## / What does the MET Office forecast mean?

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Hi, the Met Office forecasts split the day into 8 time slots and give a probability of precipitation in each slot. Often climbers would like to know not just the probability in a slot, but the probability over, say, an 8-hour period.

For example: A day's forecast is split into 8 time slots. If the probability of precipitation is 20% in each slot, I initially thought I should just simply add them up using:

P=1-(1-.2)^8

to give the probability (P) of rain in the whole 24hour period.

However I'm now thinking that rain can't always been seen as independent in each slot. For example a front comes through and dumps in the morning, then there is little chance of rain in the next time slot, however the timing of the front may have been unknown when the forecast was issued. This seems closer to a situation where there might be a near 100% chance of rain during the day (i.e. P=100%), but the chance in any slot is only P/8 = 12.5%, which most people would consider as indicating very little chance of rain, full stop.

Thanks for any help you can give. (I've sent an email to the MET Office asking much the same thing.)
"PoP is given in the 5-day forecasts for specific locations. Each line of the table in the forecast represents a 3-hour period of the day, and the Precipitation Probability is given as a percentage (%) to the nearest 10% - which indicates how likely it is that any precipitation will fall during that 3-hour period at the selected location."

http://www.metoffice.gov.uk/guide/weather/symbols

To work out the probability you need to use the system of maths in the last answer on this thread with each timeslot being a roll of the dice substituting the percentages as fractions instead of using the 1/6 of getting a 6 with each die roll.

http://mathforum.org/library/drmath/view/56502.html

ie if it was 20% in the first time slot and 30% in the second and 40% in the 3rd time slot and then dry all day

0.2 + (1 - 0.2) * 0.3 + (1 - ( 0.2 + (1 - 0.2) * 0.3 ) * 0.4 = 0.664

66.4% chance of some rain during the day.

In reply to David Coley: Sadly I have little grasp of the mathermatics, but I do know that if you are climbing in North Wales and there is a massive blob of red and yellow over the Irish Sea and Westerly winds here http://www.raintoday.co.uk/ you are very likely to get wet.
In reply to CurlyStevo: thanks. I understand the sum, but I'm not sure that the probabilities are independent. If the rain is from a front and rains at 9am, it won't rain at 11am.
There are a few more complications and the main problem is the way the met office tries to reduce the information down to probabilities rather than releasing the forecast at the more basic level - for the way you want to use this forecast so much information is lost and you'll not recover it by trying to understand the probabilities in this way.

Take, for instance, two different weather systems leading to the same chance of rain in a three hour period:

(1) a narrow band of rain with high positional uncertainty - you run loads of models, they are show the same narrow band but in different positions. You don't know where the rain is going to be and everywhere gets 30% chance of rain.

(2) a wide area of small scattered showers - you run loads of models showers pop up all over the shop "randomly" distributed and everywhere gets a 30% chance of rain.

In (1) if you get rain you are wet all day but if you are dry you stay dry (forecasts for locations are highly correlated in time) and in (2) you can't avoid the chance of rain but it will be short (uncorrelated)

Now the met office reduces this to a rainy cloud with a 30% but the experience for the climber can be completely different in the two different weather systems and they might modify their plans as a result, sadly, the met office forecast is pretty useless in helping you decide how to behave - it might pass the umbrella test (should I take an umbrella to work today?), it might tell you how many jumpers to wear but it is very limited.

This is where something like the MWIS is much more useful - the synoptic chart and commentary together with the detailed description enables you to understand what is coming and make sense of any percentages so in (1) you might change your destination based on last minute observations whereas in (2) you'll sit tight and wait for the dry to come along in a minute.

Another point where MWIS is vastly superior to many forecasts is they will tell you how reliable they think the forecast is - if it is unreliable they will say so and explain - this is really useful for mountain forecasts.

> (In reply to CurlyStevo) thanks. I understand the sum, but I'm not sure that the probabilities are independent. If the rain is from a front and rains at 9am, it won't rain at 11am.

You've never been to Wales, right?
> Now the met office reduces this to a rainy cloud with a 30%

You can still get the rainfall map, right? This is enough to distinguish between the two scenarios that you mention (and various others, I would expect). I didn't realise that the MWIS gives you confidence levels on their forecast, that would be useful!

Excellent explanation... can you simplify it and send it to the Met Office? Probably someone there might understand it
> [...]
>
> You can still get the rainfall map, right?

Yes, but not from the Mountain forecast... you have to do your own work making their effort next to useless if not dangerous

> ie if it was 20% in the first time slot and 30% in the second and 40% in the 3rd time slot and then dry all day
>
> 0.2 + (1 - 0.2) * 0.3 + (1 - ( 0.2 + (1 - 0.2) * 0.3 ) * 0.4 = 0.664
>
> 66.4% chance of some rain during the day.

