Landscape Ecology15: 145–154, 2000.© 2000Kluwer Academic Publishers. Printed in the Netherlands.

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Connectivity of forest fuels and surface fire regimes

Carol Miller1∗ & Dean L. Urban21Graduate Degree Program in Ecology, Colorado State University, Fort Collins, CO, USA2Nicholas School of the Environment, Duke University, Durham, NC, USA(∗author for correspondence: e-mail: cmiller/rmrs_missoula@fs.fed.us; current address: USDA Forest ServiceAldo 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 connectivity of a landscape can influence the dynamics of disturbances such as fire. In fire-adapted ecosystems,fire suppression may increase the connectivity of fuels and could result in qualitatively different fire patterns andbehavior. We used a spatially explicit forest simulation model developed for the Sierra Nevada to investigate howthe frequency of surface fires influences the connectivity of burnable area within a forest stand, and how thisconnectivity varies along an elevation gradient. Connectivity of burnable area was a function of fuel loads, fuelmoisture, and fuel bed bulk density. Our analysis isolated the effects of fuel moisture and fuel bed bulk densityto emphasize the influence of fuel loads on connectivity. Connectivity was inversely related to fire frequency andgenerally increased with elevation. However, certain conditions of fuel moisture and fuel bed bulk density obscuredthese relationships. Nonlinear patterns in connectivity across the elevation gradient occurred as a result of gradientsin fuel loads and fuel bed bulk density that are simulated by the model. Changes in connectivity with elevation couldaffect 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 inany landscape result from past disturbances. In turn,landscape patterns can influence the spread of futuredisturbances (Turner et al. 1989). Probabilistic modelsderived from percolation theory and cellular automatahave been very helpful for investigating the interac-tion between landscape pattern and crown fires (Green1983; Gardner et al. 1987; Turner et al. 1989). Thesemodels have demonstrated that landscape connectivityis important in controlling disturbance dynamics. Siteson a landscape are ‘connected’ if they are linked bypatterns or processes in some way. For example, iffire can spread from one site to another, those sitesare connected with respect to the process of fire. Com-puter models have revealed that nonlinear thresholdsin connectivity may exist; for very small changes in

connectivity, there can be large, sudden changes in thesystem (Turner et al. 1989; Gardner and O’Neill 1990;Turner and Dale 1990).

Patterns of fire spread and the connectivity ofa landscape with respect to fire are influenced bythe spatial arrangement of fuels (Green 1983; Davisand Burrows 1994; Turner and Romme 1994). Infire-adapted ecosystems, fire suppression may sub-stantially increase the connectivity of fuels and coulddrive qualitatively different fire patterns and behav-ior. The degree to which a landscape is connectedwith respect to fire also depends on meteorologicalconditions. Under moderate weather conditions, firespread is sensitive to the spatial arrangement of fuels;under extremely dry and windy conditions, the impor-tance of this spatial pattern may diminish (Turner andRomme 1994; Turner et al. 1994). Additional researchis needed to better delineate the range of conditionsunder which the spatial arrangement of fuels is impor-

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tant and to identify thresholds when we can expect firebehavior to change qualitatively (Turner and Romme1994).

The forests of the Sierra Nevada in California areone of the best examples of fire-adapted ecosystemsthat have been altered by fire exclusion (Vankat andMajor 1978; Parsons and DeBenedetti 1979; Skinnerand Chang 1996). Historically, these forests experi-enced frequent low- to moderate-intensity surface fireregimes. During the past century, most fires in theSierra Nevada have been suppressed. Forest structurehas become more dense, surface fuels have accumu-lated to unprecedented levels and species compositionhas shifted in favor of shade tolerant tree species.These changes have probably increased the verticaland horizontal continuity of flammable fuels and thus,increased the risk of catastrophic wildfires (McKelveyet al. 1996).

