CE 394K.2 Hydrology, Lecture 3 Water and Energy Flow

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CE 394K.2 Hydrology, Lecture 3Water and Energy
Flow

• Literary quote for today

If I should die, think only this of me    That
there's some corner of a foreign field  That is
for ever England. Rupert Brooke, English poet,
The Soldier (he died in WWI and is buried on
the island of Skyros in Greece)
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Watershed system
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Hydrologic System
Take a watershed and extrude it vertically into
the atmosphere and subsurface, Applied Hydrology,
p.7- 8 A hydrologic system is a structure or
volume in space surrounded by a boundary, that
accepts water and other inputs, operates on them
internally, and produces them as outputs
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System Transformation
Transformation Equation Q(t) ? I(t)
Outputs, Q(t)
Inputs, I(t)
A hydrologic system transforms inputs to outputs
Hydrologic Processes
I(t), Q(t)
Hydrologic conditions
I(t) (Precip)
Physical environment
Q(t) (Streamflow)
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Data Sources
NASA
Storet
Ameriflux
Unidata
NCDC
Extract
NWIS
NCAR
Transform
CUAHSI Web Services
Excel
Visual Basic
ArcGIS
C/C
Load
Matlab
Fortran
Access
Java
Applications
Some operational services
http//www.cuahsi.org/his/
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Concept of Transformation

• In hydrology, we associate transformation with
  the connection between inflow and outflow of
  water, mass, energy
• In web services, we associate transformation with
  flow of data (extract, transform, load)
• Can we link these two ideas?

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Stochastic transformation
System transformation f(randomness, space, time)
Outputs, Q(t)
Inputs, I(t)
Hydrologic Processes
I(t), Q(t)
How do we characterize uncertain inputs,
outputs and system transformations?
Hydrologic conditions
Physical environment
Ref Figure 1.4.1 Applied Hydrology
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Questions for discussion on Tuesday (from
Chapters 1 and 2 of Text)

• How is precipitation partitioned into
  evaporation, groundwater recharge and runoff and
  how does this partitioning vary with location on
  the earth?
• Can a closed water balance be developed using
  discrete time rainfall and streamflow data for a
  watershed?
• How do the equations for velocity of water flow
  in streams and aquifers differ, and why is this
  so?
• 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?

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Global water balance (volumetric)
Precipitation 100
Precipitation 385
Evaporation 424
Atmospheric moisture flow 39
Evaporation 61
Surface Outflow 38
Land (148.7 km2) (29 of earth area)
Ocean (361.3 km2) (71 of earth area)
Subsurface Outflow 1
Units are in volume per year relative to
precipitation on land (119,000 km3/yr) which is
100 units
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Global water balance (mm/yr)
Precipitation 800
Precipitation 1270
Evaporation 1400
Atmospheric moisture flow 316
Evaporation 484
Outflow 316
Land (148.7 km2) (29 of earth area)
Ocean (361.3 km2) (71 of earth area)
What conclusions can we draw from these data?
Applied Hydrology, Table 1.1.2, p.5
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Digital Atlas of the World Water
Balance(Precipitation)
http//www.crwr.utexas.edu/gis/gishyd98/atlas/Atla
s.htm
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Questions for discussion on Tuesday (from
Chapters 1 and 2 of Text)

• How is precipitation partitioned into
  evaporation, groundwater recharge and runoff and
  how does this partitioning vary with location on
  the earth?
• Can a closed water balance be developed using
  discrete time rainfall and streamflow data for a
  watershed?
• How do the equations for velocity of water flow
  in streams and aquifers differ, and why is this
  so?
• 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?

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Continuity equation for a watershed
Hydrologic systems are nearly always open
systems, which means that it is difficult to do
material balances on them
I(t) (Precip)
What time period do we choose to do material
balances for?
dS/dt I(t) Q(t)
Q(t) (Streamflow)
Closed system if
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Continuous and Discrete time data
Figure 2.3.1, p. 28 Applied Hydrology
Continuous time representation
Sampled or Instantaneous data (streamflow) truthfu
l for rate, volume is interpolated
Can we close a discrete-time water balance?
Pulse or Interval data (precipitation) truthful
for depth, rate is interpolated
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Questions for discussion on Tuesday (from
Chapters 1 and 2 of Text)

• How is precipitation partitioned into
  evaporation, groundwater recharge and runoff and
  how does this partitioning vary with location on
  the earth?
• Can a closed water balance be developed using
  discrete time rainfall and streamflow data for a
  watershed?
• How do the equations for velocity of water flow
  in streams and aquifers differ, and why is this
  so?
• 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?

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Surface and Groundwater Flow Levels are related
to Mean Sea Level
Mean Sea Level is a surface of constant
gravitational potential called the Geoid
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http//www.csr.utexas.edu/ocean/mss.html
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Vertical Earth Datums

• A vertical datum defines elevation, z
• NGVD29 (National Geodetic Vertical Datum of 1929)
• NAVD88 (North American Vertical Datum of 1988)
• takes into account a map of gravity anomalies
  between the ellipsoid and the geoid

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Energy equation of fluid mechanics
hf
energy grade line
y1
water surface
y2
bed
z1
z2
L
Datum
How do we relate friction slope,
to the velocity of flow?
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Open channel flowMannings equation
Channel Roughness
Channel Geometry
Hydrologic Processes (Open channel flow)
Hydrologic conditions (V, Sf)
Physical environment (Channel n, R)
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Subsurface flowDarcys equation
A
q
q
Hydraulic conductivity
Hydrologic Processes (Porous medium flow)
Hydrologic conditions (q, Sf)
Physical environment (Medium K)
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Comparison of flow equations
Open Channel Flow
Porous medium flow
Why is there a different power of Sf?
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Questions for discussion on Tuesday (from
Chapters 1 and 2 of Text)

• How is precipitation partitioned into
  evaporation, groundwater recharge and runoff and
  how does this partitioning vary with location on
  the earth?
• Can a closed water balance be developed using
  discrete time rainfall and streamflow data for a
  watershed?
• How do the equations for velocity of water flow
  in streams and aquifers differ, and why is this
  so?
• 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?

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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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Water Mass Fluxes and Flows

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

• Water mass m rV (Kg)
• Water mass flow rate m/T rQ (kg/s or kg/day)
• Water mass flux M/L2T rq in kg/m2-day

Water flux
Area 1 m2
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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
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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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Digital Atlas of the World Water
Balance(Temperature)
http//www.crwr.utexas.edu/gis/gishyd98/atlas/Atla
s.htm
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Digital Atlas of the World Water Balance(Net
Radiation)
Why is the net radiation large over the oceans
and small over the Sahara?
http//www.crwr.utexas.edu/gis/gishyd98/atlas/Atla
s.htm