Mesoscale Dynamics Yuh-Lang Lin Index More Information

Cambridge University Press 978-0-521-80875-0 - Mesoscale Dynamics Yuh-Lang Lin Index More information

Index

absolute deep convection (anelastic), 17 momentum, 254 Edington, 604 vorticity, 255–6 finite difference, 489–96 absolutely stable, 239–40 formulas for finite difference, 514–15 absorptivity, 597 four-stream, 604 accuracy geostrophic momentum, 387–9 first-order, 492–3 governing equations, 17–20 of finite difference methods, 494 hydrostatic, 19–20 second-order, 493, 502 incompressible (shallow convection), 16–18 aerodynamic roughness, see roughness length of advection equation, 495–508 airstream boundary, 386 of derivatives, 491–5 Andes Mountains, 341, 443 one-parameter scaling, 599 anvil pseudo-incompressible, 18 leading, 333 quasi-geostrophic (QG), 153–4 outflow, 333 two-parameter scaling, 599 Appalachian Mountains, 167, 174–6 two-stream, 604 advection area ageostrophic, of geostrophic momentum, 389 negative (NA), 247 differential moisture, 416, 453 positive (PA), 247 effect (thermal), 196–8, 205–15 atmosphere equation, 113, 192, 495 baroclinic, 265 mechanism (thermal), 196–8, 205–15 barotropic, 265 mechanism (multicell storm), 279–83 clear, 598–600, 601–3 thermal, 427–8 cloudy, 600–1, 603–4 time, 111 free, 3 advective acceleration, 16–7 isothermal, 17 air-mass thunderstorm atmospheric river, 453, 471 see single-cell thunderstorm asymmetry factor, 604 ALPEX, 158 autopropagation, 336 Alps, 157–72, 443–5 analysis baroclinic multivariate, 540 atmosphere, 265 univariate, 540 instability, 7, 25, 386 objective, 539 lee wave theory, 59–60, 160–2 Barnes objective, 539–40 wave, 160–2, 379, 386, 394–401 power spectral, 520 baroclinicity, 148–50, 380 linear stability, 73 Beer–Bouger–Lambert law, 597 numerical stability, 499 Bergeron forcing, 392 approximation Bernoulli anelastic (deep convection), 17 function, 150–1 Boussinesq, 16–19, 24 theorem, 151

618

Index 619

blackbody temperature, 596 regeneration, 279–83 Boltzmann’s constant, 596 Central Mountain Range (CMR), 168–72, 443 bora (bura), 131, 159 CFL stability criterion, 499, 503 boundary layer, 315 check friction, 352 contradiction, 539 separation, 125, 145–6, 315 buddy, 539 boundary condition gross, 539 boundedness, 39, 104, 111, 186 plausible, 539 closed, 528 chinook, 131 constant gradient, 530 circulation dynamic, 52, 70, 87, 186 ageostrophic, 392–6, 408, 422–3 free-slip, 146, 537 inland see breeze, 417 interface, 52, 70, 87, 187 secondary, 392, 408, 422–3 linear, 110, 537 solenoidal, 417 nonlinear, 110, 127, 537 thermally direct, 393, 422 no-slip, 538, 568, 576 thermally indirect, 422–5 kinematic, 52, 70, 87, 186 transverse, 392, 408, 422–3, 431 lower, 70, 110, 459, 537–8 CISK, 351–2 numerical, 490–7, 528–38 closure assumptions for KF scheme, 594 numerical upper radiation, 42, 104 cloud open, see radiation boundary condition bridge, 274 periodic, 528 cold, shield, 338 radiation, 39–42, 45, 104, 529–37 comma, 360 intensity, 597 funnel, 312 longwave (terrestrial), 596 merging, 274 shortwave (solar), 596, 603–4 microphysical processes, 444 rigid lid, 531 shelf, 278 Sommerfeld, 114, 531–3 V-shaped anvil, 207–11 sponge layer, 529, 531–3 wall, 312 time-dependent, 528 coastally trapped disturbance (CTD), 173–4, 437 zero-gradient, 530 coefficient Boussinesq fluid, 19, 53 absorption, 599 bow echo, 328 drag, 573 breeze extinction, 597 land, 215–21 heat transfer, 573 lake, 215–16 wave absorption, 88–9 sea, 215–21 wave overreflection, 88–9 bright band, 201 wave reflection 52–3, 88–9 Buckingham-Å theorem, 478 wave transmission, 88–9 Burger equation, 495 cold buoyancy, 1, 239, 302 air damming, 174–6 circulation mechanism, 279, 283 air outflow, 198, 274, 283–9, 323, 334 oscillation, 1, 39, 111 core anticyclone, 340 perturbation, 19, 211 dome, 174–6 buoyancy (Brunt–Vaisala) frequency, 16, 38, 69 front aloft (CFA), 336, 411 saturated moist, 242–4, 352, 464 columnar disturbance, 130 unsaturated moist, 244, 478 confluence mechanism, 428 -gyre, 371 conservation of mass, 12 continuity equation, 12–18, 27, 61 California Coast Range, 453–4 incompressible (shallow convection), 18, 26–7 Carnot cycle (heat engine), 353 anelastic (deep convection), 17, 302, 554 processes, 353 convection, 65 CCOPE, 72, 90, 222 cellular, 472–3 cell dry, 229 closed, 229 Rayleigh–Be´nard, 229 development, 279–83 slantwise, 264, 468 growing mode, 282 upslope, 455 open, 229–30 convective propagating mode, 282 available potential energy (CAPE), 245–6, 297, propagation, 279–83 449, 455

