Global Warming Bent-Line Regression

HadCRUT global near-surface temperatures

HadCRUtemp2lineThis graph, posted with permission, shows a bent line fitted to the HadCRUT annual data series for global near-surface temperature. Professor Thayer Watkins of San Jose State University Department of Economics posted it on his blog about 2009.

HadCRUTsmoothWithout knowing of this work, I constructed the second graph. I used data from the same HadCRUT source, but a data set smoothed by the authors.

In April 2013 I posted it to a forum thread in”weatherzone”.

Next, I added to that graph a logarithmic plot of global carbon emissions, similarly fitted with a series of straight trend lines.

Log from 1850 of world surface air temperature and carbon emissionsThis I included in posts to several forums: in a post to “weatherzone”, in a post to the Alternative Technology Association forum, and finally in a post to this blog.

Both Professor Watkins and I have fitted bent lines to the data. I fitted the lines by eye (for which I was accused of “cherry-picking”). Professor Watkins used an explicit process of Bent-Line Regression, minimising the deviations by the method of least-squares. Like me, he initially chose by eye the dates of the change points where the straight lines meet. But he then adjusted them so as to minimise the least squares deviations.
[See notes below on the method of Bent-Line Regression.]

The trend lines and change points are practically the same in the Thayer Watkins and the “Surly Bond” graphs:
1. (Up to Down) TW: 1881; SB: 1879.
2. (Down to Up) TW: 1911; SB: 1909.
3. (Up to Down) TW: 1940; SB: 1943.
4. (Down to Up) TW: 1970; SB: 1975.
As I said at the time, once straight trend lines are chosen, the dates of change points to fit this data series closely do not allow of much variation.

Relation to the IPO (or PDO) of the Pacific

Not by coincidence, Watkins and I both went on to relate the multi-decadal oscillations of Pacific Ocean temperatures to the global near-surface average temperatures.

My approach

I merely plotted my chosen global temperature change points on to the Pacific graphs (I chose to cite the IPO (Inter-decadal Pacific Oscillation)). In two posts I noted (i) the way the change points in the HadCRUT global temperature series were close to those in the IPO, and (ii) the way the IPO seemed able to explain why the trend in global warming was “bent” in 1943 and 1975 but, in that case, could only sharpen the bends of 1910 and 1880.

Professor Watkins’ approach

AGT_PDO7Professor Watkins did a separate Bent Line Regression Analysis on the Pacific graphs (He chose to cite the earlier-developed PDO (Pacific inter-Decadal Oscillation)). His analysis “A Major Source of the Near-Sixty Year Cycle in Average Global Temperatures is the Pacific (Multi)Decadal Oscillation” is here.

He admits the match is poor, with various lags and a different period. He concludes:
“Thus while the Pacific (Multi)Decadal Oscillation appears to be involved in the cycles of the average global temperature there have to be other factors also involved.”

The significance of the IPO

Continue reading

HadCRUT Global Temperature Smoothing

Graph of recent HadCRUT4

As a long-term instrumental record of global temperature, the HadCRUT4 series may be the best we have. [See Ole Humlum’s blog in the notes below.]
I like to use the published smoothed annual series of HadCRUT4.  I find that this smoothing gets rid of the “noise” that makes graphs about global warming needlessly hard to read. I used the smoothed HadCRUT series to point out the curious inverse relation between the rate of warming and the rate of carbon emissions in this post from 2014.  I will refer again to that post in discussing the use of bent-line regression to describe global warming.

The Met Office Hadley Centre published the smoothing procedure that they used for the time series of smoothed annual average temperature in the HadCRUT3 data set. The smoothing function used is a 21-point binomial filter. The weights are specified in the link above.
The authors discuss the fudge that they use to plot smoothed values up to the current year, even though a validly smoothed value for that year would require ten years of data from future years. Their method is to continue the series by repeating the final value. They had added to the uncertainty by using a final value from just part of a year.
They relate how this procedure had caused consternation when the smoothed graph published in March 2008 showed a curve towards cooling, due to the final value used being very cool.
They show the effect by displaying the graph for that date.
They maintain that the unacceptable smoothed curve (because it shows cooling, not warming) is due mainly to using a final value from an incomplete year, saying:
“The way that we calculate the smoothed series has not changed except that we no longer use data for the current year in the calculation.”
That web-page is annotated:
“Last updated: 08/04/2008 Expires: 08/04/2009”
However, this appears to be the current procedure, used with the HadCRUT4 data set.

