Rainfall in SE Asia and the PDO Index

Rainfall in Southeast Asia and the Pacific Decadal Oscillation Index

Here I compare, without comment, the maximum-month rainfall in a SE Asian country and the annual average of the PDO Index.



Hemispheric Temperature Anomalies: 1851-1980

Climate Research Unit, University of East Anglia

The Climatic Research Unit (CRU) was established in the School of Environmental Sciences (ENV) at the University of East Anglia (UEA) in Norwich in 1972.

The CRU has collected, collated and archived global climate data for over 40 years.

CRU temperature data


In 1987, the American Meteorological Society published a paper by Stanley Grotch of the Lawrence Livermore National Laboratory, University of California, that assessed the robustness of the CRU dataset for land and other datasets.

Monthly Weather Review, Volume 115 No. 7, July 1987, ISSN: 0027-0644; eISSN: 1520-0493


Three data bases of gridded surface temperature anomalies were used to assess the sensitivity of the average estimated Northern Hemisphere (NH) temperature anomaly to: 1) extreme gridpoint values and 2) zonal band contributions. Over the last 100 year, removal of either the top or bottom 10% of the gridpoint anomalies in any year changes the estimated NH average anomaly by 0.1−0.2°C. Excising extensive zonal bands also produces root-mean-square changes in the estimated NH anomaly of approximately 0.1°C. The estimated NH average anomaly appears to be robust to such perturbations.

[The following link link may not be recognized by WordPresss]

Some Considerations Relevant to Computing Average Hemispheric Temperature Anomalies (Grotch, S. L., 1987)

Alternatively, copy this link to your browser:

URL: http://journals.ametsoc.org/doi/abs/10.1175/1520-0493%281987%29115<1305%3ASCRTCA>2.0.CO%3B2

Grotch cited the paper by Jones that described the land and ocean datasets: A new compilation of monthly mean surface air temperature for the Northern Hemisphere for 1851-1984 is presented based on land-based meteorological station data and fixed-position weather ship data.

PDF: JONES, P. D., et al. Northern Hemisphere surface air temperature variations: 1851-1984. Journal of Climate and Applied Meteorology, 1986, 25.2: 161-179.

My comment:

Grotch’s paper claimed that the land (CRU) and ocean (COADS) datasets pass his tests of normality and freedom from bias. His presentation is reasonable.

However, his Figure 1 shows that the 26,000 datapoints range between plus and minus 2 degrees Celsius , while the signal (the mean temperature) ranges from approximately -0.2 C to +0.2 C over a period of 130 years, a rate of about 0.3 C per century.

The temperature increase from 1875-80 to 1935-40 was about 1.1 C, more than double the increase over the period 1851-1980. This means that the biggest change in temperature during the period was before 1950 when CO2 began to be emitted at modern levels. It also means that this rise in temperature by 1 degree C was not climate change, but merely a natural fluctuation in temperature.

The duration both 1875-80 to 1935-400 and 1935-40 to 1995-2000, is 60 years, approximately the same as the period of the Atlantic Multidecadal Oscillation (AMO).

Unfortunately, we do not know how much of the temperature change on land observed during the last 120 years was a natural response to oceanic oscillations, including the AMO.

Since no warming was observed between 1940 and 1980 and since little or no warming has been observed since about 1995 (apart from El Ninos), the 15-year period from about 1980 to 1995 is our strongest,  and perhaps only, evidence for an irreversible change in climate.

But if the warming from 1980 to 1995 was related to the warm phase of the AMO, then we can expect, first a peaking in the cycle lasting until about 2010, and then a gradual downturn in the AMO, which may have already occurred but has been masked by El Nino events.

The COADS ocean data from the period 1850-1980 revealed no global temperature trend. This may possibly reflect the crude technology in use at sea during the entire period. The change in ocean temperature was less than the errors in measurement.

