Mean Temperature Calculations

[Osbourne One-Nil]

Looking through my monthly records for October yesterday, I noticed a difference between how my Vantage Pro calculates the daily mean temperature, and how I would. Subsequently, this means my monthly mean temperature calculation differs from what the Vantage Pro tells me it is.

For example, on October 1st, the daily high was 12.7º and the low was 6.4º. I'd add the two together and divide by two, giving a daily mean temperature of 9.6º (rounded-up). However, the Vantage Pro gave it as 9.7º. The next day, the high was 13.4º and the low 8.2º, giving me a mean of 10.8º whilst the Vantage Pro gave 10.9º.

I know these are small differences, but they do add up over the course of a month. My main concern, however, is am I doing it right? If so, I'll simply ignore what the Vantage Pro says.

[johnholmes]

do it the way you are OON

[Osbourne One-Nil]

Lovely - thank you John. Not quite sure how Davis do it then, but then they're foreign so bound to be a bit odd.

I do use another piece of software which actually calculates the average temperature based on the readings at 5-minute intervals, which actually gives a more accurate indication of any given day, but I'll stick to my method.

Thanks.

[Les E]

HI Osbourne,

Thats the way I calculate means I add the minimum and maximum figures and divide by two,I seem to be in the minority as others seem to divide the mean maximas and mean minimas by two which gets a slightly differant result.

Regards Les.

[Nights King]

If you just add the min and max together and divide by 2 it can't always be that accurate?

What happens if you get 0c for 20 hours and around 10c for 4 hours would you say a fair average is +5c??

my software does every 5 mins which seems quite good.

[Osbourne One-Nil]

I've often thought it's un-representative, but I do it the simple way so it's directly comparable with everyone else. I agree that the 5-min thing is probably more realistic.

[Nights King]

Yes i find it a strange one.

We should do it for the whole year and see how a yearly average would pans out

new record low for example -25c with a mild year after and a max of 30c we could have a yearly average temperature of 2.5c

The low is abit extreme but u see my point.

[johnholmes]

I'm afraid your 'logic' is a bit out mate.

What you are taking is the Max each day, never mind how long that was recorded, and the Min overnight, again the same; for over 250 years this has been the way of doing it-I suspect that professional meteorologists, even with advanced data collection, will continue to use that system.

As to taking the Max each year and the Min and meaning it, that is pretty meaningless it seems to me.

So if you want your readings/averages to make direct comparison to professional sites then the 'old' way is the way to do it.

of course if you wish to do it a different way then its up to you but for realistic comparisons its no use suggesting a different way of doing it in my view?

[Nights King]

I'm afraid your 'logic' is a bit out mate.

What you are taking is the Max each day, never mind how long that was recorded, and the Min overnight, again the same; for over 250 years this has been the way of doing it-I suspect that professional meteorologists, even with advanced data collection, will continue to use that system.

As to taking the Max each year and the Min and meaning it, that is pretty meaningless it seems to me.

So if you want your readings/averages to make direct comparison to professional sites then the 'old' way is the way to do it.

of course if you wish to do it a different way then its up to you but for realistic comparisons its no use suggesting a different way of doing it in my view?

Ah ic so do you mean that the recording is taken from the highest temp that was recorded for longest period of time in the day and same for minimum?

Am i understanding this correctly?

[Terminal Moraine]

Ah ic so do you mean that the recording is taken from the highest temp that was recorded for longest period of time in the day and same for minimum?

Am i understanding this correctly?

No, Mullender, the highest or lowest temp' of the day might occur for only a few seconds but it is these readings which are taken as the daily max/min. These are then added, the sum is divided by two and the mean obtained.

Of course it could be argued, quite validly, that this is not the mean temp' for the day at all but is merely the point which is equidistant between the highest and lowest values of the day, but, in the days of recording before automatic stations capable of sampling every few seconds it was the best that could be achieved without an observer on site 24 hours a day to take readings every so many minutes or hours.

The most accurate mean temperature for the day ( or any other time span ) would be to make the maximum possible number of readings within that time span, sum the data and divide by the number of readings but the question then arises, how many readings are required to achieve an accurate mean? Is it every 60 seconds? every 10?, every 5? every second or every fraction of a second down to an infinitely small segment of time?

As John said above it's unlikely that the current method will be changed as it would render 300 odd years of records redundant as far as comparison is concerned. It's rather like the standard meteorological day which runs from 0900 to 0900 g.m.t. This was originally adopted in the early days of recording so that a gentleman was not obliged to sit up until midnight every day in order to finalise his day's readings. It might seem ludicrous than heavy rain falling in the early hours of one day will be accredited to the rainfall total of the previous day( or even the previous month if it occurs on the 1st of a month) but the crucial point is that, provided everyone sticks to the same system, all the readings are comparable and no problem arises.

[johnholmes]

tks TM-lucidly explained as always-you beat me to it this morning but thanks again

[Nights King]

Thanks for the in depth explanation.

Does this mean that anyone with a weather station must calculate it again after? I have virtual weather station pro which records it all and gives me avereages but i asume they are whole days recordings from 12 - 12 which means i must re do my last few months manualy.

Also on christmas day if it snows at 8am on the 26th (boxing day) that it is in fact a white christmas?

[johnholmes]

meteorology is never simple mate

re the snow=no it has to fall between 00 and 24 Xmas Day

that is how its been agreed

at odds with the rainfall stats but never mind

re the temps-depends which you want-the easy way using Davis etc or the climat way 09-09?

like I said meteorology is never easy or straightforward, or not often.

a great subject to follow though.

Edited November 3, 2009 by johnholmes

[VillagePlank]

The difference between the Vantage Pro, and OON's calculations look to me to be due to different rounding algorithms; OON, quite naturally, it appears, is using asymmetric arithmetic rounding, and the chances are that the clever programmers who wrote the software are likely using something akin to banker's rounding which, over time, reduces the error of asymmetric arithmetic rounding ...

When we think of rounding we, as we were all taught at school, round towards the nearest whole number, with five always rounded up. This is erroneous since there will always be an 'up' bias. For instance if every number is equi-probable, then 1,2,3, and 4 round down, and 5,6,7,8 and 9 always round up which means there is a 10% bias going upwards over a large data-set. This is a big problem - for instance, the entire AGW increase can be accounted for by such rounding bias - not to say it is, but it's certainly had to be accounted for (it has)

I suspect that the Vantage Pro uses either Banker's rounding (rounds to nearest number equally divisible by 2) or random rounding (rounding is determined by some predetermined random algorithm such that over a large set of data it might round up or down but over such a set it is equi-probable for either direction) If the designers were lazy they might even use truncation based rounding (just chop of the digit)

Of course, there's always the case that they might be rounding to significant digits and decimal places, too.