![Distribution of priority objective values for the individual fuel break segments for a sample of the northeastern portion of the study area: (A) wildfire hazard, computed as the product of the conditional probability of flame length > 1.25 m and annual burn probability, derived from FSim outputs [18], (B) merchantable volume, and (C) net revenue. The geographical location of these segments is shown in the red box in Figure 1.](https://www.researchgate.net/publication/366442970/figure/fig1/AS:11431281115151617@1674779279485/Distribution-of-priority-objective-values-for-the-individual-fuel-break-segments-for-a_Q320.jpg)
Available via license: CC BY 4.0
Content may be subject to copyright.
Citation: Belavenutti, P.; Ager, A.A.;
Day, M.A.; Chung, W. Multi-
Objective Scheduling of Fuel
Treatments to Implement a Linear
Fuel Break Network. Fire 2023,6, 1.
https://doi.org/10.3390/fire6010001
Academic Editor: Alistair M. S. Smith
Received: 19 October 2022
Revised: 12 December 2022
Accepted: 14 December 2022
Published: 20 December 2022
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
fire
Article
Multi-Objective Scheduling of Fuel Treatments to Implement a
Linear Fuel Break Network
Pedro Belavenutti 1, *, Alan A. Ager 2, Michelle A. Day 2and Woodam Chung 1
1Department of Forest Engineering, Resources and Management, Oregon State University,
Corvallis, OR 97331, USA
2USDA Forest Service, Rocky Mountain Research Station, Missoula Fire Sciences Laboratory,
Missoula, MT 59808, USA
*Correspondence: pedro.belavenutti@oregonstate.edu
Abstract:
We developed and applied a spatial optimization algorithm to prioritize forest and fuel
management treatments within a proposed linear fuel break network on a 0.5 million ha Western
US national forest. The large fuel break network, combined with the logistics of conducting forest
and fuel management, requires that treatments be partitioned into a sequence of discrete projects,
individually implemented over the next 10–20 years. The original plan for the network did not
consider how linear segments would be packaged into projects and how projects would be prioritized
for treatments over time, as the network is constructed. Using our optimization algorithm, we
analyzed 13 implementation scenarios where size-constrained projects were prioritized based on
predicted wildfire hazard, treatment costs, and harvest revenues. We found that among the scenarios,
the predicted net revenue ranged from USD 3495 to USD 6642 ha
−1
, and that prioritizing the wildfire
encounter rate reduced the net revenue and harvested timber. We demonstrate how the tradeoffs
could be minimized using a multi-objective optimization approach. We found that the most efficient
implementation scale was a sequence of relatively small projects that treated 300 ha
±
10% versus
larger projects with a larger treated area. Our study demonstrates a decision support model for
multi-objective optimization to implement large fuel break networks such as those being proposed or
implemented in many fire-prone regions around the globe.
Keywords:
spatial optimization; fuel breaks; multi-objective optimization; forest planning; fuel break
networks; fire management planning
1. Introduction
Linear fuel break networks are used by land managers to decrease the extent of large
fires and ultimately, reduce wildfire-related losses [
1
–
5
]. Linear fuel breaks fragment
landscapes with bands of reduced fuel that are used as control lines from which to carry out
suppression operations [
6
,
7
]. The creation of effective linear fuel break segments requires
the delineation of the connected network segments across landscapes. This is a rigorous
process that combines local expertise and spatial analyses to identify efficient fuel break
network designs [
7
–
10
]. Multiple aspects are considered when locating segments of the
fuel break network, including access, terrain, and vegetation [
4
,
11
–
14
]. Once built, there
are additional considerations for re-treatment rates to maintain low fuel loadings across
time [15,16].
A wide range of decision support tools have been applied to the problem of designing
and testing the effectiveness of fuel breaks, although studies that have examined the
problem from a linear network perspective are rare [
7
]. For instance, many studies have
analyzed the effectiveness of fuel breaks, either dispersed or arranged linearly, using fire
spread models to analyze treatment effects, including models such as FARSITE, FlamMap,
FSim [
17
,
18
], FConst MTT [
6
,
19
,
20
], BURN-P3 [
21
], and Cell2Fire [
22
]. These models are
used in planning frameworks to evaluate multiple landscape fuel break scenarios and to
Fire 2023,6, 1. https://doi.org/10.3390/fire6010001 https://www.mdpi.com/journal/fire
Fire 2023,6, 1 2 of 16
analyze tradeoffs [
7
,
23
–
26
]. A few studies have focused specifically on the design of optimal
linear fuel break networks using mathematical programming models [
27
–
29
]. Models to
test linear fuel break designs have considered the rate or probability of the success of the
fuel break segments [
20
,
30
]. In general, these and other studies suggest that fuel break
networks are effective in terms of reducing fire spread, although empirical data point to
the need for suppression resources to actually stop the fire [
4
]. Both dense vegetation
and extreme weather conditions contribute to the failure of fuel breaks under real-world
conditions [31,32].
Despite a large number of studies testing the effectiveness of fuel break networks, as
well as government proposals to build new or expand existing networks [
7
,
33
], there are
few, if any, decision support tools to prioritize project areas (i.e., sub-networks) and the
treatments within them to create the proposed networks. For instance, in Portugal, 3538 km
of proposed linear fuel breaks have been mapped, but prioritizing specific segments for
treatment from a cost and fire management standpoint has received little attention [
20
].
Studies that demonstrate models to optimize the implementation sequence and identify
economic and fire management tradeoffs for prioritizing sub-networks within the larger
networks are lacking, despite a large amount of literature on spatial forest planning [
34
,
35
].
In this study, we demonstrate a new modeling framework to prioritize treatments
and sequence project areas to implement a large linear fuel break network within a fire-
prone Western US national forest. Local fire management staff mapped a 3300 km network
within the national forest, considering terrain, roads, and suppression difficulty. The
bulk of the network will require forest and fuel management for the fuel breaks to serve
their intended purpose, and thus, the forest must now formulate priorities, estimate costs,
and build a strategic implementation plan. To support this effort, we modeled a range of
spatially explicit treatment scenarios optimized for single and multiple objectives, including
predicted wildfire hazard, treatment cost, and harvest revenue. We used these outputs to
identify optimal implementation sequences of projects and treatment segments. We discuss
how the process can provide land management organizations with a broad understanding
of tradeoffs among different prioritization schemes and provide a detailed schedule of
projects and treatments over time, with the specificity to identify the capacity and funding
required to implement the proposed networks.
2. Materials and Methods
2.1. Study Area
The study area was the 520,000 ha Umatilla National Forest (Umatilla NF) located
in the Blue Mountains ecoregion [
36
] within northeast Oregon and southeast Washington
states (Figure 1). Elevations generally range from 900 m to 1500 m, with higher peaks close
to 3000 m. Dry forests of ponderosa pine (Pinus ponderosa Lawson & C. Lawson) dominate
the lower elevations, with dry mixed conifer—grand fir (Abies grandis (Douglas ex D. Don)
Lindl) and Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco)—at higher elevations. Cold
dry forested areas are dominated by lodgepole pine (Pinus contorta Douglas ex Loudon)
at higher elevations. About 4961 ha (1%) burn annually, predominantly due to lightning-
caused wildfires (1992–2020) [37].
2.2. Fuel Break Network
The Umatilla NF designed a fuel break network (FBN) in the year 2020 using regional
guidelines and expert opinion from local fire management staff. The FBN consisted of
segments located primarily along ridgetops and roads, with an intended buffer for fuel
treatments on both sides of the 3315 km length that included grasslands, non-burnable areas,
and conifer forests. The intended width of the FBN was 300 m (150 m per side), aligning
with legislation [
38
] that maximizes fire crew safety and success rates, and consistent with
other programs elsewhere [
38
–
41
]. The FBN included fuel break sections within protected
areas where mechanical treatments are prohibited. However, these will not be implemented
due to administrative restrictions that prohibit mechanical fuel management [
42
]. About a
Fire 2023,6, 1 3 of 16
50,000 ha portion of the Umatilla NF has been prioritized for watershed-level restoration
as part of the five-year forest action plan [
43
], and the fuel breaks for these areas were not
considered for prioritization. Network density was about 0.5 km per km
2
(5 m per hectare)
over the 225,819 ha portion of the Umatilla NF where the network is being implemented.
Fire2023,5,xFORPEERREVIEW3of16
Figure1.MapoftheUmatillaNationalForestillustratingthefuelbreaknetwork(darkblacklines)
andlocalmills.
2.2.FuelBreakNetwork
TheUmatillaNFdesignedafuelbreaknetwork(FBN)intheyear2020usingregional
guidelinesandexpertopinionfromlocalfiremanagementstaff.TheFBNconsistedof
segmentslocatedprimarilyalongridgetopsandroads,withanintendedbufferforfuel
treatmentsonbothsidesofthe3315kmlengththatincludedgrasslands,non‐burnable
areas,andconiferforests.TheintendedwidthoftheFBNwas300m(150mperside),
aligningwithlegislation[38]thatmaximizesfirecrewsafetyandsuccessrates,andcon‐
sistentwithotherprogramselsewhere[38–41].TheFBNincludedfuelbreaksections
withinprotectedareaswheremechanicaltreatmentsareprohibited.However,thesewill
notbeimplementedduetoadministrativerestrictionsthatprohibitmechanicalfuelman‐
agement[42].Abouta50,000haportionoftheUmatillaNFhasbeenprioritizedforwa‐
tershed‐levelrestorationaspartofthefive‐yearforestactionplan[43],andthefuelbreaks
fortheseareaswerenotconsideredforprioritization.Networkdensitywasabout0.5km
perkm2(5mperhectare)overthe225,819haportionoftheUmatillaNFwherethenet‐
workisbeingimplemented.
2.3.ForestVegetation
WeintersectedtheFBNwiththelandscapestandpolygonlayermaintainedbythe
UmatillaNFtoidentifytheportionsoftreatmentstandswithintheFBN(Figure2).The
standboundarieswereoriginallydelineatedfromphotointerpretationandfollowed
Figure 1.
Map of the Umatilla National Forest illustrating the fuel break network (dark black lines)
and local mills.
2.3. Forest Vegetation
We intersected the FBN with the landscape stand polygon layer maintained by the
Umatilla NF to identify the portions of treatment stands within the FBN (Figure 2). The
stand boundaries were originally delineated from photo interpretation and followed natural
breaks in vegetation type and changes in stand structure from past management activi-
ties and disturbances. The landscape stand layer contains a total of 63,241 non-forested
and forested stands, which were clipped to the FBN, resulting in a network containing
22,166 interconnected potential fuel break treatment units covering 67,500 ha. Within this
area, we excluded upland hardwoods and shrublands, leaving 54,198 forested ha (80% of
the network) available as potential candidates for fuel break treatments. Areas that were
not available for treatments corresponded to mostly grass and basalt scab flats common
in much of the Umatilla NF. Inventory data for each stand was obtained from a corporate
USDA Forest Service spatial database on the Umatilla NF. These data consisted of tree
density, species, and size class in 2.54 cm increments [44].
Fire 2023,6, 1 4 of 16
Fire2023,5,xFORPEERREVIEW4of16
naturalbreaksinvegetationtypeandchangesinstandstructurefrompastmanagement
activitiesanddisturbances.Thelandscapestandlayercontainsatotalof63,241non‐for‐
estedandforestedstands,whichwereclippedtotheFBN,resultinginanetworkcontain‐
ing22,166interconnectedpotentialfuelbreaktreatmentunitscovering67,500ha.Within
thisarea,weexcludeduplandhardwoodsandshrublands,leaving54,198forestedha
(80%ofthenetwork)availableaspotentialcandidatesforfuelbreaktreatments.Areas
thatwerenotavailablefortreatmentscorrespondedtomostlygrassandbasaltscabflats
commoninmuchoftheUmatillaNF.Inventorydataforeachstandwasobtainedfroma
corporateUSDAForestServicespatialdatabaseontheUmatillaNF.Thesedataconsisted
oftreedensity,species,andsizeclassin2.54cmincrements[44].
