Update: I see that someone else had the same idea here. Copying that plot, here is a plot of the 3 hour averages (in red) and 1 hour inferred averages (in blue) for June 20 from 6am to 5pm. Though the 3 hour average high of 371 at 1pm set a new record, the peak 1 hour average wasn’t that much worse than yesterday, about 467 by my calculation.
Singapore is obsessed with numbers these days. Well, one number in particular: the pollutant standards index or PSI. PSI measures the concentration of particles of diameter 10 micrometres or less in the air, that is about one-seventh the width of a human hair. A PSI value of 50 is fairly normal in a city these days. Over 100 starts to become noticeable and unhealthy, and above 200 feels like sitting next to a campfire with the wind blowing in your face.
The National Environment Agency hourly publishes PSI values for Singapore averaged over a 3 hour period. Because of fires in Sumatra the PSI levels have been elevated all this week, and last night (June 19) the PSI reading at 10pm hit a Singaporean record high of 321 (update: since broken with a 371 today). What I found even more remarkable, however, was that from 8pm to 9pm the 3-hour average jumped from 190 to 290. Since these readings share two data points, this means the jump from the 6pm reading to the 9pm reading must have been 300 points! The averages throughout the afternoon were mid-100′s, so it stands to reason that the 9pm reading was in the mid-400′s.
For some more fun, we can try to work out all the hourly averages from the 3 hour averages. Here is a table of the 3 hour averages from yesterday June 19 (currently found on the wikipedia page about PSI).
We have more unknowns than equations, so we will have to make some assumptions to calculate the hourly values. Notice that in the morning the PSI readings are fairly flat: 77, 78, 80 at 6am, 7am, and 8am. Here the 6am value is the average PSI in the time period 3-6am. The two assumptions I will make are that the hourly values from 3-4am and 4-5am were 77. Of course, this means that the 5-6am value is also 77 since we know that is the 3 hour average. With this assumption we can set up a set of linear equations and work out the hourly averages for the rest of the day.
For example, to figure out the hourly values from 6am to 11am we have the following matrix equation.
The hourly PSI average from 8-9pm, where we saw the spike in the 3-hour average, was a whopping 452. This is in line with the prediction from our simple reasoning above. The results are quite robust to assuming different values in the early morning—if the 3 hour averages are correct, it looks like in any case we must have gotten over 400 in the 8-9pm period!