620 Index

convective (cont.) derecho, 328 boundary layer (CBL), 221–2, 414–17, 569 development for convective systems inhibition (CIN), 243–7 downscale, 265 initiation, 413–19, 592 upscale, 265 time scale, 594 diffusivity factor, 599 convergence direct numerical simulation (DNS), 563 large-scale, 328–9 discrete broadband approach, 602 moisture, 101 dispersion, 26, 28, 40, 91–7, 128, 500 conveyor dispersion relation, 31, 40, 46, 52, 94 cold, 264 dispersive, 24–6 warm, 264 tail, 119, 128 warm, belt, 330, 434–6, 448–51 dissipation, 26 cooling kinetic energy, 564 evaporative, 12 range, 547 Newtonian, 13, 531 dissipative scale, 564 radiative, 13 divergence tendency equation, 83 coordinates downburst, 272–6 eta (step-mountain), 527 downdraft geostrophic, 391–4 compensating, 196 isentropic (), 525 forward-flank (FFD), 296, 311 isobaric, 525 rear-flank (RFD), 296–7, 311 mass (hydrostatic pressure), 527 downwelling, 538 sigma (s), 525–7 drag terrain-following( s – z), 490, 525–6 form, 35 vertical, 525–8 gravity wave, 35 s – p, 525 mountain, 35, 113 s – z, 525–6 mountain wave, 35 s – , 526 pressure, 137 cooperative intensification mechanism, 350–2 surface, 35, 131 core radius, 317–18 dryline, 380, 413–20 Courant number, 498, 508 bulge, 414 covariance, 565 formation, 417 critical primary, convergence boundary (PDCB), layer, 55–7 419–20 level, 54–60, 86, 203, 329, 414, 460 level absorption, 55 echo overhang, 295 cyclone eddy Denver, 167 diffusivity of heat, 551, 570 extratropical, 349 diffusivity of water vapor, 570 Mediterranean, 359 viscosity, 217, 362, 551, 570 parent, 160 effect passage, 451 , 22–3 cyclogenesis, 406, 411, 420–1 baroclinic, on LLJ, 435 Bernoulli (venturi), 34, 157 data assimilation, 539–47 buoyancy, 289–93 ensemble-based, 546 cold pool, 334 four-dimensional (4DDA), 539–44 corner, 157 four-dimensional variational (4DVAR), directional shear, 307–9 544–5 Fujiwhara, 370–2 three-dimensional variational (3DVAR), 543–4 nonlinear advection, 425–6 deformation rotation, 203–15 depth, 211 rotational, on mountain waves, 152–7 shear, 303 shear, 203–7, 283–9, 334 stretching, 303 three-dimensionality, 203–15 total, 241 venturi (Bernoulli) effect, 34 density effective static stability, 403 current, 64, 66, 172–4, 198–9, 334 eigenvalue, 53 also see gravity current Ekman impulse, 64–71 layer, 351, 572 perturbation, 38 layer depth, 576

