Realistic Natural Atmospheric Phenomena and Weather Effects for Interactive Virtual Environments Leigh McLoughlin National Centre for Computer Animation A thesis submitted in partial fulfilment of the requirements of Bournemouth University for the degree of Doctor of Philosophy Submitted: September 2012 This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and due ac- knowledgement must always be made of the use of any material contained in, or derived from, this thesis. Abstract Clouds and the weather are important aspects of any natural outdoor scene, but existing dynamic techniques within computer graphics only offer the simplest of cloud representations. The problem that this work looks to address is how to provide a means of simulating clouds and weather features such as precipitation, that are suitable for virtual environments. Techniques for cloud simulation are available within the area of meteorology, but numerical weather prediction systems are computationally expensive, give more numerical accuracy than we require for graphics and are restricted to the laws of physics. Within computer graphics, we often need to direct and adjust physical features or to bend reality to meet artistic goals, which is a key difference between the subjects of computer graphics and physical science. Pure physically- based simulations, however, evolve their solutions according to pre-set rules and are notoriously difficult to control. The challenge then is for the solution to be computationally lightweight and able to be directed in some measure while at the same time producing believable results. This work presents a lightweight physically-based cloud simulation scheme that simulates the dynamic properties of cloud formation and weather effects. The system simulates water vapour, cloud water, cloud ice, rain, snow and hail. The water model incorporates control parameters and the cloud model uses an arbitrary vertical temperature profile, with a tool described to allow the user to define this. The result of this work is that clouds can now be simulated in near real-time complete with precipitation. The temperature profile and tool then provide a means of directing the resulting formation. 3 For Huiwen Contents List of Figures 9 List of Tables 10 1 Introduction 13 1.1 Context ................................ 13 1.2 MotivationandAims ......................... 14 1.3 Approach ............................... 15 1.4 Contributions ............................. 16 1.5 ThesisOverview............................ 16 2 Cloud Dynamics 18 2.1 Introduction.............................. 18 2.1.1 Terminology and Techniques . 18 2.2 CloudClassification.......................... 19 2.2.1 Low-LevelClouds. 22 2.2.2 Mid-LevelClouds . 22 2.2.3 High-LevelClouds . 24 2.2.4 VerticalClouds ........................ 26 2.3 TheAtmosphereandParcelTheory . 30 2.3.1 TheAtmosphere ....................... 30 2.3.2 Parcels ............................ 34 2.3.3 Parcel Buoyancy . 36 2.4 WaterandMoistAir ......................... 36 2.4.1 Categories of Water . 36 2.4.2 Water Transfers: Cloud Microphysics . 40 2.4.3 Water in Parcels: Continuity Models . 44 2.4.4 Moist Parcel Buoyancy . 47 2.5 AtmosphericStability . 47 2.5.1 AnalysisTools......................... 48 2.6 EmpiricalFormationModels . 50 5 CONTENTS 2.6.1 Convection and Thermals: Cumuliform Clouds . 50 2.6.2 Convection and Layers: Stratiform Clouds . 53 2.6.3 Ice and Snow: Cirriform Clouds . 54 2.7 Fluid Simulation for Clouds . 55 3 Related Work 57 3.1 Meteorological Approaches . 57 3.2 ComputerGraphicsApproaches . 59 3.2.1 Previous Physically-Based Simulation Work . 60 3.2.2 Procedurally-Based Techniques . 61 3.2.3 Additional Cloud-Simulation Work . 64 3.2.4 Rendering-Specific Work . 67 3.2.5 Other Weather-Related Effects . 68 3.2.6 General Fluid-Dynamics Work . 69 4 Cloud and Weather Simulation 71 4.1 InitialExperiments .......................... 71 4.1.1 AParcelModel ........................ 71 4.2 MainSimulation ........................... 78 4.2.1 Background Atmosphere . 79 4.2.2 ParcelProperties . 80 4.2.3 TemperatureProfile . 81 4.2.4 Six-StateWaterModel . 84 4.2.5 SummaryofTheCloudModel. 91 4.3 Rendering ............................... 92 4.4 Implementation ............................ 95 4.4.1 SystemDesign ........................ 95 4.4.2 System Implementation . 97 4.5 Results................................. 99 4.5.1 Performance.......................... 99 4.5.2 VisualResults......................... 100 4.5.3 TemperatureProfileTool. 110 4.6 Evaluation: A Critical Analysis . 112 4.6.1 WaterModel ......................... 112 4.6.2 TemperatureProfiles . 116 5 Conclusion 118 5.0.3 Contributions . 119 5.1 Discussion, Limitations and Further Work . 