Until the Argo system began to be deployed in 2000, oceanographers had to rely on ships at sea to measure the temperature of the world ocean. The ocean covers 70% of the Earth’s surface and the thermocline extends to a depth of about two kilometers. Thus, most of the heat in the biosphere is stored in and released from the ocean.

Argo buoys

From 2007, several thousand Argo buoys began to record ocean temperatures. Until then, the error bars on ocean temperature estimates were too large relative to the size of the anomalies to inspire much confidence. Grotch did not elaborate on the weaknesses of the COADS dataset, but the situation is clear from his paper.

The publication in an obscure minor journal of the AMS effectively buried Grotch’s paper until Richard Lindzen displayed his graph of CRU temperature in his lecture,

Global Warming, Lysenkoism _ Eugenics Prof Richard Lindzen, at 30:37.





Antarctic Temperature Anomalies

RSS (satellite) Record

The start date of the satellite record is 1979. It appears that Antarctic temperature peaked around before 1982 and has declined slightly since  then.

RSS Temp Antarctica

Source: http://data.remss.com/msu/graphics/TLT/time_series/RSS_TS_channel_TLT_Global_Land_And_Sea_v03_3.txt

Satellite temperature is actually a measure of the level of radiative energy of the atmosphere. The anomalies show the changes in the level of energy at the measured wavelengths. As a consequence, the integral of the changes may indicate the direction of change.


RSS Intergral Temp Antarctica

The integral of temperature may not have an obvious physical meaning apart from the vibration energy  of the molecules in the atmosphere. However, in some years higher temperature indicates that energy is being added to the oceans while in other year energy is being lost.

The integral of of temperature is a proxy for the running total of net energy lost and gained that indicates the direction of change more clearly than does the temperature.


Glacier response to North Atlantic climate variability during the Holocene

The Kulusuk Glacier during the Holocene

Kulusuk Lake, Greenland

Kulusuk Lake is located on Kulusuk Island off the east coast of Greenland about the same latitude as northern Iceland. The lake was the subject of a recent paper.

Glacier response to North Atlantic climate variability during the Holocene. N. L. Balascio, W. J. D’Andrea and R. S. Bradley, Clim. Past Discuss., 11, 2009-2036, 2015


The authors present a graph that shows the relative rates of change in the glacier in terms of advance and retreat since 10,000 years ago.

From about 8,000 to 4,000 years ago (during the Holocene Climate Optimum) it was too warm for a glacier to form.

After about 4,000 years ago, a glacier formed and began a series of advances and retreats up to the present as shown in their graph.

I plotted their graph and then wondered what it would look like if I accumulated the advances and subtracted the retreats. The figures are relative and not absolute. Thus the resulting curve shown below does not tell us the total mass of the glacier at any point but merely indicates how the glacier grew in mass from 4000 years ago (2000 BC) to its greatest extent around 1200 years ago (800 AD), then began to lose mass until the Medieval Warm Period around 1000 years BP.

After 1000 years BP the glacier gained mass during the Little Ice Age, which ended around 200 years ago. Since then the Earth’s climate has been getting warmer and the glacier has retreated again. Still the glacier seems to have a long way to go before reaching its extent at the end of the Roman Warming Period around 1500 years ago.



Points to Note

1.Declines in the curve correspond to increasing total ice mass and thus cooling.

2. It can be seen that the shape of the curve for the 2000-year period from 4000 BP (before the present) to 2000 BP is similar to the shape of the curve for the 2000-year period from 2000 BP until the present. The correlation coefficient is 0.78 and R-squared is 0.60 with 21 pairs of data, significant at the 1% level of confidence.

A possible explanation is given by Nicola Scafetta.

Scafetta, Nicola. “Multi-scale harmonic model for solar and climate cyclical variation throughout the Holocene based on Jupiter–Saturn tidal frequencies plus the 11-year solar dynamo cycle.” Journal of Atmospheric and Solar-Terrestrial Physics 80 (2012): 296-311. URL: http://arxiv.org/pdf/1203.4143.pdf

3. The glacier gained mass after 4000 years before the present (BP) and then lost it by 38oo BP, a date that corresponds to the Minoan Warm Period. The glacier then gained mass until about 3200 BP a time that corresponds to the end of Mycenaean civilization.

