Figure 1.2. Boulder, Colorado Hourly Windstorm Frequency Distribution ..................................................................................................5

Figure 1.3. Anemometer Trace from January 11, 1972 Boulder, Colorado Windstorm ...............................................................................6

Figure 1.4. Flow regimes for Water Flowing Over an Obstacle .................................................................................................................13

Figure 1.5. Vertical Streamline Displacement from Three Dimensional Linear Theory ...........................................................................16

Figure 1.6. Normalized Horizontal Velocity Perturbation from Heated Three Dimensional Linear Theory........................................... 20

Figure 1.7. 500mb Flow Pattern for Type-3 Boulder, CO Windstorm .......................................................................................................23

Figure 1.8. Typical Upstream Boulder CO Windstorm Sounding Profile ...................................................................................................24

Figure 2.1. Two Layer Linear Solution Graphical Representation .............................................................................................................34

Figure 2.2. Two Layer Analytical Vertical Momentum Flux ......................................................................................................................40

Figure 3.1. ARPI3D Computational Grid Box .............................................................................................................................................68

Figure 3.2. Model Domain Diagram .............................................................................................................................................................69

Figure 4.1. Model and Analytical u? Solutions and Difference Fields for a Linear Hydrostatic Mountain Wave with a Sponge Upper Boundary Condition ........................................................................................................................................................................................................82

Figure 4.2. Model and Analytical w? Solutions and Difference Fields for a Linear Hydrostatic Mountain Wave with a Sponge Upper Boundary Condition ........................................................................................................................................................................................................83

Figure 4.3. Model and Analytical u? Solutions and Difference Fields for a Linear Hydrostatic Mountain Wave with a Radiation Upper Boundary Condition ........................................................................................................................................................................................................84

Figure 4.4. Model and Analytical w? Solutions and Difference Fields for a Linear Hydrostatic Mountain Wave with a Radiation Upper Boundary Condition ........................................................................................................................................................................................................85

Figure 4.5. Vertical Momentum Flux Profiles for the Linear Mountain Wave Sponge/Radiation Tests .................................................87

Figure 4.6. Plot of ? and ? for a Non-linear Boussinesq Mountain Wave Flow ...............................................................................91

Figure 4.7. Numerical and Analytical u? Solutions and Difference Fields for Non-linear Boussinesq Test ..........................................92

Figure 4.8. Numerical and Analytical w? Solutions and Difference Fields for Non-linear Boussinesq Test .........................................93

Figure 4.9. Vertical Momentum Flux Profile for Non-linear Boussinesq Test .........................................................................................94

Figure 4.10. Model and Analytical Streamlines for Non-linear Boussinesq Test.................................................................................... 95

Figure 4.11. Model and Observed Vertical Profiles of Potential Temperature for the Wangara Day 33 Test .......................................97

Figure 4.12. Isentrope comparison for the present model and Durran and Klemp and Peltier and Clark model results at t=4000s for the January 11, 1972 Boulder Colorado Windstorm .......................................................................................................................................................101

Figure 4.13. Isentrope comparison for the present model and Durran and Klemp and Peltier and Clark model results at t=8000s for the January 11, 1972 Boulder Colorado Windstorm .......................................................................................................................................................102

Figure 4.14. Observed Isentrope East-West Cross-Section for the January 11, 1972 Boulder Colorado Windstorm Event ............103

Figure 4.15. Surface wave drag from Durran and Klemp, Peltier and Clark and the present model for the January 11, 1972 Boulder Windstorm 104

Figure 4.16. Model Isentropes for the dz=150m and dz=341m January 11, 1972 Boulder Windstorm Tests ........................................106

Figure 4.17. Surface Wave Drag for the dz=150m and dz=341m January 11, 1972 Boulder Windstorm Tests ....................................107

Figure 4.18. Vertical Momentum Flux Profiles for the dz=150m and dz=341m January 11, 1972 Boulder Windstorm Tests .............108

Figure 4.19. Upstream u? Fields for Lateral Boundary Condition Tests of the January 11, 1972 Boulder Windstorm .........................110

Figure 5.1. Sensible Heat Flux Measurements from the Boreal Forest ...................................................................................................116

Figure 5.2. Vertical Flux Profile for the Explicit and Parameterized Narrow Mountain Experiments ...................................................121

Figure 5.3. Comparison of u? for the Explicit and Parameterized Narrow Mountain Experiments ........................................................122

Figure 5.4. Isentropes for the Explicit and Parameterized Narrow Mountain Wave Experiments ........................................................123

Figure 5.5. Turbulent Kinetic Energy (e) plots for the Explicit and Parameterized Narrow Mountain Tests .......................................125

Figure 5.6. Perturbation u? Plots for the Heated Wide Mountain Tests ...................................................................................................129

Figure 5.7. Isentropes for the Control and Heated Wide Mountain Tests ...............................................................................................130

Figure 5.8. Surface Wave Drag Time Series for the Heated Narrow and Wide Mountain Parameterized Tests .................................131

Figure 5.9. Vertical Flux Profiles for the Heated Wide Mountain Experiment ........................................................................................132

Figure 5.10. Vertical Profiles of Potential Temperature for the Heated Wide and Narrow Mountain Experiments .............................133

Figure 5.11. Normalized Surface Wave Drag for the 7km Critical Layer Control and Heated h=900,750, and 600m Tests ................137

Figure 5.12. Normalized Surface Wave Drag Comparison with Linear Theory .......................................................................................138

Figure 5.13. Comparison of Linear Drag Reduction Curves with Heated Mountain Wave Flow Tests ................................................140