120 5.1.1 IssuesofControl ....................... 120 5.1.2 Wind.............................. 121 6 CONTENTS 5.1.3 Simulation Domain . 122 5.1.4 ProceduralDetail . 123 Bibliography 124 Appendix 138 A Fluid Dynamics 139 A.1 MathematicsReview . 139 A.1.1 VectorFields ......................... 140 A.2 Equations of Fluid Dynamics . 141 A.2.1 TheMomentumEquation . 141 A.2.2 Pressure ............................ 142 A.2.3 Viscosity............................ 144 A.2.4 OtherForces ......................... 144 A.2.5 Mass Continuity: Pressure in an Incompressible Fluid? . 145 A.2.6 Lagrangian and Eulerian Viewpoints . 145 A.2.7 BoundaryConditions . 147 A.3 2DVortices .............................. 147 A.3.1 Definition of vorticity . 147 A.3.2 Expressing the Navier-Stokes Equations using Vorticity . 148 A.4 SolvingTheEquations . 151 A.4.1 Solving the Eulerian Navier-Stokes Equations . 151 A.4.2 SplittingtheEquations. 152 A.4.3 Advection ........................... 152 A.4.4 BodyForces.......................... 154 A.4.5 Pressure/Incompressibility and Viscosity . 155 A.4.6 Solving the Vorticity Equation . 156 B Initial Work 159 B.1 Sheep ................................. 159 B.1.1 Solution ............................ 159 B.1.2 Background Sky-dome: Sky Colour . 159 B.2 Initial Cloud Simulation . 163 7 List of Figures 2.1 CumulusClouds. ........................... 23 2.2 StratocumulusCloud.. 23 2.3 AltocumulusCloud........................... 24 2.4 CirrusCloud. ............................. 25 2.5 Sundogs................................. 26 2.6 CirrocumulusCloud. 27 2.7 CumulonimbusClouds.. 28 2.8 Cumulonimbus Accessory Clouds. 29 2.9 TheLayersoftheAtmosphere. 30 2.10 AtmosphericStability. 48 2.11TheSkew-T............................... 49 2.12 Storm Cell Development. 51 2.13 DowndraughtFormation.. 52 2.14 CumulonimbusModel. 53 2.15CirrusModel. ............................. 55 3.1 MiddlewareSolutionScreenshots . 66 3.2 Light Paths for Cloud Rendering. 67 3.3 Blinn’sPhaseFunction. 68 4.1 Vortexdefinition. ........................... 72 4.2 VortexSystemDiagram. 73 4.3 2DVortexFluids............................ 74 4.4 2DCloudSystemDiagram. 77 4.5 2DCloudSystemResults. 77 4.6 CloudFormationProcess. 78 4.7 SystemProcessOverview. 79 4.8 DefiningtheCloudBase.. 83 4.9 ReverseSkew-T. ........................... 83 4.10 Water Transfer Diagram. 85 4.11GreenIceClouds............................ 95 8 LIST OF FIGURES 4.12 SystemOverview............................ 97 4.13 Rendering Technique Comparison. 100 4.14 SamplingMethodComparison. 101 4.15 Visual Comparison with Previous Techniques. 102 4.16 Precipitation. ............................. 103 4.17 OpticalEffectVisuals. 104 4.18 Visual Cumulonimbus Comparison. 105 4.19 Visual Precipitation Comparison. 106 4.20 Visual Anvil Comparison. 107 4.21 Visual Cloud Comparison. 108 4.22 Visual Detail Comparison. 109 4.23 AdjustingtheTemperatureProfile. 111 4.24 PaintingtheSource. 112 4.25 LayeredCloudGeneration.. 113 4.26 Water Control Comparison. 114 A.1 PressuresonaCube. ......................... 142 A.2 VorticityDefinition.. 148 A.3 FluidAdvection. ........................... 153 A.4 Streamlines. .............................. 156 A.5 Streamfunction. ............................ 157 B.1 MeadowSkyColour. 160 B.2 DynamicClouds. ........................... 162 B.3 PrototypeResults. .......................... 164 9 List of Tables 2.1 Cloud Classification Scheme. 21 4.1 WaterRenderingParameters. 93 4.2 SystemPerformance. ......................... 99 4.3 OpticalEffectTable. 103 10 Acknowledgements This work represents the single largest project that I have ever em- barked upon, yet I still feel as though I am only just at the beginning of my journey. Still, one chapter must end before another can begin. I would not have gotten to this stage without the kind help and sup- port of some incredible people and I would very much like to take this opportunity to thank them. Great thanks must be given to my supervisor, Peter Comninos, for starting me on this road, for guiding me and for never giving up on me. Without his patience and support this thesis quite simply would not exist. I would also like to thank Valery Adzhiev, my second supervisor, for his valued input and especially for his feedback on this thesis. I am also grateful to my thesis examiners, Dan Simpson and Ian Palmer, for their comments and suggestions, which have helped shape the final version of this thesis. I would like to express my gratitude to all my friends and colleagues at the NCCA for their advice, friendship and welcome distractions to broaden my knowledge and help me cling on to the last threads of my sanity. I would very much like to thank my fellow PhD students and good friends Eike Anderson and