Post-fire Tree Mortality of Western
North American Conifers:
A Review of Predictive Models
Travis J. Woolley
David C. Shaw
Lisa M. Ganio
Stephen Fitzgerald
Outline
1.
Objectives
2.
Review of literature review…
1.
2.
3.
4.
Context (geographic, species, etc.)
Variables
Compare models/structure
What is lacking from research
3.
Model Evaluation/Validation
4.
Take Home Messages
5.
Article Preparation
1.
Handouts (Outline., Tables, Annotated Bibliography)
Objectives
1. Based on an extensive literature search
•
summarize and compare characteristics of existing
models developed to predict post-fire tree mortality
Objectives
1. Based on an extensive literature search
•
summarize and compare characteristics of existing
models developed to predict post-fire tree mortality
2. Identify groups of structurally similar models
and investigate strengths
Objectives
1. Based on an extensive literature search
•
summarize and compare characteristics of existing
models developed to predict post-fire tree mortality
2. Identify groups of structurally similar models
and investigate strengths
3. Synthesize the information in a report to
WWETAC
Objectives
1. Based on an extensive literature search
•
summarize and compare characteristics of existing
models developed to predict post-fire tree mortality
2. Identify groups of structurally similar models
and investigate strengths
3. Synthesize the information in a report to the
WWETAC
4. Publish a review/synthesis of existing models
in a peer reviewed journal
Literature Review
• Peer-reviewed Journal Articles
(1986-2006)
• General Technical Reports (1980-2007)
Literature Review
• Peer-reviewed Journal Articles
(1986-2006)
• General Technical Reports (1980-2007)
• 29 Journal articles & Technical reports
– Prescribed fire (18)
– Wildfire (10)
– Both (1)
– Validation of Previous Model (2)
Study Locations
1B/1F
_ _1H/2K
1C
_ _ 1B/1F
_
2A
_ 1B/1F
_ _1E__1A
2A
_
_2B
_1B/1F
1G
2B _
_ 1B/1F
_
2H
_
2B
2K
_
_ 1B/1F
_2B
_ 2E
_ 1Q
_ 2C
2H/2I
2A
_
_ 2K
_
_1I
1B/1F
2H
_
_ 1D
2J
1J
_
_1J
_
_2J
2J
_
_1S2D
_ 1P
_ 2J
_
_ 1L
2F
_
1M
1O
1R
_
_ 2G/2H
_1N/2G
1K
Review – Species Modeled (# studies)
–
–
–
–
–
–
–
Douglas-fir(9)
ponderosa Pine(17)
sugar pine(3)
lodgepole Pine(3)
Jeffrey pine(2)
Coulter pine(1)
gray pine(1)
– incense cedar(4)
–
–
–
–
–
white fir(6)
Shasta red fir(2)
sub-alpine fir(1)
silver fir(1)
grand fir(1)
–
–
–
–
–
–
–
–
–
western larch(1)
Englemann spruce(1)
western red-cedar(1)
western hemlock(1)
coast redwood(1)
giant sequoia(1)
California black oak(3)
canyon live oak(1)
Tanoak (1)
Total # of Models (i.e., different coefficients)
(29 papers Total)
• Prescribed Fire – 59
• Wildfire – 30
Model Types
• Predictive Models
– Logistic regression
• Various variable selection procedures (or none)
• Various measures of “fit”
Pm = 1/1 + exp[-(0.392 – 0.099 DBH + 1.275 NDEAD)]
Model Types
• Predictive Models
– Logistic regression
• Various variable selection procedures (or none)
• Various measures of “fit”
Pm = 1/1 + exp[-(0.392 – 0.099 DBH + 1.275 NDEAD)]
• Others
– Discriminant Function Analysis (Classification)
– Multiple Linear Regression
– ANOVA
Fowler & Sieg (2003)
Significant Variables
…………variations on a theme
•
Crown Variables
–
–
–
–
–
Tree height
Crown ratio
Crown vigor
Crown Diameter
Pre-fire live crown
• Length
• Height to crown base
– % crown killed (scorch or consumed?)
– Crown Scorch
•
•
•
•
•
Volume
%
length
height
class
– Consumption
• %
• volume
• height
–
–
–
–
Total Crown Damage = Scorch + Consumption
Bud kill proportion
Needle scorch proportion
Live Crown proportion
Craig M. Durling 2004
Significant Variables
…………variations on a theme
•
Bole variables
–
–
–
–
–
Diameter at Breast Height (DBH)
Growth rate (pre-fire vigor)
Bark Thickness (Measured or as function of DBH)
Bole length or Height to Live branch
Bole Scorch
•
•
•
•
•
% bole
height
Circumference
max. min.
proportion
– Bole Char
•
•
•
•
•
% bole
height
ratio
severity rating,
% below DBH
– Cambium mortality – Chemical test on cambium sample
• Dead or alive vs. # dead quadrants
– Insect Damage
• Presence/Absence
• Rating
•
Many taken on several “aspects” of bole
Significant Variables
…………variations on a theme
• Plot/Fire variables
– Duff consumption
• depth
• volume
• tree and plot based
– Ground char severity
– Flame length/height
– Fireline Intensity
– Duration of lethal heat to cambium
Author’s
Evaluation/Validation
Model Evaluation/Validation
• Evaluation
– Statistical measures
• Chi-squared – e.g. Wald Stat.
