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A numerical perspective on wildfire plume-rise dynamics Moisseeva, Nadejda 2020

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A numerical perspective on wildfire plume-risedynamicsbyNadejda MoisseevaA THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Atmospheric Science)The University of British Columbia(Vancouver)December 2020© Nadejda Moisseeva, 2020The following individuals certify that they have read, and recommend to the Faculty ofGraduate and Postdoctoral Studies for acceptance, the thesis entitled:A numerical perspective on wildfire plume-rise dynamicssubmitted by Nadejda Moisseeva in partial fulfillment of the requirements for the de-gree of Doctor of Philosophy in Atmospheric Science.Examining Committee:Roland Stull, Atmospheric Science, UBCSupervisorDouw Steyn, Atmospheric Science, UBCSupervisory Committee MemberPhillip Austin, Atmospheric Science, UBCSupervisory Committee MemberAdam Kochanski, Meteorology and Climate Science, SJSUExternal ExaminerLori Daniels, Forestry, UBCUniversity ExaminerAllan Bertram, Chemistry, UBCUniversity ExamineriiAbstractThe buoyant rise of wildfire smoke and the resultant vertical distribution of emissionproducts in the atmosphere have a strong influence on downwind pollutant concentra-tions at the surface, and provide key input into regional and global chemical transportmodels. Due to inherent complexity of wildfire plume dynamics, smoke injection heightpredictions are subject to large uncertainties. One of the obstacles to the developmentof new plume rise parameterizations has been the scarcity of detailed simultaneousobservations of fire-generated turbulence, entrainment, smoke concentrations and firebehavior. This thesis makes contributions on two fronts: (i) it demonstrates the feasi-bility of using coupled fire-atmosphere large-eddy simulations tomodel wildfire smokedynamics to produce "synthetic" plume data, and (ii) develops a new energy balanceplume rise parameterization to predict the vertical distribution of smoke in the atmo-sphere.The first part of the thesis focuses on evaluating the large-eddy simulation modelused in thisworkwith a detailed observational dataset froma real prescribed burn. Thenext portion explores the effect of various fire parameters and ambient atmosphericconditions on smoke plume behavior using a range of sensitivity studies. Analysisof flow dynamics shows that the updraft is shaped by complex interactions of fire-induced winds and vorticity generated in response to a near-surface convergence, anddoes not conform to commonly used mixing and entrainment assumptions.With the knowledge gained through the above numerical experiments, the secondhalf of the thesis introduces a simple parameterization for predicting the mean cen-terline height for penetrative plumes from fires of arbitrary shape and intensity. Lastly,the proposed parameterization is extended to capture the full vertical distribution ofsmoke in the atmosphere. The broad goal of this work is to better our understandingof plume rise dynamics and improve smoke dispersion predictions within air qualityapplications.iiiLay SummaryThis work aims to improve our understanding of how smoke from wildfires spreads inthe atmosphere. The more we know about where and how the pollutants travel, thebetter we are able to predict hazardous air quality and inform downwind communities.Specifically, this thesis presents simple tools for estimating how high above the Earth’ssurface the smoke from a wildfire will rise. Thesemethods can be used within existingair quality models and help improve their accuracy.ivPrefaceThis dissertation is original work of the author, Nadejda Moisseeva, under the super-vision of Roland Stull. Below are details of how papers (published and accepted forpublication) included in thesis were modified into chapters.• Moisseeva, N.; Stull, R.: Capturing Plume Rise and Dispersion with a CoupledLarge-Eddy Simulation: Case Study of a Prescribed Burn. Atmosphere 2019,10, 579.Excerpts from the article are included in Chapter 2. Chapter 3 is based in full onthe paper, with the addition of brief introduction and ’Big picture’ sections.• Moisseeva, N. and Stull, R.: Wildfire smoke-plume rise: a simple energy balanceparameterization, Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2020-827, accepted for publication, Dec 2020.Excerpts from the article are included in Chapter 2. Chapter 4 and Chapter 6 arebased in full on the paper, with the addition of brief introduction, expandedmodelconfiguration description and ’Big picture’ sections.For both publications, I was responsible for conceptualization, experimental de-sign, methodology, analysis and visualization. Roland Stull was involved in conceptformation, manuscript composition and provided supervisory support throughout thepublishing process and the dissertation.DatasetsSynthetic wildfire plume dataset produced for this dissertation is available via Feder-ated Research Data Repository (FRDR):• Moisseeva N, (2020). WRF-SFIRE LES Synthetic Wildfire Plume Dataset. Fed-erated Research Data Repository. https://doi.org/10.20383/102.0314.vExternally-sourced graphicsThe following figures and their corresponding original sources are included in Chap-ter 2 of the dissertation:• Figure 1.1: Dalyup bushfire [48]• Figure 2.2: Smoke modelling framework schematic. Figure produced by ChrisRodell for internal report to Natural Resources Canada.• Figure 2.3: Process diagram for RxCADRE project [54]• Figure 2.4: Conceptual diagram of spatial scales captured by field campaigns[61]Open-source softwareSmoke and trajectory visualizations included in Chapter 3 and Chapter 5 were pro-duced using VAPOR open-source software [13].viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Overview of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Background: wildfire smoke in the atmosphere . . . . . . . . . . . . . . . . 42.1 Context: air quality and smoke modelling frameworks . . . . . . . . . . . 52.2 Overview of existing parameterizations . . . . . . . . . . . . . . . . . . . 72.3 Sources of evaluation data . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Related work on numerical studies of plume dynamics . . . . . . . . . . 112.5 Knowledge gaps and research questions . . . . . . . . . . . . . . . . . . 123 Proof of concept: Capturing plume rise and dispersion with a large-eddysimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1.1 Observational data . . . . . . . . . . . . . . . . . . . . . . . . . . 15vii3.1.2 Numerical configuration . . . . . . . . . . . . . . . . . . . . . . . 173.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2.1 Fire behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2.2 Plume dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.1 Vertical plume rise in the boundary layer . . . . . . . . . . . . . . 273.3.2 Importance of fire input parameters . . . . . . . . . . . . . . . . . 293.3.3 ROS and biases in modelled emissions . . . . . . . . . . . . . . . 313.3.4 Experimental design considerations . . . . . . . . . . . . . . . . . 313.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4.2 Big picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 Synthetic data: Simulating smoke plumes under a wide range of fire andatmospheric conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1 Generating plume data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1.1 Numerical configuration . . . . . . . . . . . . . . . . . . . . . . . 354.1.2 Test conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.2 Defining smoke injection height . . . . . . . . . . . . . . . . . . . . . . . 424.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3.2 Big picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 Fire-atmosphere coupling: qualitative analysis of local-scale dynamics . . 455.1 Fire-induced winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.2 Vorticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.3 Effects of fireline length . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.4 Modulation of the fire by passing ambient thermals . . . . . . . . . . . . 545.5 Plume mixing and the boundary layer . . . . . . . . . . . . . . . . . . . . 555.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.6.1 Big picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576 Smoke injection height: A simple energy balance parameterization for pen-etrative plumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.2 Model evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.2.1 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 63viii6.2.2 Model sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.2.3 Evaluation with observations . . . . . . . . . . . . . . . . . . . . . 656.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686.3.1 Context and applications . . . . . . . . . . . . . . . . . . . . . . . 686.3.2 Dimensionless relationship . . . . . . . . . . . . . . . . . . . . . . 706.3.3 Model bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.4.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726.4.2 Big picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 Beyond injection height: Modelling the distribution of smoke in the atmo-sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747.1 Plume classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747.2 Predicting smoke distribution above zCL . . . . . . . . . . . . . . . . . . . 767.2.1 Determining maximum rise . . . . . . . . . . . . . . . . . . . . . . 767.2.2 Determining spread above zCL . . . . . . . . . . . . . . . . . . . . 787.3 Predicting smoke distribution below zCL . . . . . . . . . . . . . . . . . . . 817.3.1 Accounting for ambient environmental mixing in the ABL . . . . . 817.3.2 Estimating errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 827.4 Distributing smoke laterally . . . . . . . . . . . . . . . . . . . . . . . . . . 837.5 Summary of approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877.6 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877.6.1 Big picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 888 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 898.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 918.2 What’s ahead? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93A Working with synthetic data . . . . . . . . . . . . . . . . . . . . . . . . . . . 101A.1 Initialization files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101A.2 Sample non-penetrative plume . . . . . . . . . . . . . . . . . . . . . . . . 101A.3 Identifying quasi-stationarity . . . . . . . . . . . . . . . . . . . . . . . . . 102A.4 Access to plume dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . 102ixB Plume rise scheme: mathematical formulations and implementation . . . . 103B.1 Expanded form of plume penetration equation . . . . . . . . . . . . . . . 103B.2 Expressions for w f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104B.3 Estimating model input parameters . . . . . . . . . . . . . . . . . . . . . 105B.4 Iterative solution for zCL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106xList of TablesTable 3.1 Numerical configuration for RxCADRE simulation . . . . . . . . . . . . 19Table 3.2 Fire and ignition parameters . . . . . . . . . . . . . . . . . . . . . . . . 20Table 4.1 Model configuration for synthetic dataset . . . . . . . . . . . . . . . . 37Table 4.2 Test conditions and ranges . . . . . . . . . . . . . . . . . . . . . . . . 37Table 4.3 Combinations of test conditions in LES dataset . . . . . . . . . . . . . 40Table 4.4 Fuel condition combinations and exclusions . . . . . . . . . . . . . . 41Table 7.1 Plume classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table B.1 Input variables and units . . . . . . . . . . . . . . . . . . . . . . . . . . 105xiList of FiguresFigure 1.1 Dalyup bushfire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Figure 2.1 BlueSky Canada smoke forecast map . . . . . . . . . . . . . . . . . . 6Figure 2.2 Smoke modelling framework schematic . . . . . . . . . . . . . . . . 7Figure 2.3 RxCADRE process diagram . . . . . . . . . . . . . . . . . . . . . . . . 10Figure 2.4 Field campaigns and their spatial scales . . . . . . . . . . . . . . . . 11Figure 3.1 L2G ignition pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Figure 3.2 Surface heat flux timeseries . . . . . . . . . . . . . . . . . . . . . . . 18Figure 3.3 WRF-SFIRE simulation of L2G burn . . . . . . . . . . . . . . . . . . . 21Figure 3.4 Fire behavior evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 3.5 Evaluation of WRF-SFIRE smoke dispersion . . . . . . . . . . . . . . 26Figure 3.6 Evaluation of WRF-SFIRE plume rise . . . . . . . . . . . . . . . . . . . 27Figure 3.7 Vertical smoke distribution under changing winds . . . . . . . . . . . 29Figure 3.8 Temporal evolution of domain-average smoke column . . . . . . . . 30Figure 3.9 Surface wind timeseries . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 4.1 Pre-ignition potential temperature profiles . . . . . . . . . . . . . . . 38Figure 4.2 Extracting smoke injection height from LES . . . . . . . . . . . . . . 43Figure 5.1 Fire-induced flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 5.2 Lateral vortex formation . . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 5.3 Lateral winds and fireline curvature . . . . . . . . . . . . . . . . . . . 50Figure 5.4 Fireline length and fire-induced winds: mean cross sections . . . . . 52Figure 5.5 Fire-induced winds: slice through the mixed layer . . . . . . . . . . . 53Figure 5.6 Normalized vertical smoke distributions . . . . . . . . . . . . . . . . 54Figure 5.7 Multi-vortex structure of long fireline plumes . . . . . . . . . . . . . . 55Figure 5.8 Plume vs. ambient potential temperature profile . . . . . . . . . . . . 56Figure 5.9 Conserved variable plot . . . . . . . . . . . . . . . . . . . . . . . . . . 57xiiFigure 6.1 Scatter plot of true and modelled injection heights . . . . . . . . . . 62Figure 6.2 Idealized potential temperature profile . . . . . . . . . . . . . . . . . 63Figure 6.3 Error statistics: iterative solution . . . . . . . . . . . . . . . . . . . . . 64Figure 6.4 Error statistics: explicit solution . . . . . . . . . . . . . . . . . . . . . 65Figure 6.5 Model sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 6.6 Smoke injection predictions for RxCADRE . . . . . . . . . . . . . . . 68Figure 6.7 Similarity solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Figure 7.1 Maximum plume penetration distance . . . . . . . . . . . . . . . . . 77Figure 7.2 Sample smoke profile fit: low wind . . . . . . . . . . . . . . . . . . . 79Figure 7.3 Sample smoke profile fit: high wind . . . . . . . . . . . . . . . . . . . 80Figure 7.4 MAE of parameterized smoke distributions . . . . . . . . . . . . . . . 83Figure 7.5 Lateral smoke distribution . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 7.6 Parameters affecting lateral smoke spread . . . . . . . . . . . . . . . 86Figure A.1 Sample ABL plume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101xiiiGlossaryABL atmospheric boundary layerAGL above ground levelAWI along-wind integratedCALIOP Cloud-Aerosol Lidar with Orthogonal PolarizationCAWFE Coupled Atmosphere Wildland Fire-EnvironmentCO carbon monoxideCWI crosswind-integratedFASMEE Fire and Smoke Model Evaluation ExperimentFBP fire behavior packageFIREX-AQ Fire Influence on Regional to Global Environments and Air QualityFRP fire radiative powerxivHIP Highly Instrumented PlotIQR interquartile rangeKE kinetic energy per unit massLES large-eddy simulationLHS left-hand sideLWIR Long Wave InfraredMAE mean absolute errorMINX MISR INteractive eXplorerMISR Multi-angle Imaging Spectro-RadiometerNASA National Aeronautics and Space AdministrationNOAA National Oceanic and Atmospheric AdministrationPE potential energy per unit massPM particulate matterRANS Reynolds-averaged Navier–StokesxvRHS right-hand sideROS rate of spreadRxCADRE Prescribed Fire Combustion and Atmospheric Dynamics Research Experi-mentTKE turbulence kinetic energyWFDS Wildland-Urban-Interface Fire Dynamics SimulatorWRF Weather Research and Forecasting ModelWRF-SFIRE Weather Research and Forecasting Model (WRF) combined with a semi-empirical Spread Fire modelxviAcknowledgmentsSupervisory committee: This dissertation would not be possible without my supervi-sor Roland Stull. Roland’s unwavering optimism, a firm belief that ’no challenge is toobig (or too small)’ and genuine enthusiasm have been a continuous source of moti-vation. Following his lead, I learned a tremendous amount about how to methodicallyuntangle complex scientific ideas and even more about how to communicate them.Roland’s care for the team (from uninterrupted supply of quick carbohydrates to late-night Slack consultations) and incredible passion for teaching reflect his mission ofalways putting students first. Most importantly, I want to thank Roland for giving methe opportunity to follow my own path, be it drifting off the team’s weather predictiontracks or stepping away from research altogether to grow a family. I am deeply gratefulfor his support through each and every turn along the way.Having Douw Steyn’s guidance for over a decade has been an incredible privilege.While Douw’s formal status within my academic life has continually evolved, he hasinvariably remained my mentor. Never too far away to offer advice and support, hecontinually cultivatedmy scientific curiosity and has profoundly influencedmy thinkingas a researcher. Most of the academic opportunities and experiences I have beenfortunate to enjoy, I owe to Douw’s kindhearted belief in my abilities many years priorto my making a first scientific contribution.I want to thank Phil Austin for being willing to be ’entrained’ into my advisory com-mittee at a later stage of the dissertation. While his formal membership is fairly recent,Phil’s guidance and far-sighted scientific computing advice date back tomy early yearsat UBC. His decade-long vision, mixed with extraordinary erudition and academic hu-mor, turns any of his instructional talks into an indulging intellectual workout. Phil’sability to answer questions that have yet to ripen in a young researcher’s head is trulyfascinating.I’d also like to thank Neil Balmforth for navigating me through half-century oldliterature on fluid dynamics fundamentals that curiously remained so topical, I revisitedit at every stage of this dissertation.xviiColleagues: Being a member of such a large and diverse research group has trulybeen a privilege. I want to thank Rosie Howard for her guidance on the doctoral path,her compassionate teamwork as well as for my newly acquired belief in human super-power. Thank you to Chris Rodell for his contagious enthusiasm to take on any novelchallenge, openness and virtuoso ability to connect people. The support of our ’FireTeam’ has been integral.I want to sincerely thank Julia Jiworrek for her generous help with cluster accessand Tim Chui for helping me (among a million other things) experiment with cloudcomputing. I also want to acknowledge Greg West, David Siuta andMaggie Campbellfor their guidance on my early projects.This work would not be possible without my family. I struggle to find words toexpress how deeply grateful I am to my parents. From my core values to any modestachievement, I owe it to their unconditional love and support. Thank you tomy husbandLukasz for making sure I laugh daily and to my son Alik for redefining ’curiosity’. It trulytakes a village to raise a researcher.xviiiChapter 1IntroductionWildfire smoke is a complex and dynamic pollutant. As wildfires become more fre-quent and intense under the changing global climate, smoke pollution is quickly emerg-ing as one of the key issues facing air quality in the coming decades. Our ability topredict where and how smoke travels is crucial to mitigating its negative impacts forhuman health and the environment.What is wildfire smoke plume rise? Intense heat above the fire creates updrafts,which simultaneously mix with and modify the ambient environment. These turbulentcolumns of hot air mixed with fire emissions are referred to as a plumes. The termplume rise is typically used to describe the initial buoyant phase of a smoke plume,which determines how high in the atmosphere the pollutants will travel.Why is understanding smoke plume rise important? The ability to predict wherein the atmosphere the majority of the smoke is released is key to accurately capturingsubsequent pollutant dispersion. Due to vertical wind shear, small errors in plume risepredictions can have profound consequences for downwind dispersion and forecastsmoke concentrations at the earth’s surface. Figure 1.1 is a striking example of howsharply the wind direction can change between various levels of the atmosphere. Thisis why plume rise is often the pivotal point in smoke modelling process.What are the challenges? Fundamental to understanding any physical process aregood observations. Yet detailed and temporally linked 3D measurements of smokedispersion and fire