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  • Elementos de Hidrologa SuperficialIng. Boris Ochoa Tocachi, MSc, DIC

    [email protected]

    Fotografa: Boris Ochoa Tocachi, diciembre 2011.

    Concepto, formacin y tipos de precipitacinII. Precipitacin

  • Circulacin atmosfrica

    Radiacin solar en funcin de la latitud.

    Radiacin solar

    Clleri et al, 2012; Buytaert, 2014

  • Radiacin solar media en la superficie horizontal a nivel del suelo [W m-2]. Los mximos estn en los desiertos (80% de rad. incid.).

    Radiacin solar

    Buytaert, 2014

    Circulacin atmosfrica

  • Radiacin solar

    Buytaert, 2014

    Zonas de excedentes y dficits permanentes de energa se mantienen en equilibrio por una transferencia hacia los polos.

    La radiacin recibida durante el da excede a la de salida,

    subiendo la temperatura. Lo contrario sucede en la noche.

    Circulacin atmosfrica

  • Los gases en la atmsfera obedecen las leyes simples de los gases en respuesta a los cambios de presin y temperatura.

    Ley de Boyle.

    Ley de Charles.

    Ley general de los gases.

    Leyes de los gases

    Buytaert, 2014

    Circulacin atmosfrica

  • La causa principal del movimiento del aire es el desarrollo de un gradiente de presin horizontal por diferencias espaciales en el calentamiento de la superficie y consecuentes cambios en la densidad y presin del aire.

    Estos gradientes de presin horizontales sirven como la fuerza motivadora que causa que el aire se mueva de zonas de alta presin hacia aquellas de baja presin.

    La fuerza de gradiente de presin por unidad de masa es:

    La fuerza del gradiente de presin

    Buytaert, 2014

    Circulacin atmosfrica

  • La fuerza de Coriolis es una fuerza deflectiva que se produce en una masa que se mueve hacia fuera del centro de un disco o esfera. Hay una deflexin aparente hacia la derecha de la lnea de movimiento en el hemisferio norte y hacia la izquierda en el sur.

    La fuerza deflectiva de rotacin de la Tierra

    Buytaert, 2014

    Circulacin atmosfrica

  • Aceleracin centrpeta

    Para un cuerpo siguiendo un movimiento curvo hay una aceleracin hacia el centro de rotacin.

    Se considera esta fuerza solamente en la rotacin del aire alrededor de un eje local de alta o baja presin.

    Fuerzas de friccin

    Ocurren debido a la irregularidad de la superficie de la Tierra. Son solamente importantes en altitudes bajas (bajo 500 1000 m),

    conocidas como capa lmite planetaria. La fuerza de friccin es opuesta a la velocidad del viento.

    Otras fuerzas

    Buytaert, 2014

    Circulacin atmosfrica

  • La circulacin global

    Mora, 2014

    https://www.youtube.com/watch?v=DHrapzHPCSA

    PolarSubtropical o FerrelTropical o Hadley

    ITCZInter-TropicalConvergenceZone

    Circulacin atmosfrica

  • Chow, 1994

    Circulacin atmosfricaCiclo de vida de un cicln

  • Vapor de agua

    La atmsfera contiene agua en las tres fases bsicas:vapor (gaseoso), gotas de agua (lquido), y hielo (slido).

    En una superficie de agua libre se da un intercambio constante:

    Almacenamiento y movimiento del agua

    Butler, 2014

    Vapor de agua

    Agua lquida

    Vaporizacin: molculas con alta energa escapan de la superficie y se convierten en vapor

    Condensacin: molculas de vapor colisionan con la superficie del agua y

    son absorbidas.

    Funcin de la temperatura de la superficie. Funcin de la presin de vapor.

  • El agua en la atmsfera

    Butler, 2014

    En un sistema cerrado, mientras las molculas abandonan la superficie del agua, la concentracin de vapor (y la presin) se incrementa hasta alcanzar el equilibrio.

    En un sistema abierto, el vapor puede difuminarse, y la

    evaporacin est dada por la diferenca entre las tasas de

    escape y reingreso de agua a la superficie.

    = >es En un sistema cerrado en

    equilibrio, el aire est a presin de vapor de saturacin (es).

    Vapor de agua

  • 5-40 -20 0 20 400

    20

    40

    60

    80

    e s [ m

    b ar ]

    T [oC]

    Water vapour pressureWater vapour in the atmosphere must obey the gas laws:

    MRTp U where p , U and T are the gas pressure, density and temperature, R is the gas constant (8.31 J mol-1 K-1),

    and M is the molecular weight.

