Dig and Delve Part 2: Running Detrended Data

In my last post, Dig and Delve Part1, I showed how running trends are useful for showing the linear trend to any point in a dataseries, and that trends in different regions can be compared, after the first 10 to 15 years (120 to 180 datapoints).

In this post I use running trends to derive running detrended data, and analyse data for various Land regions using UAH anomalies.  Firstly, the following figure shows global mean UAH to November 2016 detrended using the current linear trend:

Fig. 1:  Global data detrended from linear trend

This is the usual way to show detrended data.  It clearly shows where temperatures have been above or below the trend, however with each new data point the detrended data changes.  Running detrended data is calculated for each point as actual data minus  the running trend multiplied by the count of data points plus the running intercept.  Here is a plot of running detrended data and ordinary detrended data for Global UAH.

Fig. 2:  Global running detrended data and standard detrended data.

After about 1987 they differ by less than +/- 0.1C, and UAH is accurate to +/- 0.1C anyway.   Note also that when temperatures are rising, running detrended data are greater and when falling, they are lower than standard detrended data.

The benefit of running detrended data is that they never have to be recalculated.  Historic detrended values are preserved.  As well, the running trend per month is conveniently not different from zero (which is why I showed it in Part 1 as degrees per 100 years by multiplying by 1,200), so it is easy to show the detrended data with a zero line.  The detrended value is also a measure of how much each month’s data has contributed to the trend- positive values indicate warming influence, negative values indicate cooling influence on the trend.

I now turn to using running detrended data to analyse what has been happening with Land data recently.

The following plots show running detrended data for Land TLT in the Northern Hemisphere.

Fig. 3:  Northern Hemisphere Land data detrended from running trend

The large spike in February was followed by a plunge to October, but values in November have returned to trend.

Fig. 4:  Northern Extra Tropics Land data detrended from running trend

Similar to the Northern Hemisphere.

Fig. 5:  North Polar Land data detrended from running trend

Note how much North Polar data fluctuates.  However the Poles only contribute less than 7% to the Global mean.

Summing up:

• Running detrended data never have to be recalculated, and historic values are preserved.
• The detrended data show how much each month’s data has contributed to the trend at that point.
• The recent plunge in Northern Hemisphere Land anomalies is nothing to get excited about as it is the recovery from a huge spike. The November value is still on trend.

The next in this series will use an estimate of discrete Extra Tropics (20-60 North and South) to look at trends and detrended data.

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Dig and Delve Part 1: Running Trends

This is the first in a series of posts in which I look at monthly Temperature of the Lower troposphere (TLT) anomaly data from the University of Alabama- Huntsville (UAH) in different ways, which readers may find interesting and perhaps useful.

In this post, I bring together ideas from former posts- Trending Trends: An Alternative View and Poles Apart – to compare trends in TLT using running trends.

 

Running Trends

Fig. 1: Global UAH with linear trend

This is the standard presentation.  It shows the linear trend as at November 2016.  With every new month of data, the linear trend changes.

By calculating a running trend, that is, the linear trend from the start of the series to every subsequent data point, the trend at each point is preserved, and the trend at the final point is instantly calculated.

Fig. 2:  Global UAH running trend

Figure 2 shows the historical values of the linear trend at each point, and that global temperatures are demonstrably non-linear.  As I pointed out in Trending Trends: An Alternative View, each new data point will either increase, decrease, or maintain the trend.  The longer the data series, the harder it will be to change the trend: the effect diminishes with time.

(An interesting result of the diminishing effect of temperature on the running trend is that it becomes possible to identify what temperatures are doing from the shape of the running trend plot- in fact, to identify a pause or plateau.  To maintain the trend at say 1.2 degrees Celsius per 100 years, temperatures must continue to rise.  A flat-lining running trend is evidence of increasing temperatures; a rising running trend indicates a rapid increase in temperature; but a decreasing running trend is evidence of a pause or decline in temperatures.  This is not a different definition of the pause, just another indicator.)

