# Appendix C • Notation

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# Roman Symbols, Acronyms & Contractions

 A A advection of TKE albedo ampere (a unit of electrical current)  amplitude area Ball ratio = 0.2 initial analysis north-south amplitude of a wave  parameter or constant (varies by context) AAM absolute angular momentum AB Alberta, Canada postal code ABL Atmospheric Boundary Layer ACARS aircraft communication and reporting system AD albedo of dark-colored daisies AG albedo of bare ground AGL above ground level AIREP aviation report AK Alaska, USA postal code AL Alabama, USA postal code AL albedo of light-colored daisies AMDAR aircraft meteorological data relay AO Arctic Oscillation AR Arkansas, USA postal code Ar argon ARPEGE Action de Recherche Petite Echelle Grande Echelle (weather-forecast model) ASDAR aircraft to satellite data relay ASOS automatic surface observing system AT apparent temperature (heat index) AVCS arbitrary vertical cross-section Aw global albedo corresponding to an atmospheric window AWOS automatic weather observing system AZ Arizona, USA postal code acceleration attenuation coefficient length of semi-major axis of earth’s orbit = 149.457 Gm parameter or constant (varies by context) spillage distance of front (= external Rossby radius of deformation)  surface albedo $$\ \vec{a}$$ vector acceleration aH mixed-layer transport coefficient = 0.0063 arccos inverse of cosine function (cos–1) arcsin inverse of sine function (sin–1) arctan inverse of tangent function (tan–1) asin inverse of sine function (sin–1) atm atmospheres (a pressure unit) aλ absorptivity B B Beaufort wind scale bias score bowen ratio breakdown potential for dry air = 3x109 V km–1 buoyant production or consumption of TKE BC boundary conditions British Columbia, Canada postal code BLG boundary-layer gradient (wind) BRN bulk richardson number BSS Brier Skill Score Bλ black-body radiation of a certain wavelength parameter or constant (varies by context) b absorption cross section damping factor extinction cross section length of semi-minor axis = 149.090 Gm parameter or constant (varies by context) b1 parameter or constant (varies by context) bD dimensionless coefficient bH convective transport coefficient C C angular rotation in a full circle (360° or 2π radians)  circle circumference (360° or 2π radians) circulation climatological condition cost dimensionless concentration fractional area covered parameter or constant (varies by context) specific heat capacity CA air discharge California, USA postal code Ca absolute circulation CAN Canada CAPE Convective Available Potential Energy CAPPI constant altitude plan position indicator CAT clear-air turbulence CB Bernoulli’s constant CC cell circulation cloud-to-cloud CCD charge-coupled devices CCL convective condensation level CCN cloud condensation nuclei CD drag coefficient fraction of the globe covered by dark daisies CF coriolis force CFL Courant-Friedrichs-Lewy (condition for numerical stability) CG cloud-to-ground CG fractional area covered by bare ground CH bulk heat-transfer coefficient CH4 methane CI capping inversion CIN convective inhibition CL classic CL fraction of the globe covered by light daisies CMC Canadian Meteorological Center CO carbon monoxide Colorado, USA postal code CO2 carbon dioxide CP cumulative probability Cp specific heat of air at constant pressure Cpd specific heat of dry air at constant pressure = 1004.67 J·kg–2·K–1 Cpv specific heat for water vapor at constant pressure = 1875 J·kg–1·K–1 Cr relative circulation CRT video screen. Literally: Cathode Ray Tube Cs seed coverage CSI critical sucess index CT Connecticut, USA postal code Cu cumulus cloud Curv curvature Cv specific heat at constant volume Cvd air specific heat of dry air at constant volume Cw vertical drag coefficient Cy dimensionless cross-wind integrated concentration °C degrees Celsius or centigrade, a unit of temperature c concentration of a pollutant density correction factor half the distance between two foci of an ellipse maximum concentration parameter or constant (varies by context) phase speed or shallow-water wave speeds speed of light through air at sea level pressure = 299,710,000 m·s–1 speed of sound c0 speed of light in a vacuum = 299,792,258 m·s–1 c1 parameter or constant (varies by context) c2 parameter or constant (varies by context) c3 parameter or constant (varies by context) c4 parameter or constant (varies by context) cd “candela, a unit of luminous intensity” cg group speed