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Charts - Misc charts: Difference between revisions
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At least two times there was a discussion on the forum about the way the daily average for temperature was or should be calculated (see [https://cumulus.hosiene.co.uk/viewtopic.php?p=138513#p138513 here] and [https://cumulus.hosiene.co.uk/viewtopic.php?p=152909#p152909 here]). CumulusMX uses an ''integration method'' which means it samples the temperature continuously at the sampling frequency and stores the average of those samples at the logging frequency. It creates the sum of the logged entries and at the end of day it divides them by the number of observations giving the arithmetic average of all values logged which acts as an estimator of the physical average. | At least two times there was a discussion on the forum about the way the daily average for temperature was or should be calculated (see [https://cumulus.hosiene.co.uk/viewtopic.php?p=138513#p138513 here] and [https://cumulus.hosiene.co.uk/viewtopic.php?p=152909#p152909 here]). CumulusMX uses an ''integration method'' which means it samples the temperature continuously at the sampling frequency and stores the average of those samples at the logging frequency. It creates the sum of the logged entries and at the end of day it divides them by the number of observations giving the arithmetic average of all values logged which acts as an estimator of the physical average. | ||
Apparently the Meteorological Service of Britain does it still differently and does not use automatic measurement but takes manual readings twice a day and creates the daily average by <math>(Max+Min)/2</math> and the argument is that comparison with observations from before the computer era must be made. Note that the KNMI (the Dutch Meteorological Service) takes hourly measurements so there is no consistency between countries to start with. | <strike>Apparently the Meteorological Service of Britain does it still differently and does not use automatic measurement but takes manual readings twice a day and creates the daily average by</strike> <math>(Max+Min)/2</math> and the argument is that comparison with observations from before the computer era must be made. Note that the KNMI (the Dutch Meteorological Service) takes hourly measurements so there is no consistency between countries to start with. | ||
As an argument in this discussion this chart was made to make the difference between the institutional method and the Cumulus Integral Method visible. What is shown is the Cumulus Method Daily Average Temperature (one minute sampling): <math>(\sum_{minute=1}^{1440} {(Temp\ measurement)) \div 1440}</math>, the <math>(Max+Min)/2</math> and the difference between the two. It is clear that the first is the more accurate estimator of the two sample estimators (note they both are estimators for the statistic <math>average temperature of the day</math>). | As an argument in this discussion this chart was made to make the difference between the institutional method and the Cumulus Integral Method visible. What is shown is the Cumulus Method Daily Average Temperature (one minute sampling): <math>(\sum_{minute=1}^{1440} {(Temp\ measurement)) \div 1440}</math>, the <math>(Max+Min)/2</math> and the difference between the two. It is clear that the first is the more accurate estimator of the two sample estimators (note they both are estimators for the statistic <math>average temperature of the day</math>). | ||