    =

    Thus, for a concentration of water vapour, C, [g m-3], the vapour pressure, e, is :

    MRTCe

    In a closed system at equilibrium, the air is at saturation vapour pressure, es

    The saturated vapour pressure (es) is the upper limit on the density of water vapour in the air, and varies with temperature. Cs is the saturated water vapour concentration.

    es

    Attempts to introduce more vapour when the air is at es produce condensation of an equivalent amount of vapour.

    Similarly, if the temperature of some unsaturated air is reduced, at some point ereaches es. This is the dew point temperature, Td, the temperature to which air must be cooled to produce saturation (and below which condensation occurs).

    El vapor de agua v.a. en la atmsfera obedece la ley de los gases:

    Para una concentracin C de vapor de agua, la presin de vapor e:

    La presin de vapor de saturacin (es) es el lmite superior de la densidad de vapor de agua en el aire, y vara con la temperatura. Cs es la concentracin de vapor de agua saturada.

    Presin de vapor de agua

    Chow, 1994; Butler, 2014

    5

    -40 -20 0 20 400

    20

    40

    60

    80

    e s [ m

    b ar ]

    T [oC]

    Water vapour pressureWater vapour in the atmosphere must obey the gas laws:

    MRTp U where p , U and T are the gas pressure, density and temperature, R is the gas constant (8.31 J mol-1 K-1),

    and M is the molecular weight.

    =

    Thus, for a concentration of water vapour, C, [g m-3], the vapour pressure, e, is :

    MRTCe

    In a closed system at equilibrium, the air is at saturation vapour pressure, es

    The saturated vapour pressure (es) is the upper limit on the density of water vapour in the air, and varies with temperature. Cs is the saturated water vapour concentration.

    es

    Attempts to introduce more vapour when the air is at es produce condensation of an equivalent amount of vapour.

    Similarly, if the temperature of some unsaturated air is reduced, at some point ereaches es. This is the dew point temperature, Td, the temperature to which air must be cooled to produce saturation (and below which condensation occurs).

    5

    -40 -20 0 20 400

    20

    40

    60

    80

    e s [ m

    b ar ]

    T [oC]

    Water vapour pressureWater vapour in the atmosphere must obey the gas laws:

    MRTp U where p , U and T are the gas pressure, density and temperature, R is the gas constant (8.31 J mol-1 K-1),

    and M is the molecular weight.

    =

    Thus, for a concentration of water vapour, C, [g m-3], the vapour pressure, e, is :

    MRTCe

    In a closed system at equilibrium, the air is at saturation vapour pressure, es

    The saturated vapour pressure (es) is the upper limit on the density of water vapour in the air, and varies with temperature. Cs is the saturated water vapour concentration.

    es

    Attempts to introduce more vapour when the air is at es produce condensation of an equivalent amount of vapour.

    Similarly, if the temperature of some unsaturated air is reduced, at some point ereaches es. This is the dew point temperature, Td, the temperature to which air must be cooled to produce saturation (and below which condensation occurs).

    donde p, , y T son la presin, densidad y temperatura,R es la constante de los gases (8.31 J mol-1 K-1), yM es el peso molecular.

    donde v es la densidad de v.a., Rv es la constante de gas para v.a., p es la presin total del aire hmedo, p-e es la presin parcial debida al aire seco, d es la densidad del aire seco, Rd es la constante de gas para aire seco [287 J kg-1 K-1], a es la densidad del aire hmedo

    Vapor de agua

  • Una ecuacin aproximada es:

    , donde es [Pa = N m-2], T [C].Diferenciando:

    Al intentar de introducir ms vapor cuando el aire est en es produce condensacin de la cantidad de vapor equivalente.

    Si la temperatura de un aire no saturado se reduce, en algn momento e alcanza es. Este es el punto de roco, Td, la temperatura a la cual el aire debe ser enfriado para producir saturacin (y debajo de esto ocurre la condensacin).

    Presin de vapor de agua

    Raudkivi, 1979; Chow, 1994; Butler, 2014

    Vapor de agua

  • 6HumidityIt is convenient to measure the moisture content of the air using the current state relative to the saturation state at the same temperature, i.e.

    100uTe

    es

    Relative humidity:

    eTes Saturation deficit:

    [%]

    mbar

    100uTC

    CsOr

    CTCs

    [%]

    g.m-3

    In terms of vapour pressure In terms of concentration

    where e and C can be termed the absolute humidity, and es and Cs the saturation humidity.

    A useful relationship between e and C:

    An air-water vapour mixture has a total pressure, p, and partial pressures e (water vapour) and (p-e) (air). From the gas laws:

    aa M

    RTep U w

    RTe CM

    wa

    a

    MeCp e M

    U and:

    ( ) a wa

    M MRT p e eCU

    hence:

    let:18 0.6229

    w

    a

    MM

    H

    and assuming ep !!

    therefore:

    peC aHU

    31.2 kg m at STP & 20 C

    aU q

    6

    HumidityIt is convenient to measure the moisture content of the air using the current state relative to the saturation state at the same temperature, i.e.