or group velocity ci speed of light through medium i cm centimeter, a length unit cos cosine covar covariance cP continental polar air mass cy crosswind-integrated concentration cαβ intermediate calculation parameter for atmospheric optical ray paths D D daylight duration hours death rate of daisies diffusivity = 2.11x10–5 m2·s–1 for water vapor in air under standard conditions distance drop diameter duration of positive heat flux  fractal dimension modern description parameter or constant (varies by context) precipitation duration (h) size of particle width of flow DA data assimilation DC District of Columbia, USA postal code DE Delaware, USA postal code DIAL differential absorption lidars DJF “December, January, and February” DMSP defense meterological satellite program DT Daylight Savings Time DW diabatic warming rate Dφ differential heating Dϕ net radiative flux, or differential heating, at latitude ϕ d days, a time unit depth diagonal length distance between crest and trough of a wave distance between earth and sun = 149.6 Gm Julian day plume spread thickness dmax.rain total accumulated depth in a rain gauge dw precipitable water dy number of days in a year dBZ decibels of Z - units of radar reflectivity ∆d phase shift E E collision efficiency East  efficiency electric field energy incoming or outgoing radiative flux  irradiance turbine efficiency E0 theoretical efficiency E1 parameter or constant (varies by context) Ec collection efficiency ECMWF European Centre for Medium-Range Weather Forecasts EHI Energy helicity index Ein incoming flux  zonally and annually averaged incoming radiative flux Einsol annual average insolation EL equilibrium level Emax maximum efficiency Enet differential heating due to radiation net radiative flux zonally and annually averaged net radiative flux EOF Empirical Orthogonal Function Eout outgoing flux zonally and annually averaged outgoing flux EPA U.S. Environmental Protection Agency EQ equator ETS equitable threat score EU European Union Evap evaporation rate EZ entrainment zone Eϕ incoming or outgoing radiative flux at latitude ϕ (\ \bar{E}\) average daily insolation E’ coalescence efficiency E* total irradiance E*λ emittance/radiant existence/irradiance irradiance at wavelength λ e base of natural logarithms = 2.7182818285 current or voltage eccentricity eccentricity of earth’s orbit = 0.0167 vapor pressure e0 saturation vapor pressure = 0.611 kPa at 0 °C eIR IR surface emissivity es saturation vapor pressure over flat pure water saturation vapor pressure es* actual saturation vapor pressure ew equilibrium emissivity corresponding to an atmospheric window exp base of natural logarithms = 2.7182818285 eλ emissivity at wavelength λ F F flux density kinematic flux false-alarm rate force forecast Fujita tornado damage scale $$\ \vec{F}$$ vector force FA free atmosphere FAR false-alarm ratio FAS Federation of American Scientists Fc tracer flux FCF Coriolis force FCN centrifugal force FE latent heat flux from earth’s surface up into the air (in kinematic units of K·m·s–1) FFD Forward flank downdraft FG flux gradient FG molecular heat conduction  heat flux conducted from the ground up to the earth’s surface (in kinematic units of K·m·s–1) FH sensible heat flux from earth’s surface up into the air (in kinematic units of K·m·s–1) FHsfc surface kinematic heat flux FL Florida, USA postal code $$\ \vec{F}_{n e t}$$ net vector force FNMOC Fleet Numerical Meteorological and Oceanographic Center FPG Pressure gradient force FPGm mesoscale pressure-gradient force FPGs synoptic pressure-gradient force Fr Froude number Frad radiative flux at a surface FS Frontal strength FTD turbulent drag force FV3 Finite Volume - version 3 Fx kinematic heat flux component in x direction  component of net vector force toward the east Fy kinematic heat flux component in y direction meridional heat transport Fz kinematic heat flux component in z direction F* net radiative flux at earth’s surace (in kinematic units of K·m·s–1) °F Fahrenheit, a unit of temperautre $$\ \mathbb{F}$$ flux (dynamic) $$\ \mathbb{F}*$$ net radiative flux at earth’s surace (in dynamic units of W·m–2) $$\ \mathbb{F}_{diff}$$ diffusive moisture flux $$\ \mathbb{F}_{E}$$ latent heat flux from earth’s surface up into the air (in dynamic units W·m–2) $$\ \mathbb{F}_{G}$$ heat flux conducted from the ground up to the earth’s surface (in dynamic units of W·m–2) $$\ \mathbb{F}_{H}$$ sensible heat flux from earth’s surface up into the air (in dynamic units