Copyright © 2018 by Roland Stull. Practical : An Algebra-based Survey of Atmospheric Science. v1.03

APPENDIX C • NOTATION

Compiled by Alison Deere and Marjolein Ribberink University of British Columbia.

Contents AVCS arbitrary vertical cross-section CB Bernoulli’s constant Aw global albedo corresponding to an atmo- CC cell circulation Roman Symbols, Acronyms & Contractions C881 spheric window -to-cloud Greek Symbols C885 AWOS automatic weather observing system CCD charge-coupled devices Operators C887 AZ Arizona, USA postal code CCL convective condensation level Superscripts C887 a acceleration CCN cloud condensation nuclei Subscripts C887 attenuation coefficient CD drag coefficient Special Symbols C887 length of semi-major axis of earth’s orbit fraction of the globe covered by dark dai- = 149.457 Gm sies parameter or constant (varies by context) CF coriolis force spillage distance of front CFL Courant-Friedrichs-Lewy (condition for (= external Rossby radius of deforma- numerical stability) tion) CG cloud-to-ground  surface albedo CG fractional area covered by bare ground a vector acceleration CH bulk heat-transfer coefficient aH mixed-layer transport coefficient = 0.0063 CH4 methane ROMAN SYMBOLS, arccos inverse of cosine function (cos–1) CI arcsin inverse of sine function (sin–1) CIN ACRONYMS & arctan inverse of tangent function (tan–1) CL classic –1 asin inverse of sine function (sin ) CL fraction of the globe covered by light dai- CONTRACTIONS atm atmospheres (a unit) sies aλ absorptivity CMC Canadian Meteorological Center CO carbon monoxide Colorado, USA postal code A CO2 carbon dioxide A of TKE B CP cumulative probability albedo B Beaufort scale Cp specific heat of air at constant pressure ampere (a unit of electrical current) bias score Cpd specific heat of dry air at constant pressure amplitude bowen ratio = 1004.67 J·kg–2·K–1 area breakdown potential for dry air Cpv specific heat for at constant Ball ratio = 0.2 = 3x109 V km–1 pressure = 1875 J·kg–1·K–1 initial analysis buoyant production or consumption of Cr relative circulation north-south amplitude of a wave TKE CRT video screen. Literally: Cathode Ray Tube parameter or constant (varies by context) BC boundary conditions Cs seed coverage AAM absolute angular momentum British Columbia, Canada postal code CSI critical sucess index AB Alberta, Canada postal code BLG boundary-layer gradient (wind) CT Connecticut, USA postal code ABL Atmospheric Boundary Layer BRN Cu ACARS aircraft communication and reporting BSS Brier Skill Score Curv curvature system Bλ black-body radiation of a certain wave- Cv specific heat at constant volume AD albedo of dark-colored daisies length Cvd air specific heat of dry air at constant volume AG albedo of bare ground parameter or constant (varies by context) Cw vertical drag coefficient AGL above ground level b absorption cross section Cy dimensionless cross-wind integrated con- AIREP aviation report damping factor centration AK Alaska, USA postal code extinction cross section °C degrees Celsius or centigrade, a unit of AL Alabama, USA postal code length of semi-minor axis = 149.090 Gm AL albedo of light-colored daisies parameter or constant (varies by context) c concentration of a pollutant AMDAR aircraft meteorological data relay b1 parameter or constant (varies by context) density correction factor AO Arctic Oscillation bD dimensionless coefficient half the distance between two foci of an AR Arkansas, USA postal code bH convective transport coefficient ellipse Ar argon maximum concentration ARPEGE Action de Recherche Petite Echelle Grande parameter or constant (varies by context) Echelle (weather-forecast model) phase speed or shallow-water wave ASDAR aircraft to satellite data relay C speeds ASOS automatic surface observing system C angular rotation in a full circle (360° or 2π speed of light through air at sea level pres- AT apparent temperature () radians) sure = 299,710,000 m·s–1 circle circumference (360° or 2π radians) speed of sound circulation c0 speed of light in a vacuum = 299,792,258 climatological condition m·s–1 cost c1 parameter or constant (varies by context) dimensionless concentration c parameter or constant (varies by context) “Practical Meteorology: 2 fractional area covered c3 parameter or constant (varies by context) An Algebra-based Survey parameter or constant (varies by context) c4 parameter or constant (varies by context) of Atmospheric Science” specific heat capacity cd “candela, a unit of luminous intensity” by Roland Stull is licensed under a Creative CA air discharge cg group speed or group velocity Commons Attribution-NonCommercial-Sha- California, USA postal code ci speed of light through medium i reAlike 4.0 International License. View this Ca absolute circulation cm centimeter, a length unit license at http://creativecommons.org/ CAN Canada cos cosine licenses/by-nc-sa/4.0/ . This work is avail- CAPE Convective Available Potential Energy covar covariance able at https://www.eoas.ubc.ca/books/ CAPPI constant altitude plan position indicator cP continental polar air mass Practical_Meteorology/ CAT clear-air turbulence cy crosswind-integrated concentration C881 C882 NOTATION

