Transcript lecture_7
Lecture 7
Water Vapor
Water Vapor amount in the air is variable.
Concentration of water vapor can be quantified by: Vapor pressure Mixing ratio Specific humidity Absolute humidity Relative humidity Dew point depression Wet-bulb temperature
Warmer air can hold more water vapor at equilibrium than colder air. Air that holds this equilibrium amount is saturated.
If air is cooled below the saturation temperature, some of the water vapor condenses into liquid, which releases latent heat and warms the air.
Thus, temperature and water vapor interact in a way that cannot be neglected.
Saturation Vapor Pressure Vapor pressure:
Air is a mixture of gases. All of the gases contribute to the total pressure. The pressure associated with any one gas in a mixture is called the
partial pressure
.
Water vapor is a gas, and its partial pressure in air is called the
vapor pressure
.
Symbol
e
is used for vapor pressure. Units are pressure units: kPa.
Saturation
Air can hole any proportion of water vapor. For humidities greater than a threshold called the saturation humidity, water vapor tends to condense into liquid faster than it re-evaporates. This condensation process lowers the humidity toward the equilibrium (saturation) value. The process is so fast that humidities rarely exceed the equilibrium value.
Saturation
Thus, while air can hold any portion of water vapor, the threshold is rarely exceeded by more than 1% in the real atmosphere.
Air that contains this threshold amount of water vapor is
saturated
.
Air that holds less than that amount is
unsaturated
.
Saturation
The equilibrium (saturation) value of vapor pressure over a flat surface of pure water is given the symbol:
e s
For unsaturated air,
e < e
s
Air can be slightly
supersaturated
(
e > e
s
). When there are no surfaces upon which water vapor can condense.
Saturation – Technical Definition
Water Vapor Sealed Container
Liquid Water
Flux of water molecules from liquid to vapor
Water Vapor Fluxes
Flux of water molecules from vapor to liquid
Saturation
Saturation exists when these two fluxes of water vapor are equal
Flux of water molecules from liquid to vapor Flux of water molecules from vapor to liquid
Saturation Vapor Pressure
Formula for e s (T) called the
Clausius-Clapeyron Equation
Approximation:
e s
e
0 exp
L R v
1
T
0 1
T
Where e 0
R v
= 0.611 kPa, T = 273 K, = 461 J K -1 Kg -1 is the gas constant for water vapor. Absolute temperature in Kelvins must be used for T.
Clausius-Clapeyron Equation
This equation describes the relationship between temperature and saturation vapor pressure.
Because clouds can consist of liquid droplets and ice crystals suspended in air, we must consider saturations with respect to water and ice.
Teten’s Formula
Is an empirical expression for saturation vapor pressure with respect to liquid water that includes the variation of latent heat with temperature.
e s
e
0 exp
b
T
(
T
T
2
T
1 ) B = 17.2694, T1 = 276.16 K, T2 = 35.86 K
Exercise
Calculate e s (T) for T = 0 C, 10 C, 20 C, 30 C, 40 C
Graph of Clausius-Clapeyron Equation
System of Dry Air + Water Vapor
Assume system is closed i.e., no exchange of mass with environment
Dry air + water vapor
Saturation, Sub-Saturation, Super-Saturation
Super-saturated air Saturated air Sub-saturated air
Super-Saturation and Condensation
Suppose air becomes super-saturated “Excess” water vapor will condense
Supersaturation
Supersaturation occurs when e > e s Supersaturation is a temporary state Water vapor condenses until state of supersaturation is relieved
Humidity Variables
Mixing Ratio
the ratio of mass of water vapor to mass of dry air is called the mixing ratio,
r
or
w
. It is given by:
w
m m d v
(W&H 3.57) If neither condensation or evaporation take place, w of a parcel remains constant. Therefore, it is a
conserved
quantity.
Units are g/g but is usually presented as g/kg, but when solving numerical problems, must be expressed as a dimensionless quantity: kg/kg or g/g.
