, and 

elevation is shown in Table 1. 

Analysis of Stand Basal-Area Change 

Annual plot basal-area change (square feetlacre) was 

analyzed based on 87 unthinned red spruce-fir plots 

measured over two growth periods. The results shown in 

Table 2 indicate that mean plot basal-area change 

decreased from 2.29 square feetlacre during growth period 

1 to 1.29 square feetlacre in growth period 2, reflecting a 44 

percent reduction. Basal-area change rates, by geographic 

unit, reveal for growth period 1 means ranging from 1.26 

(Unit 6) to 3.62 (Unit 7) and for growth period 2, 0.26 (Unit 6) 

to 2.12 (Unit 7). Despite the spatial variability and temporal 

change which are confounded by varying stand conditions, 

it is important to note that all units declined in average plot 

basal-area change during growth period 2. Further insight is 

shown by the empirical cumulative distribution function of 

basalarea change for the growth periods (Fig. 2). For 

example, only 3 percent of the plots showed a negative 

growth in period 1 while 20 percent had negative growth for 

period 2. These empirical cumulative distribution functions 

are useful for indicating maximum potential change; for 

Analysis of Surviving-Tree Diameter Growth 

Annual tree d.b.h. growth (inches) was analyzed by 

extracting from the 87 unthinned plots all red spruce trees 

that had survived through at least one entire growth period. 

Hence, because of ingrowth and mortality, the same trees 

were not used in the analysis for both periods. The results 

(Table 3) show that annual d.b.h. growth decreased from 

0.091 to 0.076 inches between the periods, a 16 percent 

decline. Seegrist and Arner (1982) found similar annual 

d.b.h. growth during growth period 1 in their analysis of the 

FIA data, though their data base was somewhat different 

from the FIA data base due to the restrictions imposed. By 

geographical unit, the means ranged from 0.059 (Unit 3) to 

0.158 (Unit 6) for growth period 1 and 0.051 (Unit 3) to 

0.133 (Unit 6) for growth period 2. Diameter growth declined 

during growth period 2 in all units except 2 where it 

remained virtually constant. The empirical cumulative 

distribution function (Fig. 3) illustrates clearly that although 

the diameter growth distribution is basically identical for the 

growth periods at its lower tail, it is extremely skewed to the 

upper tail during growth period 1; that is, there is a greater 

proportion of faster growing trees. 

Modeling 

Stand Basal-Area Change 

The objective of our modeling effort was to develop an 

empirical prediction equation for annual stand basal-area 

change as a function of stand characteristics. The key 

variables commonly used to predict growth for most forest 

types are age, site index, and density. However, for these 

red spruce-fir forests, age and site index are not valid 

predictors since the age of most stands was indeterminate 

and soil was so variable that measures of site index were 

meaningless. Thus, to develop the basal-area model where 

BAC = annual basal-area change (square feetlacre), 

we used five stand variables that were measurable: 

BA = initial stand basal area (square feetlacre) at the 

beginning of the growth period, 

QM = initial quadratic-mean stand diameter (inches) at 

the beginning of the growth period, 

PSW = initial proportion of the plot basal area which is 

in softwood species at the beginning of the growth period, 

NT = initial number of trees per acre at the beginning 

of the growth period, and 

ELEV = elevation (feet) of the plot. 
Cumulative Proportion 

of Stands 

Annual Stand Basal-Area Change (sq. ft.lacre) 

Figure 2.-Empirical cumulative distribution function of annual stand basal-area change (square feetlacre). 

This set of variables is similar to that used by Solomon and 

others (1986, and 1987) for predicting red spruce growth 

using a matrix projection model. The first step in developing 

a growth model was to determine the relationship between 

basal-area change and each of the five stand variables. 

Graphs are shown in Figure 4 for growth period 1 and in 

Figure 5 for growth period 2. They indicate very little trend 

and a considerable amount of variation. Initial basal area 

and quadratic-mean stand diameter appeared to show 

significant correlations with basal-area change for both 

growth periods. Elevation was significantly correlated with 

basal-area change in growth period 1 but not in growth 

period 2, though the correlation was positive in both. All 

other stand variables indicated little promise as potential 

predictors. Also, no linearizing transformations were 

identified. However, all possible models of these five basic 

stand variables were examined to check predictive potential 

of various combinations of variables. There are a total of 31 

models consisting of all combinations of the five variables. 

