Kootenai, Kaniksu, and Tally Lake (KT) Variant Overview

Transcription

1 United States Department of Agriculture Forest Service Forest Management Service Center Fort Collins, CO 2008 Revised: November 2015 Kootenai, Kaniksu, and Tally Lake (KT) Variant Overview Forest Vegetation Simulator Flathead National Forest (Amanda Smiley, FS-R1-Flathead NF)

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3 Kootenai, Kaniksu, and Tally Lake (KT) Variant Overview Forest Vegetation Simulator Compiled By: Chad E. Keyser USDA Forest Service Forest Management Service Center 2150 Centre Ave., Bldg A, Ste 341a Fort Collins, CO Authors and Contributors: The FVS staff has maintained model documentation for this variant in the form of a variant overview since its release in The original authors were Renate Bush and Jim Brickell. In 2008, the previous document was replaced with this updated variant overview. Gary Dixon, Christopher Dixon, Robert Havis, Chad Keyser, Stephanie Rebain, Erin Smith-Mateja, and Don Vandendriesche were involved with this update. Robert Havis cross-checked information contained in this variant overview with the FVS source code. Current maintenance is provided by Chad Keyser. Keyser, Chad E. comp (revised November 2, 2015). Kootenai, Kaniksu, and Tally Lake (KT) Variant Overview Forest Vegetation Simulator. Internal Rep. Fort Collins, CO: U. S. Department of Agriculture, Forest Service, Forest Management Service Center. 48p. iii

4 Table of Contents 1.0 Introduction Geographic Range Control Variables Location Codes Species Codes Habitat Type, Plant Association, and Ecological Unit Codes Site Index Maximum Density Growth Relationships Height-Diameter Relationships Bark Ratio Relationships Crown Ratio Relationships Crown Ratio Dubbing Crown Ratio Change Crown Ratio for Newly Established Trees Crown Width Relationships Crown Competition Factor Small Tree Growth Relationships Small Tree Height Growth Small Tree Diameter Growth Large Tree Growth Relationships Large Tree Diameter Growth Large Tree Height Growth Mortality Model Regeneration Volume Fire and Fuels Extension (FFE-FVS) Insect and Disease Extensions Literature Cited Appendices Appendix A. Habitat Codes iv

5 Quick Guide to Default Settings Parameter or Attribute Default Setting Number of Projection Cycles 1 (10 if using Suppose) Projection Cycle Length 10 years Location Code (National Forest) 114 Kootenai National Forest Plant Association Code 571(TSHE/CLUN/CLUN) Slope 30 percent Aspect 45 degrees Elevation 35 (3500 feet) Latitude / Longitude Latitude Longitude All location codes Site Species Not used Site Index Not used Maximum Stand Density Index Based on maximum basal area Maximum Basal Area Habitat type specific Volume Equations National Volume Estimator Library Merchantable Cubic Foot Volume Specifications: Minimum DBH / Top Diameter LP All Other Species All other location codes 6.0 / 4.5 inches 7.0 / 4.5 inches Stump Height 1.0 foot 1.0 foot Merchantable Board Foot Volume Specifications: Minimum DBH / Top Diameter LP All Other Species All other location codes 6.0 / 4.5 inches 7.0 / 4.5 inches Stump Height 1.0 foot 1.0 foot Sampling Design: Basal Area Factor 40 BAF Small-Tree Fixed Area Plot 1/300 th Acre Breakpoint DBH 5.0 inches v

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7 1.0 Introduction The Forest Vegetation Simulator (FVS) is an individual tree, distance independent growth and yield model with linkable modules called extensions, which simulate various insect and pathogen impacts, fire effects, fuel loading, snag dynamics, and development of understory tree vegetation. FVS can simulate a wide variety of forest types, stand structures, and pure or mixed species stands. New variants of the FVS model are created by imbedding new tree growth, mortality, and volume equations for a particular geographic area into the FVS framework. Geographic variants of FVS have been developed for most of the forested lands in United States. The original North Idaho (NI) variant included the Kootenai, Kaniksu, and Flathead National Forests. Validation studies using the NI variant showed some biases in simulations for the Kootenai NF, Kaniksu NF, and Tally Lake Ranger District of the Flathead National Forest. As a result, Region 1 requested a new variant covering these areas. The KT variant, sometimes called the KOOKANTL variant, was developed in Data used to develop the KT variant came from growth sample trees (GST) from National Forests in northern Idaho and western Montana. Due to the small number of mountain hemlock in the database, no new small- or large-tree growth equations were formulated for this species, equations and coefficients from the North Idaho (NI) variant were used for these species. To fully understand how to use this variant, users should also consult the following publication: Essential FVS: A User s Guide to the Forest Vegetation Simulator (Dixon 2002) This publication can be downloaded from the Forest Management Service Center (FMSC), Forest Service website or obtained in hard copy by contacting any FMSC FVS staff member. Other FVS publications may be needed if one is using an extension that simulates the effects of fire, insects, or diseases. 1