W·m–2) $$\ \mathbb{F}_{rad^*}$$ net radiative flux $$\ \mathbb{F}_{x}$$ dynamic heat flux in x direction $$\ \mathbb{F}_{y}$$ dynamic heat flux in y direction $$\ \mathbb{F}_{z}$$ dynamic heat flux in z direction f oscillation frequency feedback factor fc Coriolis parameter centrifugal force fG f0 pull (force) by earth’s gravity reference Coriolis parameter at the center of the beta plane ft feet, a length unit ft H2O feet of water, a pressure unit fx fraction of cloud sizes Fz eff sfc effective surface heat flux G G cyclone graveyard gain geostrophic wind speed gravitational constant = 6.67x10–11 m3·s–2·kg–1 intermediate circulation parameter  theoretical geostrophic value GA Georgia, USA postal code GB gigabyte GCM global climate model GCM general circulation model GEM Global Environmental Multiscale (Canadian numerical model) GFS Global Forecast System GHG greenhouse gas Gm gigameter, a length unit Gm gap-geostrophic wind GMT Greenwich Mean Time GPS global positioning system (via satellite) GPU Graphics Processing Unit GSM global spectral model GSS Gilbert’s skill score GTS global telecommunication system g grams, a unit of mass gravitational acceleration = –9.8 m·s–2 (negative means downward) g’ reduced gravity H H geopotential height high pressure center high hit rate heating rate helicity unperturbed ocean depth H2 hydrogen H2O water H2O2 hydrogen peroxide H2SO4 sulfuric acid HC hurricane category He helium He e-folding depth HI heat index apparent temperature Hawaii, USA postal code HNO3 nitric acid Hp scale height for pressure HP High precipitation HRR rate of energy release over unit area of earth’s surface HSS Heidke skill score Hz “hertz, a unit of frequency” Hρ scale height for density h depth depth of cold air depth of stable boundary layer  enthalpy height hours, a unit of time wave height h0 hour angle h2 parameter or constant (varies by context) hgust gust front depth hw depth of air containing waves I [I] identity matrix I precipitation intensity current I* net longwave radiation I↑ upwelling longwave I↓ downwelling longwave I0 intensity of incident radiation parameter or constant (varies by context) I1 parameter or constant (varies by context) IA Iowa, USA postal code Ic cubic ice IC initial conditions intracloud ICSI International Classification for Seasonal Snow on the Ground ID internal dynamics Idaho, USA postal code IDF intensity-duration-frequency IFS Integrated Forecast System Ih hexagonal ice IL Illinois, USA postal code IN Indiana, USA postal code IPCC Intergovernmental Panel on Climate Change IPV isentropic potential vorticity IR infrared Iscat intensity of scattered radiation ITCZ intertropical convergence zone i grid index index number of ions per molecule time index van’t Hoff factor in inch, a unit of length in Hg “inches of mercury, a pressure unit” J J cost function Joule, a unit of energy JJA June, July, and August JNWPU Joint Numerical Weather Prediction Unit j grid index K K eddy diffusivity eddy viscosity Kelvins, a unit of absolute temperature refractive- index magnitude  total number of height levels or layers KDP specific differential phase KE eddy diffusivity for moisture KE kinetic energy KF Kalman Filter K-H Kelvin Helmholtz (waves) K↑ upwelling solar K↓ downwelling solar k absorption coefficient grid index height index molecular conductivity = 0.0253 W·m–1·K–1 parameter or constant (varies by context) vertical data point index Von Kármán constant = 0.4 k1 parameter or constant (varies by context) k2 parameter or constant (varies by context) kB Boltzmann’s constant = 1.3806x10–23 J·K–1·molecule–1 kg kilograms, a mass unit kgf kilograms of force = |g|·mass kgm kilograms of mass KH eddy diffusivity for heat km kilometers, a unit of length kPa kiloPascal, a unit of pressure KS Kansas, USA postal code kt knot (unit of speed = 1 nautical mile per hour) KY Kentucky, USA postal code L L horizontal distribution of temperature  latent heat factor length low pressure perturbation low-pressure center Obukhov length radiation out solar luminosity La attenuation factor LA Louisiana, USA postal code LCL lifting condensation level Ld latent heat of deposition or sublimation = (+/-) 2.83x106 J·kg–1 LDR linear depolarization ratio Lf latent heat of fusion or melting = (+/-) 3.34x105 J·kg–1 LFC level of free convection LFM limited-area fine-mesh LFS level of free sink LHS left hand side LOC limit of convection LP low precipitation Lv latent heat of vaporization latent heat of condensation or vaporization = (+/-) 