Atmospheric Water and
Precipitation
•
•
•
•
Global energy balance
Atmospheric circulation
Atmospheric water vapor
Precipitation
• Reading: Sections 3.1 to 3.4
Radiation
• Basic laws
– Stefan-Boltzman Law
• R = emitted radiation
(W/m2)
• T = absolute temperature
(K),
• and s = 5.67x10-8W/m2-K4
• with e = emissivity (0-1)
– Water, Ice, Snow (0.95-0.99)
– Sand (0.76)
R  sT
4
Valid for a Black body
or “pure radiator”
R  esT
4
“Gray bodies emit a
proportion of the radiation
of a black body
Net Radiation, Rn
Rn  Ri (1  a )  Re
Ri Incoming Radiation
Re
Ro =aRi Reflected radiation
a albedo (0 – 1)
Rn Net Radiation
Average value of Rn over the earth and
over the year is 105 W/m2
Net Radiation, Rn
Rn  H  LE  G
H – Sensible Heat
LE – Evaporation
G – Ground Heat Flux
Rn Net Radiation
Average value of Rn over the earth and
over the year is 105 W/m2
Energy Balance of Earth
6
70
20
100
6
26
4
38
15
19
21
51
Sensible heat flux 7
Latent heat flux 23
http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/energy/radiation_balance.html
Energy Balance in the San Marcos
Basin from the NARR (July 2003)
Note the very large amount of longwave radiation exchanged between land and
atmosphere
Average fluxes over the day
600
495
200
61
72
112
3
-400
310
bl
e
ns
i
Se
La
te
nt
un
d
G
ro
ng
_L
o
U
D
_L
o
ng
t
or
_S
h
U
_S
h
-200
or
t
0
D
Flux (W/m2)
400
415
-600
Net Shortwave = 310 – 72 = 238;
Net Longwave = 415 – 495 = - 80
Increasing carbon dioxide
in the atmosphere (from
about 300 ppm in
preindustrial times)
We are burning fossil
carbon (oil, coal) at
100,000 times the rate it
was laid down in geologic
time
Absorption of energy by CO2
Heating of earth surface
• Heating of earth
surface is uneven
– Solar radiation strikes
perpendicularly near
the equator (270 W/m2)
– Solar radiation strikes
at an oblique angle
near the poles (90
Amount of energy transferred from
W/m2)
equator to the poles is approximately
• Emitted radiation is
4 x 109 MW
more uniform than
incoming radiation
Hadley circulation
Atmosphere (and
oceans) serve to
transmit heat energy
from the equator to the
poles
Warm air rises, cool air descends creating two huge convective cells.
Atmospheric circulation
Circulation cells
Polar Cell
Ferrel Cell
1.
Hadley cell
2.
Ferrel Cell
3.
Polar cell
Winds
1.
Tropical Easterlies/Trades
2.
Westerlies
3.
Polar easterlies
Latitudes
1.
Intertropical convergence
zone (ITCZ)/Doldrums
2.
Horse latitudes
3.
Subpolar low
4.
Polar high
Shifting in Intertropical
Convergence Zone (ITCZ)
Owing to the tilt of the Earth's axis
in orbit, the ITCZ shifts north and
south.
Southward shift in January
Creates wet Summers (Monsoons)
and dry winters, especially in India
and SE Asia
Northward shift in July
Structure of atmosphere
Atmospheric water
• Atmospheric water exists
– Mostly as gas or water vapor
– Liquid in rainfall and water droplets in clouds
– Solid in snowfall and in hail storms
• Accounts for less than 1/100,000 part of
total water, but plays a major role in the
hydrologic cycle
Water vapor
Suppose we have an elementary volume of atmosphere dV and
we want quantify how much water vapor it contains
Water vapor density
Air density
mv
v 
dV
ma
a 
dV
dV
ma = mass of moist air
mv = mass of water vapor
Atmospheric gases:
Nitrogen – 78.1%
Oxygen – 20.9%
Other gases ~ 1%
http://www.bambooweb.com/articles/e/a/Earth's_atmosphere.html
Specific Humidity, qv
• Specific humidity
measures the mass of
water vapor per unit
mass of moist air
• It is dimensionless
v
qv 
a
Vapor pressure, e
• Vapor pressure, e, is the
pressure that water vapor
exerts on a surface
• Air pressure, p, is the
total pressure that air
makes on a surface
• Ideal gas law relates
pressure to absolute
temperature T, Rv is the
gas constant for water
vapor
• 0.622 is ratio of mol. wt.
of water vapor to avg mol.
wt. of dry air (=18/28.9)
e  v RvT
e
qv  0.622
p
Saturation vapor pressure, es
Saturation vapor pressure occurs when air is holding all the water vapor
that it can at a given air temperature
 17.27T 
es  611 exp 