8 2.0 Geographic Range The KT variant covers forest areas in the northern tip of Idaho and the northwestern corner of Montana. This includes Kootenai National Forest, Kaniksu National Forest, and Tally Lake Ranger District of the Flathead National Forest. The KT variant may also be used to model some forests in eastern Washington and northern Montana. The geographic range of the KT variant overlaps the range of the Inland Empire variant; however, where the variants overlap, users may choose to use the KT variant. The suggested geographic range of use for the KT and IE variants is shown in figure Figure Suggested geographic range of use for the KT and IE variants. 2

9 3.0 Control Variables FVS users need to specify certain variables used by the KT variant to control a simulation. These are entered in parameter fields on various FVS keywords usually brought into the simulation through the SUPPOSE interface data files or they are read from an auxiliary database using the Database Extension. 3.1 Location Codes Locations codes in the KT variant are delineated by Forest Service region, forest, district and compartment number. The location code is a 8-digit code where the first digit of the code represents the Forest Service Region Number(R), the next two digits represent the Forest Number (FF), the next two digits represent the district number (DD), and the last three digits represent the compartment number (CCC) resulting in the 8-digit code RFFDDCCC. The location code is used to assign a national forest code (RFF) and geographic area code that are used in the mortality model and growth equations, respectively. For example, user s having stand data in compartment 5 of the Rexford West area of the Kootenai NF should enter a location code of which would then map the stand to geographic area 2. If the location code is missing or incorrect in the KT variant, a default forest code of 114 (Kootenai National Forest) will be used and the geographic area will be set to area 8. The geographic area assignment by location code combinations recognized in the KT variant is shown in table Table Geographic area assignment by location code combinations used in the KT variant. Geographic Area Name Region (R) Forest (FF) District (DD) Compartment (CCC) 1 Rexford East, Kootenai NF Rexford West, Kootenai NF all but Yaak, Kootenai NF all 3 Fortine, Kootenai NF all 4 Troy, Kootenai NF all 4 Bonners Ferry, Idaho Panhandle NF all 5 Libby West, Kootenai NF ,8-19,27 6 Fisher River West, Kootenai NF Cabinet-Sandpoint, Kootenai NF all Cabinet-Sandpoint, Idaho Panhandle NF all 7 8 Swan Lake Island Unit, Flathead NF Tally Lake, Flathead NF all 8 Default for any other Flathead NF 1 10 Default for any other Idaho Panhandle NF Fisher River East, Kootenai NF all but Bitterroot NF Clearwater NF 1 5 3

10 8 Coeur d Alene NF Colville NF Kaniksu NF Lolo NF Nezperce NF St. Joe NF Fisher River East, Kootenai NF all but Libby East, Kootenai NF all but 1-4,8-19, Species Codes The KT variant recognizes 11 species. You may use FVS species codes, Forest Inventory and Analysis (FIA) species codes, or USDA Natural Resources Conservation Service PLANTS symbols to represent these species in FVS input data. Any valid western species code identifying species not recognized by the variant will be mapped to the most similar species in the variant. The species mapping crosswalk is available on the variant documentation webpage of the FVS website. Any non-valid species code will default to the other species category. Either the FVS sequence number or species code must be used to specify a species in FVS keywords and Event Monitor functions. FIA codes or PLANTS symbols are only recognized during data input, and may not be used in FVS keywords. Table shows the complete list of species codes recognized by the KT variant. Table Species codes used in the KT variant. Species Number Species Code Common Name FIA Code PLANTS Symbol Scientific Name 1 WP western white pine 119 PIMO3 Pinus monticola 2 WL western larch 073 LAOC Larix occidentalis 3 DF Douglas-fir 202 PSME Pseudotsuga menziesii 4 GF grand fir 017 ABGR Abies grandis 5 WH western hemlock 263 TSHE Tsuga heterophylla 6 RC western redcedar 242 THPL Thuja plicata 7 LP lodgepole pine 108 PICO Pinus contorta 8 ES Engelmann spruce 093 PIEN Picea Engelmannii 9 AF subalpine fir 019 ABLA Abies lasiocarpa 10 PP ponderosa pine 122 PIPO Pinus ponderosa 11 OT other species 999 2TREE 3.3 Habitat Type, Plant Association, and Ecological Unit Codes There are 175 habitat type codes recognized in the KT variant. If the habitat type code is blank or not recognized, the default 571 (TSHE/CLUN) will be assigned. The KT habitat type code is mapped to one of the 30 original NI variant habitat type codes. The KT and original NI variants habitat type codes are 4