–2 cαβ intermediate calculation parameter for at- Eϕ incoming or outgoing radiative flux at lat- of W·m ) mospheric optical ray paths itude ϕ FH sensible heat flux from earth’s surface up E average daily insolation into the air (in dynamic units W·m–2) E’ coalescence efficiency Frad* net radiative flux E* total irradiance Fx dynamic heat flux in x direction D E*λ emittance/radiant existence/irradiance Fy dynamic heat flux in y direction D daylight duration hours irradiance at wavelength λ Fz dynamic heat flux in z direction death rate of daisies e base of natural logarithms = 2.7182818285 f oscillation frequency diffusivity = 2.11x10–5 m2·s–1 for water va- current or voltage feedback factor por in air under standard conditions eccentricity fc Coriolis parameter distance eccentricity of earth’s orbit = 0.0167 centrifugal force drop diameter fG pull (force) by earth’s gravity duration of positive heat flux e0 saturation vapor pressure = 0.611 kPa at f0 reference Coriolis parameter at the center fractal dimension 0 °C of the beta plane modern description eIR IR surface emissivity ft feet, a length unit parameter or constant (varies by context) es saturation vapor pressure over flat pure ft H2O feet of water, a pressure unit water fx fraction of cloud sizes duration (h) saturation vapor pressure Fz eff sfc effective surface heat flux size of particle es* actual saturation vapor pressure width of flow ew equilibrium emissivity corresponding to DA data assimilation an atmospheric window DC District of Columbia, USA postal code exp base of natural logarithms = 2.7182818285 G DE Delaware, USA postal code eλ emissivity at wavelength λ G cyclone graveyard DIAL differential absorption lidars gain DJF “December, January, and February” geostrophic wind speed DMSP defense meterological satellite program gravitational constant DT Daylight Savings Time F = 6.67x10–11 m3·s–2·kg–1 DW diabatic warming rate F flux density intermediate circulation parameter Dφ differential heating kinematic flux theoretical geostrophic value Dϕ net radiative flux, or differential heating, false-alarm rate GA Georgia, USA postal code at latitude ϕ force GB gigabyte d days, a time unit forecast GCM global model depth  Fujita tornado damage scale GCM general circulation model diagonal length F vector force GEM Global Environmental Multiscale (Cana- distance between crest and trough of a FA free atmosphere dian numerical model) wave FAR false-alarm ratio GFS Global Forecast System distance between earth and sun = 149.6 FAS Federation of American Scientists GHG greenhouse gas Gm Fc tracer flux Gm gigameter, a length unit Julian day FCF Coriolis force Gm gap-geostrophic wind plume spread FCN centrifugal force GMT Greenwich Mean Time thickness FE latent heat flux from earth’s surface up GPS global positioning system (via satellite) dmax.rain total accumulated depth in a rain gauge into the air (in kinematic units of GPU Graphics Processing Unit –1 dr Julian day of summer solstice = 173 K·m·s ) GSM global spectral model dw precipitable water FFD Forward flank downdraft GSS Gilbert’s skill score dy number of days in a year FG flux gradient GTS global telecommunication system dBZ decibels of Z - units of radar reflectivity FG molecular heat conduction g grams, a unit of mass ∆d phase shift heat flux conducted from the ground up to gravitational acceleration = –9.8 m·s–2 the earth’s surface (in kinematic units (negative means downward) of K·m·s –1) g’ reduced gravity FH sensible heat flux from earth’s surface up E into the air (in kinematic units of E collision efficiency K·m·s –1) East FHsfc surface kinematic heat flux H H geopotential height efficiency FL  Florida, USA postal code electric field Fnet net vector force high pressure center energy FNMOC Fleet Numerical Meteorological and high incoming or outgoing radiative flux Oceanographic Center hit rate irradiance FPG force heating rate turbine