Upon examining each of these models and their associated 

fit statistics, R2 and mean square error, the basal-area and 

elevation model appeared to be at least as good as any 

other for both growth periods and, because of its simplicity, 

was selected as an appropriate model to predict basal-area 

change. Thus, the model for growth period 1 was 

BAC = 2.283 - 0.00887*BA + 0.00100*ELEV 

with R2 = 0.15 and MSE = 2.04 

and for growth period 2 

BAC = 2.292 - 0.01382*BA + 0.00067'ELEV 

with R2 = 0.12 and MSE = 2.33 

and all parameters were significant at the 0.05 level. 
Cumulative Proportion 

of Trees 

Growth Period 2 

A ,in. In 

0.0 0.1 0.2 0.3 0.4 0.5 0.6 

Annual DBH Growth (inches) 

Figure 3.-Empirical cumulative distribution function of annual d.b.h. growth (inches). 

Further improvements in the models were attempted by 

analyzing all two-way interactions of the five basic stand 

variables. Since the number of potential models for each 

growth period was then 32,767, it was not feasible to fit all 

models. Thus, the STEPWISE and RSQUARE procedures 

were used in SAS (SAS Institute Inc., 1985) to select the 

best possible models. The fit statistics of the newly created 

models, though, were similar to the previous two-variable 

models but were more complex, so these new models were 

rejected from further consideration. 

A graph of the annual basal-area change models is 

illustrated in Figure 6. Growth decreases the larger the 

basal area, as expected, but growth increases the higher 

the elevation, up to 2,000 feet. Growth in period 1 is more 

influenced by elevation than growth in period 2 which is more 

affected by basal area. Hence, there appears to be a change 

in the growth relationship between the two growth periods. 

To further evaluate the predictive ability of the models, 

several fit statistics were calculated to show how well the 

model could predict the data from which it was developed 

(Table 4). As expected, the bias of each model is zero since 

the bias is a function of the sum of residuals from a 

regression model. The absolute bias is of more interest 

because it expresses the amount one may expect the 

predicted basal-area growth to differ from the true observed 

value. This error amounted to approximately 1 square foot 

for both growth periods and represented a 48- and 92- 

percent error rate for growth periods 1 and 2, respectively. 

In addition, the percent bias and percent absolute bias are 

quite large. However, they must be interpreted with caution 

since they can be inflated by very small observed values. 

These statistics indicate that the predictability of the models 

is quite low due to variability inherent in the red spruce-fir 

data. 
3 I ..1 4 1 .-. 

I) LO 20 ,c 40 IO IC lo .a so 100 110 120 110 1.0 ,(I 

INrlAL STAND BASAL AREA (SQ. -/ACRE) 

iii : r=0.14 A=lpoint p = 0.18 B = 2 point 

8 : C=BpoinD .; . c 

INITIAL PROPORTION SO!7WOOD BASAL AREA 

ELEVATION (FEET) 

r = -0.17 

p = 0.11 

A = 1 point 

B=2points 

INITIAL QUADRATICMEAN STAND DIAMETER (INCHES) 

3 L 

5 .z! 4 ! ........ ............................................................................................................. .- .o 6" 80 lo< ,re 1.c .a0 xm 20" 220 >.o zm a" 300 >zo 3.0 360 3.0 400 -20 a.0 .60 4.0 500 ,zo 

INKlAL NUMBER OF TREES PER ACRE 

Figure 4.-Relationship of annual basal-area change (square feetiacre) and initial stand conditions in growth period 1. 

The correlation coefficient, r, and its associated p-value are, given. 
5 a, r = -0.28 

p = 0.01 ,. A = 1 point 

B = 2 points 

-I \ 3 -. ! 

5 -, i a ! ......................................................................................................................... 

