CE 374K HydrologyLecture 5: Precipitation

• Precipitation mechanisms• Rainall maps• Rainfall hyetographs• Nexrad measurement of rainfall• Reading for today – Applied Hydrology, Sec 3.3

and 3.4• Reading for Thursday – Applied Hydrology, Sec

3.5 and 3.6

Wind Maphttp://hint.fm/wind/gallery/

Ocean Currents

http://www.youtube.com/watch?v=oNppEPKt52E

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)

Warm 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

Shape of a Falling Raindrop

http://www.sciencemag.org/content/335/6071/925/F1.large.jpg

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

Terminal Velocity of a Raindrop

http://commons.wikimedia.org/?title=File:Rain_drop_terminal_velocity_chart.jpg

Rainfall Measurement – Tipping Bucket

http://meiyu.atmphys.howard.edu/instru.htm#

Bucket tips for each 0.01 inches of rain

Exterior of a tipping bucket gage

http://en.wikipedia.org/wiki/File:Exterior_tipping_bucket.JPG

20 cm diameter

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

Current Rainfall in Texas

http://water.weather.gov/precip/index.php?yday=1359331200&yday_analysis=0&layer%5B%5D=0&layer%5B%5D=1&layer%5B%5D=4&timetype=RECENT&loctype=STATE&units=engl&timeframe=last60days&product=observed&loc=stateTX

Percent of Normal Rainfall in Texas

http://water.weather.gov/precip/index.php?yday=1359331200&yday_analysis=0&layer%5B%5D=0&layer%5B%5D=1&layer%5B%5D=4&timetype=RECENT&loctype=STATE&units=engl&timeframe=last60days&product=observed&loc=stateTX

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 P1 = 10 mm, A1 = 12 Km2

P2 = 20 mm, A2 = 15 Km2

P3 = 30 mm, A3 = 20 km2

= 21.7 mm

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