behavior are notoriously scarce. Moreover, wildfire plume dynamicsinvolve complex nonlinear interactions and feedbacks between the fire and ambientatmosphere, which operate over a wide range of spatiotemporal scales. All thesefactors present a challenge for both modellers and experimentalists. This work aimsto explore some of these challenges with the goal of improving our understanding ofsmoke plume rise dynamics.1Figure 1.1: Dalyup bushfire January 10, 2016 (Esperance, Australia) [48]1.1 Overview of thesisWildfire dynamics are inherently an interdisciplinary scientific field. Hence, I beginby setting up the background for the thesis specifically in the context of air quality.Chapter 2 briefly summarizes the current state of knowledge and introduces smokemodelling frameworks (Section 2.1), plume rise parameterizations used within thesesystems (Section 2.2) and data sources available for their evaluation (Section 2.3).I discuss why coupled fire-atmosphere numerical models are gaining attention (Sec-tion 2.4) and outline the path forward for this thesis (Section 2.5).The next part of the thesis focuses on a numerical modelling tool key to this work:the Weather Research and Forecasting Model (WRF) combined with a semi-empiricalSpread Fire model (WRF-SFIRE). Chapter 3 summarizes my effort in evaluating themodel, while Chapter 4 provides details of how I use WRF-SFIRE to generate surrogatesmoke plume data. This "synthetic" dataset is explored in Chapter 5, to gain insightsinto how the fire interacts with the atmosphere (Section 5.1), breaks into multiple ro-tating cores (Section 5.2 - Section 5.4) and entrains ambient environmental air (Sec-tion 5.5).In the remaining part of the thesis I step away from numerics and attempt to trans-late the knowledge gained from the simulations into a simple analytical method forpredicting plume rise. Chapter 6 describes an energy-balance approach for estimating2mean injection height of a smoke plume for a fire of arbitrary shape and intensity. Iconstrain and evaluate the proposed method with both numerical and observationaldata (Section 6.1 - Section 6.2), and demonstrate that there exists a linear dimen-sionless relationship between updraft velocity and plume vertical penetration distance(Section 6.3). Chapter 7 builds on this energy-balance approach, extending themethodto parameterize the full vertical distribution of smoke in the atmosphere.I conclude with a brief summary of key contributions of this thesis.1.2 PurposeMy doctoral studies spanned some of the most devastating wildfire events both closeto home (e.g. FortMcMurray Fire of 2016) and globally (e.g. Australian "Black Summer"andCaliforniawildfires of 2020). It is no coincidence, that thewildfire smokemodellingcommunity has grown immensely in just the last few years. Yet the complex nature ofwildfires makes for a uniquely interdisciplinary challenge to the scientific community.Current state of knowledge is a product of collaborative effort between atmosphericphysicists, chemists, fire scientists, forestry and remote sensing experts, amongmanyothers.This thesis is written with air quality researchers in mind. Each chapter concludeswith a brief summary outlining its main purpose and/or contributions from a perspec-tive of an atmospheric modeller. Yet many challenges and limitations of this work layat the interface of multiple disciplines. For this reason, I added a "Big Picture" sectionat the end of each chapter. I hope this will help provide context, grasp the range ofscales and perspectives involved and establish a common ground with researchers inother disciplines working to better our understanding of wildfire dynamics.3Chapter 2Background: wildfire smoke in theatmosphereWildland fires are a fundamental global feature of the Earth system [5]. They covera broad range of spatiotemporal scales and are shaped by the complex interactionsof fuel, terrain, and meteorological conditions. Intense heat released during a wild-land fire initiates convection, creating a rising smoke plume. This vertical transport ofbyproducts of combustion, including aerosols and trace gases, combined with com-plex dynamical feedbacks between the fire and ambientmeteorological conditions, setwildfire smoke aside from other atmospheric pollutants [56].Fire emissions can be injected far above the atmospheric boundary layer (ABL),making them susceptible to long-range transport. Such penetrative smoke plumes(i.e. plumes rising above the ABL), have far-reaching effects for chemical compositionof the atmosphere, weather and climate. Plumes confined to the ABL, on the otherhand, have direct impact on air quality on a local scale [38]. Between these extremesare plumes that penetrate, but remain near the ABL, in the region often associatedwith strong vertical windshear [70]. In some cases, a significant portion of the smokeassociated with such plumes remains trapped in the ABL. Our ability to predict sub-sequent dispersion of pollutants and their impact, is hence, extremely sensitive to thedynamics of the initial buoyant phase of the smoke plume. Yet our understanding ofplume rise has been limited due to both the complex nature of the phenomenon aswell as challenges in obtaining detailed observations of smoke plumes.In this chapter, I summarize our current state of knowledge of smoke plume risedynamics. The first section sets the stage for examining plume rise in the context ofair quality, highlighting the importance of smoke modelling and it’s implications forhuman health and the environment (Section 2.1). Next, Section 2.2 provides a briefoverview of existing plume-rise parameterizations and discusses their implementation4within smoke modelling frameworks, noting the strengths and limitations of each ap-proach. Section 2.3 summarizes common data sources used for creating, evaluatingand constraining the above parameterizations, highlighting the gaps in the availableobservational data. The following Section 2.4 then takes a numerical perspective onstudying plume rise dynamics, reviewing existing tools as well as modelling experi-ments. The last portion of the chapter (Section 2.5) synthesizes the knowledge gapsand charts the forward path for this thesis.2.1 Context: air quality and smoke modelling frameworksWildfire emissions contain a wide range of pollutants, widely recognized as a hazardfor human health, including carbon monoxide (CO), nitrogen dioxide, ozone, particu-late matter (PM), polycyclic aromatic hydrocarbons, and volatile organic compoundsand many others [29, 63]. Epidemiologists have repeatedly linked smoke exposure torespiratorymorbidity, as well as overall increasedmortality from all causes [23, 30, 47].The ability of smoke dispersion models to make timely and accurate predictionsof the development, spread and intensity of smoke events is central to successfulmitigation of negative impacts for communities downwind. Typically, decision mak-ers in a wide range of sectors, including health (public advisories and evacuations),transportation (safety), tourism (nuisance), weather forecasters (public advisories),wildfire response (downwind effects), and the public (health, nuisance), rely on smokemodelling frameworks to forecast surface pollutant concentrations from wildfires.In North America several numerical air quality forecasting systems exist, which aimto capture emissions from wildfires. These include the BlueSky Framework operatedby the US Forestry Service [39] and its Canadian version (BlueSky Canada, Figure 2.1)operated by the University of British Columbia [66], High-Resolution Rapid Refresh-Smoke system from the USNational Oceanic and Atmospheric Administration [2], WRFcoupled with Community Multiscale Air Quality model (WRF-CMAQ) used by the USNational Weather Service [40], AIRPACT system operated by Washington State Univer-sity [76] and the FireWork framework developed by Environment and Climate ChangeCanada [9]. While these systems differ in their approach, they typically share keycomponents summarized in Figure 2.2.Satellite and ground observations of "hot spots" are used to identify wildfire lo-cations and sizes. This information is combined with fuel data to model emissionsproduced by combustion. Using meteorology from numerical weather forecasts, thevertical distribution of these emissions in the atmosphere is parameterized. From5Figure 2.1: Surface PM2.5 forecast produced by BlueSky Canada smokemodellingframework.there smoke dispersion is simulated (through either directly coupling chemistry withthe numerical weather model or carrying out trajectory analysis). Typically, the outputof such smoke modelling frameworks includes surface smoke concentrations (Fig-ure 2.1) or column-integrated values, which can be compared with surface pollutionobservations or satellite data, respectively.Traditionally, many operational smoke modelling frameworks relied on plume riseequations originally developed by Briggs [6] for industrial smokestacks [39, 57] to pre-dict the vertical distribution of emissions in the atmosphere. Yet several studies sug-gest that this approach may not be appropriate for wildfires [20, 22, 57, 62]. Never-the-less, the Briggs plume rise scheme remains widely used today, hosted within well-established air quality and dispersion models such as HYSPLIT, CMAQ, and in theoperational versions of BlueSky and FireWork, while often being recognized as a weaklink within these systems [9, 74]. As a result, plume rise parameterization developmentremains an active area of research.6Figure 2.2: Simple schematic showing a typical structure of a smoke modellingframework. Figure produced by Chris Rodell for internal report.2.2 Overview of existing parameterizationsExisting smoke plume prediction models span a vast range of complexity from simpleempirical relations to themore recent coupled fire-atmosphere numerical approaches.Often the choice of model is dictated by the context of its application, subject to thetrade-off between fidelity and timely execution. Typically, full-physics models, whilebeing able to resolve the complexity of wildfire plumes, are too slow or computationallyintensive to be used operationally [1]. Hence, simplified parameterizations are neededto make plume rise data available in a timely manner for large modelling domains withmultiple active emission sources.For clarity, from hereon I’ll refer to numerical models used for forecastingmeteorol-ogy (e.g. WRF) and creating highly-detailed simulations of the atmosphere (e.g. large-eddy simulations (LES)) asmodels. Simplified plume rise formulations typically hostedwithin air quality modelling systems will be referred to as parameterizations. Thedistinction is vital, as the goal of this thesis is to develop a plume rise parameterizationwith the help of a numerical model.In a recent review of existing plume rise parameterizations, Paugam et al. [56]highlight three notable schemes that stand out in literature, as that of Freitas et al. [20],Sofiev et al. [69] and Rio et al. [64]. Both Freitas and Rio’s methods use first principlesto characterize plume temperature, vertical velocity and entrainment. While the former7provides prognostic 1-D equations that can be solved as a stand-alone "offline" model,the latter is implemented as a sub-grid effect within a host chemistry transport model.Notably, both consider an idealized heat source to represent the fire. While subject toadditional complexity and computational cost, the prognostic nature of these schemesoffers an advantage over purely empirical or statistical methods under rapidly chang-ing meteorological conditions. Another strength of these parameterizations, which isparticularly important for global chemical transport modelling applications, is the in-clusion of latent heat effects. Extreme pyroconvective plumes (classified as "flamma-genitus" [52]) can gain additional buoyancy from energy released due to condensation[58]. While such events are not common [74], they can have a significant impact foratmospheric circulation on a global scale.Sofiev’s semi-empirical approach relies on energy balance and dimensional analy-sis [69], while using satellite data to both initialize and constrain the parameterization.The convenience of the method lies in the fact that it only relies on three input param-eters (ABL height, Brunt-Vaïsälä frequency of the free troposphere and fire radiativepower (FRP)) to obtain a smoke injection height estimate. The main limitation of thescheme, as expressed by Paugam et al. [56], is the exclusion of condensation andcloud formation from the scheme.Another thermodynamics-based scheme was recently introduced within the exper-imental version of FireWork model [9]. The approach is based on a method developedby Anderson et al. [4], which aims to quantify the energy release of the fire and usesenvironmental and dry adiabatic lapse rates to estimate the vertical distribution ofsmoke.Unlike Briggs’s equations, all of the above models address wildfire plumes specif-ically, yet much research is needed to reduce the large prediction uncertainties [42].Moreover, it is unclear, whether unreliable predictions should be attributed to the fire in-put parameters or the plume rise scheme itself. One of the central challenges in plumerise parameterization development has been the scarcity of comprehensive modelevaluation data [15, 54]. Key sources of observational data and their correspondinglimitations are summarized in the following section.2.3 Sources of evaluation dataOne of the challenges in obtaining a comprehensive dataset for evaluation of smokeplume-rise schemes is the fact that wildfires operate on a broad range of spatial andtemporal scales. Fuel combustion, which is affected by the size, density and chemical8properties of individual fuel elements as well as ambient environmental conditions,operates on micro- and local- scales. Smoke dispersion, on the other hand, can rangefrom local to global scales, affected by both thermodynamics of the plume and mete-orology.To date, information on wildfire smoke emissions and dispersion has largely beenderived from two distinct sources: remotely sensed data and prescribed burn cam-paigns. The "gold standard" for satellite plume observations has been the Multi-angleImaging Spectro-Radiometer (MISR) instrument on board the Terra satellite [31]. Thevertical distribution of aerosols can be reconstructed fromMISR images with a stereo-scopic altitude retrieval algorithm with roughly 500 m accuracy, typically aided by theMISR INteractive eXplorer (MINX) software tool [51]. MISR data has allowed for thedevelopment of plume "climatologies" over various global regions. Based on suchcomprehensive efforts [31, 73, 75], we know that only a small portion of wildfire smokeplumes are injected above the ABL (4-12%), and vast majority of plumes that do reachthe free troposphere (83%) remain in the stable layers just above the ABL. A majordrawback of usingMISR data is that there is noway to differentiate clouds from smokeor dust. Also, the satellite overpass times are limited to morning hours, when wildfiresare weakest and when the plumes have not fully matured [56, 75].Smoke plume heights can also be obtained from the Cloud-Aerosol Lidar with Or-thogonal Polarization (CALIOP), operated on board the CALIPSO satellite. With muchbetter spatial (120 m in the vertical) and temporal resolution, daytime overpasses andability to differentiate aerosols it offers several advantages overMISR. However, due toextremely narrow swath width (and, hence, infrequent overpasses)most of the plumesare not captured by CALIOP [31]. Apart from specific limitations of individual sensorsand satellites, a common problem with remotely sensed data is obstruction by cloudsand overall lack of direct spatiotemporal links to fire behavior [27]. As a result, untilrecently, evaluation of smoke plume models required a combination of studies, as nodataset was complete enough to rigorously constrain the problem [15].To address this critical need for a comprehensivemodel evaluation dataset severalfield campaigns have taken place in recent years, ranging in scope and scale. FireFluxexperiments I and II [10, 12] focused onmicrometeorology and fire-atmosphere interac-tions. Themain goalwas to provide detailedmeasurements for evaluating fire behaviortools and next-generation physics-based fire models.A collaborative effort between National Oceanic and Atmospheric Administration(NOAA) and National Aeronautics and Space Administration (NASA) called Fire Influ-ence onRegional to Global Environments andAir Quality (FIREX-AQ)was designedwith9Figure 2.3: Process diagram for RxCADRE project, including a partial list of mea-sured variables (figure extracted from [54]).a focus on emissions and chemistry [65]. The campaign included a strong airbornecomponent, allowing to track plumes downwind to assess chemical transformationsand air quality impacts, but failed to provide any fire characterization data critical fromthe standpoint of plume-rise modelling.Oneof themost diverse comprehensive campaigns to date has been thePrescribedFire Combustion and Atmospheric Dynamics Research Experiment (RxCADRE) [54].The project brought together researchers from a wide range of disciplines to collectdata on fuel, meteorology, fire behavior, energy, smoke emissions and fire effects. Ex-perimental burns captured by this campaign required extensive planning, managementand coordination, but produced a well-integrated dataset spanning a wide range ofmeasurement techniques, as illustrated in Figure 2.3. Another important aspect ofRxCADRE dataset is that it captures a range of spatiotemporal scales most relevant toevaluation of coupled fire-atmosphere numerical models (Figure 2.4).Due to success of RxCADRE an even more extensive and complex Fire and SmokeModel Evaluation Experiment (FASMEE) is currently underway [61]. While still in earlystages, the campaign is focused on large wildfires and aims to provide detailed mutli-10Figure 2.4: Conceptual diagram of spatial scales captured by various field cam-paigns (figure extracted from [61]).scale observations ranging from local to regional scale (Figure 2.4).While comprehensive field experiments summarized above provide the necessarylevel of detail for model evaluation studies, they typically capture a modest range offire and atmospheric conditions. Given the required coordinated effort (as shown inFigure 2.3) and high costs of such campaigns, the use of "synthetic" numerical experi-ment "data" produced by coupled fire-atmosphere models has been gaining attention,as described in the following section.2.4 Related work on numerical studies of plume dynamicsRapid increase in computational power in the recent years has aided the develop-ment of complex physics-based numerical models, that allow fire-atmosphere cou-pling. Several such models exist today, covering a range of scales and various levelsof idealization of the modelled fire and atmosphere.Wildland-Urban-Interface Fire Dynamics Simulator (WFDS) [49] and FIRETEC [41]explicitly resolve combustion and, hence, require very fine model grid (on the order ofmeters). The advantage is that fire behavior is captured without the use of simplifyingparameterizations. High computational demand of such systems, however, typicallylimits the size of modelled domains to less than 1 km2 [61].In contrast, WRF-SFIRE [45, 46], MesoNH-ForeFire [18], and Coupled Atmosphere11Wildland Fire-Environment (CAWFE) [14] have a strong focus on the atmosphere. Firebehavior is parameterized allowing faster run time and larger scale simulations thanthose performedwithWFDS and FIRETEC [61]. Plume dynamics, however, are resolvedto the level of detail which can hardly be matched by even the most extensive obser-vational campaign. This is typically made possible by the use of large-eddy simula-tions (LES): a computational fluid dynamics method that explicitly resolves turbulentatmospheric motion, while only parameterizing small-scale eddies. It is, therefore,critical to confirm whether the output of such models is physically realistic.Overall, WRF-SFIRE has been one of the most actively developed models. Severalstudies have examined its ability to capture the ground-spread behavior of a fire line,near-surface temperatures andwinds [34, 35]. Large-scale simulations of two real fireswere carried out [36], comparing modelled plume tops with satellite data. Notably,WRF-SFIRE was recently used to capture radiative feedbacks between the smoke andthe atmosphere [37] in a first study of its kind. Current developmental work includes theaddition of canopy parameterization, which accounts for the effects of modified windprofile over forested land types [44]. Promising results of the above modelling studies,as well as the presence of an active development community, were key in selectingWRF-SFIRE as the central tool for this thesis.While a growing number of evaluation studies of coupled fire-atmosphere modelsare encouraging, there remains a general lack of research focusing on the verticaldistribution of smoke emissions in the atmosphere [42]. This knowledge gap can, inpart, be explained by the difficulty of constraining potential sources of error in bothinputs and the model itself.2.5 Knowledge gaps and research questionsWhile, at first, modelling plume rise may appear to be purely an atmospheric dynamicsexercise, the subject is truly interdisciplinary in nature. Many aspects of plume risemodelling lie at the interface of atmospheric physics, fire behavior science, numericalmethods, air quality, meteorology and remote sensing. This section aims to recapwhat we know from each field and to identify the existing gaps in our knowledge, whileputting together a road map for the thesis.What are the challenges in modelling wildfire smoke? Smoke is a harmful pollu-tant. Understanding its movement in the atmosphere (and being able to predict it) iscrucial to mitigating negative air quality impacts. A weak link in our effort to modelsmoke pollution is plume rise dynamics. Remotely sensed data suggests that vast12majority of the plumes remain in or near the ABL [73]. However, the ability to determinewhich plumes will remain in the ABL vs. penetrate it and reach the free troposphereis critical for accurate downwind smoke predictions [69]. In addition, the penetrationdistance within the free troposphere canmatter significantly due to vertical wind shear[75].Complex combustion-resolvingmodels are too slow and computationally intensiveto be useful for operational air quality applications. That is why smoke modellingframeworks typically rely on simplified parameterizations to predict smoke injectionheight. Such parameterizations remain subject to large errors, due to the complexnature of the processes involved, uncertainties associated with fire behavior and thelimited observational data available.How can we address these challenges? Comprehensive model evaluation dataon wildfire smoke plume rise is extremely scarce. Recent developments in coupledfire-atmosphere models offer an opportunity to examine plume rise from a numericalperspective. This approach, however, still needs to be evaluated. This dissertationaims to make a contribution at the interface of numerical and analytical modelling,guided by the following broad research questions:• Can a coupled fire-atmosphere numerical model accurately simulate smokeplume rise from a real fire?The focus of Chapter 3 is to provide a "proof of concept" for using WRF-SFIRE tosimulate plume dynamics, using a real-life case study from the RxCADRE cam-paign. Based on the results of this model evaluation, Chapter 4 introduces asynthetic plume dataset, capturing a wide range of fire and atmospheric condi-tions.