Index 621

number, 176 overturning, 203 pumping, 352 potential (irrotational), 43–6, 110, 116–17, 187 spiral, 576 quasi-geostrophic, 153, 214 Eliassen and Palm theorem, 103, 113, 532 recirculation, 129 emittance, 597 rear-to-front, see rear-to-front jet energy reversal, 145 available potential, 399 secondary, 368 available buoyancy (CAPE), 247, 283, 292 splitting, 129, 146 convective available potential (CAPE), 245–6 stagnation, 145, 150 downdraft CAPE (DCAPE), 248, 292–3 subcritical, 33–7, 127–38 generation, 7–9 supercritical, 33–7, 127–38 kinetic, 33–4 transitional, 35 perturbation kinetic, 32 unbalanced, 83 perturbation potential, 32 upslope, 221 potential, 33–4, 311 wake, 152 propagation, 101–4, 119, 532 flux temperature, 570 static potential (CAPE), 247 foehn, 131, 444, 476 total perturbation, 32, 102, 231 deep, 476–7 transfer, 7–9, 24, 230–3 shallow, 476–7 wave, 197 forecasting ensemble deterministic, 556 averaging, 567–8 ensemble, 556 forecasting, 555–7 superensemble, 556–7 Kalman filter (EnKF), 547 force enthalpy Archimedean buoyancy, 241 specific, 353 buoyancy, 22–3, 43, 239 moist, 352–3 compression, 22–3 flux, 362–5 Coriolis, 9, 23 entrainment, 368 frictional (viscous), 13 entropy, 353 pressure gradient, 43, 301–3 equation of state, 13 restoring, 22–3 error growth, 556 forest fire, 229 Ethiopian Highlands (EH), 357 Fourier evanescent wave (disturbance), 22, 39, 52, 115 coefficient, 25 evaporative cooling, 30 component, 25–6 exchange coefficient transform, 79, 177–8 enthalpy, 362 frequency, 26 heat, 551, 570 Doppler-shifted (intrinsic) wave, 39, 45, 79, 217 local, 574 Intrinsic (Doppler-shifted) wave, 39, 45, 79, 217 momentum, 217, 362, 551, 570 front, 379–441 water vapor, 570 anafront, 383 explicit presentation of microphysical processes, 580 coastal, 214, 379 cold, 379–80 Fast Fourier Transform (FFT), 121 cross, circulation, 389–94 Fickian diffusion, 217 gust, 66, 198, 379 finite difference equation, 492 gust, updraft (GFU), 66, 279–83, 323–4 first law of thermodynamics, 12–16 katafront, 383 flow Mei-Yu, 171–2 blocked, 33–7, 451 mesoscale, 379–80, 405 blocking, 33–7, 129 passage, 451 confluent, 386 sea breeze, 215–21, 379 corner, 315–18 structure, 381 cyclostrophic, 303, 315–17 synoptic, 379 drainage, 221, 418 types, 379–80 front-to-rear, see front-to-rear jet upper-level, 380, 405–12 gap, 176–7, 476 wedge model, 380–2 irrotational (potential), 43–6, 110, 116–17, 187 warm, 379–80 katabatic, 222 wave, 27 orographic forced, 109–83 zone, 383 outer, 315 frontal passage, 170–3

622 Index

frontogenesis, 173, 380–412 continuous dynamic, adaptation (CDGA), 521–3 coastal, 214–15 interval, 491 confluence (stretchingdeformation), 384–5, 397 mesh (system), 518–25 function, 383–6 moving, 521 kinematics, 380–6 nested, 521 differential terms, 384 staggered, 522–4 frictional effects, 401–5 stretched, 520 moist effects, 401–5 system (mesh), 518–25 Petterssen, function, 385 uniform, 520 stretchingdeformation (confluence), 384–6 unstructured adaptive, 521 shearingdeformation, 384–5, 397 volume averaging, 566 three-dimensional, function, 397 tilting, 384–5 heat upper-level, 380, 405–12 capacity at constant pressure, 13, 242 vector, function, 386 capacity at constant volume, 15 vertical deformation, 385 flux, 266, 351, 569 vertical divergence, 385 island, 199–201 frontolysis, 173, 380 heating Froude number, 125 cumulus, 590 basic flow, 169 diabatic, rate, 13, 213, 384, 402, 463 critical, 130 differential, 216, 417 internal, 71 dissipative, 363 moist, 478 effective, 234 shallow-water, 33, 63, 128 latent, 13, 242, 352 thermal, 71, 195, 200 radiative, 590, 597 vortex, 33, 169 sensible, 13, 351 function helicity, 306–7 bell-shaped, 32, 495 (see also Witch of Agnesi) storm-relative environmental (SREH), 307 convective trigger, 592–3 Helmholtz equation, 126 diffusion transmission, 599 high-drag (severe-wind) state, 55, 130–8 Exner, 19, 553, 590 hook echo, 295–6, 312 frontogenetical, see frontogenesis function horizontal convective rolls (HCR), 220, 419–20 geopotential, 387, 395 hot-tower mechanism, 356 global basis, 490 Howard’s semicircle theorem, 236–8 Green’s, 70, 185–93, 207–12 hurricane, 349 influence, 118 arctic, 359 jetogenetical, see jetogenesis function extratropical, 359 local basis, 490 major, 349 Planck, 596, 599 Mediterranean, 359 Scatteringphase, 604 hydrostatic balance, 19 hydrostatic vertical wavelength, 131, 188 gas constant for dry air, 14, 242 hydraulic jump, 30, 34–5, 97, 470 geopotential, 387 downstream-propagating, 34–5, 138 geostrophic upstream-propagating, 34–5, 138 absolute momentum, 240, 254, 391 internal, 30, 36, 130–8 adjustment, 8–9, 37, 65, 74–85, 425 stationary, 34, 138 momentum equations, 389 potential vorticity, 240, 259 incident radiance, 597 vorticity, 383 indicial equation, 56 wind balance (relation), 14 inertial global energy balance, 595 advective forcing, 76 gravity current, 64, 66 subrange, 547 see also density current critical level, 55–6 gravity wave, 17 flow (oscillation), 22, 47–9, 255 acoustic, 23 oscillation (flow), 22, 47–9, 255, 434–5 parameterization, 64 initial pure, 17, 22, 37–43 condition, 10, 490, 495–7, 539–46 grid guess, 539 adaptive, 521–22 initialization, 539–40 Arkawa-A, B, C, D, E, 526 damping, 540

