Content uploaded by Carol Miller
Author content
All content in this area was uploaded by Carol Miller on May 07, 2014
Content may be subject to copyright.
Landscape Ecology 15: 145–154, 2000.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
145
Connectivity of forest fuels and surface fire regimes
Carol Miller
1∗
& Dean L. Urban
2
1
Graduate Degree Program in Ecology, Colorado State University, Fort Collins, CO, USA
2
Nicholas School of the Environment, Duke University, Durham, NC, USA
(
∗
author for correspondence: e-mail: cmiller/rmrs_missoula@fs.fed.us; current address: USDA Forest Service
Aldo Leopold Wilderness Research Institute, P.O. Box 8089, Missoula, MT 59807, USA)
(Received 10 May 1998; Revised 11 February 1999; Accepted 19 May 1999)
Key words: connectivity, correlation length, elevation gradient, fire spread, forest gap model, fuel characteristics,
mixed conifer forest, Sierra Nevada, surface fire regime
Abstract
The connectivityof a landscapecan influencethe dynamicsof disturbancessuch as fire. In fire-adaptedecosystems,
fire suppression may increase the connectivity of fuels and could result in qualitatively different fire patterns and
behavior. We used a spatially explicit forest simulation model developed for the Sierra Nevada to investigate how
the frequency of surface fires influences the connectivity of burnable area within a forest stand, and how this
connectivity varies along an elevation gradient. Connectivity of burnable area was a function of fuel loads, fuel
moisture, and fuel bed bulk density. Our analysis isolated the effects of fuel moisture and fuel bed bulk density
to emphasize the influence of fuel loads on connectivity. Connectivity was inversely related to fire frequency and
generally increased with elevation. However, certain conditionsof fuel moisture and fuel bed bulk density obscured
these relationships. Nonlinearpatterns in connectivityacross the elevation gradientoccurred as a result of gradients
in fuel loadsand fuel bed bulk density that aresimulated by themodel. Changes in connectivitywith elevationcould
affect how readily fires can spread from low elevation sites to higher elevations.
Introduction
Landscape pattern and disturbance dynamics are in-
extricably related. Many of the observed patterns in
any landscape result from past disturbances. In turn,
landscape patterns can influence the spread of future
disturbances(Turner et al. 1989). Probabilistic models
derived from percolation theory and cellular automata
have been very helpful for investigating the interac-
tion between landscape pattern and crown fires (Green
1983; Gardner et al. 1987; Turner et al. 1989). These
models have demonstratedthat landscape connectivity
is importantin controlling disturbancedynamics.Sites
on a landscape are ‘connected’ if they are linked by
patterns or processes in some way. For example, if
fire can spread from one site to another, those sites
are connected with respect to the process of fire. Com-
puter models have revealed that nonlinear thresholds
in connectivity may exist; for very small changes in
connectivity, there can be large, sudden changes in the
system (Turner et al. 1989; Gardner and O’Neill 1990;
Turner and Dale 1990).
Patterns of fire spread and the connectivity of
a landscape with respect to fire are influenced by
the spatial arrangement of fuels (Green 1983; Davis
and Burrows 1994; Turner and Romme 1994). In
fire-adapted ecosystems, fire suppression may sub-
stantially increase the connectivity of fuels and could
drive qualitatively different fire patterns and behav-
ior. The degree to which a landscape is connected
with respect to fire also depends on meteorological
conditions. Under moderate weather conditions, fire
spread is sensitive to the spatial arrangement of fuels;
under extremely dry and windy conditions, the impor-
tance of this spatial pattern may diminish (Turner and
Romme 1994; Turner et al. 1994). Additional research
is needed to better delineate the range of conditions
under which the spatial arrangement of fuels is impor-
146
tant and to identify thresholds when we can expect fire
behavior to change qualitatively (Turner and Romme
1994).
The forests of the Sierra Nevada in California are
one of the best examples of fire-adapted ecosystems
that have been altered by fire exclusion (Vankat and
Major 1978; Parsons and DeBenedetti 1979; Skinner
and Chang 1996). Historically, these forests experi-
enced frequent low- to moderate-intensity surface fire
regimes. During the past century, most fires in the
Sierra Nevada have been suppressed. Forest structure
has become more dense, surface fuels have accumu-
lated to unprecedentedlevels and species composition
has shifted in favor of shade tolerant tree species.
These changes have probably increased the vertical
and horizontal continuity of flammable fuels and thus,
increased the risk of catastrophic wildfires (McKelvey
et al. 1996).
We developed a simulation model for Sierran
forests to investigate the interactions among fire,
climate and forest pattern. Unlike the aforemen-
tioned probabilistic models which simulate crown fire
regimes, this model simulates surface fire regimes.
The model generates spatial heterogeneity in fuels
within a forest stand, making it appropriate for study-
ing the influence of fire on connectivity of burnable
area. First, we used the model to determine the ef-
fect of fire frequencyon connectivity of burnable area.
Second, we examined how this connectivity varies
along an environmental gradient. By identifying the
relationship between fire frequency and connectivity,
we may be able to suggest optimum intervals for
prescribed fires to reduce fire hazard. Improving our
understanding of how connectivity may vary with en-
vironmental conditions may help managers identify
priority areas on the landscape for strategic fire man-
agement. Furthermore, we may be able to determine
the relative importance of climatic factors versus the
spatial arrangement of fuels in influencing the spread
of large fires.
