Digital Diatribes

A presentation of data on climate and other stuff

Archive for the ‘ENSO’ Category

La Nina Reading of -1.99

Posted by The Diatribe Guy on November 1, 2010

I’ve been off the reservation as far as following climate news over the last few months. Some day I’ll fill you in on everything that’s come my way… maybe 😉

Just curious if anyone’s talking about the -1.99 La Nina reading, which (if I’m reading my numbers correctly) is the lowest number since 1955.

Just another indication to me that my long-term cyclical chart on these indices has merit.

Should make for an interesting winter.


Posted in ENSO, La Nina | Tagged: , | 3 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.


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.


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.


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.


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.


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.


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 »

It’s a Warm January – What Gives?

Posted by The Diatribe Guy on January 21, 2010

It’s kind of humorous watching the blogosphere play “It’s cold / it’s hot” tennis when these things happen. When it gets cold, the AGW-proponents grumble to themselves in silence as the skeptics/deniers/ throw out anecdote after anecdote of cold weather. Then when it gets hot, Gore’s fan club, no doubt emboldened and perturbed at the previous volley, come out swinging to once again announce the science is settled and Watts and Cavuto and others are nitwits with their collective heads in the sand.

Of course, we all try to adhere by a few rules, and few of us really adhere to them as completely as we should. The first is that “weather is not climate.” The second is that “the earth is complex, and variation happens on a day to day or month to month basis.”

But what fun is that?

And so, we delve into the question that has the pro-AGW crowd giddy with all sorts of excitement: Why did we just recently have the warmest January day in history (history meaning, since 1999), according to UAH? You can link to the site that tells us that here. You may need to recreate the chart, which is easy enough. Just hit “draw” and then select all the years and hit “redraw.” Make sure you’re on the “near surface” option.

As an official member of the community of skeptics, should I hide from this? Should I explain it away?

Nope. And the reason is simple: it is what it is. More important than any agenda-driven concerns, I’d rather give puzzling news that’s true, rather than a bunch of mumbo-jumbo that isn’t.

The truth is, I don’t know why we saw that sudden jump in temperature, just after a period where many places in the globe were seemingly getting hammered by cold and severe winter weather. And the real truth is that nobody else can possibly know why one or two days is suddenly so high. And let’s be honest – it was an impressive temperature reading. It’s not like it just barely nipped the 11-year record. It left no doubt. Further, the entire month of January promises to show a warm reading. Don’t fret about it. Accept it as the truth it is.

As I’ve said many times, we skeptics are somewhat in a corner. Most of us actually prefer warming – I know I do. But we don’t accept the AGW premise, and we see other evidence suggesting that we’re not warming – at least not catastrophically – and we have a desire to see these alarmists get their come-uppance that we, in a way, want to see it cool. But as perverse as that may be, it doesn’t hold a candle to the AGW crowd. You see, they get themselves so worked up over warming that they start seeing nice, warm, weather as a threat to existence rather than a nice, warm day. Instead of enjoying it, they lose sleep over their children’s futures and wonder why we can’t go back to the “good old days” where we had freezing rain throughout the month of April.

So, given all that introspection, let’s at least take a look at some obvious contributors to the warm beginning of 2010.

Exhibit One: El Nino.

There’s an El Nino that is impacting temperatures right now. Whenever there’s cooling during a La Nina, the pro-AGW crowd trips over themselves to point it out, but when there’s an El Nino up and about, they somehow fail to mention it when talking about -for example – how warm this January is shaping up to be.

The last 7 readings have exceeded 0.500, the traditional benchmark for El Nino. 3 readings in a row makes it official, so were well into a good old El Nino, which we know affects temps in an upward manner. And this may well make 2010 a nice, cozy year, since the December reading is the largest of the seven.

We know there’s a 4-6 month lag effect of El Nino (if I remember my facts as related to me from Bob Tisdale), so the first half of the year should reflect that, and if the El Nino persists we could see warmer temps throughout the year. This is a good thing, because my garden has had major issues the last couple years. Cool, damp weather really sucks for raising a garden.

It’s probably a stretch to suggest, as some do, that 2010 will be the warmest year ever, though. While we’ve gone up over 1.0 on the El Nino reading, it is by no means an unusually high value, and it pales in comparison to the consistently super-high values from 1997-98, which almost hit 3 at the highest point. There is nothing to indicate that we can expect such high values from this El Nino. I suppose anything can happen, though.

