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

Cool Dry April 2017

Pavonia blooms on a roadside

Roadside Pavonia

April began with cool days and nights, about three degrees below normal. However, the weather did not get any cooler until the last few days. In particular, ANZAC Day, at 27.4°, was the warmest day of the month – but that was more than a degree cooler than ANZAC Day 2002. (The average daily maximum temperature for ANZAC Day (from 2000) is 24.3°. The hottest was 28.7° (2002) and the coldest 16.8° (2012).)

Soaking rain of 10.6 mm, registered on the 26th, came with a remarkably warm night of 16.6°. Coming so late in autumn, this was 7.9° above normal, breaking the record of 7.1° above normal for an April night (20/04/06).
Further rain on the 27th (11.2 mm) fell as showers on a very cold day of 14.3°, that was 9.8° below normal. The final three nights were cold. The 30th, at 4.3°, was the coldest night of the month, but it was far from frosty.

Weather log for April 2017

Comparing April months

This month was cool, with a mean temperature of 17.0°, but not nearly as cool as April in 2008 (15.8°), 2006 (16.6°), or 1999 (15.6°). It was also rather low in moisture, with only 24 mm of rain, only 33% cloudy mornings, a daily temperature range as wide as 15.6°, and an early morning dew point of only 6.3°. What is unusual is the combination of low temperature values and low moisture values. Manilla’s climate generally swings between high temperature with low moisture (“droughts”) and low temperature with high moisture (“flooding rains”), as the poet said. (See these graphs.)
The total rainfall of 24.0 mm was at the 40th percentile, below the April average of 40 mm. There are no serious shortages of rainfall for groups of months to this date.

Climate for April 2017.


Data. A Bureau of Meteorology automatic rain gauge operates in the museum yard. From 17 March 2017, 9 am daily readings are published as Manilla Museum, Station 55312.  These reports use that rainfall data when it is available. All other data, including subsoil at 750 mm, are from 3 Monash Street, Manilla.

3-year trends to April 2017

Parametric plots of smoothed climate variables at Manilla
“Cold-Arid ‘Glacial'”

Climate trends to April 2017

April raw anomaly data (orange)

In terms of anomalies, April 2017 was even cooler than March, but much more arid. Anomalies of both daily maximum and daily minimum temperature fell by more than three degrees from February values, (They plot near the margins of the lower left graph.)
On most of the graphs, raw anomaly values for April plot towards the top left corner. Rather than moving along the top-right-to-bottom-left axis of “Droughts and flooding rains”, they combine low temperature and aridity as happened in ice ages.

 Fully smoothed data (red)

The most recent fully-smoothed data is for October 2016. Following a winter that was cool and moist, October shows a climate becoming steadily warmer and drier.
The smoothed anomaly of daily minimum temperature, which had hit a record high value in May 2016, approached a minimum value that was near normal.
Subsoil temperature anomaly was still falling rapidly, and was certain to reach a new record low smoothed value in November.


Note:

Fully smoothed data – Gaussian smoothing with half-width 6 months – are plotted in red, partly smoothed data uncoloured, and raw data for the last data point in orange. January data points are marked by squares.
Blue diamonds and the dashed blue rectangle show the extreme values in the fully smoothed data record since September 1999.

Normal values are based on averages for the decade from March 1999.* They appear on these graphs as a turquoise (turquoise) circle at the origin (0,0). A range of anomalies called “normal” is shown by a dashed rectangle in aqua (aqua). For values in degrees, the assigned normal range is +/-0.7°; for cloudiness, +/-7%; for monthly rainfall, +/-14 mm.

 * Normal values for rainfall are based on averages for the 125 years beginning 1883.

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:

Rainy days in March 2017

March 2017 had 17 rain days. In 134 years, this was beaten only by June 1950, which had 18. [More about Manilla rain days here.]

Fronds of Acacia pendula

Weeping Myall

After the record high temperatures of February, day and night temperatures in March were normal, without extremes. On a weekly basis, the first half of the month was cooler than the second half. The subsoil temperature followed the weekly air temperature down, to be a degree below normal by the 20th.
The second week had mainly clear skies and low dew points, Then the skies became persistently cloudy and dew points were high. A number of afternoons had oppressive humidity, with minimum values over 70%.
Of the 17 rain days, only three were early in the month, and they had little rain. The highest daily reading of 15.0 mm came on the 22nd.

Weather log for March 2017

Comparing March months

March had been sunny and very warm in both 2016 and 2015. This March was like that of 2014 and 2013, but with even more moisture. The mean average temperature was normal but, due to the cloudiness (58% cloudy mornings), the mean daily maximum, 29.1° was low and the mean daily minimum, 16.4°, was high, yielding the record narrow daily temperature range for March of 12.7°. The mean early morning dew point, 13.7°, was the highest March value in a decade, and the mean afternoon humidity minimum, at 53%, was far above the usual value of 30%.
The total rainfall of 113.2 mm was at the 90th percentile, far above the March average of 54 mm. The previous month, February, had only 4.1 mm, at the 4th percentile for that month. Taken together the two-month total of 117.3 mm was well above normal, at the 63rd percentile.