Study area
We focused on Sequoia-Kings Canyon National Park
in the southern Sierra Nevada, California, USA
(36.6
◦
N, 118.6
◦
W). The Park encompasses a striking
physical gradient; elevation spans 3500 m over a dis-
tance of just 100 km. Across this gradient, vegetation
ranges from foothill grassland and chaparral, through
ponderosa pine, to the mixed-conifer zone, to red fir
and lodgepole pine, and finally to high-elevation pine
near tree line. Vegetation composition is tightly cou-
pled to the soil water balance (Stephenson 1988) and
paleoecological studies have revealed that vegetation
has responded to past climatic changes (Davis et al.
1985; Anderson1990; Andersonand Carpenter 1991).
Historical fire frequencies vary across this elevation
gradient, as well (Caprio and Swetnam 1995). Prior
to the 20th century, low elevation ponderosa pine for-
est stands experienced low intensity fires every 3–4
years (Warner 1980). In the mixed conifer forest zone,
low intensity surfacefires burned through stands every
5–18 years (Kilgore and Taylor 1979). Fires in the
higher elevationred fir forests havebeen less frequent,
with fire-free intervals for individual trees averaging
around 65 years (Pitcher 1987). Mean fire return in-
tervals are over 200 years in the subalpine forests,
although evidence for fire exists in fire scarred trees
and subfossil wood. Despite the high incidence of
lightning,fuels aretoo discontinuousto sustain fires of
any appreciable size at those elevations (Keifer 1991).
Fire suppression during the 20th century has drasti-
cally disrupted the fire regime throughout the Sierra
Nevada, allowing dead fuel to accumulate and under-
story tree density to increase in many forests (Vankat
and Major 1978).
Methods
We applied the forest gap model ZELIG (Smith and
Urban 1988; Urban et al. 1991) to the Sierra Nevada
by adding a new soil moisture model (Urban et al., in
review), a new fire model (Miller and Urban 1999a;
Miller and Urban, 1999b) and parameterizing it for
Sierran tree species. Below we provide a brief descrip-
tion of the model; for furtherdetail, werefer the reader
to Miller and Urban (1999a,b) and Urban et al. (in
review).
Model Description
The model simulates a forest stand as a rectangular
grid of tree-sized (15 × 15 m) forest plots (or cells).
In this paper, we use a grid of 20 × 20 cells to sim-
ulate a 9 ha forest stand. The modeled grid has a
user-specified elevation, slope, and aspect and thus
represents a slope ‘facet’. As such, we refer to this
extension of ZELIG as the FACET Model, or sim-
ply FM. Elevation and topographic position are used
internally by FM’s weather model to adjust climate
parameters (Urban et al., in review). Radiation is ad-
justed for slope-aspect (Nikolov and Zeller 1992) and
147
precipitation and temperature are adjusted according
to locally regressed lapse rates (Running et al. 1987;
Daly et al. 1994).
Like other forest gap models, FM simulates
seedling establishment, annual diameter growth, and
mortality for individualtrees on eachplot. Treegrowth
is specified as a maximum potential which is then re-
duced to reflect suboptimal environmental conditions
(e.g., low light, low temperatures, or drought). A key
characteristic of gap models is that they simulate sys-
tem feedbacks: not only are trees affected by their
environment, but each tree exerts an influence on its
environment (e.g., through shading).
Tree growth in FM is limited by available light,
temperature, soil moisture, and nutrient availability.
Available light is estimated for each position within
the stand as a function of the leaf area, which is dis-
tributedverticallyalong eachtree’scrown(Urbanet al.
1991).Growingdegree-daysare computedand used as
an index for temperature. Soil moisture is estimated
from precipitation, potential evapotranspiration, and
the water holding capacity, from which a drought-day
index is computed (Miller and Urban, 1999b; Urban
et al., in review). The forest floor, comprising the par-
tially decomposed forest litter, is treated as the top soil
layer; the moisture content of this layer is used to es-
timate fuel moisture in the calculation of fire intensity
(see below). Finally, nutrient availability is estimated
as a ratio of nitrogen uptake and nitrogen made avail-
able through decomposition of forest litter (Miller and
Urban 1999a; Urban et al., in review). The available
light, number of drought-days, growing degree-days,
and nutrient availability on each grid cell define the
environment for each tree in that cell.
Species tolerances to shade, drought, and tempera-
ture governeach tree’s growth responseto the environ-
ment in each grid cell (Miller and Urban 1999a; Urban
et al., in review). Differential species response to nu-
trient availability has been turned off in this version of
the model to minimize the model’s sensitivity to this
uncertain parameter. Nine tree species are simulated
in this version of the model: white fir (Abies concolor
[Gord. and Glend.] Lindl. ex Hildebr.), red fir (Abies
magnificaA. Murr.), incensecedar (Calocedrusdecur-
rens [Torr.] Floren), lodgepole pine (Pinus contorta
Dougl. ssp. murryana Grev. and Balf.), Jeffrey pine
(Pinus jeffreyi Grev. and Balf.), sugar pine (Pinus lam-
bertianaDougl.), western whitepine (Pinusmonticola
Dougl.),ponderosapine (PinusponderosaLaws.), and
California black oak (Quercus kelloggii Newb.).
