Advanced Hydrology
Lecture 1: Water Balance
1:30 pm, May 12, 2011
Lecture: Pat YEH
Special-appointed Associate Professor,
OKI Lab., IIS (Institute of Industrial Science),
The University of Tokyo, Japan
Academic Experiences and Education
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Special-appointed Associate Professor (2007 Sep. ~)
OKI Laboratory, Institute of Industrial Science,
The University of Tokyo, Japan
Project Scientist (2005 Oct. ~2007 Jul.)
Dept. of Earth System Science, University of California, Irvine. USA
Research Assistant Professor (2002 Oct. ~ 2005 Sep.)
Dept. of Civil Engineering, University of Hong Kong, Hong Kong, China
Ph.D. (2003 Jan.) : Parsons Laboratory, Dept. of Civil and Environ. Eng.,
Massachusetts Institute of Technology (MIT), USA
M.S. (1994 Jun.): Inst. of Environ. Eng, National Chiao-Tung Univ.,
Taiwan
B.E. (1992 Jun.): Dept of Civil Eng, National Taiwan University, Taiwan
Working Experiences
 Special-appointed Associate Professor
(2007 Sep. ~), IIS, The University of Tokyo
 Project Scientist (2005~2007), Dept. of
Earth System Science, University of
California, Irvine. USA
 Research Assistant Professor (2003 ~
2005), Dept. of Civil Engineering,
University of Hong Kong, Hong Kong
 Ph.D.(2003 Jan.) : Dept. of Civil and
Environmental Engineering, Massachusetts
Institute of Technology (MIT), USA
Source: D. R. Maidment
Global Water Cycle
(Oki and Kanae, Science, 2006)
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Terrestrial and Atmospheric Water Balance
Terrestrial and Atmospheric Water Balance Equations
Water Balance for Soil Moisture:
nD
ds
 P  E  RS  PG
dt
(1)
Water Balance for Groundwater :
Sy
H
 PG  RG
t
(2)
Terrestrial Water Balance ( (1)+(2)): ( R  RS  RG )
nD
ds
dH
 Sy
 PER
dt
dt
(3)
Atmospheric Water Balance:
d Wa
 E PC
dt
(4)
Combined Water Balance ((3)+(4)):
nD
ds
d H dWa
 Sy

CR
dt
dt
dt
TWSC
(5)
World’s Major River Basins
North American Major River Basins
Pfafstetter level 1 basins
Pfafstetter level 2 basins
Reflectivity of the Land Surface: Albedo
1.
2.
3.
4.
Atmosphere: scatter, reflection, absorption.
Albedo (%) is the % of solar energy reflected back to the
atmosphere. It depends on the type of surface and solar
altitude (small for moist soil surface and high solar
altitude ~90 deg.)
10-20% for green forest; 15-30% for grasslands; 15-25%
for croplands; 40-50% for old, dirty snow; 80-90% for
pure and white snow;
Global average: 8% for ocean surface; 14% for earth’s
land surface; 10% for the Earth as a whole; 30% for the
planet as a whole (including atmosphere, clouds, etc)
Earth’s average annual heat balance in percentage units
Incoming solar radiation
Outgoing radiation
(Longwave)
(Shortwave)
Space
100
6 20 4
6
26
Atmospher
e
16
15
3
Land,
Ocean
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38
51
Incoming solar radiation
Absorbed by water vapor, dust, and ozone
Absorbed by clouds
Backscattered by air
Reflected by clouds
Reflected by surface
Absorbed by land and ocean
Net surface emission of longwave radiation
Absorption by water vapor
Escape into space
Net emission by water vapor, CO2
Emission by clouds
Sensible heat flux
Latent heat flux
21
7
23
100 units
16
3
6 (shortwave)
20 (shortwave)
4 (shortwave)
51
21 (longwave)
15 (longwave)
6 (longwave)
38 (longwave)
26 (longwave)
7
23
Factors Affecting Global Hydrologic Cycle
• Differential heating of the Earth’s surface
• Coriolis forces due to the rotation of the Earth
– Radial motion in a rotating frame of reference
• Pressure gradients
• Topographic effects
• Regional and local modifications due to vegetation, soilmoisture, etc.
Differential Heating of the Earth’s Surface
Difference in insolation are one of the primary factors in
determining the general circulation of the earth’s atmosphere
(radiative cooling and heating)
General Circulation of the Atmosphere
Influencing Factors of Precipitation
1.
Chief source: evaporation from ocean surfaces, not continental
evaporation (in average <10%).
2.
The location of a region with respect to the general circulation,
latitude, and distance to a moisture source (e.g. ocean) are
primarily responsible for its climate.
3.
Orographic barriers often exert more influences on the climate of
a region than the nearness to a moisture source does.
4.
These climatic and geographic factors determine the amount of
atmospheric moisture over a region, the frequency and kind of
precipitation-producing storms passing over it, and thus its
precipitation.
Conce ntrations of CO 2 and othe r gre e nhous e gas e s incre as e
Te mpe rature incre as e
Aerodynamic Formulation
Clasusius-Clapeyron Equation
Potential Evapotranspiration increase
Pre cipitation
incre as e ? de cre as e ? (how large ?)
reduced 
decrease
Actual Evapotrans piration
incre as e
Ve ge tation De s s ication
(s horte r time s cale )
Little ET change but
re duce d biomas s
Spars e r Ve ge tation
(longe r time s cale )
(ET =   EP )
Soil Mois ture de cre as e
Groundwate r
Re charge de cre as e
Surface Runoff
de cre as e
Groundwate r
Le ve l
de cre as e
Ecos ys te m Thre ate ne d, Agricultural
Productivity de cre as e
Stre amflow de cre as e
Wate r Re s ource s Thre ate ne d
Deteriorate National Economy and Human Welfare
Clausius-Clapeyron Relation
Relationship between air temperature and saturated vapor pressure
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Aerodynamic Formulation
EP = CQ·V (qG – qs)
EP:
CQ:
V:
qG:
qs:
Potential Evapotranspiration;
turbulent transfer coefficient;
wind speed;
ground level saturated specific humidity;
atmospheric specific humidity (~30m high).
ET = β EP
ET: Actual Evapotranspiration;
β : efficiency factor, depends on soil type, ground wetness and plant
properties.
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