EART30351 - University of Manchester

EART30351 Lecture 3 Moisture in the atmosphere Mass mixing ratio w, gkg-1 Volume mixing ratio x, ppmvw = x x where x = 18/29 = 0.622 Vapour pressure, mb. e = nw kT (nw = no. water molecules m-3) Dew Point TD, K. Temperature at which a parcel of air cooled at constant pressure reaches saturation. e = es(TD) Moisture in the atmosphere Mass mixing ratio w, gkg-1 Volume mixing ratio x, ppmvw = x x where x = 18/29 = 0.622 Vapour pressure, mb. e = nw kT (nw = no. water molecules m-3) Dew Point TD, K. Temperature at which a parcel of air cooled at constant pressure reaches

saturation. e = es(TD) Wet bulb temperature, Tw, K. Temperature reached at saturation when water vapour is evaporated into an air parcel, with no extra heat added. Relative humidity, % RH = 100 e/es(T) All these quantities are used in atmospheric physics! Saturated Vapour pressure, es Vapour pressure in thermo-dynamic equilibrium with the bulk liquid. It is a function only of temperature. For phase change from liquid to vapour, = v as the liquid is so much more condensed. Clausius-Clapeyron Equation:

since water vapour behaves like an ideal gas with gas constant r = 8310/18 = 462 J kg-1 K-1 So Where L is the latent heat for that phase change and the change in specific volume Solution of Clausius-Clapeyron equation Saturation vapour pressure for water and ice L = 2.5x106 -2.5x103 (T T0) J kg-1 varies slowly with temperature. So CC equation can be approximately integrated: where T0 = 273.15 K More accurate expressions take account of L(T). For ice sublimation, L(273.15 K) = 2.83 J kg-1 Saturated vapour pressure, mb

Water vapour latent heat: 15 Ice Water 10 5 -40 -30 -20 -10 Temperature 0 10

Supercooled water Saturated vapour pressure, mb Saturation vapour pressure for water and ice 10 Ice Water 1 -40 -30 -20 -10 Temperature 0

10 Water can exist in liquid form in clouds down to -37C. Liquid drops below 0C are supercooled: ice particles will grow at the expense of the liquid drops if nucleated. This is the Bergeron-Findeisen mechanism for generating snow and then raindrops. Effect of latent heating Latent heat of evaporation of water (or sublimation of ice) is very large and dominates atmospheric thermodynamics. Ascending air cools more slowly when it saturates, and so remains more buoyant Evaporating precipitation cools the air and causes downdraughts

Effect of latent heating Latent heat of evaporation of water (or sublimation of ice) is very large and dominates atmospheric thermodynamics. Ascending air cools more slowly when it saturates, and so remains more buoyant Evaporating precipitation cools the air and causes downdraughts Change of phase adds or subtracts heat to a parcel of air: dQ = -Ldw where w = mass mixing ratio of vapour Condensation, w < 0 Heat released, Q >0 Thermodynamic equation: dU = cvdT = -Ldw pdV becomes: cpdT = -Ldw +dpdpdp Example: calculation of wet bulb

temperature. Calculation of wet bulb temperature Suppose we start with air at 1000 mb, 20C with 50% relative humidity. Saturation vapour pressure of water From the graph opposite, es at 20C is 23.2 mb. Therefore e for the 30 As water evaporates, the air cools due to the latent heat of evaporation which is Lw J kg-1: cpT = -Lw = -Lx x = -Lx e/p Here w is the mass mixing ratio, x the volume mixing ratio, x =18/29 = 0.62, and x=e/p by definition This gives a linear relation between e and T: e = 11.6 0.64(T-20) Vapour pressure, mb parcel is 11.6 mb (50% of es). Saturation reached at 13.7C, 15.7 mb when the two lines meet

20 As water evaporates, e increases and T decreases with e in mb (1 mb = 100 Pa) and T in C The wet bulb temperature is that when the air becomes saturated and can cool no longer. The SVP curve was calculated using the Magnus equation. Initial e and T 10 Initial dew point, TD = 9.3 5 10 15 Temperature, degC 20 25

Saturated adiabatic lapse rate Saturated Adiabatic Lapse Rate, SALR T due to L z Can calculate a pseudo-adiabatic lapse rate from the thermodynamic equation (see handout), if we assume water droplets have no specific heat capacity. DALR = 10 K km-1 Formula is very cumbersome so to solve it we use graphical methods: the tephigram T