ARPS 4.0 User's Guide Table of Contents Welcome to the Advanced Regional Prediction System! i Copyright Notice and Disclaimer ii Trademarks iii Important Message Concerning Library Software Not Supplied by CAPS iv Required Acknowledgment When Using CAPS Software and Related Resources v Typographical Conventions Used in this Guide vi Acknowledgments vii Chapter 1. Overview of CAPS and ARPS Project 1 1.1. Purpose of this Document 1 1.2. The Mission, Goals, and Structure of CAPS 2 1.3. Project History and Model Overview 5 1.4. Project Objectives 6 1.5. Project Personnel and Their Responsibilities 6 1.6. Model Design Philosophy and Rationale 9 1.7. Subroutine Design Conventions and Constraints 10 1.7.1. ARPSÕ discrete operator methodology 10 1.7.2. Rules and conventions used in ARPS subroutines 11 1.8. ARPS 4.0 Characteristics 13 1.9. ARPS Further Development Plans 16 Chapter 2. Code Usage Restrictions and Support 19 2.1. Restrictions on Code Use 19 2.2. Code Support 19 Chapter 3. Getting Started 20 3.1. Assumptions 20 3.2. Accessing ARPS Code via Anonymous FTP 20 3.3. Examining the Files 23 3.4. Process Flowchart of ARPS Model System 24 3.5. Compiling ARPS and Supporting Programs 25 3.6. A Quick Start with ARPS 27 3.7. A Complete Run of ARPS 28 3.8. Model Output 30 3.9. Vector Graphics Analysis of ARPS Data 31 3.10.The Parallel Version of ARPS 31 3.11.Where to Get Help 34 Chapter 4. ARPS 4.0 Runtime / Configuration 35 Model Dimension Parameters 36 Experiment Identification Parameters 37 Model Run Name 38 Model Geometry Configuration Parameters 38 Model Initialization Parameters 38 Terrain Initialization Parameters 41 Model Grid Setup Parameters 42 Map Projection Parameters 44 Time Integration Control Parameters 45 Small Time Step Control Parameters 46 Options for Spatial Advection 48 Boundary Condition Parameters 49 Coriolis Force Control Parameters 51 Subgrid Scale Turbulent Mixing Parameters 52 Spatial Computational Mixing Parameters 53 Divergence Damping Parameters 55 Upper Level Rayleigh Damping Parameters 56 Moist Processes 56 Surface Layer Parameterization 58 Soil Model and Surface Energy Budget 61 Time Filter Coefficient 63 Automatic Domain Translation Parameters 63 Model I/O Control Parameters 65 Debug Parameters 68 Control Parameters for External Boundary Condition 68 Parameters Used By Program EXT2ARPS 69 Parameters Used by Program ARPSSFC 70 Chapter 5. Model Structure Reference Guide 73 5.1. Subroutine Calling Tree for ARPS 4.0 73 5.2. Program / Subroutine Glossary 80 5.3. List of All Files and Programs / Subroutines / Functions within ARPS 90 5.4. Model Structure Flow Charts 94 5.4.1. Basic Model Control 95 5.4.2. Model Initialization 96 5.4.3. Initialization Using ARPS External Data 97 5.4.4. Integration of Dynamic Equations 98 5.4.5. Momentum Equation Forcing 99 5.4.6. Forcing in Pressure and Potential Temperature Equations 100 5.4.7. Water Vapor, Liquid and Ice Water Equations 101 5.4.8. Microphysics 102 5.4.9. Turbulence Kinetic Energy Equation 103 5.4.10. Surface Physics 103 5.4.11. Model Output 104 5.4.12. History Data Output 105 5.5. Equation Schematic Charts 106 5.5.1. Momentum Equation in X Direction 106 5.5.2. Momentum Equation in Y Direction 107 5.5.3. Vertical Momentum Equation 108 5.5.4. Potential Temperature Equation 109 5.5.5. Pressure Equation 110 5.5.6. Conservation Equation for Water Substances 111 5.5.7. Turbulent Kinetic Energy Equation 112 Chapter 6. Theoretical Formulation 113 6.1. Introduction 113 6.2. Dynamic Equations and Numerical Formulations 113 6.2.1. The coordinate system 114 6.2.2. The governing equations 117 a) The model base state 117 b) The governing equations 118 6.2.3. The discretized form of the governing equations 123 a) The model grid 123 b) Numerical integration of governing equations 124 c) Terms not related to acoustic or gravity waves 127 d) The vertically implicit pressure and w solver 130 6.3. Subgrid Scale Turbulence Closure 132 6.3.1. Introduction 132 6.3.2. The turbulent mixing formulations 133 6.3.3. Smagorinsky first-order closure 138 6.3.4. 