efficiency FPGm mesoscale pressure-gradient force helicity E0 theoretical efficiency FPGs synoptic pressure-gradient force unperturbed ocean depth E1 parameter or constant (varies by context) Fr Froude number H2 hydrogen Ec collection efficiency Frad radiative flux at a surface H2O water ECMWF European Centre for Medium-Range FS Frontal strength H2O2 hydrogen peroxide Weather Forecasts FTD turbulent drag force H2SO4 sulfuric acid EHI Energy helicity index FV3 Finite Volume - version 3 HC hurricane category Ein incoming flux Fx kinematic heat flux component in x direc- He helium zonally and annually averaged incoming tion He e-folding depth radiative flux component of net vector force toward the HI heat index apparent temperature Einsol annual average insolation east Hawaii, USA postal code EL Fy kinematic heat flux component in y direc- HNO3 nitric acid Emax maximum efficiency tion Hp scale height for pressure Enet differential heating due to radiation meridional heat transport HP High precipitation net radiative flux Fz kinematic heat flux component in z direc- HRR rate of energy release over unit area of zonally and annually averaged net radia- tion earth’s surface tive flux F* net radiative flux at earth’s surace (in kine- HSS Heidke skill score EOF Empirical Orthogonal Function matic units of K·m·s–1) Hz “hertz, a unit of frequency” Eout outgoing flux °F Fahrenheit, a unit of temperautre Hρ scale height for density zonally and annually averaged outgoing F flux (dynamic) h depth flux F* net radiative flux at earth’s surace (in dy- depth of cold air EPA U.S. Environmental Protection Agency namic units of W·m–2) depth of stable boundary layer EQ equator Fdiff diffusive moisture flux enthalpy ETS equitable threat score FE latent heat flux from earth’s surface up height EU European Union into the air (in dynamic units W·m–2) hours, a unit of time Evap evaporation rate FG heat flux conducted from the ground up to wave height EZ entrainment zone the earth’s surface (in dynamic units h0 hour angle R. STULL • PRACTICAL METEOROLOGY C883

h2 parameter or constant (varies by context) KS Kansas, USA postal code second hgust gust front depth kt knot (unit of speed = 1 nautical mile per MJO Madden-Julian Oscillation hw depth of air containing waves hour) MKS metric system (SI) of units. Literally: M= KY Kentucky, USA postal code meters, K= kilograms, S = seconds ML mixed layer Mmax maximum tangential wind I MN Minnesota, USA postal code [I] identity matrix L MO Missouri, USA postal code I precipitation intensity L horizontal distribution of temperature MOS Model Output Statistics current latent heat factor Mout exit speed of wind I* net longwave radiation length Mr radial velocity I↑ upwelling longwave low pressure perturbation total gradient wind speed I↓ downwelling longwave low-pressure center Mrad radial (inflow component of velocity I0 intensity of incident radiation Obukhov length MRF medium-range forecast parameter or constant (varies by context) radiation out Ms molecular weight of solute I1 parameter or constant (varies by context) solar luminosity MS Mississippi, USA postal code IA Iowa, USA postal code La attenuation factor MSE mean squared error Ic cubic ice LA Louisiana, USA postal code MSESS mean squared error skill store IC initial conditions LCL lifting condensation level MSL mean sea level intracloud Ld latent heat of deposition or sublimation = MT monsoon trough ICSI International Classification for Seasonal (+/-) 2.83x106 J·kg–1 Montana, USA postal code Snow on the Ground LDR linear depolarization ratio Mt translation speed ID internal dynamics Lf latent heat of fusion or melting = (+/-) Mtan tangential component of velocity 5 –1 Idaho, USA postal code 3.34x10 J·kg MTH magnitude of wind IDF intensity-duration-frequency LFC level of free MUR maximum unambiguous range IFS Integrated Forecast System LFM limited-area fine-mesh MW mega Watts Ih hexagonal ice LFS level of free sink m mass IL Illinois, USA postal code LHS left hand side dimensionless diffraction parameter IN Indiana, USA postal code LOC limit of convection mass of earth = 5.9742x1024 kg IPCC Intergovernmental Panel on Climate LP low precipitation mass of satellite Change Lv latent heat of vaporization meters, a length unit IPV isentropic potential latent heat of condensation or vaporiza- mH2O meters of water, a pressure unit 6 –1 IR infrared tion = (+/-) 2.5x10 J·kg mair mass of air Iscat intensity of scattered radiation LWC liquid-water content mb millibars, a pressure unit ITCZ intertropical convergence zone