• What can we learn about the behavior of the atmosphere around the fire fromnumerical experiments?Chapter 5 examines the effects of various fire parameters and environmentalconditions onmodelled plume rise using the simulations described in Chapter 4.• Can synthetic data be used to parameterize smoke plume rise for air qualityapplications?Based on insights gained from the numerical experiments, Chapter 6 introducesa simple energy-balance plume rise parameterization to estimate themean smokeinjection height for penetrative plumes. Chapter 7 then extends this approach to13predict the full vertical distribution of smoke in the atmosphere. Lastly, Chapter 8summarizes the main contributions of this thesis.While the broad research topics above highlight the overarching goals of this work,each chapter will introduce more specific questions to help focus and guide this in-vestingation.14Chapter 3Proof of concept: Capturing plume rise anddispersion with a large-eddy simulationPlume rise is a result of a complex set of physical phenomena, spanning multiplespatiotemporal scales. Until recently comprehensive integrated datasets, combiningmeasurements of fire behavior, meteorology and smoke dispersion were not available[61]. Hence, evaluation studies of coupled fire-atmospheric models focusing on plumerise are scarce [42].RxCADRE, a recent mutli-scale prescribed burn campaign designed to address thisneed [54], provides a rare opportunity to examine the ability of a coupled fire-atmospheremodel (WRF-SFIRE) to capture smoke plume dynamics. In this chapter, I hope to pro-vide a "proof of concept" for using WRF-SFIRE simulations as a surrogate for real-lifeobservational data.Note that the main focus of this chapter is the evaluation of the model’s abilityto capture the atmospheric response to a simulated fire of known bulk properties,rather than the fire behavior itself. Effectively, the work aims to validate the relation-ship between the simulated surface forcing due to a fire and the resultant turbulentconvection.3.1 Methods3.1.1 Observational dataThe RxCADRE campaign consisted of 10 operational and 6 small replicate prescribedfires in Florida. Collected data are accessible via a US Forest Service online repository,as referenced below. Smoke dispersion and emissions measurements are availablefor three large fires: L1G and L2G grass fires and L2F sub-forest canopy surface fire.15Figure 3.1: Long Wave Infrared (LWIR) image of L2G plot during ignition (12:32:02CST) with dashed black lines denoting burn perimeters. Red scatter points cor-respond to Highly Instrumented Plot (HIP) #1 fire behavior package (FBP), eachcontaining a system of airflow, temperature and energy sensors. Data source:RxCADRE field experiment [24–26].For the purpose of model evaluation, I selected L2G (10 November 2012) grassland fireas a case study, based on its reported uniformity and consistency of flame propagation[7]. Figure 3.1 shows a sample snapshot of the burn plot during the ignition. The overallmeteorological conditions and instrumental design of the L2G experimental burn aredescribed in detail in Clements et al. [11]. The individual datasets obtained from the USForest Service online archive used for this study are summarized below.Georeferencing data, including plot location and burn perimeters, are available fromHudak and Bright [25]. Analysis of fire rate of spread (ROS) and intensity as well as a16detailed description of three Highly Instrumented Plots (HIPs) used to produce theestimates can be found in Butler et al. [7]. Locations of HIPs are available from Hudaket al. [24]. HIP1, used for this evaluation, is shown in Figure 3.1. Near-surface wind andtemperature sonic anemometer time series for in-situ and background locations areavailable fromSeto andClements [67, 68]. Ignitions timing and locationswere obtainedfrom field-grade GPS units, mounted on-board firing vehicles [26]. Fuel data usedfor this evaluation study included photographs of pre-burn samples, as well as mea-surements of size, loading and moisture content of species groups. Data collectionmethodology is detailed in [53]. Dispersion and emissions measurements includedvolume-mixing ratio of CO2, CO, CH4, and water vapor at a rate of 0.5 Hz, obtainedfrom aircraft-mounted sensors [72]. The georeferenced data consisted of horizontaltransects at multiple elevations, as well as "corkscrew" and "parking garage" flightprofiles.3.1.2 Numerical configurationI configured WRF-SFIRE [45, 46] in idealized LESmode. One of the primary advantagesof using this model is that it allows for two-way coupling between fire and the atmo-sphere. WhileWRF-SFIRE does notmodel combustion directly, the spread and intensityof the fire are parameterized using a semi-empirical approach. The latent heat flux iscomputed based on the fuel consumption and stoichiometric combustion of cellulose.Heat and moisture fluxes from the simulated burn provide forcing to the atmosphere,which in turn influences fire behavior.A 10.4 km × 14 km domain with 40 m horizontal grid spacing, 3000 m modeltop and 51 hyperbolically stretched vertical levels was initialized using the 10:00 CST(16:00 UTC) sounding [11]. While this may appear to be a shallow domain comparedto mesoscale ("Real") WRF simulations, such model top is substantially higher thanthat found in several existing published WRF-SFIRE evaluation studies [15, 32, 35].Five lowest model grid centers were located at approximately 8 m, 24 m, 42 m, 60m and 80 m above ground level (AGL). I allowed the simulation to spin up the ambientbackground flow for 2 h 23 min prior to ignition at ∼12:23 CST (time varied slightlyfor different firelines). To aid the formation of buoyancy-driven ambient backgroundturbulence typical for a daytime ABL, I imposed a lower-boundary surface thermal flux(tke_heat_flux). The value was estimated from the sonic anemometer time series ofvertical wind velocity and temperature over the time period leading up to ignition. Asshown in Figure 3.2, based on the measurements, the ambient background surfaceheat flux remained fairly constant over the entire spin-up period. Hence, the lower-1710:00 10:20 10:40 11:00 11:20 11:40 12:00 12:20time (CST) heat flux T′ w′  (Kms1 )SURFACE HEAT FLUXFigure 3.2: Five-minute averaged kinematic surface heat flux T ′w′ derived from1 Hz wind and temperature sonic anemometer time series of the backgroundambient environment. Data source: RxCADRE field experiment [68]..boundary surface forcing was idealized for the LES simulation as being uniform inspace and constant in time. I used full surface initialization (sfc_full_init =.true.), withthe lower boundary moisture flux and surface roughness characteristics set to stan-dard USGS values for "Grassland" land use category.To help trigger the ambient background convection in a horizontally uniform initialdomain, I added a small temperature perturbation "bubble". With periodic boundaryconditions, near-stationary turbulence spectrum was achieved within ∼40 min of runstart. The well-mixed modeled ABL continued to turn over and warm for a total of 2 h23 min (10:00:00 CST–12:23:00 CST). I used the restart file generated at 12:23:00 CSTas initial conditions for the main burn simulation (12:23:00 CST–13:12:00 CST), ensur-ing the fire was ignited into a well developed convective ABL. Other key configurationdetails can be found in Table 3.1, as well as in the complete namelist initialization filesin published supplementary material [50].18Table 3.1: Key parameters of numerical domain setup.Simulation Parameter Value/DescriptionModel version 24 May 2019 (git #ced5955)Horizontal grid spacing 40 mDomain size 260 grids (east-west) × 350 grids (north-south)Time step 0.1 sModel top 3000 m AGLSpinup timing 10:00:00–12:23:00 CST (CST = UTC − 6 h)Fire (restart) simulation timing 12:23:00–13:12:00 CSTSub-grid scale closure 1.5 turbulence kinetic energy (TKE)Lateral boundary conditions periodicSurface physics Monin–Obukhov similarity (sf_sfclay_physics = 1)Land surface model thermal diffusion (sf_surface_physics = 1)Ambient surface heat flux 160 W m−2 (tke_heat_flux = 0.13)Following the LES spin up, I ignited the northwestern half of the simulated L2G plotwith four roughly parallel fire lines mimicking strip head fire method used during thereal-life burn (Figure 3.1). During the campaign, the prescribed burn was ignited withdrip torches attached tomoving all-terrain vehicles (ATVs). Using GPS data from thesevehicles (available from [26]), I extracted the locations of start and end points of thefour firelines, as well as their individual start and end ignition times. While the real-lifeignition process was not perfectly uniform in time, I approximated the modeled firelines as being ignited at a constant speed, such that the time and location of the startand end points matched those of the real burn (see published supplementary material[50]). Timing varied slightly for each of the four modeled firelines. I approximated theignitions as straight lines between observed start and end points, as the ATVs’ deflec-tions from a straight path during the real burn remained within a single atmosphericgrid in my modeled domain.Ignited cells in WRF-SFIRE proceeded to spread, while each fire line continued toadvance until reaching the opposite end of the L2G plot. I excluded subsequent upwindignitions of the remaining plot area to reduce the computational load of the simulation.Taking into account the downwind location and timing of smoke plume observations,this simplification should have no effect on the proposed evaluation. The simulationwas allowed to proceed for 49 min, until the emissions reached the downwind end ofthe domain.Summary of fire and fuel parameters can be found in Table 3.2. Based on pho-tographs and average measurements of fuel size, composition and type, I determined19Table 3.2: Details of fire and ignition parameters in LES setup.Simulation parameter ValueFire mesh refinement 10Ignition duration 12:23–12:36 CST (varied for each fireline)Rate of spread during ignition 0.2 m s−1Fuel category 1 (short grass)Surface dead fuel moisture 8.46%Heat of combustion of dry fuel 1.64×107 J kg−1Anderson’s fuel Category 1 (short grass) [3] to be the best fit for L2G ground cover.Actual burn perimeters were used to mask the remaining domain as containing nofuel to prevent spread of the simulated burn outside of the burn plot. I replaced thestandard fuel loading and depth associated with Type 1 fuels with average measuredvalues of 0.267 kg m−2 and 0.18 m, respectively. Surface dead fuel moisture contentwas set to 8.46% based on observations. I adjusted the heat of combustion of dry fuelto 16.4 × 106 J kg−1 as per estimates for grasslands [55].As the central goal of this work is to evaluate the model’s ability to capture wildfiresmoke plume dynamics, I did not incorporate chemistry coupling into the simulation.Modeled "smoke plume" was represented by two passive tracers released proportion-ally to the mass and type of fuel burned. The rate of release for each tracer repre-senting CO and CO2 was controlled by assigned emission factors, based on values forgrasslands provided by Prichard et al. [60].3.2 ResultsThe overall evolution of the simulated L2G burn and the associated smoke plume isbest visualized with a 3D animation (see Animation S1 in published supplementarymaterial [50]). Figure 3.3 shows a still image of the simulated smoke plume at the endof the animation. The supplement [50] also includes an animated view of the cross-wind modeled CO2 mixing ratio (Animation S2). The latter demonstrates the ability ofthe LES to capture typical plume behavior. As seen in the animation, the initial rise ofmoist buoyant air results in a temporary overshoot of the equilibrium plume height,followed by the gradual settling of the plume to its final injection height near the top ofthe ABL (1060m at the end of LES spinup) for this case. While the ability of WRF-SFIREto qualitatively capture typical plume dynamics is reassuring, the following sectionstake a more quantitative approach to model evaluation.20Figure 3.3: WRF-SFIRE simulation of L2G burn. Modelled fire and smoke aresuperimposed on surface satellite imagery for reference. Figure produced usingVAPOR software [13].3.2.1 Fire behaviorPrior to evaluating the ability of WRF-SFIRE to capture plume rise and dispersion, it isimportant to ensure that the model is able to simulate fire behavior with reasonableaccuracy. Initial surface and fuel conditions have the potential to strongly impact firegrowth and intensity, and, hence, affect the location and buoyancy of the smoke plume.This approach does not constitute a comprehensive fire behavior evaluation study, butrather aims to ensure that WRF-SFIRE captures the bulk properties of combustion andsupplies a reasonable surface forcing to the simulated atmosphere.My evaluation is based on the analysis of fire energy transport of RxCADRE obser-vational data for L2Gburn carried out byButler et al. [7]. The study providesmeasurement-based values as well as error margins for ROS, and peak and average heat fluxes of thefire, which I use to assess the performance of the semi-empirical fire algorithm drivingthe LES simulation.Figure 3.4a,b compares LES-derived average and peak total heat fluxes for HIP1and entire burn area over the flaming period with observations. For HIP1 point-to-pointcomparison, I use output from the nearestmodelled grid points. L2G average observed21values include measurements from all three HIP lots. The corresponding simulatedestimates are calculated using the entire burn area (roughly half of the L2G plot).22L2G HIP1 LES LES HIP10510152025heat flux (kWm2)(a) AVERAGE HEAT FLUXL2G HIP1 LES LES HIP10510152025303540heat flux (kWm2)(b) PEAK HEAT FLUXL2G HIP1 LES LES HIP10. (ms1)(c) ROSFigure 3.4: Comparison of observed (blue) and modeled (red) fire behavior. The box and whiskers span interquartilerange (IQR) and 1.5 × IQR, respectively, with the notch denoting the 95% confidence interval of the median (median±1.57× IQR/n 12 ). Red line and green triangle correspond to median and mean, respectively. (a) Average heat flux duringflaming period. (b) Peak fire heat flux during flaming period. (c) Rate of spread.23The start and end times of the flaming period are defined as simulation frames atwhich total heat flux at the location exceeded 5 kW m−2 [7]. For both burn-wide andpoint comparisons, the flaming period is determined separately for each individual gridpoint. Only ignited grids are included in the analysis. This approach allowsme tomimicthe analysis performed by Butler et al. [7] in the absence of true combustion modelingin WRF-SFIRE.For the entire burn area the observed mean and peak heat fluxes associated withthe fire (not the background environment) are 11 kW m−2 and 20 kW m−2, comparedto LES-derived values of 8.9 kW m−2 and 19 kW m−2, respectively. For HIP1 lot thecorresponding values were 11.4 kW m−2 and 19.4 kW m−2 (observed) versus 8.2 kWm−2 and 13 kW m−2 (modeled). Note that, due to close proximity of the HIP1 sensorsto each other, four out of seven of them fall into the same atmospheric grid within themodeled domain. Modeled HIP1 averages should therefore be treated with caution, asthey consist of only four unique values. Moreover, the large spread of observed HIP1heat fluxes renders the differences betweenmodel andmeasurements not statisticallysignificant. Overall, the results shown in Figure 3.4 suggest that on average the surfacethermal forcing to the modeled atmosphere due to the fire is reasonably captured bythe model, subject to a slight negative bias (significant and non-significant for averageand peak heat fluxes, respectively).Observed rates of spread during the L2G burn were estimated using two methodsin the study by Butler et al. [7]: flame arrival time from ignition and video images. Theformer approach takes into account the ignition time of the nearest fire line (perpen-dicular to fire advance vector) and the distance to the individual HIP1 sensors. Theresultant values appear to have lower associated uncertainty than the latter image-derivedmethod. To ensure consistency, I mimicked the abovemethodology in my sim-ulated domain. Using the high-resolution fire domain, I calculated the upwind distancebetween each HIP1 point and the ignition line and the time it took the flame to reacheach sensor location. To estimate ROS for the entire burn area, I created a mid-firecross-section of 50 point-pairs between second and third ignition lines. Similar to theapproach above, I derived the distance and flame travel time for each pair to calculateROS. As shown in Figure 3.4c, mean LES-based HIP1 and L2G ROS values of 0.049 ms−1 and 0.087 m s−1 are significantly lower then the corresponding observed rates ofspread (0.23m s−1 and 0.30m s−1, respectively). Possible implications and sensitivityof my results to this deficiency are addressed in Section Plume dynamicsAirborne emissions data collected during RxCADRE campaign is central to my eval-uation of WRF-SFIRE’s ability to capture plume rise and dispersion. The emissionsdataset [72] contains smoke plume entry and exit points along the flight path, whichwere calculated using background CO baseline concentrations. The measurementswere taken along horizontal transects passing through the plume at various verticallevels ("parking garage" profile), beginning close to the ground and moving towardsthe top of the plume, for a total of 9 crossings.I compared the identified in-plume segments with modeled CO mixing ratios alongthe same flight path extracted from the geo- and time-referenced LES domain. Fig-ure 3.5 shows the time series of the flight path simulated emissions, overlaid withobservations-derived plume segments. The results suggest good overall agreementin both location and timing between the modeled and observed emissions dispersionthroughout majority of the ABL depth. The coinciding model CO peaks and observedsmoke segments indicate that the horizontal width of the smoke plume is well repre-sented in themodel. Potential shortcomings include excess smoke near the ground, assuggested by the early peaks (12:36 and 12:40 CST) not identified as a plume crossing,as well as a slight skew of the overall smoke distribution towards higher levels. Asmall phase shift appears in themodeled peaks toward the later parts of the simulation(12:50 CST and beyond).To evaluate the vertical distribution ofWRF-SFIRE emissions, I compared themodel-generated CO2 concentrations