Exhibit Two: The AMO cycle.

The AMO had taken a dip below zero preceding last year’s ridiculously unpleasant summer, but the values jumped back up to levels above 0.2 a couple months ago, which is likely contributing to the January temps. But the AMO cycle overall has peaked, and while it will probably remain around these current levels, it won’t continue to rise any more, at least not on a prolonged basis. But current levels will contribute to a warmer 2010 than last year, but the contribution is really no more than the couple years before that and is very unlikely to reach levels from 2005-06.

Exhibit Three: Even the PDO is joining in the fun.

The PDO has gone into its long-term cold cycle, but variations about that wave still occur for short-term periods. We can see that it was quite negative over the last couple years. Over the last five months it has increased, even above zero in four of the five months. No doubt the lack of a negative PDO influence has also contributed to our nice January, and will start off 2010 with more pleasant temps than the previous couple years. There is little likelihood, though, that this will soar to levels that push 2010 to record temps, though temps are certainly likely to be higher than the last couple years.

Now, as for the spiking temperatures of a single day, you’re just going to have ask God about that when you see Him next. Even these shorter-term variations in these indices don’t explain day-to-day variations, but they can certainly help explain our elevated temperatures in January on a general basis. I’m sure there are numerous other contributors to climate and temperature that play a part, and sometimes these things happen to align themselves in such a way that a spike or dip occurs.

Quite honestly, it’s really a silly proposition to constantly be arguing about how climate change is about long-term trends, and then trumpet a daily temperature reading, but we’re all probably guilty as charged to one extent or another.

Posted in Atlantic Multidecadal Oscillation (AMO), Atlantic Multidecadal Oscillation (AMO) Index, Climate Change, Data, Earth, El Nino, ENSO, Global Warming, PDO, Temperature Analysis | Tagged: , , , , , , | 14 Comments »

El Nino is back with the Fury of a Woman Scorned!

Posted by The Diatribe Guy on September 30, 2009

OK, not really. But the headline is kind of catchy, no?

El Nino is, in fact, back. And to hear some of the early prognostications about it, we would all melt like the Wicked Witch of the West mighty soon. And this was going to prove once and for all that global warming was real, because – we heard – the recent cooler temperatures were a byproduct of recent La Ninas. (Please forgive my laziness in not including the squiggly lines over my n).

I admit to not quite understanding that argument. The skeptics among us have pointed out that the increase in global temperatures that took place a decade ago were driven by a Super El Nino. And at the time, we heard that global warming was causing more severe El Ninos. But then the severity decreased and we had La Nina, and we were told that such statements were never really made. Or, at least, not by serious scientists. Which, if true, would mean that they should have agreed that the increase in warming at that time was exacerbated by the big and mean El Ninos. (Which, as an aside, brought very enjoyable winters in the Midwest. Why do people want to send us really cold weather all the time?) But other than some footnoted statements on page 23 of the reference section in a boring document, few people have been told the story about how El Nino affects should be viewed independently from overall warming.

That is, they didn’t know this until La Nina affects brought us some cooler temperatures. Then, suddenly, we heard about some “unusually cold” La Ninas, and how this affected global temperatures, and skeptics were being disingenuous by not properly considering that. And to the extent that such a criticism is true, they are right. But there is a strange thing that happens when ideology is part of the equation: you fail to heed your own criticism when the reverse occurs.

And so we have now seen three consecutive measures above 0.5 in the ENSO index. This is hardly unusual, but it does qualify – to my understanding – as a true El Nino. And before that, the La Nina waned, so we had a relatively neutral index for a couple months leading up to El Nino. So it’s been 5 consecutive measurements now since the La Nina has ceased. I remember when it became evident that an El Nino was on the way. This was going to prove skeptics wrong! Why? I have no idea. If El Nino had an anomaly of 1.00, 2.00, or 5,432.00 it would not prove anything other than when there is a natural warming of the Ocean, it warms our global temps. Wow… there’s a revelation. The fact that this has nothing to do with Carbon emissions is beside the point when it fits the argument.

Even stranger, skeptics tend to accept the cyclic variations as the legitimate explanation for warming. We don’t dispute warming periods. So, the skeptic will nod and agree that an elevated ENSO index will probably lead to warmer global temperatures. But then, we kindly point out, don’t blame carbon. Or people. And don’t get all in a tizzy when a La Nina comes around and we see cooler temperatures. What the hell do you expect? Sorry it doesn’t fit the model.