Lx location parameter mcondensing mass of water vapor that condensed i grid index Lε dissipation length scale mm Hg millimeters of mercury, a pressure unit index Lλ radiance that exists the atmosphere at a min minutes, a unit of time number of ions per molecule certain wavelength mole amount of substance time index l liter, a unit of volume mph miles per hour van’t Hoff factor lb buoyancy length scale mplanet mass of a planet in inch, a unit of length lb “pound, a unit of mass. Also used as a unit ms mass of solute in Hg “inches of mercury, a pressure unit” of weight (pounds-force), which is the mT maritime Tropical air mass force experienced by a pound-mass mv mass of a water molecule under the influence of gravity” mw molecular weight liter a unit of volume mwater mass of water J lm momentum length scale J cost function ln natural logarithm (base e) Joule, a unit of energy log common logarithm (base 10) JJA June, July, and August N JNWPU Joint Numerical Weather Prediction Unit N energy j grid index Newtons, a unit of force M north M actual wind number of data points mass of earth number of drops greater than a given K mean anomaly radius K eddy diffusivity number of tiles per side number of tiles through which the eddy viscosity vertical distribution of temperature perimeter passes Kelvins, a unit of absolute temperature wind speed refractivity refractive- index magnitude M0 location parameter N0 parameter or constant (varies by context) total number of height levels or layers wind speed in residual layer N1 abundance parameter –1 KDP specific differential phase M1 walking speed = 2 m·s N2 nitrogen molecule KE eddy diffusivity for moisture M2 parameter or constant (varies by context) N2O nitrous oxide KE kinetic energy Ma steady-state antitriptic wind NAAQS National Ambient Air Quality Standards KF Kalman Filter Ma Mach number NaCl salt K-H Kelvin Helmholtz (waves) MA Massachusetts, USA postal code NAM Northern Annular Mode K↑ upwelling solar MAE mean absolute error NAO North Atlantic Oscillation K↓ downwelling solar MB megabyte NB New Brunswick, Canada postal code k absorption coefficient Manitoba, Canada postal code NBV Brunt-Va_isälä frequencyon grid index MBL boundary layer wind speed NC North Carolina, USA postal code height index Mc speed of movement of a column of air NCEP National Centers for Environmental molecular conductivity MCC Mesoscale cellular convection Prediction = 0.0253 W·m–1·K–1 Mesoscale convective complex ND North Dakota, USA postal code parameter or constant (varies by context) Mcs cyclostrophic wind NE Nebraska, USA postal code vertical data point index MCS Mesoscale convective systems Ne neon Von Kármán constant = 0.4 MCV Mesoscale convective vortex NGM nested grid model k1 parameter or constant (varies by context) MD Maryland, USA postal code NH New Hampshire, USA postal code k2 parameter or constant (varies by context) ME mean error (NH4)2SO4 ammonium sulfate –23 kB Boltzmann’s constant = 1.3806x10 mechanical energy NJ New Jersey, USA postal code J·K–1·molecule–1 Maine, USA postal code NL number of layers kg kilograms, a mass unit METAR meteorological observation code Newfoundland & Labrador, Canada post- kgf kilograms of force = |g|·mass MG meridional gradient of zonal momentum al code kgm kilograms of mass Mgust gust front advancement speed NM New Mexico, USA postal code KH eddy diffusivity for heat MI Michigan, USA postal code NO2 nitrogen dioxide km kilometers, a unit of length Min incoming wind speed NOAA National Oceanographic and Atmospheric kPa kiloPascal, a unit of pressure MIPS millions of (computer) instructions per Administration C884 NOTATION

NP North Pole psf “pounds-force per square foot, a pressure rλ reflectivity at one wavelength NS Nova Scotia, Canada postal code unit” r ratio of e-folding height to inversion NSSL National Severe Storms Laboratory psi “pounds-force per square inch, a pressure strength in the stable boundary layer NT Northwest Territories, Canada postal code unit” impact parameter NU Nunavut, Canada postal code p’ pressure perturbation (deviation from hy- radius of curvature NV Nevada, USA postal code drostatic) distance of gust from downburst center NVA negative vorticity advection distance from center of earth NWP numerical weather prediction distance from axis of rotation of earth NWS National Weather Service distance from center of a hurricane NY New York, USA postal code Q mesocyclone radius n direction pointing toward the center of Q1 total amount of pollutant emitted parameter or constant (varies by