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

• 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

(Oki and Kanae, Science, 2006)3

Global Water Cycle

Terrestrial and Atmospheric Water Balance

Water Balance for Soil Moisture:

(1)Water Balance for Groundwater :

(2) Terrestrial Water Balance ( (1)+(2)):

(3) Atmospheric Water Balance:

(4)

GS PREPdt

sdDn

GGy RPt

HS

REPdt

HdS

dt

sdDn y

)( GS RRR

CPEdt

Wd a

Terrestrial and Atmospheric Water Balance Equations

RCdt

Wd

dt

HdS

dt

sdDn a

y

Combined Water Balance ((3)+(4)):

(5) TWSC

World’s Major River Basins

North American Major River Basins

Pfafstetter level 2 basinsPfafstetter level 1 basins

Reflectivity of the Land Surface: Albedo

1. Atmosphere: scatter, reflection, absorption.2. 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.)

3. 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;

4. 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 100 units• Absorbed by water vapor, dust, and ozone 16• Absorbed by clouds 3• Backscattered by air 6 (shortwave)• Reflected by clouds 20 (shortwave)• Reflected by surface 4 (shortwave)• Absorbed by land and ocean 51• Net surface emission of longwave radiation 21 (longwave)• Absorption by water vapor 15 (longwave)• Escape into space 6 (longwave)• Net emission by water vapor, CO2 38 (longwave)• Emission by clouds 26 (longwave)• Sensible heat flux 7• Latent heat flux 23

1006 20 4

16

3

51

Spac

eA

tmosphe

re

Land, Ocean

Incoming solar radiation

6 38 26

15

7 23

Outgoing radiation

(Shortwave) (Longwave)

21

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, soil-moisture, 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.

Aerodynamic Formulation Clasusius-Clapeyron Equation

C o n c e n tratio n s o f C O 2 an d o th e r g re e n h o u s e g as e s in c re as e

T e m p e ratu re in c re as e

Po te n t ia l Ev a po tra n s pira t io n in cre a s e

A c tu al E v ap o tran s p iratio nin c re as e

P re c ip itatio nin c re as e ? d e c re as e ? (h o w larg e ? )

V e g e tatio n D e s s ic atio n(s h o rte r t im e s c ale )

S p ars e r V e g e tatio n(lo n g e r t im e s c ale )

S o il M o is tu re d e c re as e

G ro u n d w ate rR e c h arg e d e c re as e S u rfac e R u n o ff

d e c re as e

G ro u n d w ate rL e v e l

d e c re as e

S tre am flo w d e c re as eE c o s ys te m T h re ate n e d , A g ric u ltu ralP ro d u c tiv ity d e c re as e

W ate r R e s o u rc e s T h re ate n e d

D e te r i o r ate N at i o nal E c o no m y and H um an W e l far e

dec

reas

e

L itt le E T c h an g e b u tre d u c e d b io m as s

(E T = E P )

red

uce

d

.

Relationship between air temperature and saturated vapor pressure

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Clausius-Clapeyron Relation

Aerodynamic Formulation

EP = CQ·V (qG – qs)

EP: Potential Evapotranspiration;

CQ: turbulent transfer coefficient;V: wind speed;

qG: ground level saturated specific humidity;

qs: 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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