Figure2.Distributionofpriorityobjectivevaluesfortheindividualfuelbreaksegmentsforasample
ofthenortheasternportionofthestudyarea:(A)wildfirehazard,computedastheproductofthe
conditionalprobabilityofflamelength>1.25mandannualburnprobability,derivedfromFSim
outputs[18],(B)merchantablevolume,and(C)netrevenue.Thegeographicallocationoftheseseg‐
mentsisshownintheredboxinFigure1.
2.4.FuelBreakTreatments
Forestandfueltreatmentswereassignedusingstandthresholdsdevelopedincol‐
laborationwithUmatillaNFstaff(Table1).Treatmentintensity,intermsofremovals,was
dependentonexistingcanopycover(CC)percentageandfuelloadings.Inshort,stands
wereeligibleforthinningifthestandcanopycoverexceeded15%(pers.comm.DonJus‐
tice,UmatillaNF).Thinningwasfrombelow(smalltreesfirst)untilthepost‐thinCCwas
15%,asperthepracticeintheBlueMountainsfuelbreakprojectsensuringthatstands
havelessthana0.10crownbulkdensity[45].Thinningfrombelowprioritizedthere‐
movalofsmallertreesoftargetedfire‐intolerantspecies(e.g.,grandfir)andreducedlad‐
derfuelstopreventtorchingandcrowningfirebehavior.Themaximumtreesizeforhar‐
vestwassetat53.3cmtomeetlate‐oldstructure(LOS)objectives,asspecifiedinlocal
harvestguidelines[46,47].ThethinningwassimulatedintwostepsuntiltheCCwasre‐
ducedto15%.Inthefirststep,allavailablespecies(<53.3cm)wereremoveduntiltheCC
wasreducedto15%ofthestand.Then,iftheCCwasstillgreaterthan15%,thesecond
stepremovedgrandfirtreesbetween53.3cmand76.2cmuntiltheCCwasreducedto
15%ofthestand.IftheCCofthestandwasstillgreaterthan15%afterthesecondstep,all
treeslessthan53.3cmandallgrandfirsunder76.2cmwouldberemoved.Surfacefuel
treatmentswereofthepileandburntype,consistingofahandormachinepilingofhar‐
vestresidueanddownedwoodymaterial[48],whichiswidelypracticedontheUmatilla
NF.Non‐forestedstandsofgrass‐shrublandswerenotassignedtoreceivetreatment.All
treatmentsweresimulatedwiththeForestVegetationSimulator(FVS),BlueMountains
variant[44].ThepileandburntreatmentsweresimulatedusingtheFuelMovekeyword,
whichhasthesameeffectasthepileburnprocessintermsofremovingfuelsfromthesite.
Figure 2.
Distribution of priority objective values for the individual fuel break segments for a sample
of the northeastern portion of the study area: (
A
) wildfire hazard, computed as the product of the
conditional probability of flame length > 1.25 m and annual burn probability, derived from FSim
outputs [
18
], (
B
) merchantable volume, and (
C
) net revenue. The geographical location of these
segments is shown in the red box in Figure 1.
2.4. Fuel Break Treatments
Forest and fuel treatments were assigned using stand thresholds developed in collab-
oration with Umatilla NF staff (Table 1). Treatment intensity, in terms of removals, was
dependent on existing canopy cover (CC) percentage and fuel loadings. In short, stands
were eligible for thinning if the stand canopy cover exceeded 15% (pers. comm. Don Justice,
Umatilla NF). Thinning was from below (small trees first) until the post-thin CC was 15%,
as per the practice in the Blue Mountains fuel break projects ensuring that stands have less
than a 0.10 crown bulk density [
45
]. Thinning from below prioritized the removal of smaller
trees of targeted fire-intolerant species (e.g., grand fir) and reduced ladder fuels to prevent
torching and crowning fire behavior. The maximum tree size for harvest was set at 53.3 cm
to meet late-old structure (LOS) objectives, as specified in local harvest guidelines [
46
,
47
].
The thinning was simulated in two steps until the CC was reduced to 15%. In the first
step, all available species (< 53.3 cm) were removed until the CC was reduced to 15% of
the stand. Then, if the CC was still greater than 15%, the second step removed grand fir
trees between 53.3 cm and 76.2 cm until the CC was reduced to 15% of the stand. If the
CC of the stand was still greater than 15% after the second step, all trees less than 53.3 cm
and all grand firs under 76.2 cm would be removed. Surface fuel treatments were of the
pile and burn type, consisting of a hand or machine piling of harvest residue and downed
woody material [
48
], which is widely practiced on the Umatilla NF. Non-forested stands of
grass-shrub lands were not assigned to receive treatment. All treatments were simulated
with the Forest Vegetation Simulator (FVS), Blue Mountains variant [
44
]. The pile and burn
treatments were simulated using the FuelMove keyword, which has the same effect as the
pile burn process in terms of removing fuels from the site.
2.5. Financial Valuation
Outputs from FVS included the population of cut trees from each treated stand by
DBH, species, and total merchantable volume. These data were post-processed with the
FVS economics extension to cut the trees into logs and calculate the small end diameter
required for financial valuation. In essence, logs are valued by the diameter of the small
end, which is not reported in standard FVS outputs. We used the LANFIN keyword file
developed by Vogler et al. [49] for this process.
Fire 2023,6, 1 5 of 16
Table 1.
Stand thresholds used to determine treatment types, as described by Belavenutti et al. (2021),
modified for fuel breaks by thinning down to 15% canopy closure.
Threshold Treatment Types
Fire2023,5,xFORPEERREVIEW5of16
Table1.Standthresholdsusedtodeterminetreatmenttypes,asdescribedbyBelavenuttietal.
(2021),modifiedforfuelbreaksbythinningdownto15%canopyclosure.
ThresholdTreatmentTypes
Standcanopyclosure(CC)>15%Availableforthinning
Merchantablevolume>35m3ha−1Commercialthinning
Thinningvolume>0m3ha−1and<35m3ha−1Non‐commercialthinning(densityreduction)
Fuelloading>3.6tonha−1inthe0–7.6cmdiametersize
classThin+Pileandburn(2yearspost‐thinning)
Standcanopyclosure(CC)<15%ANDFuelloading>3.6ton
ha−1inthe0–7.6cmdiametersizeclassPileandburnonly
Thresholdsfortreatmentsdonotapply(e.g.,standreceived
treatmentinlast15years)Recently‐treatedforest,notreatment
Standisgrass‐shrubnon‐forestNon‐forest,notreatment
2.5.FinancialValuation
OutputsfromFVSincludedthepopulationofcuttreesfromeachtreatedstandby
DBH,species,andtotalmerchantablevolume.Thesedatawerepost‐processedwiththe
FVSeconomicsextensiontocutthetreesintologsandcalculatethesmallenddiameter
requiredforfinancialvaluation.Inessence,logsarevaluedbythediameterofthesmall
end,whichisnotreportedinstandardFVSoutputs.WeusedtheLANFINkeywordfile
developedbyVogleretal.[49]forthisprocess.
Parametersforcostsandrevenuewereobtainedfromlocaltimbersaleandfuels
treatmenttransactiondataontheUmatillaNF.Wedidnotconsiderextraneousproject
implementationcosts,suchasroadreconstructionordecommissioning,sincemostofthe
proposedFBNwasco‐locatedwithestablishedroads.Weusedtheeconomicextensionof
FVStoconvertmodeledharvestvolumeoutputsintologsofspecificsizesandspecies
[50].Correspondingaveragepondvalues(USDm−3)rangingfromUSD71toUSD101
werecollectedfromtimbersalespecialistsontheUmatillaNFandusedtocalculatethe
totalvalueofdeliveredlogsfromeachstand.Logpondvalueswereonlycalculatedfor
standsthatgenerated≥35m3ha−1ofmerchantabletimber,assumingstandsproducing
lesswerenotcommerciallyviable.Althoughharvestingoperationsalongtheroadsmight
includethesestandswithlowervolume,inpractice,theassumptionsprovidedcon‐
sistencywithpriorstudiesthatprioritizedtheUmatillaNFforrestorationprojects[51].
Harvestcost(USDm−3)rangingfromUSD10toUSD110wascalculatedbasedonthe
slopeandtreesizeclass,consistentwithmethodsusedinpreviousstudies[52,53].A
ground‐basedharvestingsystemandassociatedcostswereassignedforstandshavinga
slope≤35%,andacableharvestingsystemwasassignedforallstandsthatexceededthe
35%threshold.Theaverageslopeperstandwascalculatedfromdigitalelevationdata,
witharesolutionof30m.Ifthinningwasnotcommerciallyviable(i.e.,volumeremoval<
35m3ha−1),itwasassumedtobeanon‐commercialthinning,incurringcostsofUSD1600
ha−1.ThecostofthepileandburnmethodwasassumedtobeUSD1110ha−1.
Timberhaulingcostsfromindividualstandstothenearestwoodprocessingfacility
wereestimatedusingtheroadnetworkconsistingofapproximately750,000roadsections,
whichwereclassifiedbydrivingspeed.Round‐triptraveltimebetweeneachstandand
thenearestprocessingfacilitywascomputedfortheshortestpath,usingtraveldistance
andspeed[54].Oneadditionalhourofdelaytimewasaddedforloading,unloading,and
waittimes.Roundtripcostsperonecubicmeteroftimberwerethenestimatedusing
traveltime,thetruckhourlycostofUSD100,andthetruckloadcapacityof12m3.Net
revenuewascalculatedasthedifferencebetweenthevalueofthelogsdeliveredtothe
millminusalltheothercostsassociatedwiththinningandsurfacefueltreatments.
2.6.WildfireHazard
Stand canopy closure (CC) > 15% Available for thinning
Fire2023,5,xFORPEERREVIEW5of16
Table1.Standthresholdsusedtodeterminetreatmenttypes,asdescribedbyBelavenuttietal.
(2021),modifiedforfuelbreaksbythinningdownto15%canopyclosure.
ThresholdTreatmentTypes
Standcanopyclosure(CC)>15%Availableforthinning
Merchantablevolume>35m3ha−1Commercialthinning
Thinningvolume>0m3ha−1and<35m3ha−1Non‐commercialthinning(densityreduction)
Fuelloading>3.6tonha−1inthe0–7.6cmdiametersize
classThin+Pileandburn(2yearspost‐thinning)
Standcanopyclosure(CC)<15%ANDFuelloading>3.6ton
ha−1inthe0–7.6cmdiametersizeclassPileandburnonly
Thresholdsfortreatmentsdonotapply(e.g.,standreceived
treatmentinlast15years)Recently‐treatedforest,notreatment
Standisgrass‐shrubnon‐forestNon‐forest,notreatment
2.5.FinancialValuation
OutputsfromFVSincludedthepopulationofcuttreesfromeachtreatedstandby
DBH,species,andtotalmerchantablevolume.Thesedatawerepost‐processedwiththe
FVSeconomicsextensiontocutthetreesintologsandcalculatethesmallenddiameter
requiredforfinancialvaluation.Inessence,logsarevaluedbythediameterofthesmall
end,whichisnotreportedinstandardFVSoutputs.WeusedtheLANFINkeywordfile
developedbyVogleretal.[49]forthisprocess.
Parametersforcostsandrevenuewereobtainedfromlocaltimbersaleandfuels
treatmenttransactiondataontheUmatillaNF.Wedidnotconsiderextraneousproject
implementationcosts,suchasroadreconstructionordecommissioning,sincemostofthe
proposedFBNwasco‐locatedwithestablishedroads.Weusedtheeconomicextensionof
FVStoconvertmodeledharvestvolumeoutputsintologsofspecificsizesandspecies
[50].Correspondingaveragepondvalues(USDm−3)rangingfromUSD71toUSD101
werecollectedfromtimbersalespecialistsontheUmatillaNFandusedtocalculatethe
totalvalueofdeliveredlogsfromeachstand.Logpondvalueswereonlycalculatedfor
standsthatgenerated≥35m3ha−1ofmerchantabletimber,assumingstandsproducing
lesswerenotcommerciallyviable.Althoughharvestingoperationsalongtheroadsmight
includethesestandswithlowervolume,inpractice,theassumptionsprovidedcon‐
sistencywithpriorstudiesthatprioritizedtheUmatillaNFforrestorationprojects[51].