0 I" 10 Y I" I/ SO I* 80 9G ,or 111 111 110 1.0 Ll" 160 ,,a ,I0 L1" 200 210 210 z1(/ 2.0 1 

INITIAL STAND BASAL AREA (SQ. FTIACRE) 

6. 

c ; r = -0.04 A = 1 point 

TT p= 0.70 B=Zpoints 0 ': C = 3 points i : *: .A . . . 

INITIAL PROPORTION SOFTWOOD BASAL AREA 

e. r = 011 A = 1 point 

9 >i p = 0.33 B = 2 points 

C = 3 points 9 : *: . g 1;. 5 

W ': B 8 4,vn::.: 

9 b -1 :. . . 0 0. 

5 1 

ELEVATlON (FEET) 

INITIAL QUADRATICMEAN STAND DIAMETER (INCHES) 

A = 1 point 

B = 2 pointr 

2 : Z -7 ! a 1 ............................................................. ............................................... --.--.- 0 25 ,O I> LOO 12, LX Ilr 200 2zr 210 21, IOD %1 150 3" ro9 425 rro rrr roo 52% $50 573 a00 

INITIAL NUMBER OF TREES PER ACRE 

Figure 5.-Relationship of annual basal-area change (square feetlacre) and initial stand conditions in growth period 2. 

The correlation coefficient, r, and its associated p-value are given. 
Annual Basal-Area 

Change (sq. ft./acre) 

Growth Period 1 

0 I I I I 

0 K 100 150 200 

Stand Basal Area (sq, ft.lacre) 

Annual Basal-Area 

Change (sq, ft./acre) 

Growth Pernod 2 

-1 ' I I I I 

0 50 100 150 200 

Stand Basal Area (sq. ft.lacre) 

Figure 6.-Plot of the basal area growth-prediction equation relationships. 
Predicted Annual BasalArea Change (sq, ft.lacre) 

Growth Period 1 

Predicted Annual BasalArea Change [sq, ft.lacre) 

50 100 150 

Stand Basal Area (sq. ftlacre) 

Growth Period 2 

Stand Basal Area (sq. ft.lacre) 

Figure 7.-Confidence intervals (95 percent) on the mean predicted annual basal-area change (square feetlacre) when 

elevation is kept constant at the mean of 724 feet. 
The R2, mean square error, and fit statistics provide criteria 

for model evaluation, but it is still important to analyze the 

variablility in prediction. To further address the issue, 

confidence intervals on the predicted mean response at 

various points in the sample space of the independent 

variables were developed (Fig. 7). The intervals, too, reveal 

that the models are not useful for predicting growth since 

the intervals are quite wide. They may, however, be useful 

in relative trend comparisons. 

Surviving-Tree Diameter Growth 

The approach in selecting a model for annual surviving-tree 

d.b.h. growth was similar to that used for annual basal-area 

change; that is, the relationships between diameter growth 

and the five stand variables were determined. Individual 

tree d.b.h. was included as a potential predictor. Graphic 

plots of d.b.h. growth and the six variables indicated little 

linear relationship and a considerable amount of variation. 

However, all variables except ELEV revealed a highly 

significant correlation (Table 5). No linearizing 

transformations were identified. Again, all possible models 

of the six basic variables were examined, yielding a total of 

63 models. STEPWISE and RSQUARE procedures also 

were performed on the six basic stand variables and their 

two-way interactions. Results indicated that the variables 

NT and PSW were important since they were continuously 

selected as candidates in the best models formulated by the 

variable selection procedures. Conceptually, it seemed 

reasonable to include d.b.h. as a predictor; it was a highly 

significant candidate in the variable selection procedure for 

growth period 2. The final model selected for growth period 

I was 

DBHG = 0.197 - 0.0948*PSW - 0.000122*NT + 

0.00237'DBH 

with R2 = 0.09 and MSE = 0.034 

and for growth period 2 

DBHG = 0.129 - 0.0550*PSW - 0.000097*NT + 

0.00436* DBH 

with R2 = 0.15 and MSE = 0.015 

and all parameters were significant at the 0.01 level. The 

magnitude and sign of all parameters are consistent for 

both growth periods and are biologically sensible and 

interpretable. 