2.5x106 J·kg–1 LWC liquid-water content Lx location parameter Lε dissipation length scale Lλ radiance that exists the atmosphere at a certain wavelength l liter, a unit of volume lb buoyancy length scale lb “pound, a unit of mass. Also used as a unit of weight (pounds-force), which is the force experienced by a pound-mass under the influence of gravity” liter a unit of volume lm momentum length scale ln natural logarithm (base e) log common logarithm (base 10) M M actual wind mass of earth mean anomaly number of tiles per side vertical distribution of temperature  wind speed M0 location parameter wind speed in residual layer M1 walking speed = 2 m·s–1 M2 parameter or constant (varies by context) Ma steady-state antitriptic wind Ma Mach number MA Massachusetts, USA postal code MAE mean absolute error MB megabyte Manitoba, Canada postal code MBL boundary layer wind speed Mc speed of movement of a column of air MCC Mesoscale cellular convection Mesoscale convective complex Mcs cyclostrophic wind MCS Mesoscale convective systems MCV Mesoscale convective vortex MD Maryland, USA postal code ME mean error mechanical energy Maine, USA postal code METAR meteorological observation code MG meridional gradient of zonal momentum Mgust gust front advancement speed MI Michigan, USA postal code Min incoming wind speed MIPS millions of (computer) instructions per second MJO Madden-Julian Oscillation MKS metric system (SI) of units. Literally: M= meters, K= kilograms, S = seconds ML mixed layer Mmax maximum tangential wind MN Minnesota, USA postal code MO Missouri, USA postal code MOS Model Output Statistics Mout exit speed of wind Mr radial velocity total gradient wind speed Mrad radial (inflow component of velocity MRF medium-range forecast Ms molecular weight of solute MS Mississippi, USA postal code MSE mean squared error MSESS mean squared error skill store MSL mean sea level MT monsoon trough Montana, USA postal code Mt translation speed Mtan tangential component of velocity MTH magnitude of thermal wind MUR maximum unambiguous range MW mega Watts m mass dimensionless diffraction parameter mass of earth = 5.9742x1024 kg  mass of satellite meters, a length unit mH2O meters of water, a pressure unit mair mass of air mb millibars, a pressure unit mcondensing mass of water vapor that condensed mm Hg millimeters of mercury, a pressure unit min minutes, a unit of time mole amount of substance mph miles per hour mplanet mass of a planet ms mass of solute mT maritime Tropical air mass mv mass of a water molecule mw molecular weight mwater mass of water N N energy Newtons, a unit of force north number of data points number of drops greater than a given radius number of tiles through which the perimeter passes refractivity N0 parameter or constant (varies by context) N1 abundance parameter N2 nitrogen molecule N2O nitrous oxide NAAQS National Ambient Air Quality Standards NaC salt NAM Northern Annular Mode NAO North Atlantic Oscillation NB New Brunswick, Canada postal code NBV Brunt-Va_isälä frequencyon NC North Carolina, USA postal code NCEP National Centers for Environmental Prediction ND North Dakota, USA postal code NE Nebraska, USA postal code Ne neon NGM nested grid model NH New Hampshire, USA postal code (NH4)2SO4 ammonium sulfate NJ New Jersey, USA postal code NL number of layers Newfoundland & Labrador, Canada postal code NM New Mexico, USA postal code NO2 nitrogen dioxide NOAA National Oceanographic and Atmospheric Administration NP North Pole NS Nova Scotia, Canada postal code NSSL National Severe Storms Laboratory NT Northwest Territories, Canada postal code NU Nunavut, Canada postal code NV Nevada, USA postal code NVA negative vorticity advection NWP numerical weather prediction NWS National Weather Service NY New York, USA postal code n direction pointing toward the center of curvature  index of refraction number density number of grid points being averaged  total number ni refractive index O OFM operational numerical weather forecast model OH Ohio, USA postal code OK Oklahoma, USA postal code ON Ontario, Canada postal code OR Oregon, USA postal code OSSE Observing System Simulation Experiment O2 oxygen molecule O3 ozone molecule P P ambient pressure perimeter period power pressure probability sidereal orbital period=365.256363 days P0 sea level pressure = 101.325 kPa reference pressure = 100 kPa P1 mean background pressure Pa Pascal, a unit of pressure PA Pennsylvania, USA postal code PB ambient pressure at bottom of column Pb chemical