Harvestcost(USDm−3)rangingfromUSD10toUSD110wascalculatedbasedonthe
slopeandtreesizeclass,consistentwithmethodsusedinpreviousstudies[52,53].A
ground‐basedharvestingsystemandassociatedcostswereassignedforstandshavinga
slope≤35%,andacableharvestingsystemwasassignedforallstandsthatexceededthe
35%threshold.Theaverageslopeperstandwascalculatedfromdigitalelevationdata,
witharesolutionof30m.Ifthinningwasnotcommerciallyviable(i.e.,volumeremoval<
35m3ha−1),itwasassumedtobeanon‐commercialthinning,incurringcostsofUSD1600
ha−1.ThecostofthepileandburnmethodwasassumedtobeUSD1110ha−1.
Timberhaulingcostsfromindividualstandstothenearestwoodprocessingfacility
wereestimatedusingtheroadnetworkconsistingofapproximately750,000roadsections,
whichwereclassifiedbydrivingspeed.Round‐triptraveltimebetweeneachstandand
thenearestprocessingfacilitywascomputedfortheshortestpath,usingtraveldistance
andspeed[54].Oneadditionalhourofdelaytimewasaddedforloading,unloading,and
waittimes.Roundtripcostsperonecubicmeteroftimberwerethenestimatedusing
traveltime,thetruckhourlycostofUSD100,andthetruckloadcapacityof12m3.Net
revenuewascalculatedasthedifferencebetweenthevalueofthelogsdeliveredtothe
millminusalltheothercostsassociatedwiththinningandsurfacefueltreatments.
2.6.WildfireHazard
Merchantable volume > 35 m3ha−1Commercial thinning
Fire2023,5,xFORPEERREVIEW5of16
Table1.Standthresholdsusedtodeterminetreatmenttypes,asdescribedbyBelavenuttietal.
(2021),modifiedforfuelbreaksbythinningdownto15%canopyclosure.
ThresholdTreatmentTypes
Standcanopyclosure(CC)>15%Availableforthinning
Merchantablevolume>35m3ha−1Commercialthinning
Thinningvolume>0m3ha−1and<35m3ha−1Non‐commercialthinning(densityreduction)
Fuelloading>3.6tonha−1inthe0–7.6cmdiametersize
classThin+Pileandburn(2yearspost‐thinning)
Standcanopyclosure(CC)<15%ANDFuelloading>3.6ton
ha−1inthe0–7.6cmdiametersizeclassPileandburnonly
Thresholdsfortreatmentsdonotapply(e.g.,standreceived
treatmentinlast15years)Recently‐treatedforest,notreatment
Standisgrass‐shrubnon‐forestNon‐forest,notreatment
2.5.FinancialValuation
OutputsfromFVSincludedthepopulationofcuttreesfromeachtreatedstandby
DBH,species,andtotalmerchantablevolume.Thesedatawerepost‐processedwiththe
FVSeconomicsextensiontocutthetreesintologsandcalculatethesmallenddiameter
requiredforfinancialvaluation.Inessence,logsarevaluedbythediameterofthesmall
end,whichisnotreportedinstandardFVSoutputs.WeusedtheLANFINkeywordfile
developedbyVogleretal.[49]forthisprocess.
Parametersforcostsandrevenuewereobtainedfromlocaltimbersaleandfuels
treatmenttransactiondataontheUmatillaNF.Wedidnotconsiderextraneousproject
implementationcosts,suchasroadreconstructionordecommissioning,sincemostofthe
proposedFBNwasco‐locatedwithestablishedroads.Weusedtheeconomicextensionof
FVStoconvertmodeledharvestvolumeoutputsintologsofspecificsizesandspecies
[50].Correspondingaveragepondvalues(USDm−3)rangingfromUSD71toUSD101
werecollectedfromtimbersalespecialistsontheUmatillaNFandusedtocalculatethe
totalvalueofdeliveredlogsfromeachstand.Logpondvalueswereonlycalculatedfor
standsthatgenerated≥35m3ha−1ofmerchantabletimber,assumingstandsproducing
lesswerenotcommerciallyviable.Althoughharvestingoperationsalongtheroadsmight
includethesestandswithlowervolume,inpractice,theassumptionsprovidedcon‐
sistencywithpriorstudiesthatprioritizedtheUmatillaNFforrestorationprojects[51].
Harvestcost(USDm−3)rangingfromUSD10toUSD110wascalculatedbasedonthe
slopeandtreesizeclass,consistentwithmethodsusedinpreviousstudies[52,53].A
ground‐basedharvestingsystemandassociatedcostswereassignedforstandshavinga
slope≤35%,andacableharvestingsystemwasassignedforallstandsthatexceededthe
35%threshold.Theaverageslopeperstandwascalculatedfromdigitalelevationdata,
witharesolutionof30m.Ifthinningwasnotcommerciallyviable(i.e.,volumeremoval<
35m3ha−1),itwasassumedtobeanon‐commercialthinning,incurringcostsofUSD1600
ha−1.ThecostofthepileandburnmethodwasassumedtobeUSD1110ha−1.
Timberhaulingcostsfromindividualstandstothenearestwoodprocessingfacility
wereestimatedusingtheroadnetworkconsistingofapproximately750,000roadsections,
whichwereclassifiedbydrivingspeed.Round‐triptraveltimebetweeneachstandand
thenearestprocessingfacilitywascomputedfortheshortestpath,usingtraveldistance
andspeed[54].Oneadditionalhourofdelaytimewasaddedforloading,unloading,and
waittimes.Roundtripcostsperonecubicmeteroftimberwerethenestimatedusing
traveltime,thetruckhourlycostofUSD100,andthetruckloadcapacityof12m3.Net
revenuewascalculatedasthedifferencebetweenthevalueofthelogsdeliveredtothe
millminusalltheothercostsassociatedwiththinningandsurfacefueltreatments.
2.6.WildfireHazard
Thinning volume > 0 m3ha−1and < 35 m3ha−1Non-commercial thinning (density reduction)
Fire2023,5,xFORPEERREVIEW5of16
Table1.Standthresholdsusedtodeterminetreatmenttypes,asdescribedbyBelavenuttietal.
(2021),modifiedforfuelbreaksbythinningdownto15%canopyclosure.
ThresholdTreatmentTypes
Standcanopyclosure(CC)>15%Availableforthinning
Merchantablevolume>35m3ha−1Commercialthinning
Thinningvolume>0m3ha−1and<35m3ha−1Non‐commercialthinning(densityreduction)
Fuelloading>3.6tonha−1inthe0–7.6cmdiametersize
classThin+Pileandburn(2yearspost‐thinning)
Standcanopyclosure(CC)<15%ANDFuelloading>3.6ton
ha−1inthe0–7.6cmdiametersizeclassPileandburnonly
Thresholdsfortreatmentsdonotapply(e.g.,standreceived
treatmentinlast15years)Recently‐treatedforest,notreatment
Standisgrass‐shrubnon‐forestNon‐forest,notreatment
2.5.FinancialValuation
OutputsfromFVSincludedthepopulationofcuttreesfromeachtreatedstandby
DBH,species,andtotalmerchantablevolume.Thesedatawerepost‐processedwiththe
FVSeconomicsextensiontocutthetreesintologsandcalculatethesmallenddiameter
requiredforfinancialvaluation.Inessence,logsarevaluedbythediameterofthesmall
end,whichisnotreportedinstandardFVSoutputs.WeusedtheLANFINkeywordfile
developedbyVogleretal.[49]forthisprocess.
Parametersforcostsandrevenuewereobtainedfromlocaltimbersaleandfuels
treatmenttransactiondataontheUmatillaNF.Wedidnotconsiderextraneousproject
implementationcosts,suchasroadreconstructionordecommissioning,sincemostofthe
proposedFBNwasco‐locatedwithestablishedroads.Weusedtheeconomicextensionof
FVStoconvertmodeledharvestvolumeoutputsintologsofspecificsizesandspecies
[50].Correspondingaveragepondvalues(USDm−3)rangingfromUSD71toUSD101
werecollectedfromtimbersalespecialistsontheUmatillaNFandusedtocalculatethe
totalvalueofdeliveredlogsfromeachstand.Logpondvalueswereonlycalculatedfor
standsthatgenerated≥35m3ha−1ofmerchantabletimber,assumingstandsproducing
lesswerenotcommerciallyviable.Althoughharvestingoperationsalongtheroadsmight
includethesestandswithlowervolume,inpractice,theassumptionsprovidedcon‐
sistencywithpriorstudiesthatprioritizedtheUmatillaNFforrestorationprojects[51].
Harvestcost(USDm−3)rangingfromUSD10toUSD110wascalculatedbasedonthe
slopeandtreesizeclass,consistentwithmethodsusedinpreviousstudies[52,53].A
ground‐basedharvestingsystemandassociatedcostswereassignedforstandshavinga
slope≤35%,andacableharvestingsystemwasassignedforallstandsthatexceededthe
35%threshold.Theaverageslopeperstandwascalculatedfromdigitalelevationdata,
witharesolutionof30m.Ifthinningwasnotcommerciallyviable(i.e.,volumeremoval<
35m3ha−1),itwasassumedtobeanon‐commercialthinning,incurringcostsofUSD1600
ha−1.ThecostofthepileandburnmethodwasassumedtobeUSD1110ha−1.
Timberhaulingcostsfromindividualstandstothenearestwoodprocessingfacility
wereestimatedusingtheroadnetworkconsistingofapproximately750,000roadsections,
whichwereclassifiedbydrivingspeed.Round‐triptraveltimebetweeneachstandand
thenearestprocessingfacilitywascomputedfortheshortestpath,usingtraveldistance
andspeed[54].Oneadditionalhourofdelaytimewasaddedforloading,unloading,and
waittimes.Roundtripcostsperonecubicmeteroftimberwerethenestimatedusing
traveltime,thetruckhourlycostofUSD100,andthetruckloadcapacityof12m3.Net
revenuewascalculatedasthedifferencebetweenthevalueofthelogsdeliveredtothe
millminusalltheothercostsassociatedwiththinningandsurfacefueltreatments.
2.6.WildfireHazard
Fuel loading > 3.6 ton ha−1in the 0–7.6 cm diameter size class Thin + Pile and burn (2 years post-thinning)
Fire2023,5,xFORPEERREVIEW5of16
Table1.Standthresholdsusedtodeterminetreatmenttypes,asdescribedbyBelavenuttietal.
(2021),modifiedforfuelbreaksbythinningdownto15%canopyclosure.
ThresholdTreatmentTypes
Standcanopyclosure(CC)>15%Availableforthinning
Merchantablevolume>35m3ha−1Commercialthinning
Thinningvolume>0m3ha−1and<35m3ha−1Non‐commercialthinning(densityreduction)
Fuelloading>3.6tonha−1inthe0–7.6cmdiametersize
classThin+Pileandburn(2yearspost‐thinning)
Standcanopyclosure(CC)<15%ANDFuelloading>3.6ton
ha−1inthe0–7.6cmdiametersizeclassPileandburnonly
Thresholdsfortreatmentsdonotapply(e.g.,standreceived
treatmentinlast15years)Recently‐treatedforest,notreatment
Standisgrass‐shrubnon‐forestNon‐forest,notreatment
2.5.FinancialValuation
OutputsfromFVSincludedthepopulationofcuttreesfromeachtreatedstandby
DBH,species,andtotalmerchantablevolume.Thesedatawerepost‐processedwiththe
FVSeconomicsextensiontocutthetreesintologsandcalculatethesmallenddiameter
requiredforfinancialvaluation.Inessence,logsarevaluedbythediameterofthesmall
end,whichisnotreportedinstandardFVSoutputs.WeusedtheLANFINkeywordfile
developedbyVogleretal.[49]forthisprocess.