Trends of the annual tree d.b.h. growth models are shown 

in Figure 8 where 70 and 100 percent softwood stands are 

illustrated over three density ranges (NT = 100, 300, 500). 

D.b.h. growth increases the larger the diameter of the tree, 

and the slope of this relationship is greater for growth period 

2. Diameter growth decreases with increasing tree density 

which is an expected trend in stand development. Growth 

also declines as softwood percentage in the stand 

increases. This may be attributable to the tendency of 

softwood species to dominate the poorer sites; so, as the 

softwood proportion increases, site quality and, 

consequently, growth decline. 

The fit statistics for the model indicate that once again, it is 

relatively poor for predicting growth (Table 6). As expected, 

the bias is zero but the absolute bias represents an error 

rate of approximately 50 percent when compared to the 

mean observed value in each growth period. 

Temporal Growth Change 

Stand Basal-Area Growth 

Stand basal-area growth change was assessed by 

comparing growth during growth periods I and 2. Actual 

basal area growth was 2.29 square feetlacre and 1.29 

square feetlacre for periods 1 and 2, respectively, 

representing a 1 .OO square footlacre decrease. This 

decrease may be due to changing stand conditions, the 

spruce budworm infestation during the second period, or 

pollution. Because stand conditions, such as density, are 

known to affect growth rates, any temporal comparison 

should adjust growth for these conditions. Such growth 

relationships are described with the previously formulated 

regression growth models and it is postulated that they 

describe growth during these two growth periods. Hence, to 

adjust the growth rates for varying stand conditions, growth, 

during growth period 2, was projected by using the initial 

stand conditions at period 2 and the basal-area change 

equation that describes growth in period 1. Here it is 

assumed that if the growth relationship has not changed in 

growth period 2, then the model from growth period 1 

should be unbiased in describing the observed growth in 

period 2. The results were that growth was 2.06 square 

feetlacre during period 2 when the growth relationship for 

period 1 was used while the observed was 1.29 square 

feetlacre. This is a difference of 0.77 square footlacre with 

a 95 percent confidence interval of 0.70 to 0.83 square 

footlacre, indicating a significant difference in net change 

after adjusting for stand conditions based on the 

relationships in growth period 1. 

Surviving-Tree Diameter Growth 

Similar analyses were performed for tree d.b.h. growth. 

Originally the growth was 0.091 1 inches and 0.0759 inches 

for periods 1 and 2, resulting in a change of 0.0152 inches. 

Recall that the models for diameter growth were functions 

of stand and tree characteristics through PSW, NT, and 

d.b.h. After adjusting the growth in period 2 by the growth 

model in period I, the d.b.h. growth was 0.0820 which 

resulted in a difference of only 0.0061 inches compared with 

0.0759 inches in period 2. The 95 percent confidence 

interval is 0.0051 and 0.0071, indicating a significant 

difference in d.b.h. growth after adjusting for stand and tree 

conditions. 
Annual DBH 

Growth (inches) 

0,20 F 

0.15 

0.10 

Annual DBH 

Growth (inches) 

PSW = 1.00 

PSW = 0.70 

- 

- 

__-- & __--- 

' __-- ___--- - ___--- ___--- / 

__---- _--- 

__--- __-- -____---- 

r 

0.05 

- - - - - 1970's 

I 0.00 I I 

5 10 15 2 0 

DBH (inches) 

- 

1 960's ----- 1970's 

I I 

Figure 8.-Plot of tree diameter growth-prediction equation relationships. 

0.00 1 

5 10 15 2 0 

DBH (inches) 
I Conclusions 

0 Stand basal-area change has declined from the 1960's to 

the 19701s, and the change is significant after adjusting 

for stand conditions. 

Surviving-tree d.b.h, growth has declined from the 1960's 

to the 19701s, and the change is significant after 

adjusting for stand and tree conditions. 

