(theta) dependence of intensity

theta

A’ A>

Energy per square

meter decreases

at lower sun angles

and shorter

daylight periods.

Q0

Which curve correctly describes the solar panel output power during a day?

Goal: why the earth temperature is around 300C?

--- a simple energy balance model

Q1

The earth will be a warmer place if

A) it is further away from the sun;

B) the surface temperature of the sun is lower;

C) the solar constant is bigger;

D) none of above.

Q2

Solar constant (1367W/m^2) near the earth increases if

A) the earth is closer to the sun;

B) The surface temperature increases;

C) Both a) and b) are true.

D) None is true.

Q3 (survey question)

The earth surface temperature is about 15C mainly because

A) Solar constant is 1367W/m^2;

B) Green house gases;

C) Thermal heat from the core of the earth;

D) Both A) and B)

Energy Balance

Incoming solar radiation power (depends on the value of solar constant, or how far the earth is from the Sun)

=

Outgoing radiation emitted by the earth

(depends on the earth temperature)

Power of the incoming radiation

Pin = (1-A) S π REarth2

Example from Roland B. Stull, Meteorology for Scientist and Engineers

Reflection coefficients or Albedo

• Overall average reflection coefficient of an object: Albedo

• Albedo of the Earth is about A = 0.3 which means that the Earth as a whole reflects 30% of solar radiation.

Radiation of the Earth

• Pout = σSurface TEarth4

Surface = 4 π REarth2

Earth Energy Balance Equation

A Simple model: Pin = Pout

Pin = (1-A) S π REarth2

Pout = 4π REarth2 σ TEarth

4

Q1

T4Earth = (1-A) S /4 σ

= (1- 0.3) 1367 W/m2/(4∙ 5.67∙10-8 W/m2K4)

The earth temperature according to this model is

• -100 C;• -18 C;• 30 C;• 100C.

• So we actually obtained a temperature of the Earth as seen from far away – the temperature of the atmosphere, not the surface temperature!!

• What are the effects of atmosphere ??

Atmospheric Absorption

• From: http://www.everythingweather.com/atmospheric-radiation/absorption.shtml

1

0

Earth Energy Budget Sheet