We developed a simulation model for Sierranforests to investigate the interactions among fire,climate and forest pattern. Unlike the aforemen-tioned probabilistic models which simulate crown fireregimes, this model simulates surface fire regimes.The model generates spatial heterogeneity in fuelswithin a forest stand, making it appropriate for study-ing the influence of fire on connectivity of burnablearea. First, we used the model to determine the ef-fect of fire frequency on connectivity of burnable area.Second, we examined how this connectivity variesalong an environmental gradient. By identifying therelationship between fire frequency and connectivity,we may be able to suggest optimum intervals forprescribed fires to reduce fire hazard. Improving ourunderstanding of how connectivity may vary with en-vironmental conditions may help managers identifypriority areas on the landscape for strategic fire man-agement. Furthermore, we may be able to determinethe relative importance of climatic factors versus thespatial arrangement of fuels in influencing the spreadof large fires.

Study area

We focused on Sequoia-Kings Canyon National Parkin the southern Sierra Nevada, California, USA(36.6◦N, 118.6◦W). The Park encompasses a strikingphysical gradient; elevation spans 3500 m over a dis-tance of just 100 km. Across this gradient, vegetationranges from foothill grassland and chaparral, throughponderosa pine, to the mixed-conifer zone, to red firand lodgepole pine, and finally to high-elevation pine

near tree line. Vegetation composition is tightly cou-pled to the soil water balance (Stephenson 1988) andpaleoecological studies have revealed that vegetationhas responded to past climatic changes (Davis et al.1985; Anderson 1990; Anderson and Carpenter 1991).Historical fire frequencies vary across this elevationgradient, as well (Caprio and Swetnam 1995). Priorto the 20th century, low elevation ponderosa pine for-est stands experienced low intensity fires every 3–4years (Warner 1980). In the mixed conifer forest zone,low intensity surface fires burned through stands every5–18 years (Kilgore and Taylor 1979). Fires in thehigher elevation red fir forests have been less frequent,with fire-free intervals for individual trees averagingaround 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 treesand subfossil wood. Despite the high incidence oflightning, fuels are too discontinuous to sustain fires ofany appreciable size at those elevations (Keifer 1991).Fire suppression during the 20th century has drasti-cally disrupted the fire regime throughout the SierraNevada, allowing dead fuel to accumulate and under-story tree density to increase in many forests (Vankatand Major 1978).

Methods

We applied the forest gap model ZELIG (Smith andUrban 1988; Urban et al. 1991) to the Sierra Nevadaby adding a new soil moisture model (Urban et al., inreview), a new fire model (Miller and Urban 1999a;Miller and Urban, 1999b) and parameterizing it forSierran tree species. Below we provide a brief descrip-tion of the model; for further detail, we refer the readerto Miller and Urban (1999a,b) and Urban et al. (inreview).

Model Description

The model simulates a forest stand as a rectangulargrid 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 auser-specified elevation, slope, and aspect and thusrepresents a slope ‘facet’. As such, we refer to thisextension of ZELIG as the FACET Model, or sim-ply FM. Elevation and topographic position are usedinternally by FM’s weather model to adjust climateparameters (Urban et al., in review). Radiation is ad-justed for slope-aspect (Nikolov and Zeller 1992) and

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precipitation and temperature are adjusted accordingto locally regressed lapse rates (Running et al. 1987;Daly et al. 1994).

Like other forest gap models, FM simulatesseedling establishment, annual diameter growth, andmortality for individual trees on each plot. Tree growthis specified as a maximum potential which is then re-duced to reflect suboptimal environmental conditions(e.g., low light, low temperatures, or drought). A keycharacteristic of gap models is that they simulate sys-tem feedbacks: not only are trees affected by theirenvironment, but each tree exerts an influence on itsenvironment (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 withinthe stand as a function of the leaf area, which is dis-tributed vertically along each tree’s crown (Urban et al.1991). Growing degree-days are computed and used asan index for temperature. Soil moisture is estimatedfrom precipitation, potential evapotranspiration, andthe water holding capacity, from which a drought-dayindex is computed (Miller and Urban, 1999b; Urbanet al., in review). The forest floor, comprising the par-tially decomposed forest litter, is treated as the top soillayer; 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 estimatedas a ratio of nitrogen uptake and nitrogen made avail-able through decomposition of forest litter (Miller andUrban 1999a; Urban et al., in review). The availablelight, number of drought-days, growing degree-days,and nutrient availability on each grid cell define theenvironment for each tree in that cell.