• Maximum Likelihood
• Goodness of fit tests
– Pearson’s, Hosmer, Brown etc.
Review – Model Evaluation/Validation
• Evaluation
– Classification tables
• Classification or “Decision” Criteria
– Generally 0.5, dependent on objectives
Review – Model Evaluation/Validation
Regelbrugge & Conard 1993
Observed Status
Dead
Dead
Predicted Status
Live
Total #
Live
Review – Model Evaluation/Validation
Pm= f (dbh, Char Height)
Observed Status
Dead
Live
Dead
180
14
Live
13
65
Total #
193
79
Predicted Status
Review – Model Evaluation/Validation
Pm= f (Relative Char Height)3
Observed Status
Dead
Live
Dead
160
18
Live
33
Total #
193
Predicted Status
61
79
Review – Model Evaluation/Validation
Pm= f (Relative Char Height)3
* Indicates direction
of bias in model
predictions
Observed Status
Dead
Live
Dead
160
18
Live
33
61
Total #
193
79
Predicted Status
Review – Model Evaluation/Validation
Pm= f (dbh, Char Height)
* Indicates direction
of bias in model
predictions
Observed Status
Dead
Live
Dead
180
14
Live
13
65
Total #
193
79
Predicted Status
Review – Model Evaluation/Validation
• Evaluation
– Receiver Operating Characteristic (ROC) Curves
• # of correct hits (dead:dead) vs. false alarms
(dead:alive)…
– or inverse – (alive:alive) vs. (alive:dead)
• Over a range of decision criteria
Saveland & Neuenschwander 1990
Predicted Dead|Dead
Review – Model Evaluation/Validation
Predicted Dead|Alive
Saveland & Neuenschwander 1990
Review – Model Evaluation/Validation
Predicted Dead|Dead
•Distance from chance line….
Predicted Dead|Alive
Saveland & Neuenschwander 1990
ROC Curves cont.
•Distance from chance line….
Predicted Dead|Dead
•Shape of curve…
Predicted Dead|Alive
Saveland & Neuenschwander 1990
ROC Curves cont.
•Distance from chance line….
•Area under the curve….
•Sensitivity – 0.5-1.0
•Reported in the literature
Predicted Dead|Dead
•Shape of curve…
Predicted Dead|Alive
Regglebrugge & Conard 1993
Predicted Dead|Dead
ROC example
Predicted Dead|Alive
Validation
Validation
• 4 articles validated their models
– 2 used randomly selected data from the same
fires
– 1 used new fires for validation
– 1 used old fires for validation
• 3 Articles validated previously existing
models
– 2 validated model with original coefficients
– 1 applied model form to new data set
Research Needs
• Consistent Evaluation and Validation
techniques
• Validation….at several scales
– w/in a fire
– Between fires in the same geographic locale
– Between different geographic locations
• w/in Cascades
• Between OR and WA
• Between OR, WA, CA, ID, MT, CO AZ…etc.
TABLES
2 Table Formats
• By fire type – Prescribed & Wildfire
• 1. Split into 2 “sub-tables”
– Fire and site descriptors
•
•
•
•
Year
Region
Species
Fire Size, severity, season
– Modeling characteristics
•
•
•
•
•
Sample size,
model type
measurement span/interval,
spatial scale
etc.
2 Table Formats
• By fire type – Prescribed &. Wildfire
• 1. Split into 2 “sub-tables”
– Fire and site descriptors
– Modeling characteristics
• 2. Models
– Parameters
– Coefficients
– Evaluative measures
Table Formats 1…Fire/Site Variables
Table 1 - Site, fire, and tree species characteristics of post-fire studies applying models to predict tree mortality.
Study
Code
Author(s)
Year
Region
Elevation
Fire
Size
(ha)
Season/Months
of burn
Crown Damage
(Measure)
Forest Type
Tree Species Modeled
NR
Spring, Summer,
Fall
LightModerate
Surface Fires
630-2350
0-100%
(Crown Kill)
103000
August September
NR
NR
6-85%
(Crown scorch
+/-SD)
1A
Ryan &
Reinhardt
1988
Cascades/Norther
n Rockies
NR
Douglas-fir-w.
hemlock/mixed
conifer
Douglas-fir
Western red-cedar
Western hemlock
Western larch
Engelmann spruce
Lodgeploe pine
Subalpine fire
1B
Peterson
&
Arbaugh
1986
Northern Rocky
Mountains
NR
NR
Douglas-fir
Lodgepole pine
Severity
Fireline
Intensity
(kW min-1)
Table Format 2… Model Characteristics
Table 2 – Characteristics regarding scope of inference of post-fire studies applying models to predict tree mortality.
