January 2015 CET forecasts

[Roger J Smith]

Probability theory suggests the following:

 

In a situation where you assume a steady variable climate, after 243 years of data (we are in year 244) the chance that any given day will break the existing record (either way) is one in 244. The chance that a month will see one daily record is a complex calculation that goes like this: each day has a 243/244 chance of not breaking a record. Therefore the chances of no record in a month is that statistic to the power 31. This works out to about 0.95 so that there is a 5% chance of a record high (same for a low) during the month. In pure mathematical terms, this means there is about a 1% chance of two (as we saw last month).

 

Now as to that record high being higher than all 31 of the existing values going in and not just the date itself, that probability is not governed by random distribution (realizing that random distribution is already compromised by an apparent long-term rising temperature trend). However, if we assume a bell-curve distribution of daily records around a mean for the month, then I would estimate from tables that the chance of the record high being all-time (all days) is about one in twenty or 5%. So in the 5% of months where random chance gave you a record daily high, then that would be 5% likely to be all-time, and so the chance overall is 0.25%, or 1 in 400.

 

These chances are obviously altered by the slow rising trend in temperature. A theoretical calculation is more difficult there, and an inspection of the number of record highs per year gives an easier approximation. I have such a table drawn up in the link below (historical weather section). From this I would say the actual chance in the climate we have recently is more like 7% now for one record high being set in each month and has dropped to 2 or 3 per cent for record lows to be set. This probably means that the chance of a new all-time record high is closer to 1 in 200 than the flat-trend 1 in 400.

 

The chance of a new all-time record low is almost negligible in the situation of a rising trend, and can be classified as too small to quantify (around one in a thousand or less).

 

In reality, climate does not present us with random coin toss data, record highs come in clusters, as you'll see in the same link scanning down the dates of record highs and lows, there are multiple cases where several fall consecutively or close together. For example the last six days of Jan 1776 are all date record lows. There was a longer consecutive string in the June-July 1976 heat wave. Groups of two or three are fairly common and constitute almost half the total data. This probably means that the actual chance is a bit lower since the assumption of one record high may be a sort of hybrid of the chance of one or two.

 

The frequency over any given 30 year period will adjust to the trend but with more years in the data set the chance naturally falls off slowly, so at some point in an upward trend that is not too marked, probability will flatten out. Otherwise it would always be dropping. The reverse would be true for the cold records, those will remain elusive but as time goes on, their elusiveness will intensify as the trend takes them further out of range.

 

That being said, the chance of Friday breaking a daily record is about 70% and an all-time record about 30% based on model output.

Edited January 6, 2015 by Roger J Smith

[BlueSkies_do_I_see]

Thank you for the answer! I didn't realise the mathematics behind it. Fascinating.

Edited January 7, 2015 by BlueSkies_do_I_see

[The PIT]

Are you sure about that Rodger there are 365 days in a year bar a leap year. So any of the days can break a record. Can't see where 244 comes from unless you're referring to years CET has been running.

[Summer Sun]

Up-to 5.4c to the 6th

 

1.9c above the 61 to 90 average

[TonyH]

Early on yes but I feel this month too will struggle to be below average. 

[Lettucing Gutted]

Early on yes but I feel this month too will struggle to be below average. 

I think we can already rule out a below average month.  Once the near record/record warm days have been fed in to the monthly CET data, we will be looking at a "record warm month or not" situation again unfortunately.

Edited January 7, 2015 by Craig Evans

[ItNeverSnowsInWindsor]

Unless we get a severe cold spell in the last 10 days....

Edited January 7, 2015 by prolongedSnowLover

[Roger J Smith]

Concerning the number 244 -- we are in the 244th year of CET daily records. Thus going into each day, if the temperature series is entirely random, the chance that any given day will set a record is 1/244. The rest of the discussion follows from that. The reduction ad absurdum example would be 1773, year two in the series. Each day would have a 50-50 chance of setting the new "record" at that point. Then the following year, each day a 1/3 chance, etc.

 

The probability will only involve numbers like 365 or 366 when we reach that number of years in the record.

 

Given that there is a 5% chance of a record high falling in any given month, that works out to a 46% chance that one or more will fall in a given year. Let's test that against the reality of the records in the table posted in my CET historical records. Of the 243 years listed so far, record highs occurred in 139 years or 57%. This is somewhat higher than expected which may indicate that my 5% chance should be closer to perhaps 6% (but as I noted it has already risen to 7%, the trend may be the reason, the percentage has been increasing closer to the end of the series). There have been record lows in 137 years. The trend is definitely down there, only 12 of the past 47 years have one or more.

