Atmos Water

7/30/2019 Atmos Water

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CE 394K.2 HydrologyAtmospheric Water and Precipitation

Literary quote for today:

In Khln, a town of monks and bones,

And pavements fang'd with murderous stonesAnd rags, and hags, and hideous wenches;

I counted two and seventy stenches,

All well defined, and several stinks!

Ye nymphs that reign o'er sewers and sinks,

The river Rhine, it is well known,

Doth wash your city of Cologne;But tell me, nymphs, what power devine

Shall henceforth wash the river Rhine?

Samuel Taylor Coleridge, The City of Cologne, 1800

Contributed by Eric Hersh


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Questions for today

(1) How is net radiation to the earths surface partitionedinto latent heat, sensible heat and ground heat flux andhow does this partitioning vary with location on theearth?

(2) What are the factors that govern the patterns ofatmospheric circulation over the earth?

(3) What are the key variables that describe atmosphericwater vaporand how are they connected?

(4) What causes precipitation to form and what are thefactors that govern the rate of precipitation?

(5) How is precipitation measured and described?

(Some slides in this presentation were prepared by Venkatesh Merwade)


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Questions for today








4/72

Heat energy

Energy

Potential, Kinetic, Internal (Eu) Internal energy

Sensibleheat heat content that can be

measuredand is proportional to temperature Latent heathidden heat content that is

related tophase changes

fhg

Vyz

g

Vyz

22

2

222

2

111


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Energy Units

In SI units, the basic unit of energy is

Joule (J), where 1 J = 1 kg x 1 m/s2

Energy can also be measured in calories

where 1 calorie = heat required to raise 1

gm of water by 1C and 1 kilocalorie (C) =

1000 calories (1 calorie = 4.19 Joules)

We will use the SI system of units


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MegaJoules

When working with evaporation, its more

convenient to use MegaJoules, MJ (J x

106)

So units are

Energy amount (MJ)

Energy flow (MJ/day, MJ/month)

Energy flux (MJ/m2-day, MJ/m2-month)


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Internal Energy of Water

0

1

2

3

4

-40 -20 0 20 40 60 80 100 120 140

Temperature (Deg. C)

InternalEnergy(MJ)

Heat Capacity (J/kg-K) Latent Heat (MJ/kg)

Ice 2220 0.33

Water 4190 2.5

Ice

Water

Water vapor

Water may evaporate at any temperature in range 0 100C

Latent heat ofvaporization consumes 7.6 times the latent heat offusion (melting)

2.5/0.33 = 7.6


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Latent heat flux

Water flux

Evaporation rate, E

(mm/day)

Energy flux

Latent heat flux

(W/m2), Hl

Area = 1 m2

ElH vl = 1000 kg/m3

lv = 2.5 MJ/kg

)/)(1000/1(*)/)(86400/1(*/1)/(105.2)/(1000/ 632 mmmsdaydaymmkgJmkgmW

28.94 W/m2 = 1 mm/day


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Radiation

Two basic laws

Stefan-Boltzman Law

R = emitted radiation

(W/m2)

e = emissivity (0-1)

s = 5.67x10-8W/m2-K4

T = absolute

temperature (K)

Wiens Law l = wavelength of

emitted radiation (m)

4TR es

T

3

10*90.2

l

Hot bodies (sun) emit short wave radiation

Cool bodies (earth) emit long wave radiation

All bodies emit radiation


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Net Radiation, Rn

Ri Incoming Radiation

Ro =aRi Reflected radiation

a albedo (0 1)

Rn Net Radiation

Re

ein RRR )1( a

Average value of Rn over the earth and

over the year is 105 W/m2


12/72

Net Radiation, Rn

Rn Net Radiation

GLEHRn

Average value of Rn over the earth and

over the year is 105 W/m2

GGround Heat Flux

LE

EvaporationH

Sensible Heat


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http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/energy/radiation_balance.html

Energy Balance of Earth

6

4

100 70

51

21

26

38

6

20

15

Sensible heat flux 7

Latent heat flux 23

19


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Energy balance at earths surfaceDownward short-wave radiation, Jan 2003

600Z


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900Z


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1200Z


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1500Z


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1800Z


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2100Z


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Latent heat flux, Jan 2003, 1500z


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Questions for today








22/72

Heating of earth surface

Heating of earthsurface is uneven

Solar radiation strikes

perpendicularly near

the equator (270 W/m2)

Solar radiation strikes

at an oblique angle

near the poles (90

W/m2)

Emitted radiation is

more uniform than

incoming radiation

Amount of energy transferred fromequator to the poles is approximately

4 x 109 MW


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Hadley circulation

Warm air rises, cool air descends creating two huge convective cells.