11 used in various parts of the model as identified in the sections that follow. A list of valid KT variant habitat type codes and the NI habitat type code equivalent can be found in Appendix A. 3.4 Site Index Site index is not used in the KT variant. 3.5 Maximum Density Maximum stand density index (SDI) and maximum basal area (BA) are important variables in determining density related mortality and crown ratio change. Maximum basal area is a stand level metric that can be set using the BAMAX or SETSITE keywords. If not set by the user, a default value is calculated from maximum stand SDI each projection cycle. Maximum stand density index can be set for each species using the SDIMAX or SETSITE keywords. If not set by the user, a default value is assigned as discussed below. Maximum stand density index at the stand level is a weighted average, by basal area proportion, of the individual species SDI maximums. The default maximum SDI is set based on a user-specified, or default, habitat type code or a user specified basal area maximum. If a user specified basal area maximum is present, the maximum SDI for species is computed using equation {3.5.1}; otherwise, the maximum SDI for species is computed from the basal area maximum associated with the equivalent NI original habitat type code shown in table using equation {3.5.1}. {3.5.1} SDIMAX i = BAMAX / ( * SDIU) where: SDIMAX i BAMAX SDIU is the species-specific SDI maximum is the user-specified basal area maximum or habitat type-specific basal area maximum is the proportion of theoretical maximum density at which the stand reaches actual maximum density (default 0.85, changed with the SDIMAX keyword) Table Basal area maximums by original NI habitat type code in the KT variant. Original NI Habitat Code Maximum Basal Area

12 Original NI Habitat Code Maximum Basal Area

13 4.0 Growth Relationships This chapter describes the functional relationships used to fill in missing tree data and calculate incremental growth. In FVS, trees are grown in either the small tree sub-model or the large tree submodel depending on the diameter. 4.1 Height-Diameter Relationships Height-diameter relationships in FVS are primarily used to estimate tree heights missing in the input data, and occasionally to estimate diameter growth on trees smaller than a given threshold diameter. In the KT variant, height-diameter relationships are a logistic functional form, as shown in equation {4.1.1} (Wykoff, et.al 1982). The equation was fit to data of the same species used to develop other FVS variants. Coefficients for equation {4.1.1} are shown are shown in table When heights are given in the input data for 3 or more trees of a given species, the value of B 1 in equation {4.1.1} for that species is recalculated from the input data and replaces the default value shown in table In the event that the calculated value is less than zero, the default is used. {4.1.1} For DBH > 3.0 : HT = exp(b 1 + B 2 / (DBH + 1.0)) where: HT is tree height DBH is tree diameter at breast height B1 - B2 are species-specific coefficients shown in table Table Coefficients for the logistic Wykoff equation {4.1.1} in the KT variant. Species Code Default B 1 B 2 WP WL DF GF WH RC LP ES AF PP OT Bark Ratio Relationships Bark ratio estimates are used to convert between diameter outside bark and diameter inside bark in various parts of the model. The equation is shown in equation {4.2.1} and coefficient (b 1 ) for this equation by species is shown in table