For 10 to 15 years, the running trend swings wildly, but after this it settles.  Now it becomes useful for analysis and comparison.

In Figure 2 above, note the large effect of the 1997-98 El Nino on the trend, but the 2009-10 and 2015-16 El Ninos have much less effect on the trend.  They are still identifiable by the increase in trend.

Fig. 3:  Regional UAH running trends

As we have seen previously, the North Polar and South Polar regions are distinctly different from the rest of the world and from each other.  The North Polar region has had an increasing trend (rapidly increasing temperature) from 1994 to about 2007, then a slow down with another rapid rise in the last 12 months.  All other regions have had decreasing trends since 2002-3, with an uptick in the last 12-18 months, indicating the duration of The Pause.  The trend in the South Polar region has been much lower than the others, hovering about zero for the last seven or so years, and is currently negative.

For completeness, here are the running trends for continental USA and Australia.

Fig. 4:  UAH running trends:  USA 48 States

Fig. 5:  UAH running trends:  USA 49 States

Fig. 6:  UAH running trends:  Australia

The next plots compare Land, Ocean, and Mean running trends for the UAH regions.

Fig. 7:  Global UAH running trends: Mean Land, and Ocean

Note that the mean trend is close to that of the Ocean, but since 1995 and especially 1998, the trend of global land areas is much higher.  Because of the ocean’s large thermal inertia, land areas warm and cool more quickly.  However, since the 1997-98 El Nino, land trends did not decrease but remained high until 2007.  This graph, as any Global Warming Enthusiast (GWE) will tell you, is evidence of warming.  What they won’t tell you is that it is evidence of any type of warming whether natural or anthropogenic- it is not by itself evidence of greenhouse warming.

Fig. 8:  Northern Hemisphere UAH running trends: Mean Land, and Ocean

Fig. 9:  Southern Hemisphere UAH running trends: Mean Land, and Ocean

Land trends in the Southern Hemisphere, unlike the Northern, did decrease after the 1997-98 El Nino.

Fig. 10:  Tropical UAH (20N – 20S) running trends: Mean Land, and Ocean

Fig. 11:  Northern Extra-Tropics UAH (20N – 90N) running trends: Mean Land, and Ocean

Fig. 12:  Southern Extra-Tropics UAH (20S – 90S) running trends: Mean Land, and Ocean

This region warmed rapidly to 2002-3, then trends decreased.

Fig. 13:  North Polar UAH (60N – 90N) running trends: Mean Land, and Ocean

Fig. 14:  South Polar UAH (60S – 90S) running trends: Mean Land, and Ocean

In all tropical and northern regions, Land trends have been higher than Ocean trends since 1997-98 (2002 for South Polar and Southern Extra-Tropics).  However, North Polar Ocean trends have been higher than Land since 1998.  There is a greater area of ocean than land, and ocean areas have been warming more than land.  This is the opposite of what greenhouse theory predicts.  At the poles, where warming is expected to be greatest, only the North Pole is warming, and here the warming is not greatest over land, but over the ocean.

Summing up:

• Running trends are an effective way of showing the linear trend at any given month of a data series.
• They are useful for comparison and analysis after the first 10 to 15 years (the early 1990s).
• A declining running trend indicates flat or declining temperatures, thus The Pause is visible from 2002-3 to 2014-5 in all regions apart from North Polar.
• The North and South Polar regions are distinctly different from other regions and each other.
• Apart from North Polar region, all regions show land areas warming more than ocean areas, indicating warming from whatever cause.
• In the North Polar region, TLT running trends of ocean areas have been higher than land.
• These trends, especially at the poles, are not consistent with greenhouse theory.

 

The next post in this series will use running trends to derive running detrended data.

Putting Temperature in Context: Pt 2

To show how handy my Excel worksheet is, here’s one I did in the last 15 minutes.

Apparently Sydney has had its warmest December minimum on record at 27.1 C.  The record before that was Christmas Day, 1868 at 26.3C.

