Modeling postfire conifer mortality for long-range ... - Springer Link

RESEARCH Modeling Postfire Conifer Mortality for Long-range Planning DAVID L. PETERSON* USDA Forest Service Pacific Southwest Forest and Range Experiment Station 4955 Canyon Crest Drive Riverside, California 92507, LISA KEVIN C. RYAN LJSDA Forest Service Intermountain Forest and Range Experiment Station Drawer G Missoula, Montana 59806, LISA ABSTRACT/A model is presented for predicting mortality of conifers after wildfire. The model requires stand data inputs

Relationships between fire damage and probability of mortality have been developed for ponderosa pine (Pinna ponderosa Laws) (Herman 1954, Dieterich 1979), Douglas-fir [Pseudotsuga menziesii (Mirb.) Franco] (Bevins 1980), red pine (Pinus resinosa Ait.) (Van Wagner 1970), white pine (Pinus strobus L.) (Methven 1971), and several species of Southern pine (Ferguson 1955, Storey and Merkel 1960). The relationships between crown scorch and mortality determined in these studies are species and site specific. There are currently no models that can be used to estimate fire damage or postfire condition for a wide range of conifer species and types of fires. The interaction of several forms of damage must be taken into account to predict tree mortality for a wide range of species, stands, and fires. Percentage of live crown scorched by fire is the most widely used parameter for predicting mortality in conifers (Herman 1954, Methven 1971, Van Wagner 1973, Dieterich 1979, Ryan 1982). The extent of cambial damage in stems (Hare 1965) and roots (Connaughton 1936, McConkey and Gedney 1951) is also important, although the effect of this damage on mortality has not been adequately quantified. We have developed a model that predicts postfire timber mortality for a broad range of conifer species, KEY WORDS: Crown damage; Fuels; Northern Rocky Mountains; Timber; Wildfire

*To whomcorrespondenceshouldbe addressed. EnvironmentalManagementVol. 10, No. 6, pp. 797-808

and is linked with a mathematical fire behavior model that calculates fireline intensity. Fraction of crown volume killed is calculated for each species in a stand based on mensurational data. Duration of lethal heat at the base of trees is calculated from fuel consumption and burning time values. Fraction of crown volume killed and the ratio of critical time for cambial kill to duration of lethal heat are independent variables in a function that calculates probability of mortality. The model produces reasonable estimates of stand mortality for fire and site characteristics found in the northern Rocky Mountains, USA. It has a broad resolution appropriate for use in fire management planning and has potential applications for coniferous forests throughout the United States.

stands, and fires. The mortality model was developed for a fire management planning system that estimates postfire change in resource outputs. The model is constructed with fire, site, and tree information available for the northern Rocky Mountains, USA. This region was selected for initial application of the model because of frequent fire occurrence, presence of a broad range of timber species, and potential for high postfire loss of commercial timber value.

Model Structure Site and Fire Environment Descriptors

The overall structure of the model is illustrated in Figure 1. A set of parameters describing the site and certain aspects of the fire environment is generated for each stand in which wildfire damage is estimated. These parameters include: stand cover type, stand age class (seedling/sapling, pole, and sawtimber), fuel model [a description of the mass of burnable material on the forest floor, size class distribution of fuels, and surface-to-volume ratio of fuels (Albini 1976, Anderson 1982)], slope, aspect, elevation, time of day, and time of year (Figure 1). Temperature, rdative humidity, and windspeed inputs are derived from the AFFIRMS historical weather records (Furman and Helfman 1973). Weather data are used to derive fuel moisture content. These are adjusted to account for differences in slope, aspect, elevation, time of day, and time of year (Salazar and Bradshaw 1984). 9 1986 Springer-VedagNew York Inc.

798

D.L. Peterson and K. C. Ryan

DIAMETER AND BASAL AREAOFEACHSPECIEs

m

CROW N WIDTH BARK THICKNESS

CRITICAL TIME KIL

9

CAMBIAL

(c)

FIRE BEHAVIOR PREDICTOR RATE OF SPREAD

T"EL% . 'O0~'TY

FIRELINE INTENSITy l

RACTIONAL FUEL CONSUMPTION (Cf)