Although there are significant correlations between net 

change in stand basal area and stand characteristics, it is 

doubtful that conventional regression modeling 

techniques could yield equations useful in predicting 

growth because of variability in the growth of red sprucefir stands. 

Also, despite significant correlations between tree d.b.h. 

growth and stand and tree conditions, regression 

modeling for predictive purposes yielded poor results. 

Possibly, an individual-tree, distant-dependent modeling 

approach would prove to be a more useful technique for 

predicting growth. This approach uses more precise 

information on the micro-environment of a tree and one 

does not have to rely on stand averages that may not be 

representative for an individual tree. However, the 

disadvantage of this approach would be the requirement 

of a very demanding data set and increased computer 

costs for model execution. 

References 

Ferguson, R.H.; Longwood, F.R. 1960. The timber 

resources of Maine. Upper Darby, PA: U.S. Department 

of Agriculture, Forest Service, Northeastern Forest 

Experiment Station. 77 p. 

Ferguson, R.H.; Kingsley, N.P. 1972. The timber 

resources of Maine. Resour. Bull. NE-26. Upper Darby, 

PA: US. Department of Agriculture, Forest Service. 

129 p. 

Hornbeck, J.W.; Smith, R.B. 1985. Documentation of red 

spruce growth decline. Canadian Journal of Forest 

Research. 156: 1 199-1 201. 

Powell, D.S.; Dickson, D.R. 1984. Forest statistics for 

Maine: 1971 and 1982. Resour. Bull. NE-81. Broomall, 

PA: U.S. Department of Agriculture, Forest Service, 

Northeastern Forest Experiment Station. 194 p. 

SAS Institute Inc. 1985. SAS User's Guide: Statistics. 

Version 5 edition. Cary, NC: SAS Institute, Inc. 956 p. 

Scott, J.T.; Siccama, T.G.; Johnson, A.H.; Breisch, A.R. 

1984. Decline of red spruce in the Adirondacks, New 

York. Bulletin of the Torrey Botanical Club. 11 1: 438-444. 

Seegrist, D.W.; Arner, S.L. 1982. Mortality of spruce and 

fir in Maine in 1976-78 due to the spruce budworm 

outbreak. Res. Pap. NE-491. Broomall, PA: U.S. 

Department of Agriculture, Forest Service, Northeastern 

Forest Experiment Station. 3 p. 

Siccama, T.G.; Bliss, M.; Vogelmann, H.W. 1982. 

Decline of red spruce in the Green Mountains of 

Vermont. Bulletin of the Torrey Botanical Club. 109: 

163-1 68. 

Solomon, D.S.; Hosmer, R.A.; Hayslett, Jr., H.T. 1986. 

A two-stage matrix model for predicting growth of 

forest stands in the Northeast. Canadian Journal of 

Forest Research 16: 521 -528. 

Solomon, D.S.; Hosmer, R.A.; Hayslett, Jr., H.T. 1987. 

Fiber Handbook: a growth model for spruce-fir 

and northern hardwood forest types. Res. Pap. 

NE-602. Broomall, PA: U.S. Department of Agriculture, 

Forest Service, Northeastern Forest Experiment Station. 

19 p. 

Solomon, D.S.; Hosmer, R.A.; Zarnoch, S.J.; Droessler, 

T.D. In preparation. A spatial and temporal assessment 

of forest growth decline for tree species in the 

northeast. 

Van Deusen, P.C. 1987. Testing for stand dynamic 

effects on red spruce growth trends. Canadian Journal 

of Forest Research 17: 1487-1 495. 

Vogelmann, H.W.; Badger, G.J.; Bliss, M.; Klein, R.M. 1985. 