For my own interest, I plotted the values from 1990 to 2016 of the annual series of HadCRUT4, averaged over northern and southern hemispheres. [Data sources below.]

On my graph (above), all points 1990 to 2016 are as sourced. I have plotted raw values 2017 to 2026 (uncoloured) as I believe they are used in the smoothing procedure. I have also left uncoloured the smoothed data points from 2007 to 2016, to indicate that their values are not fully supported by data.

I agree with Ole Humlum that it is very good of the Met Office to come clean on the logical shortcomings of their procedure for smoothing, but it would be even better if they ceased plotting smoothed points when the smoothing depends on data points for future years.
In my monthly series of parametric plots of smoothed monthly values of climate anomaly variables, I have faced the same problem. I smooth using a 13-point Gaussian curve. My solution is to plot “fully-smoothed” data points (in colour) up to six months ago. That gives a consistent mapping up to that date. The fifth month before now (plotted uncoloured) is smoothed with an 11-point Gaussian and so on, up to the latest month with a necessarily unsmoothed value.


Notes

1.
Ole Humlum’s blog “Climate4you”

[See: Index\Global Temperature\Recent global air temperature change, an overview\]

2.
HadCRUT4 data
Source of raw annual values:

Source of smoothed annual values:

Manilla’s Yearly Rainfall History

Lately, Manilla’s rainfall is normal, and more reliable
than it ever was.

Manilla yearly rainfall record, 21-yr smoothed

Yearly rainfall totals

The first graph helps to make sense of the history of Manilla’s rainfall, using the totals for each year. The actual figures make little sense, jumping up or down from one year to the next. The figures here have been calmed down. First, I replaced each yearly figure by an average of twenty-one years, ten years before and ten years after the date. Then I smoothed that figure some more.
The pattern is plain. There were periods in the past when there was much more or less rain than usual.
In four decades the rainfall was some 30 mm higher than normal: the 1890’s, 1950’s, 1960’s and 1970’s. In four other decades, the rainfall was some 30 mm lower than normal: the 1900’s, 1910’s, 1920’s and 1930’s.
Rainfall here collapsed about 1900. The collapse was was widespread, as was recognised half a century ago.

Using the average line drawn across the graph (at 652 mm), you can see that rainfall was below average from 1902 to 1951: almost exactly the first half of the twentieth century. After 1951, rainfall was above average for the 44 years to 1995. Since then, the annual rainfall (as plotted) has been remarkably close to the 132-year average.
Present rainfall will seem low to those who remember the 1970’s, but the 1970’s were wet times and now is normal. Few alive now will remember that Manilla’s rainfall really was much lower in the 1930’s.

Manilla yearly rainfall scatters.

Yearly rainfall scatter

The second graph also groups the data twenty-one years at a time. It shows the scatter of yearly rainfalls in each group. More scatter or spread means the rainfall was less reliable. Comparing the graphs, times of high scatter (very unreliable rainfall) were not times of low rainfall, as one might think. Annual rainfall scatter and rainfall amount were not related.
Times of very unreliable rainfall came in 1919 (dry), 1949 (normal) and 1958 (wet). Times of reliable rainfall came in 1908 and 1936 (both dry). However, by far the most reliable rainfall came since 1992, extending to 2004 and likely up to this year.

Global warming

It has been argued that human-induced climate change will cause climatic extremes to happen more often in future. Already, when any extreme climate event is reported, someone will say that climate change has caused it.

The present steady rise in global temperature began about 1975. Does this Manilla rainfall record show more extreme events since that date? Definitely not! Quite the contrary. Continue reading

House in a cold October

This October has been very cold. That has kept indoor temperature
in this solar-passive house almost too cool for comfort. I wore warmer clothes and opened windows to admit warm air.

Indoor/outdoor temperature scatter-plot.

The climate this October

The graph shows (on the x-axis) how cold this October [in red] was: the coldest of the new century.
Here on the North-west Slopes of NSW, October warms and cools more from year to year than other months. It is the month most affected by climate cycles such as the El Nino-Southern Oscillation (ENSO). As shown, October warmed by one degree each year from 2011 to 2015, then cooled by nearly six degrees from 2015 to 2016.
ENSO followed almost the same pattern, but October 2012 was warmer than October 2013.
For five months, world temperature has also been down: much lower than it was in the record-breaking months of February and March 2016. (HadCRUT4 Global monthly near-surface data set (Column 2 in the linked table.))