Fire Behavior Fuel model, slope, fuel moisture, and windspeed are inputs to the fire behavior predictor (Salazar and Bradshaw 1986) (Figure 1). Inputs are used to calculate the forward rate of spread [distance the flaming front of a fire travels over time (Rothermel 1972 and 1983)] and fireline intensity [energy release per unit time per unit length of fire front (Byram 1959)]. Scorch height, the height of lethal temperature in the convection column, is calculated from fireline intensity, air temperature, and windspeed by Van Wagner's (1973) model. Scorch height is an output of the fire behavior predictor (Salazar and Bradshaw 1986) and is subsequently used with tree morphology data to calculate the proportion of crown killed (Figure 1). Stand Composition and Structural Characteristics The Forest Service classification system for timber cover types (USDA Forest Service 1967) is used to classify cover types in the model. There are seven timber cover types in the northern Rocky Mountains dominated by ten species: ponderosa pine, Douglasfir, western white pine (Pinus monticola Dougl.), lodgepole pine (P. contorta Dougl.), western larch (Larix occidentalis Hurt.), subalpine fir [Abies lasiocarpa (Hook.) Hurt.]; grand fir [A. grandis (Dougl.) Lindl.], Engelmann spruce (Picea engelmannii Parry), western hemlock [Tsuga heterophylla (Raf.) Sarg.], and western redcedar (Thuja plicata Donn.). Forest inventory records from USDA Forest Service, Region 1 National Forests were used to compile a file of mean basal area and diameter for each species within each cover-type-ageclass combination. These even-aged distributions are generally representative of actively managed forest stands in the northern Rocky Mountains. Structural characteristics of the stand are specified in order to calculate crown kill and select the appropriate mortality function (Figure 1). Mean diameter values from the stand composition file are used by the tree morphology file to calculate tree height, crown length, and bark thickness. Tree height/diameter regression equations are from Brown and others (1977), and crown length/diameter and crown width/diameter equations are derived from data included in Brown

Figure 1. The mortality model uses stand structure and fire characteristics to calculate fire damage to conifers and estimate mortality of each species in a stand.

(1978). Bark thickness/diameter regression equations are from Ryan (1982). Crown Kill Van Wagner (1973) derived a relationship between fireline intensity (Byram 1959) and temperatures reached in the convection column above the fire (see the Appendix). This relationship is used to predict the lethal height in the canopy. Foliage is more easily killed than protected terminal buds (Methven 1971), and empirical evidence from Western conifers suggests that bud kill is more important to postfire survival than foliage scorch. Bud death is therefore used as the determinant of mortality rather than foliage death. Resistance to heat varies with bud size (Mitchell 1914, Byram 1948, Wagener 1961) and season (Wagoner 1961, Van Wagner 1973). Species and seasonal differences in resistance to crown damage are incorported in the model by assuming different lethal temperatures for each of three conditions. Condition 1 is used for species with indefinite terminal buds (western redcedar), regardless of date of fire, and for species whose buds are small or unshielded by needles during periods of active stem elongation (subalpine fir, grand fir, Engelmann spruce, western hemlock, Douglas-fir). Condition 2 is used for the above species with small buds during periods when buds are set, and for species whose buds are large or partially shielded by needles during stem elongation (ponderosa pine, lodgepole pine, western white pine, and western larch). Condition 3 is used for the above species with large or shielded buds during periods when buds have set and the meristem is insulated by bud scales. Assumed lethal temperatures for the three conditions are 60 ~ 65 ~ and 70~ respectively. Although values for lethal temperature are somewhat arbitrary, they produce adjusted values that realistically represent known differences. Dates for each condition are the average dates for initiation of shoot elongation and bud set in the northern Rocky Mountains (Schmidt and Lotan 1980). Fraction of crown volume killed as a function of height of crown kill depends on crown shape. We assume that the crown shape of all species in the model is a paraboloid with circular base for the purpose of

Modeling Postfire Conifer Mortality

calculating crown volume (Peterson 1985). Formulas for the volume of a paraboloid and frustum of a scorched crown are used to calculate fraction of crown volume killed (Figure 2) as:

(hk

-

&+

~e) (h, -

ck =

~-I-hk

hk + ~e)

c2

(1)

where

.......... i

Ck = fraction of crown volume killed

Figure 2, Height of crown kill (hk), tree height (ht), and crown length fie) are used to calculate fraction of crown volume killed (equation 1). Shaded area indicates crown kill.