1.5-order turbulent kinetic energy-based closure scheme 140 6.3.5. Dynamic eddy viscosity model - Germano scheme 143 6.4. Computational Mixing / Numerical Smoothing 146 6.4.1. Constant background mixing in physical space 146 6.4.2. Numerical smoothing in the computational space 147 a) Second order computational mixing 147 b) Fourth order computational mixing 149 c) Assigning the mixing coefficients 151 6.4.3. Upper boundary damping layer 152 6.5. Grid Structure and Boundary Conditions 153 6.5.1. Introduction 153 6.5.2. Lateral boundary conditions 155 a) Wall or mirror condition 156 b) Periodic boundary condition 157 c) Zero gradient boundary condition 158 d) Wave-radiation open boundary condition 158 e) Externally specified boundary condition 163 6.5.3. Top and bottom boundary conditions 163 6.5.4. The base state boundary conditions 165 6.6. Warm Rain Microphysics Parameterization 165 6.6.1. Autoconversion rate of cloud water to rain water 166 6.6.2. Accretion (collection)of cloud water by rainwater 166 6.6.3. Terminal velocity of rainwater 166 6.6.4. Rainwater evaporation rate 166 6.6.5. Saturation adjustment 167 6.6.6. Differencing the microphysics scheme 168 6.6.7. Other adjustments 168 6.7. Microphysics Rate Equations 169 6.8. PBL Depth Calculation 174 6.8.1. Stable boundary layer 175 6.8.2. Unstable boundary layer 175 6.9. Parameterization of the Surface Fluxes 176 6.9.1. Surface flux calculations 176 6.9.2. Surface fluxes over land 177 a) Unstable condition 178 b) Neutral condition 179 c) Free convection condition 179 d) Stable condition 180 6.9.3. Surface fluxes over ocean 180 6.9.4. Linear distribution of surface fluxes in mixing layer 181 6.10. Land-Surface Energy Budget and Soil-Vegetation Model 181 6.10.1. Land-Surface Energy and Moisture Budgets 181 6.10.2. Radiation-soil-vegetation model 182 a) Thermal coefficients 182 b) Radiation flux 182 c) Sensible heat flux 185 d) Latent heat flux 185 e) Soil surface moisture 187 6.11. Cumulus Parameterization Schemes 190 6.11.1. Modified Kuo scheme 190 Chapter 7. Map Projection, Model Grid Setup and Grid Nesting 192 7.1. Introduction 192 7.2. Map Projection 192 7.2.1. Map projection options 192 7.2.2. Map transformations 196 a) Polar stereographic projection 196 b) Lambert conformal projection 197 c) Mercator projection 198 7.3. Vertical Coordinate Transformation 199 7.3.1. The computational coordinate transformation 199 7.3.2. Vertical grid stretching 200 7.4. Adaptive Grid Refinement and Two-way Interactive Grid Nesting 206 7.5. One Way Interactive Self-Nesting 207 7.6. Grid Translation Features 208 7.6.1. User-specified grid motion 208 7.6.2. Cell tracking algorithm 208 7.6.3. Optimal pattern translation 209 7.6.4. Redefining quantities in a moving reference frame 212 7.6.5. Some practical considerations 213 Chapter 8. Model Initialization and Preprocessing 214 8.1. Introduction 214 8.2. Terrain Data Preprocessor 214 8.2.1. ARPS Terrain Data Preprocessors 215 a) ASCII to binary data conversion 215 b) Analysis of terrain data to ARPS grid - ARPSTERN 217 c) Control parameters description for terrain data preprocessors 218 8.2.2. Barnes Analysis Scheme Description 221 a) Barnes analysis scheme 222 b) Initial terrain data area requirements 223 c) Barnes response function 224 8.2.3. Example of a Multi-pass Analysis 225 8.3. Surface Characteristics Preprocessor 226 8.3.1. Introduction 226 8.3.2. Surface Characteristics Data Base 226 8.3.3. Description of ARPSSFC Program 229 8.3.4. Control Parameters for ARPSSFC 230 8.4. Horizontally Homogeneous Model Initial State 232 8.4.1. Initialization using external sounding 232 a) Example sounding 232 b) Sounding data types 234 8.4.2. Isentropic