The dynamic behaviour of wildfires is mainly influenced by weather, fuel, and topography. Based on fundamental conservation laws involving numerous physical processes and large scales, atmospheric models require substantial computational resources. Therefore, coupling wildfire and atmospheric models is impractical for high resolutions, even for small scales. Instead, a static atmospheric wind field is typically input into the wildfire model, either as boundary conditions on the control surface or distributed throughout the control volume. Wildfire propagation models may be (𝑖)data-driven ; (𝑖𝑖)theoretical ;or(𝑖𝑖𝑖)mechanisticsurrogates .Data-drivenmodelsarebeyondthescopeofthispaper. Theoreticalmodelsarebasedonconservationlaws(species,energy,mass,momentum)andtherefore are computationally expensive—e.g. the Fire Dynamics Simulator (FDS). Mechanistic surrogate modelsdonotcloselyfollowfiredynamicslawsbutadifferentsetofsomewhatrelatedlawsobserved to make predictions more efficiently and with sufficient accuracy—e.g. FARSITE and the Level-Set FDS (LS-FDS). Whethertheoretical or mechanistic surrogate,these wildfire models may becoupled withordecoupledfromwindmodels(e.g.theNavier-Stokesequations).Onlycoupledmodelsaccount fortheeffectofthefireonthewindfield.Inthispaper,aseriesofsimulationsofwildfirepropagation on grassland are performed using LS-FDS to study the impact of the fire-induced wind on the fire propagation dynamics. Results show that coupling leads to higher RoS, closer to the values reported from field experiments, with increasing wind speeds and higher terrain slopes strengthening this trend.Aimingtocapturethefire-windinteractionwithouttheheftycostofsolvingtheNavier-Stokes equations,aconceptualframeworkisproposed:1)aswarmofUAVsmeasurewindvelocitiesatflight height;2)thewindfieldisconstructedwiththeacquireddata;3)thehigh-altitudewindfieldismapped to near surface; and 4) the near-surface wind field is fed into the wildfire model periodically. As proof of concept, a series of simulations are performed using an in-house decoupled physics-based reduced-order fire propagation model (FireProM-F) enhanced by wind field "measurements". At this stage,windvelocitiesarenotactuallymeasuredbutextractedfromhigh-fidelityphysics-basedLarge EddySimulationswithinFDS,whicharetakenasgroundtruth.Unsurprisingly,highermeasurement frequencies lead to more accurate predictions of the RoS, and to more realistic formations of the propagating fire front. Finally, an initial attempt is made at studying the effect of wind measurement uncertaintyon themodel predictionsbyadding Gaussiannoise. Preliminaryresults showthathigher noise leads to the fire front displaying a less smooth shape and slower propagation. 1. Introduction The occurrence and behaviour of wildfires are greatly influenced by a combination of interrelated factors such as the ignition source, fuel composition and distribution, weather, and topography [1]. Wind—specifically, ground- level wind—is the most widely studied parameter involved in the fire-atmosphere interaction [2]. According to Gis- borne [3], surface wind affects fire behaviour via four main mechanisms: ( 𝑖) varying fuel moisture by carrying dry or humid air; (𝑖𝑖) varying the Rate of spread (RoS) of the fire; (𝑖𝑖𝑖) carrying ignited branches or embers to unburned areas thus causing the ignition of spot fires; and ( 𝑖𝑣) bringing oxygen flux to the fire flame thus boosting combustion. Sullivan [4, 5, 6] classifies wildfire propagation models into three types: ( 𝑖)physical and quasi-physical models, ∗Corresponding author tavakolsam@uni.coventry.ac.uk (M. Tavakol Sadrabadi); Mauro.S.Innocente@coventry.ac.uk (M.S. Innocente) ORCID(s):0000-0002-5938-6310 (M. Tavakol Sadrabadi); 0000-0001-8836-2839 (M.S. Innocente) 1which are based on fundamental physics or chemistry of combustion [4]; ( 𝑖𝑖)empirical and quasi-empirical mod- els, which are based on the statistical analysis of obtained data [5]; and ( 𝑖𝑖𝑖)mathematical analogues and simula- tionmodels, which are based on some mathematical con- ceit that coincidentally simulates the spread of fire [6]. Innocente and Grasso [7, 8] classify them into three types (see Figure 1, yellow boxes): ( 𝑖)theoretical models, which are physics-based and involve conservation laws; ( 𝑖𝑖)data- drivenmodels, which are constructed or fitted using actual or synthetic data; and ( 𝑖𝑖𝑖)mechanistic surrogate models, which make use of mechanisms not directly related to fire dynamics.Inturn,BakhshaiiandJohnson[9]classifywild- fire propagation models into three categories based on the leveloftheirinteractionwithwindmodels:( 𝑖)non-coupled ; (𝑖𝑖)semi-coupled ; and (𝑖𝑖𝑖)fully-coupled . A wildfire model inwhichfireandwindmodelsinteractlocallywithoutbeing coupled with an atmospheric model would fall under the semi-coupled category. In this paper, we classify wildfire models into ( 𝑖)coupledand (𝑖𝑖)decoupled depending on whether fire and wind models interact (see Figure 1, blue First Author et al.: Preprint submitted to Elsevier Page 1 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements Wildfire Propagation Models Theoretical Models Mechanistic , physics-based . Data-Driven Models Constructed from data, fitted to data, or data- driven surrogate model .White-Box Models Derived from first principles , purely physics-based models. Light-Grey-Box Models Semi-empirical , mostly based on physics-based governing laws but with some calibrated parameters. Dark-Grey-Box Models Semi-empirical , model-fitting , mostly driven by data yet incorporating principles and laws from theories. Black-Box Models Empirical , data-fitting , phenomenological , completely independent of theories.Coupled Fire and wind are coupled , affecting one another . Decoupled Fire and wind are decoupled . Typically , frozen wind af fects fire .Cellular Automata Models Computational model , rules derived from first principles or mathematical analogue . Lattice Boltzmann Models Computational model , commonly used to model fluid flow as emerging from streaming and collision among particles . Network/Graph Models Represents objects and their relationships as a graph of nodes , edges and weighs . Deterministic Same inputs always produce same outputs. Stochastic Predictions in terms of probabilities , uncertainty modelled.Agent-Based Models Computational model , typically stochastic, commonly used to model complex systems.Mechanistic Surrogate Models Mechanisms not directly related to system or phenomena being modelled. May be white-box or grey-box . Two-Dimensional Fire Growth Models e.g. perimeter representation as envelope of local ellipses and perimeter expansion by Huygens wavelet propagation based on classical fire spread models. Figure 1: Classification of fire propagation models. Modified from [7] to make it specific to wildfires, and to explicitly differentiate coupled form decoupled models. boxes). This refers to the wildfire model alone, irrespective of whether it is coupled with an atmospheric model. Seeking computational efficiency for operational use, some models such as FARSITE [10] and FireProM-F [8] aredecoupled fromwindmodels,thusneglectingtheimpact of the