(0 < ck ~< 1)

h k = height of crown kill (m) ht = tree height (m) ce = crown length (m)

When calculated scorch height exceeds the height of a tree of a given species, the species is assumed to be 100% consumed, that is, when hk > ht, the value of ck is 1.0. Foliage of trees in the northern Rocky Mountains generally begins to actively burn when fireline intensity exceeds 1000 kcal/m-s (Rothermel 1983). It is assumed that foliage and buds are consumed and trees are killed above this intensity.

Duration of Lethal Heat T h e duration of a fire affects the amount of cambial damage incurred by a tree. Duration of fire depends on the size and amount of fuel that burns. For modeling purposes, fuels (Table 1) are assumed to be woody cylinders with initial diameter D o = 4/%, where % is initial surface-to-volume ratio. T h e amount of fuel that burns is determined from initial fuelbed conditions associated with each fuel model (Table 1), that is, loading, moisture content, and an empirically derived fractional fuel consumption relationship. Proportion of fuel burned in a fire is negatively correlated with fractional fuel moisture content (ng, the ratio of wet mass to dry mass). The moisture content at which fuels no longer sustain burning is the moisture content of extinction (m,). T h e fractional amount of fuel that burns (C~) is estimated from the relationship between Cf and mf/m, (Figure 3; see the Appendix for equations). T h e r e is empirical data only for the "upper" part of the curves in Figure 3, but for modeling purposes, the relationship is extended beyond the range of the data to mf/m~ = 1.0 (that is, mf = m~), the point at which burning is assumed to stop. Because the diameters of woody fuels are small relatNe to their lengths, the ends of fuel cylinders do not contribute significantly to particle surface area. It is therefore assumed that the mass of fuel consumed can be described in terms of diameter reduction (z2xD): A D = Do (1 - [1 - Cf]~

799

(2)

Derivation of equation 2 is included in the Appendix. We assume that fuels burn at a fixed rate during both the flaming and glowing phases of a fire. T h e flaming phase residence time (-rR) is adapted from Anderson (1969) by assuming that the rate of diameter reduction is constant for the duration of 7R (see the Appendix for derivation). Total burning time (%) indudes both -rn and the time of glowing combusion (To). Glowing times are not well known "and may vary with different fuelbeds (Cheney 1981). Sandberg (1980) used the relationship vG = 7R to predict duff consumption. Cheney (1981) reported values of 7a between 4 ~R and 5 ~R, and Anderson (personal communication) suggests that Tc may approach 10 ~R. On the basis of this evidence, vc is arbitrarily fixed at 4 ~R. Burning time (vB) is therefore calculated as: 9B = 7~ + 7R = 5-rR

(3)

By substituting the value for ~R from equation 24 in the Appendix, 63

O"o

9 ~ = --(1

-

[1 -

cfl ~

(4)

Burning time is calculated for each fuel size class (the three fuel size classes used here represent average timelags for change in moisture content that correspond to specific diameter classes; see Table 1) separately because each class has different fuel loadings and different burning times. These separate burning times are weighted by the planform area of the ith fuel size class (see the A p p e n d i x ) . T h e b u r n i n g time (minutes) contributed by the ith fuel size class can be expressed as a function of the amount of fuel and its fractional moisture content: Wilt o

63

- - - (% I "rB~ = - 1.6

-

[I

-

cA] ~

= 39.4 Wi (1 - [1 - CA]~ )

(5)

(6)

800

D.L. Peterson and K. C. Ryan

Table 1. Fuelbed properties important in determining fire behavior are described for fuel models commonly found in forest stands in the northern Rocky Mountains. a

Property Surface-to-volume ratio (% [cm-1])c Loading (Wi) (g/cm 2)

Moisture of extinction (m~)

Standard fuel size classb (h)

Open timber, grass and understory (fuel model 2)

Closed timber, litter with light dead fuels (fuel model 8)

Closed timber, litter with heavy dead fuels (fuel model 10)

1 10 100 1 10 100 1 10 100

98 4 1 0.045 0.022 0.011 0.22 0.43 0.52

66 4 1 0.034 0.022 0.056 0.25 0.43 0.52

66 4 1 0.067 0.045 0.112 0.25 0.43 0.52

a Modified from fuel models in the USDA Forest Service fire behavior officers system (Albini 1976); fuel model numbers are from that system. b Standard fuel size classes are 1 b, 10 h, and, 100 h based on the average timelag for change in equilibrium moisture content. Corresponding fuel diameter classes are: ~