More meteorological shenanigans

So after I published yesterday's post, I saw something from /u/starfall-invoker on reddit that points out that the PSI is a piecewise linear function. Initially I dismissed that as not being relevant, but after seeing the data for the last few days over a larger sample size:

I'm forced to concede otherwise. Let's work our way through this slowly.

PSI vs PM₁₀

The PSI is a piecewise function of the PM₁₀, as detailed in this paper. Actually, it's the maximum of several indices, including the PM₁₀, but at the moment the PM₁₀ is most pressing. It looks something like this:

Why anyone would want to represent data using such a conversion function is beyond me. I mean, it's neither properly convex nor concave. But I digress.

Results

Using this conversion function to rebuild our hourly estimates of PSI, we obtain the following:

Compared with yesterday's initial data, the key features on the first graph remain the same. I attribute this to small sample size, and stand by my earlier statement that what results we did obtain yesterday were ultimately inconclusive. Once again, although there does look like some kind of period-3 cycle going on, in the absence of further data, it is impossible to conclusively determine that it exists.

However, we notice that, as far as the rest of the data is concerned, using the PM₁₀ and backconverting to PSI eliminates obvious period-3 cyclic instabilities. In other words, yes, it is inaccurate to directly obtain hourly PSI estimates from 3-hour averages if the readings cross breakpoints at any time. This is clearly the case with today's data. So, to pre-empt howling from the general direction of EDMW, the NEA is not evil, and the hourly PSI is not negative.

Again, in the interest of independent verification, I have uploaded my calculations for Mathematica.

Finally, the PM₁₀ metric includes the PM_2.5 metric. That is to say, PM₁₀ already accounts for particles that are also represented by the PM_2.5 metric. The use of the former is not meant to give a misleading picture of the latter.¹

EDIT: Chuyong has quite kindly included the new data in his page.

EDIT2: Fixed broken link