with airborne measurements obtained during the "park-ing garage" and "corkscrew" (spiral ascent or descent) maneuvers. As shown in Fig-ure 3.6a, there is a good overall agreement in injection heights for fire-generated emis-sions during the earlier "parking garage" profile. Plume top is accurately captured.Modeled concentrations tend to have a negative bias of ∼5 ppmv throughout the bulkof the plume thickness (500–1300 m), and be slightly over-predicted for the very topand bottom of the smoke column (at 400 m and 1500 m).The "corkscrew" profile corresponds to a time near the very end of our simulation.As shown in Figure 3.6b, the band of modeled emissions appears to be very narrowand severely under-predicts the smoke concentrations. I discuss possible reasons forthis behavior in Section 3.3.The above assessment of model performance can be easily quantified with a vari-ety of accuracymetrics. However, given the prescribed emission factors inWRF-SFIRE,the absolutemagnitudes of suchquantitativemeasureswould hardly be useful. Hence,2512:3012:3512:4012:4512:5012:5513:0013:05time (CST) concentration (ppmv)CO ALONG FLIGHT PATHWRF-SFIRE CO concentrationsobserved CO concentrations - backgroundFigure 3.5: Simulated CO mixing ratio along RxCADRE flight path. Red dashedand solid black lines correspond to LES-derived and observed values, respectively.Gray shading indicates observed smoke time periods (not magnitudes) as identi-fied from CO measurements along the flight path.this evaluation focuses on the ability of themodel to capture the relative distribution ofmodelled smoke in the atmosphere, rather than attempting to quantify concentrationprediction errors.260 5 10 15 20 25CO2 mixing ratio (ppmv)02004006008001000120014001600height (m)(a) CO2 PROFILE FROM GARAGE PROFILE0 5 10 15 20 25 30CO2 mixing ratio (ppmv)02004006008001000120014001600height (m)(b) CO2 PROFILE FROM CORKSCREW PROFILEobserved CO2 - backgroundWRF-SFIRE CO2rotated WRF-SFIRE CO2Figure 3.6: Observed (black) and modeled (red) vertical CO2 emissions distribu-tion during: (a) "parking garage" maneuver; and (b) corkscrew maneuver.3.3 DiscussionThe aim of this WRF-SFIRE evaluation is to assess its ability to capture fire-generatedemissions in the context of air quality. Hence, I examine the above results based ontheir potential applications for wildfire smoke plume rise and dispersionmodeling. Thefollowing sections discuss model performance and accuracy from the perspective ofatmospheric dynamics, as well as address potential implications of uncertainty in firebehavior and the associated input parameters.3.3.1 Vertical plume rise in the boundary layerAs demonstrated inmy results summary in Section 3.2.2, initially WRF-SFIRE produceda fairly accurate near-source emissions distribution and plume top with a slight under-prediction of concentrations (Figure 3.6a).Over time model performance appears to deteriorate. Given that the fire thermalforcing compares relatively well with observations (Section 3.2.1), a likely cause for theincreasing difference between model and observations is background ABL dynamics.The simulated atmosphere was initialized with 10:00 CST sounding, and continuallyforced with an observations-based constant surface heat flux. However, the cyclic27lateral boundary conditions maintained the same vertical wind profile as initially sup-plied by the sounding at 10:00 CST, irrespective of potentially changing mesoscaleconditions in the real atmosphere. Over the course of more than three hours betweenspin up start and the final minutes of the fire simulation, from which the "corkscrew"emissions distribution was obtained (Figure 3.6b), the real atmospheric wind profilelikely evolved.With time and further downwind the effects of any small changes in mesoscaleconditions become more pronounced, which is why initially encouraging model per-formance deteriorated towards the end of the simulation. The markedly narrow bandof emissions in Figure 3.6b suggests that the "corkscrew" location in the LES domaincorresponded to the very edge of the plume rather than the center, indicating a shift inmesoscale wind conditions.Indeed, analysis of observed background 30 m wind direction leading up to andduring the burn shows a significant shift to the west, resulting in the LES "corkscrew"profile being extracted from the edge of the plume, rather then the intended center(Figure 3.7). Accounting for this observed wind rotation, it is possible to extract a wind-corrected smoke profile, such as shownwith a red dotted line in Figure 3.6b. Assumingan average 30 degree rotation over the course of available wind observations (basedon the slope of linear regression shown Figure 3.7a), the corrected location of the"corkscrew" maneuver indeed corresponds to the center of the plume (Figure 3.7b).The wind-corrected profile shown in Figure 3.6b is a notable improvement from theoriginal non-rotated estimate. Note that this adjustment is extremely crude, as it isbased on an estimated wind rotation at one point on a single vertical level and doesnot take into account potential changes in vertical wind shear.Unfortunately, unlike the Real-mode WRF simulations, there is no way to accountfor changing lateral boundary conditions in WRF-SFIRE large-eddy mode. Hence, wecan expect the ability of themodel to accurately capture dispersion to depend stronglyon the variability of real background conditions as well as the simulation length andspatial extent of the modeled domain. Namely, an LES will provide better simulationsfor situations where that actual atmosphere is horizontally uniform and temporallysteady. While this presents a limitation for smoke plume rise and dispersionmodellers,it is important to consider it in the context of existing alternative sources of field data.Given a typical uncertainty of∼500 m associated with the most accurate widely avail-able plume height dataset from MISR [75], WRF-SFIRE provides a valuable alternativesource for generating comparatively accurate "synthetic plume height data".Moreover, unlike instantaneous observational point measurements or overpass-2811:10 11:40 12:10 12:40 13:10time (CST)406080100120140160180200220wind direction (deg)CSU (30.7m) WIND DIRECTIONlinear trend 15°/houractive burn time0 1010(a) (b)Figure 3.7: The effects of changingmesoscalewind conditions on plumeobserva-tions (a) Observed 30mwind direction prior to and during the burn (scatter points).Significant linear trend is shown with a red dashed line; active burn time shadedin red. (b) Top view of modeled smoke plume during the "corkscrew" maneuver bythe instrumented aircraft. Black dot and red star indicate the average location ofthe "corkscrew" profile from flight with and without wind-correction, respectively.limited derived satellite data, the LES allowsme to examine the domain-wide temporalevolution of the plume and identify key features, which are likely to be of interest todispersion modellers. As shown in Figure 3.8 and Animation S2 (see published sup-plementary material [50]), the vertical distribution of emissions in the domain changesthroughout the simulation. Following an initial overshoot and a period of active smokeproduction near the ground, most of the emissions rise and end up near the top of theABL (1060 m at the end of LES spinup), accumulating just above the inversion levelin a wide span of heights. While this vertical distribution may contain modelling andinitial condition biases, it is likely to offer dispersion modellers an advantage over thecommon current approach of using a single empirically derived injection height [42].3.3.2 Importance of fire input parametersAs noted in the chapter introduction, this evaluation work is focused on assessing therelationship between coupled surface forcing and the atmosphere inWRF-SFIRE ratherthan on fire behavior. However, the following discussion on fire input parametersmightbe of interest to future modellers using WRF-SFIRE.2912:23 12:29 12:36 12:43 12:49 12:56 13:03 13:09time (CST)02004006008001000120014001600height (m)EVOLUTION OF SMOKE CONCENTRATION COLUMN050,000100,000150,000200,000250,000total domain CO2 anomaly (ppmv)Figure 3.8: Temporal evolution of total column CO2 anomaly in LES domain.Similar to Kochanski et al. [34], I found that the fire behavior model is particularlysensitive to the choice of fuel moisture. This parameter inWRF-SFIRE does not dependon the selected fuel category and was based entirely on field data in my simulation. Ialso modified the standard fuel depth and loading parameters associated with Cat-egory 1 fuels to match observations, which resulted in very accurate surface heatflux forcing but substantially lower ROS values than observed or those obtained withstandard settings.Notably, similar thermal forcing to the atmosphere can be produced using a rangeof combinations of fuel categories and parameters in the model. I have not carried outa formal sensitivity analysis as it was beyond the scope of this study, however, futuremodelersmay find the following information helpful. As preliminary tests for my study,I have used Category 1 and Category 3 fuels (short and tall grass) with various combi-nations of both standard and measurement-based fuel depth and loading parametersto achieve similar surface forcing. The relationships between these parameters arehighly non-linear, which makes determining the "correct" choice (in the absence of30detailed observational data) difficult. What I found to be encouraging is that while theabsolute value of modeled concentrations and ROS changed dramatically dependingon the chosen fuel category for a given fire intensity, the relative spatial distribution ofemissions did not. The simulated atmosphere is forced solely by the parameterizedheat and moisture fluxes, so WRF-SFIRE does not discriminate which combination offuel characteristics produced a given heat flux that drives the buoyant plume rise.Given any thermal forcing, the atmospheric response appears to be fairly robust,irrespective of the particular combination of fuel parameters or ROS with which it wasachieved. While this study does not aim to establish whether the model sensitivity tofuel conditions is physical, it does suggest that the LES produces realistic plume risefor the given fire intensity.3.3.3 ROS and biases in modelled emissionsThe model’s poor performance for ROS in my case study likely resulted in reducedsimulated emissions concentrations due to lower parameterized fuel consumptionrate. This is consistent with the notable negative bias in my modeled CO2 profiles.As mentioned above, the low ROS values on my simulation are largely a result ofmy use of non-standard fuel depth and loading parameters. To eliminate alternativecauses for slow fireline advance, I compared horizontal winds at the first and secondmodel levels (at∼8mand∼25mAGL)with data obtained from2Dsonic anemometersmounted at multiple heights of the CSU-MAPS meteorological tower. As shown inFigure 3.9, the near-surface winds are generally accurately captured by the model. Atthe lowest vertical level, there tends to be a slight positive bias, which onewould expectto contribute to higher rather than lower ROS values.Apart from their dependency on ROS and fuel consumption, the absolute valuesof WRF-SFIRE emissions are also controlled by user-prescribed emission factors. Inmy case study, these factors were not derived from measurements, but were ratherbased on standard values typical for the Grassland fuel category (see Section 3.1.2).Hence, the negative bias in our modeled smoke distribution could potentially be re-duced, should observations-based emissions factors become available.3.3.4 Experimental design considerationsOne of the shortcomings of the RxCADRE dataset and this experiment is the substan-tial (nearly 2.5 h) difference in timing between the sounding balloon launch and the fireignition. Availability of an additional vertical profile for model evaluation just prior to3112:3012:3512:4012:4512:5012:5513:0013:0513:10time (CST)012345horizontal wind speed (m/s)MODELLED vs OBSERVED HORIZONTAL WINDSPEEDS WRF-SFIRE (8 m)observed (interpolated to 8m)WRF-SFIRE (25 m)observed (interpolated to 25 m)Figure 3.9: Modeled (red) and observed (black) near-surface horizontal wind.ignition would have been extremely helpful in mitigating some of the sources of errormentioned in the above sections. A similar recommendationwas offered by Kochanskiet al. [35], who suggested that an on-site sounding just prior to the burn rather than afew hours earlier would be most useful.While the challenges of coordinating balloon launches in the presence of aircraftover the fire are obvious, a potential alternative would be to include on-board temper-ature and wind sensor data from flight with the smoke dispersion measurements.3.4 SummaryThis chapter aimed to assess the ability of a coupled fire-atmosphere WRF-SFIRE LESmodel to simulate a case study of fire smoke plume growth and dispersion. I exam-ined the L2G burn from the RxCADRE 2012 campaign - a comprehensive experimentcombining simultaneousmonitoring of fuel, fire behavior, meteorology and emissions.My model evaluation demonstrates good overall agreement between the LES andthe observations, subject to accuracy and timeliness ofmodel initialization data. Usingthe emissions and dispersion data collected from an airborne platform during theRxCADRE experiment, I show that LES reasonably captures the timing, rise and dis-persion of the fire plume. I examine the possible relationships among model biases,32fire behavior and changes in ambient atmospheric conditions.This work demonstrates the feasibility of using WRF-SFIRE LES in studying fireplume dynamics. The scarcity of detailed plume observations presents one of thecentral challenges for smoke-model development. WRF-SFIRE’s ability to capture therise and spread of fire emissions for cases such as studied here has the potential toaddress this critical research need and provide alternative "synthetic" data for futuredevelopment of parameterizations for wildfire smoke plume rise.3.4.1 LimitationsRecent studies suggest that the heat extinction depth parameter in WRF-SFIRE (or e-folding distance) has a strong influence on the modeled fire and near surface plumebehavior [33, 35]. Currently, there is no clear theory in the literature on how the verticaldistribution of fire-released heat above the ground affects near-ground air tempera-tures as well as ROS. As the relationship appears to be highly non-linear, I have notexamined its implications in our simulations.Overall, my findings suggest that the ability of WRF-SFIRE to capture plume dy-namics of a specific real fire largely depends on the availability of timely atmosphericinitial conditions and accurate simulation of fire intensity. Owing to the detail andcomprehensive nature of the data provided by the RxCADRE experiment, these criticalinputs could generally be derived frommeasurements for the current case study. Thissensitivity, however, could present a challenge for future real-time fire simulations,where few or no such measurements would be available.3.4.2 Big pictureThe case study discussed in this chapter can likely be considered a good represen-tation of a "typical" smoke plume, from the perspective of remotely sensed plume"climatology" (Section 2.3). It occurred during daytime atmospheric conditions andmost of the smoke was injected into the atmospheric layers just above the ABL top.While these findings may be reassuring for regional air quality modellers, the bulkapproach to fire behavior evaluation may spark many interesting questions for com-bustion researchers.In particular, firemodellersmay consider whether it is feasible to use the fire spreadalgorithm implemented withinWRF-SFIREwith non-standard fuel category parametersand whether the produced behavior (and, in particular ROS) can be considered phys-ical. Another theoretical consideration relating to micro-scale dynamics is what the33effects of upscaling heat fluxes (and the inevitable smoothing associated with it) fromfire to atmospheric grid are. More broadly: howmeaningful is the comparison of in-situfire heat flux sensor measurements with grid-averaged values representing heat fluxin the model? These questions could serve as a helpful starting point for additionalinvestigations by fire behavior scientists.34Chapter 4Synthetic data: Simulating smoke plumesunder a wide range of fire and atmosphericconditionsIn this chapter I introduce a synthetic plume dataset produced using a coupled fire-atmosphere model WRF-SFIRE [45, 46]. The broad goal of this effort is to capture awide range of fire and atmospheric conditions and examine their effect on modelledsmoke plume rise. This surrogate "data" addresses many of the challenges of workingwith available observations (Section 2.3). The following chapter details the numericalsetup, scope of the dataset, aswell asmy approach to defining "ground truth" for plumeinjection height model evaluation.4.1 Generating plume data4.1.1 Numerical configurationWRF-SFIRE was configured in idealized large-eddy resolving mode. Much of my nu-merical setupwas adopted from the case study detailed in the previous chapter (Chap-ter 3), to ensure the simulations represent physical conditions backed by model eval-uation. Due to high computational demands of LES runs, I focused on the local- andmeso-gamma scales (1 km - 20 km), considering only the initial buoyant plume riseof smoke in typical daytime clear non-precipitating atmospheres. Key parametersvaried were ambient wind, fuel category, vertical potential temperature profile and fire-line length, denoted as conditions W,F,R and L, respectively (detailed further in Sec-tion 4.1.2).I initialize each 10 km x 20 km domain with 40 m horizontal grid spacing with35uniform ambient west wind W and vertical temperature profile R. Depending on thesounding R, the simulations were performed in either a shallow (3000 m) or a deep(5000 m) domain, with 51 or 71 hyperbolically stretched vertical levels, respectively. Aconstant uniform lower boundary surface thermal flux (tke_heat_flux) in the ambientenvironment and lateral periodic boundary conditions were imposed to produce a tur-bulent well-mixed layer in the ambient environment. I used full surface initialization(sfc_full_init =.true.), with the lower boundary characteristics set to USGS values forland use most closely matching the Anderson fuel category F [3]. The correspond-ing surface roughness lengths added various levels of wind shear to each domain toproduce amore realistic non-uniform vertical wind profile during spinup of the environ-ment before the fire was initialized in the LES.Initial convection in the ambient environment was triggered using a perturbed sur-face temperature field. On average, a near-stationary turbulence spectrumwasachievedwithin the first 30 min of run start. The "restart" file generated at the end of one hourof spinup was used to initialize the main burn simulation, ensuring the fire was ignitedin a well-mixed turbulent ABL.I initialized the fire over a one-minute interval using a straight line of length L. Theignition line was placed one kilometer downwind of the western edge of the domain(perpendicular to ambient wind) and centered in the north-south direction. With arefinement ratio of 10 in each horizontal direction, the fire was simulated on a 4 msub-grid mesh.The "smoke plume" was modelled with a passive tracer emitted proportionally tothe mass and type of fuel burned. The rate of release was controlled by an assignedemission factor representing PM2.5 for each fuel category, based on values providedby Prichard et al. [60] (see namelist.fire_emissions in downloadable supplement refer-enced in Appendix A.1).A summary of key configuration details can be found in Table 4.1, as well as insample namelist initialization files available for download (Appendix A.1).4.1.2 Test conditionsTable 4.2 summarizes the key parameters that were varied to produce the syntheticdataset.The range of ambient winds tested was bound largely by numerical constraints.Due to cyclic boundary conditions, wind speeds higher than 12 ms−1 would requirea much larger domain to prevent smoke recirculation. For the lower bound on mywind condition W, I needed to ensure that sufficient wind speed was maintained to36Table 4.1: Key parameters of numerical domain setup.Simulation Parameter Value/DescriptionModel version May 24, 2019 (git #ced5955)Horizontal grid spacing 40 mDomain size 500 grids cells (east-west) x 250 grids cells (north-south)Time step 0.1 sModel top 3000 m (shallow) / 5000 m (deep)Spinup timing 11:30:00 - 12:30:00Fire (restart) simulation timing 12:30:00 - 12:50:00 (shallow) / 12:30:00 - 13:00:00 (deep)Sub-grid scale closure 1.5 TKE (TKE = Turbulence kinetic energy)Lateral boundary conditions periodicSurface physics Monin-Obukhov similarity (sf_sfclay_physics = 1)Land surface model thermal diffusion (sf_surface_physics = 1)Ambient surface heat flux 240 W m−2(tke_heat_flux=0.2)Fire mesh refinement 10Ignition duration 13:00:10 – 13:01:10Heat of combustion of dry fuel 16.4 MJ kg−1Table 4.2: Test conditions included in synthetic plume dataset. The count indi-cates the number of unique values used within the specified range.Condition (Tag) Range Count DescriptionAmbient wind (W) 3 - 12 ms−1 10 Uniform horizontal wind magnitudeused to initialize model spinupStability profile (R) R0-R8 9 Atmospheric sounding with variableABL height, temperature and inversionstrengthFuel (F) 1 - 13 13 Anderson fuel category assigned atlower boundaryFireline length (L) 1 - 4 km 3 Length of ignition lineTotal number of experiments = 140propagate the fire. The spread algorithm used within the LES applies a correctionfactor under low wind speed conditions to prevent the fire from extinguishing itself.While necessary for numerical reasons this effect is not physical, so winds below 3ms−1 were excluded from my dataset.I used 9 different atmospheric profiles (R condition) to initialize the model. I variedthe following features for each initialization:• initial ABL height (500 m - 1600 m)37280 290 300 310 320 330potential temperature [K]05001000150020002500height [m]PRE-IGNITION ATMOSPHERIC PROFILESR0R1R2R3R4R5R6R7R8Figure 4.1: Pre-ignition potential temperature profiles (stability condition R). Col-ors correspond to initial soundings used for model spinup.