    100uTe

    es

    Relative humidity:

    eTes Saturation deficit:

    [%]

    mbar

    100uTC

    CsOr

    CTCs

    [%]

    g.m-3

    In terms of vapour pressure In terms of concentration

    where e and C can be termed the absolute humidity, and es and Cs the saturation humidity.

    A useful relationship between e and C:

    An air-water vapour mixture has a total pressure, p, and partial pressures e (water vapour) and (p-e) (air). From the gas laws:

    aa M

    RTep U w

    RTe CM

    wa

    a

    MeCp e M

    U and:

    ( ) a wa

    M MRT p e eCU

    hence:

    let:18 0.6229

    w

    a

    MM

    H

    and assuming ep !!

    therefore:

    peC aHU

    31.2 kg m at STP & 20 C

    aU q

    Es conveniente medir el contenido de humedad del aire al estado actual relativo (rh) al estado de saturacin a la misma temperatura.

    Humedad relativa:

    Dficit de saturacin:Una relacin til entre e y C:

    Humedad

    En trminos de la concentracinEn trminos de la presin de vapor

    Una mezcla de v.a.-aire tiene una presin total p y presiones parciales e (v.a.) y p-e (aire).

    entonces:

    y:

    si:

    y asumiendo

    entonces:

    6

    HumidityIt is convenient to measure the moisture content of the air using the current state relative to the saturation state at the same temperature, i.e.

    100uTe

    es

    Relative humidity:

    eTes Saturation deficit:

    [%]

    mbar

    100uTC

    CsOr

    CTCs

    [%]

    g.m-3

    In terms of vapour pressure In terms of concentration

    where e and C can be termed the absolute humidity, and es and Cs the saturation humidity.

    A useful relationship between e and C:

    An air-water vapour mixture has a total pressure, p, and partial pressures e (water vapour) and (p-e) (air). From the gas laws:

    aa M

    RTep U w

    RTe CM

    wa

    a

    MeCp e M

    U and:

    ( ) a wa

    M MRT p e eCU

    hence:

    let:18 0.6229

    w

    a

    MM

    H

    and assuming ep !!

    therefore:

    peC aHU

    31.2 kg m at STP & 20 C

    aU q

    6

    HumidityIt is convenient to measure the moisture content of the air using the current state relative to the saturation state at the same temperature, i.e.

    100uTe

    es

    Relative humidity:

    eTes Saturation deficit:

    [%]

    mbar

    100uTC

    CsOr

    CTCs

    [%]

    g.m-3

    In terms of vapour pressure In terms of concentration

    where e and C can be termed the absolute humidity, and es and Cs the saturation humidity.

    A useful relationship between e and C:

    An air-water vapour mixture has a total pressure, p, and partial pressures e (water vapour) and (p-e) (air). From the gas laws:

    aa M

    RTep U w

    RTe CM

    wa

    a

    MeCp e M

    U and:

    ( ) a wa

    M MRT p e eCU

    hence:

    let:18 0.6229

    w

    a

    MM

    H

    and assuming ep !!

    therefore:

    peC aHU

    31.2 kg m at STP & 20 C

    aU q

    6

    HumidityIt is convenient to measure the moisture content of the air using the current state relative to the saturation state at the same temperature, i.e.

    100uTe

    es

    Relative humidity:

    eTes Saturation deficit:

    [%]

    mbar

    100uTC

    CsOr

    CTCs

    [%]

    g.m-3

    In terms of vapour pressure In terms of concentration

    where e and C can be termed the absolute humidity, and es and Cs the saturation humidity.

    A useful relationship between e and C:

    An air-water vapour mixture has a total pressure, p, and partial pressures e (water vapour) and (p-e) (air). From the gas laws:

    aa M

    RTep U w

    RTe CM

    wa

    a

    MeCp e M

    U and:

    ( ) a wa

    M MRT p e eCU

    hence:

    let:18 0.6229

    w

    a

    MM

    H

    and assuming ep !!

    therefore:

    peC aHU

    31.2 kg m at STP & 20 C

    aU q

    6

    HumidityIt is convenient to measure the moisture content of the air using the current state relative to the saturation state at the same temperature, i.e.

    100uTe

    es

    Relative humidity:

    eTes Saturation deficit:

    [%]

    mbar

    100uTC

    CsOr

    CTCs

    [%]

    g.m-3

    In terms of vapour pressure In terms of concentration

    where e and C can be termed the absolute humidity, and es and Cs the saturation humidity.