4. The glacier then lost mass during the period 1200 BP to 1500 BP, a period that corresponds to the Roman Warm Period.

5. The glacier gained mass for 300 years after 500 AD (1500 BP) during which Roman civilization declined.

6. From around 700-800 AD (1200 BP) to 1000 AD (1000 BP) the glacier lost mass due to warming. This would correspond to the Medieval Warm Period in Europe.

7. During the period from 1500 BP to 1000 BP the general increase in mass of the glacier was reversed by a significant glacier retreat around 1300 BP, before retreating to its furthest point around 1000 BP. This indicated that cooling was not uniform between 1500 and 1000 BP, but broken by a warm interval around 700-800 AD. 

8. After 1000 AD the glacier gained mass during the period known as the Little Ice Age, a gain that was reversed by warming after about 1800 AD.

9. Since 1800 AD (200 BP) the glacier has recovered mass lost since the year 1000 AD but has not yet recovered the mass lost since 700-800 AD (1350 BP).


It is not certain to what extent changes in glacier mass are driven by changes in temperature or changes in precipitation.

Wind blowing over a glacier can cause sublimation of ice directly to vapour without an intervening liquid stage. The mount Kilimanjaro Glacier is known to respond to wind in this way. Whether or not the Kulusuk Glacier has responded this way is apparently not known. If so, the mass of the glacier would be less than expected from melting caused by temperature change.

Therefore this attempt at correlation between the mass changes of a Greenland glacier and European climate is merely suggestive. Nevertheless, the analysis is consistent with that of H. H. Lamb.

As for the Greenland settlements about 1000 AD, it seems that Greenland may have recovered from the  very severe climate conditions that prevailed 200 years before settlement began in 985 (1030 BP) and by around 1000 AD appeared suitable for settlement.

The settlers could not have known that climate would deteriorate for hundreds of years during the Little Ice Age, just as we do not know if climate will again deteriorate and the glaciers again advance.

The Gleissberg Cycle of Solar Activity: Part 2

Sunspot Groups and the Gleissberg Cycle

In Part 1, sunspot numbers observed from 1750 to 2015 were used to display both the 11-year cycle and the century-long Gleissberg Cycle.

Here I plot the group sunspot numbers from 1610 to 2015 to include the Maunder Minimum, a period when few sunspots were observed, named after Mr. and Mrs. Maunder, a husband and wife team. (Edward Walter Maunder and Annie Scott Dill Maunder studied but did not observe the period now called the Maunder Minimum.)

GN anomaly

As before, the data source is WDC-SILSO, Royal Observatory of Belgium, Brussels. The data is version 2, the new series. The mean value of 3.78 has been subtracted from each data point in order to show the anomalies (departures from the mean (average). The plot shows the anomalies, not the absolute values.

The Maunder Minimum is the period during the 16th century when few observations exceeded the mean. The Dalton Minimum is a similar period of shorter duration from the end of the 18th to early 19th century. Not so obvious is a period centered around 1910 when sunspots were less numerous than usual.

Cumulative Group Anomalies

I accumulated the data series by adding the second value to the first value to get the value for the second data point. To get the third data point, I added the third value to the second data point. The new series will increase as the Group Number increases and will decline as the Group Number declines.

The graphic displays a metric for CUMULATIVE number of sunspot groups.

Cumulative GN

From the start date, the cumulative total increases and then declines until the Maunder Minimum. The cumulative value then rises during the 18th century and then declines until the Dalton Minimum, rises during the first half of the 19th century and then declines until around 1940 and then rises until the end of the 20th century.