Climate for March 2017


Data. In 2016, a Bureau of Meteorology automatic rain gauge (formerly used for flood prediction) was set up in the museum yard as the official Manilla rain gauge. From 23 May 2016, its daily readings were published as if from Manilla Post Office, Station 55031. The gauge ceased transmitting five months later, on 7 October 2016. This month, after repair, it came into operation again. From 17 March 2017, daily readings are now published as Manilla Museum, Station 55312.

In these reports,the rainfall data is from Station 55031 or Station 55312 when available. Otherwise, rainfall data is from 3 Monash Street, Manilla.  All other data, including subsoil at 750 mm, are also from there. 

3-year trends to March 2017

Parametric plots of smoothed climate variables at Manilla
“Very rainy and cloudy”

3-year trends to March 2017

March raw anomaly data (orange)

March 2017 was dramatically cooler and more moist than the extremely hot and dry February. March days were cooler than normal and both rainfall and cloud were very high. Dew point and daily temperature range moved to the moist side of normal.

 Fully smoothed data (red)

The most recent fully-smoothed data is for September 2016. Following a winter that was cool and moist, September days remained cool but the climate became drier.
The smoothed anomaly of daily minimum temperature, which had hit a record high value in May 2016, approached normal. Subsoil temperature fell rapidly to below normal.


Note:

Fully smoothed data – Gaussian smoothing with half-width 6 months – are plotted in red, partly smoothed data uncoloured, and raw data for the last data point in orange. January data points are marked by squares.
Blue diamonds and the dashed blue rectangle show the extreme values in the fully smoothed data record since September 1999.

Normal values are based on averages for the decade from March 1999.* They appear on these graphs as a turquoise (turquoise) circle at the origin (0,0). A range of anomalies called “normal” is shown by a dashed rectangle in aqua (aqua). For values in degrees, the assigned normal range is +/-0.7°; for cloudiness, +/-7%; for monthly rainfall, +/-14 mm.

 * Normal values for rainfall are based on averages for the 125 years beginning 1883.

Mirrors to reflect the sun

I have begun to warm the shady side of my house with reflected sunlight in winter.

Aluminium mirrors to reflect sun

Sun Mirrors Mar-17

This winter’s set-up.

The first photo shows the present temporary set-up, done on the 10th of March 2017. That is, soon after I had changed the house from its summer regimen (to keep cool) to its winter regimen (to keep warm).
As shown, I attached aluminium foil to the courtyard wall on the south boundary of my block. The foil forms mirrors that reflect winter sun onto the south wall of the house, the edge of the floor slab, the footings and some nearby concrete paths.
The mirrors are sheets of aluminium cooking foil (“Alfoil”) 300 mm wide, cut to 900 mm lengths. I attached the foil to the wall in vertical strips with double-sided tape. As the wall is 12.6 metres long, the total mirror area is 11.3 square metres.

Last winter’s set-up.

Temporary aluminium mirrors to reflect sunlight

Sun Mirrors May-16

Last year, during April and May, I attached only 17 strips of foil 700 mm long in the same way. The total area then was 3.6 square metres. In that winter, the wind did a little damage, which I taped over. Much worse damage was caused by a magpie-lark attacking his reflection. By October, they were torn as shown in the third photo.

Aluminium foil damaged by birds

Bird Damage Oct-16

I repaired some of that damage, too, using builders’ foil, which is stronger. Early in November 2016, I removed all the foil. By then I wanted shade. not sunlight.

Effect of the mirrors

The white-painted courtyard wall reflects nearly all the sunlight it receives. However, this is diffuse reflection, going equally in every direction. Only a small part of it goes to points likely to warm the house.

Sunlight that has been reflected towards the house.

Reflected Light May-16

The aluminium foil reflects in a specular (mirror-like) way, sending nearly all of the solar energy downward at the same angle that it arrived. Because the foil is wrinkled, these mirrors spread the beam of sunlight out to about twice the width of the mirror surface. It is still quite concentrated as can be seen in the last photo, which is lit mainly by reflection from the foil.

Light reflected from these aluminium mirrors is not aimed precisely at points where it would best warm the house. The mirrors are not mobile, and their location owes a lot to chance. Furthermore, the house shades the mirrors for parts of each day; different parts as the season changes.
However, I think the warming effect will be useful, and I hope to be able to measure it.

Related Topics

The mirrors are part of the Courtyard that I have described in posts and pages listed in “My House Page”.


I raised the question of mirrors to reflect sunlight in a thread titled “Reflective Film” on a forum of the Alternative Technology Association (Melbourne).