Water Cycle

1. Formulation of the hydrological cycle

2. Equations of Hydrology

3. Observations

Formulation of the hydrological cycle

Global water content 13.1x1015kg (~2.5cm)Annual mean precipitation ~1mOverturning ~40 times/year (9 days)

Equations of HydrologyS=P-E-R0-Ru

S- rate of storage of waterP- precipitation rate (liquid and solid phase)E- evaporation rate

R0- surface runoff

Ru-subterranean runoff}R{-}E- P{}S{ 0

S {S}-time-averaging, -space-averaging

For large areas }S{ is small, thus }R{-}P{}E{ 0accuratelymeasuredmeasured

semiempiricestimates

Runoff

Balance Equations for Water Wapor

0

0

),,(p

g

dpqtW

PEQdivt

W

0

0

)(p

c g

dpvqqQ

qqc

t

WQdivSR }{0

]''[][]][[][**

vqvqvqqv

]''[][]][[][**

wqwqwqqw

-amount of precipitable water [g/m2]

-areal runoff,

-equation for the atmospheric branch of the hydrological cycle

PE couples land andatmospheric branches, thus

Globally E=P

-transport trough one parallel

-vertical transport

Water Wapor in the

Atmosphere(Horizontal

patterns)

Water Wapor in the

Atmosphere(Vertical patterns)

More than 50 percent ofthe water vapor isbelow 850mb (90 percentbelow 500mb)

NH: Summer-Winter1.2cm water

SH: Summer-Winter0.7cm water

Global meanwater content2.5cm

Transport of Water Vapor

Aerial Runoff