United States 

Department of 

Agriculture 

Forest Service 

Pacific Southwest 

Forest and Range 

Experiment Station 

General Technical 

Report PSW--115 

Ten-Year Risk-Rating 

Systems for California 

Red Fir and White Fir: 

development and use 

George T. Ferrell 
Ferrell, George T. 1989. Ten-year risk-rating systems for California 

red fir and white fir: development and use. Gen. Tech. Rep. PSW115. Berkeley, CA: Pacific Southwest Forest and Range Experiment 

Station, Forest Service, U.S. Department of Agriculture; 12 p. 

Logistic regression equations predicting the probability that a tree 

will die from natural causes--insects, diseases, intertree competition--

within 10 years have been developed for California red fir (Abies 

magnifica) and white fir (A. concolor). The equations, like those with 

a 5-year prediction period already developed for these species, are based 

on analysis of crown and bole characteristics of trees, and are readily 

programmed into pocket calculators for field use. For user convenience, 

the equations are formulated into Award-Penalty Point Systems, in 

which a tree is awarded or penalized points on the basis of ratings of its 

crown characteristics. The resulting Risk Point Total is related to the 

percentage of a hypothetical population of identical trees expected to die 

within 10 years. Three risk classes (low, medium, and high) are defined 

and depicted for rapid visual estimation of risk in applications where a 

more precise estimate is not required. 

Previous systems for these firs applied only to trees at least 10 inches 

(25.4 cm) in d.b.h. growing in mature stands. These new systems are 

applicable to firs down to 4 inches (10 cm) in d.b.h., growing in stands 

with a wide variety of size and age structure, in northern California. 

Outside this range, in central and southern California, the systems may 

be used tentatively, pending testing in these regions. 

Retrieval Terms: Abies concolor, Abies magnifica, California, mortality, risk-rating, bark-boring insects, tree diseases 

The Author: 

GEORGE T. FERRELL, a research entomologist in Berkeley, 

California, is studying pest impact assessment technology. 

Publisher 

Pacific Southwest Forest and Range Experiment Station 

P.O. Box 245, Berkeley, California 94701 

July 1989 
Ten-Year Risk-Rating 

Systems for California 

Red Fir and White Fir: 

development and use 

George T. Ferrell 

CONTENTS 

Introduction ......................................................................... 1 

Developing the Risk-Rating Systems .................................. 1 

Plot Selection .................................................................... 1 

Data Analysis ................................................................... 2

Risk Equations ..................................................................... 3

Red Fir............................................................................... 3

White Fir ........................................................................... 3

Award-Penalty Point Systems ............................................. 7 

Visual Risk Classes .............................................................. 7 

Using the Risk-Rating Systems ........................................... 8 

Applicability ...................................................................... 8

Estimating Crown Condition.............................................. 8

Live Crown Percent..................................................... 10

Crown Density ........................................................... 10

Ragged Percent ........................................................... 10

Estimating Risk of Mortality ........................................... 11

Advantages of 10-Year Systems ....................................... 11 

References .......................................................................... 12 
INTRODUCTION 

Risk-rating systems developed previously for California red fir (Abies 

magnifica A. Muff.) and white fir (A. concolor [Gord. & Glend.] 

Lindl.) predict the probability that a tree will die within 5 years (Ferrell 

1980). These systems apply to mature trees at least 10 inches (25.4 cm) 

d.b.h., growing in stands with the original overstory at least partially intact. 

Potential users, however, may want to predict risk over a somewhat longer 

time period and to use systems applicable to wider ranges of tree size, age, 

and stand structure. 

This report describes the development and use of risk-rating systems with 

a 10-year prediction period for California red fir and white fir. Based on 

ratings of crown characteristics, the systems predict the probability that a tree 

will die from natural causes--insects, diseases, intertree competition--

within 10 years. These risk-rating systems are applicable to trees at least 4 

inches (10 cm) d.b.h., growing in natural stands with a wide variety of 

structure and composition. 