    A useful relationship between e and C:

    An air-water vapour mixture has a total pressure, p, and partial pressures e (water vapour) and (p-e) (air). From the gas laws:

    aa M

    RTep U w

    RTe CM

    wa

    a

    MeCp e M

    U and:

    ( ) a wa

    M MRT p e eCU

    hence:

    let:18 0.6229

    w

    a

    MM

    H

    and assuming ep !!

    therefore:

    peC aHU

    31.2 kg m at STP & 20 C

    aU q

    6

    HumidityIt is convenient to measure the moisture content of the air using the current state relative to the saturation state at the same temperature, i.e.

    100uTe

    es

    Relative humidity:

    eTes Saturation deficit:

    [%]

    mbar

    100uTC

    CsOr

    CTCs

    [%]

    g.m-3

    In terms of vapour pressure In terms of concentration

    where e and C can be termed the absolute humidity, and es and Cs the saturation humidity.

    A useful relationship between e and C:

    An air-water vapour mixture has a total pressure, p, and partial pressures e (water vapour) and (p-e) (air). From the gas laws:

    aa M

    RTep U w

    RTe CM

    wa

    a

    MeCp e M

    U and:

    ( ) a wa

    M MRT p e eCU

    hence:

    let:18 0.6229

    w

    a

    MM

    H

    and assuming ep !!

    therefore:

    peC aHU

    31.2 kg m at STP & 20 C

    aU q

    Butler, 2014

    Vapor de agua

  • Humedad absoluta (v):masa de v.a. por unidad de volumen de aire [g m-3].

    Humedad especfica (qv):masa de v.a. por unidad de masa de aire hmedo [g kg-1].

    Radio de mezcla de humedad (x):masa de v.a. por unidad de masa de aire seco [g kg-1]

    Humedad

    Chow, 1994; Buytaert 2014

    Ra es la constante de gas para aire hmedo.

    Vapor de agua

  • La cantidad de (calor) energa que se requiere para convertir lquido a gas es conocida como el calor latente de vaporizacin, , con unidades de energa por unidad de masa [J kg-1].

    Esta energa se utiliza para incrementar la separacin de las molculas de agua, en contra de las fuerzas de atraccin.

    Para el agua, Calor especfico: 4.19 x 103 J kg-1 K-1 Calor latente de fusin: 0.334x106 J kg-1 (79,7kcal/kg) a 0C; Calor latente de vaporizacin: 2.257 x106J kg-1 (538,7kcal/kg) a 100C

    A 10 C:, cayendo 0.1% por 1C de incremento en T.

    Calor latente de vaporizacin

    Buytaert, 2014; Butler, 2014

    7

    Latent heat of vaporizationThe amount of (heat) energy that is required to convert a liquid to a gas is known as the latent heat of vaporization, O, with units of energy per unit mass, [J/kg].

    This energy is used to increase the separation of water molecules, against the forces of attraction.

    For water, O = 2.47x106 J/kg at 10C, falling by 0.1% per 1C increase in T.Exercise: Ignoring vapour pressure effects, determine the heat flux [W.m-2=1J.m-2.s-1] required to sustain an evaporation rate of 0.5 mm/d from a pond at a constant temperature of 10C (density of water is 1000 kg.m-3)

    Also note: In evaporation calculations, we commonly meet the term OE, which represents the evaporative heat flux [W.m-2]. It is important to note that the E in this expression is the evaporation rate, expressed as a mass flow rate per unit area [kg.s-1.m-2], whereas the unit of evaporation typically required by the hydrologist is in units of [mm/d], that is, a volumetric flow per unit area. The conversion between these quantities is trivial ~ but dont forget about it!

    Note the distinction between heat energy [J], and heat flux [W.m-2 = J.s-1m-2].

    Vapor de agua

  • La humedad puede ser medida usando termmetros de bulbo hmedo y seco.

    Para mover un volumen V de aire de (a) a (b), se pierde calor del aire a travs del calor latente (evaporacin).

    8

    Measuring humidityHumidity can be measured using wet and dry bulb thermometers.

    water tankwickmuslin bag

    dry bulb thermometer, Ta

    wet bulb thermometer.Tb

    To move a volume V of air from point (a) to (b), heat is lost from the air through latent heat.

    0 5 10 15 205

    10

    15

    20

    25

    e s [ m

    b ar ]

    T [oC]

    (a)

    (b)

    TCm pa 'Heat lost [J]:

    wmO'Latent heat [J]: VCTCTTVC bsbapa ))(()( OUTherefore:

    Including the relationship derived on slide 6:

    )()( eTep

    TTC bsabapa HOUU

    Hence:)( ba

    pbs TT

    pCTee OH

    )( babs TTTee Jor:Where J [mbar.C-1] is the Psychrometric constant, which can be tabulated as a function of p (or elevation).Hence, wet and dry bulb temperatures are used to find eand hence the humidity.