fire on the wind field. This increases the epistemic uncertainty. FARSITE is a mechanistic surrogate model, which mainly relies on a simplified analytical calculation of the RoS and on Huygens’ principle to approximate the propagation of the fire perimeter as if it were a wave front. FireProM-F [8, 11] is a theoretical reduced-order model based on energy and species conservation laws with some calibratedphysically-meaningfulparameters( light-grey-box model).Despitebeingphysics-based,itmayrunfaster-than- real-time under certain circumstances (scenarios, settings, computing power), although this comes at the expense of being decoupled from wind models and therefore using a frozen wind field. While decoupled models may provide fast simulations of wildfire propagation [9], they are unable to capture structures such as plume-driven fire, whirls, or horizontal roll vortices [12]. Conversely, coupledmodels such as the Fire Dynamics Simulator (FDS) [13] and FIRETEC [14] try to solve the fluid dynamics and thermo-chemical equations simultane- ously in order to capture the dynamics of a wildfire [9]. Even though some of these models (e.g. WRF-FIRE [15]) could potentially provide faster-than-real-time simulations under specific configurations and using high-performance facilities,anaccuratenumericalsolutionoveralargedomain isprohibitivelycomputationallyexpensive[9].Thisrestricts the practical use of this type of models.Eventhoughthefire-windcouplingstrategysignificantly affectsthesimulationresults,thisisrarelystudiedsystemat- ically in the literature. Lopes et al. [16] studied the effects of the mesh size and of the wind update criterion on the fire propagation dynamics. They found that the mesh size has a high impact on the RoS and propagation dynamics of the fire, though this impact becomes less noticeable as the meshsizedecreases.Nevertheless,atrulymesh-independent simulationisunlikelytobeachieved.Inturn,comparingthe resultsofaseriesofcoupledanddecoupledwildfiresimula- tions, they observed that coupled ones predict significantly smaller burned areas. Interestingly, it was also found that reducing the wind field update interval to once every five time-stepsdoesnotleadtosignificantvariationinresults,yet it notably reduces the computational effort [16]. Recently, TavakolSadrabadietal.[17]alsofoundthattheburnedarea and the RoS are smaller for coupled simulations. Thus,thechoiceoftherightwildfirepropagationmodel is highly dependent on the intended application: coupled modelsaremorerigorousthoughcomputationallyexpensive (hence with limited operational use) whereas decoupled models decrease the computational cost at the expense of disregarding the effect of the fire on the wind field (hence sacrificing prediction accuracy). In order to compensate for this drawback, efforts have been made to increase the accuracy of the wind estimations; e.g. using Numerical Weather Prediction (NWP) models together with methods to downscale and refine these estimations over the terrain of interest [18]. However, these large-scale models cannot capture wildfires local effects. First Author et al.: Preprint submitted to Elsevier Page 2 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements During the past few years, unmanned aerial vehicles (UAVs) have gained popularity in various industries and applications. They offer a low-cost option for firefighting, prevention, detection, and real-time assistance using either a single UAV or a collection of them [19, 7, 20]. Usually, UAVs(a.k.a.drones)arefittedwithsensorsthatallowthem to communicate with each other and to provide data to the ground station—e.g. GPS for navigation purposes [19], infraredanddigitalcamerasforsurveyingandfiredetection [21], and measuring sensors for aerosol concentrations [22] and wind velocities [22, 23, 24, 25]. Firefighting activities largely depend on receiving accurate real-time data such as fire propagation characteristics, fuel distribution, and wind patterns.Theavailabilityofsuchdatasignificantlyincreases the probability of success of the whole operation [26]. The use of drones in wildfire management has grown steadily in recent times, with most research focused on fire detection [27],monitoring[28],andsuppression[29,7,30].However, thesedronescouldalsobeequippedwithsensorstomeasure wind velocities while performing other tasks like fire mon- itoring and/or suppression. Therefore, this paper proposes a novel conceptual framework for improving the accuracy of decoupled wildfirepropagationmodelsusingreal-timewind field measurements carried out by a swarm of UAVs. As a proof of concept, these " measurements " are not actually taken by drones in the simulations performed in this paper but extracted from high-fidelity physics-based simulations viewed as ground truth. The proposed framework is mainly aimed at increasing the prediction accuracy of decoupled wildfire propagation models which disregard the effect of the fire on the wind field. However, it would also make it possible to capture variable atmospheric winds on site without resorting to atmospheric models. The remainder of this paper is organised as follows: Section 2 provides a brief overview of the main fire propa- gationmodelsusedinthisresearch,namelyFDSanditssub- models(LagrangianParticle,BoundaryFuel,andLevelSet), and FireProM-F; Section 3 discusses coupling strategies for fire-wind models and studies their impact on the RoS and fire propagation dynamics under different slopes and wind conditions using LS-FDS; Section 4 introduces the proposed method to improve the accuracy of decoupled wildfirepropagationmodelpredictionsusingreal-timewind measurements carried out by a swarm of UAVs; whilst Section 5 presents the results obtained from simulations using FireProM-F with and without noise in the wind mea- surements; finally, Section 6 provides a summary of the research findings and derived conclusions. 2. Fire Propagation Models This section presents a brief overview of the fire propa- gation models used for the simulations in this paper. 2.1. Fire Dynamics Simulator With a focus on smoke and heat transfer from fires, the Fire Dynamics Simulator (FDS) numerically solves avariant of the Navier-Stokes equations suitable for low- speed, thermally-driven flow. The main algorithm includes an explicit predictor-corrector method that is second-order accurateinspaceandtime.TurbulenceismodelledviaLarge Eddy Simulations (LES). A Direct Numerical Simulation (DNS) could be carried out instead, should the mesh be sufficientlyfine.FDSemploysaone-step,mixing-controlled chemical reaction with three bundled species for most ap- plications: products,fuel, andair. Reactions that are not necessarily mixing-controlled and multiple reactions could also be considered under certain conditions. To approxi- mate the governing equations and discretise the domain, a Cartesian grid is used [31]. FDS offers various models for the simulation of wildfire spread based on the desired level of physics required and the available computing resources: the Lagrangian Particle Model (LPM), the Boundary Fuel Model (BFM), and the Level-Set (LS) model. 