 

The fact that only about 4 in 7 years set a record high (or record low) but the average per year is very close to 1.5 (366/243) tells us that the average year with a record high (or low) has 2.7 of them. In fact these are the top five years of record high setters (including some cases that are just ties rather than outright winners):

 

1947,76 _ 11 dates each

1990 _ 10 dates

2011 _ 9 dates

1898 _ 8 dates

 

The recent average is something closer to 4 than 2.7, so that tells you the average month has 0.33 so the recent probability of a record high is steadily climbing. However, it's fairly obvious from the data in the table that the frequency of record highs is changing slower than the frequency of record lows. There have only been nine years since 1981 that set any record lows and only four since 1990, none between May 1996 and November 2010. At the start of the record, there were five or six years every decade with record highs. Some years in the 1770s had more record highs than most years in recent times.

[Summer Sun]

Up-to 5.6c to the 7th

 

2.1c above the 61 to 90 average

[BornFromTheVoid]

Seems unlikely now that we'll break the record for the highest daily average record in January. Temps at 9am this morning across the CET zone (when the minimum values for the 10th start) were up averaging around 9C, down from the 10-11C forecast a few days ago. This means we'd need maxima near 15C tomorrow to beat the record, which seems very unlikely.

 

Anyway, 5.9C to the 8th.

http://www.metoffice.gov.uk/hadobs/hadcet/cet_mean_est_2015

 

The minimum today is 5.4C, while maxima look like reaching the high 13s, so the CET should be on 6.3C on tomorrows update.

 

After that, the 06z GFS has the CET at:

6.7C to the 10th (10.5)

6.6C to the 11th (5.0)

6.6C to the 12th (6.4)

6.3C to the 13th (3.9)

6.2C to the 14th (4.1)

5.9C to the 15th (2.5)

5.8C to the 16th (3.7)

 

After a very mild day or 2, things look like reverting to average for while which should knock about 1C off the anomaly, but still leave us near 1.4C above the 81-10 average, and 2.3C above the 61-90 average.

[Jason M]

Given that over the last 10 - 20 years we seem to just keep clocking up above average months, an argument could be made that the averages are no longer an effective measure as there has been a climatic shift (reasons etc for a different thread!). It just seems to me that the 61-90 average CET might as well be for a different country!

Clearly some exceptions to the rule as always ie Dec 10, but we now really struggle to get a series of below average months.

I wonder if when we come to look at the 01 to 30 averages for this century they will be significantly warmer than the 81 - 10 averages.

In climate terms we are talking about short timescales but based on the limited data we have the direction of travel appears to be heading only way. I thought it interesting this morning when a forecaster on the BBC describing January night time temperatures in the low to mid teens, described them as 'rather mild'. 20 years ago, that would have been a really noteworthy event. Expectations seem to be adjusting in line with the CET!!

Edited January 9, 2015 by Jason M

[Timmytour]

If you look at the first ten days of January in the 120 years leading up to 2010, there were 19 days for which the mean CET was 10C or over. As an average, that's two in every 13 years.

Prior to this year, the 15 years of the 21st century (counting 2000) had yet to deliver such a day....the trend is reversing!!!  
 

[BlueSkies_do_I_see]

Jason

You make an interesting point.  Forecasters are reporting these temperatures on a daily basis so they are no longer getting excited about a 13C at 7am on a January morning. 

 

I keep hearing of a possible warming of upto 6C by the end of the century.  How would that affect our CET avg for the year?  Does that mean our average yearly CET will go from around 10.5C  to nearer 16.5C?

Edited January 9, 2015 by BlueSkies_do_I_see

[TonyH]

The projected rise is global, and the rise will be much less in some parts of the world, so perhaps the UK will see a more modest rise, although currently the trend upwards does seem quite sharpish!

Oh but of course we may be heading for another LIA according to a few on here

Edited January 9, 2015 by TonyH

[Timmytour]

Liam Duttonâ€@liamdutton1 min1 minute ago

Remarkable... At 7pm this evening, the temperature is 17C at Finningley, Doncaster, South Yorkshire. Yes, 17C!!!

Is there a fair chance todays mean CET could be over 10C?

[Jason M]

Jason

You make an interesting point.  Forecasters are reporting these temperatures on a daily basis so they are no longer getting excited about a 13C at 7am on a January morning. 

 

I keep hearing of a possible warming of upto 6C by the end of the century.  How would that affect our CET avg for the year?  Does that mean our average yearly CET will go from around 10.5C  to nearer 16.5C?