Having said all that, I certainly don’t expect any records to be broken in this recent El Nino. Sorry, experts. I base this simply on data analysis, admittedly knowing very little about all the climatolological influences that could prove me wrong. But what does the data indicate? Looks like it’s time for a chart:


ENSO Data as of 200908

The first observation from the data is that we’ve had four consecutive positive anomalies, and three consecutive positive anomalies greater than 0.5. Note here that a single data point is actually a two-month running average, which helps smooth out month-to-month fluctuations. The latest reading is 0.978, which is the largest of the four positive anomalies. Prior to this period, there were 9 consecutive negative anomalies, with a stretch of 7 months less than -0.50. This was on the heels of only a two month set of barely positive anomalies after a stretch of 12 consecutive negative anomalies that included an eith-month stretch less than -0.5.

So, it is pretty clear that after some real solid La Nina-esque reality, we’ve now flipped to El Nino. What is not clear is the ultimate magnitude and persistence of our new friend, Mr. Nino. But we can talk likelihoods. And for that, we observe the path of the best-fit sine wave.

The red curve below has been fitted in accordance with the other Ocean Oscillations I have observed. Take a sine wave and manipulate it in a few ways in order to ascertain the minimum least-squares deviation from the curve. You see, while El Nino exhibits noticeable short-term variation, it seems to do so about a longer-term cyclical pattern. Thus, a large deviation in one direction at point A on the curve will not produce the same magnitude El Nino at point B on the curve.

The specifics of the best-fit curve are as follows: The 1950 starting point in the data looks to be at 268 degrees in the full 360 degree cycle. The length of the best-fit curve appears to be 102 years for a full cycle. This is an imperfect estimate, since we don’t even have 102 years of data. It is also a longer fit than what was made last year when I did a similar exercise. But the calculation is what it is.

You can see from the chart that the magnitude of ENSO events can have quite a range: -2 to +3 in the data provided. The scale factor applied to the wave is +1.24 in order to achieve the best fit. However, it looks as if the anomalies in the index may be significantly overstated, at least near the beginning of the curve. The best fit line requires an upward shift of all values of the curve of +0.98. This means that the early part of the curve should have appeared “colder” than it did. The interesting thing to me is that, despite the apparent rise in the average ENSO index levels, the best-fit curve actually has a negative linear slope element to it that is pretty significant: -0.00316, or -3.792 degrees Celsius per Century. This actually means that those high El Nino anomalies are centered around a curve that, without that negative trend line, would have been significantly higher – possibly as much as a degree and a half.

So, where are we now? We are 122 degrees into the cycle, which means we have a ways to go into the negative yet, if this best-fit curve is correct. While it appears to the eye that we’re past the 180-degree point, this is not so because of the negative linear slope the curve lies along. No, if this is right, we will not reach the minimum depth of the ENSO curve until around 2050. The curve itself has a staggering implication of coldness – what was a depth of around -0.4 degrees in the 1950s would be -4.0 degrees in 2050. Should we proceed along these lines, we can continue to expect positive and negative significant deviations from the curve, as we see today. But the positive deviations will produce fewer, shorter and less severe El Ninos while the negative deviations produce more, greater and more persistent La Ninas.

OK, here’s the good news: unlike climate modelers, I don’t proclaim this analysis to be infallible. First of all, we’re fitting the best curve to data that is quite variable in its short-term fluctuations. Second of all, the best-fit curve tells us that the cycle period is a longer period than the data period for which we are evaluating. I already know that this supposed cycle period has fluctuated quite a bit from analysis a year ago.

If I had to rank my certainty on the subject, I would bet confidently that (1) there is a long-term ENSO cycle of somewhat indeterminate period, probably somewhere between 60 and 100 years, (2) that we are entering the negative phase of the cycle and we can expect less severe El Ninos and more severe La Ninas.

I am far less certain about the linear trend of the cycle, and the extent of any such trend, as I am about the shift of the curve. These elements are probably much better measured as more data arises over time.

However, in any case, I think it looks very unlikely that we will see any record-breaking El Ninos for quite some time, in either persistence or in magnitude. We may, however, see some major La Ninas surface over the next few decades.

And that won’t be our fault, either.

