Due to extensive damage to my face because of an accident, I am currently undergoing skin therapy (laser/IPL/medication), that makes my skin extremely sensitive to UV radiation. So I need to stay out of the sun, at the very least between 11:00 and 16:00, need to reapply sun screen every two hours, and generally be careful with exposure. Since that makes me hyper aware to the sun, perceived warmth, UV index and all that, it made me reasearch the subject.

I live in The Netherlands and the meteorology institute published real time UV measurements (as UV index) at https://www.rivm.nl/Onderwerpen/Z/Zonkracht However the UV index is defined as the amount energy that is radiated on the flat surface of the earth. As we humans generally have more vertical surfaces, especially sensitive surfaces like the face, would it not make more sense to not just measure in the horizontal plane? Especially during the evening and the morning the sun is at a low angle, so the (relative) energy on a vertical plane would be a lot higher than the above graph suggests.

I made a small program that parses this image, and recalculates the UV index for the vertical plain (divide the UV index by the tangent of (90 degrees minus current zenith angle). This would be the output (blue line is vertical UV index): UV index in vertical plane

  • $\begingroup$ One thing you have not considered is that at low angles (sunrise & sunset) light from the sun travels through a greater thickness of atmosphere than it does at noon. Because of this the higher frequencies of light, blue, violet & UV tend to be reflected more by the apparent thicker atmosphere. It's why sunrises & sunsets tend to be red, orange & yellow, which have the lower frequencies of light. Because of this less UV will strike any surface during low sun angles. $\endgroup$ – Fred Jul 5 '18 at 15:25
  • $\begingroup$ Hello Fred, I did consider this, but this is already part of the/measurement of the horizontal plane (the base graph). I do not need to compensate for that again, when switching to the vertical plane (the blue line). $\endgroup$ – rogerwilco Jul 5 '18 at 15:56
  • $\begingroup$ Do you think that your calculation overestimated or underestimates UV when the sun is at the angles lower than 45 degrees? I found this calculation easy and pretty good, it really does make sense. Overestimation isn't problem for me, sun safety should be everyone's priority. I made an excel calculation for personal use, with the outputs being the optimal exposure time for vitamin D production and maximal exposure time for skin damage. I can translate it and share it with you, I think you could find it useful. $\endgroup$ – lkn Mar 21 '20 at 20:18

To answer my own question: the principle is sound however the calculation does not work out, because it assumes only direct UV radiation, and not the real-world scenario of scattered UV radiation.


UVvertical Index = UVdirect Index + UVdiffuse

UVdirect Index (vertical) = cos(altitude angle)*(UVhorizontal Index)/(sin(altitude angle)+coefReflection)

UVdiffuse (vertical) = (UVhorizontal Index)/(sin(altitude angle)+coefReflection)*coefReflection*0,55+0,437*cos(altitude angle)cos(45)+0,313(cos(altitude angle)*cos(45))^2

Reflection Coefficient varies during the year, its average value is 0.1.


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