Humidity Variables
Mixing Ratio
the ratio of mass of water vapor to mass of dry air is called the mixing ratio,
r
or
w
. It is given by:
r
w
P
e e
(Stull 5.3) Where
ε
=
r d /r v
= 0.622 g vapor/g dry air is the ratio of gas constants for dry air to that for water vapor.
r
is proportional to the ratio of partial pressure of water vapor (
e
) to partial pressure of the remaining gases in the air (
P-e
).
Humidity Variables
The
saturated mixing ratio,
is where e s
r s ,
is used in place of e. Units are g/g but is usually presented as g/kg: = grams of water vapor per kilogram of dry air.
Humidity Variables
Specific Humidity
The ratio of mass of water vapor to mass of total (moist+ dry) air,
q
, to a good approximation is given by:
q
m v m v
m d
w
1
w
e P
(Stull) (W&H)
Humidity Variables
Absolute Humidity
The concentration of water vapor in air is called the
absolute humidity
, and has units of grams of water vapor per cubic meter (g/ m 3 ).
Because absolute humidity is essentially a partial density, it can be found from the partial pressure using the ideal gas law for water vapor:
v
R v e
T
e P
d
Humidity Variables
Relative Humidity
The ratio of actual amount of water vapor in the air compared to the equilibrium (saturation) amount at that temperature is called the relative humidity.
RH
100 %
e e s
q q s
s
r r s
Cooling a Parcel -- Constant Pressure
Reminder
Recall
e p
n v n
where n v = number of moles of water vapor and n = total number of moles
e
n v n
p
i.e.,
e
is proportional to
p
.
Cool the system at constant pressure Closed system n v and n remain constant e remains constant
e
Start with Sub-Saturated Air
Cool air at constant pressure
e
Cool at Constant Pressure
e
Cool at Constant Pressure
e
Cool at Constant Pressure
e
Cool at Constant Pressure
e
Cool at Constant Pressure
e
Saturation Achieved
Continue to cool air
e
Super-Saturation!
Dew
Dew forms when super-saturation occurs near a surface, e.g., a blade of grass
DEW
Dew Point (T
d
)
Definition: The temperature at which saturation would first be achieved if the air were cooled at
constant pressure
e
Temperature and Dew Point So, T d is the temperature that satisfies e s (T d ) = e.
T d T
Note
If the T d < 0 occurs,
frost
C and super-saturation forms Water vapor turns directly to ice Note: Frost is not frozen dew!
Frost
Relative Humidity (RH)
RH
100
w w s
where
w
is the mixing ratio and
w s
the saturation mixing ratio is
Relative Humidity Approximation
RH
100
e e s
Simpler, as e s is a function of T only.
Exercise
Let T = 20.0
C and e = 12.0 hPa Calculate RH using the approximate form First, calculate e s (T)
e s
( 20
C
) 6 .
112
hPa
exp 17 .
67 20 .
0
C
20 .
0
C
243 .
5
C
23 .
4
hPa RH
100 12 .
0
hPa
23 .
4
hPa
100 0 .
51 51 %
Increased Accuracy
For greatest accuracy, use the exact form of RH and use tabulated values of w s Best source:
Smithsonian Meteorological Tables (SMT)
Supersaturation
When condensation is occurring on a surface, a thin layer of air next to the surface is supersaturated i.e., RH > 100% Technically, T d occurring > T where condensation is However, T d – T is quite small and cannot be measured by standard instruments So, for practical purposes, T d T
Adiabatic Cooling
(Adiabatic expansion due to falling pressure)
Again, e
n v n p
Closed system n v /n is constant But,
p
is decreasing Therefore,
e
is decreasing
RH of Expanding Parcel
Recall,
RH
100
e e s
e
is decreasing due to expansion But, parcel is cooling e s is also decreasing
It turns out that e s decreases faster than e
z
e and e
s
for a rising parcel
e decreases as parcel rises
e s
decreases faster than
e
e e s
z
e and e
s
for a sinking parcel
e s e
RH and Adiabatic Processes
RH of a
rising
parcel
increases
condensation can occur if parcel can be lifted sufficiently RH of a
sinking
parcel
decreases
condensation will not occur if air is sinking
Lifting Condensation Level (LCL)
Definition: Level at which saturation is first achieved if an air parcel is lifted adiabatically The LCL is usually an accurate indication of the height of the cloud base
z
LCL
LCL
e e s