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Meteorology and Climate: Module 2 (5 Jan 2016)
1
Lecture by Bert Holtslag
(Thanks to Gert-Jan Steeneveld)
Thermodynamics, part I
Hydrostatics and adiabatic processes
Water vapour in air and saturation processes
Thermodynamic diagrams
Climate
Radiation
2
Heat
Precipitation
Clouds
Boundary Layer
Models & Prediction
Atmospheric Dynamics
&
Rotations
Moisture
&
Stability
Precipitation and 2 m temperatures
this morning in NL (www.knmi.nl)
3
Weather Alarm
Code Red for
North – East:
Freezing rain
and slippery
road conditions
Surface Weather at Wageningen
(www.maq.wur.nl)
4
Surface Weather at Wageningen
www.maq.wur.nl
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Surface Weather at Wageningen
www.maq.wur.nl
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Weather symbols (see also Fig 8.1)
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Wind speeds traditionally given in knots (~ 0.5 m/s)
Wind direction traditionally given with respect to
the North, and named after the direction it is
coming from.
Surface Weather at Wageningen
www.maq.wur.nl
8
Surface Weather at Wageningen
www.maq.wur.nl
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Weather Map this morning 6 UTC
(www.knmi.nl)
10
Classic low pressure system
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Formation of an occlusion
(tilted warm air)
0C
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Today’s Weather Forecast
(www.knmi.nl)
14
Tomorow’s Weather Forecast
(www.knmi.nl)
15
Understanding the vertical structure:
Last night’s sounding (Norderney): Skew T
What is the meaning of all these lines?
(weather.uwyo.edu/upperair/sounding.html)
16
Basics: How is pressure decreasing with height?
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Downward force:
p+dp
Fdown  ( p  dp) A
p
Upward force
Fdown  ( p  dp) A
dz
Fup  pA
Weight Volume of gas:
mg  Vg  Agdz
F: Force (N)
A: Area (m2)
p : pressure = F/A (N/m2)
Balance:
dp  gdz  0
dp
  g
dz
Hydrostatic equilibrium
Note constant density is assumed
Typically 1 hPa for every 8 m (near the surface):
Useful to correct pressure observations towards sea level
Figure 3.1
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dp
  g
dz

 p( z )    g dz
z
Pressure at height z is equivalent to weight
of column of air above z per unit area
How are height and pressure related?
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Start with hydrostatic equilibrium
P    z g  
with
P
z g
Rd T
P   Rd T
Integration provides:
Hypsometric equation
P
1

z g
P
Rd T
Gas law
 P1 
Rd
z2  z1 
T ln  
g
 P2 
Hypsometric equation
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 P1 
Rd
z2  z1 
T ln  
g
 P2 
Scaling height for pressure:
 P1 
For given  
 P2 
H  8 km
this means for the ‘thickness’ of a layer:
z2  z1  T
Vertical cross sections (Fig 3.3)
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solid lines are constant pressure surfaces
(larger distance in warm and smaller distance in cold regions)
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Geopotential:
work (force x distance) needed to raise 1 kg of air from
surface to actual level against gravity per unit area
dp
dp
  g  
 gdz  d
dz

z
  ( z )   g dz
0
( z )
Z
g0
 P1 
Rd
Z 2  Z1 
Tv ln  
g0
 P2 
Globally averaged
acceleration due
to gravity at the
earth’s surface
g 0  9.81 m / s 2
Geopotential height
Geopotential Height Z
Z compensates for decrease of g with z
R0  Earth Radius
z  Actual height
Z  geopotential height
z
Z
1  z R0
Z  z  16 [m]
for z=10 km!
Thus very small effect in Troposhere!
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Example Thickness Map
For
given
 P1 
 
 P2 
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the thickness of a layer:
z2  z1  T
Source: www.ecmwf.int
How does the temperature of
an air parcel change with height?
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First law of thermodynamics for air parcel of mass m
Energy change = Temp. Change + Work
Q
P
 C p T 
m

 gz (insert hydrostatic equation)
g
Q
gives : T 
z 
Cp
mC p
Q
Due to condensation, radiation etc…
Q  0 for adiabatic process
T
g
then : 

 d  1K / 100m
z C p
Dry adiabatic
lapse rate
How to compare air parcels in an honest way?
Potential temperature Temperature that a parcel
28
2900 m
will have if it is moved (dry)
adiabatically to a reference level
(P0=1000 hPa or z=0)
 P0 
  T 
P
Rd / C p
Poisson’s equation
For dry adiabatic process the
potential temperature is constant!
Actual temperature decrease (increase)
for rising (sinking) parcel
due to air expansion (compression)
How to compare air parcels in an honest way?
Potential temperature Which parcel is really the warmest?
I
500 hPa
T= -23 ºC
II
1030 hPa
T= 23 ºC
 P0 
  T 
P
Rd / C p
Poisson’s equation
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How to compare air parcels in an honest way?
Potential temperature Who is really the warmest parcel?
I
500 hPa
T= -23 ºC
 P0 
  T 
P
Rd / C p
Poisson’s equation
 1000 
 I  (23  273)