DEVELOPING THE RISK-RATING SYSTEMS 

Plot Selection 

Thirty plots, each 1-acre (0.4 ha), were established from 1975 to 1977 to 

characterize living firs and monitor their survival in subsequent years. 

Twenty-two of the plots were in "mature" stands, that is, stands retaining the 

original mature overstory at least partially intact. These plots were part of the 

sample base used previously to develop risk-rating systems for mature red fir 

and white fir. Methods by which they were selected and surveyed are fully 

described elsewhere (Ferrell 1980), and are only briefly summarized here. 

Each plot was in a natural forest stand of at least 20 acres (8.1 ha), with forest 

cover as uniform as possible. Red or white fir, or both, comprised at least 30 

percent of the overstory. The plots were located in the Cascade and Siskiyou 

USDA Forest Service Gen. Tech. Rep. PSW-115. 1989. 1 
Mountains of northern California from the vicinity of Lassen Peak north to 

the Oregon border. 

All living firs at least 10 inches (25.4 cm) in diameter at breast height 

(d.b.h.) were marked and rated for 22 crown and bole characteristics. The 

remaining eight plots sampled "released" stands, that is, stands comprised of 

former understory trees remaining after overstory removal. Methods by 

which they were selected and surveyed were identical to those of the mature 

plots, except all living firs at least 4 inches (10 cm) d.b.h. were characterized. 

All plots were resurveyed in each of the first 5 years and again in the 10th year 

after plot establishment. Mortality of marked trees, together with their 

probable cause of death (i.e., insects, diseases, intertree competition, or 

other), were recorded. Pest complexes, which were the proximal agents of 

the mortality, were the same as described previously (Ferrell 1980) and will 

therefore not be described here. 

Data Analysis

Methods of data analysis were the same as those used previously in 

developing risk-rating systems for mature red fir and white fir (Ferrell 1980). 

Tree characteristics of greatest value as risk predictors were identified using 

the computer program SCREEN (Hamilton and Wendt 1975). This program 

screens the tree variables in step-wise fashion, selecting at each step the most 

significant predictor variable based on user-supplied levels of chi-square 

probability. In both tree species, more tree variables were significant at the 

95 percent level of probability than were usable in a practical risk-rating 

system. Only those variables selected early in the step-wise process, and 

convenient for field estimation, were used as predictor variables in the 

computer program RISK (Hamilton 1974). 

RISK estimates the coefficients of a logistic regression which has the 

form: 

P=1/(1+ex

) 

in which P is the predicted probability of individual tree death, e is the base 

of natural logarithms, and X is a vector of the risk predictors of the form: 

B0 + B1X1 + ...BnXn 

where B0...Bn are regression coefficients. Graphically, the logistics equation 

is usually a sigmoid curve that is frequently more appropriate for predicting 

tree death than either discriminant or probit analysis as neither the multivariate normal assumption or continuous predictor variables are required (Monserud 1976). 

2 USDA Forest Service Gen. Tech. Rep. PSW-115. 1989. 
RISK EQUATIONS 

Red Fir 

On the basis of screening the characteristics of the sample of 1125 red firs 

(1045 live, 80 dead) for association with tree death, three were selected as 

risk predictors: 

Live Crown Percent (CPCT)--percentage of tree height in living crown. 

Crown Density (CDEN)--as one of the following codes: 

0-- Dense (normal) foliage. 

1-- Ragged, one-sided. Crown missing on one or more sides 

because of competition with neighboring trees or other causes. 

2-- Ragged, dead and flagged. Crown ragged because of dead and/ 

or dying (flagged) branches, either scattered throughout crown 

or concentrated in killed top. 

3-- Ragged because of combination of (1) and (2). 

4-- Thin. Crown uniformly thinner than normal. 

Results of the screening analysis indicated this class variable could be 

used as a regressor as coded above with little loss in predictive power. 

