Digital Diatribes

A presentation of data on climate and other stuff

Archive for the ‘Cycles’ Category

360-Month HadCrut trends as of April month-end 2011

Posted by The Diatribe Guy on June 29, 2011

Today I present the 360-month charts using the most recent HadCrut data.

The 360-month trend line is positive, with a slope of 0.1356, which translates to a temperature change of approximately 0.49 degrees Celsius over the course of 30 years.

Now that I’ve looked at all the different charts and see warming of 0.49 degrees over a 30 year period, here’s how it appears to break down by period:
May 1981 – Apr 1986: +0.10 degrees Celsius contribution to increase
May 1986 – Feb 1991: +0.05 degrees Celsius contribution to increase
May 1991 – Apr 1996: +0.24 degrees Celsius contribution to increase
May 1996 – Apr 2001: +0.17 degrees Celsius contribution to increase
May 2001 – Feb 2007: -0.18 degrees Celsius contribution to increase
Mar 2007 – Apr 2011: +0.11 degrees Celsius contribution to increase*
* – Due to an original error in the presented 60-month chart only being 50 months, the dates do not represent an equal 5-year span. The actual 5 year span was near zero. The previous 5 year period would adjust accordingly.

I’ve discussed the “step function” that seems to have taken place in 1996-97. While not presented here, a much better fit to describe the “trend” in global temperature, simply by observation, is to fit a line from 1981 to 1997-ish and then from that point forward. The best fits of those independent lines would show a very notable jump occurring at that point.

Chart below:

360-month Trend in Global Temps - HadCrut

360-month Trend in Global Temps - HadCrut

SLOPE CHANGES
In the chart below, we see the latest series of 30-year slope values since 2003. There was a steady decline in the slope value into 2009 that met the .1300 line, but has since increased to the current levels. The trend line is responding to a “fulcrum” of sorts. What I mean by that is that, even though lower anomalies are dropping off the left side of the chart (which normally would imply a lowering of the trend line) this is outweighed by anomalies on the right side of the chart staying up around the last decade’s average, and this is because of that step function that is now reaching the mid-point of the chart. If future anomalies stay around where they are at now, then when that fulcrum point moves to the left side of the chart, we will see that trend line slope value decline. We wouold not expect to see the 30 year trend line go negative unless there is a prolonged stretch of declining anomalies. Even in that scenario, it will take years to move that line around.

Chart below:

Trend of 360-month Slope values in Global Temps - HadCrut

Trend of 360-month Slope values in Global Temps - HadCrut

The entire history of 360-month slopes is shown in the chart below:

There has not been a negative trend line in the 30-year charts since the period ending November 1972. We won’t reasonably be expecting a negative trend line for another few years, even under a cooling scenario. What we can probably expect to see, however, is the slope in the trend line start to decrease soon. The slope will probably be fairly steady over the next 3-5 months, and then we’ll see some lower values emerge. In my estimation (assuming average 12-month anomaly values) we’ll see the slope on the trend line fall below 0.13 around march 2012, thus continuing the downtrend and slope values we’ve seen since 2003. We haven’t seen a slope under 0.13 in the 30-year line since April 1999.

Chart below:

History of 360-month Slope values in Global Temps - HadCrut

History of 360-month Slope values in Global Temps - HadCrut

Posted in Climate Change, Cycles, Data, Earth, Global Warming, HadCrut, Information, Science, Temperature Analysis, Updates | Tagged: , , , , , , , , , | Leave a Comment »

300-Month HadCrut trends as of April month-end 2011

Posted by The Diatribe Guy on June 28, 2011

Today I present the 300-month charts using the most recent HadCrut data.

The 300-month trend line is positive, with a slope of 0.1311, which translates to a temperature change of approximately 0.39 degrees Celsius over the course of 25 years. It’s kind of interesting to see the breakdown of the warming by looking at the different trend-lines. The 15-year chart ending in the current period attributes 0.10 degrees in temperature change in total over the last 15 years. The 20-year trend line tells us that total warming over the last 20 years equals 0.34 degrees. So, in that five year period from 1991-1996, we see a period of anomalies that were lower than both preceding and succeeding periods, which drives the slope higher on that trend line and tells us that 0.24 degrees of the 0.34 degrees can be blamed on that time period’s lower anomalies. The current slope value of the 25 year trend line adds 0.05 degrees to the total warming, so the 5 year period from 1986-91 only accounts for a total of about 0.01 degrees Celsius per year.

