atmospheric water and precipitation
DESCRIPTION
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/m 2 ) T = absolute temperature (K), - PowerPoint PPT PresentationTRANSCRIPT
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)
4TR s
“Gray bodies emit a proportion of the radiation
of a black body
4TR es
Valid for a Black body or “pure radiator”
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
Net Radiation, Rn
Rn Net Radiation
GLEHRn
Average value of Rn over the earth and over the year is 105 W/m2
G – Ground Heat Flux
LE – EvaporationH – Sensible Heat
http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/energy/radiation_balance.html
Energy Balance of Earth
6
4
10070
51
21
26
38
6
20
15
Sensible heat flux 7Latent heat flux 23
19
-600
-400
-200
0
200
400
600
D_Sho
rt
U_Sho
rt
D_Lon
g
U_Lon
g
Groun
dLa
tent
Sensib
le Flux
(W/m
2)
Energy Balance in the San Marcos Basin from the NARR (July 2003)
Average fluxes over the day
310
72
415
495
361
112
Net Shortwave = 310 – 72 = 238; Net Longwave = 415 – 495 = - 80
Note the very large amount of longwave radiation exchanged between land and atmosphere
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 itwas 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 W/m2)
• Emitted radiation is more uniform than incoming radiation
Amount of energy transferred from equator to the poles is approximately 4 x 109 MW
Hadley circulation
Warm air rises, cool air descends creating two huge convective cells.
Atmosphere (and oceans) serve to transmit heat energy from the equator to the poles
Atmospheric circulation
1. Tropical Easterlies/Trades
2. Westerlies3. Polar easterlies
1. Intertropical convergence zone (ITCZ)/Doldrums
2. Horse latitudes3. Subpolar low4. Polar high
Ferrel Cell
Polar Cell 1. Hadley cell2. Ferrel Cell3. Polar cell
Latitudes
Winds
Circulation cells
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
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 vaporSuppose we have an elementary volume of atmosphere dV and
we 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 airmv = mass of water vapor
dVmv
v Water vapor density
dVma
a Air density
Specific Humidity, qv
• Specific humidity measures the mass of water vapor per unit mass of moist air
• It is dimensionlessa
vvq
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)
TRe vv
peqv 622.0
Saturation vapor pressure, es
Saturation vapor pressure occurs when air is holding all the water vaporthat it can at a given air temperature
TTes 3.237
27.17exp611
Vapor pressure is measured in Pascals (Pa), where 1 Pa = 1 N/m2
1 kPa = 1000 Pa
Relative humidity, Rh
es
e
sh e
eR Relative humidity measures the percentof the saturation water content of the airthat it currently holds (0 – 100%)
Dewpoint Temperature, Td
e
Dewpoint temperature is the air temperatureat which the air would be saturated with its current vapor content
TTd
Water vapor in an air column• We have three equations
describing 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 to get pressure variation elevation
Column
Element, dz
aRg
TTpp
a/
1
212
1
2
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
Column
Element, dz
1
2
Adzqdm avp
Area = A
Precipitable Waterhttp://geography.uoregon.edu/envchange/clim_animations/flash/pwat.html
25 mm precipitable water divides frontal from thunderstorm rainfall
Frontal rainfall in the winter
Thunderstorm rainfall in the summer
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 air
3
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
averageP1
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 methodP1
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 gages
4. 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