Fuels accumulate as a function of site environment
and forest conditions. Each year during a simulation,
a fraction of each tree’s foliage and branchwood are
added to the fuel bed according to species-specific
allometries(Miller andUrban 1999a). Inaddition, bio-
mass from dead trees is gradually added to the fuel
bed. These ‘dead and down’ fuels are classified by
size using the conventions of fire behavior and fire
danger models (Deeming et al. 1972). Each fuel class
decays according to a constant rate which is modified
by an abiotic decay multiplier that describes the tem-
perature and moisture environment of the site. Decay
rates for each fuel class were calibrated to data from
Sequoia-Kings Canyon and Yosemite National Parks
(Parsons 1978; J. van Wagtendonk, USGS Biological
ResourcesDivision, unpublisheddata). Simulatedfuel
loads increasewith elevation to about 2300 m and then
decline as elevations approach tree line; this pattern
agrees with independent data from Sequoia National
Park (Miller and Urban 1999a).
Fine herbaceous fuels can be an important factor
in Sierra Nevada fire regimes, particularly at lower
elevations where open oak and pine woodlands can
occur. Therefore, grass production is simulated in this
version of FM as a function of precipitation, tempera-
ture, shade from overstory trees, and forest floor depth
(Miller and Urban, 1999b). Grass is included in the
fuel bed, which also contains the woody fuels and for-
est litter. A fuel bed with a large grass component may
burn more easily than a fuel bed comprised only of
forest fuels.
A number of parameters describing the physical
and chemical properties of fuel are required for calcu-
lating fire intensity: mineral content, silica-free min-
eral content, low heat value, surface area to volume
ratio, and particle density (Rothermel 1972; Albini
1976). Average values for these parameters were esti-
mated from the literature (Cohen and Deeming 1985,
Andrews 1986, van Wagtendonk et al. 1996; 1998)
and are listed in Table 1. The physical arrangement
of fuels also influences fire intensity. For example,
the loosely packed litter of long-needled ponderosa
pine forests will burn more readily than a more tightly
packed short-needled fir forest floor. To capture these
differences, we simulate bulk density of the fuel bed
as a function of species-specific bulk density (Ta-
ble 2) and tree species composition (Miller and Urban,
1999b). Bulk density is also adjusted for the grass
component of the fuel bed, which is assumed to have
a bulk density of 0.54 kg m
−3
(Miller and Urban,
1999b). Fuel bed bulk density increases with elevation
148
Table 1. Constant parameters for physical fuel properties.
Surface Particle Mineral Silica-free
area:volume density content mineral content Heat value
(cm
−1
)(gcm
−3
) (fraction) (fraction) (MJ kg
−1
)
Litter 65.6 0.51 0.055 0.011 20.93
Duff 76.1 0.51 0.055 0.011 20.93
Grass 114.8 0.51 0.055 0.011 20.93
Woody fuel classes (diameter)
<0.6 cm 65.6 0.56 0.055 0.011 20.93
0.6–2.5 cm 4.2 0.55 0.055 0.011 20.93
2.5–7.6 cm 1.1 0.52 0.055 0.011 20.93
>7.6 cm 0.4 0.42 0.055 0.011 20.93
Table 2. Species-specific fuel bed bulk density.
kg m
−3
lb ft
−3
White fir 24.83 1.55
Red fir 35.72 2.23
Incense cedar 20.82 1.30
Lodgepole pine 33.00 2.06
Jeffrey pine 21.14 1.32
Sugar pine 28.35 1.77
Western white pine 27.39 1.71
Ponderosa pine 23.55 1.47
California black oak 12.81 0.80
as species composition shifts from pine to fir and as
grass production declines (Miller and Urban, 1999b).
Because the model is implemented as a grid of for-
est plots, it can describe the spatial heterogeneity of
forest structure and composition that exists within a
stand. Fuel inputs, and therefore fuel bed conditions,
vary temporally and spatially throughout a stand ac-
cording to the number, size, and species of trees that
are present. In addition, the fuel moisture varies both
temporally and spatially with the local site water bal-
ance. Fuel moisture is derived for each grid cell from
the duff moisture content, calculated monthly in the
model’s soil water routine, with the duff layer treated
as the top soil layer. Thus, as the model generates spa-
tial heterogeneity in forest structure and condition due
to tree-level processes, this leads to heterogeneity in
fuel bed conditions, thereby generating spatial pattern
in fire intensity and effects.
We consider FM to simulate a ‘natural’ fire regime
as both fire frequency and magnitude (i.e., area
burned) are generated internally by the model and are
governed by site conditions. Fire events are simulated
as a function of three factors: probability of ignition,
fuel load and fuel moisture. The mean ignition inter-
val, in years, forthe modelgrid is specified atrun time,
and uniform-random numbers are drawn to generate
stochastic ignition events around this mean interval.
In this paper, we assume that ignitions are not limiting
and set this interval so that an ignition occurs every
year. However, for a fire to occurfrom an ignition, low
fuel moisture and sufficient fuel loadings must also
exist. Because the soil water balance – and thus fuel
moisture – becomes more positive with elevation, FM
generates a decreasing fire frequency with elevation;
the simulated pattern agrees well with independent
fire history data for the study area (Miller and Urban
1999a).