    Specific heat capacity [J.kg-1.C-1]

    (i.e. evaporation)

    Medicin de la humedad

    Butler, 2014

    8

    Measuring humidityHumidity can be measured using wet and dry bulb thermometers.

    water tankwickmuslin bag

    dry bulb thermometer, Ta

    wet bulb thermometer.Tb

    To move a volume V of air from point (a) to (b), heat is lost from the air through latent heat.

    0 5 10 15 205

    10

    15

    20

    25

    e s [ m

    b ar ]

    T [oC]

    (a)

    (b)

    TCm pa 'Heat lost [J]:

    wmO'Latent heat [J]: VCTCTTVC bsbapa ))(()( OUTherefore:

    Including the relationship derived on slide 6:

    )()( eTep

    TTC bsabapa HOUU

    Hence:)( ba

    pbs TT

    pCTee OH

    )( babs TTTee Jor:Where J [mbar.C-1] is the Psychrometric constant, which can be tabulated as a function of p (or elevation).Hence, wet and dry bulb temperatures are used to find eand hence the humidity.

    Specific heat capacity [J.kg-1.C-1]

    (i.e. evaporation)

    Termmetro de bulbo seco, Ta

    Termmetro de bulbo hmedo, Tb

    Bolsa con muselinaCordnTanque con agua

    Vapor de agua

  • Calor perdido [J]:

    Calor latente [J]:

    Entonces:

    Incluyendo la relacin derivada anteriormente:

    Entonces:

    O:

    , donde [mbar C-1] es la constante Psicomtrica, que puede ser relacionada como una funcin de p (o de la elevacin).Entonces con los termmetros de bulbo seco y hmedo, se encuentra e y la humedad.

    Medicin de la humedad

    Butler, 2014

    8

    Measuring humidityHumidity can be measured using wet and dry bulb thermometers.

    water tankwickmuslin bag

    dry bulb thermometer, Ta

    wet bulb thermometer.Tb

    To move a volume V of air from point (a) to (b), heat is lost from the air through latent heat.

    0 5 10 15 205

    10

    15

    20

    25

    e s [ m

    b ar ]

    T [oC]

    (a)

    (b)

    TCm pa 'Heat lost [J]:

    wmO'Latent heat [J]: VCTCTTVC bsbapa ))(()( OUTherefore:

    Including the relationship derived on slide 6:

    )()( eTep

    TTC bsabapa HOUU

    Hence:)( ba

    pbs TT

    pCTee OH

    )( babs TTTee Jor:Where J [mbar.C-1] is the Psychrometric constant, which can be tabulated as a function of p (or elevation).Hence, wet and dry bulb temperatures are used to find eand hence the humidity.

    Specific heat capacity [J.kg-1.C-1]

    (i.e. evaporation)

    8

    Measuring humidityHumidity can be measured using wet and dry bulb thermometers.

    water tankwickmuslin bag

    dry bulb thermometer, Ta

    wet bulb thermometer.Tb

    To move a volume V of air from point (a) to (b), heat is lost from the air through latent heat.

    0 5 10 15 205

    10

    15

    20

    25

    e s [ m

    b ar ]

    T [oC]

    (a)

    (b)

    TCm pa 'Heat lost [J]:

    wmO'Latent heat [J]: VCTCTTVC bsbapa ))(()( OUTherefore:

    Including the relationship derived on slide 6:

    )()( eTep

    TTC bsabapa HOUU

    Hence:)( ba

    pbs TT

    pCTee OH

    )( babs TTTee Jor:Where J [mbar.C-1] is the Psychrometric constant, which can be tabulated as a function of p (or elevation).Hence, wet and dry bulb temperatures are used to find eand hence the humidity.

    Specific heat capacity [J.kg-1.C-1]

    (i.e. evaporation)

    Calor especfico [J km-1 C-1]

    8

    Measuring humidityHumidity can be measured using wet and dry bulb thermometers.

    water tankwickmuslin bag

    dry bulb thermometer, Ta

    wet bulb thermometer.Tb

    To move a volume V of air from point (a) to (b), heat is lost from the air through latent heat.

    0 5 10 15 205

    10

    15

    20

    25

    e s [ m

    b ar ]

    T [oC]

    (a)

    (b)

    TCm pa 'Heat lost [J]:

    wmO'Latent heat [J]: VCTCTTVC bsbapa ))(()( OUTherefore:

    Including the relationship derived on slide 6:

    )()( eTep

    TTC bsabapa HOUU

    Hence:)( ba

    pbs TT

    pCTee OH

    )( babs TTTee Jor:Where J [mbar.C-1] is the Psychrometric constant, which can be tabulated as a function of p (or elevation).Hence, wet and dry bulb temperatures are used to find eand hence the humidity.