2.1.1. Lagrangian Particle Model In this model, vegetation is represented by a collection ofLagrangianparticlesheatedviaconvection-radiationheat transfer. These particles could be used to represent leaves, grass,trees,etc.Withsufficientgridrefinement,LPMcanbe used for simulation of the front, back, and flank fire across thesurfaceaswellashigh-levelvegetations(e.g.trees)[32]. 2.1.2. Boundary Fuel Model This model is anoption when a coarse grid is desiredto discretiseathinvegetationlayer.Inthiscase,thevegetation ismodeledasaporousboundaryconsistingofalayerofdry vegetation,air,andmoisture.Theheightofthevegetationis unresolved on the grid and may be used for grid sizes of up to 10 m [31, 32]. 2.1.3. Level Set Model Thismodelisusedforwildfirespropagatingacrosslarge areas, which cannot be discretised with a grid sufficiently fine for physics-based models. The Level Set model within FDS (LS-FDS) makes use of the same elliptical spread model used by FARSITE [33], which is based on Huygens’ principle approach for wave-front modeling. It also adopts the Rothermel-Albini’s RoS formula, and Albini’s 13 fuel models [31]. InordertodefineafuelinLS-FDS,aseriesofparameters must be set. This includes the no-wind no-slope rate of spread(𝑅𝑜𝑆0), the packing ratio (𝛽), the surface area-to- volume ratio (𝜎)in cm−1, and the fuel height (ℎ)in metres. Thesesettingswouldthenbeusedtocalculatethemid-flame wind speed(𝑢mf)as well as the wind and slope coefficients (𝜙w,𝜙s). The one-dimensional (1D) model of the RoS for uniform vegetation, wind, and slope can be estimated as in Equation (1) [33]. This assumes that the propagation of the fire, the velocity of the wind, and the slope are all aligned. 𝑅𝑜𝑆=𝑅𝑜𝑆0( 1+√(𝜙w+𝜙s)(𝜙w+𝜙s)) (1) First Author et al.: Preprint submitted to Elsevier Page 3 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements Even though 𝜙wand𝜙sare calculated based on experi- mental data, a 1D model is insufficient to provide reliable estimations in real-world applications. Therefore, it is ex- tended to a two-dimensional (2D) model as follows [33]: ϕϕϕw=(𝜙w,𝑥,𝜙w,𝑦)=𝐶(3.281𝑢mf)𝛽(𝛽 𝛽op)−𝐸 ⋅( ||𝑢mf,𝑥||𝐵sgn(𝑢mf,𝑥),|||𝑢mf,𝑦|||𝐵sgn(𝑢mf,𝑦)) ,(2) ϕϕϕs=(𝜙s,𝑥,𝜙s,𝑦)=5.275𝛽−0.3((Δ𝑧 Δ𝑥)2 ,( Δ𝑧 Δ𝑦)2) ,(3) where 𝐵=0.15988𝜎0.54, (4) 𝐶=7.47e−0.8711𝜎0.55, (5) 𝐸=0.715e−0.01094𝜎, (6) 𝛽op=0.20395𝜎−0.8189. (7) TheLS-FDSmodelisgenerallybasedontheassumption that, under specific wind, slope, and vegetation circum- stances,asurfacefirewillspreadfromasinglelocationwith an ellipse-shaped fire perimeter that has a constant length- to-breadth (𝐿𝐵) ratio for the effective wind vector [31]. Assuming𝑃𝑡denotes a point on the fire front at time 𝑡, the 𝐿𝐵ratio for elliptical fire front originating from 𝑃𝑡is as in Equation (9) [34, 33]. 𝐿𝐵=0.936e0.2566𝑢+0.461e−0.1548𝑢−0.397(8) 𝐿𝐵=max( 1,min(𝐿𝐵,8)) (9) Theratioofthefirepropagationinthewinddirectionto itspropagationinthereversedirectioniscalledtheheading- to-backing ratio (𝐻𝐵)and is calculated as in Equation (10) [34, 33], while 𝑢mfis as in Equation (11) [35, 33]. 𝐻𝐵=( 𝐿𝐵+√ 𝐿𝐵2−1)( 𝐿𝐵−√ 𝐿𝐵2−1)−1 (10) 𝑢mf=𝑢01.83 ln( 20+1.18ℎ 0.43ℎ) (11) ItisimportanttonotethatEquation(8)ignorestheeffect ofslope.Inordertoaccountforit,avirtualwindspeed(𝑢vir) is calculated as in Equation (12) [34]. The effective wind speed(𝑢eff),whichisdefinedas 𝑢eff=𝑢+𝑢vir,isthenused in Equation (8) instead of 𝑢. 𝑢vir=0.3048( 1 𝑐(𝛽 𝛽op)𝐸)1 𝐵 (𝜙s,𝑥,𝜙s,𝑦)(12)The LS fire propagation model can be linked to the FDS wind module as they both run on the same grid. This provides the capability to account for terrain-induced wind fields as well as the fire-wind interaction by presenting a simple heat source at the fire front location [33]. Thus, LS- FDS may be used in any of four modes: •MODE1: Wind field is uniform and unaffected by terrain or fire (frozen uniform wind field). Only fire model runs. Decoupled wildfire model in Figure 1. •MODE2: Wind field affected by terrain but unaf- fected by fire (frozen non-uniform wind field once fire ignites). Fire affected by frozen wind. Decoupled wildfire model in Figure 1. •MODE3: Wind field follows terrain but there is no actual fire in the simulation (just front-tracking). [31] •MODE4: Wind field affected by terrain and fire. Fire affectedbywind. CoupledwildfiremodelinFigure1. 2.2. Fire Propagation Model for Fast Simulations The physics-based Fire Pro pagation Model for Fast simulations (FireProM-F) [8] is a wildfire model developed with computational efficiency in mind, aiming for faster- than-real-time (FtRT) simulations. It is governed by a 2D reaction-diffusionequationthatdescribesthecombustionof a vegetation stratum represented by a mono-phase medium composed of pre-mixed gas of fuel and air. The latter is assumed to be composed of oxygen, carbon dioxide, water vapour, and nitrogen. The reference chemical reaction (as- sumed irreversible) is the combustion of methane in air: 𝜃1CH4+𝜃2O2→𝜃3CO2+𝜃4H2O(in air:𝜃5N2).(13) The model is formulated as a system of five partial dif- ferential equations (PDEs), where Equation (14) represents the conservation of energy whilst the four equations in (15) represent the conservation of chemical species. 𝜌𝜕 𝜕𝑡(𝑐p𝑇)=𝑅c−∇⋅(𝐪c+𝐪d+𝐪r)+𝑄c𝑧+𝑄r𝑧+𝑄w(14) 𝜕𝑋𝑖 𝜕𝑡=−𝜃𝑖 𝜃fuel𝑀𝑖 𝑀fuel𝑟;with𝑖=1,2,3,4,(15) where: 𝑅c: combustion energy source; 𝐪c: conductive heat flux; 𝐪d: interdiffusional enthalpy flux; 𝐪r: 2D radiation heat flux; 𝑄c𝑧: vertical convection heat loss; 𝑄r𝑧: vertical radiation heat loss. 𝑄w: transport term due to wind; 𝑋𝑖: mass fraction of 𝑖thchemical species. 𝑀𝑖: molar mass of 𝑖thchemical species. 𝑟: combustion rate. First Author et al.: Preprint submitted to Elsevier Page 4 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements With this dimensionality reduction, some fire dynamics phenomena like buoyancy are disregarded, though verti- cal convection ( 𝑄c𝑧) and vertical radiation ( 𝑄r𝑧) terms are added to the conservation of energy equation. FireProM-F doesnotaccountfortheconservationofmassormomentum, hence neglecting the effect of the fire on the wind field. The diffusion coefficient is augmented (via calibration) to somewhat compensate for this. The system is closed with the equations for the molar mass of the mixture, the heat capacity of the mixture, the combustion rate (modelled by the Arrhenius law), and the combustion enthalpy. Refer to [8] for more details. Thetransporttermduetowind( 𝑄w)inEquation(14)is calculated as in Equation (16): 𝑄w=−𝜌𝑐w𝐮⋅∇(𝑐p𝑇)(16) where 𝐮= (𝑢𝑥,𝑢𝑦)is the atmospheric wind velocity, 𝑐wis the wind reduction coefficient (which may also be used as a calibration parameter), 𝑇is the temperature, 𝑐pis the heat capacity coefficient at constant pressure, and 𝜌is the gas mixture density. This is solved using an upwind scheme. ThenumericalschemeforthesolutionofEquations(14) and(15)isafinitedifferencemethodwitha 2nd-ordercentral difference for space and the 4th-order Runge-Kuta method fortimediscretisations.Referto[8]forthefullformulation. This reduced-order model is adopted in this paper as a fast (yet still physics-based) simulator to test the proposed framework. The latter aims to enhance the accuracy of the transport term ( 𝑄w) by feeding the model with wind velocities ( u) measured by a swarm of UAVs. This would account for both a variable atmospheric wind and the effect of the fire on the wind field. 