CE 394K.2 Hydrology Atmospheric Water and Precipitation

1
CE 394K.2 HydrologyAtmospheric Water and
Precipitation

• Literary quote for today

In Köhln, a town of monks and bones,And
pavements fang'd with murderous stonesAnd rags,
and hags, and hideous wenchesI 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 CologneBut tell me, nymphs,
what power devineShall henceforth wash the river
Rhine? Samuel Taylor Coleridge, The City of
Cologne, 1800Contributed by Eric Hersh
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Questions for today

• (1)  How is net radiation to the earths surface
  partitioned into latent heat, sensible heat and
  ground heat flux and how does this partitioning
  vary with location on the earth?
• (2) What are the factors that govern the patterns
  of atmospheric circulation over the earth?
• (3)  What are the key variables that describe
  atmospheric water vapor and how are they
  connected?
• (4)  What causes precipitation to form and what
  are the factors that govern the rate of
  precipitation?
• (5)  How is precipitation measured and described?

(Some slides in this presentation were prepared
by Venkatesh Merwade)
3
Questions for today

• (1)  How is net radiation to the earths surface
  partitioned into latent heat, sensible heat and
  ground heat flux and how does this partitioning
  vary with location on the earth?
• (2) What are the factors that govern the patterns
  of atmospheric circulation over the earth?
• (3)  What are the key variables that describe
  atmospheric water vapor and how are they
  connected?
• (4)  What causes precipitation to form and what
  are the factors that govern the rate of
  precipitation?
• (5)  How is precipitation measured and described?

(Some slides in this presentation were prepared
by Venkatesh Merwade)
4
Heat energy

• Energy
• Potential, Kinetic, Internal (Eu)
• Internal energy
• Sensible heat heat content that can be measured
  and is proportional to temperature
• Latent heat hidden heat content that is
  related to phase changes

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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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Energy fluxes and flows

• Water Volume L3 (acre-ft, m3)
• Water flow L3/T (cfs or m3/s)
• Water flux L/T (in/day, mm/day)

• Energy amount E (Joules)
• Energy flow in Watts E/T (1W 1 J/s)
• Energy flux E/L2T in Watts/m2

Energy flow of 1 Joule/sec
Area 1 m2
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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
Water vapor
Water
Ice
Heat Capacity (J/kg-K) Latent Heat
(MJ/kg) Ice 2220 0.33 Water 4190 2.5
2.5/0.33 7.6
Water may evaporate at any temperature in range 0
100C Latent heat of vaporization consumes 7.6
times the latent heat of fusion (melting)
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Latent heat flux

• Water flux
• Evaporation rate, E (mm/day)

• Energy flux
• Latent heat flux (W/m2), Hl

r 1000 kg/m3 lv 2.5 MJ/kg
28.94 W/m2 1 mm/day
Area 1 m2
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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)

All bodies emit radiation
Hot bodies (sun) emit short wave radiation Cool
bodies (earth) emit long wave radiation
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Net Radiation, Rn
Ri Incoming Radiation

• Ro aRi Reflected radiation
• albedo (0 1)

Re
Rn Net Radiation
Average value of Rn over the earth and over the
year is 105 W/m2
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Net Radiation, Rn
LE Evaporation
H Sensible Heat
G Ground Heat Flux
Rn Net Radiation
Average value of Rn over the earth and over the
year is 105 W/m2
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Energy Balance of Earth
70
20
100
6
6
26
4
38
15
19
21
Sensible heat flux 7 Latent heat flux 23
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http//www.uwsp.edu/geo/faculty/ritter/geog101/tex
tbook/energy/radiation_balance.html
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Energy balance at earths surfaceDownward
short-wave radiation, Jan 2003
600Z
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Energy balance at earths surfaceDownward
short-wave radiation, Jan 2003
900Z
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Energy balance at earths surfaceDownward
short-wave radiation, Jan 2003
1200Z
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Energy balance at earths surfaceDownward
short-wave radiation, Jan 2003
1500Z
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Energy balance at earths surfaceDownward
short-wave radiation, Jan 2003
1800Z
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Energy balance at earths surfaceDownward
short-wave radiation, Jan 2003
2100Z
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Latent heat flux, Jan 2003, 1500z
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Questions for today

• (1)  How is net radiation to the earths surface
  partitioned into latent heat, sensible heat and
  ground heat flux and how does this partitioning
  vary with location on the earth?
• (2) What are the factors that govern the patterns
  of atmospheric circulation over the earth?
• (3)  What are the key variables that describe
  atmospheric water vapor and how are they
  connected?
• (4)  What causes precipitation to form and what
  are the factors 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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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
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Hadley circulation
Warm air rises, cool air descends creating two
huge convective cells.
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Coriolis Force
Cone is moving southward towards the pole
Camera fixed on to the globe (looking southward,
cone appears deflecting to the right)
Camera fixed in the outer space (cone appears
moving straight)
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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Atmospheric circulation
Circulation cells
Polar Cell

