Andrew–
I appreciate this attempt to briefly summarize the differences between the CF_1, CF_ATM, and ALT-CF3 algorithms. However, the difference between cF_1 and CF_ATM can not be simply a different density of indoor and outdoor particles. If that were the case, the two algorithms would differ by a constant factor, the ratio of the two densities. But in fact, the two algorithms differ in a very weird and mysterious way. First they are identical for all PM2.5 concentrations less than about 28 ug/m^3. Then at higher concentrations, strangely enough, the CF_ATM values increase more slowly than the CF_1 values. Finally, another miracle occurs at about 78 ug/m3, at which point and at all higher values the ACF_ATM algorithm remains constant at almost exactly 2/3 the value of the CF_1 algorithm (or equivalently the CF_1 is about 3/2 (1.5) times the CF_ATM algorithm.
If someone could show me an actual physical process that behaves in this way, I could nominate him/her for the Nobel Prize. Lacking that, I have to assume the following:.
I speculate that Plantower was aware that their sensor was overpredicting PM2.5. A number of studies have shown that CF_1 overpredicts PM2.5 by 50-100%. Since they could not create a new sensor, they decided to create a second algorithm, which would read lower–say 50% lower. Hence the creation of CF_ATM. It is clear that the entire relationship is just a mathematical construct with no physical reality. For unusually high concentrations, however, it does produce estimates that are closer to the actual values. But for the great majority of concentrations, it just gives us the same overpredictions of CF_1.
I hope some day PurpleAir will toss aside CF_ATM. And then, for good measure, (pun intended), CF_1 could follow its twisted partner out the door.