A Field Guide to Predict 

Delayed Mortality of FireDamaged Ponderosa Pine: 

Application and Validation 

of the Malheur Model

Walter G. Thies, Douglas J. Westlind, Mark Loewen, 

and Greg Brenner

United States 

Department of 

Agriculture 

Forest Service

Pacific Northwest

Research Station

General Technical 

Report

PNW-GTR-769

October 2008

DEPAR TMENT OF AGRICULT URE

Bole scorch

proportion = 0.15
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water, forage, wildlife, and recreation. Through forestry research, cooperation with the 

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Authors

Walter G. Thies is an emeritus scientist and Douglas J. Westlind is a forestry 

technician, U.S. Department of Agriculture, Forest Service, Pacific Northwest 

Research Station, Forestry Sciences Laboratory, 3200 Jefferson Way, Corvallis, 

OR 97331; Mark Loewen is a silviculturist, U.S. Department of Agriculture, 

Forest Service, Malheur National Forest, Emigrant Creek Ranger District, Hines, 

OR 97738. He is now at the Dixie National Forest, Cedar City, UT 84720. Greg 

Brenner is a consulting statistician, Pacific Analytics, LLC, P.O. Box 1064, 

Corvallis, OR 97339.
Abstract

Thies, Walter G.; Westlind, Douglas J.; Loewen, Mark; Brenner, Greg. 2008.

A field guide to predict delayed mortality of fire-damaged ponderosa pine: 

application and validation of the Malheur model. Gen. Tech. Rep. PNW-GTR769. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific 

Northwest Research Station. 16 p.

The Malheur model for fire-caused delayed mortality is presented as an easily 

interpreted graph (mortality-probability calculator) as part of a one-page field guide 

that allows the user to determine postfire probability of mortality for ponderosa 

pine (Pinus ponderosa Dougl. ex Laws.). Following both prescribed burns and 

wildfires, managers need the ability to predict the mortality of individual ponderosa 

pine trees based on burn damage. The model was developed from fire-caused 

delayed mortality observed for 4 years postburn in a replicated study of 12 burn 

units and 6 nonburned units near Burns, Oregon. During the fourth year, the 

percentage of mortality on burned units was not statistically different from that on 

nonburned units. Here we report validation data from 3,237 ponderosa pines in 10 

additional burns, observed for 3 years postburn, from the southern Blue Mountains 

and northern California that indicate a good fit between mortality predicted by the 

Malheur model and observed mortality. Tear-out copies of the field guide on water 

proof paper are provided. 

Keywords: Blue Mountains, fire, ponderosa pine, big trees, delayed mortality.



A Field Guide to Predict Delayed Mortality of Fire-Damaged Ponderosa Pine: Application and Validation of the Malheur Model

Introduction

The Malheur model is a two-variable model developed from data collected following prescribed burns on the Malheur National Forest near Burns, Oregon (Thies et 

al. 2005, 2006). Fire-caused delayed mortality of ponderosa pines (Pinus ponderosa

Dougl. ex Laws.) was surveyed annually for 4 years postburn. During the 4th year, 

the percentage of mortality on burned units was not statistically different from that 

on nonburned units. In the subsequent 6 years postburn (for a total of 10 years), the 

percentage of mortality on burned units remained at a low level similar to that on 

nonburned units. The model was used to generate a graph called the “mortalityprobability-calculator” or “the calculator.” The calculator allows a user to quickly 

determine the probability of mortality of fire-damaged ponderosa pine. Because 

the model predicts the probability of mortality for individual trees based on surface 

damage that reflects underlying physiological damage, it is valid for trees damaged 

by either prescribed fire or wildfire. 

Prescribed burning and wildland fire are being used as tools to achieve specific 

management objectives in western interior forests of the United States. Following a burn, managers need the ability to predict the mortality of individual trees. 

Mortality is evaluated to determine the success of burning prescriptions to achieve 

such management objectives as postfire stocking levels and to improve future 

prescriptions, and for all fires to better plan postfire activities such as hazard tree 

removal and restoration of wildlife habitat and watershed quality. Postfire mortality 

predictions need to be based on easily observable morphological and burn-damage 

characteristics that can be quickly assessed in the field. The Malheur model meets 

these criteria for ponderosa pine. Details of the model development and the study it 

was based on are published elsewhere (Thies et al. 2005, 2006).