When an ignition occurs, the fireline intensity is
computed for each of the grid cells from the accu-
mulated fuels, fuel moisture conditions, and slope
following well established equations for surface fire
behavior (Rothermel 1972; Albini 1976). Only cells
with computed intensities greater than 45 kW m
−1
(13 BTU ft
−1
s
−1
) are considered to be burnable. This
intensity is roughly equivalent to a scorch height of
about 0.5 m and we assume that fires ‘burn out’ when
intensities are less than this. Fires may spread to all
cells within the model grid, but they are restricted to
those cells which are burnable and which are also spa-
tially contiguous to a randomly located ignition point
on the grid. Thus, fires are restricted to a contagious
cluster of burnable cells, and on average, fires tend
149
to burn the largest cluster of burnable cells. Although
this approach does not simulate the complexities of
fire spread, FM successfully reproduces empirical re-
lationships between area burned and fire frequency
that have been inferred for pre-settlement fire regimes
(Miller and Urban 1999a).
Fire effects are calculated for each grid cell that
burns. Fuels are reduced as a function of pre-fire fuel
load (Brown et al. 1985), scorch height is estimated
as a function of mean daytime temperature and fire
line intensity (Van Wagner 1973) and fire mortality is
computed as a function of crown damage (Ryan and
Reinhardt 1988; Stephens 1995; Mutch and Parsons
1998).
Simulations
We conductedtwo sets of simulations. For the first set,
we ran 25simulationsfor a south-facing site at 2000 m
elevation, each with a different ignition probability to
generate a range of fire frequencies. Initially, we ran
the model from bare ground for 200 years without fire
to allow successional trends and fuel bed bulk density
to stabilize. Following this initial period, we simulated
the different fire regimes for 300 years. We chose 300
years to ensure that we would be able to average over
enough individual fire events for our analysis.
We examined how connectivity varied with eleva-
tion in the second set of simulations. As in the first
set, we ran the model for 200 years without fire and
followed it with 300 years of a natural fire regime. We
simulated 21 different south-facing sites (25% slope)
at elevations between 1000–3000 m at 100 m inter-
vals. All simulations were for Sequoia National Park
(36.6
◦
N, 118.6
◦
W)and used a homogeneoussoil map
with soil depth =1 m to emphasize the spatial pattern
created by internal forest dynamics and fire.
Analysis
We defined an area as connected if fire will burn
through it under a given set of conditions. We defined
a grid cell to be burnable if the calculated fireline in-
tensity in the model is greater than 45 kW m
−1
. Thus,
burnability is a function of the same parameters as
fireline intensity, including: fuel loads, fuel bed bulk
density, size of fuel particles, weather parameters, and
fuel moisture. The parameters that vary in this version
of FM are fuel loads, fuel bed bulk density, and fuel
moisture.
We created maps of burnable area from the fuel
load maps for each year in which a fire was simulated.
Fuel moisture and fuel bed bulk density can vary enor-
mously, however, and greatly affect whether a plot is
burnable. To emphasize the influence of fuel loads on
connectivity of burnable area, and to isolate the effects
of these two variables, we created another set of maps
of burnable area in which we held either fuel bed bulk
density or fuel moisture constant. First, we generated
sixmaps of burnablearea usingsix differentfuel mois-
tures (1, 5, 10, 15, 20, 24%) and the fuel bed bulk
density simulated by the model. Next, we generated
six maps of burnable area using six different fuel bed
bulk density values and a fuel moisture of 1 percent.
The six different bulk density values are 0.1, 0.2, 0.8,
1.1, 1.4, and 1.7 lb ft
−3
(1.6, 3.2, 12.8, 17.6, 22.4,
and27.2kgm
−3
). Figure 1 illustrates this approach
with maps of burnable area that were generated from a
single map of fuel loads using the six moisture levels.
For each set of maps, we computed the average
correlation length of burnable area for each simula-
tion. Correlationlength is an indexof connectivity and
is a measure of the averagewithin-cluster distances for
the entire map; i.e., it is the average distance that fire
can spread without leaving a patch of burnable area. A
forest plot is burnable if the calculated fire line inten-
sity is at least 45 kW m
−1
and burnableplots are in the
same patch of burnable area if they are adjacent neigh-
bors or nearest-neighbors to each other. Correlation
length is computed as:
CL =
s
6(RMS
i
)
6(S
2
i
)
, (1)
where RMS
i
is the mean-squared radius and S
i
is the
size of the ith cluster. We used the FORTRAN 77
version of RULE (Gardner, in press) to compute the
average correlationlength of burnable area for the fuel
maps.
Results
We were interested in how connectivity of burnable
area might vary with the frequencyof fire. For the sim-
ulations at 2000 m elevation, we used six sets of maps
of burnable area correspondingto 6 different moisture
levels and plotted average correlation length against
mean fire interval (Figure 2). The six distinct isolines
in Figure 2 each correspond to a different moisture
level. Correlation length generally increases as fire
frequency decreases, and for a given fire frequency,
correlation length increases with decreasingfuel mois-
tures. When fuel moisture is 1 percent, connectivity
150
Figure 1. Maps of burnable area for six levels of fuel moisture. The
fraction of the map that is burnable, p, and the correlation length,
CL, are given.
is high with average correlation lengths varying from
85 to 135 m. At the 5 percent moisture level, con-
nectivity varies most widely as average correlation
lengths range from 20 to 120 m. At moistures of 10%
and above, connectivity of burnable area is low, and
average correlation lengths are less than 50 m.
