CE 394K.2 Precipitation
• 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 lifting2. 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 liftingOrographic uplift occurs when air is forced to rise because of the physical presence of elevated land.
Convective lifting
Hot earth surface
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.
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
FdFd
Fb
Fg
D• 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 air3
6DVolume
2
4DArea
3
6DgF wg
3
6DgF ab
242
22
2 VDCVACF adadd
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
32
236246
0
DgVDCDg
WFFF
wada
DBvert
332
26624DgDgVDC
WFF
wat
ad
BD
1
34
a
w
dt C
gDV
• 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
FdFd
Fb
Fg
D
V
Re24dC
a
aVDm
Re
At standard atmospheric pressure (101.3 kpa) and temperature (20oC), w = 998 kg/m3 and a = 1.20 kg/m3
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 IntensityTime (min) Rainfall (in) Cumulative 30 min 1 h 2 h
Rainfall (in)0 05 0.02 0.0210 0.34 0.3615 0.1 0.4620 0.04 0.525 0.19 0.6930 0.48 1.17 1.1735 0.5 1.67 1.6540 0.5 2.17 1.8145 0.51 2.68 2.2250 0.16 2.84 2.3455 0.31 3.15 2.4660 0.66 3.81 2.64 3.8165 0.36 4.17 2.5 4.1570 0.39 4.56 2.39 4.275 0.36 4.92 2.24 4.4680 0.54 5.46 2.62 4.9685 0.76 6.22 3.07 5.5390 0.51 6.73 2.92 5.5695 0.44 7.17 3 5.5100 0.25 7.42 2.86 5.25105 0.25 7.67 2.75 4.99110 0.22 7.89 2.43 5.05115 0.15 8.04 1.82 4.89120 0.09 8.13 1.4 4.32 8.13125 0.09 8.22 1.05 4.05 8.2130 0.12 8.34 0.92 3.78 7.98135 0.03 8.37 0.7 3.45 7.91140 0.01 8.38 0.49 2.92 7.88145 0.02 8.4 0.36 2.18 7.71150 0.01 8.41 0.28 1.68 7.24Max. Depth 0.76 3.07 5.56 8.2Max. Intensity 9.12364946 6.14 5.56 4.1
Running Totals
Incremental Rainfall
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
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)
Incr
emen
tal R
ainf
all (
in p
er 5
min
)
Rainfall Hyetograph
Cumulative Rainfall
0
1
2
3
4
5
6
7
8
9
10
0 30 60 90 120 150Time (min.)
Cum
ulat
ive
Rain
fall
(in.)
30 min
1 hr
2 hr
3.07 in
5.56 in
8.2 in
Rainfall Mass Curve
Arithmetic Mean Method• Simplest method for determining areal average
P1
P2
P3
P1 = 10 mmP2 = 20 mmP3 = 30 mm
• Gages must be uniformly distributed• Gage measurements should not vary greatly about the
mean
N
iiPN
P1
1
mmP 203
302010
Thiessen polygon method
P1
P2
P3
A1
A2
A3
• 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 method1. Draw lines joining adjacent gages 2. Draw perpendicular bisectors to the lines created in
step 13. Extend the lines created in step 2 in both directions
to form representative areas for gages4. Compute representative area for each gage5. Compute the areal average using the following
formula
N
iiiPAA
P1
1
P1 = 10 mm, A1 = 12 Km2
P2 = 20 mm, A2 = 15 Km2
P3 = 30 mm, A3 = 20 km2
mmP 7.2047
302020151012
Isohyetal method
P1
P2
P3
10
20
30
• 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
M
iii pAP
1
A1=5 , p1 = 5A2=18 , p2 = 15
A3=12 , p3 = 25
A4=12 , p3 = 35
mmP 6.2147
35122512151855
N
iiiPAA
P1
1
Inverse distance weighting
P1=10
P2= 20
P3=30
• 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– Compute distance (di) from ungaged
point to all measurement points.
– Compute the precipitation at the ungaged point using the following formula
N
i i
N
i i
i
d
dP
P
12
12
1ˆ
d1=25
d2=15
d3=10
mmP 24.25
101
151
251
1030
1520
2510
ˆ
222
222
p
2212
2112 yyxxd
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
NEXRAD Tower
• 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
Working of NEXRAD
NEXRAD WSR-88D Radars in Central Texas(Weather Surveillance Radar-1988 Doppler)
scanning range = 230 km
Stage I: Just RadarStage II: gages, satellite, and surface temperatureStage III: Continuous mosaic from radar overlaps
NEXRAD Products:
Source: PBS&J, 2003
EWX – NEXRAD Radar in New Braunfels
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