Posted in Cycles, Data, Earth, El Nino, ENSO, La Nina, Oceans, Science | Tagged: , , , , | 13 Comments »

ENSO Update – A Bounce Upward

Posted by The Diatribe Guy on June 8, 2009

The ENSO Index has been updated for May month-end, and we see a two-month average index value of 0.344.

This is the first reading that is positive since last July, but last year the positive index values barely reached above 0 for a short, two-month stay before dipping back into La Nina territory.

The new value, strangely enough, seems to have certain pro-AGW members of the blogosphere salivating about how it looks like there is a new El Nino on the way. Interestingly, the same people who wring their hands about what warming is going to do to us can’t seem to wait for higher temperatures driven by a new El Nino. They are as much as telegraphing the fact that they will use El Nino-driven elevated temperatures, should they occur, to assist in their case for the idea that CO2 is increasing temperatures. It is unfortunate that they will likely have a voice in this claim – reasonable or not – since there is no correlation between the ENSO cycles and Carbon Dioxide levels (at least that I am aware of).

In the meantime, we can look at the data to see what’s going on with the index. El Nino and La Nina have somewhat sketchy official designations, but I think it’s a fairly common rule of thumb to say that when the index reads above 0.5 for three consecutive months, we’ve got ourselves an El Nino. When the index goes below -0.5 for three consecutive months, it’s a La Nina. I have an interesting observation regarding that a little later on. Based on that rule of thumb, it looks like we’ve come out of a recent La Nina in March. The last one wasn’t particularly strong or lengthy, though it did come on the heels of a stronger one the year before.

In April, the index increased quite a bit, though the 2-month average was still negative. The May value increased again from that level. However, talk about a new El Nino, while entirely possible, is a bit premature. We’re not even at one data point that qualifies yet.

We know that both the upside and downside happens whether we’re in a cooling or warming cycle, so regardless of what side of the argument you are on, you can’t really make any wild claims about what the latest cycle means. It’s probably more accurate to assess the ENSO index over time.

I have updated the best-fit wave pattern against the available ENSO data and shown it below:


Best-fit wave pattern against ENSO data.

The best-fit cycle shows around a 60-year wave pattern. We are now entering the downside of that wave. One thing I noticed is that the best-fit requires a vertical shift upward of the wave. This means that the zero-point of the index should probably be higher than it is. The latest maximum, for example, reached a level of 0.4687 on the crest of the wave (meaning that El Nino will be elevated by nearly half a degree during that time) and the latest trough of the wave was -0.3966 (El Nino will be lowered by about 04 tenths of a degree). The index should really be calibrated down by about 0.05 of a degree. Otherwise, the significance of El Nino will be overstated while the corresponding La Nina will be understated.

The best-fit ENSO wave pattern actually has a negative linear trend that makes a longer-term extrapolation questionable. I didn’t particularly believe that element of it. It fits the current data well, but the gut-check test tells me it would be best to simply leave this parameter at zero. When I run that, the least-squares fit is only marginally worse, but the long-term, extrapolated values make a world more sense. The graph as shown is not much affected, and the same vertical effect is still shown. Just another lesson in modeling, where simpler is often superior. The chart above excludes a linear trend assumption.

According to the chart above, the cold phase of ENSO is just beginning. Yes, we will have El Ninos, but the next 25 years or so will probably look closer to the left half of the chart than the right half of the chart in terms of magnitude of the peaks in relation to a zero index value. In relation to the wave, the peaks seem to ride the wave nicely.

Posted in ENSO, Oceans | Tagged: , | 11 Comments »

April 2009 Update on the ENSO Index

Posted by The Diatribe Guy on April 22, 2009

It’s been a few months since I’ve taken a good look at the ENSO index, so I thought I’d check that out and provide some context for that data.  First, let’s start with a couple nifty little charts (click on them for larger charts):


ENSO Chart One - Raw Anomalies with best-fit sine wave.

Smoothed ENSO

ENSO Chart Two - 5-year moving average of ENSO index readings.

I’ll discuss those in a moment. First, a little housekeeping on the data and the latest readings, and recent historical context.