Species tolerances to shade, drought, and tempera-ture govern each tree’s growth response to the environ-ment in each grid cell (Miller and Urban 1999a; Urbanet al., in review). Differential species response to nu-trient availability has been turned off in this version ofthe model to minimize the model’s sensitivity to thisuncertain parameter. Nine tree species are simulatedin this version of the model: white fir (Abies concolor[Gord. and Glend.] Lindl. ex Hildebr.), red fir (AbiesmagnificaA. Murr.), incense cedar (Calocedrus decur-rens [Torr.] Floren), lodgepole pine (Pinus contortaDougl. ssp.murryanaGrev. and Balf.), Jeffrey pine(Pinus jeffreyiGrev. and Balf.), sugar pine (Pinus lam-bertianaDougl.), western white pine (Pinus monticolaDougl.), ponderosa pine (Pinus ponderosaLaws.), andCalifornia black oak (Quercus kelloggiiNewb.).

Fuels accumulate as a function of site environmentand forest conditions. Each year during a simulation,a fraction of each tree’s foliage and branchwood areadded to the fuel bed according to species-specificallometries (Miller and Urban 1999a). In addition, bio-mass from dead trees is gradually added to the fuelbed. These ‘dead and down’ fuels are classified bysize using the conventions of fire behavior and firedanger models (Deeming et al. 1972). Each fuel classdecays according to a constant rate which is modifiedby an abiotic decay multiplier that describes the tem-perature and moisture environment of the site. Decayrates for each fuel class were calibrated to data fromSequoia-Kings Canyon and Yosemite National Parks(Parsons 1978; J. van Wagtendonk, USGS BiologicalResources Division, unpublished data). Simulated fuelloads increase with elevation to about 2300 m and thendecline as elevations approach tree line; this patternagrees with independent data from Sequoia NationalPark (Miller and Urban 1999a).

Fine herbaceous fuels can be an important factorin Sierra Nevada fire regimes, particularly at lowerelevations where open oak and pine woodlands canoccur. Therefore, grass production is simulated in thisversion 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 thefuel bed, which also contains the woody fuels and for-est litter. A fuel bed with a large grass component mayburn more easily than a fuel bed comprised only offorest fuels.

A number of parameters describing the physicaland chemical properties of fuel are required for calcu-lating fire intensity: mineral content, silica-free min-eral content, low heat value, surface area to volumeratio, and particle density (Rothermel 1972; Albini1976). 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 arrangementof fuels also influences fire intensity. For example,the loosely packed litter of long-needled ponderosapine forests will burn more readily than a more tightlypacked short-needled fir forest floor. To capture thesedifferences, we simulate bulk density of the fuel bedas 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 grasscomponent of the fuel bed, which is assumed to havea bulk density of 0.54 kg m−3 (Miller and Urban,1999b). Fuel bed bulk density increases with elevation

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Table 1. Constant parameters for physical fuel properties.

Surface Particle Mineral Silica-free

area:volume density content mineral content Heat value

(cm−1) (g cm−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 asgrass production declines (Miller and Urban, 1999b).

Because the model is implemented as a grid of for-est plots, it can describe the spatial heterogeneity offorest structure and composition that exists within astand. Fuel inputs, and therefore fuel bed conditions,vary temporally and spatially throughout a stand ac-cording to the number, size, and species of trees thatare present. In addition, the fuel moisture varies bothtemporally and spatially with the local site water bal-ance. Fuel moisture is derived for each grid cell fromthe duff moisture content, calculated monthly in themodel’s soil water routine, with the duff layer treatedas the top soil layer. Thus, as the model generates spa-tial heterogeneity in forest structure and condition dueto tree-level processes, this leads to heterogeneity infuel bed conditions, thereby generating spatial patternin fire intensity and effects.