context) curvature Q amount radius of earth (see Rearth) index of refraction Q-vector distance of hurricane eye-wall wind maxi- number density source emission rate of pollutant mum from the center of the eye number of grid points being averaged QA cumulative heating or cooling average drop radius total number QAK cumulative heating or cooling in kinemat- constant = 0.02 ni refractive index ic units earth radius = 6356.766 km QC Quebec, Canada postal code radius QE latent heat reflectivity QH heat added radius of downburst O q specific parameter or constant (varies by context) OFM operational numerical weather forecast solar forcing ratio model qs saturation specific humidity OH Ohio, USA postal code OK Oklahoma, USA postal code S ON Ontario, Canada postal code S supersaturation OR Oregon, USA postal code R solar radiative forcing OSSE Observing System Simulation ℜ gas constant in shear generation of TKE Experiment ℜd gas constant for dry air swirl ratio –1 3 –1 O2 oxygen molecule = 0.287053 kPa·K ·m ·kg South –1 –1 –2 O3 ozone molecule = 287.053 J·K ·kg solar constant = 1361 ±7 W·m ℜv gas constant for pure water vapor Snell’s Law for components = 0.4615 kPa·K–1·m3·kg–1 storm surge height of ocean surface above = 461.5 J·K–1·kg–1 normal sea level P R radius S* critical supersaturation P ambient pressure range S** Lagrangian net source/sink of water perimeter radius from centre of sphere S0 Average total solar irradiance/solar period cyclone radius constant power distance internal source of heat per unit mass or pressure R0 average radius of the earth = 6356.766 km internal latent heating rate probability smoke-stack top-radius S1 parameter or constant (varies by context) sidereal orbital period=365.256363 days net solar input SA available supersaturation P0 sea level pressure = 101.325 kPa critical radius or distance SBH sea-breeze head reference pressure = 100 kPa R1 parameter or constant (varies by context) SBL stable boundary layer P1 mean background pressure RAOB radiosonde observation SC South Carolina, USA postal code Pa Pascal, a unit of pressure RASS radio acoustic sounding system SD South Dakota, USA postal code PA Pennsylvania, USA postal code Rc radius of curvature SI International System of Units (metric PB ambient pressure at bottom of column Rearth average earth radius = 6356.766 km, or units) Pb chemical abbreviation for lead earth radius at equator = 6378 km Sinf background supersaturation at a large PBV period oscillation at the Brunt-Väisälä ref reference height distance from droplet frequency Rf flux Richardson number SK Saskatchewan, Canada postal code PC portion correct RFD Rear-flank downdraft SL surface layer Pc reference pressure at the center of an RH relative humidity SO2 sulfur dioxide anticyclone RHI range-height indicator SOI Southern Oscillation Index PCA Principal Component Analysis RHS right hand side SP South Pole Pdyn dynamic pressure RI Rhode Island, USA postal code SR equilibrium supersaturation adjacent to Pe environmental pressure Ri bulk Richardson number droplet PE primitive equation Richardson number SRH storm relative helicity Prince Edward Island, Canada postal code Ric critical Richardson number = 0.25 SSM/I Special Sensor Microwave Imagers Pearth earth orbital period = 365.25463 days RL residual layer SSROC ROC skill score PG Pasquill-Gifford RMS root mean square (error) SST stably-stratified turbulence PGm mesoscale pressure gradient Ro Rossby number PGs synoptic-scale pressure gradient ROC Relative Operating Characteristic ST standard time in the local time zone PIBAL pilot balloon Roc curvature Rossby number STP Standard Temperature and Pressure PIREPS pilot reports (of the weather in flight) RP return period Sx dimensionless spread parameter Pmoon lunar orbital period = 27.32 days RR rainfall rate s distance PMSL mean sea level pressure RxL radix layer horizontal distance POD probabilty of detection R* critical radius length of side of square PPI plan position indicator r water mixing ratio, a form of humidity path length PPM Perfect Prog Method correlation coefficient seconds, a time unit Pr precipitation rate system response slope probability reflectivity speed of sound probability of having a given wind speed r0 tornado radius streamline Prain storm period r1 parameter or constant (varies by context) total entropy PRF pulse repetition frequencies rad radians s0 parameter or constant (varies by context) Ps pressure at sea level rc critical radus (for escape) sin sine static pressure rCL cost/loss ratio sr steradian Psidereal sidereal day = 23.94 h rE excess-water mixing ratio PSTP standard sea-level pressure = 101.325 kPa average radius of the earth = 6356.766 km PT ambient pressure at top of column ri ice mixing ratio PVA positive vorticity advection rinf background mixing ratio T PVU potential vorticity unit rL liquid-water mixing ratio T temperature –6 2 –1 –1 = 10 K·m ·s ·kg rs saturation mixing ratio TORRO tornado intensity scale ppb parts per billion rT total water mixing ratio T’ amount temperature deviates from the ppm parts per million rw wet-bulb mixing ratio average value R. STULL • PRACTICAL METEOROLOGY C885