14 {4.2.1} BRATIO = b 1 where: BRATIO is species-specific bark ratio (bounded to 0.80 < BRATIO < 0.99) b 1 is a species-specific coefficient shown table Table Coefficients (b1) for the bark ratio equation {4.2.1} in the KT variant. Species Code b 1 Equation Source WP Wykoff, et. al WL Wykoff, et. al DF Wykoff, et. al GF Wykoff, et. al WH Wykoff, et. al RC Wykoff, et. al LP Wykoff, et. al ES Wykoff, et. al AF Wykoff, et. al PP Wykoff, et. al OT Wykoff, et. al Crown Ratio Relationships Crown ratio equations are used for three purposes in FVS: (1) to estimate tree crown ratios missing from the input data for both live and dead trees; (2) to estimate change in crown ratio from cycle to cycle for live trees; and (3) to estimate initial crown ratios for regenerating trees established during a simulation Crown Ratio Dubbing In the KT variant, crown ratios missing in the input data are predicted using different equations depending on tree size. Live trees less than 3.0 in diameter and dead trees of all sizes use equations { } and { } to compute crown ratio. Equation coefficients are found in table { } X = R 1 + R 2 * DBH + R 3 * HT + R 3 * BA + N(0,SD) { } CR = 1 / (1 + exp(x)) where: CR is crown ratio expressed as a proportion (bounded to 0.05 < CR < 0.95) DBH is tree diameter at breast height HT is tree height BA is total stand basal area N(0,SD) is a random increment from a normal distribution with a mean of 0 and a standard deviation of SD R 1 R 3 are species-specific coefficients shown in table

15 Table Coefficients for the crown ratio equation {4.3.1} in the KT variant. Species Code Coefficient WP WL DF GF WH RC R R R R SD Species Code Coefficient LP ES AF PP OT R R R R SD In the KT variant, equation { } is used to predict missing crown ratio for live trees 3.0 in diameter or larger. { } ln(cr) = HAB + (b 1 * BA) + (b 2 * BA^2) + (b 3 * ln(ba)) + (b 4 * CCF) + (b 5 *CCF^2) + (b 6 * ln(ccf)) + (b 7 * DBH) + (b 8 *DBH^2) + (b 9 * ln(dbh)) + (b 10 * HT) + (b 11 * HT^2) + (b 12 * ln(ht)) + (b 13 * PCT) + (b 14 * ln(pct)) where: CR is predicted crown ratio expressed as a proportion HAB is a habitat-dependent coefficient shown in table BA is total stand basal area CCF is stand crown competition factor DBH is tree diameter at breast height HT is tree height PCT is the subject tree s percentile in the basal area distribution of the stand b 1 b 14 are species-specific coefficients shown in table Table Coefficients for the crown ratio equation { } in the KT variant. Species Code Coefficient WP WL DF GF WH RC LP ES AF PP OT b b b b b b b b

16 Species Code Coefficient WP WL DF GF WH RC LP ES AF PP OT b b b b b b Table HAB values by habitat class for equation { } in the KT variant. Habitat Species Code Class WP WL DF GF WH RC LP ES AF PP OT Table Habitat class by species and habitat code for HAB values in equation { } in the KT variant. Species Code Habitat Codes WP WL DF GF WH RC LP ES AF PP OT , , 260, , , 340, , 360, , 470, ,

17 500, , 530, 545, , , , 635, 675, , 640, 650, , 660, , , 600, 690, 750, 780, 925, , , 730, 770, 790, 900, , 810, 830, , 820, Crown Ratio Change Crown ratio change is estimated after growth, mortality and regeneration are estimated during a projection cycle. Crown ratio change is the difference between the crown ratio at the beginning of the cycle and the predicted crown ratio at the end of the cycle. For live trees greater than 3 in dbh, crown change is predicted using equation { }. Crown change is checked to make sure it doesn t exceed the change possible if all height growth produces new crown. Crown change is further bounded to 1% per year for the length of the cycle to avoid drastic changes in crown ratio Crown Ratio for Newly Established Trees Crown ratios for newly established trees during regeneration are estimated using equation { }. A random component is added in equation { } to ensure that not all newly established trees are assigned exactly the same crown ratio. { } CR = * PCCF + RAN where: CR is crown ratio expressed as a proportion (bounded to 0.2 < CR < 0.9) PCCF is crown competition factor on the inventory point where the tree is established RAN is a small random component 11