First, keep in mind that the ENSO index is based on a two-month average. The data is released in terms of JanFeb, FebMar, MarApr, … So, by default, the “monthly” readings are really a two-month moving average. I don’t think that matters all that much to the analysis, but it’s worth noting. For simplicity in conversation, I’ll refer to the anomalies as “monthly” anomalies, but we all know what that means. (I’m lazy)

The current anomaly is -0.737, which is the fourth consecutive month where the reading is lower than the previous month. It is the seventh consecutive month where the reading is below -0.500, which is that point where they consider the period a “La Nina” period. It is the eighth consecutive negative anomaly. This stretch followed two readings that barely peeked above zero (0.050 and 0.028) after a previous period of 12 consecutive readings below zero. The prior stretch was colder (Spetember 2007 – December 2007 were all below -1.100).

The last time there was a stretch where 21 of the last 23 readings were below zero occurred during the period ending March 2002. However, the average anomaly during this stretch is a bit cooler than that one. The average of the last 23 readings is -0.703, and the last time we had 23 readings with at least that low of an average was the period ending September 2000.

Back to the charts…

Chart one shows the raw anomalies. We often hear of the ENSO index cycling in a somewhat irregular, short-term manner. It is evident from the chart that this is the case from a more short-term basis. However, I think we also need to recognize that there is also a longer-term cycle underlying the data. Admittedly, due to the paucity of the data period, this is based on what appears to be roughly one full cycle, and after another 200-300 years, we’ll know more. Since I won’t be around then, I can only work with what I have to work with.

The explanation makes some sense, though. Simple observation of the chart seems to indicate a general low phase and a high phase. If you look a the peaks and valleys from the zero anomaly only, recent spikes look like an aberration. If you look at them relative to the sine wave, it’s less of an aberration.

The sine curve was determined by utilizing the “Solver” add-in in Excel. It simultaneously solves for the parameter values that minimize the least square differences from the raw anomalies to the sine curve.

The sine curve was determined by solving for (1) point on the curve at January 1950, that optimally fits the rest of the data, (2) the scale of the wave, in magnitude (in terms of degrees Celisus), (3) the monthly phase reduction of the wave (basically this establishes the length of the optimal wave), and (4) vertical shift in the curve.

The results show an optimized sine curve fit that started 17.3% into its downward cycle as of January 1950, with a full (360 degree) cycle length of just over 61 years. This differs slightly from a previous analysis, and the main difference is that I did not consider a vertical shift in that previous analysis. But that needs to be considered because just because we’re told that there’s a zero anomaly for purposes of measurement doesn’t mean that it works that way in reality.

The scale of the long term curve is 0.4337. This may not seem overly large, but it is significant. From peak to trough, the difference is nearly 0.9 degrees. Consider an ENSO event that deviates in a given month positively by 2 degrees Celsius. At the trough of the longer-term cycle, this will be a 1.5-1.6 anomaly. At the peak of the cycle, it’s a 2.4-2.5 anomaly. The short-term event is no different, but it’s happening at a different point in the cycle, and the conclusions that may be drawn from it as a startlingly high event could be erroneous.

In addition to that, there is, in fact, a small bias towards higher anomalies in the data. One would expect all anomalies to balnce out to zero on a best-fit basis if there were no bias. I found that a vertical shift of 0.0325 degrees was needed in an upward direction to get the best fit of the sine wave. This is not a large amount, but in conjunction with the scale factor, it helps put the recent spikes in perspective.

Take, for example, the peak value in the index from 1997 (2.872). The sine curve vlaue at that point was 0.360, for a difference of 2.512. This is a significant deviation, to be sure. But if we review the data, is it completely out of the norm? I guess it depends on what one decides is out of the norm, but here are otehr months where the deviation was at least as large:

  • April 1983 – 2.644
  • March 1983 – 2.759
  • February 1983 – 2.615

That’s it.  So, that deviation was still pretty significant, although it was less that the deviation in each of those readings in 1983.   However, it is still not quite as significant as it first appeared.  Compare the raw anomaly of 2.872 (deviation from curve of 2.512) to a reading, for example, for the good old days of the cold and freezing 1970s.   July, 1972 showed a raw anomaly of 1.816.  That’s a decent anomaly, but it is more than a full degree less than the 1997 reading we just looked at.   However, the sine curve in 1972 had a negative value of -0.091, creating a difference of 1.907.  the gap in the difference is now only 0.6 degrees Celsius.    This in now disregards the 1997 peak value as a significant deviation, but it mitigates the degree to what the actual deviation was, and helps put it in context.