abbreviation for lead PBV period oscillation at the Brunt-Väisälä frequency PC portion correct Pc reference pressure at the center of an anticyclone PCA Principal Component Analysis Pdyn dynamic pressure Pe environmental pressure PE primitive equation Prince Edward Island, Canada postal code Pearth earth orbital period = 365.25463 days PG Pasquill-Gifford PGm mesoscale pressure gradient PGs synoptic-scale pressure gradient PIBAL pilot balloon PIREPS pilot reports (of the weather in flight) Pmoon lunar orbital period = 27.32 days PMSL mean sea level pressure POD probabilty of detection PPI plan position indicator PPM Perfect Prog Method Pr precipitation rate probability probability of having a given wind speed Prain storm period PRF pulse repetition frequencies Ps pressure at sea level static pressure Psidereal sidereal day = 23.94 h PSTP standard sea-level pressure = 101.325 kPa PT ambient pressure at top of column PVA positive vorticity advection PVU potential vorticity unit = 10–6 K·m2·s–1·kg–1 ppb parts per billion ppm parts per million psf “pounds-force per square foot, a pressure unit” psi “pounds-force per square inch, a pressure unit” p’ pressure perturbation (deviation from hydrostatic) Q Q1 total amount of pollutant emitted Q amount Q-vector source emission rate of pollutant QA cumulative heating or cooling QAK cumulative heating or cooling in kinematic units QC Quebec, Canada postal code QE latent heat QH heat added q specific humidity solar forcing ratio qs saturation specific humidity R ℜ gas constant in ideal gas law ℜd gas constant for dry air = 0.287053 kPa·K–1·m3·kg–1 = 287.053 J·K–1·kg–1 ℜv gas constant for pure water vapor = 0.4615 kPa·K–1·m3·kg–1 = 461.5 J·K–1·kg–1 R radius range radius from centre of sphere cyclone radius distance R0 average radius of the earth = 6356.766 km smoke-stack top-radius net solar input critical radius or distance R1 parameter or constant (varies by context) RAOB radiosonde observation RASS radio acoustic sounding system Rc radius of curvature Rearth average earth radius = 6356.766 km, or earth radius at equator = 6378 km ref reference height Rf flux Richardson number RFD Rear-flank downdraft RH relative humidity RHI range-height indicator RHS right hand side RI Rhode Island, USA postal code Ri bulk Richardson number Richardson number Ric critical Richardson number = 0.25 RL residual layer RMS root mean square (error) Ro Rossby number ROC Relative Operating Characteristic Roc curvature Rossby number RP return period RR rainfall rate RxL radix layer R* critical radius r water mixing ratio, a form of humidity correlation coefficient system response reflectivity r0 tornado radius r1 parameter or constant (varies by context) rad radians rc critical radus (for escape) rCL cost/loss ratio rE excess-water mixing ratio average radius of the earth = 6356.766 km ri ice mixing ratio rinf background mixing ratio rL liquid-water mixing ratio rs saturation mixing ratio rT total water mixing ratio rw wet-bulb mixing ratio rλ reflectivity at one wavelength r ratio of e-folding height to inversion strength in the stable boundary layer impact parameter radius of curvature distance of gust from downburst center distance from center of earth distance from axis of rotation of earth distance from center of a hurricane mesocyclone radius parameter or constant (varies by context) radius of earth (see Rearth) distance of hurricane eye-wall wind maximum from the center of the eye average drop radius constant = 0.02 earth radius = 6356.766 km radius reflectivity radius of downburst parameter or constant (varies by context) S S supersaturation solar radiative forcing shear generation of TKE swirl ratio South solar constant = 1361 ±7 W·m–2 Snell’s Law for components  storm surge height of ocean surface above normal sea level S* critical supersaturation S** Lagrangian net source/sink of water S0 Average total solar irradiance/solar constant internal source of heat per unit mass or internal latent heating rate S1 parameter or constant (varies by context) SA available supersaturation SBH sea-breeze head SBL stable boundary layer SC South Carolina, USA postal code SD South Dakota, USA postal code SI International System of Units (metric units) Sinf background supersaturation at a large distance from droplet SK Saskatchewan, Canada postal code SL surface layer SO2 sulfur dioxide SOI Southern Oscillation Index SP South Pole SR equilibrium supersaturation adjacent to droplet SRH storm relative helicity SSM/I Special Sensor