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

CE 394K.2 Hydrology, Lecture 3
Water 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 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”
System Transformation
Inputs, I(t)
Outputs, Q(t)
Transformation Equation
Q(t) =  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)
Data Sources
NASA
Storet
Extract
Ameriflux
NCDC
Unidata
NWIS
NCAR
Transform
CUAHSI Web Services
Excel
Visual Basic
C/C++
ArcGIS
Load
Matlab
Applications
http://www.cuahsi.org/his/
Fortran
Access
Java
Some operational services
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
Inputs, I(t)
Outputs, Q(t)
System transformation
f(randomness, space, time)
Hydrologic Processes
How do we characterize
uncertain inputs, outputs
and system transformations?
I(t), Q(t)
Hydrologic conditions
Physical environment
Ref: Figure 1.4.1 Applied Hydrology
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)
Precipitation
100
Atmospheric moisture flow
39
Precipitation
385
Evaporation
424
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
Global water balance (mm/yr)
Precipitation
800
Atmospheric moisture flow
316
Precipitation
1270
Evaporation
1400
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
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
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)
Closed system if
Q(t) (Streamflow)




 I (t )dt   Q(t )dt
Continuous and Discrete time data
Figure 2.3.1, p. 28 Applied Hydrology
Continuous time representation
Sampled or Instantaneous data
(streamflow)
truthful for rate, volume is interpolated
Can we close a discrete-time water balance?
Pulse or Interval data
(precipitation)
truthful for depth, rate is interpolated
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
Mean Sea Level is a surface of constant
gravitational potential called the Geoid
Sea surface
Ellipsoid
Earth surface
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
V12
V22
z1  y1 
 z 2  y2 
 hf
2g
2g
V12
2g
hf
2
2
V
2g
y1
energy
grade line
water
surface
y2
bed
z1
z2
L
Datum
How do we relate friction slope,
Sf 
hf
L
to the velocity of flow?
Open channel flow
Manning’s equation
1.49 2 / 3 1/ 2
V
R Sf
n
Channel Roughness
Channel Geometry
Hydrologic Processes
(Open channel flow)
Hydrologic conditions
(V, Sf)
Physical environment
(Channel n, R)
Subsurface flow
Darcy’s equation
Q
q   KS f
A
Hydraulic conductivity
Hydrologic Processes
(Porous medium flow)
Hydrologic conditions
(q, Sf)
Physical environment
(Medium K)
q
A
q
Comparison of flow equations
Q 1.49 2 / 3 1/ 2
V 
R Sf
A
n
Q
q   KS f
A
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
V12
V22
z1  y1 
 z 2  y2 
 hf
2g
2g
– 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
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 of
1 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
Internal Energy (MJ)
4
Water vapor
3
2
Water
1
Ice
-40
-20
0
0
20
40
60
80
100
120
140
Temperature (Deg. C)
Ice
Water
Heat Capacity (J/kg-K)
2220
4190
Latent Heat (MJ/kg)
0.33
2.5/0.33 = 7.6
2.5
Water may evaporate at any temperature in range 0 – 100°C
Latent heat of vaporization consumes 7.6 times the latent heat of fusion (melting)
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 flux
• 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/m2day
Area = 1 m2
Latent heat flux
• Water flux
• Energy flux
– Evaporation rate, E
(mm/day)
r = 1000 kg/m3
lv = 2.5 MJ/kg
– Latent heat flux
(W/m2), Hl
H l  rlv E
W / m 2  1000(kg / m3 )  2.5 106 ( J / kg) 1mm / day * (1 / 86400)( day / s) * (1 / 1000)( mm / m)
28.94 W/m2 = 1 mm/day
Area = 1 m2
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)
R  esT
4
All bodies emit radiation
2.90 *10
l
T
3
Hot bodies (sun) emit short wave radiation
Cool bodies (earth) emit long wave radiation
Net Radiation, Rn
Rn  Ri (1  a )  Re
Ri Incoming Radiation
Re
Ro =aRi Reflected radiation
a albedo (0 – 1)
Rn Net Radiation
Average value of Rn over the earth and
over the year is 105 W/m2
Net Radiation, Rn
Rn  H  LE  G
H – Sensible Heat
LE – Evaporation
G – Ground Heat Flux
Rn Net Radiation
Average value of Rn over the earth and
over the year is 105 W/m2
Energy Balance of Earth
6
70
20
100
6
26
4
38
15
19
21
51
Sensible heat flux 7
Latent heat flux 23
http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/energy/radiation_balance.html
Energy balance at earth’s surface
Downward short-wave radiation, Jan 2003
600Z
Energy balance at earth’s surface
Downward short-wave radiation, Jan 2003
900Z
Energy balance at earth’s surface
Downward short-wave radiation, Jan 2003
1200Z
Energy balance at earth’s surface
Downward short-wave radiation, Jan 2003
1500Z
Energy balance at earth’s surface
Downward short-wave radiation, Jan 2003
1800Z
Energy balance at earth’s surface
Downward 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)
Why is the net
radiation large
over the oceans
and small over the
Sahara?
Rn  H  LE  G
http://www.crwr.utexas.edu/gis/gishyd98/atlas/Atlas.htm