Index 623

dynamic, 540–2 jet streak, 73–7, 379–441 linear normal mode, 541, 545 balanced, 421 nonlinear normal mode, 541–2 curved, 425–7 normal mode, 540–3 entrance region, 422 static, 540–1 exit region, 422 variational, 540–1 formation, 428–31 instability four-cell, streak, 77, 423–6 absolute, 240 geostrophic, 421 air-sea interaction, 354, 538 interaction, 431–2 algebraic mode, 58 nongeostrophic, 421 baroclinic, 15, 17, 25, 265–8, 391, 398 polar, 421 barotropic, 7 propagation, 428–31 barotropic-baroclinic, 359 substropical, 421 buoyant (static), 17, 25, 130–3, 238–44, 391–5, 468 three-cell, 77, 423–5 conditional (CI), 240, 244–9, 329, 331, 457, 468 two-cell, 77, 423–6 conditional symmetric (CSI), 240, 260–5 jetogenesis, 428–31 convective (potential), 230, 240 function, 430 dry symmetric, 257–60 Jordan’s Lemma, 178 Eady baroclinic, 162 finite-amplitude, 352 Kalman–Bucy filtering, 544–5 gravitational, 17, 25, 130–3, 238–44 Kelvin hydrodynamic, 24 ship wave, 143–4 inertial, 74, 232, 240, 253–6, 345, 391 wave, 2–3, 172–4 Kelvin–Helmholtz, 17, 72, 130–4, 230, 252–3 Kelvin–Helmholtz mesoscale, 7, 65, 71–4, 229–71 billow clouds, 220–1, 253–4 moist absolute (MAI), 240–3, 331, 468 instability (KH instability), 7 moist symmetric, 260–5, 336–7 kinematic normal mode, 58 method, 423 orographic modification of baroclinic, 163–4 pressure, 19, 211, 387 static (buoyant), 17, 25, 130–3, 238–44, 391–5 kinetic energy (spectrum), 3, 10 shear, 17, 25, 65, 71, 130–4, 230, 252–3, 314 Kirchhoff’s law, 597 potential (convective) (PI), 230, 240, 329, 331–6, Kyushu Sanchi, 454–5 448–57, 468–73 potential (convective) symmetric (PSI), 240, landspout, 314 260–5, 469–70 LAPS, 546 symmetric (SI), 7, 17, 25, 74, 230, 240, 256–65, lapse rate 391, 468 actual (environmental), 239–40 Inter-Tropical Convergence Zone (ITCZ), 358 dry adiabatic, 239–44 integral theorem of stratified flows, 233–8 environmental (actual), 239–44 invertibility principle, 402 environmental saturated, 240 moist adiabatic, 240–7 Jacobian differential operator, 391 large eddy simulation (LES), 317, 564–5 jet layer African easterly, 434 advective boundary, 572 barrier, 157, 176, 436, 449 canopy layer, see roughness layer California, coastal, 434 Ekman, 572, 575 coastal, 437 inversion, 569 -front system, 410 mixed, 538, 569, 572 front-to-rear (FTR), 277, 324–5 nocturnal boundary, 569 low-level (LLJ), 215, 284, 417, 432–7, 447–57 outer, 569, 572 nocturnal, 434, 570 planetary boundary (PBL), 15, 564, 568–79 orographic, 174 roughness, 569 polar, 284 stable boundary, 570 polar, stream, 405, 420 Stoke’s boundary, 572 rear-to-front (RTF), 277 surface, 568–9 subtropical, 284 transition, 569 unbalanced, 75 viscous sublayer, 13, 21, 568–72, 572 Somali, 434 Laplace transform, 193, 224 stream, 75 lee substropical, stream, 405, 420 cyclogenesis, 157–67