• potential temperature lapse rate above inversion (0 K km−1 - 20 K km−1)• initial (pre-spinup) ABL temperature (290 K - 300 K)Following spinup (Section 4.1) under variable winds and surface conditions, thisproduced 9 sets of soundings, shown in Figure 4.1 with ABL depths of approximately600m - 2000 m. I tested all fuel categories available within the model (F condition),and varied the length of the fireline (L condition) between 1 and 4 km.Table 4.3 andTable 4.4 summarize the tested combinations of fire and atmosphericconditions captured by the synthetic plume dataset. Colored cells (blue and red) corre-spond to completed simulations. Tall boundary layers of R5 and R6 domains requiredlow winds (5 ms−1 and below) and high intensity fires (fuel categories 4, 6, 7, 12 and13) to reach ABL top within the simulation runtime and/or avoid smoke recirculation.Hence, alternative combinations (white cells in R5 and R6 columns) would require con-siderably different domain setup from other runs. For this reason these combinations38were not tested. Also, a single run was performed for R8 condition (adiabatic freeatmosphere) as an extreme case scenario.Red cells highlight simulations that were completed, but subsequently excludedfrom analysis presented in Chapter 6. This was done based on visual inspection ofLES fields. There were two possible reasons for exclusion: (i) the plume reached thetop of the domain or (ii) the plume appeared to be non-penetrative (see sample inAppendix A.2). In the former case, it’s questionable whether the fields are physical,as the plume could potentially be affected by the absorbing layer near domain top,designed to prevent numerical instability. The latter rendered the plume irrelevant forthe purpose of modelling smoke injection height (Chapter 6). These non-penetrativeruns, however, were included for testing the plume classification method presented inSection 7.1.39Table 4.3: Combinations of test conditions resulting in penetrative plumes, as captured by the LES datasets. Green cellhighlights fireline length condition (L) runs. Intensity of blue color corresponds to the number of runs for fuel condition(F) represented by the cell. Row ’W5’ is expanded in Table 4.4 below.R/W R0 R1 R2 R3 R4 R5*† R6*† R7* R8*W3 F7 F7 F7 F7 F7 F7 F7 F7W4 F7 F7 F7 F7 F7L1F7L2F7L4F7 F7 F7W5 F1 - F12,excl:F4 F1 - F13,excl:F9 F1 - F13 F2 - F13,excl:F8,F9 F1 - F13 F4 F6 F7F12 F13 F4 F6 F7F12 F13 F2 - F13,excl:F8,F9 F7W6 F7 F7 F7 F7 F7 F7W7 F7 F7 F7 F7 F7 F7W8 F7 F7 F7 F7 F7 F7W9 F7 F7 F7 F7 F7 F7W10 F7 F7 F7 F7 F7 F7W11 F7 F7 F7 F7 F7 F7W12 F7 F7 F7 F7 F7 F7*Deep domain (5 km). †Extended runtime (30 min).40Table 4.4: Tested combinations of fuel and ABL conditions (blue and red colored cells).R/W R0 R1 R2 R3 R4 R5*† R6*† R7* R8*F1 ABL plume ABL plumeF2F3F4 smoke atdomain topF5F6F7F8 ABL plume ABL plumeF9 ABL plume ABL plume ABL plumeF10F11F12F13 smoke atdomain top41Note, that varying a single condition while holding the rest constant does not resultin a controlled experiment isolating its impact on plume rise. Because WRF-SFIREincorporates fire-atmosphere coupling, the problem is not well-constrained. For ex-ample, by varying fuel type F alone, while holding the rest of test conditions constant,I obtain a set of fires with diverse shapes, sizes, intensities, fireline depths, rates ofspread and heat release. This reflects the complexity of non-linear interactions thatexist between the fire and the atmosphere (discussed further in Chapter 5). As a result,the parameter space captured within my LES dataset is much greater then the fourconditions described in Table Defining smoke injection heightGiven non-stationary fire and atmospheric conditions, determining a consistent defi-nition of an equilibrium smoke injection height is not a trivial task. It requires sepa-rating buoyant rise from dispersion, while excluding the effects of initial momentumovershoot and accounting for the advection due to varying ambient and fire-generatedwinds.A common way of examining vertical distributions of pollutants in the context ofair quality is to consider crosswind-integrated (CWI) concentrations. This allows oneto reduce the problem to two dimensions, with plume centerline being defined sim-ply as the CWI concentration maximum at each location downwind of the source.Theoretically, under stationary conditions there exists an equilibrium height, aroundwhich the centerline eventually oscillates. In reality, as well as in my LES experiments,neither the ambient nor the fire conditions are stationary. The changing location, shapeand intensity of the fire, ABL warming and growth, as well as the development of fire-coupled winds and vorticity continually modify the conditions.As a result, my approach is based on defining a region, where the concentrationdistribution is quasi-stationary. I consider the last frame of each simulation for thisanalysis. Using CWI tracer values, I locate the plume centerline (Figure 4.2a). To obtainthe quasi-stationary region for each individual plume, I first calculate the change intracer concentration along the centerline. I then use a smoothing function to reducethe effect of random turbulent oscillations in both the centerline height and the tracerconcentration gradient along the centerline. The downwind region where both of theseparameters are not changing rapidly are then then considered quasi-stationary. Addi-tional details of this filtering method are provided in Appendix A.3.420 2000 4000 6000 8000 10000 12000 14000distance [m]05001000150020002500height [m](a)plume centerlineBL height at ignition0255075100125150fire heat flux [kWm2]0 50 100 150 200CWI smoke [mg/kg]0 1000 2000 3000x distance [m]30004000500060007000y distance [m](b)0255075100125150heat flux [kW/m2]0 2000 4000 6000 8000 10000 12000 14000distance [m]0100020003000height [m](c)05001000150020002500concentration [mg/kg]averaging windowraw centerline heightsmoothed centerline height centerline concentration0 50 100CWI concentration [mg/kg]01000200030004000height [m](d)  PM profilezCLIQRW7F7R0Figure 4.2: Illustration of the approach to identifying a quasi-stationary downwind region in CWI smoke distributionusing a sample LES experiment. (a) CWI smoke concentrations. Also shown are plume centerline height (dashed),zi (dotted) and CWI fireline intensity (solid red, secondary axis). (b) Plan view of fire heat flux showing the fireline.(c) Quasi-stationary region (grey shading). Also shown are raw (dotted purple) and smoothed (solid green) centerlineheights and tracer concentrations (solid orange, secondary axis). (d) Representative downwind smoke distribution.The profile (solid blue line) is obtained by horizontally averaging the CWI smoke concentrations in the quasi-stationaryregion. Also shown are interquartile range (IQR) (light blue shading) and the derived smoke injection centerline heightzCL (dashed black).43I then average the vertical CWI distribution of tracers in the downwind direction overthe identified quasi-stationary regions (shaded in grey on the Figure 4.2c) to produce arepresentative downwind distribution for each plume (Figure 4.2d). I define the "true"injection height zCL as the mean height of smoothed centerline over the averaging re-gion. The resultant dataset of zCL values is used to constrain and evaluate the proposedsmoke injection height parameterization introduced in the following chapters.4.3 SummaryThe synthetic plume dataset (Section 4.1) and the derived injection height dataset(Section 4.2) described above provide a rich source of training and evaluation data forfuture models and parameterizations (see Appendix A.4 for access information). Theapproach introduced in this chapter allows for creation of controllable and repeatablenumerical experiments, which can capture a range of fire and atmospheric conditionsnot possible with real-life observational campaigns.4.3.1 LimitationsThe presented dataset is limited to initial plume rise fromfires occurring under daytimefair-weather conditions on a local/regional scale over flat terrain. While representativeof vastmajority of smoke plumes [73], the examples captured by the dataset are limitedto penetrative plumes, which remain in the stable layers of the free troposphere abovethe ABL. I have not considered the effects of latent heat: all plumes in the dataset arenon-condensing.4.3.2 Big pictureThe range of fire and atmospheric conditions captured here is most applicable forregional air quality applications. Future researchers interested in examining plumerise in the context of global chemical transport models, where cloud formation andpotential stratospheric injection of aerosols are of great importance, could extend theproposed approach for deeper simulated domains over complex terrain. It would beinteresting to compare plume injection heights obtained from WRF-SFIRE simulationsconfigured in LES vs Reynolds-averaged Navier–Stokes (RANS) mode and reanalysis-driven boundary conditions. Relatively fast run-time (compared to LES) and abilityof WRF to incorporate realistic initial conditions and chemistry in RANS simulations,combined with increasing computational power, could pave the way for broad use ofWRF-SFIRE in operational smoke modelling [43].44Chapter 5Fire-atmosphere coupling: qualitativeanalysis of local-scale dynamicsThe past decade has seen significant developments in complex, coupled, physics-driven atmospheric numerical models, including WRF-SFIRE, which resulted in enor-mous improvement in our ability to simulate wildfire and smoke behavior. These so-phisticated models offer the promise of giving insight into the underlying dynamics ofinteractions between the fire and the atmosphere [61]. Our current understanding ofthe subject is limited, and large uncertainties remain due to lack of observational data(Section 2.3).While the evaluation case study presented in Chapter 3 is a step towards greaterconfidence in model performance, much research is still needed to understand allthe physical processes involved. Yet without proper knowledge of what the dynam-ical mechanisms and feedbacks are, it is impossible to assess how well the currentmodels represent them. Comprehensive observational campaigns, such as FASMEE(Section 2.3) will hopefully help shed light on the subject in the near future.In the mean time, existing plume rise parameterizations have to rely on simplifyingassumptions about how the fire interactswith the ambient atmosphere. A vastmajorityof operational schemes [9, 39, 66], consider the smoke plume to be rising through astatic atmosphere, entraining ambient environmental air along its path. While suitablefor small-diameter low buoyancy sources like industrial smoke stacks, exclusion ofany possible feedbacks between the fire and the atmosphere may contribute to largeerrors associated with applying such schemes to wildfires.This chapter asks the following question: What can a coupled fire-atmospheremodel tell about dynamic interactions around wildfires? While still subject to compre-hensive evaluation, the answers to this question may help inform current and futureplume rise parameterization development.455.1 Fire-induced windsAs noted in the previous chapter, the synthetic dataset produced with WRF-SFIRE con-sists of a diverse set of smoke plumes with unique characteristics, combining theeffects of imposed initial conditions, fire-atmosphere coupling and background ABLturbulence. The detailed nature of synthetic LES data, however, allows us to identifydynamical flow features that are common to vast majority of the modelled plumes.One such effect is the formation of a convergence zone at the fire front. Shown inFigure 5.1 is a typical example of a flow pattern produced byWRF-SFIRE. The top panelrepresents cross-wind-integrated CWI smoke (Figure 5.1a), shown with ambient winddirection. The remaining subplots display horizontal and vertical flow generated by thefire (along with background turbulence), relative to mean ambient winds. I.e. the windfields displayed in the figure can be superimposed on average ambient atmosphericconditions to give the total flow field.As shown in the horizontal velocity subplot (Figure 5.1b), the fire generates a largeregion of slowing winds extending far downwind. A well-defined convergence zoneforms at the fire front, where these slowing winds meet accelerated horizontal flowfrom behind the fireline (i.e. from upwind of the fireline). Once the rising air reachesequilibrium height, the smoke is pushed into a wide range of outflow levels, marked byincreased advection relative to ambient wind. Lastly, as demonstrated in the verticalvelocity subplot (Figure 5.1c), the downwind ABL region is generally dominated bysinking air, which aids smoke recirculation and fumigation of elevated pollutants backto the surface.46Figure 5.1: Cross-wind integrated (CWI) smoke concentrations (top). Fire-induced horizontal flow relative to ambientconditions (middle). Fire-induced vertical flow relative to ambient conditions (bottom).475.2 VorticityTo examine how wildfire plumes entrain air I used the LES fields to perform trajectoryanalysis for air parcels located just outside of the fire. I placed equally spaced sourcepoints to the side of the fireline (laterally) and tracked the streaklines as they mixedwith the smoke plume. As shown Figure 5.2, clean air is pulled towards the head of thefire, creating a large lateral vortex.Examination the temporal evolution of various LES fields, the fire-atmospheric cou-pling mechanism appears to be as follows:• low pressure in the center of the updraft results in a horizontal pressure gradientforce• wind shear induces vortices that bring clean air into the plume and maintainmass continuity• cross-wind flow creates a curved fireline (eg. Figure 5.3) resulting in less occlu-sion of the firefront and decreasing the strength of the reverse flowThere is no clear theory on which buoyancy and wind conditions induce vortexformation and, in extreme cases, plume bifurcation [19]. However, Cunningham et al.[16] have previously shown using numerical experiments, that the degree to which thesmoke splits is related to surface wind shear. More importantly, they found that plumebifurcation does not affect plume rise. Though the study stops short of quantifyingthese effects, it represents the most detailed investigation of vorticity in wildfires todate.Overall, vortices appear to be a transient feature in wildfires [59]. They are con-tinually mediated by fluctuations in ambient winds (as shown in further detail in Sec-tion 5.4), and generally occur under light wind conditions [16].Notably, the lateral wind flow generated in response to the updraft and the as-sociated vorticity appear to be a very efficient mixing mechanism. The color of thestreaklines shown in Figure 5.3, corresponding to smoke concentration, indicates thatthe most rapid entrainment of ambient air occurs close to the surface. This result isinteresting, because most plume models rely on a common entrainment assumption,which suggests that mixing rate is proportional to the local vertical velocity of theupdraft [71]. Yet near the ground this velocity is still relatively low, compared to near thetop of ABL, where most of plume’s buoyancy has been converted into kinetic energy.These findings could in part explain why wildfire plume behavior differs from thatsuggested by common Gaussian plume models.48Figure 5.2: Formation of a lateral vortex around a fireline. 200mx200m trajectorysource mesh is located next to ignition line (outside of the fire) at the surface.Colors correspond to trajectory index to aid visualization. Figure produced usingVAPOR software [13]49Figure 5.3: Illustration of fire-atmosphere feedbacks between updraft, lateralwinds and fireline curvature with trajectories. Colors correspond to tracer concen-tration along each path. Equally spaced trajectory sources were placed on eachedge of the fireline, extending between 50 m and 200m AGL. Figure producedusing VAPOR software [13]505.3 Effects of fireline lengthMost existing plume rise parameterizations [4, 6, 20, 64] idealize the shape of the fire,usually assuming it’s radially symmetric. In otherwords, the plume is often representedby a cone or a cylinder. However, a wildfire often consists of an intense firefront (at theleading edge of the fire) where peak heat fluxes occur, followed by a wide smoulderingregion, and sometimes a backing fire. The length of the fireline can extend manykilometers. For modelling purposes, it is therefore convenient to consider the fire andthe smoke plume in two dimensions (x,z) as viewed from a cross-wind direction (y).This raises a question: how does the length of the fireline affect plume rise and thevertical distribution of smoke?Figure 5.4 compares the time-averaged fire-generated 2-D (x,z) horizontal flow for 1km, 2 km and 4 km firelines (in the cross-wind direction) under the same initial fire andatmospheric conditions. I found that themagnitude of the downwind region of slowingair is greater for longer firelines. Moreover, longer firelines produced a wider, strongerrange of smokeoutflow levels compared to shorter ones. Irrespective of themagnitudeof the fire-induced horizontal wind, the convergence zone remained stationary at thefirefront.51Figure 5.4: Time-averaged relative horizontal velocity plots for 1 km (top), 2 km (middle) and 4 km (bottom) firelines.Fireline-following moving averaging was performed over the last 15 min of the simulation using mean vertical crosssection of the horizontal flow field ( averaged over the central 800 m of the fireline in the y-direction) . Grey contourscorrespond to time-averaged smoke concentrations. Fireline heat flux is plotted on a secondary (red) axis. Dotted anddashed lines denote ABL height and the plume centerline, respectively.52Figure 5.5: Magnitude of fire-induced horizontal winds U ′ (relative to ambientflow) at 400 m above ground level (~half of ABL height).Figure 5.5 provides a more direct comparison of the effect of fireline length on fire-induced horizontal wind magnitude by examining a mid-ABL slice. Following a regionof brief acceleration, longer firelines produce a sharper drop across the plume, fol-lowed by a gradual convergence to average ABL conditions. This carries implicationsfor local near-fire dynamics, as it results in stronger recirculation of smoke back tothe firefront and higher relative smoke concentrations near the surface. As shown inFigure 5.6, this effect eases with downwind distance, as relative vertical smoke distri-butions converge to a fairly similar shape further away from the fire. The differencesare most pronounced close to the fire. Notably the distribution maximum (in otherwords the mean smoke injection height) is nearly identical for all three firelines.530.0 0.2 0.4 0.6 0.8 1.0normalized concentration05001000150020002500height [m]1 KM DOWNWIND0.0 0.2 0.4 0.6 0.8 1.0normalized concentration05001000150020002500height [m]3 KM DOWNWIND0.0 0.2 0.4 0.6 0.8 1.0normalized concentration05001000150020002500height [m]5 KM DOWNWIND1 km fireline2 km fireline4 km firelineTIME-AVERAGED CONCENTRATIONSFigure 5.6: Normalized vertical CWI smoke distributions at 1 km (left), 3 km(middle) and 5 km (right) downwind of the fireline for various fireline lengths.5.4 Modulation of the fire by passing ambient thermalsOne interesting observation noted in the above Section 5.3, is the fact that the locationof the horizontal wind convergence remains at the firefront, irrespective of the lengthof the fireline. From mass continuity perspective, a larger (or longer) updraft wouldrequire more air to be drawn towards the head of the fire. In part, this is supportedby higher horizontal fire-induced wind magnitudes (Figure 5.1). However, if this wasthe only mechanism, one would expect formation of larger lateral vortices as well asgreater