I'm working on adaptive thermal comfort (CIBSE TM52 / TM59). Calculating the running mean temperature using the formula Trm= 0.2Te(d-1) + 0.16Te(d-2) + 0.128Te(d-3) ... is giving me values for Trm significantly lower than the previous daily averages (Te(d-1), Te(d-2) etc).
From the formula this makes sense as we're adding 0.2 + 0.16 + 0.128 etc which is significantly less than 1.
But intuitively, this doesn't make sense. Shouldn't the running mean temperature be much closer to the previous few days' mean temperatures?
In fact, the exponentially weighted running mean temperature proposed by Nicol and Huphreys (see attached file) converges very slowly. For the recommended value α=0,8 (the one you used), the sum of the first 33 coefficients is 0,84, and the sum is only 0.75 if limited to the 10 first members. However, if the "simplified" formula
Θrm = (1- α)Θed -1 + α. Θrm-1
is used, the running mean temperature tends to the the average temperature after about 20 days if the dayly mean temperatures are constant. If the dayly mean temperatures increased in the past days, the running mean temperature is larger than the average temperature of the past days. At the contrary, if the dayly mean temperatures decreased in the past days, the running mean temperature is smaller than the average temperature.
Conclusion: Use the so-called simplified formula, introducing the dayly average temperature of the first day for Θed -1and the average tempertaure of the first two days for Θrm-1 in the first use of the equation above.
Yes, the running mean outdoor temperature is usually lower than the daily average outdoor temperature. This is because the running mean is a cumulative average of all the previous temperatures, and as such, higher temperatures from earlier in the day will eventually be brought down by lower temperatures later on. Additionally, this phenomenon is also affected by factors such as time of day and local weather patterns.