Ragged Percent (RPCT)--combined percentage of crown raggedness 

because of scattered missing, dead or dying branches, and one-sided crown. 

From regression analysis of this sample of firs, the relationship for X in the 

equation P = 1 / (1 + c), predicting the probability of death within 10 years 

was: 

X = 0.749 + 0.058 CPCT - 0.286 CDEN - 0.022 RPCT. 

A chi-square goodness-of-fit test (table 1) indicated that the probability 

distributions of predicted and observed mortality did not differ significantly 

(0.990 < p <0.995), and from a practical standpoint the equation adequately 

predicted the observed distribution of mortality in the sample. 

White Fir 

On the basis of screening the characteristics of the sample of 2239 white 

firs (2149 live, 90 dead) for association with tree death, CPCT, CDEN, and 

RPCT were selected as risk predictors for this species also. 

The relationship for X in the regression equation predicting the 10-year 

probability of death was: 

X = 1.948 + 0.043 CPCT - 0.482 CDEN - 0.026 RPCT. 

A chi-square goodness-of-fit test (table 1) indicated that the probability 

USDA Forest Service Gen. Tech. Rep. PSW-115. 1989. 3 
Table 1--Distribution of fir samples in intervals of predicted probability of death 

within 10 years, and goodness-of-fit of observed to predicted mortality, compared by chisquare for the range of prediction 

4 USDA Forest Service Gen. Tech. Rep. PSW-115. 1989. 
Table 2--Award-Penalty Risk System for Red Fir 

USDA Forest Service Gen. Tech. Rep. PSW-115. 1989. 5 
Table 3--Award-Penalty Risk System for White Fir 

6 USDA Forest Service Gen. Tech. Rep. PSW-115. 1989. 
distributions of predicted and observed mortality did not differ significantly 

(.950 < p < .975), and from a practical standpoint the equation adequately 

predicted the observed distribution of mortality in the sample. 

AWARD-PENALTY 

POINT SYSTEMS 

The risk equations were translated directly into point systems, thereby 

enabling the calculation of risk by simple arithmetic. In the point systems, 

the tree is awarded points on the basis of the estimate of live crown percent 

(CPCT), and penalized points based on estimates of crown density (CDEN) 

and ragged percent (RPCT). The difference between award and penalty 

point totals-the risk point total-is expressed as the percentage of a 

hypothetical population of identical trees expected to die within 10 years 

(tables 2, 3). 

VISUAL RISK CLASSES 

Low, medium, and high risk classes were defined, enabling rapid visual 

estimation of relative risk in applications where a more precise estimate is not 

required. The risk classes are broad, allowing a single classification to be 

used for both tree species. The risk classes were based on mortality ratios, 

defined as the percentage of mortality in a class divided by the percentage of 

the class in the original stand (Dunning 1928, Keen 1936). For the fir risk 

classes, mortality ratios were calculated from the distribution of the fir 

samples in intervals of predicted probability of death within 10 years (table 

1). The mortality ratio of each interval was calculated as its percentage 

of predicted mortality divided by its percentage in the fir sample, and 

the intervals were combined into the following classes: 

Low risk: 

Mortality ratio (MR) < 0.4 

Probability of death within 10 years (P10) < 0.05 

Approximate percentage of the fir sample (pct. sample) = 60 percent 

USDA Forest Service Gen. Tech. Rep. PSW-115. 1989. 7 
Medium risk: 

0.4 < MR < 2.0 

0.05<P 10<0.15 

Pct. sample = 22 

percent 

High risk: 

MR > 2.0 

P10 > 0. 15 

Pct. sample = 18 percent 

Representative trees in each of the risk classes are illustrated (fig. 1), 

enabling rapid classification without recourse to numerical estimation procedures. Trees with Live Crown Percentages of 80, 60, 40, and 20, and 

Ragged Percentages of 0, 20, 40, 60, and 80 are depicted, but trees with other 

estimates of these variables may be classified by interpolation or extrapolation. 