18 4.4 Crown Width Relationships The KT variant calculates the maximum crown width for each individual tree based on individual tree and stand attributes. Crown width for each tree is reported in the tree list output table and used for percent cover (PCC) calculations in the model. Crown width is calculated using equation {4.4.1} and coefficients for this equation are shown in table The minimum diameter and bounds for certain data values are given in table Equation numbers in table are given with the first three digits representing the FIA species code, and the last two digits representing the equation source. {4.4.1} Crookston (2003); Equation 03 DBH > MinD: CW = [a 1 * exp [a 2 + (a 3 * ln(cl)) + (a 4 * ln(dbh)) + (a 5 * ln(ht)) + (a 6 * ln(ba))]] DBH < MinD: CW = [a 1 * exp [a 2 + (a 3 * ln(cl)) + (a 4 * ln(mind) + (a 5 * ln(ht)) + (a 6 * ln(ba))]] * (DBH / MinD) where: BF is a species-specific coefficient based on forest code (BF = 1.0 in the EM variant) CW is tree maximum crown width CL is tree crown length DBH is tree diameter at breast height HT is tree height BA is total stand basal area EL is stand elevation in hundreds of feet MinD is the minimum diameter a 1 a 6 are species-specific coefficients shown in table Table Coefficients for crown width equation {4.4.1} in the KT variant. Species Code Equation Number* a 1 a 2 a 3 a 4 a 5 a 6 WP WL DF GF WH RC LP ES AF PP OT *Equation number is a combination of the species FIA code (###) and source (##). 12

19 Table MinD values and data bounds for equation {4.4.1} in the KT variant. Species Code Equation Number* MinD EL min EL max CW max WP n/a n/a 35 WL n/a n/a 40 DF n/a n/a 80 GF n/a n/a 40 WH n/a n/a 54 RC n/a n/a 45 LP n/a n/a 40 ES n/a n/a 40 AF n/a n/a 30 PP n/a n/a 46 OT Crown Competition Factor The KT variant uses crown competition factor (CCF) as a predictor variable in some growth relationships. Crown competition factor (Krajicek and others 1961) is a relative measurement of stand density that is based on tree diameters. Individual tree CCF t values estimate the percentage of an acre that would be covered by the tree s crown if the tree were open-grown. Stand CCF is the summation of individual tree (CCF t ) values. A stand CCF value of 100 theoretically indicates that tree crowns will just touch in an unthinned, evenly spaced stand. Crown competition factor for an individual tree is calculated using equation {4.5.1}. All species coefficients are shown in table {4.5.1} CCF equations for individual trees DBH > 1 : CCF t = R 1 + (R 2 * DBH) + (R 3 * DBH^2) 0.1 < DBH < 1.0 : CCF t = R 4 * DBH ^R 5 DBH < 0.1 :CCF t = where: CCF t is crown competition factor for an individual tree DBH is tree diameter at breast height R 1 R 5 are species-specific coefficients shown in table Table Coefficients for CCF equation {4.5.1} in the KT variant. Species Code Model Coefficients R 1 R 2 R 3 R 4 R 5 WP WL DF GF WH

20 Species Code Model Coefficients R 1 R 2 R 3 R 4 R 5 RC LP ES AF PP OT Small Tree Growth Relationships Trees are considered small trees for FVS modeling purposes when they are smaller than some threshold diameter. The threshold diameter is set to 3.0 for all species in the KT variant. The small tree model is height-growth driven, meaning height growth is estimated first and diameter growth is estimated from height growth. These relationships are discussed in the following sections Small Tree Height Growth The small-tree height increment model predicts 5-year height growth (HTG) for small trees in the KT variant. Potential height growth is estimated using equations { }, and coefficients for these equations are shown in table Species numbers 1-10 use equation { } and species 11 other species uses equation { }. { } Used for all species except species 11 HTG = HAB + LOC + c 1 * PCCF * DUM + c 2 * ln(ba) + c 3 * HT + c 4 * CR + c 5 * CR^2 + c 6 * c 13 * HT^2 + c 7 * EL + SL * (c 8 * cos(asp) + c 9 * sin(asp) + c 10 ) + c 11 * SL^2 + c 12 * BAL { } Used for species 11 where: HTG = EXP(HAB + LOC c 1 * CCF + c 3 * LN(HT) + SL * (c 8 * cos(asp) + c 9 * sin(asp) + c 10 ) + (0.01 * c 12 * BAL)) HTG is estimated height growth for the cycle LOC is a location specific coefficient shown in table HAB is a habitat type dependent coefficient shown in table CCF is stand crown competition factor BA is stand basal area CR is tree crown ratio expressed as a proportion HT is total tree height in feet EL is stand elevation in 100 s of feet BAL is total basal area in trees larger than the subject tree ASP is stand aspect SL is stand slope DUM is a dummy variable depending on whether or not the stand is managed: DUM = 0 for unmanaged stands 14