No, this is the probability that it rains in one and only one slot.
The probability that it rains in one or more slot (ie the chance of some rain during the day) is 1-(1-0.2)(1-0.3)(1-0.4).

David Coley is undoubtedly right that realistically the probabilities will be conditional.

Have you tried the Rain Alarm app? It is quite useful.
The met office describes the probabilities in an independent way. Although I agree they probably arent.

The maths I linked is for rain atleast once in the period. If you rearrange it its the same as the formulae you linked.
> The maths I linked is for rain atleast once in the period. If you rearrange it its the same as the formulae you linked.

Sorry, yes, you're right, though my version is far simpler! I wouldn't like to write down your version fot 10 slots!

Interestingly if we do treat them as independent (i.e. P=1-(1-p(t))^8)

and p(t) = 10% for all 8 time slots, P=60%.

I would have thought that most people would think that if the forecast said there was only a 10% chance of rain in each slot then it was most likely to be a dry day.
> (In reply to Robert Durran)
>
> Interestingly if we do treat them as independent (i.e. P=1-(1-p(t))^8)
>
> and p(t) = 10% for all 8 time slots, P=60%.
>
> I would have thought that most people would think that if the forecast said there was only a 10% chance of rain in each slot then it was most likely to be a dry day.

Unless is was showery weather.

I agree that MWIS is infinitely superior and in retrospect it normally correlates much better with exactly what happened with the weather out on the mountain!

On another note, the Met Office changed their website a year or so ago.. It is absolutely shockingly designed. It can be very difficult to find even basic information. Does anyone find this? For what is effectively a government funded organisation, who commissions stuff like this? Do they actually do any proper user testing before releasing the website

Still no reply on this from the Met Office (except an auto generated email, and one saying they were passing it on).

Worked well yesterday. Forecast rain at 16.00, started raining at 15.45.
It needs to be remembered as well that precipitation can form as air moves across hills and topographical features - this is the microclimates - and this is where forecasters with local knowledge area like MWIS come in handy. You can look at the rainfall radar and see no rain coming in from the sea to Skye but depending on where you are on Skye it might be raining or it might not solely based on that local topography - in fact there are some places in Skye where you can actually see cloud and precipitation forming as it hits the cuilin.

> On another note, the Met Office changed their website a year or so ago.. It is absolutely shockingly designed. It can be very difficult to find even basic information. Does anyone find this? For what is effectively a government funded organisation, who commissions stuff like this? Do they actually do any proper user testing before releasing the website

Quite interesting http://www.metoffice.gov.uk/media/pdf/0/3/Disc_Log_006.pdf
> (In reply to Robert Durran)
> The met office describes the probabilities in an independent way. Although I agree they probably arent.

The Met office website does not describe the probabilities in an independent way, it makes no mention of inter-time period relationship and they are most certainly dependent.

> The maths I linked is for rain atleast once in the period. If you rearrange it its the same as the formulae you linked.

There is no point quoting to 3 sig fig (66.3% if I recall correctly) when you are only given 1 sig fig (nearest 10%) to start.

In reply to David Coley: I've hunted for years for good weather services... but it's all about the interpretation of the data, because all forecasts are based on the same data sets.

Unfortunately, you can't look at rain in one front as having any bearing on rain volume in another, it's a mathematical paradox unfortunately that we humans fall into all too often (like the swapping of boxes in deal or no deal, the removal of a box doesn't change the standing odds of you winning - it actually creates a new game.)

From the effect of topography on the weather we know that it rains 4 times as often in the mountains (I assume that's where you're climbing) as well as 4 times as heavily.

In lowland areas, the Met office is good for area forecasts, though I find yr.no (Norwegian weather service) to add more useful interpretation of the same data, particularly in smaller time windows - it also gives minimum and maximum anticipated quantity of precipitation. The Met Office do have that data, but it's of commercial value so you have to pay for it (quite how they think that's fair when we pay for it out of tax is beyond me).

If you're climbing in the mountains, for example, probably the best thing to do (and the most tedious, unfortunately) is get good at understanding synoptic charts yourself, and reading how a front behaves in terms of fronts arriving with clouds, and how the wind, barometric pressure and clouds change before rain arrives too (The Cloud book published by the Met Office is very good), as well as the microclimates around mountains, fohne effect, and warm air. Chances are you'll be far more accurate than the Met office eventually.

Personally, I never understood why there isn't in-valley radar in the busiest mountain areas, it would be of enormous value to so many people - likewise radio repeaters for open use, but that's another issue!

Or there's the other old adage:

"If you can see across the valley, it's going to rain. If you can't see across the valley, it is raining."

What you realy REALLY need however, and requires no knowledge or technology.. and is 100% reliable, is a weather rock.