    Specific heat capacity [J.kg-1.C-1]

    (i.e. evaporation)

    8

    Measuring humidityHumidity can be measured using wet and dry bulb thermometers.

    water tankwickmuslin bag

    dry bulb thermometer, Ta

    wet bulb thermometer.Tb

    To move a volume V of air from point (a) to (b), heat is lost from the air through latent heat.

    0 5 10 15 205

    10

    15

    20

    25

    e s [ m

    b ar ]

    T [oC]

    (a)

    (b)

    TCm pa 'Heat lost [J]:

    wmO'Latent heat [J]: VCTCTTVC bsbapa ))(()( OUTherefore:

    Including the relationship derived on slide 6:

    )()( eTep

    TTC bsabapa HOUU

    Hence:)( ba

    pbs TT

    pCTee OH

    )( babs TTTee Jor:Where J [mbar.C-1] is the Psychrometric constant, which can be tabulated as a function of p (or elevation).Hence, wet and dry bulb temperatures are used to find eand hence the humidity.

    Specific heat capacity [J.kg-1.C-1]

    (i.e. evaporation)

    8

    Measuring humidityHumidity can be measured using wet and dry bulb thermometers.

    water tankwickmuslin bag

    dry bulb thermometer, Ta

    wet bulb thermometer.Tb

    To move a volume V of air from point (a) to (b), heat is lost from the air through latent heat.

    0 5 10 15 205

    10

    15

    20

    25

    e s [ m

    b ar ]

    T [oC]

    (a)

    (b)

    TCm pa 'Heat lost [J]:

    wmO'Latent heat [J]: VCTCTTVC bsbapa ))(()( OUTherefore:

    Including the relationship derived on slide 6:

    )()( eTep

    TTC bsabapa HOUU

    Hence:)( ba

    pbs TT

    pCTee OH

    )( babs TTTee Jor:Where J [mbar.C-1] is the Psychrometric constant, which can be tabulated as a function of p (or elevation).Hence, wet and dry bulb temperatures are used to find eand hence the humidity.

    Specific heat capacity [J.kg-1.C-1]

    (i.e. evaporation)

    8

    Measuring humidityHumidity can be measured using wet and dry bulb thermometers.

    water tankwickmuslin bag

    dry bulb thermometer, Ta

    wet bulb thermometer.Tb

    To move a volume V of air from point (a) to (b), heat is lost from the air through latent heat.

    0 5 10 15 205

    10

    15

    20

    25

    e s [ m

    b ar ]

    T [oC]

    (a)

    (b)

    TCm pa 'Heat lost [J]:

    wmO'Latent heat [J]: VCTCTTVC bsbapa ))(()( OUTherefore:

    Including the relationship derived on slide 6:

    )()( eTep

    TTC bsabapa HOUU

    Hence:)( ba

    pbs TT

    pCTee OH

    )( babs TTTee Jor:Where J [mbar.C-1] is the Psychrometric constant, which can be tabulated as a function of p (or elevation).Hence, wet and dry bulb temperatures are used to find eand hence the humidity.

    Specific heat capacity [J.kg-1.C-1]

    (i.e. evaporation)

    8

    Measuring humidityHumidity can be measured using wet and dry bulb thermometers.

    water tankwickmuslin bag

    dry bulb thermometer, Ta

    wet bulb thermometer.Tb

    To move a volume V of air from point (a) to (b), heat is lost from the air through latent heat.

    0 5 10 15 205

    10

    15

    20

    25

    e s [ m

    b ar ]

    T [oC]

    (a)

    (b)

    TCm pa 'Heat lost [J]:

    wmO'Latent heat [J]: VCTCTTVC bsbapa ))(()( OUTherefore:

    Including the relationship derived on slide 6:

    )()( eTep

    TTC bsabapa HOUU

    Hence:)( ba

    pbs TT

    pCTee OH

    )( babs TTTee Jor:Where J [mbar.C-1] is the Psychrometric constant, which can be tabulated as a function of p (or elevation).Hence, wet and dry bulb temperatures are used to find eand hence the humidity.