Microwave Imagers SSROC ROC skill score SST stably-stratified turbulence sea surface temperature ST standard time in the local time zone STP Standard Temperature and Pressure Sx dimensionless spread parameter s distance horizontal distance length of side of square path length seconds, a time unit slope speed of sound streamline total entropy s0 parameter or constant (varies by context) sin sine sr steradian T T temperature TORRO tornado intensity scale T’ amount temperature deviates from the average value Ts surface temperature Tsfc surface temperature T0 parameter or constant (varies by context) freezing temperature in Kelvins = 273.15 K T1 parameter or constant (varies by context) T2 parameter or constant (varies by context) TA temperature of atmosphere TB brightness temperature Td dew-point temperature TD turbulent drag tropical depression Tdyn dynamic temperature Te ambient-air absolute temperature  temperature of environment  effective radiation emission temperature = 255 K TE Tennessee, USA postal code TH thickness TIBL thermal internal boundary layer TIROS Television and InfraRed Operational (satellite) System TKE turbulence kinetic energy TL thermal low Tm absolute temperature TNT trinitrotoluene (a high explosive) Torr a measure of pressure =133.32 Pa TOVS TIROS Operational Vertical Sounder Tp temperature of katabatic layer  temperature of parcel Tr required heat transport transport of TKE by turbulence Total atmospheric and oceanic heat transport needed to compensate radiation Tr net sky transmissivity reference temperature TRL residual layer temperature TROWAL trough of warm air aloft TS Tropical Storm TSI total solar irradiance Tskin temperature of the top few molecules of the Earth’s Surface TSM total shear magnitude TSR sunrise time TSS true skill score TSTP standard sea-level temperature =15°C = 288 K Tv virtual temperature TV television TVS tornado vortex signature Tw wet-bulb temperature TX Texas, USA postal code t time  time step t0 time of onset tan tangent tcu towering cumulus td length of day/time of day tL Langrangian time scale torbit orbital time period tutc Coordinated Universal Time tutc Coordinated Universal Time tλ transmissivity at wavelength λ U U tangential velocity of earth velocity in the x-direction wind component toward the east Uag ageostrophic wind component to the east Ud destination air velocity zonal wind Ug geostrophic wind component toward the east UHF ultra-high frequency UHI urban heat island Ujet jet stream velocity UK United Kingdom UM Unified Model Ur gradient wind component toward the east URL universal resource locator (internet web address) Us zonal velocity US/USA United States of America UT Utah, USA postal code U.T Upper Tropospheric UTC Coordinated Universal Time UTH component of the thermal wind U’ velocity relative to earth u* friction velocity V V economic value vector wind velocity velocity in the y-direction verifying analysis visual range/visibility voltage (in volts) volume wind component to the north VA Virginia, USA postal code VAD Velocity Azimuth Display Vag ageostrophic wind component toward the north Vg meridional geostrophic winds geostrophic wind component toward the north VHF very high frequency Vin inflow velocity VLF very low frequency Vol volume of water Vr gradient wind component toward the North VT Vermont, USA postal code VTH component of the thermal wind VV vertical visibility v average molecular speed molecular speed total velocity along a streamline v’ deviation in meridional velocity relative to the mean var variance ve escape velocity vL velocity of current through the return stroke path in lightning W W velocity in the z-direction work thermal updrafts wave drag width Watt, a power unit West W0 stack-top exit velocity WA Washington, USA postal code WBF Wegener-Bergeron-Findeisen (cold -cloud precipitation formation process) WD Wave drag WER weak echo region WI Wisconsin, USA postal code Wmid vertical velocity across 50 kPa surface WMO World Meteorological Organization WRF Weather Research and Forecasting Ws subsidence velocity magnitude WV water vapor West Virginia, USA postal code WX Weather WY Wyoming, USA postal code w terminal velocity w0 parameter or constant (varies by context) wB buoyancy velocity scale wd downburst velocity we entrainment velocity wmax max updraft or downdraft speed ws synoptic-scale mean vertical velocity (negative for subsidence) wT terminal velocity transport velocity w* Deardorff (convective) velocity scale X X cloud