Parametersforcostsandrevenuewereobtainedfromlocaltimbersaleandfuels
treatmenttransactiondataontheUmatillaNF.Wedidnotconsiderextraneousproject
implementationcosts,suchasroadreconstructionordecommissioning,sincemostofthe
proposedFBNwasco‐locatedwithestablishedroads.Weusedtheeconomicextensionof
FVStoconvertmodeledharvestvolumeoutputsintologsofspecificsizesandspecies
[50].Correspondingaveragepondvalues(USDm−3)rangingfromUSD71toUSD101
werecollectedfromtimbersalespecialistsontheUmatillaNFandusedtocalculatethe
totalvalueofdeliveredlogsfromeachstand.Logpondvalueswereonlycalculatedfor
standsthatgenerated≥35m3ha−1ofmerchantabletimber,assumingstandsproducing
lesswerenotcommerciallyviable.Althoughharvestingoperationsalongtheroadsmight
includethesestandswithlowervolume,inpractice,theassumptionsprovidedcon‐
sistencywithpriorstudiesthatprioritizedtheUmatillaNFforrestorationprojects[51].
Harvestcost(USDm−3)rangingfromUSD10toUSD110wascalculatedbasedonthe
slopeandtreesizeclass,consistentwithmethodsusedinpreviousstudies[52,53].A
ground‐basedharvestingsystemandassociatedcostswereassignedforstandshavinga
slope≤35%,andacableharvestingsystemwasassignedforallstandsthatexceededthe
35%threshold.Theaverageslopeperstandwascalculatedfromdigitalelevationdata,
witharesolutionof30m.Ifthinningwasnotcommerciallyviable(i.e.,volumeremoval<
35m3ha−1),itwasassumedtobeanon‐commercialthinning,incurringcostsofUSD1600
ha−1.ThecostofthepileandburnmethodwasassumedtobeUSD1110ha−1.
Timberhaulingcostsfromindividualstandstothenearestwoodprocessingfacility
wereestimatedusingtheroadnetworkconsistingofapproximately750,000roadsections,
whichwereclassifiedbydrivingspeed.Round‐triptraveltimebetweeneachstandand
thenearestprocessingfacilitywascomputedfortheshortestpath,usingtraveldistance
andspeed[54].Oneadditionalhourofdelaytimewasaddedforloading,unloading,and
waittimes.Roundtripcostsperonecubicmeteroftimberwerethenestimatedusing
traveltime,thetruckhourlycostofUSD100,andthetruckloadcapacityof12m3.Net
revenuewascalculatedasthedifferencebetweenthevalueofthelogsdeliveredtothe
millminusalltheothercostsassociatedwiththinningandsurfacefueltreatments.
2.6.WildfireHazard
Stand canopy closure (CC) < 15% AND Fuel loading > 3.6 ton ha
−1
in the 0–7.6 cm diameter size class Pile and burn only
Fire2023,5,xFORPEERREVIEW5of16
Table1.Standthresholdsusedtodeterminetreatmenttypes,asdescribedbyBelavenuttietal.
(2021),modifiedforfuelbreaksbythinningdownto15%canopyclosure.
ThresholdTreatmentTypes
Standcanopyclosure(CC)>15%Availableforthinning
Merchantablevolume>35m3ha−1Commercialthinning
Thinningvolume>0m3ha−1and<35m3ha−1Non‐commercialthinning(densityreduction)
Fuelloading>3.6tonha−1inthe0–7.6cmdiametersize
classThin+Pileandburn(2yearspost‐thinning)
Standcanopyclosure(CC)<15%ANDFuelloading>3.6ton
ha−1inthe0–7.6cmdiametersizeclassPileandburnonly
Thresholdsfortreatmentsdonotapply(e.g.,standreceived
treatmentinlast15years)Recently‐treatedforest,notreatment
Standisgrass‐shrubnon‐forestNon‐forest,notreatment
2.5.FinancialValuation
OutputsfromFVSincludedthepopulationofcuttreesfromeachtreatedstandby
DBH,species,andtotalmerchantablevolume.Thesedatawerepost‐processedwiththe
FVSeconomicsextensiontocutthetreesintologsandcalculatethesmallenddiameter
requiredforfinancialvaluation.Inessence,logsarevaluedbythediameterofthesmall
end,whichisnotreportedinstandardFVSoutputs.WeusedtheLANFINkeywordfile
developedbyVogleretal.[49]forthisprocess.
Parametersforcostsandrevenuewereobtainedfromlocaltimbersaleandfuels
treatmenttransactiondataontheUmatillaNF.Wedidnotconsiderextraneousproject
implementationcosts,suchasroadreconstructionordecommissioning,sincemostofthe
proposedFBNwasco‐locatedwithestablishedroads.Weusedtheeconomicextensionof
FVStoconvertmodeledharvestvolumeoutputsintologsofspecificsizesandspecies
[50].Correspondingaveragepondvalues(USDm−3)rangingfromUSD71toUSD101
werecollectedfromtimbersalespecialistsontheUmatillaNFandusedtocalculatethe
totalvalueofdeliveredlogsfromeachstand.Logpondvalueswereonlycalculatedfor
standsthatgenerated≥35m3ha−1ofmerchantabletimber,assumingstandsproducing
lesswerenotcommerciallyviable.Althoughharvestingoperationsalongtheroadsmight
includethesestandswithlowervolume,inpractice,theassumptionsprovidedcon‐
sistencywithpriorstudiesthatprioritizedtheUmatillaNFforrestorationprojects[51].
Harvestcost(USDm−3)rangingfromUSD10toUSD110wascalculatedbasedonthe
slopeandtreesizeclass,consistentwithmethodsusedinpreviousstudies[52,53].A
ground‐basedharvestingsystemandassociatedcostswereassignedforstandshavinga
slope≤35%,andacableharvestingsystemwasassignedforallstandsthatexceededthe
35%threshold.Theaverageslopeperstandwascalculatedfromdigitalelevationdata,
witharesolutionof30m.Ifthinningwasnotcommerciallyviable(i.e.,volumeremoval<
35m3ha−1),itwasassumedtobeanon‐commercialthinning,incurringcostsofUSD1600
ha−1.ThecostofthepileandburnmethodwasassumedtobeUSD1110ha−1.
Timberhaulingcostsfromindividualstandstothenearestwoodprocessingfacility
wereestimatedusingtheroadnetworkconsistingofapproximately750,000roadsections,
whichwereclassifiedbydrivingspeed.Round‐triptraveltimebetweeneachstandand
thenearestprocessingfacilitywascomputedfortheshortestpath,usingtraveldistance
andspeed[54].Oneadditionalhourofdelaytimewasaddedforloading,unloading,and
waittimes.Roundtripcostsperonecubicmeteroftimberwerethenestimatedusing
traveltime,thetruckhourlycostofUSD100,andthetruckloadcapacityof12m3.Net
revenuewascalculatedasthedifferencebetweenthevalueofthelogsdeliveredtothe
millminusalltheothercostsassociatedwiththinningandsurfacefueltreatments.
2.6.WildfireHazard
Thresholds for treatments do not apply (e.g., stand received
treatment in last 15 years) Recently-treated forest, no treatment
Fire2023,5,xFORPEERREVIEW5of16
Table1.Standthresholdsusedtodeterminetreatmenttypes,asdescribedbyBelavenuttietal.
(2021),modifiedforfuelbreaksbythinningdownto15%canopyclosure.
ThresholdTreatmentTypes
Standcanopyclosure(CC)>15%Availableforthinning
Merchantablevolume>35m3ha−1Commercialthinning
Thinningvolume>0m3ha−1and<35m3ha−1Non‐commercialthinning(densityreduction)
Fuelloading>3.6tonha−1inthe0–7.6cmdiametersize
classThin+Pileandburn(2yearspost‐thinning)
Standcanopyclosure(CC)<15%ANDFuelloading>3.6ton
ha−1inthe0–7.6cmdiametersizeclassPileandburnonly
Thresholdsfortreatmentsdonotapply(e.g.,standreceived
treatmentinlast15years)Recently‐treatedforest,notreatment
Standisgrass‐shrubnon‐forestNon‐forest,notreatment
2.5.FinancialValuation
OutputsfromFVSincludedthepopulationofcuttreesfromeachtreatedstandby
DBH,species,andtotalmerchantablevolume.Thesedatawerepost‐processedwiththe
FVSeconomicsextensiontocutthetreesintologsandcalculatethesmallenddiameter
requiredforfinancialvaluation.Inessence,logsarevaluedbythediameterofthesmall
end,whichisnotreportedinstandardFVSoutputs.WeusedtheLANFINkeywordfile
developedbyVogleretal.[49]forthisprocess.
Parametersforcostsandrevenuewereobtainedfromlocaltimbersaleandfuels
treatmenttransactiondataontheUmatillaNF.Wedidnotconsiderextraneousproject
implementationcosts,suchasroadreconstructionordecommissioning,sincemostofthe
proposedFBNwasco‐locatedwithestablishedroads.Weusedtheeconomicextensionof
FVStoconvertmodeledharvestvolumeoutputsintologsofspecificsizesandspecies
[50].Correspondingaveragepondvalues(USDm−3)rangingfromUSD71toUSD101
werecollectedfromtimbersalespecialistsontheUmatillaNFandusedtocalculatethe
totalvalueofdeliveredlogsfromeachstand.Logpondvalueswereonlycalculatedfor
standsthatgenerated≥35m3ha−1ofmerchantabletimber,assumingstandsproducing
lesswerenotcommerciallyviable.Althoughharvestingoperationsalongtheroadsmight
includethesestandswithlowervolume,inpractice,theassumptionsprovidedcon‐
sistencywithpriorstudiesthatprioritizedtheUmatillaNFforrestorationprojects[51].
Harvestcost(USDm−3)rangingfromUSD10toUSD110wascalculatedbasedonthe
slopeandtreesizeclass,consistentwithmethodsusedinpreviousstudies[52,53].A
ground‐basedharvestingsystemandassociatedcostswereassignedforstandshavinga
slope≤35%,andacableharvestingsystemwasassignedforallstandsthatexceededthe
35%threshold.Theaverageslopeperstandwascalculatedfromdigitalelevationdata,
witharesolutionof30m.Ifthinningwasnotcommerciallyviable(i.e.,volumeremoval<
35m3ha−1),itwasassumedtobeanon‐commercialthinning,incurringcostsofUSD1600
ha−1.ThecostofthepileandburnmethodwasassumedtobeUSD1110ha−1.
Timberhaulingcostsfromindividualstandstothenearestwoodprocessingfacility
wereestimatedusingtheroadnetworkconsistingofapproximately750,000roadsections,
whichwereclassifiedbydrivingspeed.Round‐triptraveltimebetweeneachstandand
thenearestprocessingfacilitywascomputedfortheshortestpath,usingtraveldistance
andspeed[54].Oneadditionalhourofdelaytimewasaddedforloading,unloading,and
waittimes.Roundtripcostsperonecubicmeteroftimberwerethenestimatedusing
traveltime,thetruckhourlycostofUSD100,andthetruckloadcapacityof12m3.Net
revenuewascalculatedasthedifferencebetweenthevalueofthelogsdeliveredtothe
millminusalltheothercostsassociatedwiththinningandsurfacefueltreatments.
2.6.WildfireHazard
Stand is grass-shrub non-forest Non-forest, no treatment
Parameters for costs and revenue were obtained from local timber sale and fuels
treatment transaction data on the Umatilla NF. We did not consider extraneous project
implementation costs, such as road reconstruction or decommissioning, since most of the
proposed FBN was co-located with established roads. We used the economic extension of
FVS to convert modeled harvest volume outputs into logs of specific sizes and species [
50
].
Corresponding average pond values (USD m
−3
) ranging from USD 71 to USD 101 were
collected from timber sale specialists on the Umatilla NF and used to calculate the total
value of delivered logs from each stand. Log pond values were only calculated for stands
that generated
≥
35 m
3
ha
−1
of merchantable timber, assuming stands producing less were
not commercially viable. Although harvesting operations along the roads might include
these stands with lower volume, in practice, the assumptions provided consistency with
prior studies that prioritized the Umatilla NF for restoration projects [51].
Harvest cost (USD m
−3
) ranging from USD 10 to USD 110 was calculated based on
the slope and tree size class, consistent with methods used in previous studies [
52
,
53
]. A
ground-based harvesting system and associated costs were assigned for stands having
a slope
≤
35%, and a cable harvesting system was assigned for all stands that exceeded
the 35% threshold. The average slope per stand was calculated from digital elevation
data, with a resolution of 30 m. If thinning was not commercially viable (i.e., volume
removal < 35 m
3
ha
−1
), it was assumed to be a non-commercial thinning, incurring costs of
USD 1600 ha−1. The cost of the pile and burn method was assumed to be USD 1110 ha−1.