We present the Malheur model here in graph form as a two-factor mortalityprobability calculator, and describe its use in a one-page field guide (app. 1) along 

with a list of cautions. Tear-out copies of the field guide are provided at the back 

of this GTR. In addition, a test of the efficacy of this model using data from 10 

validation stands from the south end of the Blue Mountains in eastern Oregon and 

the east side of the Cascade Range in northern California is provided (app. 2). The 

10 validation stands were not the same as those used for model development (fig. 1). 

Postfire mortality 

predictions need 

to be based on 

easily observable 

morphological 

and burn-damage 

characteristics 

that can be quickly 

assessed in the field. 

The Malheur model 

meets these criteria 

for ponderosa pine.
GENERAL TECHNICAL REPORT PNW-GTR-769

Using the Mortality-Probability Calculator

A tree is evaluated by first measuring the proportion of both bole and crown scorch. 

Bole scorch proportion is the maximum bole scorch (blackened) height as a 

proportion of total tree height (fig. 2). Crown scorch proportion is the length of the 

scorched (scorched or consumed needles) portion of the crown as a proportion of the 

total crown (fig. 2). The crown base is taken as the lower height of live crown (whorl 

of three or more live branches) as it existed prefire. The layer of scorched crown 

is often asymmetrical. The height of the scorched crown is taken as the average 

height for that layer measured at the bole. The proportion can be calculated by using 

heights measured with an instrument, such as a laser rangefinder with inclinometer 

or hand-held clinometer, or determined directly by something as simple as the 

proportion gauge provided on the one-page field guide. The mortality-probability 

calculator is used by locating a tree’s bole scorch proportion on the left vertical 

axis (the y-axis) and then moving horizontally to the right until reaching the crown 

scorch proportion. The value of the intercept point is the probability of mortality for 

that tree, determined from the nearest upper and lower diagonal lines of equal probability of mortality. The probability of mortality could be interpolated to the nearest 

0.01 although that degree of precision may exceed most operational requirements.

Figure 1—Location of stands used to collect Malheur model development and validation data.
A Field Guide to Predict Delayed Mortality of Fire-Damaged Ponderosa Pine: Application and Validation of the Malheur Model

This two-variable mortality-probability calculator was derived for each 0.1 

increment of probability of mortality from 0.0 to 1.0 (plus probabilities of 0.05 and 

0.95) by holding the probability constant while proportion of crown scorch was 

increased by increments of 0.1 and using the model to solve for the corresponding 

proportion of bole scorch. The points were plotted resulting in straight lines representing points of equal probability of mortality. 

Management Decision Tool

Use of the information from the Malheur model is determined by the objectives and 

needs of the land manager. Individual trees can be evaluated for probability of mortality, or a stand can be surveyed (sampled) and the proportion of trees projected to 

die can be determined. Probability of mortality for trees can be determined in the 

field using the calculator, or stem and crown scorch proportions can be recorded in 

the field and probability of mortality can be calculated in a spreadsheet. 

This tool can be used to monitor (1) whether objectives were met for prescribed 

burns and wildland fire use, or (2) to determine if economical salvage opportunities 

exist after wildfire in consideration of other management objectives. 

Figure 2—Measuring the proportions of bole scorch and crown scorch.
GENERAL TECHNICAL REPORT PNW-GTR-769

Individual tree example—

A management objective may require that all trees with a probability of mortality 

greater than 0.6 be marked for removal. Example 1: Proportion of bole scorch is 

determined to be 0.3; proportion of crown scorch is determined to be 0.5. Enter 

the calculator at 0.3 for bole scorch and 0.5 for crown scorch and find the intercept 

point. Note from the diagonal lines that the probability of mortality is slightly more 

than 0.3. If the designated probability limit is 0.6, the example tree would not be 

marked. 

Example 2: Proportion of bole scorch is 0.6; proportion of crown scorch is 0.6. 