Chart below:

300-month Trend in Global Temps - HadCrut

300-month Trend in Global Temps - HadCrut

SLOPE CHANGES
In the chart below, we see the latest series of 25-year slope values since 2007. There has been a steady decline in the slope value, with only a short lull (flat) in 2008. In the last half-year, the rate at which the trend line is decreasing has accelerated as some older, lower anomalies drop off the front end. The last time the slope value has reached current levels was January 2002.

In all likelihood, the 25-year trend line will remain positive for the next few years to come. In a scenario of just using a 12-month average going forward, the trend line would not become negative until 2020. Obviously, if temperature readings decline that would accelerate. If temps drift upward, it’s possible that we won’t see a 25-year trend line reach zero or negative at all.

Chart below:

Trend of 300-month Slope values in Global Temps - HadCrut

Trend of 300-month Slope values in Global Temps - HadCrut

The entire history of 300-month slopes is shown in the chart below:

There has not been a negative trend line in the 25-year charts since March 1969. Now, more than 42 years later, we will not reasonably expect any possibility of seeing a negative slope for at least another 5 years or more. Things got real close in 1976, but at its low point the trend stayed slightly positive.

Looking at the history, the last prolonged stretch above zero trend started in January 1922 and lasted until July 1954. That was a stretch of 32.5 years, so we are well past that at this point. We are in a period where the current retracement is the largest since 1976, but despite that we are still well above the zero line.

Chart below:

History of 300-month Slope values in Global Temps - HadCrut

History of 300-month Slope values in Global Temps - HadCrut

Posted in Climate Change, Cycles, Data, Earth, Global Warming, HadCrut, Information, Science, Temperature Analysis, Updates | Tagged: , , , , , , , , | 4 Comments »

240-Month HadCrut trends as of April month-end 2011

Posted by The Diatribe Guy on June 24, 2011

Today I present the 240-month charts using the most recent HadCrut data.

The 240-month trend line is positive, with a slope of 0.1399, which translates to a temperature change of approximately 0.34 degrees Celsius over the course of 20 years. This is fairly significant warming over that period. Since the 15-year chart shows less than a third of that amount in total warming, the majority of the slope value is attributable to the lower anomalies in the first five years. The current slope value of the 20 year trend line is at about the same level as it’s been for the last year and a half or so. It would certainly appear that if temperatures do not dramatically increase, the slope value will decrease as some of those lower anomalies drop off. Every single anomaly for the next three years is lower than every anomaly since mid-2001. However, since no anomalies have since exceeded the peak value in 1998, the trend line certainly looks to have a high probability of decreasing in slope.

Chart below:

240-month Trend in Global Temps - HadCrut

240-month Trend in Global Temps - HadCrut

CORRECTION ON CURRENT FLAT/COOLING TREND

As I was reviewing the above chart, and eyeballing the data since 1997, I was a bit surprised that there wasn’t a trend line that was flat or negative going back to 1997/98. So, I went back to the data and am embarrassed to say that there is. In my first post back after a long hiatus, I didn’t offer my best work, apparently.

Extending a trend line backwards from April month-end, the best fit trend line does in fact switch from negative to positive between July and August 2000. What I missed was that there is a stretch from May 1997 to November 1997 where the best fit trend line is negative. In other words, we can extend a negatively sloped trend line back in the HadCrut data to May 1997. That is exactly 14 years (which better explains why it looks like the 15-year trend line will go negative within the next year).

I know that there are issues with linear fit and all that stuff, but when the current line goes back 14 years, you’d think that would make some people pause a bit and wonder where this exponential warming is.

My apologies for the erroneous statement in my initial post of this series. I suppose I’ll need to update that chart with May month-end data.

SLOPE CHANGES
In the chart below, we see the latest series of 20-year slope values since 2004. There was a steady decline in the slope value until late 2009, at which point it’s vaccilated around where the current value is. Unless temperature anomalies start to meet and exceed the 1998 peak, we can expect a continued decline in the slope value. Since longer-period slopes take a longer time to adjust, we will need to see anomalies around current averages for the next 5 years or so before we’d see an actual declining trend line. If temperatures drop, this would obviously accelerate. Likewise, if temperatures spurt upwards, we may not see a negative trend line at all in the foreseeable future. Even under a very aggressive cooling scenario, it would take nearly three years to see a negative trend line. So, like it or not, global warming proponents will be able to use 20+ year trend lines to make their point for a few years.