    Specific heat capacity [J.kg-1.C-1]

    (i.e. evaporation)

    Vapor de agua

  • MxMn

    Seco Hmedo

    Medicin de la humedad

    Butler, 2014; Weather station with Stephenson screen housing dry, wet, max & min thermometers (CEH Wallingford)

    Vapor de agua

  • 10

    Exercises1.Using the graph below, for each air-water vapour mixture given, identify the

    saturation vapour pressure, es, the dew point temperature, Td, and relative humidity

    0 2 4 6 8 10 12 14 16 18 206

    8

    10

    12

    14

    16

    18

    20

    22

    24

    e s [ m

    b ar ]

    T [oC]

    a) T = 16C, e = 14 mbar;

    b) T = 12C, e = 10 mbar;

    c) T = 4C, e = 8 mbar;

    2. Calculate the psychometric constant and use it to calculate the vapour pressure (in kPa & mbar) and humidity of the air, given wet and dry bulb temperatures of 12C and 18C respectively.

    Cp 1013 J.kg-1. C-1

    O 2.47x106 J.kg-1H 0.622 [-]p 101 kPa = 1010 mbar

    1. Usando el grfico siguiente, para cada combinacin dada de v.a.-aire, identifica la presin de vapor de saturacin es, la temperatura del punto de roco Td, y la humedad relativa rh.

    2. Calcular la constante

    Ejercicio en clase

    Butler, 2014

    a) T = 16 C, e = 14 mbar;b) T = 12 C, e = 10 mbar;c) T = 4C, e = 8 mbar;

    psicomtrica y usarla para calcular la presin de vapor e (en kPa & mbar), la humedad del aire especfica y relativa (qv y rh), y la densidad del aire (a), dado que las temperaturas de bu lbo hmedo y seco son 12C y 18C, respectivamente.

    10

    Exercises1.Using the graph below, for each air-water vapour mixture given, identify the

    saturation vapour pressure, es, the dew point temperature, Td, and relative humidity

    0 2 4 6 8 10 12 14 16 18 206

    8

    10

    12

    14

    16

    18

    20

    22

    24

    e s [ m

    b ar ]

    T [oC]

    a) T = 16C, e = 14 mbar;

    b) T = 12C, e = 10 mbar;

    c) T = 4C, e = 8 mbar;

    2. Calculate the psychometric constant and use it to calculate the vapour pressure (in kPa & mbar) and humidity of the air, given wet and dry bulb temperatures of 12C and 18C respectively.

    Cp 1013 J.kg-1. C-1

    O 2.47x106 J.kg-1H 0.622 [-]p 101 kPa = 1010 mbar

  • 10

    Exercises1.Using the graph below, for each air-water vapour mixture given, identify the

    saturation vapour pressure, es, the dew point temperature, Td, and relative humidity

    0 2 4 6 8 10 12 14 16 18 206

    8

    10

    12

    14

    16

    18

    20

    22

    24

    e s [ m

    b ar ]

    T [oC]

    a) T = 16C, e = 14 mbar;

    b) T = 12C, e = 10 mbar;

    c) T = 4C, e = 8 mbar;

    2. Calculate the psychometric constant and use it to calculate the vapour pressure (in kPa & mbar) and humidity of the air, given wet and dry bulb temperatures of 12C and 18C respectively.

    Cp 1013 J.kg-1. C-1

    O 2.47x106 J.kg-1H 0.622 [-]p 101 kPa = 1010 mbar

    1. Usando el grfico siguiente: identifica es, Td, y rh.a) Td = 12 C; es = 18 mbar; rh = e/es * 100 = 14/18 * 100 = 66.67 %b) Td = 7 C, es = 14 mbar; rh = 10/14 * 100 = 71.43 %c) Td = 4 C, es = 8 mbar; rh = 100 %

    2. Calcular la constante psicomtrica.

    Solucin: Ejercicio en clase

    Butler, 2014

    = pCp/ = (101*1013)/(2.47*106*0.622)

    [kPa][J kg-1 C-1][J kg-1] = 66.595*10-3 [kPa C-1]

    Calcular e, rh, y qv, a.e = es - (Ta - Tb)

    e = 1.4 - 66.595*10-3 (18 - 12) [kPa]e = 1.4 - 0.3996 [kPa]

    e = 1.00043 [kPa] = 10.0043 [mbar]r = e/es * 100 = 10/20.5 * 100 = 48.8 %

    qv = (e/p) = 0.622*(1/101)qv = 0.0062 [kg agua/kg aire hmedo]

    Ra = 287*(1+0.608*qv) = 288.07 [J kg-1 K-1]a = p/RaT = 101*103/(288*291) = 1.204 [kg m-3]

  • Ley del gas ideal (1) y ley de la presin hidrosttica (2):V.a. en una columna atmosfrica esttica

    Chow, 1994

    1

    3

    45

    2

    Vapor de agua

  • D.J. Jacob, Introduction to Atmospheric Chemistry Princeton University Press, 1999; Buytaert, 2014

    Vapor de agua en una columna atmosfricaVapor de agua

  • Agua precipitable

    Chow, 1994

    Cantidad de humedad contenida en una columna atmosfrica.