Enter the calculator at 0.6 for bole scorch and 0.6 for crown scorch and find the 

intercept point. Note from the diagonal lines that the probability of mortality is 

approximately 0.82. If the management designated mortality probability limit is 

0.6, the tree would be marked for removal. The probability limit is established from 

management considerations. 

If access to the subject trees makes frequent returns possible, the limit may be 

established high (e.g., 0.9) with a plan to return to remove additional trees that die. 

If the area is remote, thereby making frequent returns difficult, the limit may be 

established low (e.g., 0.3) with an intent to cut most of the trees that will likely die 

from the fire with a single entry.

Survey example—

A management objective may require that an estimate be made of the proportion of 

trees in a stand that will die. Perhaps the manager needs to learn at an early date the 

success of a particular prescription or to evaluate the need to replant. It is important 

that sample trees be randomly selected and representative of the stand or the portion 

of the stand of interest. Each sample tree would be evaluated and its probability of 

mortality recorded. A mean of the probabilities will be an estimate of the proportion of the trees in the stand that can be expected to die. For example, assume that 

10 trees are representative and randomly selected from an area of interest and they 

have the following probabilities of mortality: 0.40, 0, 0, 0.55, 0, 0, 1.0, 0, 0.65, and 

0.55. The total is 3.15; the proportion of trees likely to die in the stand is 3.15/10 or 

0.315. Although the sample size in this example is unrealistically small, it illustrates 

the math involved. 


A Field Guide to Predict Delayed Mortality of Fire-Damaged Ponderosa Pine: Application and Validation of the Malheur Model

Cautions

Every model must be used with caution to ensure that the sample population being 

tested is within the limits of the data used to develop the model. The following 

considerations are provided for the Malheur model:

1. Evaluate only ponderosa pine. Although results for other species may 

appear to conform to the results for ponderosa pine, it is unlikely that such 

is the case. Additional testing would be required to adjust the model for 

other species. 

2. Sample within the geographic area of model development or where validation data from representative stands have been tested and results from the 

model have been shown to be a good fit to the observed data. (Note: At this 

writing the successfully tested geographic area of inference for the Malheur 

model ranges from the southern Blue Mountains of eastern Oregon south 

into northern California (app. 1, fig. 2). 

3. Obtain the most accurate measurement possible to determine the bole and 

crown scorch proportions consistent with management objectives. Avoid 

ocular estimates as they will likely differ by observer and thus not yield 

consistent results.

4. The model provides a probability of mortality for a given tree and not an 

absolute indication that a tree will live or die. A probability of 0.6 means 

that if 1,000 trees have crown and bole scorch proportions that fall on the 

0.6 line of probability, about 600 of them can be expected to die. All trees 

with a bole and crown scorch proportion that places them above the 0.6 

probability line have a greater than 0.6 probability of mortality. 

5. Because the model provides a probability, some trees predicted to live will 

die and some that are predicted to die will live. This was observed in stands 

used for both model development and validation. With or without fire, a 

few trees are likely to die in a stand each year because of other natural 

processes such as insects, disease, or limited resources. Additionally, a 

few trees with crown or bole scorch proportion equal to 1.0 will survive. 

Because of these anomalies, the model predicts a probability of mortality 

within the range from 0.011 to 0.972, rather than 0.0 to 1.0. The Malheur 

model will predict fire-caused mortality close to what would be observed 

in the next 3 years if the stand were undisturbed; however, the stands are 

biological systems and some small variation from the predicted mortality 

should be expected.

The model provides a 

probability of mortality 

and not an absolute 

indication that a tree 

will live or die.
GENERAL TECHNICAL REPORT PNW-GTR-769

6. The model predicts probability of mortality based on damage to individual trees and is not related to fire type or season of the burn. Data used to 

develop the model were collected from areas of prescribed burns; however, 

the sample trees encompassed the full range of burn-induced-damage from 

mild heat exposure and no visible damage to extreme burn damage with no 

chance of recovery. To access the full range of responses in these stands, 

data were collected from both spring and fall burns. The tested explanatory 

variables represented tree morphology, fire damage, and season of burn. 

