Name:__Master   Correction  _                                                                             GEO 302c

                                                                                                                        Lab 1

 

Climate:  Past, Present, and Future

Lab#1: Energy Reflectance and Absorption

 

Definitions:

 

Blackbody: A blackbody is a hypothetical body (a coherent mass of any material) comprising a sufficient number of molecules absorbing and emitting electromagnetic radiation in all parts of the electromagnetic spectrum so that

 

·        all incident radiation is completed absorbed (hence the term BLACK), and

·        in all wavelength bands and all directions the maximum possible

       emission is realized.

 

Solar radiation: Solar radiation is comprised of electromagnetic waves having magnetic and electrical properties.  They do not need molecules to propagate them.  In a vacuum, they travel at a constant speed of nearly 300,000 km (186,000 mi) per second -- the speed of light.  Solar radiation releases "heat" energy when it is absorbed by an object; this energy released from earth into space is in the form of infrared energy.  By the Law of Conservation of Energy, flux in is equal to flux out.

 

Albedo: The albedo of a planet is defined as the ratio of reflected, or outgoing, solar radiation to incoming solar radiation. Snow has a high albedo, hence, a greater capacity to reflect light than say, a woodland forest, or a rocky desert.

 

 

 

                                               

 

Case 1: Blackbody Earth

 

Consider a spherical planet “Earth” with no atmosphere. Energy from the sun (solar radiation) pours down onto earth and is reflected back from the surface as infrared light.

 

The amount of energy coming into the planet is given by

 

Flux In = (1-a) pr2S

 

where:

a=albedo (reflectivity)

S = intensity of sunshine, 1380 W/m2

r = radius of a circle

pr2 = the area of the circle onto which the sun’s radiation falls

 

Assuming this “Earth” is a blackbody, the Stefan-Boltzmann law describes the rate of energy being lost by outgoing infrared light as a function of surface temperature, by

 

Flux Out = 4pr2 sTe4

 

Where:

s = Stefan-Boltzmann constant, 5.7 x 10-8 W/m2K4

Te = Temperature of the earth’s surface

4pr2 = the area of a sphere (Earth)

 

Since the radiation flux in must equal the flux out, we can write

 

(1-a) pr2S = 4pr2 sTe4

 

and simplify this to

 

S(1-a)/4 = sTe4

 

Problems:

 

1. Express your answers in degrees Kelvin (K)

 

a)      Calculate Earth’s equilibrium temperature Te for an average albedo of 0.33.  Why is the temperature lower/higher than the observed average temperature of about 16°C or 289.15 K ?

 

b)      Calculate the Earth’s equilibrium temperature Te during a glacial period, where albedo = 0.75.

 

2.  On any available computer, go to the website

 

http://www.worc.ac.uk/Departs/Envman/Staff/Rowland/ums/env/mec/Models/albedo.html

 

Read the pop up window, “Hints on Using the Model”. 

 

Using the albedo values given for different landscapes, calculate reflected energy out for the following:

 

a)      average earth

b)      equatorial marine environment

c)      the Sahara Desert

d)      alpine forest

e)      Antarctica

 

Bonus:

f)        White Sands, New Mexico (gypsum sand known for its bright white color)

g)      What would you guess is the typical range of albedo values for Austin, TX and the surrounding area? You may use a range, i.e., more than one, of albedo values if you feel it is appropriate. Please include an explanation.

 

Notes

·        “Energy In” should remain a constant, 1370 W/m2

·        Please use only albedo values listed on website.

 

Answers for Question #2

 

Environment

Albedo Value

Energy In

Energy Out

a) Average Earth

 

1370

 

b) Equatorial Marine

 

1370

 

c) The Sahara Desert

 

1370

 

d) Alpine Forest

 

1370

 

e) Antarctica

 

1370

 

f) White Sands, NM

 

1370

 

g) Austin, TX

 

1370

 

 

 

 

 

 

3. Thought Question:

 

Knowing what you know now about solar radiation loss to reflection, and it’s dependency on the albedo of the planet…

 

a)      Would you expect the temperature of an ice-covered planet to increase or decrease over time? Why? What would be the result of this trend?

 

b)      Give some brief reasons other than the albedo as to why the Earth’s mean temperatures fluctuate through time. How is the Earth able to recover from extensive periods of glaciation or greenhouse conditions? A full treatise on the dynamics of Earth’s climate is not necessary, just a few brief observations taken from readings and lectures as to why the “Blackbody Earth” is not a complete picture.