To examine how connectivity varies with elevation
for a natural fire regime, we plotted average corre-
lation length against elevation for the simulations of
sites between 1000 m to 3000 m elevation. For each
simulation, we again generated six sets of maps of
burnable area corresponding to six different moisture
Figure 2. Connectivity as a function of fire frequency. Correlation
length was computed for simulations conducted for 2000 m, 25%
slope and 180
◦
azimuth. Isolines represent different levels of fuel
moisture; fuel bed bulk density was allowed to vary within the stand.
levels; each isoline represents a different moisture
level (Figure 3a). For these sets of maps, we used the
bulk density that is simulated by model (Figure 3b).
Correlation lengths tend to increase with elevation,
with the exception of a range of elevations between
1500 m to 1750 m. Between 1500 m and 1750 m,
correlation lengths decrease abruptly before increas-
ing again at higher elevations. As in the previous set
of runs, correlation lengths are higher at lower levels
of fuel moisture.
Fuel bed bulk density varies dramatically with ele-
vation (Figure 3b). To see how connectivity compared
among elevations when fuel bed bulk density was held
constant with elevation, we generated sets of maps
correspondingto six bulk densitiesand plottedaverage
correlation length computed from these maps against
elevation (Figure4). Each isoline corresponds to a dif-
ferent bulk density value. For the set of results shown
here, fuel moisture was held constant at 1 percent.
Correlation length generally increases with elevation,
and at a given elevation, correlation length increases
with decreasing bulk density. Abrupt increases in con-
nectivity are apparent around 1700 m and 2600 m
elevation.
Discussion
Fire frequency
Fire frequency influenced the connectivity of burnable
area (Figure2). This result is not surprising,and in fact
has been inferred from fire scars in the tree-ringrecord
by Swetnam (1993). He found an inverse relationship
between fire frequency and fire extent in giant sequoia
151
Figure 3. Elevational gradients in connectivity, fuel bed bulk den-
sity and fuel loads. (a) Connectivity measured by correlation length.
Isolines represent different levels of fuel moisture; fuel bed bulk
density was allowed to vary within the stand and with elevation. (b)
Mean fuel bed bulk density simulated during fire years. (c) Mean
fuel loads for litter and grass fuels simulated during fire years.
Figure 4. Changes in connectivity with elevation. Isolines represent
different levels of fuel bed bulk density; fuel moisture was held
constant at 1 percent.
groves and suggested that decreased fire frequency al-
lows greater fuel accumulation between fires, which
increases the connectivity of the fuel bed and leads to
wider spreading fires. Fires have been excluded from
most Sierran forests for several decades. As a result,
the connectivity of these forests with respect to fire
is expected to have increased (McKelvey et al. 1996).
However, our analysis suggests that connectivity may
be related to fire frequency only when fuel moisture
is intermediate in value. When fuel moisture is very
low, fire frequency is irrelevant; the forest stand is
almost completely burnable regardless of time since
the previous fire. Conversely, if fuel moisture is high,
fire frequency is irrelevant because so little of the for-
est is burnable. Therefore, even in the past before fire
suppression, widely spreading fires probably occurred
during droughtswhen the effects of low fuel moistures
overwhelmed the spatial arrangementof fuels. Coinci-
dent fire dates in the tree-ring record at different sites
support this hypothesis (Swetnam 1993; Caprio and
Swetnam 1995).
Elevation
Fire intensity is a complex function of many variables
including fuel moisture, fuel loads, and the bulk den-
sity of those fuels. These variables tend to vary with
elevation in the Sierra Nevada. Our definition for the
connectivity of burnable area is a function of these
same variables, and our analysis allowed us to em-
phasize the importance of fuel load while isolating the
effects of two variables: fuel moisture and fuel bed
bulk density.
The effect of fuel moisture on the connectivity
of burnable area across the elevation gradient can
be seen in the difference among the isolines in Fig-
ure 3a. When conditions were dry enough, burnable
area increased and nearly all sites across the elevation
gradient had high connectivity. Conversely, when con-
ditions were moist, there was little burnable area and
connectivity as low.
When we held fuel bed bulk density constant
across elevation, connectivity of burnable area gen-
erally increased with elevation (Figure 4) as fuel
loads increased (Figure 3c). Fuels at elevations be-
low 1700 m were sparse and thus these sites had low
connectivity except when bulk density was very low
(Figure 4). On the other hand, fuels were abundant
at elevations from 2500 m to 3000 m. These sites
had high connectivity even when bulk densities were
1.4lbft
−3
(22.4 kg m
−3
) or higher (Figure 4).
152
Bulk density, however, was not constant across el-
evation (Figure 3b). Fuel bed bulk density increased
with elevation (Figure 3b) because species composi-
tion shifted from long needled pine to short needled
fir, under which a compact forest floor developed(van
Wagtendonk et al. 1998). In addition, grass, which
tends to reduce the overall fuel bed bulk density, de-
creased with elevation. When we allowed fuel bed
bulk density to vary with elevation in our analysis,
connectivity increased above 1700 m as fuel loads
increased. At the lowest elevations, however, it is ap-
parent that the bulkdensity of fuels can overwhelmthe
effect of absolute values of fuel loads on connectivity.