We consider FM to simulate a ‘natural’ fire regimeas both fire frequency and magnitude (i.e., areaburned) are generated internally by the model and aregoverned by site conditions. Fire events are simulatedas a function of three factors: probability of ignition,fuel load and fuel moisture. The mean ignition inter-val, in years, for the model grid is specified at run time,and uniform-random numbers are drawn to generatestochastic ignition events around this mean interval.In this paper, we assume that ignitions are not limitingand set this interval so that an ignition occurs everyyear. However, for a fire to occur from an ignition, lowfuel moisture and sufficient fuel loadings must alsoexist. Because the soil water balance – and thus fuelmoisture – becomes more positive with elevation, FMgenerates a decreasing fire frequency with elevation;the simulated pattern agrees well with independentfire history data for the study area (Miller and Urban1999a).

When an ignition occurs, the fireline intensity iscomputed for each of the grid cells from the accu-mulated fuels, fuel moisture conditions, and slopefollowing well established equations for surface firebehavior (Rothermel 1972; Albini 1976). Only cellswith computed intensities greater than 45 kW m−1

(13 BTU ft−1 s−1) are considered to be burnable. Thisintensity is roughly equivalent to a scorch height ofabout 0.5 m and we assume that fires ‘burn out’ whenintensities are less than this. Fires may spread to allcells within the model grid, but they are restricted tothose cells which are burnable and which are also spa-tially contiguous to a randomly located ignition pointon the grid. Thus, fires are restricted to a contagiouscluster of burnable cells, and on average, fires tend

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to burn the largest cluster of burnable cells. Althoughthis approach does not simulate the complexities offire spread, FM successfully reproduces empirical re-lationships between area burned and fire frequencythat have been inferred for pre-settlement fire regimes(Miller and Urban 1999a).

Fire effects are calculated for each grid cell thatburns. Fuels are reduced as a function of pre-fire fuelload (Brown et al. 1985), scorch height is estimatedas a function of mean daytime temperature and fireline intensity (Van Wagner 1973) and fire mortality iscomputed as a function of crown damage (Ryan andReinhardt 1988; Stephens 1995; Mutch and Parsons1998).

Simulations

We conducted two sets of simulations. For the first set,we ran 25 simulations for a south-facing site at 2000 melevation, each with a different ignition probability togenerate a range of fire frequencies. Initially, we ranthe model from bare ground for 200 years without fireto allow successional trends and fuel bed bulk densityto stabilize. Following this initial period, we simulatedthe different fire regimes for 300 years. We chose 300years to ensure that we would be able to average overenough individual fire events for our analysis.

We examined how connectivity varied with eleva-tion in the second set of simulations. As in the firstset, we ran the model for 200 years without fire andfollowed it with 300 years of a natural fire regime. Wesimulated 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 homogeneous soil mapwith soil depth=1 m to emphasize the spatial patterncreated by internal forest dynamics and fire.

Analysis

We defined an area as connected if fire will burnthrough it under a given set of conditions. We defineda 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 asfireline intensity, including: fuel loads, fuel bed bulkdensity, size of fuel particles, weather parameters, andfuel moisture. The parameters that vary in this versionof FM are fuel loads, fuel bed bulk density, and fuelmoisture.

We created maps of burnable area from the fuelload 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 isburnable. To emphasize the influence of fuel loads onconnectivity of burnable area, and to isolate the effectsof these two variables, we created another set of mapsof burnable area in which we held either fuel bed bulkdensity or fuel moisture constant. First, we generatedsix maps of burnable area using six different fuel mois-tures (1, 5, 10, 15, 20, 24%) and the fuel bed bulkdensity simulated by the model. Next, we generatedsix maps of burnable area using six different fuel bedbulk 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,and 27.2 kg m−3). Figure 1 illustrates this approachwith maps of burnable area that were generated from asingle map of fuel loads using the six moisture levels.

