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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