Moisture in the Atmosphere and Its Impact on Weather
EART30351
Lecture 3
Moisture in the atmosphere
•
Mass mixing ratio w, gkg
-1
•
Volume mixing ratio x, ppmv
w =
ε
x where
ε
= 18/29 = 0.622
•
Vapour pressure, mb.
e = n
w
kT
(n
w
= no. water molecules m
-3
)
•
Dew Point T
D
, K. Temperature at
which a parcel of air cooled at
constant pressure reaches
saturation. e = e
s
(T
D
)
Moisture in the atmosphere
•
Mass mixing ratio w, gkg
-1
•
Volume mixing ratio x, ppmv
w =
ε
x where
ε
= 18/29 = 0.622
•
Vapour pressure, mb.
e = n
w
kT
(n
w
= no. water molecules m
-3
)
•
Dew Point T
D
, K. Temperature at
which a parcel of air cooled at
constant pressure reaches
saturation. e = e
s
(T
D
)
•
Wet bulb temperature, T
w
, K.
Temperature reached at
saturation when water vapour is
evaporated into an air parcel,
with no extra heat added.
•
Relative humidity, %
RH = 100 e/e
s
(T)
All these quantities are used in
atmospheric physics!
Saturated Vapour pressure, e
s
Solution of Clausius-Clapeyron equation
Supercooled water
Water can exist in liquid form in
clouds down to -37°C. Liquid
drops below 0°C 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
Thermodynamic equation:
dU = c
v
dT = -Ldw – pdV becomes:
c
p
dT = -Ldw +
α
dp
Condensation,
Δ
w < 0
Heat released,
Δ
Q >0
E
x
a
m
p
l
e
:
c
a
l
c
u
l
a
t
i
o
n
o
f
w
e
t
b
u
l
b
t
e
m
p
e
r
a
t
u
r
e
.
Suppose we start with air at 1000 mb, 20°C with 50% relative humidity.
From the graph opposite, e
s
at 20°C is 23.2 mb. Therefore e for the parcel
is 11.6 mb (50% of e
s
).
As water evaporates, the air cools due to the latent heat of evaporation
which is LΔw J kg
-1
:
c
p
ΔT = -LΔw = -LεΔx = -LεΔe/p
Here w is the mass mixing ratio, x the volume mixing ratio, ε=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)
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.
Saturated adiabatic lapse rate
Can calculate a pseudo-adiabatic
lapse rate from the
thermodynamic equation (see
handout), if we assume water
droplets have no specific heat
capacity.
Formula is very cumbersome so to
solve it we use graphical methods:
the
tephigram
T
z
DALR = 10 K km
-1
Saturated
Adiabatic Lapse
Rate, SALR
Δ
T due to L
Explore the dynamics of moisture in the atmosphere, including concepts like mass mixing ratio, volume mixing ratio, dew point, wet bulb temperature, and saturated vapor pressure. Learn about the Clausius-Clapeyron equation, supercooled water phenomena, and the effects of latent heating on atmospheric thermodynamics. Gain insights into how these factors influence weather patterns and atmospheric behavior.
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Presentation Transcript
EART30351 Lecture 3
Moisture in the atmosphere Mass mixing ratio w, gkg-1 Volume mixing ratio x, ppmv w = x where = 18/29 = 0.622 Vapour pressure, mb. e = nwkT (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, ppmv w = x where = 18/29 = 0.622 Vapour pressure, mb. e = nwkT (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, = vas the liquid is so much more condensed. ??=? ? ?? Clausius-Clapeyron Equation: ??? ??= ? Where L is the latent heat for that phase change and the change in specific volume since water vapour behaves like an ideal gas with gas constant r = 8310/18 = 462 J kg-1K-1 ??? ??= ? ?= ? ? ??? ? ?2 So
Solution of Clausius-Clapeyron equation Saturation vapour pressure for water and ice Water vapour latent heat: L = 2.5x106-2.5x103(T T0) J kg-1varies slowly with temperature. So CC equation can be approximately integrated: Saturated vapour pressure, mb 15 Ice Water 10 ? ? 1 ?0 1 ??? ~???0??? ? 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 5 -40 -30 -20 -10 0 10 Temperature
Supercooled water Water can exist in liquid form in clouds down to -37 C. Liquid drops below 0 C 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. Saturation vapour pressure for water and ice Saturated vapour pressure, mb 10 Ice Water 1 -40 -30 -20 -10 0 10 Temperature
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 + dp
Example: calculation Example: calculation of wet bulb temperature. of wet bulb temperature. Calculation of wet bulb temperature Suppose we start with air at 1000 mb, 20 C with 50% relative humidity. From the graph opposite, es at 20 C is 23.2 mb. Therefore e for the parcel is 11.6 mb (50% of es). Saturation vapour pressure of water 30 As water evaporates, the air cools due to the latent heat of evaporation which is L w J kg-1: Saturation reached at 13.7 C, 15.7 mb when the two lines meet Vapour pressure, mb cp T = -L w = -L x = -L e/p Here w is the mass mixing ratio, x the volume mixing ratio, =18/29 = 0.62, and x=e/p by definition 20 As water evaporates, e increases and T decreases This gives a linear relation between e and T: e = 11.6 0.64(T-20) with e in mb (1 mb = 100 Pa) and T in C Initial e and T 10 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 dew point, TD = 9.3 5 10 15 20 25 Temperature, degC
Saturated adiabatic lapse rate Can calculate a pseudo-adiabatic lapse rate from the thermodynamic equation (see handout), if we assume water droplets have no specific heat capacity. Saturated Adiabatic Lapse Rate, SALR T due to L z DALR = 10 K km-1 Formula is very cumbersome so to solve it we use graphical methods: the tephigram T