2.3. Calibration and Validation 2.3.1. Experimental Data Numerical simulations are validated against the flat ter- rain grassland fire spread experiments carried out by the Commonwealth Scientific and Industrial Research Organi- sation(CSIRO)[36].TheselectedexperimentsaretheC064 andF19.Thesewereperformedinthemiddleofthedrysea- sononflatlandsof 100×100 m2coveredwithdryKerosene grassandof200×200 m2coveredwithdryKangaroograss, respectively. Measured properties in [36] and unmeasured properties assumed in [32] are shown in Table 1. Most simulations are performed using LS-FDS to study the effect of coupling/decoupling fire-fuel models. Albini’s FuelModel 1(shortgrass)and FuelModel 3(tallgrass)are used for the simulated C064 and F19 experiments, respec- tively [31]. Some modifications are performed to resolve mismatches between the characteristics of the fuel models in [31] and actual experimental measurements. 2.3.2. Boundary Conditions and Grid Sensitivity Open boundary conditions are used at the top, outlet, right, and left boundaries. The ambient wind is simulated within the domain using the Monin-Obukhov similarity theory, with Obukhov length scale 𝐿=−500, aerodynamicroughness height 𝑧0= 0.03, and wind speed at a reference height of 2 m above ground level (AGL) 𝑢r=4.6m/s. Structured Cartesian grids with equal spacing in 𝑥,𝑦,𝑧 directionsareusedtodiscretisea 120×120×40 m3domain fortheC064experiments,anda 240×240×100 m3domain for the F19 experiments. In order to study the sensitivity of the simulated fire propagation to the grid cell size, sizes between1×1×1 m3and5×5×5 m3aretestedusingLS- FDS,andofsizes 0.5×0.5×0.5m3and1×1×1 m3using BFM-FDS and LPM-FDS. The evolution of the fire front for different cell sizes is shown in Figure 2 for the (a) C064 and (b) F19 CSIRO ex- perimentsusingthethreeFDSsub-models.Inparticular,LS- FDSisrunusingboththecoupledanduncoupledstrategies. As a general trend, it can be observed that increasing the mesh/cellsizeresultsinincreasingtheRoSofthefire,which is consistent with the results in [32]. 2.3.3. Level-Set No-Wind No-Slope RoS Calibration The analysis in Section 2.3.2 shows that the no-wind no-slope RoS ( 𝑅𝑜𝑆0) is sensitive to the refinement of the grid (i.e. to the mesh/cell size). Though less evident in the C064 experiments, it can also be observed in Figure 2 that coupled(C)wildfiremodelspredictfasterRoS(andcloserto the experimental results) than the corresponding decoupled (D)ones.Theremainingsimulationsinthispaperarecarried out for the F19 experiment due to its larger area and longer duration, which results in more meaningful comparisons. In order to calibrate the LS-FDS, the default values of the𝑅𝑜𝑆0in Albini’s fuel models are tuned so that the model outputs RoS values comparable to those obtained from the CSIRO experiments. Figure 3 shows the position and perimeter of the fire obtained for the simulated CSIRO F19 experiment using the coupled LS-FDS (M ODE4) with calibrated𝑅𝑜𝑆0for 2 m, 3 m, and 5 m grid sizes at three different times from ignition. Results obtained using BFM- FDS and LPM-FDS are also included in the figure. 3. Coupling Strategies for Fire-Wind Models Figure3showsthatthecoupledLS-FDSwithcalibrated 𝑅𝑜𝑆0predicts the CSIRO F19 experiment accurately under no-slopecondition.Theeffectsoffire-windcouplingonthe headfire position and the corresponding RoS for a range of wind speeds and topography slopes during up-slope prop- agation can be observed in Figure 4, where 2×2×1 m3 cellsareusedforspatialdiscretisation.GiventhatFDSuses structured grids, a sloped topography is modelled using a staircase of cubic blocks. Figure 4 shows (a) the headfire position (distance trav- elled) for eight different wind speeds and (b) their corre- spondingRoSforhorizontaltopography.Italsoshows(c)the headfire position and (d) their corresponding RoS for a fire propagating up slope for all nine possible combinations of three slopes ( 5%,15 %, 30%) and three wind speeds (1 m/s, 5 m/s, 10 m/s). Both coupled (C) and decoupled (D) LS- FDS are used in each case. Note that wind speed refers to atmospheric horizontal wind, whilst the resulting up-slope First Author et al.: Preprint submitted to Elsevier Page 5 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements Table 1 Measured properties of CSIRO experiments [36] and utilized values for simulations based on [13, 32] .Property Unit Case C064 Case F19 Wind speed m/s 4.6 4 .8 Ambient Temperature °C 32 34 Surface Area to Volume Ratio m−19,770 12 ,240 Grass Height m 0.21 0 .51 Bulk Mass Per Unit Area kg m−20.283 0 .313 Moisture Fraction % 6.3 5 .8 Measured RoS m s−11.2 1 .5 Fuel - Cellulose (C6H10O5) Cellulose (C6H10O5) Heat of Combustion kJ kg−115,600 15 ,600 Soot Yield kg kg−10.015 0 .015 Char Yield kg kg−10.2 0 .2 Specific Heat kJ kg−1K−11.5 1 .5 Conductivity kJ kg−1K−10.1 0 .1 Density kg m−3512 512 Heat of Pyrolysis kJ kg−1418 418 Pyrolysis Temperature °C 200 200 Obukhov Length m −500 −500 Aerodynamic Roughness Length m 0.03 0 .03 Drag Coefficient - 2.8 2 .8 Soil Specific Heat kJ kg−1K−12.0 2 .0 Soil Conductivity W m−1K−10.25 0 .25 Soil Density kg m−31,300 1 ,300 Figure 2: Evolution of the fire front for different mesh sizes using LS-FDS with coupled (C) and decoupled (D) strategies, LPM-FDS, and BFM-FDS models for (a) C064 and (b) F19 CSIRO experiments. wind is always higher. As expected, higher wind speed and higher topography slope (for up-slope propagation) lead to higherRoS.Furthermore,higherwindspeedsofupto10m/s and higher surface slopes of up to 30% also result in larger differences between predictions by corresponding coupled and decoupled fire-wind models (in agreement with exper- imental results [37]). For example, the difference between coupled and decoupled predictions of the RoS is 0.44m/s for 30% slope and 5m/s wind, whereas it is 1.51m/s for 30% slope and 10m/s. The RoS predicted by coupled LS- FDS appears to be generally higher than the one predictedby decoupled LS-FDS for wind speeds of up to 12 m/s. For horizontal topography in Figure 4 (b), this trend seems to invert for wind speeds approximately between 12 m/s and 20 m/s, with the coupling strategy making little to no difference for a wind speed of 20 m/s. However, more data- points would be required to support this observation. It is important to note that these simulations using LS- FDS seem to indicate that increasing wind speeds always leads to increasing RoS. However, experimental results [2, 38] showed that a turning point and a reduction of the RoS is to be expected. Since LS-FDS is not physics-based, it First Author et al.: Preprint submitted to Elsevier Page 6 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements Figure 3: (a) Position and (b) perimeter of fire for CSIRO F19 experiment using BFM-FDS, LPM-FDS, and coupled LS-FDS with calibrated 𝑅𝑜𝑆0for three grid sizes at three different times after ignition. Experimental results also provided for reference. is reasonable to infer that it does not capture some of the relevantunderlyingfirepropagationdynamics,andtherefore may make unreliable predictions for higher