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Appendix C • Notation

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    Roman Symbols, Acronyms & Contractions



    advection of TKE


    ampere (a unit of electrical current)



    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


    Arizona, USA postal code


    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


    Beaufort wind scale

    bias score

    bowen ratio

    breakdown potential for dry air = 3x109 V km–1

    buoyant production or consumption of TKE


    boundary conditions

    British Columbia, Canada postal code

    BLG boundary-layer gradient (wind)
    BRN bulk richardson number
    BSS Brier Skill Score


    black-body radiation of a certain wavelength

    parameter or constant (varies by context)


    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


    angular rotation in a full circle (360° or 2π radians)

    circle circumference (360° or 2π radians)


    climatological condition


    dimensionless concentration

    fractional area covered

    parameter or constant (varies by context)

    specific heat capacity


    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


    cell circulation


    CCD charge-coupled devices
    CCL convective condensation level
    CCN cloud condensation nuclei


    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


    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


    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


    daylight duration hours

    death rate of daisies

    diffusivity = 2.11x10–5 m2·s–1 for water vapor in air under standard conditions


    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


    days, a time unit


    diagonal length

    distance between crest and trough of a wave

    distance between earth and sun = 149.6 Gm

    Julian day

    plume spread



    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


    collision efficiency



    electric field


    incoming or outgoing radiative flux


    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


    incoming flux

    zonally and annually averaged incoming radiative flux

    Einsol annual average insolation
    EL equilibrium level
    Emax maximum efficiency


    differential heating due to radiation

    net radiative flux

    zonally and annually averaged net radiative flux

    EOF Empirical Orthogonal Function


    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


    emittance/radiant existence/irradiance

    irradiance at wavelength λ


    base of natural logarithms = 2.7182818285

    current or voltage


    eccentricity of earth’s orbit = 0.0167

    vapor pressure

    e0 saturation vapor pressure = 0.611 kPa at 0 °C
    eIR IR surface emissivity


    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


    flux density

    kinematic flux

    false-alarm rate



    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


    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


    kinematic heat flux component in x direction

    component of net vector force toward the east


    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


    oscillation frequency

    feedback factor


    Coriolis parameter

    centrifugal force



    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


    cyclone graveyard


    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


    grams, a unit of mass

    gravitational acceleration = –9.8 m·s–2 (negative means downward)

    g’ reduced gravity

    geopotential height

    high pressure center


    hit rate

    heating rate


    unperturbed ocean depth

    H2 hydrogen
    H2O water
    H2O2 hydrogen peroxide
    H2SO4 sulfuric acid
    HC hurricane category
    He helium
    He e-folding depth


    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



    depth of cold air

    depth of stable boundary layer



    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] identity matrix
    I precipitation intensity current
    I* net longwave radiation
    I↑ upwelling longwave
    I↓ downwelling longwave


    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


    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


    grid 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”


    cost function

    Joule, a unit of energy

    JJA June, July, and August
    JNWPU Joint Numerical Weather Prediction Unit
    j grid index


    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


    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


    horizontal distribution of temperature

    latent heat factor


    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


    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)


    actual wind

    mass of earth

    mean anomaly

    number of tiles per side

    vertical distribution of temperature

    wind speed


    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



    Manitoba, Canada postal code

    MBL boundary layer wind speed
    Mc speed of movement of a column of air


    Mesoscale cellular convection

    Mesoscale convective complex

    Mcs cyclostrophic wind
    MCS Mesoscale convective systems
    MCV Mesoscale convective vortex
    MD Maryland, USA postal code


    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


    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

    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



    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



    Newtons, a unit of force


    number of data points

    number of drops greater than a given radius

    number of tiles through which the perimeter passes


    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


    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

    direction pointing toward the center of curvature

    index of refraction

    number density

    number of grid points being averaged

    total number

    ni refractive index
    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


    ambient pressure






    sidereal orbital period=365.256363 days


    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


    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


    precipitation rate


    probability of having a given wind speed

    Prain storm period
    PRF pulse repetition frequencies


    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)
    Q1 total amount of pollutant emitted