After accounting for the fire damage variables, there was no indication of a 

difference in mortality between fall and spring burns. This was interpreted 

to mean that trees with similar degrees of damage from either burn season 

would have about the same probability of delayed mortality. We concluded 

that the mortality is related to the damage inflicted on each tree rather than 

the season as it relates to the physiological state of the trees. Because mortality is related to the damage inflicted, the type of fire is not important, and 

this model, although developed with data from prescribed burns, will work 

equally well with trees burned by a wildfire. One of the fires in the validation data set reported in appendix 1 was a prescribed burn that escaped and 

burned the stand as a wildfire. The data from that fire fit the Malheur model 

well and supports use of the model on trees damaged by wildfire. 

Acknowledgments

Creation of the Malheur model has taken a sustained effort from 1996 through 

2008 by many individuals through a variety of funding channels. The authors 

thank the Malheur National Forest, the Emigrant Creek Ranger District, and the 

Burns Interagency Fire Zone for their support throughout this effort. Without 

their constant and unselfish support this project would not have been possible. 

Fieldwork was conducted with funds provided by Forest Health Protection of the 

U.S. Department of Agriculture, Forest Service, through the Special Technology 

Development Program, the Pacific Northwest Research Station, and the Joint 

Fire Sciences Program. Special thanks to Mike Dubrasich of Forest Analytics of 

Lebanon, Oregon, for statistical review of the manuscript and to Karen Esterholdt 

for editing the manuscript. We also thank Paul Anderson, Erik Berg, Kenneth 

Higle, and Rick Kelsey for review and helpful comments during manuscript 

preparation. 
A Field Guide to Predict Delayed Mortality of Fire-Damaged Ponderosa Pine: Application and Validation of the Malheur Model

English Equivalents

When you know Multiply by To find

Centimeters (cm) 0.394 Inches

Meters (m) 3.28 Feet

Literature Cited

Hosmer, D.; Lemeshow, S. 2000. Applied logistic regression. 2nd ed. 

New York: John Wiley and Sons. 373 p.

Regelbrugge, J.C.; Conard, S.G. 1993. Modeling tree mortality following 

wildfire in Pinus ponderosa forests in the central Sierra of California. 

International Journal of Wildland Fire. 3: 139–148.

Ryan, K.C.; Peterson, D.L.; Reinhardt, E.D. 1988. Modeling long-term 

fire-caused mortality of Douglas-fir. Forest Science. 34: 190–199.

Saveland, J.M.; Neuenschwander, L.F. 1990. A signal detection framework 

to evaluate models of tree mortality following fire damage. Forest Science. 

36: 66–76.

Thies, W.G.; Westlind, D.J.; Loewen, M. 2005. Season of prescribed burn in 

ponderosa pine forests: impact on pine mortality. International Journal 

of Wildland Fire. 14: 223–231.

Thies, W.G.; Westlind, D.J.; Loewen, M.; Brenner, G. 2006. Prediction of 

delayed mortality of fire-damaged ponderosa pine following prescribed fires 

in eastern Oregon, USA. International Journal of Wildland Fire. 15: 19–29.

van Mantgem, P.J.; Stephenson, N.L.; Mutch, L.S. [et al.] 2003. Growth rate 

predicts mortality of Abies concolor in both burned and unburned stands. 

Canadian Journal of Forest Research. 33: 1029–1038.
Appendix 1—Field Guide
A Field Guide to Predict Delayed Mortality of Fire-Damaged Ponderosa Pine: Application and Validation of the Malheur Model

Appendix 2: Malheur Model Validation

Introduction

The Malheur two-factor model, presented here in graph form as the mortalityprobability calculator, predicted 96.4 percent of the observed mortality caused 

by the prescribed burns used for model development (Thies et al. 2006). But a 

model remains a hypothesis until it is validated by using data unrelated to the 

developmental data. We report here the results of an effort to validate the Malheur 

model in a limited area by evaluating sample trees in burns in 10 ponderosa pine 

(Pinus ponderosa Dougl. ex Laws.) stands in the southern Blue Mountains of 

eastern Oregon and the east side of the Cascade Range in northern California. 

The 10 validation burns are in different stands than the 12 burns used to collect 

data for model development. 