The following seven plots show this in context.

Fig. 1:  The annual range in Sydney’s minima:

Extremes in minima can occur any time between October and March.

Fig. 2:  The first 2 weeks of December

Plainly, a new record was set this morning, but apart from Day 340 the other days are within the normal range.

Fig. 3:  7 day mean of Tmin in this period

Extreme, but a number of previous years had warmer averages.

Fig. 4:  Consecutive days above 20C Tmin.

But there have been longer periods of warm minima in the past.

Now let’s look at the same metric, but for all of December.

Fig. 5:  All Decembers (including leap years).

A record for December, with 1868 in second place.

Fig. 6:  7 day mean of Tmin for Decembers

Seven day periods of warm nights are not new.  The horizontal black line shows the average to this morning (20.6C) is matched or exceeded by a dozen other Decembers.  (Of course this December isn’t half way through yet.)  Also note what appears to be a step change about 1970.

Fig. 7:  Consecutive days above 20C Tmin in December.

I doubt if 15 December will be as warm as today, but could still be over 20C.

This is weather, not global warming.

 

Putting Daily Temperature in Context

In this post I demonstrate a simple way of comparing current temperatures for a particular location with those previously recorded.  In this way it is possible to show the climatic context.

Using data from Climate Data Online, I plot maximum temperature for each day of the year, and then for a particular short period: in this case the last week of November and the first week of December, which coincides with the recent very warm spell here in Queensland.  To account for leap and ordinary years this period is 15 days.  In ordinary years 24^th November is Day 328 and 7^th December is Day 341, while in leap years this same calendar period is Day 329 to 342.  I also calculate the running 7 day mean TMax for this period, and the number of consecutive days above 35C.

To put the recent heatwave in context, I have chosen six locations from Central and Southern Queensland which regularly feature on ABC-TV weather: Birdsville, Charleville, Roma, Longreach, Ipswich (Amberley RAAF), and Rockhampton.

Birdsville:

Fig. 1

The Police Station data are from 1954 to 2005, and the Airport from 2000.  This shows the range of temperatures throughout the year.  The red arrow indicates the current period.   The next plot shows data only for the period in question.

Fig. 2:  24 November- 7 December: Airport data

Note there were three days where the temperature this year was the highest for those days since 2000, but didn’t exceed the highest in this time period, which was in November.  The other days were well within the historic range.

For interest, let’s now see how this year compares with the Police Station record.  (The average difference in TMax during the overlap period was 0.0 to 0.3C.)

Fig. 3:  24 November- 7 December: Police Station data

In a similar range.

Fig. 4

This heatwave was the third hottest since 2000 and fifth overall.

Fig. 5

Five previous periods had more consecutive days above 35C.  2006 had 22.

Charleville:

Fig. 6: Charleville Aero since 1942

Temperatures in this period reached the extremes of the range on three days.

(Although the Post Office record begins in 1889, there are too many errors in the overlap period so the two records can’t be compared.)

Fig. 7:

A new record for early December was set, but note this was the same temperature as 29^th November 2006.

Fig. 8:

Definitely the hottest for this period since 1942.

Fig. 9:

Note this was not the longest warm spell by a mile: there were many previous periods with up to 26 consecutive days above 35C.

Roma

Fig. 10:

Although there is not one day of overlap so the two records can’t be compared, you can see that Airport (from 1992) and Post Office records are similar.

Fig. 11:

A new record for this time of year was set: 44.4C, and six days in a row above 40C.  Pretty hot….

Fig. 12:

…but there were longer hot periods in the past (since 1992).

Longreach

Fig. 13:  Longreach Aero since 1966.

Fig. 14:

Hot, but no record.

Although there is good overlap with the Post Office, temperatures for this period differ too much: from -1 to +0.7C.

Fig. 15:

Fifth hottest period since 1966.

Fig. 16:

And in the past there have been up to 47 consecutive days above 35C at this time of year.

Ipswich (Amberley RAAF):

Fig. 17:

Fig. 18:

Not unusually hot for this time of year.