Indoor climate this October

As shown on this graph beginning 2005, the indoor mean temperature in October months has varied with outdoor mean temperature. This coldest October outdoors (15.9 degrees) was also the coldest indoors (20.8 degrees). (But see Note below.)
October is the final month that I keep the house in its winter warming regimen. In 2014 and 2015 it had been almost ideally warm, but in 2016 it was just above the comfort minimum. Since this figure is just an average, there were times when the house was too cool for comfort, especially in the mornings.

Successive unfavourable months this year

As in other seasons, I intend the indoor climate to be comfortable through each spring season.
As I posted in “Hard Winter for Solar-passive” this very cloudy winter had reduced solar gain, making heaters needed much more than usual. However, the mean indoor temperature at winter’s end (August) was normal, although the heat bank was 0.7 degrees cooler than normal.
In September months, the warmth indoors still depends on solar gain through the north windows. This time,the sky continued very cloudy, and the daytime temperature was a record low value. As a result, the indoor temperature was 0.9 degrees down and the heat bank 0.7 degrees down.
By October, there is no solar gain through the north windows: warmth is gained from the surroundings in daytime by conduction, convection and radiation and retained by closed curtains at night. This time, both day and night temperatures were three degrees below normal, reducing daily heat gain and increasing nightly loss. As a result, the indoor temperature was 1.2 degrees down and the heat bank 0.9 degrees down.

What I did

Continue reading

Is There Any Drought Now?

No. In Manilla just now, there is no drought of any kind: not a short drought, a medium-length drought, or a long drought; not an extreme drought, a severe drought, or even just a serious drought.

A new comprehensive graph of the severity of drought at one site.

In this graph, each line of data points is for one particular month. The middle line, joining the red squares, shows the whole rainfall drought situation for last month: September 2016.
This is a new kind of graph. (See Note 1 below.) It can show how severe a drought is, not only during the last month or two, but during the last year, and during the last many years. That is a lot of information.

How to read the graph

A month of extreme drought would have data points very low down on the graph. The scale on the left side is amount of rainfall. It must be a “percentile” value. For example: if the amount of rain that fell is just more than has been seen in the driest 5% of all months, it has a value in the 5th percentile. (See Note 2 below.)

Along the top and bottom of the graph I have plotted a number of months.
The number does not show time passing. It shows the number of months I included in a calculation. For each month on record I did many calculations. I added up the total rainfall for:
* the month itself;
* two months including the previous month;
* three months including the month before that;
* … and so on.
I found the totals for larger groups of months extending back as far as 360 months (30 years).
Using all these rainfall totals, I calculated percentile values to plot on the graph. For example, for groups of 12 months, all groups of 12 consecutive months are compared with each other, to find the percentile value of the 12-month period ending in a given month. (See Note 3 below.)

Which months had the most drought and least drought?

The worst drought there could ever have been would be one with data points along the bottom line of the graph. In such a disastrous month, all the rainfall totals would be the lowest on record, not just the one-month total, but also the two-month total and so on up to the 360-month total. Every one of them would be the lowest total on record. It has never been as bad as that.
The “best” time, in terms of being free of drought, would be a month with all its data points along the top edge of the graph. For that month, every rainfall total, for a short period or a long period, would be the wettest on record.
From the Manilla rainfall record, I have chosen to display the most drought and the least drought that actually occurred.

The most drought: August 1946

The month of August 1946 had no rain. Of course, that was the lowest rainfall for any August month (One among 13 months on record that had no rain.). As a result, the percentile rank for that month’s rainfall is zero. Most totals for groups of any number of months ending in August 1946 are also on the “zero-th” percentile, that is, the lowest on record. Thus, it was an extreme drought in the short term, medium term and long term.
For this month, percentile values that are above the third percentile occur in the totals for 48, 60, and 72 months, as shown. These figures, while not extremely low, were still well below normal (Normal is the 50th percentile.). They occur because these totals include some wet months in 1940, 1941, and 1942.