Forest decline on Camels Hump, Vermont. Bulletin of 

the Torrey Botanical Club. 11 2: 274-287. 
Table 1 .-Distribution of 87 remeasured red spruce-fir plots by stand characteristics at inventory 1 

Quadratic-mean stand diameter (inches) 

Stand basal 

area (ft2/a) 5 6 7 8 9 10 11 Total 

0-40 

40-80 

80-1 20 

120-1 60 

Total 

Proportion softwood per stand basal-area 

Stand basal 

area (ft2/a) 0.65- 0.70- 0.80- 0.90- 

0.70 8.80 0.90 1 .OO Total 

0-40 

40-80 

80-1 20 

120-1 60 

Total 

Number of trees per acre 

Stand basal 0- 100- 200- 300- 400- 500- 

area (ft2/a) 1 00 200 300 400 500 600 Total 

0-40 

40-80 

80-1 20 

1 20-1 60 

Total 

Elevation (feet) 

Stand basal 0- 400- 800- 1200- 1600- 2000- 

area (ft2/a) 400 800 1200 1600 2000 2400 Total 

0-40 7 2 1 3 1 14 

40-80 11 6 6 2 3 1 29 

80-1 20 8 6 8 5 1 28 

120-1 60 4 1 10 1 16 

Total 30 15 25 11 4 2 87 
Table 1 (continued) 

Proportion softwood per stand basal-area 

Quadratic-mean 

stand diameter 0.65- 0.70- 0.80- 0.90- 

(inches) 0.70 0.80 0.90 1 .OO Total 

5 

6 

7 

8 

9 

10 

11 

Total 

Quadratic-mean Number of trees per acre 

stand diameter 0- 100- 200- 300- 400- 500- 

(inches) 100 200 300 400 500 600 Total 

5 

6 

7 

8 

9 

10 

11 

Total 

Quadratic-mean Elevation (feet) 

stand diameter 0- 400- 800- 1200- 1600- 2000- 

inches 400 800 1200 1600 2000 2400 Total 

5 2 1 3 

6 12 3 8 5 2 30 

7 10 10 9 1 2 2 34 

8 4 1 5 4 14 

9 2 1 1 4 

10 1 1 

11 1 1 

Total 30 15 25 11 4 2 87 
Table 1 (continued) 

Proportion softwood Number of trees per acre 

per stand 0- 100- 200- 300- 400- 500- 

basal area 100 200 300 400 500 600 Total 

0.65-0.70 4 4 8 

0.70-0.80 1 5 9 1 1 17 

0.80-0.90 5 7 5 3 20 

0.90-1 .OO 2 9 16 11 3 1 42 

Total 3 19 36 21 7 1 87 

Proportion softwood 

per stand 

basal area 

0.65-0.70 

0.70-0.80 

0.80-0.90 

0.90-1 .OO 

Total 

Elevation (feet) 

0- 400- 800- 1200- 1600- 2000- 

400 800 1200 1600 2000 2400 Total 

Elevation (feet) 

Number of trees 0- 400- 800- 1200- 1600- 2000- 

per acre 400 800 1200 1600 2000 2400 Total 

0-1 00 

100-200 

200-300 

300-400 

400-500 

500-600 

Total 
Table 2.-Annual stand basal-area change (square feetlacre) and mean stand initial growth-period conditions for 

red spruce-fir stands 

Geographic Growth Stand basal-area growth Mean stand conditions 

unit period Na Mean S.D.* BA~ QM~ PSW~ NT~ ELEV~ 

Total 1 87 2.29 1.53 8 1 7.5 0.88 258 724 

2 87 1.29 1.61 107 7.8 0.89 324 724 

*Standard deviation 

aN = Number of plots used in analysis. 

bBA = lnitial stand basal-area (ft21acre) at beginning of 

growth period. 

CQM = lnitial quadratic-mean stand diameter (inches) at 

beginning of growth period. 

dPS~ = lnitial proportion of plot basal area in softwood 

species at beginning of growth period. 

eNT = Initial number of trees per acre at beginning of the 

growth period. 

'ELEv = Elevation (feet) of plot. 
Table 3.-Individual annual surviving-tree d.b.h. growth, and mean tree and stand initial growth-period conditions 

for red spruce 

Geographic 

unit 

1 

Growth 

period 

D.b.h. growth Tree d.b.h. Mean stand conditions 

Na Mean S.D.* Mean BAb QMC pSwd NTe ELEV 

Total 

*Standard deviation 

W = Number of plots used in analysis. 

bBA = lnitial stand basal-area (ft2/acre) at beginning of 

growth period. 

