Salby M.L. Fundamentals of Atmospheric Physics

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600

Answers to Selected Problems

17. (a) o) =

-pgw,

(b) w = -18 mm s -1.

~ { [~soo 2~, sin(~r x2+y2)] [2~rx _, ( x2+y2)] }

18. (a) Vsoo =

a L 2

Zsoo --gr- i + --LrZsooSin zr--zr- j ,

+ rr (x2+Y:)L2

COS (TrX2~ y2)~ ql + f0-

24. (a) 16 m s -1, (b) 14.3 m s -1.

25. (a) 768 m s -1, (b) 45 m s -1.

2y [ 2]

27. (b) s r = ~ exp - (Y)

exp[i(kx -

o-t)];

exp [-(y)2]

exp[i(kx -

~rt)];

V. v h

[ ]

iOx

exp - (y)2

exp[i(kx -

~rt)]; q, - f,

oy"

__ O,

30. (a) 950-850: 52~ = 0, N=~ -0.032 K km -1", 850-750:52

o__r = +.028 K km -1 (b) 950-850:32 K day -1" 850-750:

Oy '

-28 K day -1,

32. Positive (negative) feedback between changes of e, and ~2

--Off ~"

{1]2r2 ~

35. p = poexp

\2RT]"

36. (a) v = + (~)~~-e~e6.

37. (a) zsoo

=R Y

_..U_) [A + ~ ln(2)] ] '

T 2y

n ln(2) [--a +

exp

( - X2+y2

(b) U5oo = -7 L-r --Zr-) [A + ~ ln(2)] },

vs00 ~ ln(2) { 2x exp ( - xi+y2

= L-r L2 )[A + ~ ln(2)] ], (c) p 430 mb.

38. 33 ~ .

o~y

t~ 0, (b)

y(x) Aei] -~x + Be -iv/-~x

39. (a) ~-r + u Y = = 9

d__~ ~ _ fV . Vh"

9 dt

47. (a) s r =-7.5 x 10 -5 s -1, (b) ~" =-8.3 x 10 -5 s -1.

48. (b) Solenoidal production is absent in isobaric coordinates as well, but

tilting remains.

50. (a)dM

_~o (ep)dA

= const.

(ep)dA,

(b)dr

d,faA)

-- ~ ~ d--['- dt "

54. (c) Diffusion.

Chapter 13

1. (a) 0.003, (b) 108, (c) 5.0 x 1011

3. 87 km for H --7.3 km.

5. 105 MW (!).

15. 8.9 mms -1

16. 0.08 N m -2.

Answers to Selected Problems

601

17. (a) KK- f-~ - 0;

K~ + f(-~ - ug)

= 0; K - cel~l (b) ~ - u-----s-g

h ' ,+~ (i + ~j),

18. (a) 20 m s-akm -1, (b) 50 m s -1 km -1.

19. 4.5 days.

drt 1

20. (a) ~ + zrt -- lra, (b) rt(x ) -- ro e-x/L -Jr- ra; T(x) -- To e-x/L + Ta,

9.4- 2354

(c)

rw(X ) -

0.622 10

Toexp(-~+Ta)

-NO--

Chapter 14

' gH(y)

19. (a) k and cg are both horizontal, (b) k points downward and

is horizon-

tal.

(a) vertical propagation: z <

zt,

external: z >

zt; zt = h~/1

k2ff 2

24.

-- N~'

28. (a)

= 18 km, (c) wave activity disperses for E -+ ec.

30. (a) 0.0004 mb, (b) 5.1 m s -1.

32. [pff[2 _ K 2 [wff[ 2ez/H

K 2

[Wff[ 2efT-2&z _rh2 1 N 2 k 2

__ H--- ~ o.2K(K_I)WN2k2H 2 ~ o.2H 2 [89 ; ~ 4H 2 "- o.---- ~- .

41. (a) Through divergence, the mountain acts as a vorticity source,

exp - 2

(b) o V2~, o$' Q0 exp x2+y2~ i .

-Jr- fl 3x -- 27rL 2 --~1,

(c)

~st- -~Qo

ff(ks2+/2)_/3 ,

ks l

> 0, y > 0;

k sl < O, y < O.

1 O (Oq/) l d (Nf_~ ~) --0;

46. (a)

a2 cos ~b 0-~b COS ~ ~ --[- P ~-~ p _.[../,,2 ~t

1 3 (Off) 13 (f2~off)

/,,2

-- u-cfle

k2; fie -- fl a2~s-~- ~

cos~b~

~rt,~ , (b) 74 ~

driven to zero, reflection can occur at both high and low

47. With

fie -- -~-

latitudes, supporting the existence of horizontal modes. Since propagation

is also trapped vertically, normal modes can exist as well.