Methods

Validation stands (fig. 1, table 1) were identified and data collection begun within 

a month following their respective burns from fall 2002 through fall 2004. Stands 

were selected according to accessibility of a prescribed burn, available cooperation from Forest Service ranger districts, and geographic distribution of sites. The 

number of trees tagged in each stand was dependent on staff time and funding.

Within each stand, a starting point was selected near an access road in a portion 

of the stand typical of that burn. A random starting azimuth was selected within 

the azimuth range that would encompass the range of fire damage observed. If the 

first transect was not long enough to provide adequate numbers of trees, the crew 

Table 1—Stand summary for validation stands 

Stand name Latitude/longitude Area Elevation Burn date Mean d.b.h.a Mean height 

Hectares Meters Centimeters (range) Meters

Black Rock 1 43.88N, 118.86W 60 1595 Fall 2004 27.8 (8.9–85.1) 13.9

Black Rock 2 43.95N, 118.82W 90 1650 Fall 2004 24.1 (7.6–96.5) 12.2

Curry Springs 1 43.93N, 119.63W 30 1685 Fall 2002 37.8 (12.2–101.9) 19.3

Curry Springs 2 43.91N, 119.61W 30 1670 Spring 2003 41.2 (8.6–95.0) 20.7

Gabe 44.11N, 118.75W 55 1585 Fall 2004 43.2 (10.4–95.0) 21.3

Skookum 1 44.10N, 118.41W 30 1645 Fall 2002 42.7 (15.7–78.7) 21.3

Skookum 2 44.12N, 118.42W 30 1650 Spring 2003 43.6 (8.9–104.6) 21.2

Squaw Meadow 44.50N, 118.43W 90 1760 Fall 2004 24.6 (7.6–76.5) 13.8

Tennant 1 41.58N, 121.93W 240 1240 Fall 2004 39.1 (7.9–192.0) 18.3

Tennant 2 41.65N, 121.67W 45 1480 Fall 2004 34.9 (8.6–208.3) 16.8

a

 d.b.h. = diameter at breast height.
10

GENERAL TECHNICAL REPORT PNW-GTR-769

offset 50 to 100 m within the burn and continued along the back azimuth. The 

strip sampled extended 5 m to either side of the transect centerline. All standing 

ponderosa pine greater than 7.5 cm diameter breast high (d.b.h.) within the sampling 

strip were tagged. A numbered aluminum tag was placed on each tree, in numerical 

order, at breast height toward the transect centerline. 

Each tagged tree was evaluated and marked at the time of transect establishment as either alive (if the tree had some green needles) or dead (if all needles were 

scorched or discolored owing to heat from the fire). Dead trees were categorized by 

time of death as preburn mortality (based on bark condition, presence of decay, and 

lack of needles and fine twigs), immediate mortality (alive at the time of the burn 

but dead when tagged), and delayed mortality (found dead in later exams, table 2).

Table 2—Summary of tree means sampled from the 10 validation stands 

Stand name Trees alive at burn Trees dead after 3 years Mortality

Percent

Black Rock 1 298 42 14.1

Black Rock 2 294 35 11.9

Curry Springs 1 121 12 10.0

Curry Springs 2 249 24 9.6

Gabe 300 17 5.7

Skookum 1 289 35 12.1

Skookum 2 296 14 4.7

Squaw Meadow 300 80 26.7

Tennant 1 731 91 12.5

Tennant 2a 359 71 19.8

a The Tennant 2 burn began as a prescribed burn; however, the fires got out of control and created a wildfire 

situation. Sampling on this unit was done in the area of the wildfire using the same protocol as for other 

validation units. 

At the time of tagging, morphological variables were recorded for each tagged 

tree. The d.b.h. of each tagged tree was measured to the nearest 0.25 cm on the 

uphill side of the tree at 1.37 m above mineral soil, and the height was measured 

to the nearest 3.0 cm with a laser rangefinder with inclinometer (table 1). Two 

measures of fire-caused damage were recorded for each tree: crown scorch 

proportion and bole scorch proportion. 