 237.3  T 
Vapor pressure is measured in Pascals (Pa), where 1 Pa = 1 N/m2
1 kPa = 1000 Pa
Relative humidity, Rh
es
e
e
Rh 
es
Relative humidity measures the percent
of the saturation water content of the air
that it currently holds (0 – 100%)
Dewpoint Temperature, Td
e
Td
T
Dewpoint temperature is the air temperature
at which the air would be saturated with its current
vapor content
Water vapor in an air column
• We have three equations
describing column:
2
– Hydrostatic air pressure,
dp/dz = -ag
– Lapse rate of temperature,
dT/dz = - a
– Ideal gas law, p = aRaT
• Combine them and
integrate over column to
get pressure variation
elevation
Column
Element, dz
1
 T2 
p2  p1  
 T1 
g / aRa
Precipitable Water
• In an element dz, the
mass of water vapor
is dmp
• Integrate over the
whole atmospheric
column to get
precipitable water,mp
• mp/A gives
precipitable water per
unit area in kg/m2
2
Column
Element, dz
1
Area = A
dm p  qv  a Adz
Precipitable Water
http://geography.uoregon.edu/envchange/clim_animations/flash/pwat.html
Frontal rainfall in the winter
Thunderstorm rainfall in the summer
25 mm precipitable water divides
frontal from thunderstorm rainfall
Precipitation
• Precipitation: water falling from the
atmosphere to the earth.
– Rainfall
– Snowfall
– Hail, sleet
• Requires lifting of air mass so that it cools
and condenses.
Mechanisms for air lifting
1. Frontal lifting
2. Orographic lifting
3. Convective lifting
Frontal Lifting
• Boundary between air masses with different properties is
called a front
• Cold front occurs when cold air advances towards warm
air
• Warm front occurs when warm air overrides cold air
Cold front (produces cumulus cloud)
Cold front (produces stratus cloud)
Orographic lifting
Orographic uplift occurs when air is forced to rise because of the physical
presence of elevated land.
Convective lifting
Convective precipitation occurs when the air near the ground is heated by the
earth’s warm surface. This warm air rises, cools and creates precipitation.
Hot earth
surface
Condensation
• Condensation is the change of water vapor into
a liquid. For condensation to occur, the air must
be at or near saturation in the presence of
condensation nuclei.
• Condensation nuclei are small particles or
aerosol upon which water vapor attaches to
initiate condensation. Dust particulates, sea salt,
sulfur and nitrogen oxide aerosols serve as
common condensation nuclei.
• Size of aerosols range from 10-3 to 10 mm.
Precipitation formation
• Lifting cools air masses
so moisture condenses
• Condensation nuclei
– Aerosols
– water molecules
attach
• Rising & growing
– 0.5 cm/s sufficient to
carry 10 mm droplet
– Critical size (~0.1
mm)
– Gravity overcomes
and drop falls
Forces acting on rain drop
• Three forces acting on
rain drop
– Gravity force due to
weight
– Buoyancy force due to
displacement of air
– Drag force due to friction
with surrounding air
Fg   w g

6
D3
Fb   a g
2
V2
2  V
Fd  Cd  a A
 Cd  a D
2
4 2

6
D3
D
Fb
Fd
Fd
Fg
Volume 
Area 

4

6
D3
D2
Terminal Velocity
• Terminal velocity: velocity at which the forces acting on the raindrop
are in equilibrium.
• If released from rest, the raindrop will accelerate until it reaches its
terminal velocity
 Fvert  0  FB  FD  W