I do not see a centennial-scale cycle here. The first cycle seems closer to 200 years, which would make it a Suess cycle (or de Vries cycle). Which is why I think of the Gleissberg and Suess/de Vries Cycle as pseudo-cycles.

The lack of regularity can mean either that the phenomenon is chaotic (like turbulence) or that other factors are operating, such as changes in gravity acting upon the Sun caused by the orbital motions of the planets.

[Ann Maunder noted the apparent association of sunspot appearances with the motions of the inner planets.]

I interpret the long sunspot cycles as indications of increases and decreases of the amount of energy entering the oceans and the ice caps of the Earth. The reason is that the atmosphere and uppermost few meters (yards) of land can store very little energy. I mention “ice” because when ice melts it absorbs a lot of energy as latent heat. So during the upward swing of the Gleissberg Cycle I expect an increase in solar energy entering the oceans in the tropics and melting ice at or near the poles.

The controversial aspect is the claim that changes in solar activity have a significant impact on the climate of the Earth. This question I leave until later in the series.

The model presented here shows a proxy (substitute) for solar activity. There are other proxies for solar activity that can be used alone or as “predictors” for sunspots. These I will discuss in Part 3 of this series.

First I ask the question, “Are counts of sunspot groups consistent with counts of sunspot numbers?” The reason I ask this question is that Group Number (GN) and the Sunspot Number (SSN) are two related but different proxies for solar activity.




The Gleissberg Cycle of Solar Activity: Part 1

What is the Gleissberg Cycle?

The Gleissberg cycle of solar activity spans roughly 80 to 90 years. Because it is not regular, it is probably better described as quasi-periodic or as a pseudo-cycle.

You can easily discover it for yourself.

How to Plot the Gleissberg Cycle

I found the newly corrected sunspot series here:  SILSO sunspot data (by remembering the name “Clette”, a scientist who has been doing research in this field for a long time.)

I entered the monthly data into a spreadsheet and plotted it.

SSN 175-2015

The 11-year cycle is apparent but the Gleissberg Cycle is not.

To display the Gleissberg Cycle, I standardized the values as described below and then cumulated the standardized values. In the following graph, the 11-year cycles appear in clusters of increasing or decreasing numbers of sunspots. A full cycle up and down is defined as a Gleissberg Cycle after Wolfgang Gleissberg.


To obtain Z-scores, I calculated the mean and standard deviation (using the functions AVERAGE() a.nd STDEV()). The Z-scores for every month, is defined as:


The key to the graph is this: After calculating Z-scores I cumulated the scores by recording the first Z-score by itself. Then for the second data point, I added the second Z-scores and so on. At some points the up scores added to the down scores should cancel and the line values should be zero (the line should cross the X-axis).

This method is very crude because the vertical position and the location of the high and low points depends on the starting value. The starting point itself is arbitrary, determined by the point in time when the observers started recording carefully enough and regularly enough for today’s scientists to report sunspot numbers instead of groups of sunspot numbers.

One way to improve would be to add 100 years or so of data going back to the Maunder Minimum, a period of 650 years from 1645 to 1715 when few sunspots were observed.

Because the Maunder Minimum was such a long period with few sunspots the graph would start around zero and a starting point near zero would be roughly correct according to our best current knowledge.


The 11-year solar cycles can be seen, usually 4 to 7 one after the other increasing and decreasing. The peaks occurred around 1790, 1880, and 2005, 90 and 125 years apart. The troughs are 105 years apart.

The average of these intervals (90, 125 and 105) is 107 years, rather longer than the usual value cited of 87 or 88 years.

The cause of the Gleissberg Cycle is speculative. Possibly the process is chaotic, resulting from changes in magnetism deep in the Sun that cause turbulence at the surface. The chaotic nature of the cycle may result from two dynamos within the Sun that are interacting. The Gleissberg Cycle may be displaying the beat frequency of these two dynamos. Alternatively, the gravitational pull of the planets may affect the Sun’s activity.