N2 L k2 1 -- 0.

51. (a)m

b -o g, (b) g~

-Jr-U2 (c_ff) 2 --

Chapter 15

4. de = cpTd

In 0e.

5. -9.8 x 104 J kg -1.

11. (b) 2.6 x 1021 J.

12. 0.0013.

13. 81 m s -1.

602

Answers to Selected Problems

18. (b) Phase lines tilt SW-NE in the Northern Hemisphere, so that wave

activity propagates equatorward with

Cgy < O.

19. (a) 2.9 m s -1.

23. (a) 6 days.

26. (a) 9.2 x 103 J kg -1, (b) 7.8 x 102 J kg -1, (c) 13.3 km; 4.4 km.

Chapter 16

3.-f(f-~)y'.

4. (a) low latitudes.

5. (a) positive, (b) 4) = cos -1

l_f2 a202" .

U2 a-~

16.-~ = coth (-~-)

17. (b)

(kCi)k=l --'-~1 (kCi)l=O

19. 6.1 days, 3.2 days, 2.25 days, 1.86 days, 1.71 days, 1.77 days, 2.22 days, oo.

25. (a) unstable (stable) equatorward (poleward) of 25 ~

Chapter 17

__ 1 . 1 -- 37

min;

-- 32 years,

1. z03 - J3+~3[01'

ZOx

2k3[0]'

(a) Zo3

ZOx

(b) ~'o3 = 21 min; ~'Ox = 15 days, (c) Zo3 = 2.4 min;

~Ox

= 3.8 hr.

9. (a) 16.4 ppmv, (b) 1.6 ppmv, (c) 3.3 ppmv.

11. 1.26 ppmv.

1 . J2[o2]

13. (a) fOx

2k3[O]+2ka[Cl] ,

[O]--

k3[O3]+kb[ClO] ,

(a) 8

years, (b) 3.1 days.

Index

Absolute concentration, 6-7

Absolute humidity, 26, 118

Absolute vorticity, 388, 389-392

Absorption

atmospheric waves, 468-472

by gases, characteristics, 216-224;

see also

specific gases

graybody, 211-212

heat, 65-66, 81-87

plane parallel atmosphere, 226, 228-230,

232

radiation, LW, 46, 200, 469, 472

radiation, SW, 48-49, 200, 243, 244, 263,

307

radiative, 199-200, 207-208, 243-244, 246

strong, 230, 232

Absorption coefficient, 207

Absorption cross section, 207

Absorptivity, 208, 211, 216

cloudy atmosphere, 298, 300

plane parallel atmosphere, 229

Acceleration, 335-336

centrifugal, 143, 144-145, 336

centripetal, 384-385

Coriolis, 351, 355, 371, 385

material, 347-348, 355, 382-384, 409

Accumulation particle, 261

Acid rain, 41

Acoustic cutoff frequency, 441

Acoustic-gravity wave, 441, 444

Acoustic wave, 439-446

Activated droplet, 268

Adiabat, 69, 71, 128

pseudo-adiabatic process, 132, 134, 135

Adiabatic cooling, 283

Adiabatic layer, 155

Adiabatic process, 58, 63, 68-75, 128-129

Carnot cycle, 82-84

control surface, 58

603

entropy, 87, 93

equation of motion, 352

equilibrium conditions, 91

isentropic coordinates, 364, 367

lapse rate, 171

dry, 74, 135, 151

saturated, 132-133, 151

path independence, 63

potential energy, 493-495

potential temperature, 71-73, 74, 93, 352

pseudo-adiabatic, 130-132, 134-148

stratification, 130-131, 156-160

Advection, 27, 552

material derivative, 328, 338

Aerosol, 33, 35, 46;

see also

Clouds, droplet

growth

chemical processes, role, 314-315

cloudy atmosphere, 295-305

global energy budget, role, 312-314

ice nuclei, 275-276

LW and SW radiation, 244, 263, 312-313

Mie scattering, 291-295

morphology, 258-264, 270-271

thermal structure, 275-305

as trace constituent, 35

Ageostrophic motion, 394, 422, 502

?fir, see also

Dry air; Moist air

compressibility, 2, 6-7, 152-153

constituents, 3-4, 12, 14;

see also

Geopotential height;