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Coriolis ForceCone is moving southward towards the pole

Camera fixed in the outer space

(cone appears moving straight)

Camera fixed on to the globe

(looking southward, cone

appears deflecting to the right)

the force that deflects the path of the wind on account of earth

rotation is called Coriolis force. The path of the wind is deflected

to the right in the Northern Hemisphere and the to left in the

Southern Hemisphere.


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Effect of land mass distribution

A) Idealized winds generated by pressure gradient and Coriolis Force. B) Actual

wind patterns owing to land mass distribution

Uneven distribution of land and ocean, coupled with different thermal properties

creates spatial variation in atmospheric circulation

Shifti i I t t i l


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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

Northward shift in July

Creates wet Summers (Monsoons)

and dry winters, especially in India

and SE Asia


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ITCZ movement

http://iri.ldeo.columbia.edu/%7Ebgordon/ITCZ.html
http://ingrid.ldgo.columbia.edu/expert/SOURCES/.NOAA/.NCEP/.CPC/.CAMS_OPI/.climatology/.prcp/X/Y/1/SM121/DATA/40/80/120/160/200/240/280/320/360/400/VALUES/0/400/green10colorscale/figviewer.html?map.T.plotvalue=Jan+to+Dec&map.Y.units=degree_north&map.Y.plotlast=90N&map.url=X+Y+fig:+colors+|++contours+black+medium+coasts++:fig&map.domain=+%7B+/T+0.5+11.5+plotrange+X+340.+700.+plotrange+%7D&map.domainparam=+/plotaxislength+450+psdef+/plotborder+72+psdef+/XOVY+null+psdef&map.zoom=Zoom&map.Y.plotfirst=90S&map.X.plotfirst=20W&map.X.units=degree_east&map.X.modulus=360&map.X.plotlast=20W&map.prcp.plotfirst=0&map.prcp.units=mm/month&map.prcp.plotlast=400&map.plotaxislength=450&map.plotborder=72&map.fnt=Helvetica&map.fntsze=12&map.XOVY=auto&map.color_smoothing=auto&map.iftime=150&map.mftime=150&map.fftime=200


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Questions for today








30/72

Structure of atmosphere


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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


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Water vapor

Suppose we have an elementary volume of atmosphere dV andwe want quantify how much water vapor it contains

Atmospheric gases:

Nitrogen 78.1%

Oxygen 20.9%

Other gases ~ 1%

http://www.bambooweb.com/articles/e/a/Earth's_atmosphere.html

dV

ma = mass of moist air

mv = mass of water vapor

dV

mvv Water vapor density

dV

maa Air density


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Specific Humidity, qv

Specific humidity

measures the mass of

water vapor per unit

mass of moist air It is dimensionless

a

v

vq


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Vapor pressure, e

Vapor pressure, e, is thepressure that water vaporexerts on a surface

Air pressure, p, is thetotal pressure that air

makes on a surface Ideal gas law relates

pressure to absolutetemperature T, Rv is thegas constant for water

vapor 0.622 is ratio of mol. wt.

of water vapor to avg mol.wt. of dry air

TRe vv

p

eqv 622.0


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Daltons Law of Partial Pressures

John Dalton studied the effect of gases in amixture. He observed that the Total Pressure of

a gas mixture was the sum of the Partial

Pressure of each gas.

P total = P1 + P2 + P3 + .......Pn

The Partial Pressure is defined as the pressure

of a single gas in the mixture as if that gas

alone occupied the container. In other words,

Dalton maintained that since there was an

enormous amount of space between the gas

molecules within the mixture that the gasmolecules did not have any influence on the

motion of other gas molecules, therefore the

pressure of a gas sample would be the same

whether it was the only gas in the container or if

it were among other gases.http://members.aol.com/profchm/dalton.html


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Avogadros law

Equal volumes of gases at the same temperature and pressure contain

the same number of molecules regardless of their chemical nature and

physical properties. This number (Avogadro's number) is 6.023 X 1023

in 22.41 L for all gases.

Dry air

Water vapor

Dry air ( z = x+y molecules) Moist air (x dry and y water vapor)

d = (x+y) * Md/Volume m = (x* Md + y*Mv)/Volume

m < d, which means moist air is lighter than dry air!