Ts surface temperature U.T. Upper Tropospheric receptor from source Tsfc surface temperature UTC Coordinated Universal Time ratio of heat flux into the ground to the net T0 parameter or constant (varies by context) UTH component of the thermal wind radiative flux at the earth’s surface freezing temperature in Kelvins = 273.15 K U’ velocity relative to earth Xe Xenon T1 parameter or constant (varies by context) u* friction velocity x abscissa value T2 parameter or constant (varies by context) distance TA temperature of atmosphere distance downwind TB brightness temperature distance from centreline Td dew-point temperature V distance from front TD turbulent drag V economic value distance toward east tropical depression vector wind velocity path length Tdyn dynamic temperature velocity in the y-direction travel distance Te ambient-air absolute temperature verifying analysis x’ distance east from arbitrary longitude temperature of environment visual range/ effective radiation emission temperature voltage (in volts) = 255 K volume TE Tennessee, USA postal code wind component to the north Y TH thickness VA Virginia, USA postal code Y dimensionless crosswind distance of the TIBL thermal internal boundary layer VAD Velocity Azimuth Display receptor from plume centerline TIROS Television and InfraRed Operational Vag ageostrophic wind component toward the time period of orbit (satellite) System north YT Yukon Territory, Canada postal code TKE turbulence kinetic energy Vg meridional geostrophic y distance toward north TL thermal low geostrophic wind component toward ordinate value Tm absolute temperature the north year TNT trinitrotoluene (a high explosive) VHF very high frequency yr year Torr a measure of pressure =133.32 Pa Vin inflow velocity y’ north-south displacement from center lat- TOVS TIROS Operational Vertical Sounder VLF very low frequency itude Tp temperature of katabatic layer Vol volume of water temperature of parcel Vr gradient wind component toward the Tr required heat transport North transport of TKE by turbulence VT Vermont, USA postal code Z Total atmospheric and oceanic heat trans- VTH component of the thermal wind Z dimensionless receptor height port needed to compensate radiation VV vertical visibility radar reflectivity factor horizontal transport parameter v average molecular speed Zulu Time (= UTC time) Tr net sky transmissivity molecular speed ZCL dimensionless plume centreline height reference temperature total velocity along a streamline ZDR differential reflectivity TRL residual layer temperature v’ deviation in meridional velocity relative Zs dimensionless souce (smoke stack) height TROWAL trough of warm air aloft to the mean ZT tropospheric depth (=11km) TS Tropical Storm var variance z depth TSI total solar irradiance ve escape velocity effective atmospheric thickness Tskin temperature of the top few molecules of vL velocity of current through the return height the Earth’s Surface stroke path in vertical distance TSM total shear magnitude z0 aerodynamic roughness length TSR sunrise time z1 initial amplitude TSS true skill score zc reference height at the centre of an TSTP standard sea-level temperature =15°C W anticyclone = 288 K W velocity in the z-direction zCL plume centerline height Tv work zi depth of convective mixed layer TV television thermal updrafts depth of the atmospheric boundary layer TVS tornado vortex signature wave drag mixed-layer depth Tw wet-bulb temperature width zLCL lifting condensation level (km) TX Texas, USA postal code Watt, a power unit zs physical source (smoke stack) height t time West zstn station elevations above sea level time step W0 stack-top exit velocity zT depth of troposphere =11 km t0 time of onset WA Washington, USA postal code height of topography tan tangent WBF Wegener-Bergeron-Findeisen (cold -cloud zTrop depth of troposphere =11 km tcu towering cumulus precipitation formation process) td length of day/time of day