Timber hauling costs from individual stands to the nearest wood processing facility
were estimated using the road network consisting of approximately 750,000 road sections,
which were classified by driving speed. Round-trip travel time between each stand and the
nearest processing facility was computed for the shortest path, using travel distance and
speed [
54
]. One additional hour of delay time was added for loading, unloading, and wait
times. Round trip costs per one cubic meter of timber were then estimated using travel
time, the truck hourly cost of USD 100, and the truckload capacity of 12 m
3
. Net revenue
was calculated as the difference between the value of the logs delivered to the mill minus
all the other costs associated with thinning and surface fuel treatments.
Fire 2023,6, 1 6 of 16
2.6. Wildfire Hazard
We used wildfire simulation raster outputs generated with the FSim [
18
] model, as
part of prior work on the Umatilla NF [
55
]. FSim captures spatial characteristics regarding
topography, surface fuels, and historical weather conditions to quantitatively assess wildfire
hazards [
56
]. FSim uses an ignition density grid to indicate the spatial likelihood of large-fire
occurrence, regardless of ignition source. We measured wildfire hazard as the probability
of a fire with a flame length greater than 1.25 m, a threshold at which direct attack is
avoided in fire suppression operations due to crown fire occurrence. Testing revealed that
the prioritization results were relatively insensitive to higher or lower thresholds. This
particular hazard metric has been described and used in other studies [
57
,
58
]. Wildfire
hazard (Haz) was calculated using the flame length probability outputs that report the
conditional probability of a fire of a given flame length category in 20 0.5 m classes. Wildfire
hazard was then calculated by summing the flame length weighted conditional probabilities
from the flame length classes above 1.25 m and then multiplying by the annual burn
probability for the pixel.
Haz =
FLi>20
∑
FLi=1.25
(BPixFLi)(1)
where FL
i
is the flame length midpoint of the ith category, and BP
i
is the annual burn
probability.
We transferred the calculated raster pixel values for wildfire hazard to the fuel break
treatment units and multiplied the area to create a metric that measured the area-weighted
hazard, henceforth, fire hazard.
2.7. Treatment Unit Aggregation for Project Areas
We modified the ForSysR package ‘Patchmax’ [
59
] to aggregate treatment units (forest
stands within the FBN) into project areas, maximizing one or multiple objectives. Patchmax
is a multicriteria spatial planning model developed to explore landscape management
scenarios for forest restoration. Patchmax was specifically modified to sequence multi-
objective optimal project areas, found by minimizing the Euclidean distance from the
maximum possible objective values, as described with linear equations in the work of
Diaz-Balteiro et al. [
60
]. Patchmax employs the breadth-first search (BFS) algorithm [
61
]
to explore combinations of adjacent treatment units and build potential optimal project
areas. During the first iteration, the algorithm considers each of the treatment units as a
seed polygon that links to the adjacent units, growing a project configuration of desirable
size. Among all resulting feasible projects, the one with the highest objective contribution
(i.e., lower deviations from the maximum objective values) is identified and removed
from further consideration, and this process is repeated until a desired number of optimal
project areas is met. Here, multi-objective optima (Equations (2)–(6)) are found by searching
the objectives obtained in the feasible project configurations, as described above, and
identifying the one that minimizes the Euclidean distance between the absolute optimum
objective values achieved for a particular project. Equations (2) and (3) are used to calculate
the total deviation from the optimum objective values of each feasible project p. Equation
(4) calculates the contribution of treatment units tto the objective values of each project.
Equations (5) and (6) are the treatment area constraints that allow a deviation of 10% from
the treated area target per project. The user supplies a scenario in terms of objectives
(e.g., maximize net revenue and fire hazard) and constraints (e.g., project area size, stand
treatment thresholds), and the model outputs a sequenced prioritized set of project areas
and identifies treatment units within them, as well as the associated objective contribution.
D=
j
∑
Obj=1
dpj (2)
Fire 2023,6, 1 7 of 16
dpj =vpj −vjmax (3)
vpj =∑t p
t=1ctj xtp (4)
tp
∑
t=1
atxtp ≤1.1 Prjare a (5)
tp
∑
t=1
atxtp ≥0.9 Prjare a (6)
where
dpj
is the deviation for the
pth
feasible project from the maximal
jth
objective value,
vpj
is the objective value for the
pth
feasible project for the
jth
objective,
vjmax
is the maximum
observed value among all feasible project configurations for the
jth
objective, tp is the total
number of available treatment units in the study area for project p,xis a binary vector
indicating whether the t
th
treatment unit is included in the project p(
xtp
= 1) or not (
xtp = 0
),
c
tj
is the contribution of the t
th
treatment unit to the
jth
objective, a
t
is the area of the t
th
treatment unit, and Prjarea is the project treatment area target.
2.8. Scenarios
We simulated 13 scenarios, or project strategies, that collectively examined the effect
of different project objectives and treatment areas on prioritization outcomes when treating
40,000 ha, or ca. 75% of the available forested fuel break network (Table 2). Treating
more than 75% of the FBN resulted in scenarios where the 1000 ha per project treatment
constraint could not be met, and for smaller projects, these lowest ranking projects were
of low value and did not contribute substantially to any of the priority objectives. Each
scenario maximized one of the following objectives, or a combination of objectives using
our multi-objective approach, as previously described: net revenue (revenue), merchantable
volume (volume), and fire hazard (hazard). Then, we varied the treatment area per project
by constraining the total to 100, 300, 600, and 1000 ha
±
10% to understand how the scale of
project implementation affected objective attainment. For instance, environmental planning
on national forests allows for a wide range of project sizes, although administrative and
legal efficiencies are associated with specific project sizes and associated treated areas. We
focused on the scenarios with a 300 ha treatment area per project to examine the tradeoffs
and the efficiency of multi-objective solutions. We saved all intermediate feasible project
configurations generated by Patchmax to examine the tradeoffs between objectives. Feasible
project configurations are generated when Patchmax tests each treatment unit as a seed
polygon to grow a project in the adjacent treatment units. These latter solutions were then
prioritized to examine production frontiers and analyze optimum multi-objective projects.
Table 2.
Description of scenarios simulated to prioritize project areas. See the methods section for
additional description of the scenario details.
Objective Treatment Area Per Project
(ha) Number of Project Areas
Wildfire hazard 100 400
Wildfire hazard 300 133
Wildfire hazard 600 66
Wildfire hazard 1000 40
Merchantable timber volume 100 400
Merchantable timber volume 300 133
Merchantable timber volume 600 66
Merchantable timber volume 1000 40
Net revenue 100 400
Net revenue 300 133
Fire 2023,6, 1 8 of 16
Table 2. Cont.
Objective Treatment Area Per Project
(ha) Number of Project Areas
Net revenue 600 66
Net revenue 1000 40
Multi-objective 300 133
3. Results
3.1. Effect of Treatment Area Per Project on Objective Values
To examine the effect of treatment area per project on the outcomes, we simulated
scenarios to build the complete network, while varying the area treated per project (Table 2).
The results showed that the area treated per project only had a minor impact on the
objective values when considered on a per-hectare basis. Figure 3shows the efficiency of
treated area per project when cumulatively assessing objective attainment across treatment
implementation. Increasing treatment area per project from 100 to 1000 ha proportionally
reduced the number of projects required to complete the total treated area of 40,000 ha
and decreased the per area objective value. Wildfire hazard resulted in smaller cumulative
differences due to the abundance and distribution of high-hazard units in the study area,
making it easier to build efficient spatial projects. Based on the high efficiency in terms of
the objective achieved per ha treated and additional input from the Umatilla NF staff, we
chose the 300 ha treatment area per project for subsequent sensitivity analysis.
Fire2023,5,xFORPEERREVIEW8of16
Netrevenue300133
Netrevenue60066
Netrevenue100040
Multi‐objective300133
3.Results
3.1.EffectofTreatmentAreaPerProjectonObjectiveValues
Toexaminetheeffectoftreatmentareaperprojectontheoutcomes,wesimulated
scenariostobuildthecompletenetwork,whilevaryingtheareatreatedperproject(Table
2).Theresultsshowedthattheareatreatedperprojectonlyhadaminorimpactonthe
objectivevalueswhenconsideredonaper‐hectarebasis.Figure3showstheefficiencyof
treatedareaperprojectwhencumulativelyassessingobjectiveattainmentacrosstreat‐
mentimplementation.Increasingtreatmentareaperprojectfrom100to1000hapropor‐
tionallyreducedthenumberofprojectsrequiredtocompletethetotaltreatedareaof
40,000haanddecreasedtheperareaobjectivevalue.Wildfirehazardresultedinsmaller
cumulativedifferencesduetotheabundanceanddistributionofhigh‐hazardunitsinthe
studyarea,makingiteasiertobuildefficientspatialprojects.Basedonthehighefficiency
intermsoftheobjectiveachievedperhatreatedandadditionalinputfromtheUmatilla
NFstaff,wechosethe300hatreatmentareaperprojectforsubsequentsensitivityanaly‐
sis.
(A)(B)(C)
Figure3.Changeinobjectiveattainmentwithincreasingareatreatedforfourdifferentamountsof
treatedareaperprojectandthreescenarioswhereeachoftheobjectiveswasoptimized:(A)wildfire
hazard,(B)merchantablevolume,and(C)netrevenue.
3.2.TradeoffsbetweenFireHazardandRevenue
Figures4andS1showthetradeoffsbetween300hafeasibleprojectconfigurations
thatweretestedaspartofidentifyingoptimalsingleandmulti‐objectivesolutions.Our
scenariosaresubsetsofnon‐overlappingprojectsthatweresequenced,dependingonthe
priorityobjectives(i.e.,singleandmulti‐objective).Fromthetotalnumberofover20,000
simulatedprojectswith300hatreatedareas,only11,083ofthesolutions(50%)generated
positivenetrevenue,withamaximumofUSD6642ha
−1
.Theharvestedmerchantablevol‐
umerangedfrom<1to43m
3
ha
−1
,with6072(27%)oftheprojectsproducingmorethan20
m
3
ha
−1
.Incontrast,simulatedprojectsweremoreeffectiveattreatinghighhazardstands,
asmeasuredbythenumberofprojectsthatexceeded50%oftheoptimalsolution(11,340,
51%).Theproportionoftotalprojectsthatsubstantiallycontributedtomultipleobjectives
wasrelativelysmall,with4690solutions(21%)contributingtoallthreeobjectives(i.e.,
generatingpositivenetrevenue,expressingmorethan20m
3
ha
−1
ofmerchantablevolume,
andexceeding50%ofthemaximumfirehazardsolution).
Figure 3.
Change in objective attainment with increasing area treated for four different amounts of
treated area per project and three scenarios where each of the objectives was optimized: (
A
) wildfire
hazard, (B) merchantable volume, and (C) net revenue.
3.2. Tradeoffs between Fire Hazard and Revenue
Figures 4and S1 show the tradeoffs between 300 ha feasible project configurations
that were tested as part of identifying optimal single and multi-objective solutions. Our
scenarios are subsets of non-overlapping projects that were sequenced, depending on
the priority objectives (i.e., single and multi-objective). From the total number of over
20,000 simulated projects with 300 ha treated areas, only 11,083 of the solutions (50%) gener-
ated positive net revenue, with a maximum of USD 6642 ha
−1
. The harvested merchantable
volume ranged from <1 to 43 m
3
ha
−1
, with 6072 (27%) of the projects producing more
than 20 m
3
ha
−1
. In contrast, simulated projects were more effective at treating high hazard
stands, as measured by the number of projects that exceeded 50% of the optimal solution
(11,340, 51%). The proportion of total projects that substantially contributed to multiple
objectives was relatively small, with 4690 solutions (21%) contributing to all three objectives
(i.e., generating positive net revenue, expressing more than 20 m
3
ha
−1
of merchantable
volume, and exceeding 50% of the maximum fire hazard solution).