D

2

3
2V
  a g D  Cd  a D
  w g D3
6
4
2
6
FD  FB  W
 2 Vt2


Cd  a D
 a g D3  w g D3
4
2
6
6
Vt 
4 gD   w 

 1
3Cd   a

Fb
Fd
At standard atmospheric pressure (101.3 kpa) and temperature (20oC),
w = 998 kg/m3 and a = 1.20 kg/m3
Fd
Fg
V
• Raindrops are spherical up to a diameter of 1 mm
• For tiny drops up to 0.1 mm diameter, the drag force is specified by
Stokes law
Cd 
24
Re
 VD
Re  a
ma
Rainfall patterns in the US
Global precipitation pattern
Spatial Representation
• Isohyet – contour of constant rainfall
• Isohyetal maps are prepared by
interpolating rainfall data at gaged points.
Austin, May 1981
Wellsboro, PA 1889
Texas Rainfall Maps
Temporal Representation
• Rainfall hyetograph – plot of rainfall
depth or intensity as a function of time
• Cumulative rainfall hyetograph or
rainfall mass curve – plot of summation
of rainfall increments as a function of time
• Rainfall intensity – depth of rainfall per
unit time
Rainfall Depth and Intensity
Time (min)
Rainfall (in)
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
150
Max. Depth
Max. Intensity
0.02
0.34
0.1
0.04
0.19
0.48
0.5
0.5
0.51
0.16
0.31
0.66
0.36
0.39
0.36
0.54
0.76
0.51
0.44
0.25
0.25
0.22
0.15
0.09
0.09
0.12
0.03
0.01
0.02
0.01
0.76
9.12364946
Cumulative
Rainfall (in)
0
0.02
0.36
0.46
0.5
0.69
1.17
1.67
2.17
2.68
2.84
3.15
3.81
4.17
4.56
4.92
5.46
6.22
6.73
7.17
7.42
7.67
7.89
8.04
8.13
8.22
8.34
8.37
8.38
8.4
8.41
Running Totals
30 min
1h
2h
1.17
1.65
1.81
2.22
2.34
2.46
2.64
2.5
2.39
2.24
2.62
3.07
2.92
3
2.86
2.75
2.43
1.82
1.4
1.05
0.92
0.7
0.49
0.36
0.28
3.07
6.14
3.81
4.15
4.2
4.46
4.96
5.53
5.56
5.5
5.25
4.99
5.05
4.89
4.32
4.05
3.78
3.45
2.92
2.18
1.68
5.56
5.56
8.13
8.2
7.98
7.91
7.88
7.71
7.24
8.2
4.1
Incremental Rainfall
0.8
Incremental Rainfall (in per 5 min)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150
Time (min)
Rainfall Hyetograph
Cumulative Rainfall
10
9
Cumulative Rainfall (in.)
8
7
6
5
3.07 in
4
8.2 in
30 min
3
5.56 in
2
1 hr
1
2 hr
0
0
30
60
90
Time (min.)
Rainfall Mass Curve
120
150
Arithmetic Mean Method
• Simplest method for determining areal
average
P1 = 10 mm
P1
P2 = 20 mm
P3 = 30 mm
1
P
N
P
N
P
i 1
P2
i
10  20  30
 20 mm
3
P3
• Gages must be uniformly distributed
• Gage measurements should not vary greatly about
the mean
Thiessen polygon method
•
•
•
Any point in the watershed receives the same
amount of rainfall as that at the nearest gage
Rainfall recorded at a gage can be applied to
any point at a distance halfway to the next
station in any direction
Steps in Thiessen polygon method
1. Draw lines joining adjacent gages
2. Draw perpendicular bisectors to the lines
created in step 1
3. Extend the lines created in step 2 in both
directions to form representative areas for
gages
4. Compute representative area for each gage
5. Compute the areal average using the following
formula N
P
1
Ai Pi

A i 1
P
12 10  15  20  20  30
 20.7 mm
47
P1
A1
P2
A2
P3
A3
P1 = 10 mm, A1 = 12 Km2
P2 = 20 mm, A2 = 15 Km2
P3 = 30 mm, A3 = 20 km2
Isohyetal method
• Steps
– Construct isohyets (rainfall
contours)
– Compute area between
each pair of adjacent
isohyets (Ai)
– Compute average
precipitation for each pair of
adjacent isohyets (pi)
– Compute areal average
using the following formula
1M N
PP  
P
Ai pA
i i i
A
i 1 i 1
P
5  5  18 15  12  25  12  35
 21.6 mm
47
10
20
P1
A1=5 , p1 = 5
A2=18 , p2 = 15
P2
A3=12 , p3 = 25
30
P3
A4=12 , p3 = 35
Inverse distance weighting
• Prediction at a point is more
influenced by nearby
measurements than that by distant
measurements
• The prediction at an ungaged point
is inversely proportional to the
distance to the measurement
points
• Steps
P1=10
P2= 20
d2=15
– Compute distance (di) from
ungaged point to all measurement
points.
d12 
d1=25
P3=30
p
d3=10
x1  x2 2   y1  y2 2
N


i 1
 di 
P
 i2 
10
20 30
– Compute the precipitation at the

d 


ungaged point using the following Pˆ  i 1  i  Pˆ  25 2 152 10 2  25.24 mm
N 
1
1
1
1 
formula


 2 
2
2
2
25
15
10
Rainfall interpolation in GIS
• Data are generally
available as points with
precipitation stored in
attribute table.
Rainfall maps in GIS
Nearest Neighbor “Thiessen”
Polygon Interpolation
Spline Interpolation
NEXRAD
• NEXt generation RADar: is a doppler radar used for obtaining
weather information
• A signal is emitted from the radar which returns after striking a
rainfall drop
• Returned signals from the radar are analyzed to compute the rainfall
intensity and integrated over time to get the precipitation
NEXRAD Tower
Working of NEXRAD
NEXRAD WSR-88D Radars in Central Texas
(Weather Surveillance Radar-1988 Doppler)
scanning range = 230 km
NEXRAD Products:
Stage I: Just Radar
Stage II: gages,
satellite, and surface
temperature
Stage III:
Continuous mosaic
from radar overlaps
EWX – NEXRAD Radar in New Braunfels
Source: PBS&J, 2003
NEXRAD data
• NOAA’s Weather and Climate Toolkit (JAVA
viewer)
– http://www.ncdc.noaa.gov/oa/wct/
• West Gulf River Forecast Center
– http://www.srh.noaa.gov/wgrfc/
• National Weather Service Precipitation
Analysis
– http://www.srh.noaa.gov/rfcshare/precip_analysis_new.php