Fig. 19:

Ninth hottest since 1941.

Fig. 20:

Hotter for longer in the past.

Rockhampton:

Fig. 21:

Fig. 22:

Very hot, but no records.  (The heat lasted another two days, with 36.6 and 37.3 on 8^th and 9^th.)

Fig. 23:

Fourth hottest 7 day average on record (since 1939).

Fig. 24:

Again, a number of hot days, but there were as many and more in the past.

To conclude: the recent heatwave was very hot certainly, and was extreme in southern inland Queensland.  While Charleville had the highest seven day mean temperature on record, NO location had as many consecutive hot days (above 35C) as in the past.

This is a handy method for showing daily data in context.  It can used for any period of the year, can be tuned to suit (I chose TMax above 35C, but temperatures below a set figure could be found), and can be used for any daily data.

If you would like a comparison done for a location that interests you, let me know in comments including time period and parameters of interest (e.g. Sydney, first 2 weeks of December, TMax above 30C say, or Wangaratta, September, daily rainfall over 10mm say.)

The Pause Update: November 2016

The complete UAH v6.0 data for November were released yesterday evening- the quickest ever. I present all the graphs for various regions, and as well summaries for easier comparison. The Pause has ended globally and for the Northern Hemisphere, and the Tropics, and may soon disappear from the USA, but still refuses to go away in the Southern Hemisphere.

These graphs show the furthest back one can go to show a zero or negative trend (less than 0.1 +/-0.1C per 100 years) in lower tropospheric temperatures. I calculate 12 month running means to remove the small possibility of seasonal autocorrelation in the monthly anomalies. Note: The satellite record commences in December 1978- now 38 years long- 456 months. 12 month running means commence in November 1979. The y-axes in the graphs below are at December 1978, so the vertical gridlines denote Decembers. The final plotted points are October 2016.

[CLICK ON IMAGES TO ENLARGE]

Globe:

The Pause has ended. A trend of +0.28 C/100 years (+/- 0.1C) since March 1998 is creeping up.

And, for the special benefit of those who think that I am deliberately fudging data by using 12 month running means, here is the plot of monthly anomalies:

Northern Hemisphere:

The Northern Hemisphere Pause has well and truly ended.

Southern Hemisphere:

For well over half the record, the Southern Hemisphere still has zero trend.  The Pause has shortened by two months and may end shortly.

Tropics:

The Pause in the Tropics (20N to 20S) has ended and the minimal trend is now +.27C/ 100 years.

Tropical Oceans:

The Pause has ended for ocean areas.

Northern Extra Tropics:

The minimal trend is up to +0.56C/ 100 years.

Southern Extra Tropics:

The Pause persists.

Northern Polar:

The trend has increased a lot to +2.32C and since February 2003 +0.7C/100 years.

Southern Polar:

The South Polar region has been cooling for the entire record.

USA 49 States:

The Pause has shortened by one month and is about to disappear altogether.

Australia:

One month longer- 21 years 5 months.

The next graphs summarise the above plots. First, a graph of the relative length of The Pause in the various regions:

Note that the Pause has ended by my criteria in all regions of Northern Hemisphere, and consequently the Globe, and the Tropics, but all southern regions have a Pause for over half the record, including the South Polar region which has been cooling for the whole record.

The variation in the linear trend for the whole record, 1978 to the present:

Note the decrease in trends from North Polar to South Polar.

And the variation in the linear trend since June 1998, which is about halfway between the global low point of December 1997 and the peak in December 1998:

The imbalance between the two hemispheres is obvious. The lower troposphere over Australia has been strongly cooling for more than 18 years- just shy of half the record.

Global TLT anomalies have remained stubbornly high.  The next few months will be interesting. The Pause may disappear from the USA and Southern Hemisphere soon, but not the Southern Extra-Tropics or Australia. El Nino tropical heat is strongly affecting the North Polar region now, and will begin to affect the Southern Hemisphere early next year.