Fire 2023,6, 1 9 of 16
Fire2023,5,xFORPEERREVIEW9of16
Figure4.Plotofthe22,166different300hafeasibleprojectconfigurations.Firehazard,harvestvol‐
ume,andnetrevenueobjectivecontributionsarepresentedperhectare,duetothe±10%variation
inprojectsize.
3.3.OptimizingPotentialRevenueTreatments
Figure5showsthetreatmentprescriptionsrequiredtoimplementtheoptimalpro‐
jectsforthe300hascenariothatgeneratedthehighestrevenueoutofthe20,000simulated
projectsolutions.Themaxrevenuescenarioresultedin59projectswithapositivenet
revenue,comparedto42forthemulti‐objectivescenario(Figure5D).Thehigherrevenue
fortheformerscenarioresultedfromtheselectionofalargerproportionofprofitable
commercialthinningtreatments.Therevenuesurplusfromcommercialthinningde‐
creasedinthehighest‐priorityprojectsinthescenariothatoptimizedthetreatmentof
high‐hazardunits(Figure5C).
Figure 4.
Plot of the 22,166 different 300 ha feasible project configurations. Fire hazard, harvest
volume, and net revenue objective contributions are presented per hectare, due to the
±
10% variation
in project size.
3.3. Optimizing Potential Revenue Treatments
Figure 5shows the treatment prescriptions required to implement the optimal projects
for the 300 ha scenario that generated the highest revenue out of the 20,000 simulated
project solutions. The max revenue scenario resulted in 59 projects with a positive net
revenue, compared to 42 for the multi-objective scenario (Figure 5D). The higher revenue
for the former scenario resulted from the selection of a larger proportion of profitable
commercial thinning treatments. The revenue surplus from commercial thinning decreased
in the highest-priority projects in the scenario that optimized the treatment of high-hazard
units (Figure 5C).
3.4. Multi-Objective Scenario
The multi-objective scenario generated the smallest reduction in attainment compared
to the single objective for all three objectives examined (Figure 6). For example, the
best-performing scenario for revenue was the scenario that maximized revenue, but the
second-best was the multi-objective (Figure 6C). Similarly, the wildfire hazard scenario
resulted in only a slight improvement compared to the multi-objective scenario, but also
resulted in the largest reductions in volume and revenue. The multi-objective scenario was
therefore, near optimal, regardless of the single objective. Thus, the multi-objective function
was able to schedule the most efficient projects to contribute to all objectives simultaneously,
unlike the other cases in which scheduled projects maximized one single objective.
Fire 2023,6, 1 10 of 16
Fire2023,5,xFORPEERREVIEW10of16
Figure5.Treatmentprescriptionswithinprojectswith300haoftreatedareascheduledforfour
scenarios:maxnetrevenue,maxvolume,maxhazard,andmulti‐objective.
3.4.Multi‐ObjectiveScenario
Themulti‐objectivescenariogeneratedthesmallestreductioninattainmentcom‐
paredtothesingleobjectiveforallthreeobjectivesexamined(Figure6).Forexample,the
best‐performingscenarioforrevenuewasthescenariothatmaximizedrevenue,butthe
second‐bestwasthemulti‐objective(Figure6C).Similarly,thewildfirehazardscenario
resultedinonlyaslightimprovementcomparedtothemulti‐objectivescenario,butalso
resultedinthelargestreductionsinvolumeandrevenue.Themulti‐objectivescenario
wastherefore,nearoptimal,regardlessofthesingleobjective.Thus,themulti‐objective
functionwasabletoschedulethemostefficientprojectstocontributetoallobjectivessim‐
ultaneously,unliketheothercasesinwhichscheduledprojectsmaximizedonesingleob‐
jective.
(A)(B)(C)
Figure6.Comparisonofsolutionsobtainedundersingleversusmulti‐objectiveprioritiesforthree
responsemetrics(A)cumulativewildfirehazard,(B)cumulativemerchantablevolume,and(C)cu‐
mulativerevenue,withincreasingareatreatedandprojectsimplemented.Alloutputsarefrom
Figure 5.
Treatment prescriptions within projects with 300 ha of treated area scheduled for four
scenarios: max net revenue, max volume, max hazard, and multi-objective.
Fire2023,5,xFORPEERREVIEW10of16
Figure5.Treatmentprescriptionswithinprojectswith300haoftreatedareascheduledforfour
scenarios:maxnetrevenue,maxvolume,maxhazard,andmulti‐objective.
3.4.Multi‐ObjectiveScenario
Themulti‐objectivescenariogeneratedthesmallestreductioninattainmentcom‐
paredtothesingleobjectiveforallthreeobjectivesexamined(Figure6).Forexample,the
best‐performingscenarioforrevenuewasthescenariothatmaximizedrevenue,butthe
second‐bestwasthemulti‐objective(Figure6C).Similarly,thewildfirehazardscenario
resultedinonlyaslightimprovementcomparedtothemulti‐objectivescenario,butalso
resultedinthelargestreductionsinvolumeandrevenue.Themulti‐objectivescenario
wastherefore,nearoptimal,regardlessofthesingleobjective.Thus,themulti‐objective
functionwasabletoschedulethemostefficientprojectstocontributetoallobjectivessim‐
ultaneously,unliketheothercasesinwhichscheduledprojectsmaximizedonesingleob‐
jective.
(A)(B)(C)
Figure6.Comparisonofsolutionsobtainedundersingleversusmulti‐objectiveprioritiesforthree
responsemetrics(A)cumulativewildfirehazard,(B)cumulativemerchantablevolume,and(C)cu‐
mulativerevenue,withincreasingareatreatedandprojectsimplemented.Alloutputsarefrom
Figure 6.
Comparison of solutions obtained under single versus multi-objective priorities for three
response metrics (
A
) cumulative wildfire hazard, (
B
) cumulative merchantable volume, and (
C
) cu-
mulative revenue, with increasing area treated and projects implemented. All outputs are from
treating 300 ha per project. Note that within each panel, we graph the results of four scenarios where
each of the priority objectives (lines) are maximized individually. For example, panel A shows the
effect on treating wildfire hazard from four different prioritization scenarios.
These scenarios also illustrated a steep tradeoff between financial and fire hazard
objectives (Figure 6C), showing that projects with high fire hazard objective contribution
do not necessarily generate positive net revenue. As projects were implemented in the
max revenue scenario, the decline in revenue was steeper compared to that of the multi-
objective scenario. Non-profitable commercial thinning is the most expensive treatment,
but contributed significantly to treatments targeting fire exposure and harvested wood.
The multi-objective scenario scheduled projects with a larger proportion of non-profitable
commercial thinning more regularly to balance the objectives. Figure 7illustrates project
Fire 2023,6, 1 11 of 16
number 99 from the multi-objective scenario treating 122 ha (40%) with commercial thinning
using the pile and burn method and 178 ha (60%) using non-commercial thinning and
the pile and burn method, resulting in a net revenue of USD 412 thousand and USD
142 thousand, respectively.
Fire2023,5,xFORPEERREVIEW11of16
treating300haperproject.Notethatwithineachpanel,wegraphtheresultsoffourscenarioswhere
eachofthepriorityobjectives(lines)aremaximizedindividually.Forexample,panelAshowsthe
effectontreatingwildfirehazardfromfourdifferentprioritizationscenarios.
Thesescenariosalsoillustratedasteeptradeoffbetweenfinancialandfirehazard
objectives(Figure6C),showingthatprojectswithhighfirehazardobjectivecontribution
donotnecessarilygeneratepositivenetrevenue.Asprojectswereimplementedinthe
maxrevenuescenario,thedeclineinrevenuewassteepercomparedtothatofthemulti‐
objectivescenario.Non‐profitablecommercialthinningisthemostexpensivetreatment,
butcontributedsignificantlytotreatmentstargetingfireexposureandharvestedwood.
Themulti‐objectivescenarioscheduledprojectswithalargerproportionofnon‐profitable
commercialthinningmoreregularlytobalancetheobjectives.Figure7illustratesproject
number99fromthemulti‐objectivescenariotreating122ha(40%)withcommercialthin‐
ningusingthepileandburnmethodand178ha(60%)usingnon‐commercialthinning
andthepileandburnmethod,resultinginanetrevenueofUSD412thousandandUSD
142thousand,respectively.
Figure7.Illustrationofthe133sequencedprojectsfromthe300hatreatedareascenarioprioritizing
multi‐objectives.(A)FullextentofthefuelbreaknetworkontheUmatillaNationalForest.(B)Pro‐
jectareadistributioninthesouthwesternpartoftheforest.(C)Fuelbreaktreatmentunitswithin
projectarea99overlaidonaerialphotosacrossforestandnon‐forestgrass‐shrubvegetation.Stand
treatmentsincludecommercialthinningwiththepileandburnmethod;non‐commercialthinning,
withthepileandburnmethod;andnotreatment(conductedinforestedstandswith<15%CCor
grassland/shrubs).
Figure 7.
Illustration of the 133 sequenced projects from the 300 ha treated area scenario prioritizing
multi-objectives. (
A
) Full extent of the fuel break network on the Umatilla National Forest. (
B
) Project
area distribution in the southwestern part of the forest. (
C
) Fuel break treatment units within
project area 99 overlaid on aerial photos across forest and non-forest grass-shrub vegetation. Stand
treatments include commercial thinning with the pile and burn method; non-commercial thinning,
with the pile and burn method; and no treatment (conducted in forested stands with < 15% CC or
grassland/shrubs).
4. Discussion
We described the development and application of a new multi-objective decision
support model to prioritize a large fuel break network on a fire-prone Western US national
forest. The model fills a void in the operational fuels planning community where the current
prioritization of linear fuel breaks is largely, if not entirely, based on subjective evaluation
and expert opinion. Although we do not discount the value of expert opinion from wildfire
planners on the location of fuel breaks, broad scale (e.g., 500,000 ha) understanding of
priorities, tradeoffs, and economic factors requires landscape scale scenario planning
models to efficiently schedule projects and treatments and to predict outcomes. Our new
algorithm sequenced and optimized projects for the study area in less than 5 seconds per
optimized scenario and was implemented in an globally available open source programing
platform [62].
Fire 2023,6, 1 12 of 16
Prioritization is an important process in the implementation of forest and fuel man-
agement programs due to administrative, legal, and operational constraints that require
subdividing and scaling activities to create project areas. In contrast to our prior work on
simulating spatial landscape restoration projects with Patchmax (Belavenutti et al. 2022), we
modified the evaluation function to sequence multi-objective optimal project areas and also
saved the entire population of project solutions for a given scenario, rather than just identi-
fying and analyzing the most optimal scenarios concerning one or more objectives. The
purpose of this was to provide additional information to assess how capable the optimiza-
tion was in leveraging the algorithm to pinpoint projects in a way that optimized multiple
objectives. The importance of identifying the feasible solutions within pareto frontiers
and the efficiency of multi-objective (i.e., goal programming) techniques for multicriteria
decision making has been discussed in previous studies [63–65].
Our results showed significant tradeoffs between financial and fire management
objectives and revealed that the multi-objective approach degrades the attainment of
individual objectives, while offering a robust global solution. Tradeoffs such as these have
been reported elsewhere [
66
,
67
]. Our scenarios maximizing either volume or revenue were
also effective for treating wildfire hazard, since overstocked stands in the study area were
typically also rated as high fire hazard due to excessive surface and canopy fuels. Prioritized
projects aggregated fuel break subunits with different treatment compositions, including
a variety of non- and commercial thinning. Our simulation method essentially exploited
the spatial variation of treatment subunits on the landscape to design projects, rather than
simply ranking treatments according to their objective contribution, as observed with
predefined project areas (i.e., individual fuel break sections) in previous studies [
19
,
20
].
The results also show that implementing many smaller projects is more efficient than
conducting fewer large projects in increasing the rate of attainment in the earlier phases
of implementation. This latter result is not surprising, but the performance reduction
with an increase in the area treated per project has previously not been analyzed, and it
is an important consideration when designing future management scenarios to respond
to growing wildfire risks and other threats. However, there are many other efficiencies of
scale, both economic and administrative, that also need to be considered along with the
attainment of primary project objectives when determining the most efficient project sizes.