624 Index

lee (cont.) k-distribution, 600, 603 cyclogenesis types, 159 Lagrangian, 489–90 cyclogenesis theories, 160–7 Lagrangian parcel, 593 vortex, 144–52 line-by-line (LBL), 600 wave, 54, 59 normal modes, 29, 31, 44, 51 wave theory, 160–2 of images, 194 leeside convergence zone (LCZ), 222–3 slice, 249 LES–RANS, 565 spectral, 490 level of upstream interpolation, 491 free convection (LFC), 101, 240–4 WKBJ, 55, 122 free slantwise convection, 403 Mexican Plateau, 413 neutral buoyancy (LNB), 245 microburst, 275 lifting dry, 275 condensation level (LCL), 242–4, 329 wet, 275 layer, 329, 339, 452–7, 468 Miles’ theorem, 236 parcel, 329 Miles–Howard criterion, 72 longwave assumption, 103 microphysical processes longitudinal wave, 27 accretion, 475, 580–4 low-level wind maximum (LLWM), 175 aggregation, 475 autoconversion, 581–4 macroburst. 275 Bergeron process, 581–4 Madden–Julian Oscillation (MJO), 358 coalescence, 475 MAP, 449 condensation, 580–3 MAPS, 546 drop breakup, 580 Marshall–Palmer distribution, 581 dry growth of graupel, 581–4 Margule’s formula, 382 evaporation, 580–3 mass fallout, 580–4 flux, 100, 350, 592–3 freezing, 581–4 source/sink, 14, 99 melting, 581–4 transport, 12 riming, 475 maximum potential intensity (MPI), 362 sublimation, 581–4 maximum tangential wind scale, 5 vapor diffusion, 580 medium of wave propagation, 22 wet growth of graupel, 581–4 mesoscale misocyclone, 419–20 mesoscale convective elements (MBES), 347 mixinglength, 572 cellular convection, 229, 419 hypothesis, 572 convective complex (MCC), 322, 336–47 mixingratio convective line, 322, 325–6, 334 saturation, 242 convective vortex (MCV), 328, 340, 345–7 total water, 242 defined, 1–6 water vapor, 244 convective complex (MCC) development, 341–7 mode convective complex (MCC) formation, 341–7 computational, 506 convective complex (MCC) genesis, 340–2 forced, 217 lee cyclogenesis, 166–7 free, 217 mesocyclone, 293, 309, 312 physical, 506 mesohigh, 198, 273, 326–8 model mesolow, 326–8 balanced, 401 mesoscale convective system (MCS), 322–78 band, 600 formation mechanisms, 328–31 elevator-escalator, 264 front-fed leadingstratiform (FFLS), 327 Eady, 15, 163, 398 leadingstratiform (LS) precipitation, 325–7, 333 Hoskins–Bretherton, 404 parallel stratiform (PS) precipitation, 325–7 hydrodynamical, 10 rear-fed leadingstratiform (RFLS), 327 Long’s, 126–8 trailingstratiform precipitation (TS), 325–7, 333 moist Eady, 403 method Moncrieff’s squall line, 326 adjoint, 545 primitive equation (PE), 12–16, 401 finite element, 490, 527 semi-geostrophic, 396 finite difference, 489–96 Shapiro’s, 410–11 finite volume, 491 moist Galerkin, 489–90 adiabat, 590–1

Index 625

absolute instability (MAI), 240–3 diffusion, see numerical smoothing absolutely unstable layer (MAUL), 243 instability, 497–500, 510 convection, 65–71 modelingof geophysicalfluid systems, 518 geostrophic PV, 240 phase speed, 499–500, 525, 534 static energy, 587 smoothing, 548–51 moisture weather prediction (NWP), 10, 23, 518, 539 accession, 590 convergence, 588–91 occlusion downdraft, 312 flux, 458–61, 569 optical gradient, 414–17, 448 path, 599 molecular thickness, 598, 604 thermal diffusion, 568 optimal viscosity, 568 interpolation, 540 molecular weight state, 287–9, 333 water vapor, 244 orographic dry air, 244 cumulus, 472 momentum lifting, 448–55 equations, 12–16 modification, 446 forcing, 78 modification of baroclinic instability, 163–7 flux, 101–4, 113, 189–92, 569 ridging, 174 Monin–Obukhov orographic precipitation, 442–488 length, 571 climatological distribution, 442–6 similarity theory, 571 combined thermal and orographic forcing, 471–2 morningglory, 66, 92 common ingredients, 458 mountain control parameters, 477–8 anticyclone, 154, 169 dynamical-microphysical interaction, 475–7 drag, 35 enhanced by turbulence, 476 effective, 383, 472 formation and enhancement mechanisms, 461–77 half-width, 116 low-level upward motions, 458–9 -induced high pressure, see mountain anticyclone mountain geometry, 449–60, 470–1, 499 -plains solenoidal circulation (MPS), 221–4, 343 over larger mountains, 442 wave, 24, 35, 55 over small hills, 444 upslope, 483 Navier–Stokes equations of motion, 13, 563 release of moist instabilities, 466–70 nesting seeder–feeder mechanism, 472–5 one-way, 521, 529 stratiform, 483 two-way, 521, 529 stable ascent mechanism (model), 462–6 Newton’s second law of motion, 12 Newtonian parameter cooling, 56 control, flow over mountains, 34, 128 relaxation (nudging), 544 control, tropical cyclogenesis, 359 nocturnal inversion, 221 Coriolis, 4 node entrainment, 351 of attachment, 145 intercept, 581 of separation, 145 Scorer, 103, 110, 121, 532 nondispersive, 26, 28 shape, 585 nondimensional slope, 581 mountain height, 34, 63, 125–8, 478 parameterization time, 130 bulk aerodynamic, 573 nonlinear bulk microphysical processes (BMP), 580–5 aliasing, 518, 539, 547–51 cumulus (CP), 201, 585–94 balance equation (NLBE), 83 K-theory, 574 computational instability, 518 microphysical processes, 580–5 instability, 547–51 moist processes, 579–94 interaction, 65, 85, 548–9 physical processes, 563–609 nonlinearity, 91–7 PBL, 568–78 nudging (Newtonian relaxation), 544 radiative transfer processes, 594–604 numerical surface layer, 570–2 damping, 500–7 Parseval theorem, 117, 179 dispersion, 500–7 path length, 597