Height

coordinate systems, 146

pseudo-adiabatic chart, 134

Amazon basin, global energy budget, 307

Angle

scattering, 288-289

zenith,

see

Zenith angle

Angular momentum

absolute vorticity, 391

coordinate systems, 350, 352

general circulation, 486, 502

quasi-biennial oscillation, 557

Angular velocity

earth, 579

reference frame, 334

Answers, to selected problems, 593-600

Antarctic plateau, 552

Anthropogenic impact

aerosol, 35, 258, 262, 271

albedo, 312

carbon dioxide, 23-24

chlorofluorocarbons, 33, 542

greenhouse effect, 252

heterogeneous chemistry, 567, 569

methane, 32

nitric oxide, 35, 541

nitrous oxide, 34-35

Anticyclone, 187, 192;

see also

Cyclone

Anticyclonic motion, 374;

see also

Cyclonic

motion

geostrophic equilibrium, 380, 386-387, 388

stratospheric warming, 554-556

tropical circulation, 508

Anvil cirrus cloud

global energy budget, 307

radiative cooling, 304

Archimedes' principle, 167

Arctic haze, 312

Asymmetry factor, scattering, 297

Asynoptic satellite observation, 404

Atacama desert, LW radiation, 211

Atmospheric behavior,

see also

Atmospheric

motion

influencing mechanisms, 2-3

perspectives, 1-2, 321-323

Atmospheric energy,

see

General circulation,

atmospheric energy

Atmospheric motion,

see also

Equations of

motion; Horizontal motion; Large-scale

motion; Vertical motion

Cauchy's equations, 331-334

conservation of mass, 330-331

descriptions, 321-323

first law of thermodynamics, 336-338

fluid motion, kinematics, 323-328

material derivative, 328

momentum budget, 331-336

Reynolds' transport theorem, 329-330

rotating reference frame, 334-336

Atmospheric window, 200, 203

absorption characteristics, 216

Auxiliary function, 88

Avogadro's number, 579

Axisymmetric circulation, 495-503

Band, spectrum, 218-220

Band absorptivity, 229

Band model, 217, 229-230

Band transmissivity, 228

Baroclinic instability, 493, 505, 521-523;

see

also

Eady problem

Baroclinic stratification, 378--379, 389-393

potential energy, 491, 494

Barotropic instability, 521-523

Barotropic nondivergent motion, 387-388

Barotropic nondivergent vorticity equation,

388

Barotropic nondivergent wave, 459-461

Barotropic stratification, 378

Beta effectiveness, 466

Beta-plane approximation, 394

Blackbody radiation theory, 208-212

Blackbody spectrum, 209

Blackbody temperature, 43, 44, 208-212

Boltzmann constant, 579

Boundary layer,

see

Planetary boundary

layer

Boussinesq approximation, 394-395

Break temperature, 193

Brewer-Dobson circulation, 547-548

Brightness temperature, 209

Brunt-V~iis/iill/i frequency, 175

Bulk viscosity, 340

Buoyancy

cloud dissipation, 286-287

cloud formation, 277-281

conditional instability, 178-179

Buoyancy

(continued)

entrainment, 181, 184

vertical stability, 166-170, 174-176, 189

Buoyancy wave, 440--456

CAPE,

see

Convective available potential

energy

Carbonaceous aerosol, 258, 260, 262

Carbon dioxide (CO2)

absorption by, 200, 201, 203, 216-217, 232,

244

greenhouse effect, 249-250, 252

line broadening, 224

LW radiation, 46, 242

as trace constituent, 22-25

Carbon monoxide (CO), absorption by, 216

Carnot cycle, 82-84, 159

Carnot's theorem, 84-85

Cartesian coordinates

rectangular, 341

transformations, 341-342, 344-346

Cauchy's equations of motion, 331-334

CCN,

see

Cloud condensation nuclei

Centrifugal acceleration, 143, 144-145, 336

Centripetal acceleration, 384-385

CFCs,

see

Chlorofluorocarbons

Chapman layer, 243, 246, 304

Chappuis band, 219, 220

Chemical equilibrium, 118, 120;

see also

Photochemical equilibrium

Gibbs function, 102-103, 105-106

heterogeneous system, 99, 102-104

Chemical potential, 102-104, 105, 109

Chinook wind, 138

Chlorine chemistry, 35, 41;

see also

Chlorofluorocarbons; Heterogeneous

chemistry

odd chlorine family, 543-544

Chlorofluorocarbons (CFCs)

absorption by, 216, 220

greenhouse effect, 252

heterogeneous chemistry, 569

increased levels, 33-34

middle atmosphere, 542-544

mixing ratio, 33

ozone destruction, 34

radiative equilibrium, 43

as trace constituents, 33-34

Chromosphere, 201

Circulation, 2, 41;

see also

Atmospheric

motion; General circulation;

