It won't be hard if the effects are as large as claimed in the original study.
The study shows minor effects at 1000 ppm and pronounced effects at 2500 ppm. I don't think changes in weather would drive your CO2 concentration to these levels.
And if you interpret the effect of weather as mostly open vs closed windows, there is a whole bunch of other factors in play like the balance of indoor and outdoor contaminants, etc.
I am sceptical of these results, anyway, they look too big. And the authors mention another study:
Researchers in Hungary have questioned this assumption (Kajtar et al. 2003, 2006). The authors reported that controlled human exposures to CO2 between 2,000 ppm and 5,000 ppm, with ventilation rates unchanged, had subtle adverse impacts on proofreading of text in some trials, but the brief reports in conference proceedings provided limited details.
which implied ("subtle") small effect size.
Why do you call the effects at 1000ppm minor? They are easily big enough to measure statistically with a realistic sample size for an observational study, even if the effect of weather on CO2 was only say a 5% change in P(windows open).
Opening my window moves CO2 levels in my room from around 1400 to around 400ppm.
I agree the results look too big.
One or two research groups have published work on carbon dioxide and cognition. The state of the published literature is confusing.
Here is one paper on the topic. The authors investigate a proprietary cognitive benchmark, and experimentally manipulate carbon dioxide levels (without affecting other measures of air quality). They find implausibly large effects from increased carbon dioxide concentrations.
If the reported effects are real and the suggested interpretation is correct, I think it would be a big deal. To put this in perspective, carbon dioxide concentrations in my room vary between 500 and 1500 ppm depending on whether I open the windows. The experiment reports on cognitive effects for moving from 600 and 1000 ppm, and finds significant effects compared to interindividual differences.
I haven't spent much time looking into this (maybe 30 minutes, and another 30 minutes to write this post). I expect that if we spent some time looking into indoor CO2 we could have a much better sense of what was going on, by some combination of better literature review, discussion with experts, looking into the benchmark they used, and just generally thinking about it.
So, here's a proposal:
Some clarifications:
(Thanks to Andrew Critch for mentioning these results to me and Jessica Taylor for lending me a CO2 monitor so that I could see variability in indoor CO2 levels. I apologize for deliberately not doing my homework on this post.)