626 Index

pendulum day, 1 approximation, 153–4 period of buoyancy oscillation, 25, 38–42 balance, 75 phase flow, 153–5, 214 angle, 25 omega equation, 397 error, 503, 506 Q vector, 397, 423 line, 55, 495–6 theory, 153–4 of wave, 25 speed, 25, 40–1, 500 radiation tilt, 113, 203–13, 232, 266 longwave, 598–601 Planck constant, 596 shortwave, 601–4 Poincare´wave, 23 radiative Poisson’s equation, 13, 20, 239 cooling, 595 point transfer processes, 595 attachment, 145 warming, 595 saddle, 145 rain shadow, 442 stagnation, 145 rainbands, 323–38, 360–1, 369, 403, 412 polar radiative flux, 597–9 front theory, 380, 398 longwave, 598–9 low, 359–60 radius low formation, 360 of local curvature, 345 polarization relations, 42, 48 of updraft, 315, see also core radius potential rate dynamic, 359 conversion, cloud water to thermal, 359 precipitation, 589 potential temperature precipitation, 589 defined, 14 radiative heating, 590 environmental saturated equivalent, 240–2 storage, 589 equivalent, 240–2 surface evaporation, 589 saturation equivalent, 245–51 ray path, 53–4 virtual, 244, 478 Rayleigh friction, 13, 56, 218, 531 wet-bulb, 250, 453 Raymer hailstorm, 277 potential vorticity (PV) 149, 160, 266, 354, 391–5 rear inflow, see rear-to-front jet advection, 164 reduced gravity, 61 banner (streamer), 164 reflectivity, 532–3, 597 conservation of, 150 regime dissipative generation of, 150 evanescent flow, 186, 217 equation, 266 flow, 43–7 Ertel’s, 345 flow-around, 147, 470–1 geostrophic, 259 flow-over, 146, 470–1 perturbation, 78, 266 flow splitting, 148 streamer (banner), 164, 448 hydrostatic gravity wave, 153 tendency, 346 intermediate (mesoscale mountain precipitable water, 459 wave), 155 precipitation lee vortex, 148 efficiency, 274, 458, 475 linear mountain wave, 148 loading, 276, 299, 302 mesoscale mountain wave (intermediate), 155 predictability, 10–11, 555–7 moist flow, 478–83 mesoscale, 556 nonlinear flow, 125–31 pressure nonrotatingevanescent flow, 153–5 dynamic, 241, 302–9 supercell, 290 buoyancy, 241, 302–3 vertically propagating wave, 186–7 problem wave, 43–7 closure, 567 wave breaking, 148 initial-boundary value, 539 weakly nonlinear mountain wave, 129 net heating, 185 relaxation period, see convective time scale partitioning, 259 remainder, 492 pseudo-adabatic process, 242 resonance, 55 amplification theory, 131–5 quality control, 539 off, 132 quasi-geostrophic (QG) on, 132

Index 627

partial, 55, 132 Grell, 594 wave, 122–4, 183 Heun, 504 Reynolds higher-order closure, 578 averaging, 563–8 implicit, 508–11 number, 21, 145, 533, 563–4 Kain–Fritsch (KF), 592–4 stress, 132, 234 Kessler warm rain, 581 -averaged Navier–Stokes equations (RANS), Kuo, 588–91 564–5 Lax–Wendroff, 501 Richardson number Leapfrog(centered-in-time), 496, 504 gradient, 56, 72, 204, 236, 259 Lin–Farley–Orville (LFO), 581–5 bulk, 290–7 mesoscale CP, 591–4 Riemann–Lebesgue Lemma, 161, 178 multi-stage, 503 right mover, see severe right (SR) storm one-and-a-half-order closure, 576 Rocky Mountains, 165–6, 341, 413 one moment BMP, 584 Rossby number quasi-Lagrangian, see semi-Lagrangian scheme Eulerian, 1, 152, 211, 343 Runge–Kutta, 504 Lagrangian, 4, 84, 388 second-order closure, 578 Rossby radius of deformation semi-implicit, 510–11 internal (stratified fluid), 9, 75–6, 268, 322, 343, 425 semi-implicit semi-Lagrangian, 513–14 external (shallow water), 9, 75–6 semi-Lagrangian, 511–14 orographic, 156–9 third-order closure, 578 Rossby (planetary) wave, 22–3 three-time level, 496, 504 topographic, 157 TKE closure, 578 rotor, 124–5 three-moment BMP, 585 roughness length, 538 two-moment BMP, 585 trapezoidal semi-implicit, 510 SALLJ, 433–4 two-time level, 496 saturated upstream in space, 499–501 adiabatic process, 247 Scorer’s equation, 110, 186 geostrophic potential vorticity, 240, 262 sea surface temperature (SST), 538 moist Brunt–Vaisala (buoyancy) frequency, 242 anomaly (SSTA), 358 Sawyer–Eliassen equation, 390–3, 408 semi-geostrophic scale equations, 396 analysis, 14, 554 model, 396 definitions, 1–6 omega equation, 397, 441 height, 16–17, 29 potential vorticity equations, 398 interaction, 7–9 vorticity equations, 397 Orlanski, 2, 4 separation vector, 386 selection, 101 severe-wind (high-drag) state, 55, 130–8 scattering, 597 shallow water phase function, 604 dispersion relation, 31 scheme internal, wave speed, 71 Adam–Bashforth, 504 waves, 29–37 Anthes–Kuo, 591 wave equations, 29–33, 60 Arakawa–Schubert, 591 wave speed, 31–2, 524 backward difference, 492 shear Betts–Miller CP, 588 directional, 304–8 bulk microphysical parameterization (BMP), 580–5 downshear, 285 centered difference, 393 environmental wind, vector, 304–9 centered in time (leapfrog), 496, 504 speed, 304 centered in space 496, 504 unidirectional, 308 convective adjustment, 586–8 upshear, 287, 309, 324–5 Crowley, 503 vector, 304–9 cumulus parameterization (CP), 585–94 single-scattering albedo, 604 Euler’s implicit, 509 size distribution, 581, 585 explicit, 508 slantwise convective forward difference, 492 available potential energy (SCAPE), 261 forward-backward, 504 inhibition (SCIN), 261 forward in time, 496–501 smoother, fourth-order centered difference, 507 numerical, 548–51

