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### #1 Asbytec

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Posted 16 October 2016 - 07:41 AM

This is a great light pollution map, and it has a nice feature with it. It gives a measure of radiance in W/cm^2 * sr.

http://www.lightpoll...&layers=B0TFFFF

Is there a way to convert radiance to an approximate calculated magnitude per square arcsecond to determine the sky brightness that may result from the indicated radiance value?

### #2 Jon Isaacs

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Posted 16 October 2016 - 10:19 AM

Norme:

Interesting challenge. One issue I see is that magnitude is a relative scale. Somehow one has to calibrate it. If you knew the radiance of the sun then it could be used but one has to be careful in keeping the definitions consistent, the radiationof the sun is mmeasured in terms of watts falling on a surface, surface brightness is a relative measure based on the area of the object.

What is sr?

The maps legend is somewhat confusing.. The sky brightness shows a black zone but it seems to be actually gray, the underlying map is probably gray.

Here's a couple of numbers:

- my house in North Clairemont shows as yellow which on the legend is listed as 3-6 x 10-9 watt/cm2 *sr.  A good night measure 18.7 MPSAS on my SQM-L.

- my house in Boulevard California shows as gray which I assume to be black and is listed as being < 0.25 x 10-9 watt/cm2 *sr.  It generally measures between 21.2 and 21.5 MPSAS on my SQM-L. The skies are dark but not super dark.

I suspect this map was made by taking a photo from above, I question the validity of doing this.  It shows you the local sources of light but it does not show how all the light from all sources integrates into a measure of the sky brightness. When I look at the local Indian Casino, it shows as being brighter than my San Diego backyard but that light is very local and I am quite sure that standing in the Casino parking lot I have a much better chance of seeing the Milky Way than I do from my San Diego backyard.

So thinking about it, I am not sure a conversion is possible.  The light pollution map appears to my eye to be a map of the radiance from a particular point on the earth, a Sky Brightness measurement is a measure of the brightness of the sky taken at that point on the earth, these are two different quantities and cannot be converted.

Jon

### #3 Asbytec

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Posted 16 October 2016 - 10:49 AM

Jon, I have no idea what the term sr is other than a unit of radiance. Magnitude being a logarithmic scale does need some sort of calibration, as does arcsecond to cm^2. But it seems like it can be done if it hasn't been done already.

My location shows the edge of an orange zone, but it does not seem to behave that way with yellow and green nearby. NELM 5.2 suggests 19.5 MPSAS which is a orange zone, but not sure how much NELM is lost due to astigmatism. So, kinda hard to really lock it down. It may be (have been) darker.

One reason I kind of want to use objective measurements, for whatever they are worth, is to determine whether new construction and LP encroachment is becomming a problem and I actually am in an orange zone, now, since earlier this year.

Had a great season last year, but it turned south beginning this year. Not sure whether its light pollution or humid climate related pulling NELM down to about 4.5 or about a red zone (not accounting for astig.) If light pollution, will consider moving.

Just anxious waiting for the monsoon to break to see whats up. Hopefully it will be the same as last year and I can stay put.

In the end, though, such a conversion could be helpful for many folks who want to get a second opinion on their sky brightness or a dark site nearby.

### #4 Asbytec

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Posted 16 October 2016 - 11:15 AM

Thinking further, if the radiance value is used to determine the Bortle class by clicking on a point, then a conversion is availble. Might find in the HTML source for the page.

Edited by Asbytec, 16 October 2016 - 11:16 AM.

### #5 Jon Isaacs

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Posted 16 October 2016 - 11:26 AM

Norme:

My point is that this map appears to be a map of the light sources on the surface of the earth. This is not a map of the light pollution that you would see standing on the ground looking up at the sky. An SQM-L measure the brightness of the sky, that is what we are interested in.

These are two totally different measurements and therefore cannot be converted from one to other. One is looking down at the earth's surface from above, one is looking up at the sky from below..

Even if one could convert the units, it would have no meaning,

Jon

### #6 Asbytec

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Posted 16 October 2016 - 12:25 PM

Understood. It may be a map of the surface albedo measured from space, as such it has to include any sky brightness, as well, possibly factoring out the surface albedo leaving only the sky brightness displayed.

Looking down through the pollution is not so different than looking up through it, except the background is different. Seem to remember there may have been some technical discussion about how sky brightness was determined a long time ago in this forum.

The idea of using the sun,s irradiance as a measure speaks to the right idea. It seems to be a measure of how bright the surface is looking down on it, probably the same method used in the map. But the suns irradiance at the surface does not inlude the sky brihtness above which is what we're after.