USING THE RISK-RATING SYSTEMS 

Applicability 

These risk-rating systems predict the probability of individual tree death 

within 10 years as a result of natural causes--insects, diseases, or intertree 

competition (fire, windthrow, or other are not included). The systems apply 

to firs at least 4 inches (10 cm) d.b.h., growing in natural stands with a wide 

variety of age, size, and species composition. Geographically, the systems 

are applicable to the southern Cascade Mountains from Lassen Peak north to 

Mt. Shasta and to the eastern Siskiyou Mountains near the Oregon border. 

Based on similarity in weather patterns, pests complexes, and tree growing 

sites, these systems should apply also to firs in the Warner Mountains and 

nearby ranges in northeastern California, in the Salmon-Trinity and Marble 

Mountains in northwestern California, and in the Sierra Nevada north of 

Lake Tahoe. Outside this region, they should be used only tentatively, 

pending studies to test them in other regions. 

Estimating Crown Condition 

Estimation procedures are identical for red fir and white fir, and are the 

same as used in the risk-rating and growth classification systems developed 

previously for these species (Ferrell 1980, 1983). 

8 USDA Forest Service Gen. Tech. Rep. PSW-115. 1989. 
Figure 1--Risk classes for rapid visual prediction of 10-year mortality in California 

red fir and white fir: (left to right) low, medium, and high risk. 

USDA Forest Service Gen. Tech. Rep. PSW-115. 1989. 9 
Live Crown Percent 

Live crown percent (CPCT) is the percentage of a tree's total height 

occupied by live crown, estimated to nearest 10 percent. The live crown is 

defined as extending from the tree's top, regardless of whether live or dead 

(topkill, spiketop), to the lower limit of the living crown. If the top is missing 

(broken off), the live crown extends downward from the point of breakage. 

To set the lower limit of live crown: 

• Exclude isolated lower branches 

• For one-sided crowns, use longer side 

• If branches droop, use horizontal projection of branch tips onto bole. 

Crown Density 

Crown density (CDEN) categorizes the crown as to shape, and foliage 

condition and density. 

Dense--foliage with needles normal in length, number, and color. Dead, 

dying, off-color, or thin foliage, if present, amounting to less than 5 percent 

of total crown. 

Ragged--localized reduction in foliage density because of 

• One-sidedness--one side of crown or portion thereof missing because of 

shading or crown injury resulting from falling neighbor tree (crownraking) 

• Dead and dying branches, either scattered throughout crown, or concentrated in top (topkill, spiketop) or other section of crown (ignore missing, 

broken tops) 

• Combination of one-sidedness and scattered dead or dying branches 

Thin--crown uniformly sparser than normal from reduced number and 

length of needles. 

Ragged Percent 

Ragged percent (RPCT) is the combined percentage of crown missing and 

dead or dying, estimated to nearest 10 percent of crown. Include missing 

portions of crown above lower limit of live crown, whether contributing to 

one-sidedness or not. Include portions of crown that are dead or missing 

because of topkilling, regardless of whether topkill is recent (dead foliage 

retained) or older (dead foliage missing as in spiketop). 

Variation in estimates of Live Crown Percent and Ragged Percent tend to 

compensate for one another in the calculation of risk for any individual tree. 

For example, including isolated lower branches in the live crown, while 

leading to higher estimates of Live Crown Percent, will be compensated for 

by resultant increases in estimates of Ragged Percent. Trials indicate that the 

same, or closely similar estimates of risk will be obtained regardless of such 

differences in the height at which the observer sets the lower limit of the live 

crown. 