21 DUM = 1.0 for managed stands c 1 c 13 are species-specific coefficients shown in table Table Coefficients (c 1 c 13 ) for equation { } in the KT variant. Species Code Coefficient WP WL DF GF WH RC LP ES AF PP OT c c c c c c c c c c c c c Table LOC values for equation { } in the KT variant. Location Class Species Code WP WL DF GF WH RC LP ES AF PP OT Table Location class by species and geographic area (table 3.1.1) in the KT variant. Alpha Code Geographic area WP WL DF GF WH RC LP ES AF PP OT

22 Table HAB values for equation { } in the KT variant. Habitat Class Species Code WP WL DF GF WH RC LP ES AF PP OT Table Habitat class by species and habitat code in the KT variant. Habitat Code Species Code WP WL DF GF WH RC LP ES AF PP OT

23 Habitat Code Species Code WP WL DF GF WH RC LP ES AF PP OT

24 Habitat Code Species Code WP WL DF GF WH RC LP ES AF PP OT

25 Habitat Code Species Code WP WL DF GF WH RC LP ES AF PP OT

26 Habitat Code Species Code WP WL DF GF WH RC LP ES AF PP OT For all species, a small random error is then added to the height growth estimate. The estimated height growth (HTG) is then adjusted to account for cycle length, user defined small-tree height growth adjustments, and adjustments due to small tree height model calibration from the input data. Height growth estimates from the small-tree model are weighted with the height growth estimates from the large tree model over a range of diameters (X min and X max ) in order to smooth the transition between the two models. For example, the closer a tree s DBH value is to the minimum diameter (X min ), the more the growth estimate will be weighted towards the small-tree growth model. The closer a tree s DBH value is to the maximum diameter (X max ), the more the growth estimate will be weighted towards the large-tree growth model. If a tree s DBH value falls outside of the range given by X min and X max, then the model will use only the small-tree or large-tree growth model in the growth estimate. The weight applied to the growth estimate is calculated using equation { }, and applied as shown in equation { }. The range of diameters for each species is shown in table { } 20

27 DBH < X min : XWT = 0 X min < DBH < X max : XWT = (DBH - X min ) / (X max - X min ) DBH > X max : XWT = 1 { } Estimated growth = [(1 - XWT) * STGE] + [XWT * LTGE] where: XWT DBH X max X min STGE LTGE is the weight applied to the growth estimates is tree diameter at breast height is the maximum DBH is the diameter range is the minimum DBH in the diameter range is the growth estimate obtained using the small-tree growth model is the growth estimate obtained using the large-tree growth model Table Diameter bounds by species in the KT variant. Species Number Specie s Code X min X max 1 WP WL DF GF WH RC LP ES AF PP OT Small Tree Diameter Growth As stated previously, for trees being projected with the small tree equations, height growth is predicted first, and then diameter growth. So both height at the beginning of the cycle and height at the end of the cycle are known when predicting diameter growth. Small tree diameter growth for trees over 4.5 feet tall is calculated as the difference of predicted diameter at the start of the projection period and the predicted diameter at the end of the projection period, adjusted for bark ratio. By definition, diameter growth is zero for trees less than 4.5 feet tall. For western white pine, western larch, Douglas-fir, grand fir, western hemlock, western redcedar, lodgepole pine, Engelmann spruce, subalpine fir, and ponderosa pine, these two predicted diameters are estimated using equations { }, { } { }, and coefficients shown in table For other species, these two predicted diameters are estimated using equations { } { }, and coefficients shown in table { } DHAT = c 1 + c 2 * HT + DADJ { } DHAT = c 1 * (HT 4.5) c2 + DADJ 21

28 { } DADJ = DELMAX * RELH * RELH 2 * DELMAX * RELH { } RELH = (HT 4.5) / (AH 4.5) { } DELMAX = (AH / 36) * ( * CCF 1.75) where: DHAT is estimated tree diameter at breast height HT is tree height DADJ is an adjustment factor to correct for bias, relative tree size, and stand density RELH is relative tree height (bounded 0 < RELHT < 1) AH is average height of the 40 largest diameter trees DELMAX is an adjustment factor based on relative tree size and stand density (bounded DELMAX < 0) CCF is stand crown competition factor Table Coefficients (c 1 c 2 ) by species for equation { } in the KT variant. Species Code C 1 C 2 WP WL DF GF WH RC LP ES AF PP OT Large Tree Growth Relationships Trees are considered large trees for FVS modeling purposes when they are equal to, or larger than, some threshold diameter. This threshold diameter is set to 3.0 for all species in the KT variant. The large-tree model is driven by diameter growth meaning diameter growth is estimated first, and then height growth is estimated from diameter growth and other variables. These relationships are discussed in the following sections Large Tree Diameter Growth The large tree diameter growth model used in most FVS variants is described in section in Dixon (2002). For most variants, instead of predicting diameter increment directly, the natural log of the periodic change in squared inside-bark diameter (ln(dds)) is predicted (Dixon 2002; Wykoff 1990; Stage 1973; and Cole and Stage 1972). For variants predicting diameter increment directly, diameter increment is converted to the DDS scale to keep the FVS system consistent across all variants. 22