Index

605

Large-scale motion; Meridional

circulation; Middle atmosphere

Brewer-Dobson, 547-548

Hadley, 39, 51, 505

secondary, 395, 420

structure, 17-22

thermally direct, 51

time-mean, 19-21, 51

Walker, 51

zonal-mean, 17-18

Circumpolar flow, 18-19, 21, 51, 150

Cirriform cloud, 277, 307

Cirrus cloud, 300, 304, 305

dissipation, 287

global energy budget, 307

microphysical properties, 285-286

Mie scattering, 295

Cirrus uncinus cloud, 286

Clausius-Clapeyron equation, 112-114

distribution of water vapor, 122

greenhouse effect, 250

saturation properties, 120

Clausius inequality, 85-86

Closed system, 55

Cloud condensation nuclei (CCN), 268,

270-271, 275

chemical species, 314

Cloud cover, 250, 306-312

Cloud radiative forcing, 308-310

Clouds, 39, 41, 259;

see also

Lifting

condensation level; Moist air; Water

vapor

aerosol formation, 261

droplet growth, 264-273, 274

ice particle growth, 276

pseudo-adiabatic chart, 137-138

pseudo-adiabatic process, 130-132

Conditional instability, 173, 176-181, 189

Conservation of mass, 330-331

Conserved property, 7-8

Constants, physical, 579

Continental aerosol, 258, 260-263, 270-271

Continental cloud

droplet growth, 271

glaciation, 275

reflective properties, 300

Continuity equation, 331, 338

incompressible motion, 352

isentropic coordinates, 366-367

isobaric coordinates, 360, 361

log-pressure coordinates, 363

quasi-geostrophic motion, 396

turbulence, 409

Control surface, 55, 58

Convection, 27

boundary layer, 419

cumulus, 39, 190-191

entrainment, 181, 183-184

free, 178, 179, 189, 415, 508

Rayleigh-B6nard, 282

sloping, 39, 505

stratification, 159

vertical stability, 176, 189

Convective available potential energy

(CAPE), 179, 189

Convective cloud, 38, 127, 136

Convective mixing, 189-191, 192-193

Convective overshoot, 180-181

Convective overturning, 236-240

Conversion, to SI units, 577

Cooling,

see also

Longwave radiation;

Shortwave radiation

adiabatic, 283

cirrus, 304

evaporative, 45

Newtonian, 76, 248, 469, 472, 552

Cooling rate, 160-161

Cooling to space, 241, 246-248

Cool-to-space approximation, 246

Coordinates

Cartesian, 341-342, 344-346

curvilinear, 341-344, 581-582

cylindrical, 581-582

fluid motion, kinematics, 323-326

geopotential, 145-147, 336

isentropic, 364-368, 372

isobaric, 151, 357-362

log-pressure, 362-364

orthogonal, 343, 344, 346

spherical, 146, 344-352, 581

thermodynamic, 357-368

trajectory, 383

Coriolis acceleration, 335-336, 351, 355, 371

cyclostrophic motion, 385

inertial motion, 385

Coriolis force, 336

general circulation, 502

geostrophic equilibrium, 372-374

Rossby waves, 459

Coriolis parameter, 351

Critical level, 13-15

gravity waves, 473

Rossby waves, 465

wave activity, 450, 454-456

Critical line

quasi-biennial oscillation, 557-560

shear instability, 522

Critical point, water, 108

Critical radius, droplet formation, 268

Critical supersaturation, 268

Crustal aerosol, 258, 260, 261, 262, 275

Cumuliform cloud, 277;

see also

Cumulus

cloud

Cumulonimbus cloud, 180-181, 277,

280-281

global energy budget, 307

microphysical properties, 285-286

troposphere-stratosphere interaction, 562,

563

Cumulus cloud, 39, 128;

see also

Stratocumulus cloud

albedo, 299

dissipation, 286, 287

droplet growth, 271, 274

formation, 277-281

global energy budget, 307, 310, 311

microphysical properties, 285-286

Mie scattering, 293-295

transmissivity, 299

Cumulus convection, 39, 190-191

Cumulus tower, 180-181

Curl, motion field, 326

Curvature effect, droplet growth, 268

Curvilinear coordinates, 341-344, 581-582

Curvilinear motion, 382-387

Cyclic process, 59, 62;