Chart below:

Trend of 240-month Slope values in Global Temps - HadCrut

Trend of 240-month Slope values in Global Temps - HadCrut

The entire history of 240-month slopes is shown in the chart below, with the following observations:

There has not been a negative trend line in the 20-year charts since February 1979. Now, more than 32 years later, we will not reasonably expect any possibility of seeing a negative slope for at least another 3 years.

Looking at the history, the last prolonged stretch above zero trend started in October 1919 and lasted until August 1950. That was a stretch of almost 31 years, a length of time we’ve already passed. It will be interesting to see if a downward plunge is in store for us, as a cyclical mindset might think is the case. However, even with a cyclical mindset, it has to be recognized that we’re comparing to exactly one previous similar cycle, so it’s hardly a credible sample.

Chart below:

History of 240-month Slope values in Global Temps - HadCrut

History of 240-month Slope values in Global Temps - HadCrut

Posted in Climate Change, Cycles, Data, Earth, Global Warming, HadCrut, Information, Science, Temperature Analysis, Updates | Tagged: , , , , , , , , , | 1 Comment »

180-Month HadCrut trends as of April month-end 2011

Posted by The Diatribe Guy on June 23, 2011

Today I present the 180-month charts using the most recent HadCrut data.

15 years starts to get to a point where some of those short-term cyclical variations start to get eliminated. Mind you, because I believe there are some clear longer-term cycles in the temperature data that span as long as 60 years, I think ANY trend line shorter than that has questionable value for extrapolation purposes.

The 180-month trend line is positive, with a slope of 0.0555, which translates to a temperature change of approximately one tenth of one degree Celsius over the course of 15 years. (Sounds like enough to melt a glacier or two, eh?) The current slope value of the 15 year trend line is actually at its lowest value since the period ending October 1994. The left side of the graph has some lower anomalies that will be dropping off over the next few months, and barring extremely high anomaly measures over the next few months, it is almost certain that the trend line slope will continue to decline for at least a bit.

Chart below:

180-month Trend in Global Temps - HadCrut

180-month Trend in Global Temps - HadCrut

In the chart below, we see the latest series of 15-year slope values since 2007. As noted above, we’re now at the lowest slope value in almost 17 years, and it has every likelihood of continuing lower. In fact, if I look forward and simply assume an average 12-month anomaly going forward for each month, this trend line will go negative in less than a year. That’s not a prediction, because I don’t know what the future of anomalies will bring, it’s just an observation. Still, it’s a fairly remarkable possibility that in the course of the next 10 months our “look back” negative trend line would go from just over 11 years to 15 years. We’ll just have to wait and see what happens.

Chart below:

Trend of 180-month Slope values in Global Temps - HadCrut

Trend of 180-month Slope values in Global Temps - HadCrut

The entire history of 180-month slopes is shown in the chart below, with the following observations:

1) Since 1960, there has very clearly been a continued positive trend measured in 15-year time increments. It’s too bad we don’t have good data prior to 1850 so we can see if there was a period of time where most of the trends were negative over a long span. If so, something seemed to “flip” around 1910. I suppose AGW proponents would point to this as the onset of CO2 emission expansion.

2) From October 1915 to November 1948 the 15-year trend line was positive. (33 years, 2 months)
3) From December 1948 to July 1959 the trend line was negative.
4) That period was followed by some fluctuation around zero.
5) The current stretch of positive trend lines began in May 1977. So, our current stretch above the zero trend is at exactly 34 years.

Chart below:

History of 180-month Slope values in Global Temps - HadCrut

History of 180-month Slope values in Global Temps - HadCrut

Posted in Climate Change, Cycles, Data, Earth, Global Warming, HadCrut, Information, Science, Temperature Analysis, Updates | Tagged: , , , , , , , , , | 2 Comments »

120-Month HadCrut trends as of April month-end 2011

Posted by The Diatribe Guy on June 22, 2011

Today I present the 120-month charts using the most recent HadCrut data.

While 10 years still doesn’t have the significance that longer term trends will have, there is some value in looking at the last decade, at least in the sense that if temperatures don’t appreciate significantly for a 10 year stretch or more, it allows for a bit more of a skeptical eye towards claims of future temperature increases of 1, 2, or 5 degrees by the end of the century. I already showed in my “Overall” post that temperatures have been flat for almost 11 years.

