I would love to give you my calculations, but I do not know how to upload pics or files (an excel sheet) here, so I would need advise with that too. Let me just describe how I get to these results.

I started with that information on the emissivity of water presented here:

https://scienceofdoom.com/2010/12/27/emissivity-of-the-ocean/

Then I wanted to have a function which would be in line with the measured data quoted there, so that i would not have guess the specific data points from the chart and insert those values in my excel sheet for every single degree from 0 to 90. The trial & error approach gave me those parameters: starting with 1.3105 and incrementing it at the power of 1.032 yields 99.94 at 90°. 100 – these results almost perfectly draws the curve I searched for.

This graph is actually very similar to the albedo or reflectivity of water, only inverted of course. And as I need absorptivity, I actually have to invert it.

As I was mainly interested in the geometric aspect, I ignored these minor differences and just weighted this function

a) according to the distribution of solar radiation, which apparently is one directional, only a small fraction of it will hit at the very low angles. For example the 80 to 90° range only accounts for 1 – sin(80)^2 = 3% of total light received. Thus low absorptivity at these angles play a minor role, and total hemispheric absorptivity would then be 93.95%.

b) according to the surface of a hemisphere, thereby representing all the possible directions radiation may go from the surface. The formula hereto would be 1 – cos(x) with x being the specific angle. In this case the 80 to 90° range would account for 17.3% of the total surface of hemisphere, and low emissivity at there angles would have a much higher weight. Total hemispheric emissivity would then be 84.39%.

If we assume that a perfect black body would have 280°K at earths position, then water should be (93,95 / 84,39) ^0.25 * 280 = 287.61°K

This figure is almost exactly the temperature earth has, and that would mean the oceans were causing the “greenhouse effect”, which then of course would not even exist. I must be wrong! What is my mistake?

]]>Great post – I needed a laugh this morning!

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