Crown scorch proportion is the proportion of damaged crown length based 

on scorched or consumed needles. The total crown length is the distance from the 

tree tip to the lower height (whorl of three or more live branches) of live crown as 

it existed prefire. Immediately postfire, crowns that are alive but damaged show 

two layers: an upper green layer and a lower brown layer of scorched or consumed 

needles. Damage layers often were asymmetrical. The scorch height was taken as 
11

A Field Guide to Predict Delayed Mortality of Fire-Damaged Ponderosa Pine: Application and Validation of the Malheur Model

the average height for that layer measured at the bole. Heights were measured to the 

nearest 3.0 cm with a laser rangefinder with inclinometer. Crown scorch proportion 

as a measure of crown damage has been used by others and allowed reproducible 

results with a minimum of training of field crews (Thies et al. 2006). 

Bole scorch proportion is the maximum bole scorch height as a proportion of 

total tree height. Bole scorch is the distance from mineral soil to the highest point 

of bole blackening measured to the nearest 15 cm. 

Only those tagged trees living at the time of the prescribed burns were included 

in this validation evaluation. Each fall, starting with the first growing season after 

the burn, sample transects were revisited and delayed mortality recorded; trees 

without any green needles, and not previously marked as dead, were recorded as 

having died that growing season. 

We tested the agreement between the mortality predicted by the Malheur 

model and the mortality observed 3 years postburn of tagged trees from the 10 

validation stands using the Hosmer-Lemeshow goodness of fit test, the receiver 

operating characteristic (ROC) scores, and percentage of correctly classified trees. 

The Hosmer-Lemeshow goodness of fit test was used to evaluate the fit of the full 

and reduced (Malheur) models to the development data (Thies et al. 2006) and the 

Malheur model to the validation data. The data were first partitioned into groups 

based on the predicted probability of mortality (table 3). We classified the mortality 

probabilities from 0.0 to 1.0 into 10 groups identified by the midpoints (0.5 to 0.95). 

The sum of the predicted probability of mortality of all trees in a decile was used 

as the projected number of trees expected to die in that class. The actual observed 

status of the trees 3 years postburn (alive, dead) was recorded for each decile 

from the observed dead trees. If the Malheur model is accurate, then the projected 

Table 3—Calculated mortality and observed mortality for the Malheur model across the range of probability 

of mortality classes 

Probability-of-mortality classes, by midpoint percentage

Data set 5 15 25 35 45 55 65 75 85 95 Total

Number

Validation data set:

Total trees in class— 2,380 304 151 94 65 58 52 44 37 52 3,237

Projected dead 75 44 37 33 29 32 33 33 32 50 398

Observed dead 72 31 24 34 33 36 39 37 34 46 386

Development data set:a

Total trees in class—a 2,315 280 162 130 153 99 82 78 59 57 3,415

 Projected deada 64 41 40 46 69 54 53 59 50 54 530

 Observed deada 80 44 29 43 60 67 56 61 55 55 550

a From Thies et al. 2006.
12

GENERAL TECHNICAL REPORT PNW-GTR-769

number of dead trees should be close to the observed number of dead trees. The 

Hosmer-Lemeshow test statistic (HL) was calculated by comparing the observed 

and expected frequencies of the dead trees in the decile groups. The test statistic 

has a chi-square distribution with a desirable outcome of nonsignificance (P > 0.05), 

thereby indicating that the model prediction does not significantly differ from the 

observed data (Hosmer and Lemeshow 2000, van Mantgem et al. 2003). The ROC 

analysis paralleled that done by Saveland and Neuenschwander (1990) to evaluate 

models of tree mortality following fire damage. The ROC curve is a plot of the 

sensitivity (y-axis) and 1-specificity (x-axis) over all possible mortality probability 

cutoff values. Sensitivity is the ability to correctly predict a tree to die (proportion 

of tree deaths that were predicted). Specificity is the ability to correctly predict a 

tree to live (proportion of surviving trees that were predicted). The area under the 

curve is a measure of the ability of the model to discriminate between dead and 

alive trees. The ROC area values range from 0 to 1.0. A value for the area under the 

curve of 1.0 indicates a perfect model, which would yield no false positives. The 

ROC values ≥0.7 are acceptable; values ≥0.9 are indicative of outstanding discrimination (Hosmer and Lemeshow 2000). 