For each set of maps, we computed the averagecorrelation length of burnable area for each simula-tion. Correlation length is an index of connectivity andis a measure of the average within-cluster distances forthe entire map; i.e., it is the average distance that firecan spread without leaving a patch of burnable area. Aforest plot is burnable if the calculated fire line inten-sity is at least 45 kW m−1 and burnable plots are in thesame patch of burnable area if they are adjacent neigh-bors or nearest-neighbors to each other. Correlationlength is computed as:

CL=√6(RMSi)

6(S2i )

, (1)

whereRMSi is the mean-squared radius andSi is thesize of theith cluster. We used the FORTRAN 77version of RULE (Gardner, in press) to compute theaverage correlation length of burnable area for the fuelmaps.

Results

We were interested in how connectivity of burnablearea might vary with the frequency of fire. For the sim-ulations at 2000 m elevation, we used six sets of mapsof burnable area corresponding to 6 different moisturelevels and plotted average correlation length againstmean fire interval (Figure 2). The six distinct isolinesin Figure 2 each correspond to a different moisturelevel. Correlation length generally increases as firefrequency decreases, and for a given fire frequency,correlation length increases with decreasing fuel mois-tures. When fuel moisture is 1 percent, connectivity

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Figure 1. Maps of burnable area for six levels of fuel moisture. Thefraction of the map that is burnable, p, and the correlation length,CL, are given.

is high with average correlation lengths varying from85 to 135 m. At the 5 percent moisture level, con-nectivity varies most widely as average correlationlengths range from 20 to 120 m. At moistures of 10%and above, connectivity of burnable area is low, andaverage correlation lengths are less than 50 m.

To examine how connectivity varies with elevationfor a natural fire regime, we plotted average corre-lation length against elevation for the simulations ofsites between 1000 m to 3000 m elevation. For eachsimulation, we again generated six sets of maps ofburnable area corresponding to six different moisture

Figure 2. Connectivity as a function of fire frequency. Correlationlength was computed for simulations conducted for 2000 m, 25%slope and 180◦ azimuth. Isolines represent different levels of fuelmoisture; fuel bed bulk density was allowed to vary within the stand.

levels; each isoline represents a different moisturelevel (Figure 3a). For these sets of maps, we used thebulk density that is simulated by model (Figure 3b).Correlation lengths tend to increase with elevation,with the exception of a range of elevations between1500 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 setof runs, correlation lengths are higher at lower levelsof fuel moisture.

Fuel bed bulk density varies dramatically with ele-vation (Figure 3b). To see how connectivity comparedamong elevations when fuel bed bulk density was heldconstant with elevation, we generated sets of mapscorresponding to six bulk densities and plotted averagecorrelation length computed from these maps againstelevation (Figure 4). Each isoline corresponds to a dif-ferent bulk density value. For the set of results shownhere, fuel moisture was held constant at 1 percent.Correlation length generally increases with elevation,and at a given elevation, correlation length increaseswith decreasing bulk density. Abrupt increases in con-nectivity are apparent around 1700 m and 2600 melevation.

Discussion

Fire frequency

Fire frequency influenced the connectivity of burnablearea (Figure 2). This result is not surprising, and in facthas been inferred from fire scars in the tree-ring recordby Swetnam (1993). He found an inverse relationshipbetween fire frequency and fire extent in giant sequoia

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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 bulkdensity was allowed to vary within the stand and with elevation. (b)Mean fuel bed bulk density simulated during fire years. (c) Meanfuel loads for litter and grass fuels simulated during fire years.

Figure 4. Changes in connectivity with elevation. Isolines representdifferent levels of fuel bed bulk density; fuel moisture was heldconstant at 1 percent.

groves and suggested that decreased fire frequency al-lows greater fuel accumulation between fires, whichincreases the connectivity of the fuel bed and leads towider spreading fires. Fires have been excluded frommost Sierran forests for several decades. As a result,the connectivity of these forests with respect to fireis expected to have increased (McKelvey et al. 1996).However, our analysis suggests that connectivity maybe related to fire frequency only when fuel moistureis intermediate in value. When fuel moisture is verylow, fire frequency is irrelevant; the forest stand isalmost completely burnable regardless of time sincethe 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 firesuppression, widely spreading fires probably occurredduring droughts when the effects of low fuel moisturesoverwhelmed the spatial arrangement of fuels. Coinci-dent fire dates in the tree-ring record at different sitessupport this hypothesis (Swetnam 1993; Caprio andSwetnam 1995).