fireline curvature for longer firelines. Yet neither of these features differ greatlybetween the various fireline length simulations.In an attempt to explain how longer updrafts are supported, I repeated the trajec-tory analysis for the 4 km fireline now placing equally spaced sources upwind of theignition. The results are shown in Figure 5.7: as clean air is accelerated towards thehead of the fire, the flow breaks up into multiple cores. This multi-vortex structure istransient: individual cores are not stationary in space or time. This behavior is likelythe result of interaction between the plume and the passing ambient ABL thermals.Random velocity perturbation due to ABL turbulence allow for fireline "fingering",as certain portions of an initially uniform ignition line are advected faster/slower bylocal eddies relative to their surroundings. Because WRF-SFIRE spread algorithm re-sponds to local winds, these turbulent fluctuations naturally distort the fireline, aidingthe formation of multiple cores. While the parameterized fire behavior in WRF-SFIREremains subject to evaluation, this tendency for more prominent fingering for longerfirelines appears to be supported by models with explicitly resolved combustion [8]. Inreal life, this effect is likely further enhanced by fuel and surface heterogeneity.54Figure 5.7: Trajectory analysis of clean air entrainment frombehind a 4 kmfireline.Individual paths are colored by smoke concentration. Figure produced usingVAPOR software [13]5.5 Plume mixing and the boundary layerThe trajectory analysis discussed in the previous sections suggests that most rapidmixing of the plume with clean environmental air occurs near the surface. In otherwords, based on the observed kinematics, onewould expectmost of the plume dilution(and, hence, cooling) to occur in the lower levels of the ABL as well.Using the synthetic plume dataset (Chapter 4) I examined the vertical distributionof plume centerline potential temperature for each run. Shown in Figure 5.8 is a typicalexample of such a profile. It suggests that rapid cooling of the plume’s core indeedoccurs in the lower half of the ABL, after which its potential temperature remainslargely unchanged (or on the order of random turbulent perturbations).Apart from radiative cooling and effective mixing due to fire induced winds andvorticity, this may also be attributed to growth and widening of the smoke plume. Asthe edges of the plume move further away, the core becomes less and less affectedby the ambient environmental conditions. A penetrative plume entering the free tro-55Figure 5.8: Vertical potential temperature profile of the mean ambient pre-ignitionenvironment (light blue) and plume core (orange) temperature. Also shown: ABLheight zi before ignition (dotted grey) and smoke injection height zCL (dashed red),based on the definition provided in Section 4.2posphere above the ABL is still warmer then the surrounding atmosphere, hence itcontinues to move up into the stable layers. However, our LES simulations suggestthat there is relatively little cooling and mixing occurring above the ABL. Followinga momentum-driven overshoot the plume centerline eventually oscillates around itsequilibrium height, where its core temperature roughly matches that of the ambientenvironment. This concept is best demonstrated with conserved variable plots, suchas one shown in Figure 5.9.Scatter point color in Figure 5.9 indicates the relative height (normalized by theheight of the ABL) of the plume centerline, from which the dry static energy and tracerconcentrations were obtained. Note that the theoretical mixing line connecting warm,smokey points (lower right) and the equilibrium cluster (upper left) is generally brown,suggesting that most dilution occurs below mixed layer top zi.56305 310 315 320 325dry static energy ( Cp) [kJ/kg]0500100015002000PM mixing ratio [mg/kg]CONSERVED VARIABLE PLOT: W5F12R00.000.250.500.751.001.251.501.752.00z/z iFigure 5.9: Dry static energy vs. concentration along the CWI plume centerline.Values are obtained at 20 min after simulation start. Scatter point color corre-sponds to relative (to ABL top zi) height from which the values were obtained.5.6 SummaryThis chapter provided a qualitative discussion of several fire-atmosphere dynamicalfeedback mechanisms observed in LES plume data. Key features included the for-mation of horizontal flow convergence at the firefront and the associated lateral windshear and vorticity. Fireline curvature and fingering appear to be influenced by ambientABL conditions as well as fire geometry. Based on LES data, most of plumemixing anddilution occurs in the lower levels of theABL, beyondwhich the plume core temperatureremains largely unaffected by the ambient environment.5.6.1 Big pictureSome of the fire-atmosphere interactions discussed in this chapter may help informplume rise parameterization development (including the one introduced in this thesis).57However, most still lack evaluation with observational data. While this may require anexceptionally complex and expensive effort, numerical simulations, similar to thoseused in this chapter, could potentially facilitate planning field experiments. Optimizinginstrument placement as well as anticipating weather impacts could help save costand increase the chance of collected data being useful and relevant.58Chapter 6Smoke injection height: A simple energybalance parameterization for penetrativeplumesThis chapter introduces a new simple parameterization for predicting the mean injec-tion level of wildfire smoke plumes. The method is derived from basic energy bal-ance, using simplifying assumptions motivated by numerical insights from the previ-ous Chapter 5.6.1 FormulationA common approach to predicting the final equilibrium centerline height of wildfiresmoke is to first estimate the initial buoyant energy of the hot rising smoke [4, 6, 69].After the smoke plume entrains surrounding ABL environmental air and cools, theremaining energy is spent doing work to push the cooled smoke plume up into thestatically stable capping inversion.The relationship between final and initial energies is often rewritten to show thatthe potential energy per unit mass (PE) of smoke penetration equals some fraction c1of initial heat released from the fire. In kinematic units, the initial heat input has unitssimilar to kinetic energy per unit mass (KE). The empirical parameter c1 is usuallyestimated based on concepts of entrainment into the rising smoke plume [17].PE = c1KE (6.1)The PE of smoke-plume penetration into the capping inversion can be written asPE = g′z′ (6.2)59where the penetration distance z′ of the final equilibrium smoke centerline zCL abovereference height zs (near the top of the well-mixed portion of ABL) isz′ = zCL− zs (6.3)The static-stability variable g′ for the plume-penetration region isg′ = gθCL−θsθs= gθ ′θs(6.4)where θCL and θs are the potential temperatures of the ambient environment at zCL andzs, respectively, and θCL−θs = θ ′.Typically, expression for plume buoyancy includes a potential temperature pertur-bation relative to ambient environmentwithin the same vertical level in the atmosphere.However, as discussed in Section 5.5, based on LES data, little cooling occurs beyondupper ABL. This allows me to express θ ′ in Equation 6.4 in terms of plume core poten-tial temperature θCL at injection level.The KE can be estimated using a velocity scale w f asKE = 0.5w2f (6.5)Typically, the bulk potential-temperature difference across the smoke-plume penetra-tion region θ ′ is expected to be relevant for only the PE portion of Equation 6.1. How-ever, I found from the LES runs for a wide range of fire and environment conditions thatthe KE also depends on the same potential temperature difference. This dependencecan be expressed in the velocity scale:w f =Iziθ ′(6.6)This velocity scale is related to the fireline intensity parameter I = ∫ rHdr, which is thekinematic heat flux into the atmosphere H integrated across the fireline depth r ( inunits of K m2 s−1), and to the mixed-layer depth zi. The mathematical form of w f isdiscussed further in Appendix B.2.One could speculate that this interesting result is because smoke from a fire doesnot rise through a passive environment, as is often assumed for Briggs types of plumeentrainment models. Instead, the fire and the environment interact in many complexways. Some of these, detailed in Chapter 5 include: vertical-to-bent-over vortices onthe ends of the fire line that rapidly mix environmental air into the buoyant smoke60plume; modulation of fire intensity and fire updrafts by translation of ambient thermalsacross the fire line; plumes of enhanced convergence and updraft along the fire line;mass conservation as descending air beneath the extended smoke plume lowers thelocal mixed-layer depth; and possibly other factors.Thus, Equation 6.1 becomesg′z′ = c2[Iziθ ′]2 (6.7)where c2 = 0.5c1.The above can be rearranged into the following form (see Appendix B.1):zCL− zs =C[g(θCL−θs)θs (zCL− zs)]− 12 {gI (zCL− zs)θszi} 13 (6.8)whereC is a dimensionless empirical parameter. The factors in square and curly brack-ets with their corresponding powers have units of time and velocity, respectively. Thisrelationship is plotted in Figure 6.1. It provides quite an acceptable fit to the data over awide range of 140 combinations of fire and atmospheric conditions simulated. Scatterpoints largely fall close to 1:1 line, suggesting C ≈ 1. Model bias will be addressed infurther detail in Section 6.2.2.Equation 6.8 suggests that the relevant length and temperature scales (z′,θ ′) de-pend not on the capping inversion strength alone, or on the tropospheric lapse rateabove the capping inversion alone, but on the bulk potential-temperature differencesacross the smoke-plume penetration region, z′. Equation 6.8 is implicit, in that thedesired plume centerline equilibrium height zCL appears in both the left and right sidesof the equation. The plume centerline height also defines where θCL is retrieved fromthe atmospheric sounding; namely, zCL is implicit in both Equation 6.7 and Equation 6.8.However, for any specific fire and environment conditions, values of zCL are easily foundby iteration (see Appendix B.4). Steps to estimating input parameters required for theproposed injection model from the LES data are summarized in Appendix B.3.Alternatively, for a small sacrifice in accuracy, it is possible to obtain an explicitsolution by considering an idealized version of the atmospheric profile, consistingof an adiabatic mixed layer, entrainment zone and a stable uniformly stratified freeatmosphere above (Figure 6.2). In such case γ is defined as the overall potentialtemperature gradient of the free atmosphere and zs as the height corresponding to theintercept of γ and the well mixed portion of the ABL profile. Then, using Equation 6.8,61500 1000 1500 2000 2500 3000model zCL [m]50010001500200025003000true z CL [m]MODELLED SMOKE INJECTION HEIGHTSlinear regression fit1:1 line20000400006000080000100000120000140000fireline intensity [K m2 /s]Figure 6.1: Comparison of true (as shown in Figure 4.2) and modelled (fromEquation 6.8) smoke injection heights. Scatter points represent the 140 individualplume experiments within the LES dataset, with colors corresponding to firelineintensity I. Solid black and grey dashed lines denote linear regression fit and unity,respectively.zCL can be found explicitly as:zCL =[θsg] 14[Izi] 12[1γ] 34+ zs (6.9)62000ssiCLCLzzzz0aFigure 6.2: Idealized potential temperature profile θ vs. height with constantstable layer lapse rate. γ .6.2 Model evaluationToassess the accuracy of the proposed smoke injection height parameterization (Equa-tion 6.8), I perform two sets of verification studies. The first approach is based onusing the synthetic plume dataset from Chapter 4 to carry out model evaluation, biascorrection and sensitivity analysis with idealized data. The second portion of thissection applies my approach to the case study of a real prescribed burn (RxCADRE2012) discussed in Chapter Numerical resultsShown in Figure 6.1 are "true" and parameterized smoke injection heights. The formeris obtained directly from the LES, as per Section 4.2. The latter is determined iterativelyusing the proposed smoke injection height parameterization (see Appendix B.4 forimplementation details).Individual prediction errors do not appear to be a function fireline intensity, as indi-cated by scatter point color in Figure 6.1, or ambient winds (not shown). While overallthe scheme’s performance is encouraging, the small discrepancy between the unityand regression lines suggests a linear bias. This can be remedied by applying biascorrection using regression parameters from the fit shown in Figure 6.1. This optimizedmodel produces errors on the order of 20 - 30m for equilibrium plume centerline heightzCL, as suggested by the interquartile range shown in Figure 6.3d. Model bias will be63500 1000 1500 2000 2500 3000zCL [m]2000200error [m](a) Error as f(zCL): RAWzCL2000200error [m](b) Error Statistics500 1000 1500 2000 2500 3000zCL [m]2000200error [m](c) Error as f(zCL): BIAS CORRECTEDzCL2000200error [m](d) Error StatisticsITERATIVE SOLUTIONFigure 6.3: Performance of the smoke injection height parameterization based onthe iterative solution (Equation 6.8). (a) Non-bias corrected prediction error (true- modelled zCL ) as a function of zCL. (b) Error statistics for non-bias correctedvalues. The box and whiskers span IQR and 1.5 x IQR, respectively. Median valueshown in orange. (c) Bias-corrected prediction error as a function of zCL. (d) Errorstatistics for bias-corrected values.addressed in further detail in Section 6.3.Given smooth averaged profiles from the synthetic dataset and excluding condi-tion R8 (adiabatic free atmosphere), the explicit solution using Equation 6.9 offerscomparable accuracy to the iterative version for both raw and bias corrected datasets(Figure 6.4) . I address the limitations of using the explicit approach in Section Model sensitivityTo asses how sensitive the smoke injection model performance is to the particularchoice of bias correction parameters, I partition my original plume dataset into train-ing and testing groups through random sampling. I obtain the linear bias correctionparameters using training data only (80% of runs). I then apply our bias-correctediterative solution to the test group (remaining 20% of the runs) and assess model64500 1000 1500 2000 2500 3000zCL [m] 2000200error [m](a) Error as f(zCL): RAWzCL2000200error [m](b) Error Statistics500 1000 1500 2000 2500 3000zCL [m] 2000200error [m](c) Error as f(zCL): BIAS CORRECTEDzCL2000200error [m](d) Error StatisticsEXPLICIT SOLUTIONFigure 6.4: Performance of the smoke injection height parameterization based onthe explicit solution (Equation 6.9)). (a) Non-bias corrected prediction error (true- modelled zCL ) as a function of zCL. (b) Error statistics for non-bias correctedvalues. The box and whiskers span IQR and 1.5 x IQR, respectively. Median valueshown in orange. (c) Bias-corrected prediction error as a function of zCL. (d) Errorstatistics for bias-corrected values.accuracy. Figure 6.5 summarizes the performance and sensitivity of the proposedparameterization, based on 10 trials of sampling with replacement. Consistently highPearson correlation shown in the trial histogram in Figure 6.5c, are encouraging, andsuggest that the particular choice of simulations used in bias correction does not havea strong impact on accuracy.6.2.3 Evaluation with observationsNext, I apply the proposed parameterization to a real-life case-study. I use observa-tional data from the RxCADRE L2G prescribed burn (Section 2.3) and it’s numericalsimulation detailed in Chapter 3.Recall the strip headfire pattern used to ignite the grass lot (shown in Figure 3.1). Iestimate the burn’s input fireline intensity parameter I for this complex ignition in two651 2 3 4 5 6 7 8 9 10trial no.2001000100200error in zCL [m](a) TRIAL ERROR1all runs2001000100200error in zCL [m](b) ALL TRIALS0.991 0.992 0.993R-value012345count(c) R-VALUE SENSITIVITYFigure 6.5: Analysis of model sensitivity to the choice of bias correction parame-ters. (a) Error distributions for individual trials using independent (test) data. (b)Error distribution for all trials using independent (test) data. (c) Sensitivity of R-value (correlation coefficient) for all trials.66different ways: from raw data collected during the burn as well as from the numericalsimulation. The observations-based value Iobs is derived from the integral heat fluxdata obtained from the Highly Instrumented Plots (HIPs) fire behavior package (FBP)sensors [28]. I use the provided time-integrated values, averaging between all sensorswith confirmed fire at the sensor location (as indicated by video footage [7]). I thenobtain the mean value (in kinematic units) of 236 K ms−2 and multiply it by the aver-age measured rate of spread (ROS) value of 0.38 m s−1 [7] for the same sensors toconvert to spatially-integrated heat flux for a single fire line. I assume that this value isrepresentative of the remaining three firelines, hence:Iobs = 236 ·0.38 ·4= 359 (6.10)in units of K m2s−1. Note, that raw data for both heat fluxes and ROS values haveextremely large associated uncertainties. Observed ROS values vary by nearly a factorof two, depending on the measurement technique used. While I have included onlylocations with ignition confirmed by video footage in my calculations, heat fluxes stillvary up to a factor of four between sensors.For comparison, I also obtain an LES-based integrated fireline intensity value ILES.Due to wind shear, as measured by the sounding launched prior to the burn, the CWIdirection at the surface differs from the one used to estimate CWI smoke. ILES was,hence, estimated by assuming 125 degree rotation of LES fields, based on the lowestavailable wind direction measurement. I use trapezoidal rule to numerically integratethe mean crosswind heat flux along the depth of the fireline (see Appendix B.3) andfind ILES = 1002 K m2s−1.I apply the iterative solution (Equation 6.8) to find two zCL estimates based on Iobsand ILES, and compare them to the CWI smoke injection height obtained from the LES.The results are shown in Figure 6.6. The parameterized injection heights are under-predicted by 20 m and 70 m for LES- and observations- derived I values, respectively.670 500 1000 1500 2000 2500 3000CO2 concentration [ppm]02505007501000125015001750height [m]EVALUATION OF INJECTION MODEL USING RxCADREvertical CO2 profileIQRLES zCL = 1130 mmodelled zCL = 1110 m,  using ILESmodelled zCL = 1060 m,  using IobsFigure 6.6: Model evaluation using a case-study of a real prescribed burn(RxCADRE 2012). CWI smoke concentration profile shown in blue. "True" zCLobtained directly from LES shown in solid black. Solid orange and dashed redlines correspond to zCL estimates obtained using the iterative solution of theproposed smoke injection height parameterization (Equation 6.8), based on LES-and observations- derived fireline intensities, respectively.6.3 Discussion6.3.1 Context and applicationsThe abovemodel evaluation indicates encouraging performance for the proposed smokeinjection parameterization (Equation 6.8) at little computational cost. An additionaladvantage of the method is that it does not require making simplifying assumptionsregarding the shape and heat flux distribution of the fire. This allowsme to easily applythis approach to complex heat sources, such as one produced with the strip head fireignition pattern during the RxCADRE L2G prescribed burn (Figure 3.1).Notably, this also makes direct comparison of the proposed method with exist-68ing schemes difficult. A vast majority of established plume-rise parameterizationsconsider a simplified fire geometry and a uniform (or total) heat flux as input param-eters. [4, 6, 9, 20, 64]. Hence, applying these methods to my synthetic data wouldrequire making many simplifying assumptions regarding the heat source. Subsequentintercomparison would hardly be useful, as each scheme’s performance would largelyreflect how well the inputs are calibrated to the given plume-rise formulation.Unlike most existing plume rise parameterizations, [6, 20, 64] I focus on a CWIcenterline. The proposed scheme can be viewed as a "bulk method", having somecommon ground with the thermodynamic approach used in the FireWork modellingframework [4, 9] and the energy balance approach proposed by Sofiev et al. [69]. Morespecifically, I make no attempt to predict the full evolution of the rising plume centerlinevelocity or temperature before it reaches its equilibrium height. Rather, I focus on theenergy balance of the plume within a "penetration layer".Through analysis of the 140 LES experiments for plumes under variable fire andatmospheric conditions detailed in Chapter 5, I found that near-surface and boundary-layer plume dynamics are extraordinarily complex. While some aspects of plume mix-ing can be reasonably accounted for by making common entrainment assumptions,complicated features resulting from fire-atmosphere