wind speeds (in these experiments, higher than 12–13 m/s). Wildfires can propagate up slope surprisingly fast due to the heating of unburned fuel ahead of the fire as the plumeattachestotheslopesurface;i.e.tothefuelbed[39]. The RoS increases with the increase in the length of the plume attachment, which grows as the angle between the fire plume and the the fuel bed shrinks. This angle shrinks with increasing flame tilt angle (𝜃)and with increasing fuel bed inclination angle (𝛼), where𝜃is defined as the angle between the centerline of the individually pioneering flame andtheverticalaxis[40].Inturn, 𝜃increaseswithincreasing uphillwind speed and with increasing 𝛼due to the result- ing asymmetry of the air entrainment . Since the buoyancy force has an uphill component, the air entrainment into the fire from the burned side (upstream) is greater, tilting the plume towards the unburned downstream vegetation [41]. Therefore, higher uphill wind speeds and higher surface slopeslead to faster uphill fire propagation (higher RoS) due to the resulting larger plume attachment length . Under no ambient wind condition, the plume attachment length is more sensitive to fuel bed inclination angles higher than 15◦, increasing dramatically for angles higher than 24◦(the so-called critical inclination angle ) [42]. Similar values are reportedintheliterature,obtainedfromdifferentlaboratory and field burns. The general conclusion is that the critical slopeis in the20◦–25◦range [39]. Even though LS-FDS doesnotmodeltheflameorradiativeheattransfer,thelarger RoS predicted for larger surface slopes when coupling fire and wind models during uphill fire propagation is likely due to the released latent heat from the fire front inducing convective wind patterns up slope.Thus, higher wind speeds and larger inclinations of the fuel bed lead to faster up-slope fire propagation. Coupled models predict higher values of the RoS than decoupled ones, presumably being able to better capture the relevant phenomenaassociatedwithfire-inducedwind.Furthermore, Figure5showsthattheshapeofthepredictedfireperimeter alsodiffers,withthedecoupledmodeldisplayingasmoother perimeter.Thisfigurealsoconfirmsthatthecoupledwildfire model predicts faster propagation. 4. Enhancement for Decoupled Models In Section 3, the influence that the fire has on the wind field has been shown to have a strong effect on its RoS, and therefore should not be neglected when predicting its propagation. Yet, this is precisely what decoupled wildfire modelsdo.Aimingtocapturethefire-windinteractionwith- out incurring the hefty cost of solving the Navier-Stokes equations,amethodologyisproposedheretoenhancewild- firemodelpredictionsbyprovidingitwithnear-surfacewind fieldsapproximatedfromUAVmeasurementsathigheralti- tudes. A top level description of the proposed methodology is shown in Figure 6. 4.1. System Overview Theproposedmethodologyismodelagnostic,andthere- fore can be implemented as a stand-alone module to be integrated with any wildfire model that includes wind in its governing equations. Since its aim is to mimic the effect of fire-windcoupling,itisoriginallyproposedwithdecoupled wildfiremodelsinmind.Nonetheless,itcouldbeappliedto coupled models as well, potentially using data assimilation tocorrectthewindfieldpredictedbythemodel.Atop-level description of the methodology is shown in Figure 6 and summarised below: First Author et al.: Preprint submitted to Elsevier Page 7 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements Figure 4: (a) Headfire position (distance travelled) for eight different wind speeds and (b) their corresponding RoS for horizontal topography; and (c) headfire position for nine different slope-wind combinations and (d) their corresponding RoS with fire propagating up slope. Both coupled (C) and decoupled (D) LS-FDS are tested in each case. Figure 5: Fire perimeter as predicted by coupled (C) and decoupled (D) LS-FDS at three different times for three different slopes, namely (a) 𝑆=5%, (b)𝑆=15%, (c)𝑆=30%. 1. A swarm of UAVs measure wind velocity at different 2D locations at flight height at a given time 𝑡=𝑡𝑖. 2. The measured wind velocities are used to generate a high-resolution wind field using a data-driven super- resolution approach.3. The high-resolution wind field at flight height is used to approximate the near-surface wind field by means of a mapping method such as a neural network. 4. Thedownscalednear-surfacewindfieldisfedintothe FtRT simulator, which forecasts the fire propagation First Author et al.: Preprint submitted to Elsevier Page 8 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements High-Altitude Wind Field Measurement High-Altitude Wind Field Generation Wildfire Behaviour Predictions Near-Surface Wind Field MappingDownscaling Data-Driven Modelling Other Model Inputs - Boundary conditions. - Initial conditions. - Fuel bed descriptors. - Topography descriptors. - Et cetera. ANN Mapping Figure 6: Top-level description of the proposed methodology to enhance decoupled wildfire model predictions using near-surface wind fields approximated from measurements at a high altitude (specifically, at flight height). for the desired prediction horizon (). Thus, the fire propagation is simulated in the interval (𝑡𝑖,𝑡𝑖+]. 5. Once the desired time increment (Δ𝑡)for updates has elapsed, swarm-based measurements are re-taken at time𝑡𝑖+1=𝑡𝑖+Δ𝑡,andtheprocessisrepeatedtopre- dictthefirepropagationinthe (𝑡𝑖+1,𝑡𝑖+1+]interval. Thus, the prediction horizon recedes by Δ𝑡<< . Thefirepropagationforecastduringthepredictionhori- zon()can be used to assist firefighting operations, with the surface wind field remaining frozen during this time. Nonetheless,theoutputsofthesimulatorafterthetimeincre- ment(Δ𝑡)haselapsedtogetherwiththeupdatednear-surface windfieldwillcomprisetheinputsintothesimulator,which can then forecast the fire propagation during the next . Although it may be often infeasible to have a swarm of UAVs airborne solely to take wind measurements, equip- pingthemwithappropriatesensors(andpossiblyactuators) would enable the swarm to perform more than one task simultaneously. For example, consider the swarm of self- organising drones proposed by Innocente and Grasso [7] or thedronefleetsystemproposedbyAusonioetal.