The least drought: March 1894

March 1894, with 295 mm of rain, was one of the the wettest months ever, ensuring a 100th percentile value. The rainfall totals for groups of months ending in that month included six other “wettest ever” values, and all other groups of months were also very wet. No group of months was below the 95th percentile. (See Note 4 below.)

Current drought situation (September 2016)

This month’s rainfall total of 122.4 mm puts it in the 92nd percentile of all monthly rainfall values, far above the median value marked as “normal” on the graph. The 2-month rainfall total (203 mm), and the 4-month rainfall total (350 mm) are almost as high, each in the 90th percentile.
Continue reading

Climate trends for thermal soaring

For pilots who soar at Lake Keepit or Mount Borah: relevant summer climate data for Manilla, NSW, since 1999.

Graph of some summer climate variables 1999 to 2015.

Variables relevant to thermal soaring

From my data I have selected three variables that are relevant to success in soaring flight using thermals. I have chosen to use values for summer: a total or average for the three months of December, January and February.
The variables are:

  • The number of hot days, when the maximum temperature was over 33°C;
  • The number of sunny days, when the cloud amount seen at 9 am was less than two octas;
  • The average daily temperature range in degrees celsius.

Changing values of the variables

The graph shows that each variable fluctuated wildly, with each summer very different from the last. These variables often moved in the same sense.
Two summers had high values of all three variables: 2006-07 and 2013-14. Two summers had low values of all three variables: 2007-08 and 2011-12. I would expect that longer and faster thermal soaring flights would have been achieved in the summers with high values, compared to those with low values.

Trends

I have fitted linear trend lines, and displayed their equations within the graph.
All three trend lines slope down. This suggests that summer thermal soaring conditions have been getting worse.
I have cited the values of “R-squared”, the Coefficient of Determination. All three R-squared values are abysmally low. Even the best is below 20%, which can be taken to mean that more than 80% of the variation has nothing to do with the trend line shown.
You could say that the trends are nonsense, but we are dealing with Climate Change here!

The future

In the spirit of Mark Twain, we can extend the trend lines forward to where they come to zero:

  • There will be no hot days above 33° by the summer of 2118;
  • There will be no sunny mornings with less than 2 octas of cloud by 2073;
  • Days will be no warmer than nights by 2423.

That last date seems too remote to worry about. However, the daily temperature range will be unacceptable when it gets down to 11°. That is the current summer value for Lasham, England, after all. According to the trend, the daily temperature range will be worse than at Lasham by 2117. That is the same year that the very last 33° day is expected.

Global Warming

You may be surprised that the linear trend lines fitted to this data set slope downwards. It seems to contradict Global Warming. Continue reading

Manilla’s Droughts, 1884 to 1916

Graphical log of droughts, 1884 to 1916

The catastrophic droughts in 1902 and 1912-16 were quite different.

In the years before 1917 shown here, Manilla had several times of extreme drought. They came in 1888, 1895, 1902, and in a cluster that began in 1912.
(1.) The 1888 extreme droughts were of 2-, 3-, 4-, 5-, 6- and 9-month duration. The 2-month event was in August, and other events came later as they became longer, until the 9-month event came in December (having begun in April).
(2.) In 1895, drought was extreme only for durations of 5-months (June) and 6-months (July and August). Although droughts of 2-, 3-, 4-, and 9-month duration also occurred, they were not extreme, but merely “severe”.
(3.) Manilla’s 1902 (“Federation”) drought was phenomenal. Extreme droughts of nearly all durations from 2 months through to 96 months occurred (and ended) at practically the same time. The 2-month event plots at May 1902. The 96-month extreme drought plots at February-March 1903. None of the drought events around 1902 extended far into 1903; all ceased abruptly. The rainfall shortages began earlier according to a simple pattern; the longer the duration of the extreme event, the earlier it began. The 1902 extreme 1-year drought began in September 1901, and the extreme 8-year drought began in 1895.
(4.) The cluster of drought events extending through 1912 and 1916 was as bad as the events of 1902, but quite different. Merely “severe” short-duration events began in April 1911. Events of increasing duration came at later dates, forming a smooth curve on the graph. Beyond 12-month duration, and up to 72-month duration, there were extreme events at nearly all classes of duration. By the 72-month duration, the date of plotting had drifted forward in time to January-July 1916. The beginning of these 72-month events would have been during Continue reading