1. Hadley cell
2. Ferrel Cell
3. Polar cell

Ferrel Cell
Winds

1. Tropical Easterlies/Trades
2. Westerlies
3. Polar easterlies

Latitudes

1. Intertropical convergence zone (ITCZ)/Doldrums
2. Horse latitudes
3. Subpolar low
4. Polar high

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Effect of land mass distribution
Uneven distribution of land and ocean, coupled
with different thermal properties creates spatial
variation in atmospheric circulation
A) Idealized winds generated by pressure gradient
and Coriolis Force. B) Actual wind patterns
owing to land mass distribution
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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
Creates wet Summers (Monsoons) and dry winters,
especially in India and SE Asia
Northward shift in July
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ITCZ movement
http//iri.ldeo.columbia.edu/7Ebgordon/ITCZ.html
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Questions for today

• (1)  How is net radiation to the earths surface
  partitioned into latent heat, sensible heat and
  ground heat flux and how does this partitioning
  vary with location on the earth?
• (2) What are the factors that govern the patterns
  of atmospheric circulation over the earth?
• (3)  What are the key variables that describe
  atmospheric water vapor and how are they
  connected?
• (4)  What causes precipitation to form and what
  are the factors 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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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 and we want quantify how much
water vapor it contains
Water vapor density
dV
ma mass of moist air mv mass of water vapor
Air density
Atmospheric gases Nitrogen 78.1 Oxygen
20.9 Other gases 1
http//www.bambooweb.com/articles/e/a/Earth's_atmo
sphere.html
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Specific Humidity, qv

• Specific humidity measures the mass of water
  vapor per unit mass of moist air
• It is dimensionless

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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

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Daltons Law of Partial Pressures
John Dalton studied the effect of gases in a
mixture. 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 gas
molecules 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 ( z xy molecules)
Moist air (x dry and y water vapor)
Dry air
Water vapor
rd (xy) Md/Volume
rm (x Md yMv)/Volume
rm lt rd, which means moist air is lighter than
dry air!
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Saturation vapor pressure, es
Saturation vapor pressure occurs when air is
holding all the water vapor that it can at a
given air temperature
Vapor pressure is measured in Pascals (Pa), where
1 Pa 1 N/m2
1 kPa 1000 Pa
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Relative humidity, Rh
es
e
Relative humidity measures the percent of the
saturation water content of the air that it
currently holds (0 100)
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Dewpoint Temperature, Td
e
Td
T
Dewpoint temperature is the air temperature at
which the air would be saturated with its current
vapor content
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Water vapor in an air column

• We have three equations describing column
• Hydrostatic air pressure, dp/dz -rag
• Lapse rate of temperature, dT/dz - a
• Ideal gas law, p raRaT
• Combine them and integrate over column to get
  pressure variation elevation

2
Column
Element, dz
1
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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

2
Column
Element, dz
Area A
1
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Precipitable Water, Jan 2003
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Precipitable Water, July 2003
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January
July
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Questions for today

• (1)  How is net radiation to the earths surface
  partitioned into latent heat, sensible heat and
  ground heat flux and how does this partitioning
  vary with location on the earth?
• (2) What are the factors that govern the patterns
  of atmospheric circulation over the earth?
• (3)  What are the key variables that describe
  atmospheric water vapor and how are they
  connected?
• (4)  What causes precipitation to form and what
  are the factors that govern the rate of
  precipitation?
• (5)  How is precipitation measured and described?

(Some slides in this presentation were prepared
by Venkatesh Merwade)
46
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

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Definitions

• Air mass A large body of air with similar
  temperature and moisture characteristics over its
  horizontal extent.
• Front Boundary between contrasting air masses.
• Cold front Leading edge of the cold air when it
  is advancing towards warm air.
• Warm front leading edge of the warm air when
  advancing towards cold air.

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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)
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Orographic lifting
Orographic uplift occurs when air is forced to
rise because of the physical presence of elevated
land.
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Convective lifting
Convective precipitation occurs when the air near
the ground is heated by the earths warm surface.
This warm air rises, cools and creates
precipitation.
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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.

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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 to carry 10 mm droplet
• Critical size (0.1 mm)
• Gravity overcomes and drop falls

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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
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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

D
Fb
Fd
Fd
Fg
At standard atmospheric pressure (101.3 kpa) and
temperature (20oC), rw 998 kg/m3 and ra 1.20
kg/m3
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

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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

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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
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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 summation of rainfall increments
  as a function of time
• Rainfall intensity depth of rainfall per unit
  time

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Rainfall Depth and Intensity
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Incremental Rainfall
Rainfall Hyetograph
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Cumulative Rainfall
Rainfall Mass Curve
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Arithmetic Mean Method

• Simplest method for determining areal average

P1 10 mm P2 20 mm P3 30 mm
P1
P2
P3

• Gages must be uniformly distributed
• Gage measurements should not vary greatly about
  the mean

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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
• Draw lines joining adjacent gages
• Draw perpendicular bisectors to the lines created
  in step 1
• Extend the lines created in step 2 in both
  directions to form representative areas for gages
• Compute representative area for each gage
• Compute the areal average using the following
  formula

P1
P2
P3
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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

10
20
P1
A15 , p1 5
A218 , p2 15
P2
A312 , p3 25
P3
30
A412 , p3 35
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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
• Compute distance (di) from ungaged point to all
  measurement points.
• Compute the precipitation at the ungaged point
  using the following formula

P110
P2 20
d125
P330
d215
d310
p
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Rainfall interpolation in GIS

• Data are generally available as points with
  precipitation stored in attribute table.

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Rainfall maps in GIS
Nearest Neighbor Thiessen Polygon Interpolation
Spline Interpolation
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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
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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