[30],which couldeasilybetakingimageryandmeasuringenvironmental variables like wind, temperature or pressure whilst engaged infiresuppressionand/ormonitoringactivities.Ourprelim- inary vision of how the system in Figure 6 could blend into a potential fire management system is shown in Figure 7. Evidently,thesmallerthe Δ𝑡betweenmeasurementsthe better,asthewindiskeptfrozenforshorterperiodsoftime. ArangeofsimulationsarecarriedoutinSection5.1tostudy the effect of Δ𝑡on a flat grassland covered with a uniform fuel bed. Since actual wind measurements are certain to be uncertain,Section5.2providesaninitialattemptatstudying the effect of uncertainty on the wildfire model predictions.4.2. Swarm-Based Wind Field Measurement Current technology to measure wind velocities include traditional methods like cup anemometers and weather bal- loons, as well as more modern ultrasonic and laser-based systems. Conventional measurements above 60m AGL re- quire the building of costly towers, which motivates the useofalternativetechnologiessuchas drone-mountedwind LiDARs[24] and drone-mounted ultrasonic anemometers [25].Asopposedtomechanicalanemometers,windLiDARs measure the wind speed remotely, without direct contact with the atmosphere [43]. There are two types of Doppler wind LiDARs: (𝑖)continuous wave LiDARs emit a high- frequency concentrated laser beam at the specified location forrangesof 10mto250mAGL,whilst (𝑖𝑖)pulsedLiDARs generateavolleyoflow-frequencylaserpulsessothatwind velocity can be measured along a line at different locations simultaneously for ranges of 50m to10km AGL [24]. Airborneatmosphericmeasurementsmaybetakenusing fixed-wing or rotor-based drones. The former are especially suitable for long-range and long-endurance flights, as they canreachconsiderablyhigherlift-to-drag (𝐿∕𝐷)ratios.This translates to much lower thrust requirements than similar- sized rotor-based drones, and therefore to longer endurance [25]. On the other hand, rotor-based drones do no require a runway to take off, they offer greater maneuverability, and they have the ability to hover [22]. Measurements can be taken (𝑖)indirectly by evaluating the drone response to the surrounding wind field [44], or ( 𝑖𝑖)directlyby means of dedicated sensors [23, 25]. The most common sensors used in UAVs include pitot tubes and multi-hole pressure probes [45], mechanical and sonic anemometers [44, 46], and LiDAR systems [24]. Wind speed measurement errors havebeenreportedtobearound3%underhorizontalinflows and ideally levelled conditions [44, 47], around 10–20% for hardersituations[48,49],andintherangeof20–50%when mounted on quadrotors [44]. First Author et al.: Preprint submitted to Elsevier Page 9 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements High-Altitude Wind Field Measurement Near-Surface Wind Field MappingHigh-Altitude Wind Field Generation Fire Detection using a range of systems, including UAV-based ones Other Model Inputs - Boundary conditions. - Initial conditions. - Fuel bed descriptors. - Topography descriptors. - Et cetera. Model Inputs - Boundary conditions. - Initial conditions. - Fuel bed descriptors. - Topography descriptors. - Uniform, frozen wind fieldFire Management decisions and planning Suppression & Monitoring ActivitiesFire Ignition Wildfire Behaviour Predictions Downscaling Figure 7: System view of an envisioned fire management system empowered by UAV swarms, which assimilates the proposed methodology shown in Figure 6 to enhance fire propagation model predictions. Wetz et al. [23] proposed using multiple UAVs for syn- chronised wind velocity measurements in the atmospheric boundary layer (ABL), where a small swarm of 10 UAVs operate simultaneously to provide the spatial distribution in thevicinityofwindturbines.Theiralgorithmestimateswind velocity making use of the principle of aerodynamic drag and related quadcopter dynamics. Since the air flow around a wildfire is highly turbulent andhot,itmaybearguedthatflyingdronesinthoseregions presents a high risk of failure, especially for small-sized UAVs [50]. In order for the latter to cope with hazardous and all-weather conditions, there is substantial work being carriedoutonthedesignofmorerobustcontrollers[51]and of more resilient structures and materials [50, 52, 53]. This paper proposes the use of UAV swarms to period- ically take multiple, simultaneous, real-time wind velocity measurementswhichwillbesubsequentlyusedtoconstruct the wind field to be fed into a wildfire propagation model. Thisremovestheneedtocoupleawindmodel,andcouldbe performed while carrying out other fire management tasks such as fire perimeter monitoring, fire suppression, or evac- uation assistance. UAVs are particularly suitable because they do not require preinstalled infrastructure, whilst they cancarryarangeofsensors,reachhard-to-accessareaswith ease,andkeephumanfirefightersfurtherawayfromdanger. In turn, swarms are particularly suitable because they allow formultiplesimultaneousmeasurementstohelpcapturethe generaltrendofthewindfield.ThespecificUAVandsensor technologies to take the measurements and the swarming behaviour are beyond the scope of this paper.4.3. Wind Field Downscaling The accurate estimation of the wind field is of great importance in numerous applications. However, numeri- cal weather models require powerful computing resources, which restricts the feasibility of fine-scale (high-resolution) forecasts [18]. This has led to coarse-scale weather models often being employed in wildfire decision-support systems. Adomain-averagewindfieldmaybeconstructedusingsuch models, usually in the form of uniform wind fields [54]. Downscaling methods aim to avoid costly high- resolution simulations across large geographic scales by inferring high-resolution from low-resolution data [18]. They may be either dynamic orstatistical [55], with dynamic methods falling into either the prognostic or the diagnostic categories. Prognosticmethodssuchasthoseemployedinnumerical weather forecasting solve mass, momentum, energy, and moisture conservation equations and advance in time. They often include detailed models for the dynamics of bound- arylayers,land–atmosphereinteractions,radiation,thermo- dynamics, and cloud processes. Therefore, these methods demand a substantial amount of computational power, have complicated initial and boundary conditions, and require highly skilled operators for their use [54, 56]. Alternatively, statistical downscaling makes use of re- sultsfromlarge-scalesimulationswithcoarsespatialresolu- tion (predictor data ) to derive predictions at smaller scales with fine resolution ( predictand data ). These methods are trained on a given set of predictor–predictand data pairs to learn the correlations between coarse and fine data [18]. First Author et al.: Preprint submitted to Elsevier Page 10 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements Machine Learning (ML) and Deep Learning (DL) tech- niques are particularly useful in this domain. Specifically, Convolutional Neural Networks (CNNs) have found vast applicationsindownscalingatmosphericparameterssuchas wind fields for both, the construction of the wind field at a highaltitudefrompointmeasurements[57]andtheimprove- mentofthewindfieldresolution[18,58,59].Sincetheaim oftheproposedmethodologyistoenhancepredictionsmade by FtRT simulations, statistical downscaling methods are preferred. They can be trained in advance and be efficiently evaluated in real-time under operational conditions. Since this paper aims to demonstrate how the proposed methodology enhances FtRT decoupled model predictions by providing them with multiple simultaneous wind mea- surements, the development and training of a specific sta- tistical downscaling method is beyond its scope. Therefore, windvelocitiesarenotactuallymeasuredanddownscaledin this paper but extracted from three-dimensional (3D) high- fidelity physics-based Large Eddy Simulations in FDS. 5. Simulations and Analysis of Results 5.1. Enhancing Wildfire Model Predictions A series of 3D grassland fire propagation