see also

Circuit, heat

transfer

first law, 64-65

second law, 80-82, 85

Cyclic work, 57

Cyclone, 20, 72;

see also

Anticyclone

Eady model, 525

potential energy, 493

vertical instability, 188

Cyclonic motion,

see also

Anticyclonic

motion

geostrophic equilibrium, 374, 380,

386-387, 388

Rossby waves, 460

Cyclostrophic equilibrium, 385-386

Cylindrical coordinates, 581-582

Dalton's law, 5

Deforestation, 191

Deformation. tensor, 326

Degrees of freedom, 59

barotropic stratification, 378

heterogeneous system, 99, 106-107

homogeneous system, 99

moist air, 123

water, 108-109

Density, number,

see

Number density

Deposition, 276

Desert dust, 312-314

Dew point, 121, 135-136

Index

607

Diabatic process, 75-76, 156

changes of state, 63-65

entrainment, 181

momentum budget, 332

stratification, 160-162

Diagnostic equation, 387

Diffuse flux transmission function, 229

Diffuse radiation, 205, 295-296;

see also

Scattering

Diffusive transport, 11-12

Diffusivity, 232, 333, 411, 412

Dilatation, motion field, 326

Dipole moment, scatterer, 287

Direction,

see also

Reversibility

thermodynamic process, 85, 87, 90

Dispersion

turbulent, 174, 189-193

wave, 434-438

Dissipation, 392

cloud, 286-287

frictional, 50, 52

Dobson units, ozone abundance, 31

Doppler broadening, 224

Doppler shift, 432, 447, 472

Drag

frictional, 381

Stokes, 317

turbulent, 420

Drag coefficient, 424

Drag force, 334

Droplet growth, 264-275

Dry adiabatic lapse rate, 74, 135, 151

Dry air, 4, 7

equation of state, 118

thermodynamic properties, 578

Dynamical structure, 16-22

Dynamic condition, free surface, 428-429

Eady problem, 523-529, 531

Earth

angular velocity, 579

radius, 579

rotation,

see

Rotation, earth

Eddy diffusivity, boundary layer, 411, 412

Eddy momentum, 409-411, 428

Edge wave, 434, 442, 526

Effective gravity, 143-145, 336;

see also

Height

Eigenfrequency, shear instability, 520

Einstein notation, 325

Ekman balance, 498, 501

Ekman layer, 412-413, 501, 502, 503

608

Index

Ekman number, 495-496

Ekman pumping, 420-423

Ekman spiral, 413, 499

E1 Chichon volcano, 263, 315

Elevation,

see

Altitude; Geopotential height;

Height

El Nifio, 467-468, 509-510

E1 Nifio Southern Oscillation (ENSO), 510

Emission

Lyman-c~, 201

radiative, 208-212

plane parallel atmosphere, 226, 228, 232

Emissivity, 211

Energy transfer,

see

General circulation;

Global energy budget; Heat transfer;

Radiation; Radiative transfer

ENSO,

see

El Nifio Southern Oscillation

Enthalpy, 65, 11 0-111

ideal gas law, 67

specific heat capacity, 66

Entrainment, 181, 183-184

cloud dissipation, 286-287

cloud formation, 280

Entropy

changes, 87-88

potential temperature, 91-96, 337

saturated behavior, 126

second law, 84-87, 91-96

Environmental lapse rate, 151-153, 168

Environmental temperature, 169-170

Equations of motion, 331-334, 338;