Study
Code
1A
1B
# of measurements/temporal scale
Four/Three Annually
1 monitoring in year 7 or 8
Two/Annually
# trees
2356
302 (PSME)
243 (PICO)
Spatial scope
Sample Plot Size
07-9.0 ha
Point-centered
quarter method
on transects
Model Type
Variables Tested
Replicated?
Validated
Logistic
Tree Height
DBH
Bark Thickness
Scorch Height
% Crown Killed
No
No
Logistic
Discriminant
Analysis
DBH
Bole length
Crown ratio
Crown diameter
Crown scorch
Bark thickness
Basal scorch (% circ.)
Bark char (depth)
Bark char ratio (depth char/depth bark)
Insect (low, med, high based on 3 of
entries)
No
No
Table Formats…Models
Table 3 – Post-fire tree mortality models with variable coefficients and accuracy values.
Study
Code
Species
Sample
Size
Model
Statistical Measures Used
Accuracy/Error
(Criteria)
ROC Curve
Value
Validation
Accuracy
1A
All
2356
Pm = 1/1 + exp(-1.466 + 1.190 BT – 0.1775 BT2 - 0.000541CK2)
Maximum Likelihood
Wald Statistic
0.14-0.49
(0.50)
NA
NA
1A
PSME
1488
Pm = 1/1 + exp(-0.9245 + 1.0589 PSME + 0.9407BT – 0.0690 BT2 - 0.000542 CK2)
Maximum Likelihood
Wald Statistic
0.14
NA
NA
1A
LAOC
287
Pm = 1/1 + exp(-0.9245 + 1.5475 LAOC + 0.9407BT – 0.0690 BT2 - 0.000542 CK2)
Maximum Likelihood
Wald Statistic
0.12
NA
NA
1A
PIEN
96
Pm = 1/1 + exp(-0.9245 - 1.495 PIEN + 0.9407BT – 0.0690 BT2 - 0.000542 CK2)
Maximum Likelihood
Wald Statistic
0.12
NA
NA
1A
PICO
144
Pm = 1/1 + exp(-0.9245 - 0.1472 PICO + 0.9407BT – 0.0690 BT2 - 0.000542 CK2)
Maximum Likelihood
Wald Statistic
0.20
NA
NA
1A
ABLA
172
Pm = 1/1 + exp(-0.9245 – 1.1269 ABLA + 0.9407BT – 0.0690 BT2 - 0.000542 CK2)
Maximum Likelihood
Wald Statistic
0.14
NA
NA
1A
THPL
69
Pm = 1/1 + exp(-0.9245 + 0.8860 THPL + 0.9407BT – 0.0690 BT2 - 0.000542 CK2)
Maximum Likelihood
Wald Statistic
0.13
NA
NA
1A
TSHE
100
Pm = 1/1 + exp(-0.9245 - 0.7231 TSHE + 0.9407BT – 0.0690 BT2 - 0.000542 CK2)
Maximum Likelihood
Wald Statistic
0.11
NA
NA
1B
PSME
302
Ps = 1 + exp(-6.944 + 0.063CS + 1.004ID)
Pearson’s goodness of fit
Hosmer goodness of fit
Brown goodness of fit
NA
NA
NA
1B
PICO
243
Ps = 1 + exp(-3.874 + 0.039CS + 0.023BS)
Pearson’s goodness of fit
Hosmer goodness of fit
Brown goodness of fit
NA
NA
NA
Take Home Messages…So far.
• Validation is needed!
– Consistency with evaluation measures
Take Home Messages…So far.
• Validation is needed!
– Consistency with evaluation measures
• All models are not created equally…
– Consistency of variables
– Consistency with statistical procedures (i.e., use
of variable selection procedures)
Take Home Messages…So far.
• Validation is needed!
– Consistency with evaluation measures
• All models are not created equally…
– Consistency of variables
– Consistency with statistical procedures (i.e., use
of variable selection procedures)
• Not all papers are written equally…
Take Home Messages…So far.
• Validation is needed!
– Consistency with evaluation measures
• All models are not created equally…
– Consistency of variables
– Consistency with statistical procedures (i.e., use
of variable selection procedures)
• Not all papers are written Equally…
• Wildfires < Prescribed
– More data needed???
Deliverables to date…
• Literature Database (i.e., Endnote & Pdf’s)
• Annotated Bibliography
– Wider geographic range
• “The List”
– More limited geographic range
• Map of study areas in the western U.S.
• Descriptive Tables of Models
Article Outline
1. Introduction
2. Overview
2.1 General Structure of Models
2.2 Context
- Prescribed vs. Wildfire
- Geographic
- Species
- Fire characteristics
3. Scope of Inference and Interpretation
4. Author’s Model Evaluation
5. Author’s Model Validation
6. Management Implications – Previous Use of models in Management Scenarios
6.1 Examples
- Nomograms (Reinhardt and Ryan 1988)
- FOFEM (Reinhardt et al. 1997)
-“Scott Guidelines” (Scott et al. 2002)
- FVS (Ryan & Crookston 2003)
- Hood & Bentz 2007
7. Management Implications – Choosing models for use in Future Management Scenarios