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Saturation vapor pressure, esSaturation vapor pressure occurs when air is holding all the water vaporthat it can at a given air temperature

T

Tes

3.237

27.17exp611

Vapor pressure is measured in Pascals (Pa), where 1 Pa = 1 N/m2

1 kPa = 1000 Pa


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Dewpoint Temperature, Td

e

Dewpoint temperature is the air temperature

at which the air would be saturated with its current

vapor content

TTd


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Water vapor in an air column

We have three equationsdescribing column: Hydrostatic air pressure,

dp/dz = -ag

Lapse rate of temperature,dT/dz = - a

Ideal gas law, p = aRaT

Combine them and

integrate over column toget pressure variationelevation

Column

Element, dz

aRg

T

Tpp

a/

1

212

1

2


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Precipitable Water

In an element dz, themass of water vaporis dmp

Integrate over thewhole atmosphericcolumn to getprecipitable water,mp

mp/A gives

precipitable water perunit area in kg/m2

Column

Element, dz

1

2

Adzqdm avp

Area = A


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Precipitable Water, Jan 2003


43/72

Precipitable Water, July 2003


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January

July


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Questions for today




(4) What causes precipitation to form and what are the

factors that govern the rate of precipitation?




46/72

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.


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Mechanisms for air lifting

1. Frontal lifting

2. Orographic lifting

3. Convective lifting

Definitions


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Definitions

Air mass :A large body of air with similar temperatureand moisture characteristics over its horizontal extent.

Front: Boundary between contrasting air masses.

Cold front: Leading edge of the cold air when it isadvancing towards warm air.

Warm front: leading edge of the warm air whenadvancing towards cold air.

F t l Lifti


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Frontal Lifting

Boundary between air masses with different properties is

called a front Cold frontoccurs when cold air advances towards warm

air

Warm frontoccurs when warm air overrides cold air

Cold front (produces cumulus cloud) Cold front (produces stratus cloud)


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Orographic liftingOrographic uplift occurs when air is forced to rise because of the physical

presence of elevated land.

C f
http://www.physicalgeography.net/physgeoglos/o.htmlhttp://www.physicalgeography.net/physgeoglos/o.html


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Convective lifting

Hot earth

surface

Convective precipitation occurs when the air near the ground is heated by the

earths warm surface. This warm air rises, cools and creates precipitation.


52/72

Condensation

Condensation is the change of water vapor intoa 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 ascommon condensation nuclei.

Size of aerosols range from 10-3 to 10 mm.


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Precipitation formation

Lifting cools air masses

so moisture condenses Condensation nuclei

Aerosols

water molecules

attach Rising & growing

0.5 cm/s sufficient tocarry 10 mm droplet

Critical size (~0.1mm)

Gravity overcomesand drop falls


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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 air

3

6DVolume

2

4DArea

3

6DgF wg

3

6DgF ab

242

22

2 VDC

VACF adadd

Terminal Velocity


55/72

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

23

6246

0

DgV

DCDg

WFFF

wada

DBvert

332

2

6624DgDg

VDC

WFF

wat

ad

BD

1

3

4

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 byStokes law

FdFd

Fb

Fg

D

V

Re

24dC

a

aVD

m

Re

At standard atmospheric pressure (101.3 kpa) and temperature (20oC),

w= 998 kg/m3 and a = 1.20 kg/m3


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Precipitation Variation

Influenced by

Atmospheric circulation and local factors

Higher near coastlines

Seasonal variation annual oscillations in some

places

Variables in mountainous areas

Increases in plains areas More uniform in Eastern US than in West

Rainfall patterns in the US


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Rainfall patterns in the US


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Global precipitation pattern


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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


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Texas Rainfall Maps


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Temporal Representation

Rainfall hyetograph plot of rainfall

depth or intensity as a function of time

Cumulative rainfall hyetograph or

rainfall mass curve plot of summationof rainfall increments as a function of time

Rainfall intensity depth of rainfall per

unit time

Rainfall Depth and Intensity


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Rainfall Depth and IntensityTime (min) Rainfall (in) Cumulative 30 min 1 h 2 h

Rainfall (in)