There are very few of these data points to draw any kind of conclusion, but the peak positive deviations (+2.0 or more) do outweight the “peak” negative deviations (-2.0 or less).  1983 and 1997 experienced those peak positive deviations, while  1988 experienced the sole negative deviation of at least two degrees.  Note that, while 1988 was in fact the largest negative deviation from the wave in the data, it is only the 5th lowest trough point on a raw basis.  

As for Chart 2, it is simply a 5-year smoothed presentation of the ENSO data.  Purely for observation, it basically corresponds to the idea that there is a longer-term cyclical nature to the ENSO index.   Pre-1990, anomalies, on average, were negative.   Post-1980, anomalies, on average, have been positive.  It is much more akin to a step function, or what could be expected with a cycle, than any sort of linear trend.   What is happening on the right hand side of the chart indicates a potential transition point, though one should be a little careful about declaring positive anomalies dead.  On the left side of the chart, I don’t know how far back the actual anomalies fell below the zero line.   Looking at the double peak in the periods ending 1960 and 1970 may have looked like a transition point at that time.  But La Nina wasn’t quite done yet, giving us one last good blast in the mid 1970s.   After that, there was a clear transition into a stronger El Nino phase.   The 2003 and current dip looks similar in nature to me.   However, the double maximum peak in 1983 – 1997 looks similar to the double negative trough in 1957 and 1976, as well.  So, this is where I could go either way on whether or not the transition is now or in another 5-10 years.   But if I consult Chart 1,  1976 was just entering the positive phase of the cycle, and we’re just now entering the negative phase.  So if I had to wager my 3rd child, I’d go with “the transition is now.”

Of course, entering the cold phase doesn’t mean there will be no more El Ninos (or at the very least, positive deviations from the wave).  They still occur, perhaps as frequently, but the deviations from a negative phase wave translates into a lower raw anomaly.

At least, that’s how I see it.

Posted in Cycles, Earth, El Nino, ENSO, La Nina, Oceans, Science | Tagged: , , , , , , | Leave a Comment »

Deconstructing the HadCrut Data

Posted by The Diatribe Guy on February 10, 2009

In this post I took a look at the PDO, AMO, and ENSO data and went through the exercise of fitting a sine wave to see how the fit looked.  On all three, the fit seemed to be a good and reasonable way of estimating the general level of the curves at a given time.  Obviously, there are fluctuations about those curves, but all in all it seemed to be fairly adequate.

So, the other day I was thinking about the implications of hypothesizing the contribution of these
periodic elements to the temperature data, and I figured that it may be an interesting exercise to deconstruct the HadCrut data in the same way.  Understanding that there may be multiple oscillations going on, I set out to fit multiple waves to the data to see what I could make of it.

I used HadCrut because their records data back the furthest.  And also because the older data has not undergone the continual adjustments that the GISS data has.  Since HadCrut protects their process in determining the anomaly, it is not transparent to the user of the data what kind of spreading and adjustments they make to it.  However, I am inclined to place a little more trust in it than I do GISS because the data is more in line over the last 30 years with the satellite data than GISS is.  (Admittedly, based on observation.  I haven’t done a rigorous analysis on that).

Let me start by introducing the most recent chart that shows the overall linear trend on HadCrut over time. I didn’t do a January update, but the additional data point won’t have much of an effect.

Overall Trend

The overall trend since January 1850 has a slope of 0.0003649, which corresponds to warming of 0.4378 degrees Celsius per Century. Light blue lines are raw anomalies, and the black line is a 12-month smoothed number.

Here are the required parameters and procedures to get the best fit:

  1. A parameter that assigns the optimal wave length. This is done by determining a degree increment per month that gets added to the previous degree amount. That value is then converted to radians, and the sine value is calculated.
  2. A wave scale factor is used to determine amplitude of the wave.
  3. The starting wave position in January 1850
  4. Linear trend that the wave is centered on
  5. Vertical wave shift – since the anomalies over time aren’t necessarily centered about zero, and even if they were there may still be a shift needed depending on wave cycle weights, the wave needs to be shifted up or down to achieve optimal fit.
  6. Parameters 1-3 are wave specific when optimizing multiple waves, while parameters 4 and 5 are applied after the cooperative effect of all the waves tested are determined.
  7. To determine the best fit, I set up my calculations using the parameters above to compare against the historical HadCrut anomalies, determine the difference, and square the result. I then minimized the sum of the squares.

The first run I did was against only one wave. Even this fit provides substantial improvement over a simple linear fit, and starts to demonstrate the fact that there are clear cycles in the data.

