Hydrology I

Jozsef Szilagyi, Professor of Hydrology Department of Hydraulic and Water

Resources Engineering Budapest University of Technology and

Economics

Lecture #3: Basics of meteorologySimplified radiation balance of the earth’s land-atmosphere

system:Rc = solar constant (1367 W/m2)

Rscattered

Rdirect

αRc

Rthermal_up

Rthermal_down

Short-wave radiation Long-wave (thermal) radiation

Short-wave:

In: Rsc + Rd = Rc

Out: αRc

Balance(in – out):Rc – αRc = Rc(1-α)

Long-wave:

In: Rtd = εaσTa4

Out: Rtu = εsfσTsf4

Balance: Rtd – Rtu

ε is emissivity (close to 1) of the atmosphere (a) and the land surface (sf), respectively. It is defined as the ratio of energy radiated by the body over the energy radiated by a perfect black body at the same temperature. α is albedo (Rout/Rin), σ is the Stefan-Boltzman constant: 5.78·10-8 W / m2K4.

Net radiation (radiation balance): Net shortwave + net longwave Rn = Rc(1-α) + Rtd – Rtu (for a unit area)

Q1: Why are black cars hotter than white ones?Q2: Why is it that in the winter time (in the northern hemisphere) when the earth is closer to the Sun, it is colder than in the summer, when it is farther away from it?

30% 70%

Log-log scale

• Lab2: (a) What is the mean temperature of the earth’s surface? (b) What would be the same temperature without the presence of the atmosphere and greenhouse gases in it?

(a) Rn = Rc(1-α) + Rtd – Rtu, over a long-term the earth is in a radiation equilibrium (not considering the present climate change), thus Rn is zero. Therefore

0 = Rc(1-α)Acr + εaσTa4A - εsfσTsf

4A

= 1367(1-0.3)Acr + σ23344Acr - σ Tsf4 4Acr

where Acr is the cross-sectional area (this is what blocks the incoming radiation from the Sun) of the globe, while A is the surface area (=4Acr) of it.

(b) 0 = 1367(1-0.3)Acr - σTsf44Acr (Here we assume that the

albedo would be the same)

H

H

H

H

ITCZ in July

ITCZ in January