Hypothesis

CO₂ data from a single CO₂ sensor suggests that I can consider the air in my living room ideally mixed (i.e. mixing is substantially fast that the concentration of CO₂ at any point in the room is roughly equal). However, to “proof” this hypothesis I decided to spend my monthly savings on a second sensor. First, I positioned the sensors next to each other to obtain a “base case scenario”, because the absolute readings of the different sensors might deviate due to measurement errors, differences in (auto)-calibration and probably other reasons.

Base case scenario

When we position the two sensors next to each other we see that the measurement values from both sensors match reasonably well, see Figure 1. There appears to be some offset in the slope, which is probably the result of different calibration values.

Figure 1: Parity plot for two CO₂ sensors positioned directly next to each other for a single day. Every minute a measurement is registered.

After a series of ~20 days I collected a vast amount of data which resulted in Figure 2. It is obvious that the deviation between the two sensors has increased. However, most importantly, the trend is still similar.

Figure 2: Parity plot for two CO₂ sensors positioned directly next to each other for ~20 days. Every minute a measurement is registered.

The first question that came to my mind whether the deviation between the two sensors increases as function of time. However, it turns out that this is not the case, because the first day of measurement (blue) and the last day of the campaign (yellow) in Figure 3 perfectly overlap. The deviation was bigger hallway during the campaign (red) in Figure 3.

Figure 3: Parity plot for first day of measurement (blue), after ~10 days of measurement (red) and after ~20 days of measurement (yellow). Every minute a measurement is registered.

Sensors at different locations

After the initial campaign I positioned the second sensor at a different position in the room. One would expect the sensors to give the same reading, provided that mixing within this room is relatively fast. Ideally, the sensors are placed as far away from each other as possible, but there are practical considerations here at play as well. The sensors need a power socket and they have to fulfil the WAF criteria (Wife Acceptance Factor). I did my best. A schematic representation of the sensors positioned in the room is depicted in Figure 4.

Figure 4: Schematic representation of the room with sensor one in blue (default location) at a height of ~2 m and sensor two in red at a height of ~0.5 m

Figure 5 shows the CO₂ measurement for a randomly selected day at the two different positions in the room. The trend is very similar and the absolute deviations are probably within the sensors error margin as displayed in Figure 2. This observation gives a proper confirmation that the air in my living room is properly mixed.

Figure 5: CO₂ profile as function of time for two sensors positioned as depicted in Figure 4. Every minute a measurement is registered.

Alternatively to Figure 5, I created a parity plot, by now you must have recognized that I kind of like these type of plots. This plot, Figure 6, essentially provides the same message: both sensors typically give a very comparable reading and thus the air in this room is well mixed.

Figure 6: Parity plot for two sensors positioned as depicted in Figure 4 for a single day. Every minute a measurement is registered.

Figure 7 shows a parity plot for a campaign of 20 days. Although not clearly visible the majority of the measurements falls between the parity and dotted line. Or is at least close to these lines. Yes, the spread is more than when the sensors are positioned directly next to one another (Figure 2), but it still confirms that the air in the room is well mixed. There is also a bunch of data deviating. I suspect that big deviations emerge when there is a “source” (i.e. a person) is close to one of the sensors (but obviously not to the other one).

Figure 7: Parity plot for two sensors positioned as depicted in Figure 4 for a campaign of 20 days. Every minute a measurement is registered.

To conclude, yes, my living room is pretty well mixed.