0 0

5 0.02 0.02

10 0.34 0.36

15 0.1 0.46

20 0.04 0.5

25 0.19 0.69

30 0.48 1.17 1.17

35 0.5 1.67 1.65

40 0.5 2.17 1.81

45 0.51 2.68 2.22

50 0.16 2.84 2.34

55 0.31 3.15 2.46

60 0.66 3.81 2.64 3.81

65 0.36 4.17 2.5 4.15

70 0.39 4.56 2.39 4.2

75 0.36 4.92 2.24 4.46

80 0.54 5.46 2.62 4.96

85 0.76 6.22 3.07 5.53

90 0.51 6.73 2.92 5.56

95 0.44 7.17 3 5.5

100 0.25 7.42 2.86 5.25

105 0.25 7.67 2.75 4.99

110 0.22 7.89 2.43 5.05

115 0.15 8.04 1.82 4.89

120 0.09 8.13 1.4 4.32 8.13

125 0.09 8.22 1.05 4.05 8.2

130 0.12 8.34 0.92 3.78 7.98

135 0.03 8.37 0.7 3.45 7.91

140 0.01 8.38 0.49 2.92 7.88

145 0.02 8.4 0.36 2.18 7.71

150 0.01 8.41 0.28 1.68 7.24

Max. Depth 0.76 3.07 5.56 8.2

Max. Intensity 9.12364946 6.14 5.56 4.1

Running Totals

Incremental Rainfall


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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)

IncrementalRa

infall(inper5min)

Rainfall Hyetograph


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Cumulative Rainfall

0

1

2

3

4

5

6

7

8

9

10

0 30 60 90 120 150

Time (min.)

CumulativeRainfall(in.)

30 min

1 hr

2 hr

3.07 in

5.56 in

8.2 in

Rainfall Mass Curve

Arithmetic Mean Method


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Arithmetic Mean Method

Simplest method for determining areal

average

P1

P2

P3

P1 = 10 mm

P2 = 20 mm

P3 = 30 mm

Gages must be uniformly distributed

Gage measurements should not vary greatly about

the mean

N

i

iPN

P1

1

mmP 203

302010

Thi l th d


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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 method

1. Draw lines joining adjacent gages2. 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

i

iiPAA

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


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Isohyetal method

P1

P2

P3

10

20

30

Steps Construct isohyets (rainfall

contours)

Compute area betweeneach pair of adjacentisohyets (Ai)

Compute averageprecipitation for each pair ofadjacent isohyets (pi)

Compute areal averageusing the following formula

M

i

iipAP1

A1=5 , p1 = 5

A2=18 , p2 = 15

A3=12 , p3 = 25

A4=12 , p3 = 35

mmP 6.2147

35122512151855

N

i

iiPAA

P1

1

Inverse distance weighting


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Inverse distance weighting

P1=10

P2= 20

P3=30

Prediction at a point is moreinfluenced by nearby

measurements than that by distantmeasurements

The prediction at an ungaged pointis inversely proportional to thedistance to the measurement

points Steps

Compute distance (di) fromungaged point to all measurementpoints.

Compute the precipitation at theungaged point using the followingformula

N

ii

N

i i

i

d

d

P

P

1

2

1

2

1

d1=25

d2=15

d3=10

mmP 24.25

10

1

15

1

25

110

30

15

20

25

10

222

222

p

22122112 yyxxd


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Rainfall interpolation in GIS

Data are generallyavailable as points with

precipitation stored in

attribute table.

Rainfall maps in GIS


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Rainfall maps in GIS

Nearest Neighbor Thiessen

Polygon InterpolationSpline Interpolation


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NEXRAD

NEXRAD Tower

NEXt generation RADar: is a doppler radar used for obtainingweather information

A signal is emitted from the radar which returns after striking arainfall drop

Returned signals from the radar are analyzed to compute the rainfallintensity and integrated over time to get the precipitation

Working of NEXRAD


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NEXRAD data

NCDC data (JAVA viewer) http://www.ncdc.noaa.gov/oa/radar/jnx/

West Gulf River Forecast Center

http://www.srh.noaa.gov/wgrfc/ National Weather Service Animation

http://weather.noaa.gov/radar/mosaic.loop/DS.p19r0/ar.us.conus.shtml
http://www.ncdc.noaa.gov/oa/radar/jnx/http://www.srh.noaa.gov/wgrfc/http://weather.noaa.gov/radar/mosaic.loop/DS.p19r0/ar.us.conus.shtmlhttp://weather.noaa.gov/radar/mosaic.loop/DS.p19r0/ar.us.conus.shtmlhttp://www.srh.noaa.gov/wgrfc/http://www.ncdc.noaa.gov/oa/radar/jnx/

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