The 10-year trend line is negative. Again, this is a shorter term line that can adjust between positive and negative, so fluctuations are to be expected, and a negative trend line isn’t at this point indicative of a trend that we could feel confident projecting forward. Whereas the trough in the anomaly measure at the end of 2007 helped spur on a positive trend in the 60-month line, the same phenomenon coupled with lower anomalies very recently are helping to pull that best-fit trend line down.

Chart below:

120-month Trend in Global Temps - HadCrut

120-month Trend in Global Temps - HadCrut

Much more significant in a longer term view of what’s been happening over the last few years with the 10-year trend lines is the next chart, which plots the slope vlaues since 2002. Even though the 10-year trend line has been positive for most of that time period, the slope value has steadily declined (very steady, in fact, shown by the very high R-squared value). So, even though (until a few months ago) the trend line showed warming, it showed warming at continually lower rates. This is quite different from the view of acceleration in the rate of warming. This indicates the exact opposite.

Over the last few months, the trend line took another plunge into negative territory. As those troughs in the chart above move to the left side of the chart, we can expect the trend line to flatten, and unless there are continually lower troughs on the way, the trend will likely be positive again within the next couple years. The question is whether that will be the start of a continually increasing slope or if that will be another soft bump on the way to lower trend readings.

Chart below:

Trend of 120-month Slope values in Global Temps - HadCrut

Trend of 120-month Slope values in Global Temps - HadCrut

Finally, I present the entire history of the slope values to put the current downtrend into perspective. The current value of -0.0578 is a bit difficult to see on the right side because I have a thicker border obfuscating that, but there are some interesting observations to be made:

1) The last negative slope reading occurred with the period ending May 1997. This was a very short-lived stay in negative territory. The 10-year slope was only there for 6 months and never reached a value below -0.01.
2) The last time the slope was as negative as it is now occurred with the period ending April 1977 – exactly 34 years ago. Once that stretch of negative trend lines ended in August 1979, the period of almost unbroken strings of positive 10-year trends continued with that brief exception noted in (1) until November 2010. That’s a period of 31 years, 4 months.
3) A similar period began in January 1915. With the exception of a brief and shallow period of negative trend lines in the 1920s (lasted 5 months) there was continued positive 10-year trend lines through July 1946. That is a period of 31 years, 7 months.
4) At the end of the period in (3) we saw the steepest decline in temperatures (on a 10-year trendline basis) in the history of the chart going back to 1850. The negative trend lines continued through October 1957, a period of about 11 years. I have no basis to say that history will repeat itself, but i do find the parallels in the chart interesting.

Chart below:

History of 120-month Slope values in Global Temps - HadCrut

History of 120-month Slope values in Global Temps - HadCrut

Posted in Climate Change, Cycles, Data, Earth, Global Warming, HadCrut, Information, Science, Temperature Analysis, Updates | Tagged: , , , , , , , , , | Leave a Comment »

60-Month HadCrut trends as of April month-end 2011

Posted by The Diatribe Guy on June 21, 2011

In my previous post I mentioned that there was a two year stretch of year-over-year increasing anomalies until the latest 9 months.

NOTE: In reviewing the data after I made this post, I realized that the chart presented below is based on 50 months, not 60 months. I have edited the text below to reference 50 months, and the chart is mis-labeled. The slope charts are correct.
On the 50-month chart we can see this detail a bit clearer. A trough occurs about 3 years ago, followed by increasing anomaly readings. The current downtrend is not enough to offset a positive uptrend.

By itself, a raw, fitted 50-month trend in the world of temperature statistics is fairly meaningless. But I’m just showing the charts and letting the reader decide what kind of mental effort is worth putting into it. Probably isn’t worth much more than a noteworthy point of interest.

Chart below:

60-month Trend in Global Temps - HadCrut

50-month Trend in Global Temps - HadCrut

Of a bit more interest to me (but not much more…) is the current trend in how the 60-month slope values have been changing. This tells us whether or not there is an acceleration or deceleration in the trendline. I find this more interesting because it puts the current trend line in context with previous readings. The actual trend line is probably not as meaningfull as the graph itself, but it’s a nice visual.