simulations are performed using LPM-FDS and BFM-FDS (described in Section 2.1), with the resulting wind field extracted at different time-steps and provided to FireProM-F (described in Section 2.2) as if it were the output of the wind field downscaling module in Figure 6. The effect of feeding the decoupled wildfire propagation model with the wind field is studied for a range of time intervals between consecutive "measurement" updates (Δ𝑡). Thus, the CSIRO C064 experiment is simulated using LPM-FDSandBFM-FDSwithcellsizesof 1×1×1m3and 0.5×0.5×0.5m3. Figure 8 shows the simulated wildfire at three time instants using 0.5×0.5×0.5m3cells, with both models predicting similar RoS despite their different representations of the fuel bed. Since both simulators rely on LES to model turbulence, they include stochasticity and therefore predict fire perimeters which are not perfectly symmetrical. This is more noticeable on the flanks of the fire. Given that LPM-FDS is expected to be a more realistic representationoftherealphenomena,andalsothatitappears to predict slightly more symmetrical fire perimeters, the wind "measurements" for the following experiments are extracted from the wind field generated by this model. In order to investigate the effect of the time increment between wind measurements, the CSIRO C064 experiment issimulatedwithFireProM-Ffor 120sandforfivedifferent values ofΔ𝑡. The specific settings are provided in Table 2, whilst the temperature distributions are shown in Figure 9 at three points in time: 27s,53s, and100s after ignition. In the first case, there is a single wind field input at the beginningofthesimulation,whicheffectivelymeansthatthe wind is frozen. The other cases consider decreasing values ofΔ𝑡between measurements (and therefore between wind field inputs into the wildfire model) in order to somewhatTable 2 Wind field inputs/updates during a 120s simulation of wildfire propagation for different values of the time increment Δ𝑡. No. Wind Δ𝑡(s) Wind Input Times (s) Inputs 1 120 0 4 30 0, 30, 60, 90 6 20 0, 20, 40, 60, 80, 100 12 10 0, 10, 20, 30, 40, 50, ..., 100, 110 24 5 0, 5, 10, 15, 20, ..., 110, 115 accountforthefire-inducedwindwithouthavingtocouplea computationally expensive wind model. For example, there are four wind field inputs into FireProM-F during the 120s simulation for Δ𝑡=30s. The results for a uniform, frozen wind field are shown in Figures 9 (a), (b) and (c), providing a baseline against which to evaluate the effect of Δ𝑡. It can be observed that the fire front resulting from using a frozen wind field, thus disregarding the fire-induced wind, has a pointy shape that differs from the actual and simulated shapes respectively observedinboth,thefieldexperimentsandFigure8.Instead, the proposed periodic update of the wind field constructed from measurements every Δ𝑡leads to more credible fire front formations. Comparing the shapes at 𝑡= 27s in Figures 8 and 9, it is clear that smaller values of Δ𝑡(i.e. higherfrequencyofupdates)predictmorerealisticshapesof the fire front. For larger values of Δ𝑡, the fire front reaches the counter-rotating vortex pairs which form downstream (not shown here), affecting the formation of the fire front and the pace of its propagation. Therefore, reducing the value ofΔ𝑡, consequently increasing the frequency of wind fieldupdatesprovidedtothedecoupledwildfirepropagation model, may prevent or reduce the effect of this numerical (artificial) phenomenon. Furthermore, a visual comparison of Figures 9 (g), (h) and (i) (Δ𝑡= 20s), Figures 9 (j), (k) and (l)(Δ𝑡= 10), and Figures 9 (m), (n) and (o) (Δ𝑡=5s)suggeststhatreducing Δ𝑡resultsinslightlyfaster propagation (i.e. higher RoS of the fire). ItisinterestingtonotethatFireProM-Fisdeterministic. Therefore, the fire perimeter is symmetric for uniform wind (and uniformly distributed fuel), as can be observed in Figures 9 (a), (b) and (c). The asymmetries displayed in the remainingfigures,inwhichthewindfieldisupdatedduring thesimulation,areduetoFDSrelyingonLEStomodeltur- bulence(thereforeintroducingstochasticity).Infact,thefire perimeterspredictedbyLPM-FDSandbyBFM-FDSinFig- ure 8 are also asymmetric. Recall that these simulated wind fieldsaretakenasgroundtruthinthenumericalexperiments in this paper to represent actual measurements provided to FireProM-Ftoenhanceitspredictions.Furthermore,agiven wind field extracted from the simulations corresponds to a specific point in time, which means that it is not time- averaged and is therefore affected by the oscillations of the dynamiccombustionphase.Thisalsocontributes,albeittoa First Author et al.: Preprint submitted to Elsevier Page 11 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements Figure 8: Simulated wildfire propagation at three points in time for the CSIRO C064 experiment using LPM-FDS (top) and BFM-FDS (bottom) models and 0.5×0.5×0.5m3cells. lesser extent, to the asymmetries observed in the simulated fire perimeters. Figure10showsthesimulatedfireperimetercorrespond- ing to the CSIRO C064 experiment at three points in time predicted by FireProM-F enhanced by wind field inputs derivedfromwindmeasurementsevery Δ𝑡=5s(reddotted lines). These predictions are in agreement with actual field measurements shown in the figure by black markers. Figure 11 shows the size of the burned area at three points in time after ignition experimentally measured; pre- dicted by LPM-FDS (coupled); predicted by FireProM-F (decoupled) with frozen and uniform wind; and predicted by FireProM-F (decoupled) enhanced by wind field inputs derivedfromwindmeasurementswithdifferentvaluesof Δ𝑡. As can be observed, the size of the burned area simulated by LPM-FDS is larger than that of actual experimental measurements.Onesourceofthissignificantdiscrepancyis the fact that the "atmospheric wind" velocities are variable both in intensity and direction during the field experiments, whereastheyarekeptconstantduringthesimulations.Note that "atmospheric wind" here means without accounting for the fire-induced wind. It can also be observed that the burned area size predicted by the enhanced FireProM-F is closer to the one predicted by LPM-FDS than it is to the one experimentally measured. This makes sense, since the wind fields provided to FireProM-F were extracted from the LPM-FDS simulations. In fact, the smaller the Δ𝑡the better the agreement between them, whereas the decoupled Fire-ProM-F returns a burned area size similar to the one measured from the field experiments. With regards to the computational effort, it is worth mentioningthatsimulatingawildfirepropagationfora 100× 100m2areadiscretisedinto10,0002Dcellsisperformedup to 3.33 times faster than real time. That is to say that 1 min of wildfire propagation is simulated in 18 s on a single-core CPU. This may be reduced by orders of magnitude if im- plementedonparallelprocessingframeworks,whichmakes this approach especially suitable for operational settings.5.2. Effect of Wind Measurement Uncertainty Wind speed measurement errors have been reported to be in the range of 20–50% when mounted on quadrotors [44].Inordertoperformapreliminarystudyoftheeffectof these measurement uncertainties on the simulated wildfire propagation, two scenarios are considered: (𝑖)30% and (𝑖𝑖)50% Gaussian noise added to the "measurements". In other words, noise is sampled from a normal distribution with standard deviation equal to 30% and 50% of the wind velocity, respectively. Figures 12 and 13 show the tempera- turedistributionatthreepointsintimeafterignitionreturned byFireProM-FsimulatingtheCSIROC064experimentwith noisy wind field inputs every 30s and10s, respectively. As can be observed, the general shape of the burned area remains despite the noise, with the fire front displaying a more defined shape and faster propagation (higher RoS) for lowerlevelsofnoise(seealsoFigure9).Thisisinagreement withtheburnedareadecreasingwhen50%noiseisaddedto the "measurements" in Figure 11. 