If the rise ends up at 6c we will be into geo engineering territory. At some point I suspect we will end up having to scrub the excess greenhouse gasses out of the atmosphere. I believe the technology exists already, but obvoiusly decades away from viability. Anyway, moving way off topic now so I'll stop there.

17c though at 7pm in early January. Wow!

[Summer Sun]

Up-to 6.3c to the 9th

 

2.8c above the 61 to 90 average

[kev238]

Amazing to be so far above average! If you were reading the model output thread you would believe this month to be far closer to average with the constant screaming of cold, cold, cold.

The issue is that during cold zonal periods daytime temperatures may be slightly below average but due to Strong winds nighttime lows don't drop too far. Therefore the cold zonal periods are slightly below average whilst the milder days are way above average more than counter balancing the cold.

One exceptionally mild day might need 5 slightly below days to balance it.

The next five or six days are a good case in point- a couple of pretty mild days and 4 or so pretty average or just below periods ( looking at the daytime and nighttime averages) . Net result a cet that will be slightly above the long term average ( though the running average for this month will certainly lower)

[reef]

Amazing to be so far above average! If you were reading the model output thread you would believe this month to be far closer to average with the constant screaming of cold, cold, cold.

The issue is that during cold zonal periods daytime temperatures may be slightly below average but due to Strong winds nighttime lows don't drop too far. Therefore the cold zonal periods are slightly below average whilst the milder days are way above average more than counter balancing the cold.

One exceptionally mild day might need 5 slightly below days to balance it.

The next five or six days are a good case in point- a couple of pretty mild days and 4 or so pretty average or just below periods ( looking at the daytime and nighttime averages) . Net result a cet that will be slightly above the long term average ( though the running average for this month will certainly lower)

 

Indeed, not to mention the cold interludes are barely 24 hours long, so you get high maxima on most days and the wind prevents cold minima too. Certainly here like in the majority of the CET zone you just get a sunny day in these polar maritime spells as the hills to the west kill off any shower activity so maxima on the 'colder' days are pretty average in reality.

Edited January 10, 2015 by reef

[DAVID SNOW]

I think we have reached the high point for the month now imo, with a general decline to months end.

[BlueSkies_do_I_see]

I agree David. I think the only way is down from here.

[Summer Sun]

Up-to 6.6c to the 10th

 

3.1c above the 61 to 90 average

[BornFromTheVoid]

Seems the cold arrived a little earlier than forecast yesterday, causing the maximum to be just 10C, barely higher than the minimum of 9C.

 

The minimum today is 3.0C, while maxima look like reaching over 9C, so remaining on 6.6C on tomorrows update.

 

After that, the 06z GFS parallel has the CET at:

6.6C to the 12th (7.0)

6.5C to the 13th (4.3)

6.3C to the 14th (3.9)

6.2C to the 15th (5.4)

6.1C to the 16th (3.9)

5.9C to the 17th (2.8]

5.7C to the 18th (2.3)

5.4C to the 19th (-0.2)

5.1C to the 20th (-0.6)

 

So, an average, trending to below average, week or so coming up. The CET could take a real battering should get a few sub zero values but, given that they occurred well outside of the reliable range, there isn't much confidence in them occurring yet.

[reef]

Seems the cold arrived a little earlier than forecast yesterday, causing the maximum to be just 10C, barely higher than the minimum of 9C.

 

The minimum today is 3.0C, while maxima look like reaching over 9C, so remaining on 6.6C on tomorrows update.

 

After that, the 06z GFS parallel has the CET at:

6.6C to the 12th (7.0)

6.5C to the 13th (4.3)

6.3C to the 14th (3.9)

6.2C to the 15th (5.4)

6.1C to the 16th (3.9)

5.9C to the 17th (2.8]

5.7C to the 18th (2.3)

5.4C to the 19th (-0.2)

5.1C to the 20th (-0.6)

 

So, an average, trending to below average, week or so coming up. The CET could take a real battering should get a few sub zero values but, given that they occurred well outside of the reliable range, there isn't much confidence in them occurring yet.

 

I wouldn't be surprised if we're still in the high 5s by the 20th. The ECM seems to keep us in more of the same with polar maritime incursions which seem to downgrade as they come to T+0. The parallel seems to be out on its own this morning too.

[BornFromTheVoid]

I wouldn't be surprised if we're still in the high 5s by the 20th. The ECM seems to keep us in more of the same with polar maritime incursions which seem to downgrade as they come to T+0. The parallel seems to be out on its own this morning too.

 

Agreed, though at the same time, I wouldn't take anything beyond 5+ days too seriously from any model.