What we see here is that the 60-month trend line had achieved a minimum slope value of just under -0.3 about halfway through 2008. We then saw the slope values increase to near 0.15 by the end of 2010. Over the last few months, we’ve seen a fairly sharp reversal, and it looks as if slopes are back on a downturn.

Again, the 60-month slopes are pretty variable, so there’s still no real stunning conclusions to be had here.

Chart below:

Trend of 60-month Slope values in Global Temps - HadCrut

Trend of 60-month Slope values in Global Temps - HadCrut

Probably the most meaningful and interesting chart regarding 60-month trends is the entire historical view on how the slope values change over time. I find it interesting because one can see that there are a constant series of peaks and valleys in the 60-month slope values. Observation of this chart highlights a couple things of note:

1) The highest 60-month slope occurred back around 1880. Subsequent peaks were of lower magnitude until around 1930, at which point peaks increased in magnitude until the late 1990s.
2) The minimum 60-month trend value followed a series of lower minimums that started in the 1860s and ended around 1905. From that point until around 1940 the minimums were higher.
3) There was a sudden plunge in the 60-month slope that reached a minimum around 1950. This then started an upward trend in minimums until 2000. The chart of minimums from 1905 – 1945 looks very similar to the stretch from 1950 – 2000.
4) If the current peak fizzles at under a 0.2 maximum following a minimum below -0.2, it would mark the first time since the early 1920s that this would have happened. I have no idea what this means, but I thought I’d point it out.
5) More importantly, if you observe what I’ll call the “major peaks” since 1950, which increase over one another, and then observe the “minor peaks” which increase over one another, then a fizzling at under 0.2 would represent the first instance of a significantly separated “minor peak” from previous peak to (a) not be a “major peak” and (b) to decline from previous “minor peak.” This also hasn’t happened since the 1920s.
6) It is apparent that since the mid-1970s a lot more time has been spent in the “positive slope” territory of the chart than in the “negative slope” area. This shouldn’t be surprising, given the fact that the anomalies saw their most significant increases in the 1980s and 1990s.

Chart below:

History of 60-month Slope values in Global Temps - HadCrut

History of 60-month Slope values in Global Temps - HadCrut

Peace, dudes.

Posted in Climate Change, Cycles, Data, Earth, Global Warming, HadCrut, Information, Science, Temperature Analysis, Updates | Tagged: , , , , , , , , , | Leave a Comment »

The Best of Digital Diatribes (In one man’s opinion…)

Posted by The Diatribe Guy on July 15, 2010

Over the course of my time here, there seem to be a handful of posts that I keep referring to. These posts are referred to because of other studies that arise, or questions that come up.

I don’t consider my blog to, for the most part, have provided a plethora of new information to the discussion on climate, climate change, or the science behind the data. Most of my posts on the subject are more of a curiosity. “Hey, here’s a bunch of data. Here’s a bunch of trends at different lengths. Here’s how those trends are changing.” Most people with an understanding of Excel and statistics could do something similar. I guess maybe others aren’t as interested to just look through a bunch of numbers to see if any interesting things jump out, so to the extent I’ve been able to add something, that’s great.

There have been times, though, where I do an analysis and put together a post that I’m particularly proud of. I believe it actually does add to the debate.

Interestingly, those more complex posts with an actual interesting conclusion seem to get less attention than a simple trend line chart. I continue to be astonished by the debates that can ensue over a simple line chart.

But nevertheless, since there are a few posts that (a) I really like, (b) refer to quite a bit – and every time I do I have to dig through and remember where it is, and (c) I think actually add a new insight to the debate, I thought I’d highlight these posts again, while putting them all into one post.

So, with that introduction, here they are:
(1) Sunspot study that derives a correlation between sunspots and temperature

(2) A best fit of sine waves to HadCrut data that clearly shows cycles within the temperature data

(3) A look at the AMO data, demonstrating where we are in the current cycle, and where we’re headed

(4) A look at a few ocean cycles, but the focus here is the PDO analysis

(5) A demonstration of the fallacy of a singular trend-line fit in the recent temperature data, and how most of the increase in temps has come from a single step

Posted in Climate Change, Cycles, Data, Earth, Global Warming, Information, Oceans, Science, Temperature Analysis | 10 Comments »

Uh Oh… Does the plummetting ENSO Index portend a cold winter?

Posted by The Diatribe Guy on July 10, 2010

We’ve had a wetter than average summer, but the temperatures here have been glorious. Out East, they have been scorching temps as of late, and a lot of people are making a lot of hay about that (I’ve never really understood that expression).