WD Wave drag tL Langrangian time scale WER weak echo region torbit orbital time period WI Wisconsin, USA postal code tutc Coordinated Universal Time Wmid vertical velocity across 50 kPa surface tλ transmissivity at wavelength λ WMO World Meteorological Organization WRF Weather Research and Forecasting GREEK SYMBOLS Ws subsidence velocity magnitude WV water vapor U West Virginia, USA postal code U tangential velocity of earth WX Weather velocity in the x-direction WY Wyoming, USA postal code Α, α Alpha wind component toward the east w terminal velocity α angle of ray above horizon Uag ageostrophic wind component to the east w0 parameter or constant (varies by context) angle of tilt of wave crests Ud destination air velocity wB buoyancy velocity scale relative to vertical zonal wind wd downburst velocity component angle Ug geostrophic wind component toward we entrainment velocity elevation angle the east wmax max updraft or downdraft speed local azimuth angle UHF ultra-high frequency ws synoptic-scale mean vertical velocity (neg- parameter or constant (varies by context) UHI urban heat island ative for subsidence) slope angle Ujet jet stream velocity wT terminal velocity specific volume = 1/ρ UK United Kingdom transport velocity spread parameter UM Unified Model w* Deardorff (convective) velocity scale terrain slope Ur gradient wind component toward the east relative to north URL universal resource locator (internet α1 rotation angle about the column axis of web address) an ice crystal U zonal velocity s X α3 intermediate calculation parameter US/USA United States of America X cloud diameter/depth α5 intermediate calculation parameter UT Utah, USA postal code dimensionless downwind distance of C886 NOTATION Θ, θ, ϑ Theta

Β, β Beta θ angle of light ray Ρ, ρ Rho mixed-layer ∆β beamwidth potential temperature ρ density –3 β beta parameter (rate of change of Coriolis θ1 viewing angle average sea-level density = 1.225 kg·m parameter with latitude) incident angle ρ0 density of air at sea-level component angle θ2 viewing angle density of object constant or parameter (varies by context) refracted angle ρair density of air divergence θ3 reflected angle ρd density of dry air growth rate θa ambient potential temperature ρf density of fluid Kalman gain θc critical angle ρHV co-polar correlation coefficient rotation angle θe equivalent potential temperature ρi ice density β1 intermediate calculation parameter potential temperature of the environment ρL density of liquid water β3 intermediate calculation parameter θH horizontal angle ρm number density of molecules –3 β5 intermediate calculation parameter θh horizontal viewing angle ρSTP standard sea-level density = 1.225 kg·m βc wedge angle θL liquid-water potential temperature ρv absolute humidity constant or parameter (varies by context) θML mixed-layer potential temperature = density of water vapor θp initial gas temperature of effluent from a ρve excess water vapor density smoke stack ρvs saturation value of absolute humidity potential temperature of an air parcel ρwater density of water Γ, γ Gamma θsfc surface potential temperature θv vertical angle Γ ( = –∆T/∆z) vertical viewing angle Γd dry adiabatic lapse rate virtual potential temperature Σ, σ, ς Sigma Γps pre-storm lapse rate θw wet-bulb potential temperature Γ s saturated (moist) lapse rate Σ summation Γa standard atmospheric lapse rate σ backscatter cross-section area = 6.5 K km–1 parameter of constant (varies by context) γ crystal orientation with respect to the Ι, ι Iota standard deviation compass direction of the incoming surface tension light ray wavenumber depth parameter σo standard deviation of raw observation environmental lapse rate σ1 standard deviation of drop radii potential temperature gradient above the Κ, κ Kappa σ2 variance atmospheric boundary layer σf standard deviation of errors associate psychrometric constant with first guess from previous forecast –1 = 0.4 (gwater vapor/kgair)·K σg standard deviation of errors associated volume extinction coefficient with first guess Λ, λ Lambda σH cloud-cover fraction of high σL cloud-cover fraction of low clouds Λ parameter or constant (varies by context) σM cloud-cover fraction of middle clouds Δ, δ Delta λ wavelength σSB Stefan-Boltzmann constant (see App. B) dimensionless wave parameter σy lateral standard deviation of smoke-plume ∆ change of true longitude angle spread 2 2 ∆ Laplacian operator climate sensitivity factor σy lateral variance of smoke-plume spread δij Kronecker delta horizontal scale σyd dimensionless