Next I will try to improve the graphic by adding more data. SILSO provides annual data back to the 17th century.


To analyze the graphic we should keep in mind that it displays a metric for CUMULATIVE number of sunspots.

I interpret this as long-term (century) increases and decreases of the amount of energy entering the oceans and the ice caps of the Earth. The reason is that the atmosphere and uppermost few meters (yards) of land can store very little energy. I mention “ice” because when ice melts it absorbs a lot of energy as latent heat.

So during the upward swing of the Gleissberg Cycle I expect a lot of solar energy entering the oceans in the tropics and a lot of melting ice at or near the poles.

Ocean currents tend to distribute energy from tropical to polar regions. So I would expect to see ice melting in the Arctic Ocean. I would expect to see less ice melting in the Antarctic. Why?

First, the southern oceans are bigger and so the heat is distributed less densely.

Second, the existing ice is more extensive than in the Arctic and therefore the Antarctic ice reflects more light back into space preventing it from converting into heat energy. In effect, the 100-year length of the Gleissberg Cycles  is not long enough to have much impact on the Antarctic ice cap.

Further, ice in the Antarctic is mostly land-based and is therefore less affected by ocean heating. By contrast, ice at the margins that is not grounded on the seafloor would be subject to increased melting.

These theoretical predictions are confirmed by observations.

Finally, I conclude that even if one solar cycle of 11-years does not greatly affect climate, a series of 5 sunspot cycles either up or down may be expected to have a cumulative effect. What makes it so difficult to determine the effect is the fact that ocean currents must be integrally involved because only the oceans can store solar energy for 50 years and then release it.

The oceans therefore act as a low-pass filter for variability in solar output.

There is an interesting paper by Nir Shaviv, Using the Oceans as a Calorimeter to Quantify the Solar Radiative Forcing. He estimated that the variation in ocean temperature within one solar cycle is about 0.1 degree Celsius.

We can see from inspection of the Gleissberg Cycle graphic that from 1935 to 2005 the time span is about 70 years compared to 7 solar cycles, giving a duration of 10 years per cycle. The vertical span of the upward swing is 7 bars, and each cycle averages one vertical bar.

If each cycle from top to bottom represents 0.1 degree Celsius, that would give a span of 0.7 degrees Celsius between 1935 and 2005. This may be compared with the rise in ocean heat content estimated to have raised the temperature by about 0.8 degrees Celsius per decade, 056 degrees C in 70 years (1935-2005). This rough comparison suggests that from 1935 to 2005 the Earth’s oceans should have heated by 0.7 degrees Celsius from excess solar energy alone, whereas the oceans heated only 0.56 degrees Celsius.

This analysis seems to be flawed because that would be too great a rise in temperature. The variation in one 11-year cycle may overlap the variation in the next. Assuming only 50% of the figure estimated by Dr Shaviv (o.o5 degrees Celsius) the heating from solar variation over 7 cycles would be 0.35, 60% of total observed oceanic heating.

This analysis suggests that the percentage of total heating by increased solar activity between 1935 and 2005 was between 60% and 100%.

There remains the possibly that much of the increase in solar energy:

… was reflected back into space by ice and clouds

… melted ice without increasing temperature

… evaporated water at the surface that rose into the upper troposphere and was there emitted into space

OR Sunspots are not so tightly correlated with the Sun’s energy flux as hitherto believed.

Still the Gleissberg Cycle is important because at least some approaches to analyzing Sunspots cycles suggest that solar energy accumulates over many cycles sufficient to affect global warming.

This is a highly controversial subject that I leave until later in this series.

Part 2 will attempt to extend the analysis back to 1610. This will correct some of the bias at the beginning of the series because the zero point on the graph will coincide with a time when there were few sunspots observed.

Statistics with R Using Atmospheric Gases: Part 4 Reviewing the Scientific Literature


Literature Review of the Mauna Loa CO2 Series

I deliberately explored the data before delving into the literature. But even so, I found it difficult to set aside general knowledge acquired from study of geoscience.