diameter/depth dimensionless downwind distance of receptor from source ratio of heat flux into the ground to the net radiative flux at the earth’s surface Xe Xenon x abscissa value distance distance downwind distance from centreline distance toward east path length travel distance x’ distance east from arbitrary longitude Y Y dimensionless crosswind distance of the receptor from plume centerline  time period of orbit YT Yukon Territory, Canada postal code y distance toward north ordinate value year yr year y’ north-south displacement from center latitude Z Z dimensionless receptor height radar reflectivity factor Zulu Time (= UTC time) ZCL dimensionless plume centreline height ZDR differential reflectivity Zs dimensionless souce (smoke stack) height ZT tropospheric depth (=11km) z depth effective atmospheric thickness  height vertical distance z0 aerodynamic roughness length z1 initial amplitude zc reference height at the centre of an anticyclone zCL plume centerline height zi depth of convective mixed layer  depth of the atmospheric boundary layer mixed-layer depth zLCL lifting condensation level (km) zs physical source (smoke stack) height zstn station elevations above sea level zT depth of troposphere =11 km height of topography zTrop depth of troposphere =11 km

# GREEK SYMBOLS

 Α, α Alpha α angle of ray above horizon angle of tilt of wave crests relative to vertical component angle elevation angle local azimuth angle parameter or constant (varies by context) slope angle specific volume = 1/ρ spread parameter terrain slope wind direction relative to north α1 rotation angle about the column axis of an ice crystal α3 intermediate calculation parameter α5 intermediate calculation parameter Β, β Beta ∆β beamwidth β beta parameter (rate of change of Coriolis parameter with latitude) component angle constant or parameter (varies by context) divergence growth rate Kalman gain rotation angle β1 intermediate calculation parameter β3 intermediate calculation parameter β5 intermediate calculation parameter βc wedge angle constant or parameter (varies by context) Γ, γ Gamma Γ lapse rate ( = –∆T/∆z) Γd dry adiabatic lapse rate Γps pre-storm lapse rate Γs saturated (moist) lapse rate Γa standard atmospheric lapse rate = 6.5 K km–1 γ crystal orientation with respect to the compass direction of the incoming light ray depth parameter environmental lapse rate potential temperature gradient above the atmospheric boundary layer psychrometric constant = 0.4 (gwater vapor/kgair)·K–1 volume extinction coefficient Δ, δ Delta ∆ change of ∆2 Laplacian operator δij Kronecker delta δs solar declination angle Ε, ε Epsilon ε dissipation rate of TKE effective emissivity intermediate calculation parameter obliquity (tilt of earth’s axis) = 23.439° ratio of gas constants for dry air and water vapor = 0.633 (gwater vapor/gair)·K–1 viscous dissipation rate of TKE ε0 permittivity of free space (see Appen. B) Ζ, ζ Zeta ζ zenith angle vertical vorticity ζa absolute vorticity ζg relative geostrophic vorticity ζIPV isentropic potential vorticity ζp potential vorticity ζr relative vorticity ζ* dimensionless height Η, η Eta η‘ vertical displacement of a wave Θ, θ, ϑ Theta θ angle of light ray mixed-layer potential temperature potential temperature θ1 viewing angle incident angle θ2 viewing angle refracted angle θ3 reflected angle θa ambient potential temperature θc critical angle θe equivalent potential temperature potential temperature of the environment θH horizontal angle θh horizontal viewing angle θL liquid-water potential temperature θML mixed-layer potential temperature θp initial gas temperature of effluent from a smoke stack potential temperature of an air parcel θsfc surface potential temperature θv vertical angle vertical viewing angle virtual potential temperature θw wet-bulb potential temperature Ι, ι Iota Κ, κ Kappa Λ, λ Lambda Λ parameter or constant (varies by context) λ wavelength dimensionless wave parameter true longitude angle climate sensitivity factor horizontal scale λd internal Rossby radius of deformation λr longitude λR external Rossby radius of deformation λmax wavelength of peak emission λ2 parameter or constant (varies by context) Μ, μ Mu μij ratio of refractive indicies ni and nj µm micrometer, a unit of length Ν, ν Nu ν frequency true anomaly Ξ, ξ Xi Ο, ο Omicron Π, π Pi π math constant = 3.141 592 653 589 793 238 462 643 dimensionless group Ρ, ρ Rho ρ density average sea-level density = 1.225 kg·m–3 ρ0 density of air at sea-level density of object