lateral standard deviation δs solar declination angle λd internal Rossby radius of deformation of smoke plume λr longitude σz vertical standard deviation of smoke- λR external Rossby radius of deformation plume spread 2 λmax wavelength of peak emission σz vertical variance of smoke-plume spread Ε, ε Epsilon λ2 parameter or constant (varies by context) σzc vertical standard deviation of cross- wind-integrated concentration of ε dissipation rate of TKE pollutant effective emissivity σzdc dimensionless vertical standard deviation intermediate calculation parameter Μ, μ Mu of crosswind-integrated concentra- obliquity (tilt of earth’s axis) = 23.439° tion ratio of gas constants for dry air and water μij ratio of refractive indicies ni and nj –1 vapor = 0.633 (gwater vapor/g air)·K µm micrometer, a unit of length viscous dissipation rate of TKE ε0 permittivity of free space (see Appen. B) Τ, τ Tau

Ν, ν Nu τ optical thickness stress Ζ, ζ Zeta ν frequency perihelion date true anomaly time scale ζ zenith angle e-folding time vertical vorticity τ^ transmittance ζa absolute vorticity ζg relative geostrophic vorticity Ξ, ξ Xi ζIPV isentropic potential vorticity ζp potential vorticity Υ, υ, ϒ Upsilon ζr relative vorticity ζ* dimensionless height Ο, ο Omicron

Φ, ϕ, φ Phi Η, η Eta Φ geopotential η‘ vertical displacement of a wave Π, π Pi Φr tilt of Earth’s axis relative to the ecliptic = 23.44° π math constant = ϕ angle between wind direction and 3.141 592 653 589 793 238 462 643 sound-propagation direction dimensionless group direction R. STULL • PRACTICAL METEOROLOGY C887

latitude bottom of troposphere λ at one wavelength intermediate calculation parameter black or dark daisies ϕ at latitude _ BL boundary layer °C in degrees celsius BLG boundary layer gradient (wind) ∞ at a far or infinite distance away C of parcel C Χ, χ Chi °C in degrees Celsius CCN cloud condensation nuclei CF Coriolis Force CN centrifugal force cond conduction Ψ, ψ Psi d destination SPECIAL SYMBOLS flow in the most narrow part of a channel ψ elevation angle or mountain pass § computer spreadsheet should be used to E latent heat solve this homework exercise e environment ℑ dynamic flux earth ℜ gas constant in ideal gas law earth of the earth Ω, ω Omega ℜd gas constant in ideal gas law for dry air eff effective ℜv gas constant in ideal gas law for pure Ω ohms, a measure of resistance eq equilibrium water vapor Ωd angular velocity final final state • key equation or concept angular rotation rate of the earth G ground · multiply operator ω angular frequency bare ground ωE Earth’s rotation rate = 0.0043633 radians/ g geostrophic minute first guess H of heat ia rays going from ice to air destination index ϖ Variant Pi init initial j source index ϖ equinox precession = angle of the K in Kelvin perihelion from the vernal equinox k data point index L liquid LCL lifting condensation level left at the left side of a volume or box liq liquid max maximum mid mid-level OPERATORS at midpoint of column initial value d( ) total derivative ML mixed layer ∂( ) partial derivative mtn of a mountain ∆( ) difference, or change of o mean background value or reference () (overbar) average or mean of state ( )’ (prime) deviation from the mean observation [ ] matrix initial condition p parcel |z at height z | | absolute value PG pressure gradient () amplitude (of wave) R reference condition ∫( ) integral of rad of radiation ∑( ) sum of ref reference condition ∏( ) product of right at the right side of a volume or box · multiplication RL residual layer RxL radix layer s surface source index upstream flow SBF of the sea-breeze front sfc surface skin at the top molecules of the earth’s sur- SUPERSCRIPTS face SL surface layer ( )’ (prime) deviation from the mean SL or sl sea level first guess SST sea surface temperature perturbation STP strandard temperature and pressure turbulent variation sun of the sun T top of troposphere t at time t TD turbulent drag TH thickness thermal turb turbulent or turbulence SUBSCRIPTS u u component of wind v v component of wind 1 at height 1 virtual 2 at height 2 W white or light daisies A any quantity w vertical component of wind of parcel A water of water a analysis X of parcel X ABL, abl atmospheric boundary layer x variable in the x direction AD advection component toward the east adv advection y variable in the y direction ai rays going from air to ice component toward the north air of air z variable in the z direction avg average component in upward direction B of parcel B θ potential temperature C888 NOTATION