Sky Quality Data and Analysis with SQM-L

[Captain Scarlet]

Last year I was given a Unihedron SQM-L, the narrow field of view version of their gadget for measuring night-sky brightness. Since then, I’ve nipped outside to take zenith readings whenever I’ve been able, often a few times per night. As a result I now have 85 data-points, all from my back garden in Sunbury on Thames which rates a 19.04 on www.lightpollutionmap.info . As it turns out, this agrees well with the data I’ve collected.

The darkest I’ve measured at this location has been 19.13, with 4 records better than 19.05 and 10 better than 19.00.
Plotted against Moon altitude, it looks like:

One thing I noticed very early on was that the reading generally gets darker and darker as the night goes on. The chart below suggests the data agrees, but how strongly I’m not adept enough yet with my statistics to work out. If anyone fancies doing this for me, I’d be grateful, I’ve attached the data .csv file I think to the end of this post.

The data itself: each record contains date, time[GMT], SQM value, Moon phase, Moon altitude . For the purposes of my analysis, I’ve converted the time value into hoursafter6pm, which allows the intercept of the regression solution to be loosely considered as the “6pm starting point” for the darkness estimation, which is OK for this dataset as my data is all from this latest Autumn/Winter.

I’ve done an “ordinary least-squares” regression with multiple input variables. At first glance it seems to me that the SQ vs altitude chart above should not behave well with that: there’s a clear kink, intuitively obvious I guess, at the point the Moon altitude goes negative.

To cope with that, I divided my data into two and did three separate regressions: “Moon up” data, “Moon down”, and “All data” but treating phase and altitude as zero if the Moon is below -5 degrees (I chose -5 degrees arbitrarily).

With Moon up, I decided the SQM value will depend on Time of Night, Moon Altitude and Phase. With Moon down, it only needs to depend on time of night.

Thus my regression model is:

SkyQual = a + b.timeafter6pm + c.phase + d.altitude + residual

or rearranged

residual = a + b.timeafter6pm + c.phase + d.altitude – SkyQual

The analysis involves minimizing the sum of (the squares of the) residuals, by hunting around for the appropriate values of a, b, c & d which yields this minimum. I used MS Excel’s built-in Solver to do the “hunting around”.
The following table summarizes the results:

In words, using “Moon Up” as my subject, my Sky Quality, in magnitudes per arc-second, can be estimated as

19.28 mags/arc-sec
plus 0.0314 /hour
minus 0.864 /full-phase (or 0.216 /quarter)
minus 0.0186 /degree above horizon (or 0.186 /10 degrees).

This is a pretty simple analysis. I’m sure there’s theory and formulae available relating Moon-altitude and -phase to extra sky brightness, but I haven’t used any of that here. And the “error model” I’ve used implicitly assumes that the relationships between SQM-reading and the variables are linear.

If anyone is curious and wishes to do their own analysis, my raw-ish data is available as a .csv file attachment at the end of this post.

Cheers,

Magnus

 

A note about the data collection: each reading is an average of a few readings at a given time, with outliers rejected. For instance, often the first press yields an outlier, and over the following few seconds subsequent ones tend to settle down. So the series of readings 19.05 (me getting excited), 18.85, 18.86, 18.86 , which is a quite typical pattern, would cause me to record 18.86. My highest recorded reading, 19.13, was indeed where it settled down.

Other “one-on-one” charts:

   

SQMLdata201903.csv

[vlaiv]

Just a couple of remarks from me:

- did you account for astronomical darkness in your readings? Check out this website for astronomical darkness times on particular dates for your location:

https://www.timeanddate.com/sun/serbia/novi-sad

(link is for my town, but you can select your location on top) - note that for my location, astronomical darkness starts at 17:45 only for a few days in December - rest of time it starts past 6pm, so depending on this, you might want to exclude some early measurements.

- Looking at the plot of SQM vs time (past 6) with moon down - its obvious how much human made LP contributes - notice the dip 3-4 hours past 6pm - which corresponds to 9-10pm - time when most people keep their house lights on in the evening.

[Captain Scarlet]

Thanks Vlaiv.

29 minutes ago, vlaiv said:

Just a couple of remarks from me:

- did you account for astronomical darkness in your readings? Check out this website for astronomical darkness times on particular dates for your location: ...

Yes I did, by omission ... I checked that for (almost) every record, the Sun was >16 degrees below the horizon, so decided to ignore the Sun's elevation as a factor. I say "almost" because there are perhaps 2  is one record where it was 13.5 below the horizon, but I decided the effect on the totality of my results so far was likely to be too small to bother re-doing all the numbers. As I gather more data further into the spring and summer, I'll have to add sun elevation as an input too.

I have built myself a calculator to be able to compute star and planet positions for any time and any place, in fact that's how I derived my Moon phase and altitude data here. I used a site very like the link you supply to check it whilst developing it ... I posted about it a while back (search for "building my own sky stargazers lounge").

In fact in relation to that link, I'm Safety Adviser at my rowing club, and part of the rationale for "building my own sky" was to be able to produce a chart just like that, of when rowers must put lights on their boats, ie when the Sun is +/-3 degrees from horizon.

 

[knightware2]

Hi Captain,

Very interesting experiment. I hope you can continue a bit longer before the summer time brightness interrupts.

As regards the outlier readings...

As I understand it, the meter continuously integrates data. The darker your sky, the longer it takes to integrate a reliable reading. Depending on how long you point the meter at the zenith, your first reading or so may definitely be statistically 'bad'. I hope that makes sense. Anyway, an average of multiple readings is a good idea, and outliers are a possibility.

I hope you'll post here on your progress.

- Phyllis

[devdusty]

Very interesting but what does it indicate in visibility of stars with the naked eye and their magnitude.?

Chris P

 

[laser_jock99]

The SQM-L is a great idea although I found (in a dark sky site) the results were somewhat variable. Point it near the Milky Way or a brightish star and a 21.8 sky suddenly becomes a 20 sky- such is the sensitivty. In the urban setting they are more consitant. Your idea of taking multiple average readings is a good one. Long term it will also track if your sky is changing in any way. Keep going!

[Captain Scarlet]

13 hours ago, devdusty said:

Very interesting but what does it indicate in visibility of stars with the naked eye and their magnitude.?

Chris P

Generally the time it takes me, or I have available, to get an SQM reading is too short to look around and decide on the dimmest star, so thus far I haven't got any NELM alongside to compare. The purpose of this to start with was to see how my area compared to lightpollutionmap.info and how variable the brightness readings are.

[Captain Scarlet]

6 hours ago, laser_jock99 said:

The SQM-L is a great idea although I found (in a dark sky site) the results were somewhat variable. Point it near the Milky Way or a brightish star and a 21.8 sky suddenly becomes a 20 sky- such is the sensitivty. In the urban setting they are more consitant. Your idea of taking multiple average readings is a good one. Long term it will also track if your sky is changing in any way. Keep going!

Yes I was in our place in SW Ireland very shortly after I got it, the place is supposedly 21.8 by lightpollutionmap.info . I did notice precisely what you say, MW or stars affect the number quite a lot, in which case to collect data one might have to find a patch away from zenith...