Atmosphere 234 8.4.3. Isothermal Atmosphere 235 8.4.4. Constant Static Stability Atmosphere 235 8.4.5. Analytic Moist Thermodynamic Sounding 235 8.5. Initialization Using 3-D Analysis 236 8.5.1. Generalized data interpolator 236 8.5.2. Using External Data Sets in ARPS 239 8.6. Time-Dependent Boundary Conditions 239 Chapter 9. Thermodynamic Recovery and Forward Assimilation 241 9.1. Introduction 241 9.2. Thermodynamic Recovery 242 9.3. Numerical Solution of the Poisson Equation 246 9.4. Evaluation of the Local Derivative Terms 248 9.5. Variational Wind Adjustment with Single-Doppler Data 249 9.6. Direct Insertion Technique 253 9.7. File and Subroutine List for the Assimilation Package 255 9.8. Assimilation Subroutine Glossary 255 9.9. Subroutine Calling Tree for the Assimilation package 256 9.10 Examining the Assimilation Code 258 Chapter 10. Data I/O and Post-Processing Utilities 259 10.1. ARPS History Data Format and I/O 259 10.2. Graphic Plotting Program 264 10.3. Data Conversion Program 266 10.4. Formatted Printing Program for Examining History Data Dumps 266 10.5. Other Utility Programs 267 10.6. ARPSTOOLS 268 10.6.1 ARPSSKEWT 268 10.7. Savi3D 270 10.8. GrADS 270 Chapter 11. ARPS Performance and Optimization on Single and Multiple Processor Systems 272 11.1. Introduction 272 11.2. General Performance Statistics 272 11.3. Basics of Optimization on Uniprocessor Systems 277 11.4. Economizing Computer Time Through a Judicious Choice of Model Parameters 280 11.5. Implementation of ARPS on Parallel Systems: Strategies 280 11.6. Implementation of ARPS on Parallel Systems: Timing 284 11.7. Publications Describing the Construction, Efficiency, Operational Application, and Parallelization of ARPS 290 Chapter 12. The ZXPLOT Graphics Package 292 12.1. What is ZXPLOT 292 12.2. How to Access ZXPLOT Library 293 Chapter 13. Validation and Benchmark Cases 295 13.1. Introduction 295 13.2. Symmetry Tests with Random Initial Perturbations 295 13.3. A Viscous Beltrami Flow Test 297 13.4. A Test of the Coriolis Formulation 301 13.5. A Test with the Taylor-Green Solution 304 13.6. May 20, 1977 Del City Supercell Storm 304 13.7. Inertia-Gravity Waves in a Constant Flow 308 13.8. Mountain Wave Validation Experiments 311 13.8.1. Linear Mountain Waves 311 a) Analytic Solution 311 b) Numerical Results 312 c) Momentum Flux 315 13.8.2. Finite Amplitude Non-Hydrostatic Non-Rotating Mountain Waves 317 a) Analytic Solution 317 b) Numerical Results 318 13.8.3. Additional Notes on the Lateral Boundary Conditions 322 13.9. 1-D Benchmark Tests on Soil Model 323 13.10. A Real Data Example 327 Chapter 14. Educational Program 329 Chapter 15. Answers to Frequently-Asked Questions 330 Appendix A. Use of Operators 337 Appendix B. Coordinate Transformation 342 B.1. Coordinate Transformation Relations 342 B.1.1. Covariant Equations 344 B.1.2. Relations Between Covariant and Contravariant Forms 345 B.2. Application of the Transformation Relations to a Boussinesq System of Conservation Laws 349 B.2.1. Scalar Transport Equation 349 B.2.2. Momentum Equation 350 Appendix C. Description of ARPS Supported Terrain Data Sets 356 C.1. Global 1 Degree Resolution Data 356 C.2. North American/European 5 Minute Resolution Data 357 C.3. United States 30 Second Resolution Data 357 Appendix D. List of Model Variables and Their Definitions 358 Table D.1. Global Time-Dependent Prognostic Variables 358 Table D.2. Time-Dependent Diagnostic Variables Local to Each Time Step 358 Table D.3. Time-Dependent Diagnostic Variables Not Local to a Single Time Step 359 Table D.4. Time-Independent Variables 360 Table D.5. Time-Independent Parameters 361 Table D.6. Parameters that May Change with Time 362 Software Usage Agreement 363 1. Data on Institution and Contact Person 363 2. Conditions 364 3. Acknowledgment of Software Use 364 4. Software Usage 364 References Cited 365 Index 375