For example, there is a high degree of connectivity
at elevations below 1500 m, despite the low overall
fuel loads. Miller and Urban (1999) suggested that
high fuel moistures are the primary factor that limits
burnable area at higher elevations. Indeed, the effect
of high fuel moistures on connectivity can be seen in
the differences among the isolines in Figure 3a; low
connectivity occurs when fuel moistures are high. Our
results here suggest that in addition to fuel moisture,
bulk density (and by extension, species composition)
can play a role in controlling burnable area.
Grass can be an important player in Sierran fire
regimes. Grass lowers the bulk density of the fuel bed
and contributes fine fuels for combustion, enhancing
flammability. Without grass, these low elevation sites
(<1500 m) would have low connectivity and experi-
ence fires of small spatial extent. Grass can provide
a high degree of connectivity and allow for widely
spreading fire (Figure 3a). Grass can influence fire fre-
quencyat lowerelevations, as well. Fire scar data from
the tree-ring record has shown an inverse relationship
betweenelevation and fire frequencydespite a reduced
ignition rate at lower elevations (Caprio and Swetnam
1995). A grassy understory at lower elevations would
enable fire to spread rapidly over large areas and to
recur frequently.
We observed nonlinear patterns in connectivity
across the elevation gradient for intermediate values
of bulk density and fuel moisture (Figures 3a, 4).
These nonlinear patterns are consistent with expecta-
tions from percolation theory (Stauffer 1985; Gardner
et al. 1987). Rapid changes in the size and shape
of burnable patches occur near a critical density of
burnable plots when the largest patch is able to ex-
tend across the map from one edge to the other. Once
the proportion of the forest stand that is burnable ex-
ceeds this critical value, the fire can percolate across
the map and the map is highly connected. Our results
suggest that a critical threshold may exist in the lower
mixed conifer forest, between 1700–1900 m, where
fuel loads increase. There may be another critical
threshold between 1500–1700 m (Figure 3a). Connec-
tivity of burnablearea decreasessharply with elevation
in this zone because both grass production and litter
production from forest trees are quite low (Figure 3c).
We did not anticipate this result, and would be inter-
ested in finding out if such a threshold really exists in
the ecotone between the oak-pine savanna and closed
mixed conifer forest in the Sierra Nevada.
In the past, many fires burned across the eleva-
tion gradient in the Sierra Nevada (Caprio and Swet-
nam 1995), perhaps linking disparate vegetation types
along the elevation gradient. The fire regime and veg-
etation pattern in one elevation zone could influence
the fire regime and vegetation pattern in other zones.
Although this model does not explicitly link forest
stands from one site to another across the elevation
gradient, our finding of differences in connectivity
with elevation may have important implications for
fires that spread throughout the landscape. For exam-
ple, if there is a zone of low connectivity between
1500 m and 1700 m, then we might expect this zone
to act as a natural fire break for fires burning up-slope
from sites below this zone, except, of course, dur-
ing conditionsof extremely dry weather. Furthermore,
because fire suppression represents a drastic decrease
in fire frequency throughout the Sierra Nevada, con-
nectivity may have increased considerably between
1500–1700 m. If connectivity has increased in this
zone, there may be more opportunities today for fires
to burn very large areas than in the past.
Model uncertainties
Fuel bed bulk density is probably not the only fuel
property that varies with elevation in the Sierra
Nevada. For example, surface-area-to-volume ratios
for woody fuels vary among species (van Wagten-
donk et al. 1996) but we have not simulated these
differences here. Elevational gradients in other fuel
properties could either enhance or offset the influence
of fuel bed bulk density on connectivity of burnable
area that we have demonstrated here.
Connectivity of burnable area is very responsive to
the amount of grass in the fuel bed. Although we have
improved the ability to simulate fire regimes where
grass may be important, the treatment of grass dynam-
ics is still crude. We have not included competitive
interactions with tree seedlings for soil water in the
153
model. Nor have we distinguished betweenannual and
perennial grasses, which may respond differently to
fire. Shrubs may also be very important in Sierran for-
est fire regimes, especially where forest grades into
chaparral, but we have not attempted to incorporate
shrubs in this model.
Fire spread in the model does not account for the
variability in weather conditions that occur during a
fire. In reality, a single fire can flareup and die downas
wind, temperatureand relative humidity vary. We have
limitedouranalysisof connectivityto areasof9 ha and
a range of average weather conditions, represented by
six different levels of fuel moisture.
Conclusion
Simulation results confirmed our expectations that fire
frequency can influence the connectivity of burnable
area. By allowing mean fuel loads to increase, fire
suppression increases connectivity and could lead to
wider spreading fires. Our results also demonstrated
that very low or very high levels of fuel moisture
can override the influence of the spatial arrangement
of fuels. Although fires were frequent in the Sierra
Nevada before European settlement, connectivity was
probably high during times of drought and individual
fires spread widely. Even if land managers reduce fuel
loads, they cannot control the variability in weather
conditions. A significant degree of risk of large fires
always exists, no matter how much fuel reduction is
performed.