Global temperatures have been warmer. It is what it is. No use pretending otherwise.

But this wasn’t completely unexpected. In fact, as a resident skeptic, I personally suggested prior to last winter that we’d have mild one. It isn’t rocket science. The ENSO index was into persistent El Nino territory and that was that. My prediction turned out to be right. Oh, sure, as always in Wisconsin, we had our extremely cold days, but all in all it was warmer, we had more days than normal get into temps that melted snow, and we had an early spring. And thanks, at least in part, to an ENSO index that stayed above the 0.5 mark from the 2009 May/June reading to the 2010 April/May reading we have continued to see warm temps.

So, imagine my surprise when I just randomly clicked on the index to see a May/June reading of -0.412.

Now, without any other context, this isn’t an extraordinarily low number. But there is a bit of context here that makes this a fairly fascinating number.

First, the index tracks on a two-month average basis. Thus, going from an April/May value of 0.539 to a May/June value of -0.412 (a drop of 0.951) must imply a very dramatic cooling in June. It’s one thing to see that kind of number when the previous one was -0.2, it’s quite another to see it after an El Nino-esque reading in the prior period.

So, I was curious to see how this compared to previous drops in the index.

I was both surprised, and not surprised, to see that this drop is the largest single month-to-month negative change in the index since the beginning of the readings in 1950.

Ouch.

I am not entirely sure what this means, and I suppose we need to see what happens over the next couple months. But I don’t like the timing. The impact of La Nina will have a few month lag, which puts us squarely in line for a harsh winter.

If you’re curious about the other laregest drops and what happened after those drops:

2nd place: -0.915 May/June 1998. This was a drop from an extremely high index reading to a still high reading. (From 1.982 tp 1.067) Within 3 months we saw La Nina, and it persisted 19 months, if you include one reading just above -0.5.
3rd place: -0.825 Apr/May 1954. This was a shift from a shallow La Nina value (-0.598) to a deep La Nina reading (-1.423). Including the initial value, this started a La Nina that persisted for 34 months.
4th place: -0.799 Oct/Nov 1950. This was a move from a negative reading (-0.381) to La Nina (-1.180). Something seems odd here. Deep La Nina readings are in place from the first month of 1950, then we had a jump, and then this drop. La Nina persisted another 5 months.
5th place: -0.775 May/June 1988. This was a move from barely positive (0.090) to La Nina negative (-0.685). This started a La Nina that persisted for 12 months.

Not to be a pessimist, but if you’re in my area, enjoy the next 2-3 months while you can.

Posted in Cycles, Data, Earth, El Nino, ENSO, La Nina, Oceans | Tagged: , , , , , | 10 Comments »

Curve-Fitting the ENSO Index Suggests We Have the Highest El Nino Event since 1998

Posted by The Diatribe Guy on January 28, 2010

ENSO 200912

ENSO Index and Fitted Curves @ 12/31/2009

I’ve continued to work, as I have the time to, on pulling the Oceanic Oscillation data, developing a fitting spreadsheet for each index, to get some idea of what the underlying cyclical nature of the oscillations may be.

I decided to post the above chart on ENSO, since I (a) completed it, (b) we’re currently in the midst of an El Nino, and (c) most amateur climatologists know about it and occasionally like to take a look at it.

The source for the data can be found on the right side of this page. The largest hurdle in the curve-fitting is that good(?) data only goes back to 1950. Even this may be a little questionable, and from what I’ve read, any proxied data prior to that is even less reliable. But, we’ll run with the data we have with the caveat that is always there about analysis only being as good as the accuracy of the data and all that.

I’ve been very interested in trying to understand the tendency of these oscillations to cycle (or not cycle, as the case may be). The ENSO index, in particular, can have the appearance of a random variation with no particular pattern.

At this point, I need to explain what I did here, and then I need to explain what I am saying and what I am not saying regarding the conclusions.

PROCESS

1) I have simultaneouosly fitted a long-period wave and a short-period wave to the ENSO data
2) The following elements have been fitted:

For the long period wave:

  1.  Best fit sine wave with a period of at least 30 years
  2. A scale factor to determine amplitude of the wave
  3. A phase increment amount to determine the length of the wave
  4. A starting point on the wave cycle to be fitted at the beginning of the data
  5. A vertical shift, to account for bias in the zero-anomaly base assumption
  6. A slope of linear trend

For the short wave:

  1. Best fit sine wave with a period less than 30 years
  2. A scale factor for amplitude
  3. A phase increment amount to determine cycle length
  4. A start point on the wave at the beginning of the data

There is no shift or trend determined on the short wave determination, since this will follow the path of the long wave.

