CE 394K.2
Precipitation
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•
•
•
Precipitation mechanisms
Rainall maps
Rainfall hyetographs
Nexrad measurement of rainfall
Reading: Applied Hydrology Sections 3.5 to 3.6 on
Evaporation for Thursday
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
D
Fb
Fd
Fd
Fg
Volume 
Area 
Fg   w g

6
D3
Fb   a g
2
V2
2  V
Fd  Cd  a A
 Cd  a D
2
4 2

6
D3

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
• Gages must be uniformly distributed
• Gage measurements should not vary greatly about the
mean
P3
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
1 N
P   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
d1=25
d2=15
– Compute distance (di) from ungaged
point to all measurement points.
P3=30
p
– Compute the precipitation at the
ungaged
2   y1the
2
d12  point
x1  x2using
 y2following
formula
 Pi 
 2



i 1  d i 
ˆ
P
N 
1 
 2

i 1  d i 
d3=10
N
10
20 30

 2
2
2
Pˆ  25 15 10  25.24 mm
1
1
1


25 2 152 10 2
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