The connectivity of burnable area is influenced by
at leastthree variables, all of which vary with elevation
in the Sierra Nevada: fuel loads, fuel moisture and the
bulk density of the fuel bed. We showed that connec-
tivity tends to increase with elevation as mean fuel
loads increase. However, we also demonstrated how
other fuel bed parameters may outweigh this influ-
ence and thus control burnable area. We demonstrated
the potential influence of fuel bed parameters using
fuel bed bulk density, which is controlled by species
composition. Our results also illustrated the important
influence that grass can have on connectivity at lower
elevations. Finally, we identified thresholds where fire
behavior may change qualitatively as a result of non-
linear changes in connectivity. These thresholds could
affect the potential for fires to spread throughout the
landscape.
As the local or regional climate changes, extremes
in climate may be more important than the changes
in mean climate (Rind et al. 1989). Fuel moisture
responds to the variance in weather and can greatly
affect the connectivity of burnable area. When pro-
jecting impacts of global climatic change on forest
dynamics, we should consider how the variability
in climate might change. Although climate directly
affects fire regimes through its influence on fuel mois-
ture, its indirect effects on the fire regime may be
equally important. As global climate changes, species
composition is likely to change and could affect the
fire regime via its influence on the bulk density of the
fuel bed. Therefore,climate changeprojectionsshould
also address potential shifts in species composition.
Acknowledgements
Funding for this research was provided by the United
States Geological Service/ Biological Resources Divi-
sion Sierra Nevada Global Change Research Program
under contract CA8800-1-9004.This research benefit-
ted from the incredibly rich collaborative environment
of the Sierra Nevada Global Change Research Pro-
gram. Bob Gardner suggested using correlation length
to measure connectivity and providedan advancecopy
of the computer program RULE. This work was com-
pleted as part of Carol Miller’s doctoral degree at Col-
orado State University. Thoughtful comments by Jim
Lenihan and an anonymousreviewergreatly improved
the manuscript.
References
Albini, F. A 1976. Estimating wildfire behavior and effects. USDA
Forest Service General Technical Report INT-30.
Anderson, R. S 1990. Holocene forest development and paleocli-
mates within the central Sierra Nevada, California. J Ecol 78:
470–489.
Anderson, R. S. and Carpenter, S. L. 1991. Vegetation change in
Yosemite Valley, Yosemite National Park, California, during the
protohistoric period. Madrono 38: 1–13.
Andrews, P. L 1986. BEHAVE: fire behavior prediction and fuel
modeling system. USDA Forest Service General Technical Re-
port INT-194.
Brown, J. K., Marsden, M. A., Ryan, K. C. and Reinhardt, E. D.
1985. Predicting duff and woody fuel consumed by prescribed
fire in the northern Rocky Mountains. United States Department
of Agriculture Forest Service Research Paper INT-337.
Caprio, A. C. and Swetnam, T. W. 1995. Historic fire regimes along
an elevational gradient on the west slope of the Sierra Nevada,
California. pp 173–179. In Proceedings: Symposium on Fire in
Wilderness and Park Management, Missoula, MT, March 30-
April 1, 1993. J. K. Brown, Mutch, R. W., Spoon, C. W. and
Wakimoto, R. W., technical coordinators.
154
Cohen, J. D. and Deeming, J. E. 1985. The national fire-danger
rating system: basic equations. USDA Forest Service General
Technical Report PSW-82.
Daly, C., Neilson, R. P. and Phillips, D. L. 1994. A digital topo-
graphic model for distributing precipitation over mountainous
terrain. J Appl Metero 33: 140–158.
Davis, F. W. and Burrows, D. A. 1994. Spatial simulation of fire
regime in Mediterranean-climate landscapes. pp 117–139. it In
The Role of Fire in Mediterranean-type Ecosystems. Edited by
J. M. Moreno and W.C. Oechel. Springer-Verlag, New York.
Davis, O. K., Anderson, R. S., Fall, P. L., O’Rourke, M. K.
and Thompson, R. S. 1985. Palynological evidence for early
Holocene aridity in the southern Sierra Nevada, California. Quat
Res 24: 322–332.
Deeming, J. E., Lancaster, J. W., Fosberg, M. A., Furman, R. W.,
and Schroeder, M. J. 1972. National fire-danger rating system.
USDA Forest Service Research Paper RM-84.
Gardner, R. H. RULE: a program for the generation and analysis
of landscape patterns. In Landscape Ecological Analysis: Issues
and Applications. Edited by J. M. Klopatek and R. H. Gardner.
Springer-Verlag, Berlin (in press).
Gardner, R. H., Milne, B. T., Turner, M. G. and O’Neill, R. V.
1987. Neutral models for the analysis of broad-scale landscape
patterns. Landscape Ecol 1: 19–28.
Gardner, R. H. and O’Neill, R. V. 1990. Pattern, process and
predictability: the use of neutral models for landscape analy-
sis. pp 289–307 In Quantitative Methods in Landscape Ecology.
Edited by M. G. Turner and R. H.Gardner. Springer-Verlag, New
York.
Green, D.G, 1983. Shapes of simulated fires in discrete fuels. Ecol
Modelling 20: 21–32.
Keifer, M, 1991. Age structure and fire disturbance in the south-
ern Sierra Nevada subalpine forest. M.S. Thesis University of
Arizona, Tucson.
Kilgore, B. M. and Taylor, D. 1979. Fire history of a sequoia-mixed
conifer forest. Ecology 60: 129–142.