    Masa total de agua precipitable en la columna entre z1 y z2 es (1).

    Se calcula usando intervalos de altura z, dando masa incremental.

    Ver ejemplo 3.2.2 de Ven te Chow.

    1

    2

    Vapor de agua

  • PrecipitacinConcepto

    Chow, 1994; Clleri et al, 2012

    Precipitacin es la cantidad de agua que cae de la atmsfera sobre la superficie terrestre (hidrometeoro) a travs de varios procesos:

    Para la formacin de precipitacion se requiere la elevacin de una masa de agua en la atmsfera en forma de humedad, de tal manera que una parte se enfre, se condense y precipite. Elevacin frontal: aire caliente es elevado por un aire fro. Orogrfica: aire hmedo es elevado por una cadena montaosa. Convectiva: aire arrastrado hacia arriba por una accin convectiva (calor

    enfocado en un punto, centro de una celda de una tormenta elctrica).

    Precipitacin Condesancin (NO)Lluvia.Llovizna.Nieve.AguanieveGranizo.

    VirgaNeblinaRoco

  • PrecipitacinFormacin de la precipitacin

    Mora, 2014

  • Mora, 2014

    PrecipitacinFormacin de la precipitacin

  • Chow, 1994

    Formacin de precipitacin en las nubes El aire sube, se enfra,

    y se puede congelar.

    Ncleos de condensacin: Partculas de polvo. Iones. Partculas de sal. Compuestos de sulfuro y

    nitrgeno.

    Ciclo condensacin-cada-evaporacin-elevacin se repite en promedio 10 veces.

    Precipitacin

  • PrecipitacinFormacin de la precipitacin

    Chow, 1994

    Corrientes de viento de solo 0.5 cm/s son suficiente para arrastrar gotas de agua 10 micras.

    En las nubes puede existir gotas de agua lquida superfra por debajo del punto de congelamiento, hasta ~ -35C, que luego se congelan sin la presencia de ncleos de congelamiento.

    La presin de vapor de saturacin del v.a. es menor en hielo que en agua lquida.

    La siembra de nubes se realiza al nuclear artificialmente las nubes para inducir la precipitacin.

  • PrecipitacinVelocidad terminal

    Chow, 1994

    Tres fuerzas actan en una gota de lluvia que cae:

    Fg: peso (gravitacional);

    Fb: empuje (desplazamiento del aire);

    Fd: fuerza de arrastre (friccin con el aire circundante).

    Cd es un coeficiente de arrastre adimensional.

  • PrecipitacinVelocidad terminal

    Si la gota parte del reposo, se acelerar hasta que alcance su velocidad terminal Vt, las fuerzas se balancean:

    Haciendo V = Vt:

    Resolviendo para Vt:

    Chow, 1994

  • PrecipitacinVelocidad terminal

    Chow, 1994

    Ver ejemplo 3.3.1 de Ven te Chow.

    Velocidad terminal de gotas de lluvia a condiciones atmosfricas estndar al nivel del mar.

    La velocidad terminal aumenta con el tamao de gota hasta un nivel asinttico a 5 mm de ~9 m/s.

    En aire ms tenue (menor presin, mayor elevacin), Vt aumenta.

  • PrecipitacinModelos de celdas de tormentas elctricas

    Chow, 1994

    Regin de salida (flujo del aire mas fro y seco sale de la celda).

    Regin de elevacin (donde la humedad se condensa y se precipita).

    Regin de entrada de flujo (airea caliente es arrastrado a una celda).

    Circulacin de celda convectiva.

    3

    1

    2

  • PrecipitacinModelos de celdas de tormentas elctricas

    Chow, 1994

    La tormenta elctrica se analiza con la ecuacin de continuidad para vapor de agua:

    Si una precipitacin de intensidad i case sobre un rea A debajo de una celda de tormenta, y la derivada temporal es 0 en flujo permanente:

    La celda es un cilindro de dimetro D, en el cual el aire entra a travs de un incremento de altura z. Si la densidad del aire y humedad especfica son constantes en cada incremento:

  • PrecipitacinModelos de celdas de tormentas elctricas

    Chow, 1994

    En forma similar, puede escribirse una ecuacin de continuidad para el aire seco que mueve el vapor:

    Sustituyendo:

    Ver ejemplo 3.3.2 de Ven te Chow.

  • TareaLectura

    Captulo 3, Hidrologa aplicada, Ven Te Chow.

    Subcaptulos 3.1 a 3.3.

  • [email protected]

    Preguntas y discusin