coupling, such as formation oflateral vortices and fireline wind convergence zone, are difficult to parameterize di-rectly. Hence, I apply the energy balance approach to a layer well above the surface,starting from a reference height zs close to the top of the ABL.As noted in Section 6.1, the implicit functional form of my solution (Equation 6.8)can be interpreted as a characteristic timescalemultiplied by the characteristic velocityscale w f . By rearranging Equation 6.7 and substituting Equation 6.8 for z′ it can beshown (see Appendix B.2) that the two expressions for w f are equivalent, namely:w f =[Iziθ ′]=[gIz′θszi] 13 (6.11)The scaling relationship between vertical plume velocity and cubic root of fire heat hasbeen previously established with both Rio’s and Freita’s models [20, 64] (discussed inSection 2.2), although my formulation includes different variables inside the radical.While both ofmy forms forw f and bothmodel formulations (the simplified Equation 6.7and the expanded Equation 6.8) are mathematically equivalent, conversion from oneform to another requires repeated exponentiation. This results in large prediction er-rors; hence, for practical applications, the full Equation 6.8 should be used.696.3.2 Dimensionless relationshipAs discussed in Section 6.1, I can obtain an explicit solution for zCL by making addi-tional assumptions about the vertical profile of potential temperature above the ABL.This allows me to reduce Equation 6.9 to a similarity relationship with two dimension-less groups z and H , denoting the left-hand side (LHS) and right-hand side (RHS) ofEquation 6.12, respectively. Nondimensional z and H are linearly related, as shown inFigure 6.7. The simple relationship suggests that my modelling results could fairlyeasily be scaled to a wider range of fire and atmospheric conditions, beyond thosecaptured by the synthetic dataset presented in Chapter 4.z′zi︸︷︷︸z=[θsgγ3] 14[Iz3i] 12︸ ︷︷ ︸H(6.12)6.3.3 Model biasThe raw, non-bias- corrected form of the proposed parameterization suffers from apositive bias for tall plumes, as suggested by Figure 6.3c and Figure 6.4c. In otherwords, zCL is overpredicted for plumes injected high above the ABL. One could spec-ulate that this is due to the simplifying assumption that most of the cooling, mixing,and dilution occurs below the reference level zs in upper portion of the ABL.As the distance between zs and zCL increases for tall plumes and as the smoketravels further into the free atmosphere, this assumption becomes increasingly lessaccurate. Additional radiative cooling and entrainment of ambient air is, therefore,unaccounted for, resulting in over-prediction for zCL.This issuemaypartially be corrected formydatasetwith the applied bias-correction.However, cases with strong shear turbulence and active smoke mixing above the ABLare still likely to be overestimated.700.0 0.2 0.4 0.6 0.8 1.0H0. RELATIONSHIP1:1 line20000400006000080000100000120000140000fireline intensity [Km2 /s]Figure 6.7: Similarity solution for dimensionless groupsH and z, corresponding tothe RHS and LHS of Equation 6.12, respectively. Scatter points represent individualLES runs, colored by fireline intensity parameter I. 1:1 line is shown in dashed greyfor reference.6.4 SummaryIn this chapter I present a simple parameterization (Equation 6.8) for predicting CWIsmoke-plume centerline height from a wildfire of an arbitrary shape and intensity. Iconstrain and evaluate the proposed approach using the synthetic LES-derived plumedataset developed for a wide range of fire and atmospheric conditions detailed inChapter 4. Based on the results of cross-evaluation with LES data as well as a realprescribed burn case study, the parameterization offers reasonable accuracy at littlecomputational cost.716.4.1 LimitationsThe most significant limitation of the proposed smoke injection height parameteriza-tion is that it applies only to smoke plumes with no water vapor condensation. Latentheat effects are not considered. Hence, smoke injection level for extreme pyroconvec-tive events (e.g. flammagenitus clouds [52]) will likely be grossly under-predicted withthe given formulation.Another limitation is the inherently implicit form of the full model Equation 6.8.While I have not encountered any issues using an iterative solver to find zCL, atypical(or extremely noisy) ambient atmospheric soundings could potentially affect conver-gence. The explicit form (Equation 6.9) derived using the idealizing ambient sounding(Figure 6.2) offers a possible solution for such cases. However, it fails forweakly stableand adiabatic free atmosphere (eg. condition R8 in Figure 4.1), as θs is extrapolatedinto lower levels of ABL.Lastly, the parameterization has been developed and tested only for typical daytimefair-weather atmospheric conditions. I have not assessed model performance for sta-ble night-time atmospheric profiles or in the presence of strong vertical windshear.6.4.2 Big pictureGiven the above limitations, a reasonable question to ask is: how useful is the pro-posed approach? In its current form (without latent heat effects), it’s unlikely to be suit-able for large-scale applications (e.g. global chemical transport models). However, ithas the potential to improve regional air quality tools, since wildfire emissions sourcesare largely dominated by in- or near- ABL non-condensing smoke plumes (Section 2.3).The method can also be applied as a classifier to distinguish penetrative vs. non-penetrative plumes, which is often vital for subsequent dispersion modelling [69], asdiscussed further in Chapter 7.Given the energy-balance formulation of this plume rise parameterization, it maybe possible to incorporate latent heat effects by including an extra PE term in Equa-tion 6.1. Similarly to the iterative process for finding a level of neutral buoyancy withEquation 6.8 using potential temperature, it may be possible to predict plume conden-sation level using ambient humidity profile. A big obstacle to this development, how-ever, is ensuring that WRF-SFIRE can capture aerosol microphysics, while accuratelysimulating input fire moisture fluxes. As noted in Section 3.2.1, my model evaluationof fire behavior within WRF-SFIRE is fairly primitive. Greater confidence in fire inputparameters, following comprehensive evaluation of model microphysics, would most72certainly pave the way for further plume rise parameterization improvement.73Chapter 7Beyond injection height: Modelling thedistribution of smoke in the atmosphereThe parameterization introduced in Chapter 6 enables one to predict the initial cen-terline height of a wildfire smoke plume. However, wildfire emissions are actuallydeposited over a greater depth between the surface and the equilibrium level, withsignificant portion remaining above the mean smoke injection height. Moreover, thephysics that govern mixing and dispersion within the ABL differ from those in theentrainment layer and the free troposphere. Hence, in order to accurately predict down-wind concentrations from awildfire, we first need to know: (i) Which plumes will pene-trate the ABL? Once penetrative plumes are identified, we then need to determine: (ii)How far above the equilibrium level does the plume extend? and (iii) What fractionof wildfire emissions remains in the ABL?. The following sections aim to answerthese questions using ideas inspired by numerical experiments of Chapter 5, equationsderived in Chapter 6 and synthetic data from Chapter 4.7.1 Plume classificationPrevious Chapter 6 applied an energy balance parameterization to predict the meansmoke injection height zCL of a given penetrative plume. For this purpose, only plumesrising above ABL top zi were included in the synthetic plume dataset used to constrainand evaluate the approach (see Table 4.3). In this section, I step back and consider allperformed simulations, to determine whether the same equations can also be used toclassify penetrative vs. non-penetrative plumes.The synthetic dataset described in Chapter 4 consisted of 140 runs and excluded7 simulations, where the plume remained trapped in the ABL (see Table 4.3 and Ta-ble 7.1). I determined this by visual analysis of CWI centerline and smoke fields. The ex-74cluded plumes typically exhibited oscillatory or irregular centerline behavior (within theABL) with little or no smoke injected above zi (see sample ABL plume in Appendix A.2).For several combinations of fire and atmospheric conditions, however, making thedistinction was challenging. For this reason, I included these "marginally-penetrative"plumes in the dataset.In real-world applications, classification is a fundamental first step in plume rise pa-rameterization process [69]. A viable automated method for categorizing penetrativevs. non-penetrative plumes requires that the distinction be made based on availableinput parameters, rather then smoke observations (as such are typically not availableat the time of making a forecast).Conveniently, I can use Equation 6.8 to obtain a zCL estimate for any combinationof input parameters without prior knowledge of plume type. It can, hence, be appliedas a classifier by requiring that for a penetrative plumezCL > zi+ (7.1)where zi+ denotes the height of the upper edge of the numerical grid box (or ambientatmospheric sounding) containing zi. In other words, this definition ensures that zi andzCL are not in the same vertical model level. If this condition is not satisfied, the plumeis assumed to be non-penetrative.This approach correctly classifies all non-penetrative plumes that had been iden-tified by visual analysis (Table 7.1). In addition, several plumes exhibiting marginalbehavior are also classified by Equation 7.1) to be non-penetrative.For the purpose of subsequent dispersionmodelling within real-world applications,non-penetrative plumes (i.e. all plumes listed in Table 7.1) would be assumed to be-come uniformly mixed in the vertical within a few convective turnover distances down-wind of the fire. Turbulent eddies within the ABL produce a well-mixed layer, resultingin relatively homogeneous vertical distribution of pollutants between the surface andzi. In contrast, predicting the downwind smoke behavior for plumes that extend abovezi, spanning the ABL, the entrainment layer, and/or the free troposphere, is significantlymore difficult. The goal of the following sections is, therefore, to parameterize the ver-tical smoke profiles of the remaining 133 synthetic plumes classified as "penetrative"by Equation 7.1.75Table 7.1: Identifying non-penetrative plumes using visual analysis vs. automatedclassification. Plume name denotes wind condition W, fuel type F and initialatmospheric profile R.Plume Visual analysis Automated classificationW5F9R1 X XW5F1R3 X XW5F8R3 X XW5F9R3 X XW5F1R7 X XW5F8R7 X XW5F9R7 X XW5F1R0 XW5F1R1 XW5F8R1 XW5F10R3 XW5F11R3 XW5F1R4 XW5F11R4 X7.2 Predicting smoke distribution above zCLFrom hereon, for the identified penetrative plumes I will treat smoke injection heightzCL and plume penetration distance z′ as "known". Hence, I will use the LES-derived,rather than estimated zCL and z′ values. This ensures that the errors associated withmodelling the vertical smoke profile C(z) are independent of mean plume rise param-eterization.7.2.1 Determining maximum riseRecall from Section 5.5, that above ABL the plume core (represented by the center-line) experiences little mixing with the ambient environment. Yet due to momentumacquired during the initally-buoyant rise, the plume typically overshoots its equilibriumlevel. Naturally, one can expect some of the smoke to be detrained in the atmosphericlevels between the peak centerline height ztop and zCL. In other words, ztop is potentiallya useful estimate for the upper edge of a given CWI smoke profile.Amplitude of the initial centerline oscillation about its equilibrium level is likely tobe roughly equal to the original "displacement" of the plume from zCL. Therefore, Ihypothesize that:ztop = zCL+ z′ (7.2)761000 1500 2000 2500 3000 3500 4000 4500zCL+ z′ [m]10001500200025003000350040004500z top from LES [m]PREDICTING DISTRIBUTION TOP: R=0.9940060080010001200z′ [m]Figure 7.1: Estimation of plume top ztop using plume penetration distance z′."Truth" value was obtained from the LES dataset of 133 penetrative plumes,assuming ztop is the height at which smoke concentration is equal to 0.15% ofthe maximum value at zCL (≈3 standard deviations from the peak for Gaussiandistributions). Colors correspond to penetration distance z′. Unity slope (dashedgrey) is shown for reference.This relationship is plotted in Figure 7.1, suggesting a good fit to LES data (Pearsoncorrelation coefficient R=0.99). To determine the "true" top of CWI smoke profiles fromLES , I defined the upper plume edge such thatC(ztop) = 0.0015 ·C(zCL). This, assumingGaussian spread, corresponds to a smoke concentration three standard deviationsfrom the peak. Based on this definition, the scatter points generally fall on or closeto the unity line (dashed grey), suggesting the above hypothesis (Equation 7.2) is notunreasonable. Greater overshoot distance (as indicated by scatter point color) tendsto be associated with increased scatter about unity. However, overall this appears tobe a viable approach for predicting ztop.777.2.2 Determining spread above zCLIn order tomodel CWI smoke distribution above themean injection level, I assume thatthe concentration drop off between the maximum at zCL and ztop is roughly Gaussian.In such case, the upper portion of the smoke profile C(z) can be described with thefollowing equation:C(z)|z>zCL = Ae−(z−µ)2/(2σ2top) (7.3)where A =C(zCL) is the distribution amplitude, µ = zCL is the location parameter, andσtop is a scale factor representing mean smoke spread above zCL.Typically, actual absolute concentration values of wildfire emissions are calculatedoutside of plume rise parameterization scheme (by corresponding fuel consumptionand emissions modules) within the host smoke modelling framework. Therefore, forthe purpose of this chapter I assume C(zCL) is known. For air quality applications, thenormalized dimensionless smoke profilesCN(z) can be obtained by setting A= 1.Based on the definition of ztop from Section 7.2.1 (i.e. upper edge of the plume cor-responds to concentrations 3 standard deviations below themaximum), I can estimateσtop as:σtop =(ztop− zCL)3=z′3(7.4)Given Equation 7.4 and assuming Gaussian functional form of Equation 7.3, I canparameterize the smoke distribution above zCL using only z′ value obtained from Equa-tion 6.8. Sample fits producedwith this approach are shown in Figure 7.2 and Figure 7.3for typical low and high wind conditions, respectively.For the low wind case (Figure 7.2), I have intentionally selected a run with apprecia-ble error in ztop. Notably, as indicated by the relatively small discrepancy between themodelled (orange) and LES-derived (dotted grey) curves above zCL, this error doesn’ttranslate into large differences between the distributions.The vertical smoke profile in Figure 7.2 appears to be well-captured by a singleGaussian curve. Namely, the profile below and above zCL can be modelled using thesame σ . In contrast, the distribution in Figure 7.3 is markedly wider below zCL thanabove. The following section explores possible explanations for this behavior.780 20 40 60 80CWI concentration [ g kg 3]0500100015002000250030003500height [m]W4F7R5TEsmoke profilezCLztop LESztop modelledbased on LES ztopbased on modelled ztopIQRFigure 7.2: LES-derived (blue) and parameterized (orange) smoke distributionunder low (4 ms−1) ambient wind conditions. LES-derived and parameterizedztop values are plotted in dashed orange and dashed grey, respectively. Alsoshown, IQR range of LES smoke profile (blue shading), zCL (dash-dotted blue) andparameterized distribution based on LES-derived ztop.790 10 20 30 40 50 60 70CWI concentration [ g kg 3]0500100015002000250030003500height [m]W12F7R3smoke profilezCLztop LESztop modelledbased on LES ztopbased on modelled ztopIQRFigure 7.3: LES-derived (blue) and parameterized (orange) smoke distributionunder high (12 ms−1) ambient wind conditions. LES-derived and parameterizedztop values are plotted in dashed orange and dashed grey, respectively. Alsoshown, IQR range of LES smoke profile (blue shading), zCL (dash-dotted blue) andparameterized distribution based on LES-derived ztop.807.3 Predicting smoke distribution below zCL7.3.1 Accounting for ambient environmental mixing in the ABLWeknow fromboundary layer theory thatmixingwithin the ABL is typically governed bysurface buoyancy flux andwind stress [70]. Due to strong near-surface shear, highwindconditions are typically associated with mechanically-generated turbulence (forcedconvection). In contrast, under calm conditionsmixing is largely the result of continualturnover of buoyant thermals rising from the surface (free/convective turbulence). Of-ten the relative importance of each type of convection is expressed as the dimension-less Richardson numberRi, corresponding to the ratio of buoyant and shear productionof TKE.In a similar fashion, LES data suggests that the width of the smoke distribution be-low zCL appears to be a function of the relative magnitudes of fire updraft and ambientconvection. Previously, in Section 6.3, I introduced an expression for the characteristicfire velocity w f (Equation 6.11). Using w f I can estimate the relative (to backgroundthermals) updraft speed wr aswr = w f −w∗ (7.5)where w∗ is the Deardorff velocity scale, representing the mean vertical velocity ofbackground thermals, given byw∗ =[gziSTv] 13 (7.6)Tv and S denote virtual absolute temperature of the ABL and kinematic surface sensibleheat flux, respectively. To obtain a characteristic horizontal ABL wind Ua, I use theaverage value from the ambient sounding between 0.5zi and zi. I exclude the bottomhalf of the ABL, as various roughness lengths associated with different fuel typesproduce variable surface layer depths. I then define a dimensionless ratio Rw, suchthatRw =Uawr,w fw∗ ≥ 1.5Uaw f,w fw∗ < 1.5(7.7)This conditional formulation ensures that Rw remains reasonable for cases with w f ≈wr. I determined the absolute threshold based on informal sensitivity analysis of LESdata. Finally, I define the spread of the smoke profile below zCL as:σbot = Rwσtop (7.8)81Substituting σbot in place of σtop in Equation 7.3, I can obtain the bottom portion of thesmoke profile, as shown in Figure 7.2 and Figure 7.3. For low wind case (Figure 7.2)Rw ≈ 1, producing a roughly symmetrical (about zCL) Gaussian curve. For high windcase with Rw > 1 (Figure 7.3) there is an obvious skew in the distribution, with largerportion of smoke remaining in the ABL.In the following section I examine howaccurately this approach partitions the smokebetween the ABL and the free troposphere under the variety of fire and wind conditionscaptured by the synthetic plume dataset.7.3.2 Estimating errorsUsing the approach introduced in this chapter, I parameterize the normalized verticalsmoke distributions of all penetrative plumes in the LES dataset (as identified by theclassification condition in Section 7.1). To isolate potential sources of error, I calculatetwo separate solutions using (i) LES-derived ztop and (ii) modelled ztop values. Samplecurves representing the two solutions are plotted in dotted grey and solid orange inFigure 7.2 and Figure 7.3.For each solution, I then calculate mean absolute error (MAE) separately for valuesbelow and above zi, as well as over the entire depth of the smoke column. The resultsare summarized in Figure 7.4.As expected, LES-derived ztop generally produces slightly more accurate solutionsthan the modelled ztop, though the differences are not statistically significant. Overall,the proposed approach appears to properly partition smoke between the ABL and thefree atmosphere above, accurately allocating 90-95% of normalized emissions.82ABL FREE ATM TOTAL0. (normalized concentration)LES-derived ztopABL FREE ATM TOTAL0. (normalized concentration)Modelled ztopNORMALIZED DISTRIBUTION MAEFigure 7.4:MAEof parameterized smoke distributionsCN(z)based on LES-derived(left) and modelled (right) ztop. Orange line corresponds to median value. The boxand whiskers span IQR and 1.5×IQR, respectively, with the notch denoting the 95%confidence interval of the median (median±1.57×IQR/n 12 ).7.4 Distributing smoke laterallyThe parameterizations presented in the previous and current chapters focused entirelyon CWI smoke vertical distributions. This approach is largely motivated by its mostlikely application: a smoke modelling framework.My numerical plume dataset contained fires with lengths ranging from 1 to 4 kilo-meters in the cross-wind direction. For comparison, typical grid-spacing of a regionalsmoke dispersionmodelling system is≈10 km [9, 66]. While common in the real world,the simulated fires captured by the dataset would, therefore, be treated as a subgrid-scale effect within these systems. Thismeans that the smoke distribution in the cross-wind (y) direction would be considered to be uniform across the width of the cell