Twilight Derivatives

Since change is the nature of the universe, I'm always interested in looking at how things change.

Measuring how things change is simply looking at the difference between two adjacent data points, either in time or space.

In the case of looking at twilight, I'm interested in seeing how the brightness changes as a function of time.  If you want to put this in terms of motion, the dimming of the sky after sunset is a lot like a velocity.  I can calculate the 'velocity' of the dimming by calculating the derivative, or difference, between two adjacent points in time.

I also like to make various forms of spectra -- also called 'histograms'.  I can make a spectrum of the velocities, and then break them up in time so I can see how the brightness is changing at different times of night.

Here's a recent sunset (x-axis is hours after sunset, y-axis is ADU):

and here are the differences for the same time period:

Notice that the 'velocity' is negative when the brightness is dropping, just as expected.

Here's the entire night's derivatives (x-axis is hours after sunset, y-axis is in ADU per 10 seconds):

I can then divide this up into 1000 second (16m 40s) chunks, and make a spectrum (histogram) of the derivatives:

times goes left to right, top to bottom.

At this point, I'm just looking at the data in as many ways as I can think of.  I'm not interested (yet) in understanding or explaining what I'm seeing with this data.

Maybe there's nothing interesting at all.

One thing I definitely want to do is a running average to smooth the derivative plot a little to see if there's any underlying structure.  If you look at the darkest part of the plot you get an idea of how dynamic the velocity is.

So yeah the velocity is changing, too.