• Paul C. Peh

Albedo And Greenhouse Gases

Much is known today regarding the negative effects of greenhouse gases such as carbon dioxide, methane and nitrous oxide. But without them, earth's surface temperature will be too low to sustain life.

There are some large numbers to think about when we deal with objects as big as our sun. The average solar radiation ( electromagnetic wave) arriving on earth is approximately 1361 watts / meter squared. Since our earth's surface area ( a spherically shaped surface) is 4 times the surface of a 2-D disk per given radius, r ( pi*r squared versus 4*pi*r squared), we need to divide that number by 4. So, 1361/4=340.25 watts /m^2. Applying the Stefan-Boltzmann equation for all black-body objects, we can conclude that the EM energy absorbed by earth is equal to the radiation emitted by earth. Also, we have to take note of an effect called albedo, or percentage of heat being reflected back to space by an astronomical object like earth, which very much depends on the type of surface. Ice, on the arctic circle, is nature's best albedo. As for earth, it is roughly 30%. Hence, only 340.25 * 70% or 238.175 watts/m^2 are absorbed by our earth's surface. By applying the Stefan-Boltzmann and Wien's Law,

238.175= radiation emitted by earth= Stefan-Boltzmann constant*T^4.

Hence, T^4= (238.175 watts /m^2) / (5.670367*10^-8 wm^-2K^-4).

=> T^4= 4.20035*10^9

=> T= 254.578 Kelvin or -18.5 celcius or -1.42 Fahrenheit.

That's cold!!!!! Thanks to clouds ( and gases) and their greenhouse effect, our earthly average temperature is about 15 celcius or 59 Fahrenheit (288.15 K) and not below freezing point. That's a difference of 33.57 Kelvin!

Another good example of greenhouse effect is by comparing planet Venus and Mercury. Albeit being closer to the Sun, Mercury's surface temperature is cooler than Venus's. Venus's atmosphere is made up of almost 96 % carbon dioxide, which suffice to say it traps almost all the heat it absorbed from the sun. Below is a comparison of equilibrium temperatures calculated using the Stefan-Boltzmann and Wien's Law of our 4 inner planets against their actual surface temperatures.

Earth and Venus shows the largest discrepancy as the black-body radiation laws did not take into account the effects of greenhouse gases.

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About Me

I was born and raised in Penang, Malaysia. I came to the U.S. to pursue my undergraduate studies at The College Of Wooster in Ohio. I moved to Hawaii in the early 90's and attended the University of Hawaii at Manoa for my graduate studies. In 2005, I became a naturalized U.S. citizen. Hiking and outdoor photography are some of my favorite past times. All photos presented in this site were taken by myself or by my spouse, Rosemary, with a Canon 5D MK III, Sony 7R IV, DJI Inspire drone and Apple Iphone. Welcome to my personal website!

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