628 Index

smoother (cont.) TAMEX, 443 five-point, 550 Taylor series expansion 118, 490–2 three-point, 548–50 Taylor–Goldstein equation, 38, 54, 73, time, 550 203, 463 solar theory flux, 602 hydraulic, 131, 135–8 irradiance, 601 K, 570 radiation, 594 layer, 249 solid-body rotation, 315 local K, 575 solitary wave mechanism, 91–7 Monin–Obukov similarity, 571 soliton, 92 non-local, 575 Sommerfeld radiation condition, 104 parcel, 238 southerly buster, 174 RKW theory, 283–99, 333 sound wave, 554 semi-geostrophic (SG), 387, 390, 430 speed, 15–17 thermal specific heat capacity of dry air buoyancy, 241 at constant pressure, 13, 610 emission, 597 at constant volume, 610 thermodynamic squall line, 323–38 diagram, 245–6, 298 classifications, 323–8 efficiency, 363 maintainence, 324, 332–4 thunderstorm, see storm movement, 335–6 thunderstorm outflow, see cold air outflow stationary phase, 118–20 time scale steeringlevel, see critical level advection, 463, 475 Stefan–Boltzmann cloud growth, 463 constant, 596 Eulerian, 4 law, 596 Lagrangian, 19, 388 storm raindrop falling, 463 air-mass, 273 time splitting, 504, 506, 554 classical supercell, 296 tornado, 293–7, 309–18 left-moving, 299 core, 315 high precipitation supercell (HP), 296–7 gust-front (type II), 313–18 initial, 290 nonsupercell, 313–18 isolated convective, 272–309 supercell (type I), 313 low precipitation supercell (LP), 296–7 vortex, 309–12, 315–18 multicell, 276–83 tornadic vortex signature (TVS), 312 multicell, generation, 279–83 tornadogenesis propagation, 304–9 nonsupercell (type II), 313–18 relative helicity (SRH), 297 supercell (type I), 309–13 right-moving, 299, 305 total (material) derivative, 13 right-moving multicell, 278 track rotation, 301, 304–9 cyclone, 167–70 secondary, 290 MCC, 342 severe right (SR), 300–7 storm, 157 single-cell, 272–6 transmissivity, 597 splitting, 290, 299–3–4 transverse wave, 27 nondimensional, strength, 291 tropical supercell, 293–313 cyclogenesis, 348–60 streamfunction, 127, 163, 231 cyclone movement, 370–2 streamline depression, 349 critical, 136 mesovortex, 361–9 critically steepened, 132 storm, 349 dividing, 135–6 unified mechanism for, cyclogenesis, deflection, 125 356–8 steepening, 128 upper tropospheric trough (TUTT), 349 subgrid-scale correction terms, 548 vertical velocity scale, 365 subgrid mixing, 501 wave, 349 subharmonic excitation, 85 tropical cyclone (TC), 347–77 sublimation, 581–4 eye, 360–1 swirl ratio, 315–16 eyewall, 360–1