Elevation

Fire intensity is a complex function of many variablesincluding fuel moisture, fuel loads, and the bulk den-sity of those fuels. These variables tend to vary withelevation in the Sierra Nevada. Our definition for theconnectivity of burnable area is a function of thesesame variables, and our analysis allowed us to em-phasize the importance of fuel load while isolating theeffects of two variables: fuel moisture and fuel bedbulk density.

The effect of fuel moisture on the connectivityof burnable area across the elevation gradient canbe seen in the difference among the isolines in Fig-ure 3a. When conditions were dry enough, burnablearea increased and nearly all sites across the elevationgradient had high connectivity. Conversely, when con-ditions were moist, there was little burnable area andconnectivity as low.

When we held fuel bed bulk density constantacross elevation, connectivity of burnable area gen-erally increased with elevation (Figure 4) as fuelloads increased (Figure 3c). Fuels at elevations be-low 1700 m were sparse and thus these sites had lowconnectivity except when bulk density was very low(Figure 4). On the other hand, fuels were abundantat elevations from 2500 m to 3000 m. These siteshad high connectivity even when bulk densities were1.4 lb ft−3 (22.4 kg m−3) or higher (Figure 4).

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Bulk density, however, was not constant across el-evation (Figure 3b). Fuel bed bulk density increasedwith elevation (Figure 3b) because species composi-tion shifted from long needled pine to short needledfir, under which a compact forest floor developed (vanWagtendonk et al. 1998). In addition, grass, whichtends to reduce the overall fuel bed bulk density, de-creased with elevation. When we allowed fuel bedbulk density to vary with elevation in our analysis,connectivity increased above 1700 m as fuel loadsincreased. At the lowest elevations, however, it is ap-parent that the bulk density of fuels can overwhelm theeffect of absolute values of fuel loads on connectivity.For example, there is a high degree of connectivityat elevations below 1500 m, despite the low overallfuel loads. Miller and Urban (1999) suggested thathigh fuel moistures are the primary factor that limitsburnable area at higher elevations. Indeed, the effectof high fuel moistures on connectivity can be seen inthe differences among the isolines in Figure 3a; lowconnectivity occurs when fuel moistures are high. Ourresults 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 fireregimes. Grass lowers the bulk density of the fuel bedand contributes fine fuels for combustion, enhancingflammability. Without grass, these low elevation sites(<1500 m) would have low connectivity and experi-ence fires of small spatial extent. Grass can providea high degree of connectivity and allow for widelyspreading fire (Figure 3a). Grass can influence fire fre-quency at lower elevations, as well. Fire scar data fromthe tree-ring record has shown an inverse relationshipbetween elevation and fire frequency despite a reducedignition rate at lower elevations (Caprio and Swetnam1995). A grassy understory at lower elevations wouldenable fire to spread rapidly over large areas and torecur frequently.

We observed nonlinear patterns in connectivityacross the elevation gradient for intermediate valuesof bulk density and fuel moisture (Figures 3a, 4).These nonlinear patterns are consistent with expecta-tions from percolation theory (Stauffer 1985; Gardneret al. 1987). Rapid changes in the size and shapeof burnable patches occur near a critical density ofburnable plots when the largest patch is able to ex-tend across the map from one edge to the other. Oncethe proportion of the forest stand that is burnable ex-ceeds this critical value, the fire can percolate acrossthe map and the map is highly connected. Our results

suggest that a critical threshold may exist in the lowermixed conifer forest, between 1700–1900 m, wherefuel loads increase. There may be another criticalthreshold between 1500–1700 m (Figure 3a). Connec-tivity of burnable area decreases sharply with elevationin this zone because both grass production and litterproduction 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 inthe ecotone between the oak-pine savanna and closedmixed 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 typesalong the elevation gradient. The fire regime and veg-etation pattern in one elevation zone could influencethe fire regime and vegetation pattern in other zones.Although this model does not explicitly link foreststands from one site to another across the elevationgradient, our finding of differences in connectivitywith elevation may have important implications forfires that spread throughout the landscape. For exam-ple, if there is a zone of low connectivity between1500 m and 1700 m, then we might expect this zoneto act as a natural fire break for fires burning up-slopefrom sites below this zone, except, of course, dur-ing conditions of extremely dry weather. Furthermore,because fire suppression represents a drastic decreasein fire frequency throughout the Sierra Nevada, con-nectivity may have increased considerably between1500–1700 m. If connectivity has increased in thiszone, there may be more opportunities today for firesto burn very large areas than in the past.