Through a simultaneous and recursive process, all these elements are simultaneously solved to produce the minimum value of squared differences from the point on the short wave to actual ENSO index readings.   The ultimate solution is not necessarily incorporating the best-fitted long wave taken in isolation.   I initially ran the long-wave fit first, and then separately ran the best fit short wave along that curve.   Moving to running everything simultaneously helped the overall fit and actually reduced the length of the long-wave.    The difference is not huge, but since it is the best fit and the results appear reasonable, I went with that.

RESULTS

The results of this analysis show a 50.5 year ENSO cycle that underlies the shorter-term variations.   I have shown this before, and it is an interesting consideration in evaluating the relative magnitude of certain ENSO events, not so much as it relates to the zero value, but as it relates to the long-term wave.   The current long-term wave is on a decline, and may, in fact, be bottoming out in another four or five years.

The starting point is just past the halfway mark of the cycle, so we see a lower-index period at the beginning of the chart.  The amplitude of the wave is about 0.32 at its peak.   So, from top to bottom (with no linear trend) there is a difference of 0.64 in the magnitude contributed to ENSO events from one period to another, depending on where the long-term cycle is at.

There seems to be, in addition to the cycle, a linear trend in the data for which the long-term cycle moves along, at least since 1950.   It may be that there is a third cycle that is substantially longer that is being mistaken for a linear trend.   This may matter in the long run, but for a 60-year time period the linear approximation should suffice.   However, it may well be that we need a number of additional years of data to better fit this and judge whether or not there is a linear trend, or some other cycle at work.  For now, though, I go with the best fit, and for that the rate of change is 0.7 degrees Celsius per century.

This long wave is being fit simultaneously with a short wave placed on its path.   The period of this short wave is 4.93 years.  Its scale is 0.49.   So, at the top of this wave, plus the top of the long wave, we are adding 0.81 degrees to the ENSO index.   The first wave starts at about the 220 degree mark of a cycle.

Key Assumptions (What I’m doing versus what I’m suggesting)

There are a couple key assumptions here.  The primary assumption is the selection of a sine wave for fitting.  I am not saying this is the best assumption.  All I am saying is, given this assumption, there is a best fit.   As I look at the data, it actually doesn’t do too bad a job in aligning with peaks and valleys.  However, it is far from perfect.   There are other ways to manipulate this, if desired.  One can select a skewing assumption so that the wave peaks earlier or later in the cycle than at 90/270 degrees.   Or, once can assume that there is a factor that compresses or expands length over time (or both in some oscillating pattern over years).   Another thing to look at is to see if the length of sunspot cycles impacts the difference in timing of ENSO peaks/valleys, as I’ve seen suggested.

All these are potential refinements that could improve results.   However, all that said, I still think there are some interesting results here.   The most significant El Nino events do seem to correspond well with peaks in both waves.

The other assumption is that there are two cycles to consider.  A third assumption that can be questioned is the validity of a linear trend in the data.

DEVIATIONS

One may think that the waves represent the anticipated direction of the ENSO index.  That is actually not what the waves imply.  The red wave pattern marks the “starting point” for the current index.  From there, deviations may go up or down.    This may be the most confusing aspect on how to read the chart.   It’s not so much about predicting El Nino or La Nina, it’s about showing how the ultimate magnitude is affected.

Examples:

June 1955 ENSO index = -2.270; Wave value = -0.76.  Negative deviation = -1.51

September 1973 ENSO index = -1.71; Wave value = +0.20.  Negative deviation = -1.91.

One could argue that the 1973 event was substantially more profound than the 1955 event, even though the actual ENSO index reading was lower in 1955.

Likewise:

The most profound El Nino event, in terms of a deviation from the underlying wave, actually occurred in 1983 – not 1998.  The March 1983 reading = 3.11, and the wave value = 0.77, for a differential of 2.34.    The maximum deviation during the “Super El Nino” was actually August 1997 – a difference of 2.03.

In fact, we actually have a fairly significant event occurring right now.   The December 2009 deviation from the wave is +1.54, which is the largest difference since April of 1998!