Somehow, though, there has to be a conversion from wattage per unit measure to Bortle zones. The map uses it to display the appropriate color and there is a scale shown.

You may well be right, though, Jon. I am not sure how it's done or what it actually measures, just guessing at this point. But, yes, we want the sky brightness as seen from the surface.

Edited by Asbytec, 16 October 2016 - 12:30 PM.

### #7 Asbytec

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Posted 16 October 2016 - 01:39 PM

Oh, I see what you're driving at. There is no scale between watts/cm^2 and magnitude. We dont know what magnitude 3 watts is at a distance that 1 cm^2 subtends 1" arc^2. We couldn't take 1" arc^2 of the moons avg albedo and convert it to watts?

Edited by Asbytec, 16 October 2016 - 01:43 PM.

### #8 Asbytec

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Posted 17 October 2016 - 06:21 AM

Jon, getting closer. Check out this chart. It seems to link many things together, from NELM to Mag/arcsecond^2 to even what looks like a radiance measure mcd/m^2 (which might be a SQM reading.)

That's a square surface area similar to the watts/cm^2 above. Now, if there was just a way to convert mcd/m^2 to watts/cm^2 used in the LP map, we might have a conversion to MPSAS.

Lux? Lumens? Candela? Foot candles? It's so confusing...

Still have to sort this looking up and down thing.

http://www.darkskies...ss-nomogram.gif

Edited by Asbytec, 17 October 2016 - 06:24 AM.

### #9 Jon Isaacs

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Posted 17 October 2016 - 10:07 AM

>>>>Looking down through the pollution is not so different than looking up through it, except the background is different. Seem to remember there may have been some technical discussion about how sky brightness was determined a long time ago in this forum.>>>>

On the contrary, I think it very different and the map shows this very clearly. The map is showing individual light sources and these are far brighter that the sky brightness. Looking down is a transmission measurement, looking up is a reflection measurement.

This is the reason for the seeming anomalies. According to the map there are places withina few miles of my place in the high desert that are as bright or brighter than my place here in San Diego. That simply cannot be a measure of sky brightness. One thing i learned as the child of a well known oceanographer was to look closely as the data and apply some common sense. Over the my years in science, thishas been valuable.

The units are a key, understanding the units means understanding something about the measurement. A radiance map has units of energy per unit area because that is what you measure with an aerial photograph. It doesn't measure the reflected light that you see looking up into the sky from below.

Jon

### #10 Asbytec

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Posted 17 October 2016 - 11:22 AM

I was hopeful the graphic above might hold a clue as it offered a measurement in units of area.

I gotta give this one a rest, I just dont have the math skill to work it. But I am convinced there is a relation with surface radiance (looking down) and sky glow (looking up.) Just don't know what it is.

Edited by Asbytec, 17 October 2016 - 11:42 AM.

### #11 Jon Isaacs

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Posted 18 October 2016 - 01:47 PM

I was hopeful the graphic above might hold a clue as it offered a measurement in units of area.

I gotta give this one a rest, I just dont have the math skill to work it. But I am convinced there is a relation with surface radiance (looking down) and sky glow (looking up.) Just don't know what it is.

Think about it..  it's a measurement issue.   If the sky were perfectly transparent with no reflection, I could be standing next to a bright light and as long as I was looking up,  I could not see that there was a light next to me, it would havr no effect on sky brightness. On the radiance meter,  it would measure its full brightness.

Ponder why it is that on the chart,  places where there is little light pollution and dark skies can have greater radiance than places with a great deal of light pollution.

In theory one could develop a model that would look at all the light sources within maybe 100 miles,  the geography,  the various properties of the various atmospheric layers etc and predict the sky brightness..   that would be an educated guess and rather complicated mathematically.

Jon

### #12 Asbytec

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Posted 18 October 2016 - 08:20 PM

Sure, we could use an standard atmosphere and somehow determine the amount of light reflected back down from all the surface lighting shining up. If we know the level of the surface lighting within some radius, especially by looking down on it, we could model how much we might expect to be driven back down to our eye.

We might have to measure the lighting and the albedo of the surface we see from above, as I believe the LP map does, or just a simple measure of total radiance as seen from space.  I agree, it's more straightforward to just measure the light that is raining back down on us. But, surely surface radiance can be modeled to that amount of light reflected back down by standard or average atmospheric properties.

I like the map above, even if it (or all models) might not be completely accurate. I especially like the radiance measure, I am thinking it might be as useful looking down on all those lights as measuring the sky itself with a meter, if we have one. The meter is more accurate, surely, and more real time. But, I don't have one.