 500 
II
1030 hPa
T= 23 ºC
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 1000 
 II  (23  273)

 1030 
 I   II  Stable
0.286
 305 K
0.286
 293.6 K
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Potential Temperature
structure of lower part
standard atmosphere
with turbulent
boundary layer below
(see Chapter 9 book)
With strong mixing the
potential temperature
becomes constant with
height (in daytime
boundary layer with
convection)
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Break
Relation between Pressure, Temperature and
Potential temperature (Fig 3.6)
 P0 
  T 
P
Rd / C p
Blue area
normally
used in
Meteorology
34
Snapshot of relation between Pressure,
Temperature and Potential temperature
on a skew T - ln p diagram (Fig 3.7)
Skew T diagram is introduced to enhance
difference between isotherms and adiabats
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Snapshot of relation between Pressure,
Temperature and Potential temperature
on a skew T - ln p diagram (Fig 3.7)
How to incorporate the effects of water vapour
saturation in this diagram?
36
Water on Planet Earth
37
Oceans
97.2%
Glaciers
2.0%
Ground water
0.6%
Lakes and
Rivers
Atmosphere
0.02%
0.001%
Boxes with air (un-) saturated of water vapour (Fig 3.8)
(dots represent water molecules)
Evaporation > Condensation
at plane water surface
Evaporation = Condensation
at plane water surface
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Saturation water vapor pressure es
over a flat surface of pure water
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Relation (1)
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Temp. – max. Vapor Pressure
In GENERAL, Clausius Clapeyron equation:
es  eo exp( (  ))
L
Rv
1
To
To = 273.13 K
eo = es(To) = 0.611 kPa
Rv = R*/Mv = 8300/18 = 461 J/kg/K
1
T
See book page 99
for derivation
Relation (2)
Temp. – max. Vapor Pressure
Vapor over Liquid Water:
L = Lv = 2.50 106 J/kg (Latent heat of vaporization)
L/Rv = 2.50 106/(8300/18) = 5423 K
Vapor over Ice:
L = Ld = (2.50+0.33) 106=2.83 106 J/kg
(Latent heat of vaporization and ice melting)
L/Rv = 6139 K
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Water Vapor versus Ice Vapor
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Fig 3.9
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Max at -12
Important for
cloud formation
Practical Relation
Temp. – max. Vapor Pressure
Tetens Formula (fitting relation)
b(T  T1 )
es  eo exp(
)
T  T2
T1 = 273.16 K
Accounts for Lv(T),
See also study guide
T2 = 35.86 K
eo = es(To) = 0.611 kPa; b = 17.2694
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Clausius Clapeyron vs. Tetens for liquid water
45
Paths to Saturation
46
Dew-point
Wet-bulb temperature
Humidity in air: Various Measures
1. Absolute Humidity
2. Specific Humidity
47
soundings
1. (T, Td )
3. Mixing Ratio
2. (T, Tw )
4. Relative Humidity
3. (T, RH)
instruments
Absolute Humidity
(concentration of water vapor in air)
Given air with
water vapor pressure e,
temperature T, and
pressure p (apply gas law)
R is gas constant, and
M is molecular mass
Both are different
for vapor (index v)
and dry air (d)!
e
v 
RvT
pe
d 
Rd T
[ mkg3 ]
kg
[ m3 ]
v
Rd e
e


 d Rv ( p  e)
pe
Rd M v
18



 0.622
Rv M d 28.9
48
Mixing Ratio r (and also w in book)
mv  v
e
r


md  d
pe
Solution for e
r
e
p
 r
  r than :
e
r 
p
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Specific Humidity
50
mv
r
e kg
q

r 
[ kg ]
md  mv 1  r
p
also
qsat
esat kg
 rsat  
[ kg ]
p
Numerical values of r and q very similar!
Relative Humidity
51
RH
e
q v r
 


100% es qs  s rs
RH
g
r
rs 1000..........[ kg ]
100
es (T )
g
r  10 RH
......[ kg ]
p
Relative Humidity (2)
52
Dew Point Temperature
53
Temperature which occurs after cooling of air
(at constant pressure)
Dew Point : e  es (Td )
e  eo exp( RLv ( T1o  T1d ))
1 Rv
e 1
Td  [  ln( )]
To L
eo
Lifting Condensation Level (LCL)
54
In rising parcel q is constant (not Td) ,
and temperature decreases with 1 K/100m
until saturation occurs at dew point
z LCL  125(T  Td )....[m]
LCL is also measure for humidity!
Useful to estimate cloud base height
for Cumulus type clouds
Lifting Condensation Level (LCL)
55
In rising parcel q is constant (not Td) ,
and temperature decreases with 1 K/100m
until saturation occurs at dew point
z LCL  125(T  Td )....[m]
What is typical value for cloud base on
summer day at noon?
ZLCL= 125*(35-16.8)=
2275 m
Noon: T= 35.0 °C; Td =16.8°C
What is the height of the tower of Babylon?
Or is het likely that the clouds were formed at indicated height?
"Little" Tower of Babel painting by Pieter Bruegel the Elder, circa 1563
Museum Boijmans Van Beuningen, Rotterdam, NL
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Wet Bulb temperature
59
Temperature which occurs after cooling
of air due to evaporation of liquid water
in air (without adding energy)
Psychrometric equation
e  ew   (T  Tw )
Cp p
Pa

 65[ ]
L 
K
Fig 3.11
60
Yellow line represents the Dry Adiabat
Green line represents a “Saturated Adiabat” for which a parcel
remains saturated when it is moved vertically
Thermodynamic diagram
61
Moist adiabat
Isohume
Dry adiabat
Pressure
Temperature
Last night’s sounding (Norderney, DE): Skew T
(weather.uwyo.edu/upperair/sounding.html)
62
Last night’s sounding (Essen, DE): Skew T
(weather.uwyo.edu/upperair/sounding.html)
63
Practical tomorrow:
64
Application of hypsometric equation
Construct air parcels paths on thermodynamic diagram yourself
Analysis of radiosoundings with ROAB program (as in real-world weather rooms)
Collection of thermodynamic diagrams
65
Collection of thermodynamic diagrams
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Summary
67
Many moisture and humidity variables
(use depends on observation type and
application)
Thermodynamic diagrams are useful
practical tools to judge cloud formation
and stability
(Exercises in Practical)
More on this tomorrow!