Results and Discussion

Within the 10 validation stands, 3,237 ponderosa pine were evaluated. The Malheur 

model had a good fit to the data from the validation stands (table 3): HL = 10.31, d.f. 

= 8, P = 0.244. The Malheur model predicted a total mortality of 398 trees based 

on the two measured variables of fire damage. Three growing seasons postburn the 

actual observed mortality was 386 trees, a difference of 3.1 percent of the predicted 

mortality from the observed mortality. Table 3 illustrates the fit of the model across 

the range of probability-of-mortality classes. These results closely parallel the 

Malheur model fit to the data from the 3,415 ponderosa pine in the model development data set (Thies et al. 2006).

The ROC curve is presented as figure 3; the area under the curve is 0.8815 

(standard error 0.01134; 95-percent confidence interval of 0.8593 to 0.9038; P < 

0.0001) indicating a good fit between the predicted and the observed outcomes.

We used classification tables as a supplemental measure of model fit. For our 

analyses, 0.5 was selected a priori as the decision criterion. That is, trees with 

predicted probability of mortality, ≥0.5 are predicted dead. We used this cutoff 

criterion because we had no reason for selecting otherwise. A cutoff of 0.5 was 

used previously for fire-killed ponderosa pine (Regelbrugge and Conard 1993), for 

fire-killed Douglas-fir (Ryan et al. 1988), and is considered the most common cutoff 

used in a variety of applications (Hosmer and Lemeshow 2000). A classification 
13

A Field Guide to Predict Delayed Mortality of Fire-Damaged Ponderosa Pine: Application and Validation of the Malheur Model

Table 4—Classification table of the validation data set 

based on the Malheur model logistic regression using a 

cutoff of 0.5 probability of mortality

Observed

Predicted Alive Dead Total

Alive P(m) <0.5 2,800 194 2,994

Dead P(m) >0.5 51 192 243

 Total 2,851 386 3,237

Overall rate of correct classification = [(2,800 + 192)/3,237] × 100 = 92.4 percent.

Overall rate of correctly predicting mortality = 192/243 × 100 = 79.0 percent.

Figure 3—The ROC curve representing the relationship between the Malheur model and the 

validation data with the area under the curve being equal to 0.8815 (n = 3,237). Sensitivity is 

the false positive and specificity is the false negative.

table was prepared for the validation data set (table 4). The overall rate of correct 

classification was 92.4 percent. The overall rates of correctly predicting mortality 

of individual trees was 79.0 percent. 

The Malheur model fits the available data for wildfire-like conditions. One 

of the stands included in the validation set (Tennant 2) was a prescribed fire that 
14

GENERAL TECHNICAL REPORT PNW-GTR-769

escaped and burned much of the unit as a wildfire. The sample transects were 

placed in the wildfire portion of the stand, and the data were collected from sample 

trees (n = 359) using the same protocols followed for the other nine stands from 

which validation data were collected. The area under the ROC curve for Tennant 

2 is 0.8925 (standard error 0.02379; 95-percent confidence interval of 0.8459 to 

0.9391; P < 0.0001) indicating a good fit between the predicted and the observed 

outcomes. A classification table was prepared for the Tennant 2 data (table 5). The 

Table 5—Classification table of the Tennant 2 data set 

based on the Malheur model logistic regression using a 

cutoff of 0.5 probability of mortality

Observed

Predicted Alive Dead Total

Alive P(m) <0.5 272 25 297

Dead P(m) >0.5 16 46 62

 Total 288 71 359

Overall rate of correct classification = [(272 + 46)/359] × 100 = 88.6 percent.

Overall rate of correctly predicting mortality = 46/72 × 100 = 74.2 percent.

overall rate of correct classification was 88.6 percent. The overall rate of correctly 

predicting mortality was 74.2 percent. Similar results were observed for the 

nearby (fig. 2) Tennant 1 successfully conducted prescribed burn. The Tennant 1 

unit (n = 731) has an area under the ROC curve of 0.9378 (standard error 0.0125; 

95-percent confidence interval of 0.9132 to 0.9623; P < 0.0001. A classification 

table was prepared for the Tennant 1 data (table 6). The overall rate of correct 

classification was 93.6 percent, and the overall rate of correctly predicting mortality was 83.3 percent (table 6). We consider this evidence that individual trees 

respond to their fire-induced damage and trees with similar damage characteristics will have a similar probability of mortality whether the damage is induced 

by a prescribed fire or a wildfire. 