6. Conclusions The accuracy of wildfire propagation models’ predic- tions is influenced by numerous factors such as the fidelity of the fuel descriptors, adequate initial and boundary con- ditions, the coupling with atmospheric models, and the couplingwithwindmodelssuchasNavier-Stokesequations to account for the interaction between wind and fire. This paperfocusedonthelatter.Moreprecisely,onenhancingthe prediction accuracy of a given wildfire propagation model that is not coupled with a wind model—a.k.a. decoupled wildfire propagation model—by periodically providing it with wind fields constructed from UAV swarm-based wind measurements. This made it possible to account for fire- windinteractionswithoutresolvingcomputationallyexpen- sive mass and momentum balance equations as in full- blown computational fluid dynamics (CFD) simulations. This means that the decoupled wildfire propagation model predictions were enhanced while still retaining its ability First Author et al.: Preprint submitted to Elsevier Page 12 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements Figure 9: Temperature profile at three points in time from a 120s simulation of the CSIRO C064 experiment by FireProM-F (decoupled) enhanced by wind fields inputs derived from wind measurements with update intervals (Δ𝑡)as in Table 2. Note that "X DW" stands for "X dynamic wind field inputs during the simulation". First Author et al.: Preprint submitted to Elsevier Page 13 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements Figure 10: Three time instants of the CSIRO C064 experiment, where actual measurements are shown by black markers whilst the fire perimeter predicted by FireProM-F enhanced by wind field inputs derived from wind measurements every Δ𝑡= 5s are shown by red dotted lines. Figure 11: Burned area of CSIRO C064 experiment at three time instants after ignition experimentally measured, predicted by LPM-FDS (coupled), predicted by FireProM-F (decoupled) with frozen wind, and predicted by FireProM-F (decoupled) enhancedbywindfieldinputsderivedfromwindmeasurements with different update intervals (Δ𝑡). Note that "X DW" stands for "X dynamic wind field inputs during the simulation", whilst the percentage refers to Gaussian noise. toperformfaster-than-real-time(FtRT)simulationstoassist fire management operations. A range of numerical experiments were performed to simulate the CSIRO C064 and F19 field experiments underdifferent conditions and using a range of wildfire propa- gation models: (𝑖)LPM-FDS (full-blown CFD simulator); (𝑖𝑖)LS-FDS (level set model within FDS); (𝑖𝑖𝑖)FireProM- F (2D physics-based simulator) with frozen wind field; and (𝑖𝑣)FireProM-F enhanced by periodic inputs of wind fields constructed from UAV swarm-based wind measurements. Simulations performed using coupled and decoupled LS-FDSshowedthatcouplingleadstohigherRoS,closerto the values reported from field experiments. The difference in RoS increases with increasing atmospheric horizontal wind speeds and with higher terrain positive slopes. This is presumed to be due to coupled models being able to better capture fire-induced convective wind patterns up slope (i.e. downstream).Furthermore,thecouplingofaturbulentwind modelresults,unsurprisingly,inthepredictedfireperimeter being less smooth. In order to study the effect of the proposed method to enhance decoupled wildfire propagation model predictions, a series of wind fields generated by LPM-FDS were used to stand for actual wind measurements. FireProM-F was used as an example of a decoupled FtRT simulator whose predictions are to be enhanced by the proposed method. Thus, a series of fire propagation simulations were per- formed periodically providing the model with "measured" wind fields. The resulting fire fronts and burned areas were then compared against those predicted by full-blown CFD simulations(LPM-FDS),whichweretakenasgroundtruth. Thismakessensebecausetheyhadprovidedthewindfields asasurrogateofthemeasuredones.Resultsdemonstratethat the enhanced FireProM-F makes more accurate predictions than the plain one, and that the higher update frequencies, namelyΔ𝑡= 10s andΔ𝑡= 5s, predict burned areas very similar to the ground truth. Furthermore, the fire front predicted by the enhanced FireProM-F was shown to track the experimental ones accurately. Sincewindwasnotmeasuredinthefieldfortheseexper- iments but extracted from LPM-FDS simulations, Gaussian noisewasaddedtoperformapreliminarystudyoftheeffect ofmeasurementuncertainty.Resultsshowedthatthegeneral shapeoftheburnedarearemainsmoreorlessthesamewhen adding 30%–50% noise, with the fire front displaying a less smooth shape and slower propagation as noise increases. Thus, the proposed method has been shown to enhance decoupled wildfire propagation model predictions, as it had beenhypothesised.Still,thisisaconceptualframeworkand considerable work remains to be done to bring the concept closer to deployment. The next steps in our research are the design of the wind downscaling mechanism, and the inves- tigation of the performance of the proposed methodology when measurements are less regular; e.g. when the swarm is performing other activities while taking measurements. First Author et al.: Preprint submitted to Elsevier Page 14 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements Figure 12: Temperature profile at three points in time from a 120s simulation of the CSIRO C064 experiment by FireProM-F (decoupled) enhanced by wind fields inputs with 30 % (top) and 50 % (bottom) Gaussian noise with update interval Δ𝑡=30s. Note that "X DW" stands for "X dynamic wind field inputs during the simulation". Figure 13: Temperature profile at three points in time from a 120s simulation of the CSIRO C064 experiment by FireProM-F (decoupled) enhanced by wind fields inputs with 30 % (top) and 50 % (bottom) Gaussian noise with update interval Δ𝑡=10s. Note that "X DW" stands for "X dynamic wind field inputs during the simulation". First Author et al.: Preprint submitted to Elsevier Page 15 of 17 Enhancing Wildfire Propagation Model Predictions Using Aerial Swarm-Based Wind Measurements CRediT authorship contribution statement Mohammad Tavakol Sadrabadi: Conceptualization, Methodology, Software, Writing, Investigation, Visualization. Mauro Sebastián Innocente: Conceptualization, Methodology, Software, Writing, Supervision, Resources, Visualization.