Index 629

intensity, 361–3 dynamic, coefficient, 13 mesoscale structure, 363–70 kinematic, coefficient, 13, outflow, 369–70 563, 572 passage, 453–7 molecular, 13 vortex, 347, 366 turbulent eddy, 13 tropopause von Ka´rma´n folding, 406–7 constant, 538, 571 dynamic, 406, 430 vortex street, 152 trough vortex Atlantic, 157 bookend, 347 dry, 412–16 breakdown, 316 lee, 171, 412–16 interaction mechanism, 355–6 monsoon, 358 multiple, 316 Pacific, 157 one-cell, 315 passage, 447 outer, 360 secondary, 171 secondary, 360–1 short wave, 160, 406 sheet, 252 synoptic, 159 shedding, 152–7 upper-level, 164 two-cell, 316 truncation error, 501 vorticity turbulence, 421 absolute geostrophic, 255, 395 closure, 564, 567 advection, 169, 304 clear air (CAT), 24, 64 equation, 110 first-order, 570 crosswise, 306 PBL, 564 geostrophic, 383 three-dimensional, 10 shrinking, 168 turbulent streamwise, 306–7 exchange coefficient, 564, 570 stretching, 168, 304 kinetic energy (TKE), 576–8 tendency, 168, 304 heat flux, 234, 565 tilting, 304 mixing, 134, 520 vector, 149–51, 241 momentum flux, 538, 565 vertical, 168, 304 Reynolds number, 564 two-phase deepeningprocess, 159–64 West African disturbance line (WADL), 349–50 typhoon, 349 waterspout, 314 super, 349 wave absorption, 55, 88–9 U-shapted disturbance, 208 African easterly (AEW), 349 ultraviolet radiation (UV), 601, 603 amplitude, 25 undular bore, 93–7 breaking, 55, 95, 129–37 upwelling, 538 -CISK, 97–101, 230, 336, 470 updraft duct, 58, 86–91 buoyant, 315 ducting, 134 phase-lagged, 84 easterly (tropical), 349 source layer (USL), 592 frequency, 25 generation mechanisms, 64–85 ventilation, 363, 372 -induced critical level, 55 velocity length, 26 Doppler, 296 -like solution, 28 friction, 5, 538, 570 maintenance mechanisms, 85–101 group, 2–6, 41, 119–20, 197, 208 mixed Rossby-gravity, 358 phase, 27, 40–1 motion, 12, 64–107 storm-relative environmental number, 25, 40 wind, 304 number vector, 27 terminal, 584 of depression. 64, 69, 71 vertical of elevation, 64, 71 displacement, 9, 32–3, 70–1 overreflection, 55, 88–9, 206 flux divergence, 597 overturning, 37, 129, 134 virtual temperature, 14, 244 packet, 53, 64 viscosity plane, 38

630 Index

wave (cont.) nonhydrostatic, 128 propagation, 23, 27, 201, 208–11 planetary Rossby, 369 reflection, 50–4, 88–9, 134, 519 pure gravity, 17, 22 reflection level, 50–4 shallow water, 29–37 regimes with inertial critical level, 59–60 ship, 143–4 resonance, 130–8 solitary, 91–7 steepening, 36–7, 95 sound (acoustic), 17, 22–9 transmission, 50, 88–9 surface trapped, 40 tropical (easterly), 349 trapped, 143, 160 wave interaction, 548 transverse, 27, 143 2Dt, 550 vertically propagating, 39–42, 115, 130, 2Dx, 494 140, 202 wave ducting vortex Rossby, 367–9 linear, 86–91 weak echo region (WER), 294 nonlinear, 135 also bounded weak echo region (BWER), 294 waves wind acoustic, 17 ageostrophic, 75, 422 acoustic-gravity, 17, 23 advective, 422 algebraic (BDO) solitary, 71, 80, 91–7 downslope, 34, 436 BDO (algebraic) solitary, 71, 80, 91–7 gap. 436 classical (KdV) solitary, 71, 80, 91–7 gradient, 349, 362–6 cnoidal, 95 isallobaric, 422, 436 dispersive, 25 kabatic, 65 dissipative, 25 mistral, 159 diverging, 143–4 mountain-gap, 176–7 electromagnetic, 595–6 mountain-valley, 221 evanescent, 39–40, 117, 140, 214 slope, 221 gravity, 22, 37–43, 230 radius of maximum (RMW), 5, 354, 364 hydrostatic, 115 severe downslope, 34–6 hydrostatic mountain, 117, 156 straight-line, 274 internal gravity, 37–50, 69 thermal, 15, 257, 380 inertia-gravity, 17, 23, 27, 43–50, 74–7, 217–18, upslope, 221 230, 540 wind reversal level, 131 KdV (classical) solitary, 71, 80, 91–7 windstorm Lamb, 29, 63 Boulder, 35–6, 137 lee, 54, 59, 122–5, 143 severe downslope, 35, 131–8 longitudinal, 27 wind-induced mesoscale, 22–4, 64–107 critical level, 131–8 mixed acoustic-gravity, 23 surface heat exchange (WISHE), 352–5 moist Eady, 403 Witch of Agnesi, 32 mountain, 65, 109–83 see also bell-shaped function nondispersive, 25, 495 nondissipative, 25 zonda, 131