ρair density of air ρd density of dry air ρf density of fluid ρHV co-polar correlation coefficient ρi ice density ρL density of liquid water ρm number density of molecules ρSTP standard sea-level density = 1.225 kg·m–3 ρv absolute humidity = density of water vapor ρve excess water vapor density ρvs saturation value of absolute humidity ρwater density of water Σ, σ, ς Sigma Σ summation σ backscatter cross-section area parameter of constant (varies by context) standard deviation surface tension wavenumber σo standard deviation of raw observation σ1 standard deviation of drop radii σ2 variance σf standard deviation of errors associate with first guess from previous forecast σg standard deviation of errors associated with first guess σH cloud-cover fraction of high clouds σL cloud-cover fraction of low clouds σM cloud-cover fraction of middle clouds σSB Stefan-Boltzmann constant (see App. B) σy lateral standard deviation of smoke-plume spread σy2 lateral variance of smoke-plume spread σyd dimensionless lateral standard deviation of smoke plume σz vertical standard deviation of smokeplume spread σz2 vertical variance of smoke-plume spread σzc vertical standard deviation of crosswind-integrated concentration of pollutant σzdc dimensionless vertical standard deviation of crosswind-integrated concentration Τ, $$\ \tau$$ Tau $$\ \tau$$ optical thickness stress perihelion date time scale e-folding time $$\ \hat{\tau}$$ transmittance Υ, υ, ϒ Upsilon Φ, ϕ, φ Phi Φ geopotential Φr tilt of Earth’s axis relative to the ecliptic = 23.44° ϕ angle between wind direction and sound-propagation direction direction latitude intermediate calculation parameter Χ, χ Chi Ψ, ψ Psi ψ elevation angle Ω, ω Omega Ω ohms, a measure of resistance Ωd angular velocity angular rotation rate of the earth ω angular frequency ωE Earth’s rotation rate = 0.0043633 radians/ minute ϖ Variant Pi ϖ equinox precession = angle of the perihelion from the vernal equinox OPERATORS d( ) total derivative ∂( ) partial derivative ∆( ) difference, or change of ( ) (overbar) average or mean of ( )’ (prime) deviation from the mean [ ] matrix |z at height z | | absolute value $$\ \widehat{()}$$ amplitude (of wave) ∫( ) integral of ∑( ) sum of ∏( ) product of · multiplication

# SUPERSCRIPTS

 ( )’ (prime) deviation from the mean first guess perturbation turbulent variation

# SUBSCRIPTS

 1 at height 1 2 at height 2 A any quantity of parcel A a analysis ABL, abl atmospheric boundary layer AD advection adv advection ai rays going from air to ice air of air avg average B of parcel B bottom of troposphere black or dark daisies BL boundary layer BLG boundary layer gradient (wind) C of parcel C °C in degrees Celsius CCN cloud condensation nuclei CF Coriolis Force CN centrifugal force cond conduction d destination flow in the most narrow part of a channel or mountain pass E latent heat e environment earth earth of the earth eff effective eq equilibrium final final state G ground bare ground g geostrophic first guess H of heat ia rays going from ice to air destination index init initial j source index K in Kelvin 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 at midpoint of column initial value ML mixed layer mtn of a mountain o mean background value or reference state observation initial condition p parcel PG pressure gradient R reference condition rad of radiation ref reference condition right at the right side of a volume or box RL residual layer RxL radix layer s surface upstream flow SBF of the sea-breeze front sfc surface skin at the top molecules of the earth’s surface SL surface layer SL or sl sea level SST sea surface temperature STP strandard temperature and pressure sun of the sun T top of troposphere t at time t TD turbulent drag TH thickness thermal turb turbulent or turbulence u u component of wind v v component of wind virtual W white or light daisies w vertical component of wind water of water X of parcel X x variable in the x direction component toward the east y variable in the y direction component toward the north z variable in the z direction component in upward direction θ potential temperature λ at one wavelength ϕ at latitude _ °C in degrees celsius ∞ at a far or infinite distance away

# SPECIAL SYMBOLS

 § computer spreadsheet should be used to solve this homework exercise ℑ dynamic flux ℜ gas constant in ideal gas law ℜd gas constant in ideal gas law for dry air ℜv gas constant in ideal gas law for pure water vapor • key equation or concept · multiply operator