ycontaining the fire. In other words:C∗N(y j,z) =CN(z)∆y(7.9)where j denotes subgrid-scale index, CN(z) is normalized CWI concentration in unitsof mass/area,C∗N(y j,z) is normalized concentration in units of mass/volume and ∆y isthe horizontal resolution of the host model in the cross-wind direction. The parame-terized CWI smoke profile would be applied to the vertical column directly above the83ignited cell (i.e. plume tilt and/or other local-scale effects would not be relevant withinthese coarse-grid applications). Dispersion and plume growth would be subsequentlyhandled by the appropriate modules within the host smoke modelling framework.A wide range of factors affect the lateral distribution of smoke within the plume.Among them are the shape and curvature of the fireline, ambient convection, verticalpotential temperature profile, winds, vorticity, fire intensity and many others. Whilebeyond the scope of both the synthetic dataset and of this dissertation, the remainderof this section offers some ideas for future investigation.Shown in Figure 7.5a is the total normalized smoke of a sample simulated plume,as integrated over the depth of the domain in the along-wind direction. For most ofmy simulations along-wind integrated (AWI) plumes are not symmetrical, as the fireswere not ignited instantaneously. A representative lateral smoke distribution can beobtained by taking a cross-section at zCL (Figure 7.5b). By comparing cross-sectionsof different simulated plumes, I can examine the effects of some parameters in mysynthetic dataset on the width and shape of the lateral (cross-wind) distribution (Fig-ure 7.6).Specifically, I compare runs with different (a) fire intensities, (b) fireline lengths and(c) ambient winds, while holding other simulation conditions constant (Figure 7.6). Ofcourse, as many of the parameters interact in complex non-linear ways, these compar-isons do not constitute true controlled experiments. Generally, LES data suggests thatthe extent to which the plume widens is largely governed by the shape and intensity ofthe fire.Recall from Chapter 5 that wildfire plumes often exhibit anvil-like behavior, withsmoke outflow levels marked by increased advection relative to ambient winds. Onecan speculate, that this radial outflowmay contribute to plume widening. Hence, moreintense fires, associated with stronger updrafts and fire-induced winds appear to havebroader lateral smoke distributions than weaker fires (Figure 7.6a).In a similar fashion to Section 7.2, I can characterize the strength of the updraftand the associated lateral spread using the fire velocity scale w f (Equation 6.11). Thisdoes not in any way constitute a method for parameterizing the smoke distribution inthe cross-wind direction. However, an extremely crude normalized approximation canbe described as follows:C∗N(y,z) = e−(y−y f )2(2σ2y ) (7.10)where y f is the cross-wind location of the center of the fire and σy = 1870+215∗w f . Idetermined the fit parameters for σy (Equation 7.10) from linear regression on LES data840 2000 4000 6000 8000cross-wind distance [m]0100020003000height [m](a) AWI SMOKEzCL0.0 0.5 1.0normalized concentration0 2000 4000 6000 8000 10000cross-wind distance [m] concentration(b) CROSSSECTION AT zCLFigure 7.5: Lateral smoke spread from a sample simulated wildfire plume. (a) To-tal normalized along-wind (y,z) smoke. Dashed grey line denotes smoke injectionlevel zCL (b) Horizontal cross-section obtained from above at zCL.(R=0.80). The approximated lateral smoke distributions obtained using this approachare shown as dotted lines in Figure 7.6.In conclusion, although parameterizations for the initial lateral spread of the smokecan be devised, most operational applications, with coarse-grid dispersionmodels, willinject the smoke plume into one grid column. Hence, initial lateral spread is not needed,because the injected smoke is assumed to to be distributed uniformly within each gridcell.850 2000 4000 6000 8000 10000cross-wind distance [m] concentration(b) FIRELINE LENGTH EFFECT1 km4 km0 2000 4000 6000 8000 10000cross-wind distance [m] concentration(c) AMBIENT WIND EFFECT3 m/s12 m/s0 2000 4000 6000 8000 10000cross-wind distance [m] concentration(a) FIRELINE HEAT EFFECTlow intensityhigh intensityFigure 7.6: Parameters affecting lateral smoke spread from a wildfire. Solid anddotted lines denote true (LES) and approximated (Equation 7.10) cross-sections,respectively. (a) Low (blue) vs. high (orange) fireline intensity. (b) 1 km (blue) vs.4 km (orange) firelines. (c) Low (blue) vs. high (orange) winds.867.5 Summary of approachIn this chapter I introduce a simplemethod for predicting the normalized vertical distri-butionCN(z) of CWI smoke from a wildfire under known daytime ambient atmosphericconditions. The approach can be summarized with the following steps:1. For a given wildfire, obtain zCL and z′ (Equation 6.8)2. Perform automated plume classification (Equation 7.1)(a) For non-penetrative plumes assume uniform smoke distribution betweenthe surface and zi(b) For penetrative plumes proceed to the following steps3. Calculate σtop (Equation 7.4)4. Calculate σbot(a) Calculate w f (Equation 6.11)(b) Obtain w∗ andUa from ambient atmospheric and surface data(c) Calculate Rw (Equation 7.7) and σbot (Equation 7.8)5. Model the full normalized vertical smoke profile of CWI concenration:CN(z) = e−(z−zCL)2/(2σ2) (7.11)whereσ =σtop, z≥ zCLσbot , z< zCLTo obtain actual concentrations, it may be necessary to make additional assump-tions about how the smoke is distributed in the cross-wind direction (Section 7.4),although most dispersion models will not need the initial lateral spread.7.6 LimitationsThe overall encouraging error statistics presented in Section 7.3.2 should be treatedwith caution, as all simulations in the synthetic plume dataset were initialized with thesame ambient sensible heat flux at the lower domain boundary. Various ABL depthsand temperatures corresponding to different R conditions produce a wide range of w∗values, however, S is constant for the entire dataset.87The dependence of the parameterization on w∗ is in itself a limitation, as in real-world (rather then numerical modelling) applications observations of surface fluxesare typically not available. However, rough estimates can be made in the field usingPasquill-Gifford methods [21], such as considering insolation, cloud cover and windspeed. Also, while the approach doesn’t appear to be very sensitive to errors in ztop,it, never-the-less, relies on the relative definition of the plume penetration distance z′from the previous Chapter 6.Lastly, Section 7.4 merely skims the surface of the complex analysis required tounderstand what processes govern smoke distribution in the cross-wind direction.7.6.1 Big pictureA truly robust assessment of uncertainties associated with the proposed parameter-ization would require expanding the parameter space of the LES plume dataset. Inparticular, it would be important to include directional shear in the imposed ambientwinds, while also varying the surface sensible heat flux. Never-the-less, even in itscurrent form it is likely going to offer an advantage over "single-level" smoke injectionschemes or those relying on "uninformed" assumptions (e.g. linear interpolation ofconcentrations between the injection height and the surface; single Gaussian distribu-tion with a fixed spread).While encouraging, these results are still dependent on accurate input parametersfrom other components of smokemodelling systems. Namely, themethods presentedhere rely on fire behavior information to predict the mean smoke injection level andplume penetration distance, as well as emissions estimates to convert the normalizedprofiles to absolute concentration values. Moreover, much theoretical work is neededto understand how the smoke is distributed in the cross-wind direction. More broadly,the tools presented in this chapter are merely small elements of a complex modellingchain.88Chapter 8ConclusionsModelling plume rise from wildfires is a complex challenge that lies at the interfaceof fluid dynamics, atmospheric physics and fire behavior science. To date, it remainsone of the weakest links in our ability to predict where and how smoke from wildfirestravels in the atmosphere. This dissertation was guided by a set of research questions,aiming to fill the knowledge gaps in our current state of knowledge on the subject. AsI revisit them below, I hope that my answers contribute to the interdisciplinary effort toimprove our understanding of wildfire atmospheric dynamics.• Can a coupled fire-atmosphere numerical model accurately simulate smokeplume rise from a real fire?In short, yes. The model evaluation case study presented in this thesis (Chap-ter 3) compared fire and smoke behavior from a WRF-SFIRE simulation to obser-vations from a comprehensive field experiment (RxCADRE). While rudimentaryin some aspects, the analysis suggested that the model reasonably capturesplume kinematics and can serve as a useful tool for learning about the physicalprocesses involved.• What can we learn about the behavior of the atmosphere around the fire fromnumerical experiments?Detailed synthetic data produced by WRF-SFIRE (Chapter 4) allowed me to ex-periment with a range of fire and atmospheric conditions well beyond the ca-pacity of any observational campaign. Complex dynamical features (includingflow convergence, vorticity, interactionswith boundary layer turbulence) revealedby these numerical experiments challenge several common assumptions abouthow smoke plumes mix with the atmosphere (Chapter 5). Most aspects of fire-atmosphere interactions detailed in this work remain to be quantified.89• Can synthetic data be used to parameterize smoke plume rise for air qualityapplications?Based on insights gained from the numerical experiments, I developed a simpleenergy-balance approach, which allows to determine:– What is the mean smoke injection height of a given wildfire plume?The proposed parameterization (Chapter 6) allows to predict the centerlineheight of a CWI penetrative plume froma fire of arbitrary shape and intensityunder a wide range of ambient conditions. I demonstrated that for daytimefair-weather plumes there exist a linear dimensionless relationship and acharacteristic fire velocity scale, which govern the vertical penetration dis-tance of the plume in the atmosphere above the ABL.– Which plumes will penetrate the ABL?Using equations fromChapter 6, I showed that the proposed energy-balanceapproach can also be applied as an automated classifier to distinguish pen-etrative vs. non-penetrative plumes.– How are wildfire emissions vertically distributed in the atmosphere?In Chapter 7 I demonstrated that parameterized plume penetration distanceand fire velocity scale can be used to predict the full vertical profile of smokeemissions above and below the mean injection height.In Section 7.5 I provide a complete set of algorithms needed to incorporate thenew plume rise parameterization into an air quality model.The natural next step beyond this thesis is the implementation of the new plumerise scheme within a regional smoke prediction system (e.g. BlueSky Canada). Muchwork remains to be done to ensure that the new methods are calibrated to work wellwith the existing fire behavior and emissions models. Moreover, the inherently numer-ical perspective of this thesis is bound to be challenged, when the ideas and methodspresented here are put to trial in real-world applications.As extreme wildfire events become more common under a changing climate, ourability to reduce the health risks and mortality associated with smoke exposure willbecome critically important. My hope is that the contributions presented here will helpadvance our current smokemodelling tools andmitigate some of the negative impactsof wildfires for human health and the environment.908.1 ContributionsThe specific contributions of this thesis are as follows:• Analysis of WRF-SFIRE model performance using an integrated observationalRxCADRE dataset (Chapter 3). The results and methods (as well as sampleinitialization files) of this evaluation study can be used for model developmentand improvement.• A synthetic plume dataset consisting of 133 penetrative and 14 non-penetrativeplumes over a wide range of atmospheric and fire conditions (Chapter 4, Ta-ble 4.3), to facilitate smoke dispersion research in the absence of detailed ob-servational data.• Ananalyticalmethod for determining themean injection height of a smoke plumefrom an arbitrarily shaped wildfire in a daytime atmosphere (Chapter 6). The ap-proach canbe applied as a classifier to distinguish penetrative and non-penetrativeplumes (Section 7.1) aswell as a plume rise parameterizationwithin a host smokemodelling system.• A Gaussian-based method for predicting the vertical distribution of CWI wildfireemissions in the atmosphere (Chapter 7), which can be applied within air qualityand dispersion models.8.2 What’s ahead?Methods and ideas presented in this thesis are aimedat improving a single link in a longand complex modelling chain of smoke prediction systems. Due to lack of scientifictheory connecting the numerous physical processes involved, many components ofthese frameworks still rely on simplifying parameterizations. Hence, in the short term,I hope that the methods contributed by this work can be implemented within existingair quality systems and help improve their accuracy.Yet I imagine that the next generation of smoke modelling frameworks could har-ness the power of increasinglymore affordable cloud computing resources. Thiswouldeventually allow us to replace parameterized components (like combustion and smokedynamics) of our numerical systems with directly computed full-physics models. This,in turn, could help capture many dynamical feedbacks that exist between the fire, thesmoke and the atmosphere. The importance of understanding these feedbacks ex-91tends well beyond air quality, and carries fundamental consequences for climate pre-diction.Hence, my long-term vision and hope is that accurate and intelligent smoke mod-elling systems of the future will have no need for parameterizations akin to ones con-tributed by this thesis.92Bibliography[1] G. L. Achtemeier, S. A. Goodrick, Y. Liu, F. 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Bulletin of the AmericanMeteorological Society, 85(4):549–562, 2004. → page 5100Appendix AWorking with synthetic dataA.1 Initialization filesSample initialization files used to generate a smoke plume can be obtained from Sup-plementary Material available at:https://acp.copernicus.org/preprints/acp-2020-827/acp-2020-827-supplement.zipA.2 Sample non-penetrative plumeShown in Figure A.1 is an example of a simulated plume classified as non-penetrativeby visual analysis. Note that the centerline exhibits oscillatory behavior and very littlesmoke is injected above ABL top. Such plumes are likely to remain trapped in the ABLand eventually become uniformly mixed throughout the depth of the convective mixedlayer.Figure A.1: True aspect ratio plot of CWI smoke from a sample non-penetrativeplume. Plume centerline and zi shown in dashed and dotted grey, respectively.101A.3 Identifying quasi-stationarityI define the quasi-stationary downwind region for each plume based on two factors:the height of the centerline and tracer concentration gradient along the centerline. Myfilter attempts to extract only those portions of the downwind CWI smoke distribution,where both of these factors are changing slowly.First, I remove the effect of random turbulent oscillations by applying a smoothingfunction (Savitzky-Golay filter provided by SciPy library with polynomial order set to 3)to both the concentration gradient along the centerline and the centerline height. I varythe size of the smoothing window as a function of mean ambient wind condition W,such that window_length= max(W ·10+1,51) grid points.The filter then applies the following criteria to extract quasi-stationary regions:• smoothed tracer concentration along the plume centerline varies by less then10% of the maximum concentration gradient• smoothed centerline height varies by less then a 100 m• the location is downwind of the maximum tracer concentration gradient• the location is at least 10 grid points away from the maximum in smoothed andnon-smoothed centerline height• the location is at least 50 grid points away from the downwind endpoint of thecenterlineThe above thresholdswere determined through an informal sensitivity analysis (notshown), based on the filter’s ability to effectively identify regions of near-stationaryplume centerline height for all simulations in our dataset.A.4 Access to plume datasetData archive is available at:https://doi.org/10.20383/102.0314102Appendix BPlume rise scheme: mathematicalformulations and implementationB.1 Expanded form of plume penetration equationEnergy-balance formulation for plume penetration distance (Equation 6.1) can be con-verted into expanded form Equation 6.8) as follows:z′gθ ′θs= c[Iziθ ′]2 (B.1)Rearranging givesz′gθ ′3θs= c[Izi]2Multiplying both sides by z′z′[gz′θ ′3θs] 12= c˜[Iz′zi]and rearranging givesz′ = c˜[gz′θ ′3θs]− 12 [ Iz′zi]Expanding the RHSz′ = c˜[gz′θ ′3θs]− 12 [gIz′ziθs][θsg]and rearranging givesz′ = c˜[1z′θ ′3] 12[gIz′ziθs][θsg] 32103Multiplying both sides by z′2z′3 = c˜[z′θ ′] 32[gIz′ziθs][θsg] 32and taking a cube root of the above expressionz′ =C[θsz′gθ ′] 12︸ ︷︷ ︸1N[gIz′ziθs] 13︸ ︷︷ ︸w fwhereN is Brunt-Vaïsälä frequency (units of s−1) over the penetration regionwithmeanatmospheric lapse rate θ ′z′ and w f is the fire velocity scale (in ms−1). Expanding z′ andθ ′ giveszCL− zs =C[g(θCL−θs)θs (zCL− zs)]− 12 {gI (zCL− zs)θszi} 13 (B.2)B.2 Expressions for w fI have two expressions for convective fire velocity w f :w f1 =Iziθ ′(B.3)andw f2 =[gIz′θszi] 13 (B.4)Using Equation 6.7 and setting C ≈ 1 (based on LES data), I can rewrite Equation B.3asw f1 =[z′gθ ′θs] 12= z′[gθ ′z′θs] 12104Now substituting Equation 6.8 for z′ into the above and cancelling terms in squarebrackets I obtain:w f1 =[gθ ′θsz′]− 12 {gIz′θszi} 13[gθ ′z′θs] 12={gIz′θszi} 13= w f2Hence, the two expressions are equivalent.B.3 Estimating model input parametersSummarized in Table B.1 are parameters associated with an iterative solution for zCLusing Equation 6.8. Below is my approach to estimating these parameters from LESdata.As noted above, I consider the problem in crosswind direction. Given a three-dimensional fire of an arbitrary shape (eg. Figure 4.2b) and an ambient atmosphericsounding, I first average the fire kinematic heat flux for all ignited cells (where heat flux> 1 kW m−2) over the crosswind (y) direction at the surface (red line on Figure 4.2a).Due to surface wind shear this direction may differ from the one used for calculatingCWI smoke concentrations (as shown in Section 6.2.3). To obtain fireline intensityparameter I I numerically integrate the crosswind averaged heat fluxes over the depthof the fireline in the along-wind (x) direction.I use pre-ignition potential temperature profile (i.e. the ambient environment up-wind of the fire) averaged over the entire LES domain as an environmental sounding.Table B.1: Variable descriptions and units used in smoke injection parameteriza-tion.Variable Unit DescriptionI K m2s−1 fireline integrated heat fluxg ms−2 gravity constant = 9.81θCL K ambient potential temperature at zCLθs K ambient potential temperature at zszCL m smoke injection heightzi m boundary layer heightzs m reference height105All model fields are interpolated to have a 20 m vertical increment. zi is defined asthe height of the strongest environmental lapse rate gradient, and zs = 34zi, based oninformal model sensitivity analysis (not shown). The exact choice of zs has little effecton model performance as long as it remains within the upper portion of the uniformpotential temperature well-mixed layer.The values of θs and θCL are then determined from the pre-ignition sounding foreach simulation using the definitions of zs and zCL (as described in Section 4.2).B.4 Iterative solution for zCLThe numerical implementation of my iterative solution using SciPy’s fsolve function(scipy.optimize.fsolve) is as follows. I rewrite bias corrected Equation 6.8 into an inputfunction toSolve as:toSolve= lambda z : z−B1(zs+[g(T0[int( zdz)]−θs)θs(z− zs)]− 12 [gI(z− zs)θszi] 13)−B2 (B.5)where B1 = 0.919 and B2 = 137.919 are bias correction parameters, T0 is the potentialtemperature sounding vector, dz is the vertical step and int() is a standard Pythonfunction converting the bracketed value into an integer.A possible issue for some solvers is that we are, effectively, iterating over the ver-tical index of the column vector T0 corresponding to zCL. As the numerical solverattempts to converge on a solution it may query a non-existent index and fail. I am ableto obtain a fast and consistent performance by ensuring I set zi as the initial guess forzCL and by minimizing the initial step bound option of the solverzCL = f solve(toSolve,zi, f actor = 0.1) (B.6)106


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