Pieter Tans of the ESRL provides references to the two most important seminal papers.

Related papers

The literature is substantial, especially since the measurement of atmospheric gases now covers several more species of gas collected by a global network of observatories. Charles Keeling was a leader in the field for many years.

There is now a substantial literature based on data series from the observatories in the global network, useful to give perspective to other oceanic and land influences in addition to North America and northern Europe.

Google Scholar is a virtual Who’s Who in the study of CO2 worldwide.

Lessons from Thoning, Tans and Komhyr 1989

The literature is extensive, too extensive to review here. I conclude that all my exploratory observations were discovered by Keeling and others more than 40 years ago. The techniques of separating the trend from the annual cycle are various and complex.

The record of CO2 at Mauna Loa is basically a combination of three signals: a long-term trend, a non sinusoidal yearly cycle, and short-term variations from several days to several weeks that are due to local and regional influences on the CO2 concentration. (Thoning, Tans  and Komhyr, 1989)

The analysis must therefore be complex as illustrated by the methodology used to decompose the data:

The curves used for selecting data and calculating monthly and annual means were obtained using a procedure described by Thoning et al. [1989]. Briefly, the curves are a combination of a quadratic fit to the trend and a fit of sines and cosines to the annual cycle and its first three harmonics. The residuals from these fits are then digitally filtered with a filter having a full width half maximum cutoff at 40 days to remove high-frequency variations. The results of the filtering are then added to the fitted curves. At this point the residual standard deviation of the points from the curve is calculated, and points lying more than +3 [sigma] from the curve are flagged as not representative of background or regionally well-mixed conditions. The procedure is repeated on the unflagged values until no more points are flagged.(Conway, Tans, Waterman, and Thoning, 1994)

This paper describes an approach using Fourier analysis, followed by filtering in the frequency domain and then reversing the process to convert the smoothed data back to the time domain. To discover something that has not already been discovered seems a daunting task, the reason Einstein said, “If at first, the idea is not absurd, then there is no hope for it”.

I do have an absurd idea, a couple of absurd ideas, in fact. The most absurd of my ideas is to use the annual minima and maxima to estimate the trend. My ideas are inspired by comments made by Thoning, Tans, and Komhyr in 1989.

It can be seen from Figure 8 that the annual cycle has the same basic shape from year to year, although with some small but significant variations. For example, the peaks of the cycles can vary from a sharp point to a more rounded shape…. The mean peak-to-peak amplitude for the 12 years from 1974 to 1985 was 6.77 ppm, with a standard deviation about the mean of 0.32 ppm.

Enting [1987] found a correlation between the peak heights for each spring and the following fall for SIO [Scripps Institution of Oceanography] monthly mean data from 1960 to 1981. Low-amplitude peaks in the spring were followed by low-amplitude troughs in the following fall. He did not find any correlation between the fall troughs and the following spring peak. If we plot the absolute values of the maximum and minimum values for the seasonal cycle (Table 3) in a manner analagous to that of Enting, we find a correlation opposite to that stated by Enting. We see no correlation between the size of the peaks and troughs in the same year (correlation coefficient = 0, Figure 11a), but we do find a correlation for the size of the fall troughs followed by the spring peak…(pp.8559-8556).

The dates at which the minima of the annual cycle occur are more consistent than the dates of the maxima. The dates at which the seasonal cycle crosses the trend line are also more consistent for the drawdowns in July than for the increases in January.  Peterson et al. [1986] found a similar consistency for the continuous CO 2 measurements at Barrow, Alaska. This suggests that the forces that drive the summer CO 2 drawdown in the northern hemisphere are stronger and more regular than any interannual variability in CO 2 but that during the winter and spring the release of CO 2 by the biosphere and atmospheric transport are more variable in time and more easily affected by regional or hemispheric variations in CO 2. This can also be seen in Figure 4, where there tend to be larger and more frequent excursions from the filtered curve during the first half of the year than in the latter half.