McKelvey, K. S., Skinner, C. N., Chang, C., Erman, D. C., Husari,
S. J., Parsons, D. J., van Wagtendonk, J. W. and Weather-
spoon, C. P. 1996. An overview of fire in the Sierra Nevada.
In Sierra Nevada Ecosystem Project: final report to Congress,
Vol. II, Assessments and Scientific Basis for Management Op-
tions. pp 1033–1040. University of California, Centers for Water
and Wildland Resources, Davis.
Miller, C. and Urban, D. L. 1999a. A model of surface fire, cli-
mate and forest pattern in the Sierra Nevada, California. Ecol
Modelling: 114: 113–135.
Miller, C. and Urban, D.L. 1999b. Interactions between forest
heterogeneity and surface fire regimes in the southern Sierra
Nevada. Can J Forest Res 29: 202-212.
Mutch, L. S. and Parsons, D. J. 1998. Mixed conifer forest mortal-
ity and establishment before and after prescribed fire in Sequoia
National Park, California. Forest Scie 44: 341–355.
Nikolov, N. T. and Zeller, K. F. 1992. A solar radiation algorithm
for ecosystem dynamic models. Ecol Modelling 61: 149–168.
Parsons, D. J. 1978. Fire and fuel accumulation in a giant sequoia
forest. J Forestry 76: 104–105.
Parsons, D. J. and DeBenedetti, S. H. 1979. Impact of fire sup-
pression on a mixed-conifer forest. Forest Ecol Manage 2:
21–33.
Pitcher, D. C, 1987. Fire history and age structure in red fir forests
of Sequoia National Park, California. Can J Forest Res 17: 582–
587.
Rind, D., Goldberg, R. and Ruedy, R. 1989. Change in climate
variability in the 21st century. Climatic Change 14: 5–37.
Rothermel, R. C, 1972. A mathematical model for predicting fire
spread in wildland fuels. United States Department of Agricul-
ture Forest Service Research Paper INT-115.
Running, S. W., Nemani, R., and Hungerford, R. D, 1987. Extrap-
olation of meteorological data in mountain terrain, and its use
for simulating forest evapotranspiration and photosynthesis. Can
J Forest Res 17: 472–483.
Ryan, K. C. and Reinhardt, E. D, 1988. Predicting postfire mortality
of seven western conifers. Can J Forest Res 18: 1291–1297.
Skinner, C. N. and Chang, C. 1996. Fire regimes, past and present.
In Sierra Nevada Ecosystem Project: final report to Congress,
Vol. II, Assessments and Scientific Basis for Management Op-
tions. pp 1041–1070. University of California, Centers for Water
and Wildland Resources, Davis.
Stauffer, D. 1985. Introduction to percolation theory. Taylor and
Francis, London.
Stephens, S. L. 1995. Effects of prescribed and simulated fire
and forest history of giant sequoia (Sequoiadendron giganteum
[Lindley] Buccholz.)-mixed conifer ecosystems of the Sierra
Nevada, California. Ph.D. Dissertation. University of California,
Berkeley, CA.
Stephenson, N. L. 1988. Climatic control of vegetation distribution:
the role of the water balance with examples from North Amer-
ica and Sequoia National Park, California. Ph.D. Dissertation.
Cornell University, Ithaca.
Swetnam, T. W, 1993. Fire history and climate change in giant
sequoia groves. Science 262: 885–889.
Turner, M. G. and Dale, V. H. 1990. Modeling landscape distur-
bance. In Quantitative Methods in Landscape Ecology. Edited by
M. G. Turner and R. H. Gardner. pp 323–352. Springer-Verlag,
New York.
Turner, M. G., Gardner, R. H, Dale, V. H and O’Neill, R. V.
1989. Predicting the spread of disturbance across heterogeneous
landscapes. Oikos 55: 121–129.
Turner, M. G., Hargrove, W. W., Gardner, R. H. and Romme, W. H.
1994. Effects of fire on landscape heterogeneity in Yellowstone
National Park, Wyoming. J Veg Sci 5: 731–742.
Turner, M. G. and Romme, W. H. 1994. Landscape dynamics in
crown fire ecosystems. Landscape Ecol 9: 59–77.
Urban, D. L., Bonan, G. B., Smith, T. M. and Shugart, H. H. 1991.
Spatial applications of gap models. Forest Ecol Manage 42: 95–
110.
Vankat, J. L. and Major, J. 1978. Vegetation changes in Sequoia
National Park, California. J Biogeogr 5: 377–402.
Van Wagner, C. E, 1973. Height of crown scorch in forest fires. Can
J Forest Res 3: 373–378.
van Wagtendonk, J. W., Benedict, J. M. and Sydoriak, W. M. 1996.
Physical properties of woody fuel particles of Sierra Nevada
conifers. Int J Wildland Fire 6: 117–123.
van Wagtendonk, J. W., Benedict, J. M. and Sydoriak, W. M. 1998.
Fuel bed characteristics of Sierra Nevada conifers. Western J
Appl Forestry 13: 73–84.
Warner, T. E, 1980. Fire history in the yellow pine forest of Kings
Canyon National Park. Pages 89–92 in Proceedings of the Fire
History Workshop, USDA Forest Service General Technical
Report RM-81.