29 The KT variant predicts diameter growth using equation { }. Coefficients for this equation are shown in tables { } Used for all species in the KT variant ln(dds) = b 1 + (b 2 * EL) + (b 3 * EL^2 ) + (b 4 * sin(asp) * SL) + (b 5 * cos(asp) * SL) + (b 6 * SL) + (b 7 * SL^2) + (b 8 *CCF) + (b 9 * ln(dbh)) + (b 10 * CR) + (b 11 * CR^2) + (b 12 * BAL / (ln(dbh + 1.0))) + (b 13 * CCF^2) + (b 14 * DBH^2) + (b 15 * ln(ba)) + (b 16 * PCCF * DUM 1 ) + (b 17 * PCCF * DUM 2 ) + HAB where: DDS is the predicted periodic change in squared inside-bark diameter EL is stand elevation in hundreds of feet ASP is stand aspect SL is stand slope (for other species, SL = 0) CR is a tree s live crown ratio (compacted) expressed as a proportion DBH is tree diameter at breast height BA is total stand basal area BAL is total basal area in trees larger than the subject tree For species 11, BAL = 0.01 * BAL CCF is stand crown competition factor PCCF is crown competition factor on the inventory point where the tree is established HAB is a plant association code dependent coefficient shown in table LOC is a location-specific coefficient shown in table DUM 1-2 are dummy variables depending on whether or not the stand is managed: DUM 1 = 0, DUM 2 = 1.0 for unmanaged stands DUM 1 = 1.0, DUM 2 = 0 for managed stands b 1 is a location-specific coefficient shown in table b 2 -b 17 are species-specific coefficients shown in tables Table Coefficients (b 2 -b 17 ) for equation in the KT variant. Species Code Coefficient WP WL DF GF WH RC LP ES AF PP OT b b E b b b b b b b b b b E E E E E E b

30 Species Code Coefficient WP WL DF GF WH RC LP ES AF PP OT b b E b Table b1 values by location class for equation { } in the KT variant. Location Class Species Code WP WL DF GF WH RC LP ES AF PP OT Table Location class by species and geographic area (table 3.1.1) for equation { } in the KT variant. Species Code Geographic Area WP WL DF GF WH RC LP ES AF PP OT Table HAB values for equation { } in the KT variant. Habitat Class Species Code WP WL DF GF WH RC LP ES AF PP OT

31 Habitat Class Species Code WP WL DF GF WH RC LP ES AF PP OT Table Habitat class by species and habitat code in the KT variant. Habitat Code Species Code WP WL DF GF WH RC LP ES AF PP OT

32 Habitat Code Species Code WP WL DF GF WH RC LP ES AF PP OT

33 Habitat Code Species Code WP WL DF GF WH RC LP ES AF PP OT

34 Habitat Code Species Code WP WL DF GF WH RC LP ES AF PP OT

35 Habitat Code Species Code WP WL DF GF WH RC LP ES AF PP OT Large Tree Height Growth In the KT variant, equation { } is used to estimate large tree height growth for all species. { } HTG = exp(hab + b 0 + (b 1 * HT^2) + (b 2 * ln(dbh)) + (b 3 * ln(ht)) + (b 4 * ln(dg))) where: HTG is estimated height growth for the cycle HAB is a plant association code dependent intercept shown in table HT is tree height at the beginning of the cycle DBH is tree diameter at breast height at the beginning of the cycle DG is 10-year diameter growth for the cycle b 0, b 2, b 3 are species-specific coefficients shown in table b 1, b 4 are habitat-dependent coefficients shown in table Table Coefficients (b 0, b 2 and b 3 ) for the height-growth equation in the KT variant. Species Code Coefficient WP WL DF GF WH RC LP ES AF PP OT b b b