Posted in Cycles, Earth, El Nino, ENSO, Oceans, Pacific Ocean, Science | Tagged: , , | 4 Comments »

Eastern Pacific Oscillation and Random Stuff – Believe it or not, a New Post…

Posted by The Diatribe Guy on December 1, 2009

Ah, it’s been a while, hasn’t it? My friend Jeff at The Air Vent asked me if I’m giving up. I understand the appearance of this, given my lackluster performance (or more accurately, zero performance) as of late.

Before I present a chart of the EPO Index, which most of us probably don’t care all that much about anyway (if we’ve even heard of it), I have a few random observations:

1) To Docattheautopsy: Ha! I told you! (Check out comment #6 here: https://digitaldiatribes.wordpress.com/2009/09/30/el-nino-is-back-with-the-fury-of-a-woman-scorned/#comments). Good thing, too, because I get enough spam. Anyway, as complex as climate is, it is actually kind of amazing that so much of the simplicity can be missed among the complexity. I know it doesn’t always hold, but there are some rules of thumb that stand up pretty well. La Nina in spring/summer ==> cold Wisconsing Winter. El Nino in Spring/Summer ==> mild Wisconsin winter. It’s not really rocket science. So, each of the last two years gave us frigid temps and lots of snow, and so far this year we have above average temperatures in November. It’s supposed to cool off soon, but nothing unusual. I admit I was nervous in October – it was a very cold and wet October, but November has been beautiful.

2) Climategate: I love it. I don’t “love it” in the sense that it should have ever happened. That part ticks me off, because it’s simply a blight on the scientific process and public trust, and a validation of the more underhanded aspects of the whole thing – it’s about money, politics, control and power. That’s a major shame. But I do “love” the fact that this has been exposed. It may well be true that much of their analysis doesn’t change, and they may actually believe their conclusions. But what is lost in making that simple argument of dismissal about the relevance of the situation is that there are other scientists who have reached different conclusions who were essentially shut of of the public debate, and in doing this it led to a global, incessant mantra that brainwashed policymakers and citizens alike. It’s not whether or not their studies are meritorious, it’s about the fact that the full debate and scientific process was not implemented, and the full range of views were shut out of attaining credibility through reprehensible methods of collusion and intimidation. And really, it just shows the overall poor character of the participants in these exchanges, which also leads to a lack of trust.

3) Where are the temperature charts? Well, I’ll get back to them. I really wanted to spend time on the Oscillation Data, so I’m continuing down that path at the moment. The trends don’t change so much from month to month, and I am in no way avoiding it due to recent uptick in temperatures. I don’t do that, even if Phil Jones and Michael Mann may suggest implementing a trick to disguise the uptick, if they were skeptics.

And so, with that, let me explain the following chart: The Eastern Pacific Oscillation Data are available since 1950 (link to the right) and is just another one of the Oceanic Oscillations. It’s not one we hear about much, and may well not be highly important in the climate discussion. That’s OK. By plowing through the different indices, I hope to isolate the ones that do have an apparent oscillation pattern, because it seems to me that this is an indication that the Oscillation is a driver of temperature, rather than the other way around. The interesting thing about most of the oscillation patterns is that they tend to cycle on a longer time period. Even ENSO, with its shorter term spikes (not on particularly predictable intervals, it seems) has a longer term cycle. The EPO index suggests something else – an 8.9 year cycle.

Caveat: there are no December values in the data set. I have adjusted this by using the average of the November and January values. I have sent an e-mail to NOAA seeking an explanation for this. If I receive a response, I’ll either comment about it or update the post.

EPO_200910_raw

EPO Data as of 200910

It’s hard to say how much impact this metric has on global temperatures, and I probably won’t know until I can do a full correlation analysis of all the oscillations, solar index, and CO2, at minimum. But it may have some impact. There is almost no linear trend whatever on this, and the index seems well-centered around a zero anomaly.

There also does seem to be a very shallow 40-year cycle, if I expand the analysis out to look at that, but nothing worth more than a note. The driving cycle is the shorter-term one.

Hope all is well with everyone. If I find I cannot get to data analysis, I will try to do better at posting some fluff just to let you know I’m still here ;).

Posted in Cycles, Data, Earth, EPO, Oceans, Pacific Ocean, Science | Tagged: , , , | 6 Comments »