Enting, I. G., The interannual variation in the seasonal cycle of carbon dioxide concentration at Mauna Loa, J. Geophys. Res., 92, 5497-5504, 1987.

In my opinion, with 25 years more data, it is time to revisit both Enting and Thoning, Tans and Komhyr.

Besides, the peaks and troughs are intrinsic to the underlying physical and biological processes. From a certain point of view, the historical and continuing anthropogenic emission of CO2, (the long-term trend) is a nuisance because it complicates the task of estimating the natural sources and sinks. It seems to me that improving the estimation of the trend would contribute to improving estimates of the variation in the cyclical changes in the sources and sinks. At least, that seems to me a good place to start.

The SIO and MLO CO2 Data Series Compared

Thoning and Tans also discussed the Scripps CO2 (SIO) data series and how some of the SIO data was used to fill gaps in the Mauna Loa Observatory (MLO) series. The SIO weekly data extends from March 19 1958 to the present. Therefore, at least in principle, there is data from this locale for 57 years. Inspection of the two data series revealed the following:

  • The MLO series (from May 1974) has more regular intervals of 7 days than the SIO series (from March 1958)
  • The MLO series has fewer gaps than the SIO series for the period May 1974 to the present.
  • The mean absolute difference between the series since May 1974 is about 0.5%.
  • The differences between the series are probably randomly distributed, something to be verified.
  • A reasonable working hypothesis is that both series are drawn from the same population with normal sampling error but the MLO series has benefited from marginally better control.
  • Both data series use a calendar year of 365 days. The MLO-week runs from Monday to Sunday and the SIO-week from Sunday to Saturday. Thus, the two date series can be synchronized by aligning observations with one day difference. (I am not certain, but I think there may be only 12 hours difference, between midnight and noon,)

Note: The year adopted by SIO and MLO is close to the tropical year. The International Union of Pure and Applied Chemistry and the International Union of Geological Sciences have jointly recommended using the length of the tropical year in the year 2000, approximately 365.24219 days.

The Gregorian Calendar has 365 regular days, but with the leap day has 365.2425 days. The difference of 3 days in 10,000 years is not the problem in aligning the weekly data. Rather the number of weeks per year is the problem.

Some years have 53 weeks and to analyze the series, it is convenient to drop the 53rd week. But a 52-week year has only 364 days, whereas these series are based on 365 days. After 57 years the series would be approximately 5.7 weeks out of synchronization. That’s the problem.

For analysis, my year overlaps two calendar years by aligning the series so that the week of the vernal equinox is week 1. My years is 52 weeks, extending into the following calendar year. For the SIO data this adjustment results in an average departure of the mean time of observation at the vernal equinox of 0.07+/-1.99 days and maximum departure of +/-3 days. This variation in observation time is approximately equal to half of the 7-day period over which the daily observations were averaged. 


I expect that, after appropriate testing and verification, I will be able to  obtain a series of 56 years of nominally continuous weekly observations of CO2. Prior to 1974, 19 gaps in the SIO data must be interpolated to standardize the time to 7 days between observations. Inspection of the SIO data post-1973 suggests that very little interpolation will be needed.

For the initial analysis, I intend to work with the annual maxima and annual minima.  Using the SIO series will permit me to apply a version of the Fourier transform (the FFT) that requires the length of the series to be an even power of 2. This can be achieved by padding the series to 64 years (2 to the power of 6). The standard padding method is to extend the series using zeros.

But I  wonder if this series is so regular that other approaches might be possible. Study of the literature will take up to 3 months. This is an essential step because several papers have passed peer review even though the numerical techniques were faulty to the extent that the authors reported their artifacts as scientific results.

There is not much point in exerting a lot of effort in data preparation and analysis only to cause confusion by using faulty procedures.

In process ….