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)
Watershed system
Hydrologic System
Take a watershed and extrude it vertically into the atmosphereand 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”
System Transformation
Transformation EquationQ(t) = I(t)
Inputs, I(t) Outputs, Q(t)
A hydrologic system transforms inputs to outputs
Hydrologic Processes
Physical environment
Hydrologic conditions
I(t), Q(t)
I(t) (Precip)
Q(t) (Streamflow)
NWISNWIS
ArcGISArcGIS
ExcelExcel
NCARNCAR
UnidataUnidata
NASANASAStoretStoret
NCDCNCDC
AmerifluxAmeriflux
MatlabMatlabAccessAccess JavaJava
FortranFortran
Visual BasicVisual Basic
C/C++C/C++
Some operational services
CUAHSI Web ServicesCUAHSI Web Services
Data SourcesData Sources
ApplicationsApplications
Extract
Transform
Load
http://www.cuahsi.org/his/
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?
Stochastic transformation
System transformationf(randomness, space, time)
Inputs, I(t) Outputs, Q(t)
Ref: Figure 1.4.1 Applied Hydrology
How do we characterizeuncertain inputs, outputsand system transformations?
Hydrologic Processes
Physical environment
Hydrologic conditions
I(t), Q(t)
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 earth’s surface partitioned into latent heat, sensible heat and ground heat flux and how does this partitioning vary with location on the earth?
Global water balance (volumetric)
Land (148.7 km2)(29% of earth area)
Ocean (361.3 km2)(71% of earth area)
Precipitation100
Evaporation61
Surface Outflow38
Subsurface Outflow1
Precipitation385
Evaporation424
Atmospheric moisture flow 39
Units are in volume per year relative to precipitation on land (119,000 km3/yr) which is 100 units
Global water balance (mm/yr)
Land (148.7 km2)(29% of earth area)
Ocean (361.3 km2)(71% of earth area)
Precipitation800
Evaporation484
Outflow316
Precipitation1270
Evaporation1400
Atmospheric moisture flow 316
What conclusions can we draw from these data?
Applied Hydrology, Table 1.1.2, p.5
Digital Atlas of the World Water Balance(Precipitation)
http://www.crwr.utexas.edu/gis/gishyd98/atlas/Atlas.htm
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 earth’s surface partitioned into latent heat, sensible heat and ground heat flux and how does this partitioning vary with location on the earth?
Continuity equation for a watershed
I(t) (Precip)
Q(t) (Streamflow)dS/dt = I(t) – Q(t)
dttQdttI )()(Closed system if
Hydrologic systems are nearly alwaysopen systems, which means that it isdifficult to do material balances on them
What time period do we chooseto do material balances for?
Continuous and Discrete time data
Continuous time representation
Sampled or Instantaneous data(streamflow)truthful for rate, volume is interpolated
Pulse or Interval data(precipitation)truthful for depth, rate is interpolated
Figure 2.3.1, p. 28 Applied Hydrology
Can we close a discrete-time water balance?
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 earth’s surface partitioned into latent heat, sensible heat and ground heat flux and how does this partitioning vary with location on the earth?
Surface and Groundwater Flow Levels are related to Mean Sea Level
Earth surface
EllipsoidSea surface
Geoid
Mean Sea Level is a surface of constant gravitational potential called the Geoid
http://www.csr.utexas.edu/ocean/mss.html
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
Energy equation of fluid mechanics
gV2
21
fhgVyz
gVyz
22
22
22
21
11
Datum
z1
y1
bed
water surface
energy grade line
hf
z2
y2
gV2
22
L
How do we relate friction slope, Lh
S ff to the velocity of flow?
Open channel flowManning’s equation
2/13/249.1fSR
nV
Channel Roughness
Channel Geometry
Hydrologic Processes(Open channel flow)
Physical environment(Channel n, R)
Hydrologic conditions(V, Sf)
Subsurface flowDarcy’s equation
fKSAQq
Hydraulic conductivity
Hydrologic Processes(Porous medium flow)
Physical environment(Medium K)
Hydrologic conditions(q, Sf)
Aq q
Comparison of flow equations
2/13/249.1fSR
nAQV
fKSAQq
Open Channel Flow
Porous medium flow
Why is there a different power of Sf?
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 earth’s surface partitioned into latent heat, sensible heat and ground heat flux and how does this partitioning vary with location on the earth?
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
fhgVyz
gVyz
22
22
22
21
11
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 1°C and 1 kilocalorie (C) = 1000 calories (1 calorie = 4.19 Joules)
• We will use the SI system of units
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 of1 Joule/sec
Area = 1 m2
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)
Internal Energy of Water
0
1
2
3
4
-40 -20 0 20 40 60 80 100 120 140
Temperature (Deg. C)
Inte
rnal
Ene
rgy
(MJ)
Heat Capacity (J/kg-K) Latent Heat (MJ/kg)Ice 2220 0.33Water 4190 2.5
Ice
Water
Water vapor
Water may evaporate at any temperature in range 0 – 100°CLatent heat of vaporization consumes 7.6 times the latent heat of fusion (melting)
2.5/0.33 = 7.6
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 = V] (Kg)
• Water mass flow rate [m/T = Q] (kg/s or kg/day)
• Water mass flux [M/L2T = q] in kg/m2-day
Water flux
Area = 1 m2
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
Radiation
• Two basic laws– Stefan-Boltzman Law
• R = emitted radiation (W/m2)
= emissivity (0-1) = 5.67x10-8W/m2-K4
• T = absolute temperature (K)
– Wiens Law = wavelength of
emitted radiation (m)
4TR
T
310*90.2
Hot bodies (sun) emit short wave radiationCool bodies (earth) emit long wave radiation
All bodies emit radiation
Net Radiation, Rn
Ri Incoming Radiation
Ro =Ri Reflected radiation
albedo (0 – 1)
Rn Net Radiation
Re
ein RRR )1(
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
Energy balance at earth’s surfaceDownward short-wave radiation, Jan 2003
600Z
Energy balance at earth’s surfaceDownward short-wave radiation, Jan 2003
900Z
Energy balance at earth’s surfaceDownward short-wave radiation, Jan 2003
1200Z
Energy balance at earth’s surfaceDownward short-wave radiation, Jan 2003
1500Z
Energy balance at earth’s surfaceDownward short-wave radiation, Jan 2003
1800Z
Energy balance at earth’s surfaceDownward short-wave radiation, Jan 2003
2100Z
Latent heat flux, Jan 2003, 1500z
Digital Atlas of the World Water Balance(Temperature)
http://www.crwr.utexas.edu/gis/gishyd98/atlas/Atlas.htm
Digital Atlas of the World Water Balance(Net Radiation)
http://www.crwr.utexas.edu/gis/gishyd98/atlas/Atlas.htm
Why is the net radiation largeover the oceans and small over the Sahara?
GLEHRn
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