CQM = lnitial quadratic-mean stand diameter (inches) at 

beginning of growth period. 

dPSW = Initial proportion of plot basal area in softwood 

species at beginning of growth period. 

eNT = Initial number of trees per acre at beginning of the 

growth period. 

'ELEV = Elevation (feet) of plot. 
Table 4.-Mean values of fit statistics for annual basal-area change models based on observed (Oi) and predicted 

(Pi) values 

Percent 

Growth Absolute Percent absolute 

period Observed Predicted Biasa biasb biasC biasd 

aBias = (Pi - Oi) / N 

bAbsolute Bias = ]Pi - Oil I N 

CPercent Bias = 100 (Pi - Oi) 1 NOi 

dPercent Absolute Bias = 100 )Pi - Oil I NOi 

Table 5.-Correlation of annual tree d.b.h. growth (inches) with tree and stand conditions. Figures in parentheses 

are probability values associated with testing hypothesis: correlation coefficient is zero 

Growth Tree 

period d.b.h. 

aBA = Initial stand basal area (ft2/acre) at beginning of 

growth period. 

bQM = lnitial quadratic-mean stand diameter (inches) at 

beginning of growth period. 

CPSW = lnitial proportion of plot basal area in softwood 

species at beginning of growth period. 

d~~ = lnitial number of trees per acre at beginning of 

growth period. 

eELEV = Elevation (feet) of plot. 
Table 6.-Mean values of fit statistics for annual diameter-growth models based on observed (Oi) and predicted 

(Pi) values 

Percent 

Growth Absolute Percent absolute 

period N Observed Predicted Biasa biasb biasC biasd 

aBias = (Pi - Oi) 1 N 

bAbsolute Bias = [Pi - Oi 1 / N 

CPercent Bias = 100 (Pi - Oi) I NOi 

dPercent Absolute Bias = 100 JPi - Oil / NOi 

eBased on N = 91 1 observations due to elimination of 

observations when Observed is zero. 

'~ased on N = 1219 observations due to elimination of 

observations when Observed is zero. 
Zarnoch, S.J.; Gansner, D.A.; Powell, D.S.; Birch, T.A. 1990. Stand 

basal-area and tree-diameter growth in red spruce-fir forests in 

Maine, 1960-80. Res. Pap. NE-633. Radnor, PA: U.S. Department of 

Agriculture, Forest Service, Northeastern Forest Experiment Station. 

18 p. 

Stand basal-area change and individual surviving red spruce d.b.h. growth 

from 1960 to 1980 were analyzed for red spruce-fir stands in Maine. 

Regression modeling was used to relate these measures of growth to stand 

and tree conditions and to compare growth throughout the period. Results 

indicate a decline in growth. 

Keywords: stand basal-area; tree-diameter growth; red spruce; fir; Maine 

*U. S. GOVERNMENT PRINTING OFFICE: 19901748-070100017 
Headquarters of the Northeastern Forest Experiment Station is in Radnor, Pennsylvania. Field laboratories are maintained at: 

Amherst, Massachusetts, in cooperation with the University of Massachusetts 

Berea, Kentucky, in cooperation with Berea College 

Burlington, Vermont, in cooperation with the University of Vermont 

Delaware, Ohio 

Durham, New Hampshire, in cooperation with the University of New Hampshire 

Hamden, Connecticut, in cooperation with Yale University 

Morgantown, West Virginia, in cooperation with West Virginia University 

Orono, Maine, in cooperation with the University of Maine 

Parsons, West Virginia 

Princeton, West Virginia 

Syracuse, New York, in cooperation with the State University of New York, College of Environmental Sciences and Forestry at Syracuse University 

University Park, Pennsylvania, in cooperation with The Pennsylvania State University 

Warren, Pennsylvania 

Persons of any race, color, national origin, sex, age, religion, or with any handicapping condition are welcome to use and enjoy ail facilities, programs, and services of 

the USDA. Discrimination in any form is strictly against agency policy, and should be 

reported to the Secretary of Agriculture, Washington, DC 20250.