"...places where there is little light pollution and dark skies can have greater radiance than places with a great deal of light pollution."

I have to ponder that. I can't get my head around why a dark sky would have greater radiance than a light polluted sky given the idea we're looking down on all of that light, much of which is driven through the sky as radiance from the surface. That light is traveling into space where we observe it, some of it is redirected toward the ground. In a dark sky, this is also happening, but at a much lower radiance because there are few things radiating at visual frequencies.

Once we get past all that, we still have the problem of converting units of surface area in cm^2 looking down to units of magnitude per arcsecond^2 looking up. And whether the units of either measure are even compatible. (I just went in over my head.

### #13 fsr

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Posted 01 October 2017 - 08:37 AM

Hi,

I was recently searching about this, and found that lightpollutionmaps.info did publish a response, but prepare to be dissapointed:

How do you convert VIIRS data to MPSAS (magnitudes per square arc second) or Bortle scale? What does W/cm2 * sr mean anyway?
W/cm2 * sr is a SI radiometry unit for radiance. Radiance is radiant flux emitted, reflected, transmitted or received by a surface, per unit solid angle per unit projected area. It sounds complicated right? Well that's because it is. Things get a bit more (actually a lot more) complicated if you want to do a simple conversion to MPSAS. I'm not even going to touch the Bortle scale issue because it is highly subjective scale. Anyway if you are still interested in a "conversion" I can try to explain the problem. Imagine you have a small light source aimed at the sky and this light source gets picked up by the VIIRS detector detector. The VIIRS detector is monochromatic and has its own spectral response curve. It has no idea of the spectral curve of the light source. MPSAS or more specific magnitude is a measure that is measured in a “specific wavelength or passband”. See the problem? That's one major issue. The other major issue is that light from the light source passes through the atmosphere and while doing this it scatters due to air molecules and aerosols. So you need to create a model of light propagation for the entire Earth taking into the account local air conditions, earth curvature, light absorption, Earth terrain and what not. You can read more about it here. If you got skills to do this and willing share the result I'll be glad to include it! If not be sure to check the World Atlas (WA 2015) overlay.

However, there is another site with a similar map, but with data from 2006 which was modelled and is available in surface brightness units.

This is the map: http://darksitefinde...maps/world.html

Data seems to come from here: http://djlorenz.gith...tronomy/lp2006/

And that data has this scale in magnitudes per square arcsecond: http://djlorenz.gith...006/colors.html

mag/arcsec^2 can be converted to mag/arcmin^2 simply by substracting 8.89

So, even if the data is old and light sources probably did change, and just a mathematical model based on satellite measurements, it does at least give an answer in surface brightness units.

Regards

### #14 jdupton

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Posted 01 October 2017 - 12:56 PM

fsr,

https://www.cloudyni...utionmap-sites/

In essence, there is no simple conversion between the two map styles and what they measure. In the above thread there is a link to the conversion methodology as detailed in a journal article but but it is computationally intensive and the most recent data dates from 2013 - 2014.

John

### #15 Asbytec

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Posted 20 October 2017 - 07:13 AM

Thank both of you for replying. A lot more complex than a rule of thumb that I thought might exist. It would be nice to have some actual data on radiance to predict sky brightness, but maybe the most efficient way is just to go look.

### #16 CrazyPanda

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Posted 24 October 2017 - 03:55 PM

This is a great light pollution map, and it has a nice feature with it. It gives a measure of radiance in W/cm^2 * sr.

http://www.lightpoll...&layers=B0TFFFF

Is there a way to convert radiance to an approximate calculated magnitude per square arcsecond to determine the sky brightness that may result from the indicated radiance value?

I know that this discussion has evolved somewhat, but that map actually does have an SQM in mag/arcsec2 option. No idea if that is actually referring to the sky brightness or not, but it does what you're looking for.

### #17 caveman_astronomer

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Posted 24 October 2017 - 04:38 PM

I would use the "radiance" data to identify places to try to avoid, if one is looking for dark skies or darker skies.

But, a dark-looking area with light-polluted areas in the immediate vicinity is obviously less desirable that one without.

SQM is obviously a very different measurement from the radiance, very loosely correlated, if at all.

### #18 Tele

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Posted 23 February 2018 - 12:38 PM

Found this thread by asking the same question, discovered this graphic which is a fun general idea type thing that gives me a ballpark idea of how different locations stack up to places I've taken measurements. I think just calculating your mag/sq sec using a DSLR and a histogram is a right way to verify.

### #19 Asbytec

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Posted 26 February 2018 - 08:10 AM

Yea, that's a great chart. Got it. Thank you.

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