## An Introduction to Boundary Layer MeteorologyPart of the excitement in boundary-layer meteorology is the challenge associated with turbulent flow - one of the unsolved problems in classical physics. An additional attraction of the filed is the rich diversity of topics and research methods that are collected under the umbrella-term of boundary-layer meteorology. The flavor of the challenges and the excitement associated with the study of the atmospheric boundary layer are captured in this textbook. Fundamental concepts and mathematics are presented prior to their use, physical interpretations of the terms in equations are given, sample data are shown, examples are solved, and exercises are included. The work should also be considered as a major reference and as a review of the literature, since it includes tables of parameterizatlons, procedures, filed experiments, useful constants, and graphs of various phenomena under a variety of conditions. It is assumed that the work will be used at the beginning graduate level for students with an undergraduate background in meteorology, but the author envisions, and has catered for, a heterogeneity in the background and experience of his readers. |

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### Contents

Mean Boundary Layer Characteristics | 1 |

11 A BoundaryLayer Definition | 2 |

12 Wind and Flow | 3 |

13 Turbulent Transport | 4 |

14 Taylors Hypothesis | 5 |

15 Virtual Potential Temperature | 7 |

16 Boundary Layer Depth and Structure | 9 |

17 Micrometeorology | 19 |

83 Structure Function | 300 |

84 Discrete Fourier Transform | 303 |

85 Fast Fourier Transform | 310 |

86 Energy Spectrum | 312 |

87 Spectral Characteristics | 318 |

88 Spectra of Two Variables | 329 |

89 Periodogram | 335 |

810 Nonlocal Spectra | 336 |

18 Significance of the Boundary Layer | 21 |

19 General References | 23 |

110 References for this Chapter | 25 |

111 Exercises | 26 |

Some Mathematical Conceptual Tools Part 1 Statistics | 29 |

22 The Spectral Gap | 33 |

24 Some Basic Statistical Methods | 35 |

25 Turbulence Kinetic Energy | 45 |

26 Kinematic Flux | 47 |

27 Eddy Flux | 51 |

28 Summation Notation | 57 |

29 Stress | 63 |

210 Friction Velocity | 67 |

211 References | 68 |

212 Exercises | 70 |

Application of the Governing Equations to Turbulent Flow | 75 |

31 Methodology | 76 |

33 Simplifications Approximations and Scaling Arguments | 80 |

34 Equations for Mean Variables in a Turbulent Flow | 87 |

35 Summary of Equations with Simplifications | 93 |

36 Case Studies | 97 |

37 References | 110 |

38 Exercises | 111 |

Prognostic Equations for Turbulent Fluxes and Variances | 115 |

42 Free Convection Scaling Variables | 117 |

43 Prognostic Equations for Variances | 120 |

44 Prognostic Equations for Turbulent Fluxes | 134 |

45 References | 147 |

46 Exercises | 148 |

Turbulence Kinetic Energy Stability and Sealing | 151 |

52 Contributions to the TKE Budget | 153 |

53 TKE Budget Contributions as a Function of Eddy Size | 166 |

54 Mean Kinetic Energy and Its Interaction with Turbulence | 168 |

56 The Richardson Number | 175 |

57 The Obukhov Length | 180 |

58 Dimensionless Gradients | 183 |

59 Miscellaneous Scaling Parameters | 184 |

510 Combined Stability Tables | 186 |

511 References | 187 |

512 Exercises | 189 |

Turbulence Closure Techniques | 197 |

62 Parameterization Rules | 200 |

63 Local Closure Zero and Half Order | 202 |

64 Local Closure First Order | 203 |

65 Local Closure Oneandahalf Order | 214 |

66 Local Closure Second Order | 220 |

67 Local Closure Third Order | 224 |

68 Nonlocal Closure Transilient Turbulence Theory | 225 |

69 Nonlocal Closure Spectral Diffusivity Theory | 240 |

610 References | 242 |

611 Exercises | 245 |

Boundary Conditions and Surface Forcings | 251 |

72 Heat Budget at the Surface | 253 |

73 Radiation Budget | 256 |

74 Fluxes at Interfaces | 261 |

75 Partitioning of Flux into Sensible and Latent Portions | 272 |

76 Flux To and From the Ground | 282 |

77 References | 289 |

78 Exercises | 292 |

Some Mathematical Conceptual Tools Part 2 Time Series | 295 |

82 Autocorrelation | 296 |

811 Spectral Decomposition of the TKE Equation | 340 |

812 References | 342 |

813 Exercises | 344 |

Similarity Theory | 347 |

92 Buckingham Pi Dimensiortal Analysis Methods | 350 |

93 Scaling Variables | 354 |

94 Stable Boundary Layer Similarity Relationship Lists | 360 |

95 Neutral Boundary Layer Similarity Relationship Lists | 364 |

96 Convective Boundary Layer Similarity Relationship Lists | 368 |

97 The Log Wind Profile | 376 |

98 Rossbynurnber Similarity and Profile Matching | 386 |

99 Spectral Similarity | 389 |

910 Similarity Scaling Domains | 394 |

911 References | 395 |

912 Exercises | 399 |

Measurement and Simulation Techniques | 405 |

102 Sensor Lists | 407 |

103 Active Remote Sensor Observations of Morphology | 410 |

104 Instrument Platforms | 413 |

105 Field Experiments | 417 |

106 Simulation Methods | 420 |

107 Analysis Methods | 427 |

108 References | 434 |

109 Exercises | 438 |

Convective Mixed Layer | 441 |

111 The Unstable Surface Layer | 442 |

112 The Mixed Layer | 450 |

113 The Entrainment Zone | 473 |

114 Entrainment Velocity and Its Parameterization | 477 |

115 Subsidence and Advection | 483 |

116 References | 487 |

117 Exercises | 494 |

Stable Boundary Layer | 499 |

122 Processes | 506 |

123 Evolution | 516 |

124 Other Depth Models | 518 |

125 LowLevel Nocturnal Jet | 520 |

126 Buoyancy Gravity Waves | 526 |

127 Terrain Slope and Drainage Winds | 534 |

128 References | 538 |

129 Exercises | 542 |

Boundary Layer Clouds | 545 |

132 Radiation | 555 |

133 Cloud Entrainment Mechanisms | 558 |

134 Fairweather Cumulus | 562 |

135 Stratocumulus | 570 |

136 Fog | 576 |

137 References | 578 |

138 Exercises | 583 |

Geographic Effects | 587 |

142 Geographically Modified Flow | 595 |

143 Urban Heat Island and the Urban Plume | 609 |

613 | |

145 Exercises | 617 |

Appendices | 619 |

Scaling Variables and Dimensionless Groups | 621 |

Notation | 629 |

Useful Constants Parameters and Conversion Factors | 639 |

Derivation of Virtual Potential Temperature | 645 |

649 | |