One limitation of our study is that the priority of specific planned fuel break projects
will be altered over time by the implementation of nearby fuel breaks, restoration projects,
and wildfires. Forest managers can identify areas where extreme or impactful wildfires will
likely occur, but specific fire perimeters are more difficult to predict due to the uncertainty
regarding future ignitions and weather forecasts [
68
–
70
]. These unpredictable wildfires
will intersect with projects before or after implementation, suggesting that any long-term
plan (+10 years) will undergo significant revision during its implementation [
71
]. This
requires forest managers to adjust the planned projects after identifying significant changes
in landscape conditions. It is expected that implemented projects will alter fire exposure
in the same vicinity of the fuel break network because fuel break projects are designed
to facilitate suppression resources that will contain the fire, preventing it from spreading
to other areas. Whether or not this is a real limitation in the modeling depends on how
close the fuel break sections are from each other and the sequence of implementing projects
that have interdependent fire exposures [
20
]. Our assessment of the space–time sequence
of the optimized fuel break network is included in Figure S2. Further research is needed
to extend our modeling framework to reevaluate fire hazard objective values with fire
spread models each time a project is implemented in the simulation. Previous studies
developed decision support tools with potential adjustments for this problem, such as the
method of Chung et al. [
23
] that implemented the OptFuels system, a heuristic process that
integrates FVS and FlamMap with a treatment optimization module for spatial projects
that included the timing of fuel treatments, while considering changes in forest conditions,
such as forest growth, wildfire behavior, and spread, over time. Forest landscape models
such as LSim [
72
] considered the dynamics of wildfire and treatments over time, and the
Fire 2023,6, 1 13 of 16
current work can be implemented into this system as the treatment scheduling module to
optimize treatments under uncertain wildfire events and a changing climate. For instance,
Mina et al. [
73
] used the forest landscape model LANDIS-II to simulate climate-smart
management policy scenarios that promote warm-adapted species, but the system lacks a
treatment optimization module.
There are many avenues for further research on fuel break networks and their ap-
plication across a wide range of fire frequent ecosystems. Questions relating to network
density, width, location, effectiveness, and financial cost all need to be addressed with em-
pirical and simulation studies. Optimal network densities from a cost and fire management
standpoint [
74
] may exist, as identified by diminishing returns for implementing pro-
posed networks in their entirety. The co-prioritization of linear fuel breaks with landscape
restoration and forest health treatments on US federal forests [
75
] will also be a challenging
problem for planners, and case studies are needed that demonstrate the effective coupling
of alternative treatment strategies [
76
]. Future work along these lines will facilitate the
work of many government organizations tasked with designing long-range fuel treatment
strategies to address wildfire risk in a wide range of fire frequent ecosystems.
Supplementary Materials:
The following supporting information can be downloaded at: https://www.
mdpi.com/article/10.3390/fire6010001/s1, Figure S1: Plot of the 22,166 different 300 ha feasible
project configurations; Figure S2: Our assessment of the space-time sequence of the optimized
fuel break.
Author Contributions:
P.B.: conceptualization, methodology, validation, formal analysis,
writing—original
draft; A.A.A.: resources, conceptualization, writing—review and editing, supervision; M.A.D.: con-
ceptualization, writing—review and editing, supervision; W.C.: conceptualization,
writing—review
and editing, supervision. All authors have read and agreed to the published version of the manuscript.
Funding:
This work was funded by the USDA Forest Service, Rocky Mountain Research Station,
National Fire Decision Support Center.
Acknowledgments:
This work was funded by the USDA Forest Service, Rocky Mountain Research
Station, and the National Fire Decision Support Center. We thank the national forest staff, including
Andrew Stinchfield, Richard Gardner, and Don Justice from the Umatilla National Forest, for con-
tributing to many aspects of this and prior related studies. We also would like to thank Ana Barros,
Fermin Alcasena, and Rachel Houtman for assisting with technical insights.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Ascoli, D.; Russo, L.; Giannino, F.; Siettos, C.; Moreira, F. Firebreak and Fuelbreak. In Encyclopedia of Wildfires and Wildland-Urban
Interface (WUI) Fires; Manzello, S.L., Ed.; Springer International Publishing: Cham, Switzerland, 2018; pp. 1–9.
2.
Maestas, J.; Pellant, M.; Okeson, L.; Tilley, D.; Havlina, D.; Cracroft, T.; Brazee, B.; Williams, M.; Messmer, D. Fuel Breaks to Reduce
Large Wildfire Impacts in Sagebrush Ecosystems; USA-NRCS: Boise, ID, USA, 2016.
3.
Shinneman, D.J.; Germino, M.J.; Pilliod, D.S.; Aldridge, C.L.; Vaillant, N.M.; Coates, P.S. The ecological uncertainty of wildfire
fuel breaks: Examples from the sagebrush steppe. Front. Ecol. Environ. 2019,17, 279–288. [CrossRef]
4.
Syphard, A.D.; Keeley, J.E.; Brennan, T.J. Factors affecting fuel break effectiveness in the control of large fires on the Los Padres
National Forest, California. Int. J. Wildland Fire 2011,20, 764–775. [CrossRef]
5.
Xanthopoulos, G.; Caballero, D.; Galante, M.; Alexandrian, D.; Rigolot, E.; Marzano, R. Forest fuels management in Europe.
In Fuels Management. How to Measure Success; Andrews, P.L., Butler, B.W., Eds.; Portland, OR, USA, 2006. Available online:
https://www.fs.usda.gov/rm/pubs/rmrs_p041.pdf (accessed on 10 October 2022).
6.
Oliveira, T.M.; Barros, A.M.G.; Ager, A.A.; Fernandes, P.M. Assessing the effect of a fuel break network to reduce burnt area and
wildfire risk transmission. Int. J. Wildland Fire 2016,25, 619–632. [CrossRef]
7.
Zong, X.; Tian, X.; Wang, X. An optimal firebreak design for the boreal forest of China. Sci. Total Environ.
2021
,781, 146822.
[CrossRef]
8.
Green, L.R. Fuelbreaks and Other Fuel Modification for Wildland Fire Control; US Department of Agriculture, Forest Service:
Washington
,
DC, USA, 1977. Available online: https://www.fs.usda.gov/research/treesearch/33461 (accessed on 10 October 2022).
9.
Eastaugh, C.S.; Molina, D.M. Forest road and fuelbreak siting with respect to reference fire intensities. For. Syst.
2012
,21, 153–161.
[CrossRef]
Fire 2023,6, 1 14 of 16
10.
O’Connor, C.D.; Calkin, D.E.; Thompson, M.P. An empirical machine learning method for predicting potential fire control
locations for pre-fire planning and operational fire management. Int. J. Wildland Fire 2017,26, 587–597. [CrossRef]
11.
Caggiano, M.D. Collaboratively Engaging Stakeholders to Develop Operational Delineations; CFRI-1908; Colorado State
University
:
Fort Collins, CO, USA, 2019; Available online: https://cfri.colostate.edu/wp-content/uploads/sites/22/2019/08/PODs-
Collaborative-Engagement-Final-Report.pdf (accessed on 10 October 2022).
12.
Varela, E.; Giergiczny, M.; Riera, P.; Mahieu, P.A.; Solino, M. Social preferences for fuel break management programs in Spain: A
choice modelling application to prevention of forest fires. Int. J. Wildland Fire 2014,23, 281–289. [CrossRef]
13.
Price, O.F.; Edwards, A.C.; Russell-Smith, J. Efficacy of permanent firebreaks and aerial prescribed burning in western Arnhem
Land, Northern Territory, Australia. Int. J. Wildland Fire 2007,16, 295–305. [CrossRef]
14.
O’Connor, C.; Thompson, M.; Rodríguez y Silva, F. Getting ahead of the wildfire problem: Quantifying and mapping management
challenges and opportunities. Geosciences 2016,6, 35. [CrossRef]
15.
Aubard, V.; Pereira-Pires, J.E.; Campagnolo, M.L.; Pereira, J.; Mora, A.; Silva, J. Fully automated countrywide monitoring of fuel
break maintenance operations. Remote Sens. 2020,12, 2879. [CrossRef]
16.
Rodríguez-Puerta, F.; Ponce, R.A.; Pérez-Rodríguez, F.; Águeda, B.; Martín-García, S.; Martínez-Rodrigo, R.; Lizarralde, I.
Comparison of Machine Learning Algorithms for Wildland-Urban Interface Fuelbreak Planning Integrating ALS and UAV-borne
LiDAR Data and Multispectral Images. Drones 2020,4, 21. [CrossRef]
17.
Finney, M.A. An overview of FlamMap fire modeling capabilities. In Fuels Management-How to Measure Success, Proceedings RMRS-
P-41, Fort Collins, CO, USA, 28–30 March 2006; Andrews, P.L., Butler, B.W., Eds.; USDA Forest Service, Rocky Mountain Research
Station: Fort Collins, CO, USA, 2006; pp. 213–220. Available online: https://www.fs.usda.gov/research/treesearch/25948.
(accessed on 10 October 2022).
18.
Finney, M.A.; McHugh, C.W.; Grenfell, I.C.; Riley, K.L.; Short, K.C. A simulation of probabilistic wildfire risk components for the
continental United States. Stoch. Environ. Res. Risk Assess. 2011,25, 973–1000. [CrossRef]
19.
Ager, A.A.; Lasko, R.; Myroniuk, V.; Zibtsev, S.; Day, M.A.; Usenia, U.; Bogomolov, V.; Kovalets, I.; Evers, C.R. The wildfire
problem in areas contaminated by the Chernobyl disaster. Sci. Total Environ. 2019,696, 133954. [CrossRef]
20.
Aparício, B.A.; Alcasena, F.; Ager, A.A.; Chung, W.; Pereira, J.M.C. Evaluating priority locations and potential benefits for building
a nation-wide fuel break network in Portugal. J. Environ. Manag. 2022,320, 115920. [CrossRef] [PubMed]
21.
Parisien, M.A.; Parks, S.A.; Miller, C.; Krawchuk, M.A.; Heathcott, M.; Moritz, M.A. Contributions of ignitions, fuels, and weather
to the spatial patterns of burn probability of a boreal landscape. Ecosystems 2011,14, 1141–1155. [CrossRef]
22.
Pais, C.; Carrasco, J.; Martell, D.L.; Weintraub, A.; Woodruff, D.L. Cell2Fire: A Cell Based Forest Fire Growth Model. 2019, p. 47.
Available online: https://www.frontiersin.org/articles/10.3389/ffgc.2021.692706/full (accessed on 10 October 2022).
23.
Chung, W.; Jones, G.; Krueger, K.; Bramel, J.; Contreras, M. Optimising fuel treatments over time and space. Int. J. Wildland Fire
2013,22, 1118–1133. [CrossRef]
24.
Ager, A.A.; Vaillant, N.M.; Finney, M.A. Integrating fire behavior models and geospatial analysis for wildland fire risk assessment
and fuel management planning. J. Combust. 2011,2011, 572452. [CrossRef]
25.
Massada, A.B.; Radeloff, V.C.; Stewart, S.I. Allocating fuel breaks for optimal protection of structures in the wildland-urban
interface. Int. J. Wildland Fire 2011,20, 59–68. [CrossRef]
26.
Benali, A.; Sá, A.C.L.; Pinho, J.; Fernandes, P.M.; Pereira, J.M.C. Understanding the impact of different landscape-level fuel
management strategies on wildfire hazard in Central Portugal. Forests 2021,12, 522. [CrossRef]
27.
Pais, C.; Carrasco, J.; Elimbi Moudio, P.; Shen, Z.-J.M. Downstream protection value: Detecting critical zones for effective
fuel-treatment under wildfire risk. Comput. Oper. Res. 2021,131, 105252. [CrossRef]
28.
Russo, L.; Russo, P.; Siettos, C.I. A complex network theory approach for the spatial distribution of fire breaks in heterogeneous
forest landscapes for the control of wildland fires. PLoS ONE 2016,11, e0163226. [CrossRef] [PubMed]
29.
Wei, Y. Optimize landscape fuel treatment locations to create control opportunities for future fires. Can. J. For. Res.
2012
,42,
1002–1014. [CrossRef]
30.