Model uncertainties

Fuel bed bulk density is probably not the only fuelproperty that varies with elevation in the SierraNevada. For example, surface-area-to-volume ratiosfor woody fuels vary among species (van Wagten-donk et al. 1996) but we have not simulated thesedifferences here. Elevational gradients in other fuelproperties could either enhance or offset the influenceof fuel bed bulk density on connectivity of burnablearea that we have demonstrated here.

Connectivity of burnable area is very responsive tothe amount of grass in the fuel bed. Although we haveimproved the ability to simulate fire regimes wheregrass may be important, the treatment of grass dynam-ics is still crude. We have not included competitiveinteractions with tree seedlings for soil water in the

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model. Nor have we distinguished between annual andperennial grasses, which may respond differently tofire. Shrubs may also be very important in Sierran for-est fire regimes, especially where forest grades intochaparral, but we have not attempted to incorporateshrubs in this model.

Fire spread in the model does not account for thevariability in weather conditions that occur during afire. In reality, a single fire can flare up and die down aswind, temperature and relative humidity vary. We havelimited our analysis of connectivity to areas of 9 ha anda range of average weather conditions, represented bysix different levels of fuel moisture.

Conclusion

Simulation results confirmed our expectations that firefrequency can influence the connectivity of burnablearea. By allowing mean fuel loads to increase, firesuppression increases connectivity and could lead towider spreading fires. Our results also demonstratedthat very low or very high levels of fuel moisturecan override the influence of the spatial arrangementof fuels. Although fires were frequent in the SierraNevada before European settlement, connectivity wasprobably high during times of drought and individualfires spread widely. Even if land managers reduce fuelloads, they cannot control the variability in weatherconditions. A significant degree of risk of large firesalways exists, no matter how much fuel reduction isperformed.

The connectivity of burnable area is influenced byat least three variables, all of which vary with elevationin the Sierra Nevada: fuel loads, fuel moisture and thebulk density of the fuel bed. We showed that connec-tivity tends to increase with elevation as mean fuelloads increase. However, we also demonstrated howother fuel bed parameters may outweigh this influ-ence and thus control burnable area. We demonstratedthe potential influence of fuel bed parameters usingfuel bed bulk density, which is controlled by speciescomposition. Our results also illustrated the importantinfluence that grass can have on connectivity at lowerelevations. Finally, we identified thresholds where firebehavior may change qualitatively as a result of non-linear changes in connectivity. These thresholds couldaffect the potential for fires to spread throughout thelandscape.

As the local or regional climate changes, extremesin climate may be more important than the changes

in mean climate (Rind et al. 1989). Fuel moistureresponds to the variance in weather and can greatlyaffect the connectivity of burnable area. When pro-jecting impacts of global climatic change on forestdynamics, we should consider how the variabilityin climate might change. Although climate directlyaffects fire regimes through its influence on fuel mois-ture, its indirect effects on the fire regime may beequally important. As global climate changes, speciescomposition is likely to change and could affect thefire regime via its influence on the bulk density of thefuel bed. Therefore, climate change projections shouldalso address potential shifts in species composition.

Acknowledgements

Funding for this research was provided by the UnitedStates Geological Service/ Biological Resources Divi-sion Sierra Nevada Global Change Research Programunder contract CA8800-1-9004. This research benefit-ted from the incredibly rich collaborative environmentof the Sierra Nevada Global Change Research Pro-gram. Bob Gardner suggested using correlation lengthto measure connectivity and provided an advance copyof 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 JimLenihan and an anonymous reviewer greatly improvedthe manuscript.

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