see also

Perturbation equation

adiabatic motion, 352

balances

scale analysis, 354-357

stratification, 353-354

Cav,:hy's, 331-334

coordinates

curvilinear, 341-344

spherical, 344-352

thermodynamic

isentropic, 364-368

isobaric, 357-362

log-pressure, 362-364

incompressible motion, 352

traditional approximation, 350-352

turbulence, 407-408, 409

Equations of radiative transfer, 215, 233, 295

Equations of state, 5-7, 59

dry air, 118

heterogeneous system, 106, 112-113

moist air, 119

water, 107-108, 112, 113

Equilibrium

stable, 90

true, 90, 91

Equilibrium phase transformation, 110-114

Equilibrium supersaturation, 268, 269

Equilibrium temperature, 236

Equilibrium vapor pressure, 109, 112-114

Equivalent potential temperature, 131-132,

136

Ertel potential vorticity, 392

Escape velocity, 13-15

Eulerian derivative, 328

Eulerian description

versus Lagrangian, 1-2, 322-323, 324

material derivative, 328, 329-330

Evanescent wave, 441--442

Evaporation

cloud dissipation, 286-287

droplet growth, 265-268

Evaporative cooling, 45

Exact differential theorem, 61

Exchange integral, 241

Exner function, 369

Exosphere, 13-15

Expansion work, 56-58

adiabatic conditions, 63, 73

diabatic conditions, 75

Exponential kernel approximation, 232

Extensive property, 55-56, 99-101

External wave, 441-442

Extinction, 206

Extinction coefficient, 214, 293

Extinction cross section, 213-214

Extinction efficiency, 292

Fair weather cumulus cloud, 281

Feedback, greenhouse effect, 250-252

Ferrell cell, 502-503

Field variable, 322, 331, 338;

see also

Atmospheric motion

Final warming, 557

Finite-energy condition, 457

First law of thermodynamics, 63-65, 85

atmospheric motion, 336-338

forms, 66

adiabatic process, 68-69, 132

diabatic process, 75, 76

isochoric process, 87

Fluid motion, 1-2, 321-328;

see also

Atmospheric motion

Flux Richardson number, 415

f-plane motion, 374--375

Forcing

cloud radiative, 308-310, 311

Fourier's law of heat conduction, 337

Fourier synthesis, 429-432

Fourier transform, 431

Fractus cloud, 282

Free atmosphere, 405

Free convection, 178, 179, 189, 415, 508

Free energy, 89, 265-267

Free surface, 426-429

Freezing level, 136-137

Freezing nucleus, 275

Frictional convergence, 420, 421

Frictional dissipation, 50, 52

Frictional geostrophic equilibrium, 381

Friction velocity, 413

Frost point, 121

Fundamental relations, 88-90

heterogeneous system, 104-106

Gases, thermodynamics,

see

Thermodynamics of gases

Gas phase properties, 117-120

Gas-to-particle conversion, 35

General circulation, 50-52, 486-487;

see also

Circulation

atmospheric energy

moist static, 487-489

potential, available, 491-495

potential, total, 489-491

heat transfer

axisymmetric circulation, 495-503

laboratory simulations, 503-506

radiative transfer, 198

tropical, 506-513

General circulation model (GCM), 24, 362

Geological evidence

carbon dioxide, 24-25

ozone, 29-30

Geometric altitude,

see

Altitude

Geometric optics method, 451-456

Geopotential coordinates, 145-147, 336

Geopotential height, 146-147;

see also

Gravity; Potential energy

Geostrophic balance, 377

Geostrophic equilibrium

curvilinear motion, 382-384, 386-387

frictional, 381

large-scale motion, 371-377

thermal wind balance, 380

weakly divergent motion, 388, 394-395

Index

609

Geostrophic motion, 372, 374, 377-381;

see

also

Quasi-geostrophic motion

Geostrophic paradox, 372, 486

Geostrophic streamfunction, 376, 461

Geostrophic velocity, 371-373, 374, 378-379

quasi-geostrophic motion, 394

Geostrophic wind, 370, 377-381

Gibbs-Dalton law, 117, 120

Gibbs free energy, 265-267

Gibbs function, 88-89

chemical equilibrium, 102-103, 105-106

equilibrium conditions, 91

Gibbs' phase rule, 107, 109, 123

Glaciated cloud, 275

Global energy budget,

see also

Momentum

budget; Vorticity budget

aerosol, role, 312-314, 315

clouds, role, 306-312

global-mean energy balance, 44--46

radiative transfer, 198

Global-mean energy balance, 44-46

Global warming, 23-24

Governing equations,

see

Continuity

equation; Equations of motion;

Equations of state; Perturbation

equation

Gradient equilibrium, 386

Gradient motion, 386-387

Gradient Richardson number, 417

Gradient wind speed, 386

Grauple, 276

Gravity, 2, 8, 44;

see also

Height; Hydrostatic

equilibrium; Potential energy

centrifugal acceleration, 336

effective, 143-145, 336

escape velocity, 13-15

standard, 579

Gravity wave, 440-450

critical level, 473

dynamical structure, 22

nonlinear conditions, 477

Gray atmosphere,

see also

Plane parallel

atmosphere

greenhouse effect, 248-249

radiative equilibrium, 233-236

Graybody absorption, 211-212

Greenhouse effect, 43, 203, 248-252

global energy budget, 45, 306

runaway, 250

Group speed, 435

Group velocity, 436

acoustic waves, 439-440

gravity waves, 441