Rashidi, E.; Medal, H.; Hoskins, A. An attacker-defender model for analyzing the vulnerability of initial attack in wildfire
suppression. Nav. Res. Logist. 2018,65, 120–134. [CrossRef]
31.
Penman, T.; Collins, L.; Price, O.; Bradstock, R.; Metcalf, S.; Chong, D. Examining the relative effects of fire weather, suppression
and fuel treatment on fire behaviour–A simulation study. J. Environ. Manag. 2013,131, 325–333. [CrossRef]
32. Syphard, A.D.; Keeley, J.E.; Brennan, T.J. Comparing the role of fuel breaks across southern California national forests. For. Ecol.
Manag. 2011,261, 2038–2048. [CrossRef]
33.
AGIF. National Plan for Integrated Wildfire Management 2020–2030; Agency for Integrated Rural Fire Management: Lisbon, Portugal,
2020; p. 166.
34. Baskent, E.Z.; Keles, S. Spatial forest planning: A review. Ecol. Model. 2005,188, 145–173. [CrossRef]
35. Crooks, K.R.; Sanjayan, M.A. Connectivity Conservation; Cambridge University Press: Cambridge, UK, 2006; p. 736.
36.
USDA Forest Service. Bailey’s Ecoregions of the Conterminous United States. United States Geological Survey. Available online:
https://www.sciencebase.gov/catalog/item/54244abde4b037b608f9e23d (accessed on 10 October 2022).
37.
Short, K.C. Spatial Wildfire Occurrence Data for the United States, 1992-2020 [FPA_FOD_20221014], 6th ed.; Forest Service Research
Data Archive: Fort Collins, CO, USA, 2022. [CrossRef]
Fire 2023,6, 1 15 of 16
38.
Infrastructure Investment and Jobs Act, Public Law 117-58. 2021. Available online: https://www.congress.gov/117/plaws/
publ58/PLAW-117publ58.pdf (accessed on 10 October 2022).
39.
Dennis, F.C. Fuelbreak Guidelines for Forested Subdivisions & Communities; Colorado State Forest Service, 2005; p. 8. Available online:
https://mountainscholar.org/handle/10217/45082 (accessed on 10 October 2022).
40.
Mooney, C. Fuelbreak Effectiveness in Canada’s Boreal Forests: A Synthesis of Current Knowledge. 2010, p. 53. Available online:
https://library.fpinnovations.ca/media/FOP/9438.pdf (accessed on 10 October 2022).
41.
Ingalsbee, T. Fuelbreaks for wildland fire management: A moat or a drawbridge for ecosystem fire restoration. Fire Ecol.
2005
,1,
85–99. [CrossRef]
42.
USDA Forest Service, Pacific Northwest Region. Land and Resource Management Plan. Umatilla National Forest; USDA Forest
Service, Pacific Northwest Region: Portland, OR, USA, 1990.
43.
Belavenutti, P.; Chung, W.; Ager, A.A. The economic reality of the forest and fuel management deficit on a fire prone western US
national forest. J. Environ. Manag. 2021,293, 112825. [CrossRef]
44.
Keyser, C.E.; Dixon, G.E. Blue Mountains (BM) Variant Overview—Forest Vegetation Simulator; USDA Forest Service, Forest
Management Service Center: Fort Collins, CO, USA, 2015; p. 56.
45.
Keyes, C.R.; O’Hara, K.L. Quantifying stand targets for silvicultural prevention of crown fires. West. J. Appl. For.
2002
,17, 101–109.
[CrossRef]
46.
USDA and USDI. Record of Decision for Amendments to Forest Service and Bureau of Land Management Planning Departments within the
Range of the Northern Spotted Owl; USDA Forest Service and USDI Bureau of Land Management: Portland, OR, USA, 1994.
47.
USDA Forest Service, Pacific Northwest Region, Management Direction for Large Diameter Trees in Eastern OR & Southeastern WA;
USDA Forest Service, Pacific Northwest Region, 2021. Available online: https://www.fs.usda.gov/detail/r6/landmanagement/
planning/?cid=FSEPRD710229 (accessed on 10 October 2022).
48.
Jain, T.B.; Battaglia, M.A.; Han, H.S.; Graham, R.T.; Keyes, C.R.; Fried, J.S.; Sandquist, J.E. A Comprehensive Guide to Fuel
Management Practices for Dry Mixed Conifer Forests in the Northwestern United States; U. S. Department of Agriculture, Forest Service:
Fort Collins, CO, USA, 2012; p. 331.
49.
Vogler, K.C.; Ager, A.A.; Day, M.A.; Jennings, M.; Bailey, J.D. Prioritization of forest restoration projects: Tradeoffs between
wildfire protection, ecological restoration and economic objectives. Forests 2015,6, 4403–4420.
50.
Martin, F. User Guide to the Economic Extension (ECON) of the Forest Vegetation Simulator; U. S. Department of Agriculture, Forest
Service, Forest Management Service Center: Fort Collins, CO, USA, 2013; p. 43.
51.
Ager, A.A.; Houtman, R.; Day, M.A.; Ringo, C.; Palaiologou, P. Tradeoffs between US national forest harvest targets and fuel
management to reduce wildfire transmission to the wildland urban interface. For. Ecol. Manag. 2019,434, 99–109. [CrossRef]
52. Rummer, B. Assessing the cost of fuel reduction treatments: A critical review. For. Policy Econ. 2008,10, 355–362. [CrossRef]
53.
Rainville, R.; White, R.; Barbour, J. Assessment of Timber Availability from Forest Restoration within the Blue Mountains of Oregon; Gen.
Tech. Rep. PNW-GTR-752; USDA Forest Service, Pacific Northwest Research Station: Portland, OR, USA, 2008; p. 65.
54. Dijkstra, E.W. A note on two problems in connexion with graphs. Numer. Math. 1959,1, 269–271. [CrossRef]
55.
USDA Forest Service. Umatilla Landscape Wildfire Strategy; USDA Forest Service, Umatilla National Forest: Pendleton, OR,
USA, 2015.
56.
Ma, F.; Lee, J.Y.; Camenzind, D. Probabilistic Wildfire Risk Assessment Methodology and Evaluation of a Supply Chain Network.
Int. J. Disaster Risk Reduct. 2022,82, 103340. [CrossRef]
57.
McEvoy, A.; Kerns, B.K.; Kim, J.B. Hazards of risk: Identifying plausible community wildfire disasters in low-frequency fire
regimes. Forests 2021,12, 934. [CrossRef]
58.
Alcasena, F.J.; Salis, M.; Nauslar, N.J.; Aguinaga, A.E.; Vega-García, C. Quantifying economic losses from wildfires in black pine
afforestations of northern Spain. For. Policy Econ. 2016,73, 153–167. [CrossRef]
59.
Belavenutti, P.; Ager, A.A.; Chung, W.; Day, M.A. Designing forest restoration projects to optimize the application of broadcast
burning. Ecol. Econ. 2022,201, 107558. [CrossRef]
60.
Diaz-Balteiro, L.; Belavenutti, P.; Ezquerro, M.; González-Pachón, J.; Nobre, S.R.; Romero, C. Measuring the sustainability of a
natural system by using multi-criteria distance function methods: Some critical issues. J. Environ. Manag.
2018
,214, 197–203.
[CrossRef]
61. Cormen, H.T.; Rivest, R.L.; Stein, C. Introduction to Algorithms, 3rd ed.; MIT Press: Cambridge, MA, USA, 2009.
62.
R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2019; Available
online: http://www.R-project.org/ (accessed on 10 October 2022).
63.
Borges, J.G.; Garcia-Gonzalo, J.; Bushenkov, V.; McDill, M.E.; Marques, S.; Oliveira, M.M. Addressing multicriteria forest
management with Pareto frontier methods: An application in Portugal. For. Sci. 2014,60, 63–72. [CrossRef]
64.
Diaz-Balteiro, L.; Romero, C. Making forestry decisions with multiple criteria: A review and an assessment. For. Ecol. Manag.
2008,255, 3222–3241. [CrossRef]
65.
Marques, M.; Reynolds, K.M.; Marques, S.; Marto, M.; Paplanus, S.; Borges, J.G. A Participatory and Spatial Multicriteria Decision
Approach to Prioritize the Allocation of Ecosystem Services to Management Units. Land 2021,10, 747. [CrossRef]
66.
Belavenutti, P.; Romero, C.; Diaz-Balteiro, L. Integrating Strategic and Tactical Forest-Management Models within a Multicriteria
Context. For. Sci. 2019,65, 178–188. [CrossRef]
Fire 2023,6, 1 16 of 16
67.
Triviño, M.; Pohjanmies, T.; Mazziotta, A.; Juutinen, A.; Podkopaev, D.; Le Tortorec, E.; Mönkkönen, M. Optimizing management
to enhance multifunctionality in a boreal forest landscape. J. Appl. Ecol. 2017,54, 61–70. [CrossRef]
68.
Barros, A.M.G.; Day, M.A.; Preisler, H.K.; Abatzoglou, J.T.; Krawchuk, M.A.; Houtman, R.; Ager, A.A. Contrasting the role of
human- and lightning-caused wildfires on future fire regimes on a Central Oregon landscape. Environ. Res. Lett.
2021
,16, 064081.
[CrossRef]
69.
Dillon, G.K.; Menakis, J.; Fay, F. Wildland fire potential: A tool for assessing wildfire risk and fuel management needs. In
Large Wildland Fire Conference, RMRS-P-73, Proceedings of the Large Wildland Fires Conference, Missoula, MT, USA, 19–23 May 2014;
Keane, R.E., Jolly, M., Parsons, R., Riley, K., Eds.; USDA Forest Service, Rocky Mountain Research Station: Fort Collins, CO, USA,
2015; pp. 60–76.
70.
Barros, A.M.G.; Ager, A.A.; Day, M.A.; Palaiologou, P. Improving long-term fuel treatment effectiveness in the National Forest
System through quantitative prioritization. For. Ecol. Manag. 2019,433, 514–527. [CrossRef]
71.
Ager, A.A.; Evers, C.R.; Day, M.A.; Alcasena, F.J.; Houtman, R. Planning for future fire: Scenario analysis of an accelerated fuel
reduction plan for the western United States. Landsc. Urban Plan. 2021,215, 104212. [CrossRef]
72.
Ager, A.A.; Barros, A.M.; Houtman, R.; Seli, R.; Day, M.A. Modelling the effect of accelerated forest management on long-term
wildfire activity. Ecol. Model. 2020,421, 108962. [CrossRef]
73.
Mina, M.; Messier, C.; Duveneck, M.J.; Fortin, M.J.; Aquilué, N. Managing for the unexpected: Building resilient forest landscapes
to cope with global change. Glob. Change Biol. 2022,28, 4323–4341. [CrossRef]
74.
Finney, M.A.; Seli, R.C.; McHugh, C.W.; Ager, A.A.; Bahro, B.; Agee, J.K. Simulation of long-term landscape-level fuel treatment
effects on large wildfires. Int. J. Wildland Fire 2007,16, 712–727. [CrossRef]
75.
Butler, W.H.; Esch, B. Collaborative forest landscape restoration in action. In A New Era for Collaborative Forest Management: Policy
and Practice Insights from the Collaborative Forest Landscape Restoration Program; Butler, W.H., Schultz, C.A., Eds.; Routledge: London,
UK, 2019; p. 25. Available online: https://www.researchgate.net/publication/330725598_Collaborative_forest_landscape_
restoration_in_action_Policy_and_Practice_Insights_from_the_Collaborative_Forest_Landscape_Restoration_Program. (accessed
on 10 October 2022).
76.
Stephens, S.L.; Battaglia, M.A.; Churchill, D.J.; Collins, B.M.; Coppoletta, M.; Hoffman, C.M.; Lydersen, J.M.; North, M.P.;
Parsons, R.A.; Ritter, S.M.; et al. Forest restoration and fuels reduction: Convergent or divergent? BioScience
2021
,71, 85–101.
[CrossRef]
Disclaimer/Publisher’s Note:
The statements, opinions and data contained in all publications are solely those of the individual
author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to
people or property resulting from any ideas, methods, instructions or products referred to in the content.