    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


    specific humidity

    solar forcing ratio

    qs saturation specific humidity
    gas constant in ideal gas law
    d gas constant for dry air = 0.287053 kPa·K–1·m3·kg–1 = 287.053 J·K–1·kg–1
    v gas constant for pure water vapor = 0.4615 kPa·K–1·m3·kg–1 = 461.5 J·K–1·kg–1




    radius from centre of sphere

    cyclone radius



    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


    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


    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


    water mixing ratio, a form of humidity

    correlation coefficient

    system response


    r0 tornado radius
    r1 parameter or constant (varies by context)
    rad radians
    rc critical radus (for escape)
    rCL cost/loss ratio


    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


    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 of downburst

    parameter or constant (varies by context)




    solar radiative forcing

    shear generation of TKE

    swirl ratio


    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


    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


    stably-stratified turbulence

    sea surface temperature

    ST standard time in the local time zone
    STP Standard Temperature and Pressure
    Sx dimensionless spread parameter



    horizontal distance

    length of side of square

    path length

    seconds, a time unit


    speed of sound


    total entropy

    s0 parameter or constant (varies by context)
    sin sine
    sr steradian



    TORRO tornado intensity scale

    T’ amount temperature deviates from the average value
    Ts surface temperature
    Tsfc surface temperature


    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


    turbulent drag

    tropical depression

    Tdyn dynamic temperature


    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


    temperature of katabatic layer

    temperature of parcel


    required heat transport

    transport of TKE by turbulence

    Total atmospheric and oceanic heat transport needed to compensate radiation


    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



    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


    tangential velocity of earth

    velocity in the x-direction

    wind component toward the east

    Uag ageostrophic wind component to the east


    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


    economic value

    vector wind velocity

    velocity in the y-direction

    verifying analysis

    visual range/visibility

    voltage (in volts)


    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


    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


    velocity in the z-direction


    thermal updrafts

    wave drag


    Watt, a power unit


    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


    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)


    terminal velocity

    transport velocity

    w* Deardorff (convective) velocity scale


    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


    abscissa value


    distance downwind

    distance from centreline

    distance toward east

    path length

    travel distance

    x’ distance east from arbitrary longitude


    dimensionless crosswind distance of the receptor from plume centerline

    time period of orbit

    YT Yukon Territory, Canada postal code

    distance toward north

    ordinate value


    yr year
    y’ north-south displacement from center latitude


    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)



    effective atmospheric thickness


    vertical distance

    z0 aerodynamic roughness length
    z1 initial amplitude
    zc reference height at the centre of an anticyclone
    zCL plume centerline height


    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


    depth of troposphere =11 km

    height of topography

    zTrop depth of troposphere =11 km


    Α, α Alpha


    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


    beta parameter (rate of change of Coriolis parameter with latitude)

    component angle

    constant or parameter (varies by context)


    growth rate

    Kalman gain

    rotation angle

    β1 intermediate calculation parameter
    β3 intermediate calculation parameter
    β5 intermediate calculation parameter


    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


    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


    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


    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


    angle of light ray

    mixed-layer potential temperature

    potential temperature


    viewing angle

    incident angle


    viewing angle

    refracted angle

    θ3 reflected angle
    θa ambient potential temperature
    θc critical angle


    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


    initial gas temperature of effluent from a smoke stack

    potential temperature of an air parcel

    θsfc surface potential temperature


    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)



    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



    true anomaly

    Ξ, ξ Xi
    Ο, ο Omicron
    Π, π Pi


    math constant = 3.141 592 653 589 793 238 462 643

    dimensionless group

    Ρ, ρ Rho



    average sea-level density = 1.225 kg·m–3


    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


    backscatter cross-section area

    parameter of constant (varies by context)

    standard deviation

    surface tension


    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


    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°


    angle between wind direction and sound-propagation direction



    intermediate calculation parameter

    Χ, χ Chi
    Ψ, ψ Psi
    ψ elevation angle
    Ω, ω Omega
    Ω ohms, a measure of resistance


    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
    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


    ( )’

    (prime) deviation from the mean

    first guess


    turbulent variation


    1 at height 1
    2 at height 2


    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


    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



    flow in the most narrow part of a channel or mountain pass

    E latent heat




    earth of the earth
    eff effective
    eq equilibrium
    final final state



    bare ground



    first guess

    H of heat


    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



    at midpoint of column

    initial value

    ML mixed layer
    mtn of a mountain


    mean background value or reference state


    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



    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




    turb turbulent or turbulence
    u u component of wind


    v component of wind


    W white or light daisies
    w vertical component of wind
    water of water
    X of parcel X


    variable in the x direction

    component toward the east


    variable in the y direction

    component toward the north


    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


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