DavorJ
commented
4 years ago Drifts 15: Behaviour of median in function of x observations
To verify my concerns above about the median, I assume the KNMI series has perfect measurements and is always on the same altitude. Subsequently, I bootstrap its medians in function of the # of observations, and observe how they behave:
About 1500 observations (=2 years) are needed to reduce the standard error of the median pressure to +/- 1 cmH2O. Note that from analysis #53, based on the barometric formula, we know that 1 cmH2O corresponds to almost 10 m altitude change. So based on 2 years of pressure data our uncertainty of the median is about +/- 2 cmH2O (95% conf.), which is equivalent to an error of approximately 40 m in altitude.
In other words, the above analysis 14 is mostly useless once we take these expected errors of the median in function of the number of observations into account, since the differences between the medians are within the error margins due to the limited number of observations.
As a sidenote: the distribution of the medians doesn't seem to be Gaussian.
Drifts 14: differences in median pressure on the same location
In light of the subsequent analysis 15 below, this analysis is inaccurate and obsolete.
This is a preliminary analysis to compare barometers on the same location to see what effect the medians have on altitude calculation. Given enough data, I would expect the medians to be around the same pressure (and thus altitude). Something like this:
BAOL006X_179843 and BAOL006X_555569 also seem OK based on #51, although the former seems a bit jumpy at the end.
The altitude difference based on the medians is computed using barometric formula from #53 and should only be indicative.
These two match perfectly and are also perfect according to #51:
While in this case the difference is too high:
But both barometers are broken anyway according to #51.
The more interesting cases are the ones which are both OK according to #51, but which are off in this analysis. For example:
This could indicate wrong units. On the other hand I think I have too little observations to make any real conclusions. I think the analysis would be better if done based on offset comparison of the red line from analysis #51 or #57.
All the plots are available here.