Figure 5.14. Maximum Surface Wind Speed for the 7km Critical Layer h=900,750, 600m Control and Heated Experiments .............141

Figure 5.15. Plot of u? for the Heated h=750m 7km Critical Layer Test ..................................................................................................143

Figure 5.16. Isentropes for the Heated h=750m 7km Critical Layer Test at Ut/a=160............................................................................144

Figure 5.17. Isentropes for the Heated h=750m 7km Critical Layer Test at Ut/a=240 ...........................................................................145

Figure 5.18. Normalized Surface Wave Drag for the 17km Critical Layer h=1000, 600, and 200m Control and Heated Experiments..147

Figure 5.19. Maximum Surface Wind Speed for the 17km Critical Layer h=100, 600, 200m Control and Heated Experiments ..........149

Figure 5.20. Perturbation u for the Heated h=1000m 17km Critical Layer Test ......................................................................................150

Figure 5.21. Isentrope Plot for the Heated h=1000m 17km Critical Layer Test ......................................................................................151

Figure 5.22 Summary of Normalized Surface Wave Drag for all Critical Layer Tests ...........................................................................155

Figure 5.23. Summary of Normalized Surface Wave Drag for Two Dimensional Non-Linear Parameter Experiments ......................158

Figure 5.24. Time series of Normalized Surface Wave Drag for the Two-Layer Experiments .............................................................161

Figure 5.25. Time series of Maximum Surface Wind Speed for the Two-Layer Experiments ..............................................................162

Figure 5.26. Model Predicted Control and Heated Potential Temperature Comparison for the Two-Layer Tests ..............................163

Figure 5.27. Barnes Response Function for the Two Dimensional January 9, 1989 Boulder Colorado Windstorm Terrain Profile .....166

Figure 5.28. Peak Observed winds from the roof of the NOAA Building in Boulder ...............................................................................169

Figure 5.29. Doppler Lidar Observations ....................................................................................................................................................170

Figure 5.30. Vertical Profile of E-W Wind Component and Potential Temperature Observed from the Craig, CO 2305 UTC ...........171

Figure 5.31. Surface Wave Drag for the Two Dimensional January 9, 1989 Boulder Windstorm Simulations .....................................173

Figure 5.32. Maximum Surface Wind Speed for Two Dimensional January 9, 1989 Boulder Windstorm Simulations .........................174

Figure 5.33. Model Predicted Control and Heated Potential Temperature Comparison in the vicinity of Boulder, CO ........................175

Figure 5.34. Total Horizontal Velocity Comparison for the 2-D January 8, 1989 Boulder Colorado Windstorm 2305UTC Control and Heated Simulations at t=70000s ...............................................................................................................................................................................176

Figure 5.35. Total Horizontal Velocity Time Series Plot in the Lee of the Mountain for the January 9, 1989 Boulder Windstorm 2305UTC Control Test ................................................................................................................................................................................................................178

Figure 5.36. Total Horizontal Velocity Time Series Plot in the Lee of the Mountain for the January 9, 1989 Boulder Windstorm 2305UTC Heated Test ................................................................................................................................................................................................................179

Figure 5.37. Domain Wide Isentropes for the 2305UTC 2-D January 9, 1989 Boulder Windstorm Control and Heated Tests ...........180

Figure 6.1. Normalized Surface Wave Drag Summary for the Three Dimensional Mountain Wave Experiments ................................187

Figure 6.2. Surface Horizontal Velocity Vector Plot for the Nh/U = 3.0 Circular Ridge Test .................................................................189

Figure 6.3. Vertical X-Z Cross Section Isentrope Comparison for the Present Model and Reference Solution from Reisner and Smolarkiewicz for the Nh/U = 3.0 Circular Mountain Flow Tests .......................................................................................................................................190

Figure 6.4. Surface Wave Drag Time Series for the Nh/U = 1.0 Two and Three Dimensional Circular and Finite Ridge Simulations ..193

Figure 6.5. Surface Maximum Wind Speed Time Series for the Nh/U = 1.0 Two and Three Dimensional Circular and Finite Ridge Simulations 194

Figure 6.6. X-Z Cross-Sections of E-W Velocity for the Two and Three Dimensional Ridge Nh/U=1.0 Tests Prior to Surface Heating. 195

Figure 6.7. X-Z Cross-Sections of Potential Temperature for the Two and Three Dimensional Ridge Nh/U=1.0 Tests Prior to Surface Heating. ...........................................................................................................................................................................................................................196

Figure 6.8. X-Z Cross-Sections of E-W Velocity for the Two and Three Dimensional Ridge Nh/U=1.0 Tests near the end of the Heating Cycle. ...........................................................................................................................................................................................................................197

Figure 6.9. X-Z Cross-Sections of Potential Temperature for the Two and Three Dimensional Ridge Nh/U=1.0 Tests near the end of the Heating Cycle. ...................................................................................................................................................................................................198

Figure 6.10. Plot of Vertical Velocity at the Surface and Aloft for the Three Dimensional Ridge Nh/U=1.0 Test Prior to Surface Heating. 199

Figure 6.11. Surface Wave Drag Time Series Summary for the Nh/U = 0.2 Two and Three Dimensional Circular and Finite Ridge Simulations 201

Figure C.1. Streamline Test Plots of the Trajectory Formulation ...................................................................................................................231

Figure D.1. Pie Chart of CPU Time Requirements for a Three Dimensional Mountain Wave Simulation Using ARPI3D and the ECAS Cray J-90 ..............................................................................................................................................................................................................................234

Figure D.2. ARPI3D CRAY T3D Scalability ...................................................................................................................................................239