10 USDA Forest Service Gen. Tech. Rep. PSW-115. 1989. 
Estimating Risk of Mortality 

For field use, the risk equations are readily programmed into pocket 

calculators. Those which retain the program after being switched off 

(constant memory) are preferable, to conserve battery power. Equations for 

the two species differ only in their coefficients; thus a single program can be 

devised which will estimate risk for both. Also, as the risk equations use 

virtually the same predictors as the growth classification equations previously developed for these firs (Ferrell 1983), reasonably concise calculator 

programs can be designed to predict both risk and growth classes of either 

species. Pocket calculators have the advantage of providing precise estimates without the use of mental arithmetic. For applications where a less 

precise estimate of risk is satisfactory, either the award-penalty point 

systems or the visual risk classification can be used. 

ADVANTAGES OF 

10-YEAR SYSTEMS 

These risk-rating systems have several advantages over those previously 

developed for California red fir and white fir (Ferrell 1980). There are fewer 

predictor variables requiring estimation, decreasing the time needed to rate 

trees. Also, the 10-year prediction period is more in concert with preferred 

intervals between stand entries for management purposes. Finally, to 

develop the 10-year systems, trees were surveyed over a longer time. The 

previous systems were based on a single year's survey, followed by estimation of 1-year probabilities of death, which were mathematically extrapolated to 5 years under the assumption that they remained constant from year 

to year. This assumption may not always be realistic, however, as fir mortality rates can vary in response to environmental variables such as weather 

(Ferrell and Hall 1975). And, in fact, trials suggest that for some trees, the 

5-year probabilities predicted by the previous systems may be too high as 

they exceed the 10-year probabilities predicted by the new systems. Estimates of risk obtained with the new systems are therefore probably more 

reliable, as they involve no such assumption or extrapolation. 

These risk systems are expected to be useful in marking trees for partial 

cuts intended to reduce mortality and maintain adequate stocking in residual 

stands. Predictions for trees, if integrated with appropriate growth data and 

summarized on a stand-wide basis, could also prove to be of value in stand 

yield prognoses. 

USDA Forest Service Gen. Tech. Rep. PSW-115. 1959. 11 
REFERENCES 

Dunning, Duncan. 1928. A tree classification for the selection forests of the Sierra Nevada. 

Journal of Agricultural Research 36: 755-771. 

Ferrell, George T. 1980. Risk-rating systems for mature red fir and white fir in northern 

California. Gen. Tech. Rep. PSW-39. Berkeley, CA: Pacific Southwest Forest and Range 

Experiment Station, Forest Service, U.S. Department of Agriculture; 29 p. 

Ferrell, George T. 1983. Growth classification systems for red fir and white fir in northern 

California. Gen. Tech. Rep. PSW-72. Berkeley, CA: Pacific Southwest Forest and Range 

Experiment Station, Forest Service, U.S. Department of Agriculture; 18 p. 

Ferrell, George T.; Hall, Ralph C. 1975. Weather and tree growth associated with white fir 

mortality caused by fir engraver and roundheaded fir borer. Res. Paper PSW-109. 

Berkeley, CA: Pacific Southwest Forest and Range Experiment Station, Forest Service, 

U.S. Department of Agriculture; 11 p. 

Hamilton, David A., Jr. 1974. Event probabilities estimated by regression. Res. Paper INT152. Ogden, UT: Intermountain Forest and Range Experiment Station, Forest Service, U.S. 

Department of Agriculture; 18 p. 

Hamilton, David A., Jr.; Wendt, Donna L. R. 1975. SCREEN: A computer program to 

identify predictors of dichotomous dependent variables. Res. Paper INT-22. Ogden, UT: 

Intermountain Forest and Range Experiment Station, Forest Service, U.S. Department of 

Agriculture; 10 p. 

Keen, F. P. 1936. Relative susceptibility of ponderosa pines to bark beetle attack. Journal 

of Forestry 34: 919-927. 

Monserud, Robert A. 1976. Simulation of forest tree mortality. Forest Science 22: 438-444. 

12 USDA Forest Service Gen. Tech. Rep. PSW-115. 1989. 
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