Table 6—Classification table of the Tennant 1 data set 

based on the Malheur model logistic regression using a 

cutoff of 0.5 probability of mortality

Observed

Predicted Alive Dead Total

Alive P(m) <0.5 629 36 665

Dead P(m) >0.5 11 55 66

 Total 640 91 736

Overall rate of correct classification = [(629 + 55)/731] × 100 = 93.6 percent.

Overall rate of correctly predicting mortality = 55/66 × 100 = 83.3 percent.

The Malheur model 

can be used to 

determine probability 

of fire-caused delayed 

mortality in individual 

trees regardless of 

whether the fire is a 

prescribed fire or a 

wildfire. 
15

A Field Guide to Predict Delayed Mortality of Fire-Damaged Ponderosa Pine: Application and Validation of the Malheur Model

The Malheur model did well in predicting the delayed mortality of “big” 

ponderosa pine (>53.3 cm). These big trees currently are being protected in U.S. 

Forest Service Region 6 and are of special concern to managers. Both the development and the validation stands contained big ponderosa pine. The validation 

stands contained 522 big trees of which 23 died; the Malheur model predicted that 

25 big trees would die. The largest tree in the validation data set was 208.3 cm 

dbh. The model development data set contained 213 big trees of which 15 died. A 

classification table was prepared for the combined big tree data (table 7). The overall rate of correct classification and the overall rate of correctly predicting mortality were 95.2 percent and 66.6 percent, respectively. The big trees were not given 

any special treatment or protection during either the development or the validation 

burns (n = 22 burns) yet the mortality rate of big trees was 5.2 percent (n = 735 ) 

while the mortality rate of all sample trees was 14 percent (n = 6,652). 

Table 7—Classification table for large ponderosa pine 

(over 53.3 cm d.b.h.) based on the Malheur model logistic 

regression using a cutoff of 0.5 probability of mortality

Observed

Predicted Alive Dead Total

Alive P(m) <0.5 694 32 726

Dead P(m) >0.5 3 6 9

 Total 697 38 735

Overall rate of correct classification = [(694 + 6)/735] × 100 = 95.2 percent.

Overall rate of correctly predicting mortality = 6/9 × 100 = 66.6 percent.

There were 735 big (over 53.3 cm d.b.h) trees in the original and the validation 

data sets, of which 38 died; the two-factor model predicted 33.5 would die.

Ponderosa pine that have had all needles consumed or scorched but have not 

had significant bark consumption have a small but real probability of survival. 

In the validation data set (n = 3,237), 162 trees had all needles consumed or 

scorched; of these, 95 regreened (new needles formed) within a season of the 

burn, and 14 were still living 3 years later. In the development data set, 278 trees 

had all needles consumed or scorched; of these, 30 regreened within a season 

and 10 were still living 8 years later. 

The Malheur model 

can be used to 

determine the 

probability of firecaused mortality of 

big ponderosa pine.
16

GENERAL TECHNICAL REPORT PNW-GTR-769

Conclusions

1. There is good agreement between the delayed mortality predicted by 

the Malheur model and the mortality observed 3 years following the 

burn in the 10 validation stands. 

2. The geographic area of inference for using the Malheur model has 

been expanded north of the development stands and south into 

northern California.

3. The Malheur model can be used to determine probability of fire-caused 

delayed mortality in individual trees regardless of whether the fire is a 

prescribed fire or a wildfire. 

4. The Malheur model can be used to determine the probability of 

fire-caused mortality of big ponderosa pine. 

5. The observed proportion of big ponderosa pine killed by fire was 

about 5 percent. 

Epilogue

An additional validation study was begun in summer 2007 to broadly sample 

burns in eastern Washington and Oregon. The sample burns are expected to 

include equal numbers of wildfires and prescribed burns. Each ponderosa pine 

stand will be evaluated by using both conventional height-measurement instruments as well as the simple proportional system shown on the field guide. 
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