Single Sine Wave Fit Against HadCrut

The best-fit single sine wave along a linear trend.

While we can see visually that it is not entirely perfect, we can definitely see the general wave it’s tracing. The parameters on this wave are as follows:

  • Wave length parameter = 0.45658. This corresponds to a 788.5 month complete cycle, or 65.7 years. This fit lines up right along with the cycle lengths determined in the PDO/AMO/ENSO study.
  • Wave scale parameter = 0.13222. Basically, this means that the overall wave doesn’t deviate from the trend line by more than this value.
  • Start Wave position = -31.71316. (0 would be right on the trend line, and +/-90 would be max deviation from the trend line in either direction.)
  • Linear trend = 0.00037. This is spot on with the overall linear trend observed without the sine curve applied.
  • Vertical Wave Shift = -0.53644 means that the start of the sin wave had to be shifted downward by this amount.

The least squares result was 56.18. This compares to the least squares fit on the linear trend line only of 72.58. This is nearly a 25% improvement.

The conclusions of this:

  • there is still a definite linear trend, but most of the fluctuation about that trend can be explained by adding a single sin wave.
  • the most recent decade or two is not satisfactorily explained by the sine wave, and the latest anomalies are above the wave. This could be consistent with the idea that the something has changed (e.g. increased Carbon Dioxide has accelerated what had been a linear trend).  Alternatively, it may simply be that a single sine wave is insufficient and there are other periodic influences that need to be examined.

An interesting exercise is to extrapolate the linear trend with the single sine curve forward. Taking this to 2050 shows us the following:

Single Sine Wave Fit Against HadCrut Extrapolated

The best-fit single sine wave along a linear trend, extrapolated to 2050.


  • The graph indicates that we are at or near the peak of the single sine curve fit, and that the next 23 years will cool. 
  • There is still the linear trend line observed at just over 0.4 degrees Celsius per Century, so the anticipated trough won’t be as severe, but we will still be cooler than today for the next 30 years or so.
  • The trough of the curve occurs October 2032, where single-digit anomalies would be the norm.

While the single sine wave fit provides interesting information, from observing the AMO/PDO information, it seemed clear that there would likely be at least one additional periodic wave in the data. So I added an additional wave and the following chart ensued:

Double Sine Wave Fit Against HadCrut

The best-fit double sine wave along a linear trend.

The interesting thing about this fit is that the cycles of both waves are shorter than the singularly combined wave (59.1 years and 58.5 years), and the amplitude of both waves is around 1.5. The combined wave is only 0.13222 because the phases of these two waves at the start of the period are almost perfectly offset (182 degrees apart). The linear trend is still apparent, though just a shade less (0.42 degrees per century). The vertical wave shift is nearly the same as the single wave. Overall least squares fit isn’t remarkably better, at 54.118.

All in all, the waves do seem to do a pretty good job of fitting the curve. In the early 1900s, the wave seemed to ride above the curve a bit and in the last decade or two the wave rides below a bit. So, it’s not perfect. It is possible that a linear curve is not the best approximation to have the sine curve fluctuate around. I may do further tests with other alternatives, such as geometric or exponential approaches.

The extrapolated chart, though, shows a little more severity in projected cooling (the title is wrong – it should read “Double Sin”  I would have corrected it except that I need to re-create it and don’t have time at the moment.  My apologies for the oversight:

Double Sine Wave Fit Against HadCrut Extrapolated

The best-fit double sine wave along a linear trend, extrapolated to 2050.


  • The shifting of the wave phases over time lead to more fluctuation in the peaks and troughs, which explains why the right hand side of the chart fluctuates more than the left.  Since the amplitudes of these waves are 1.5, one can imagine a time centuries from now where there would be astonishing swings in the temperature trends over 50-year periods of time.
  • The projected trough in temperature is expected to be June 2030 according to this chart.   Average anomalies at that time would be slightly negative.   The last half of next century would warm considerably.
  • All this fluctuation occurs over a linear trend that is less than a haf-degree Celsius per Century.

I didn’t stop there. I tested three waves. However, the results that provide the best fit don’t make a lot of sense. The fit of existing data is certainly impressive, so let’s look at that first:

Triple Sine Wave Fit Against HadCrut

The best-fit triple sine wave along a linear trend.

Adding a third sine wave certainly appears to put our temperature observations spot on with the generated curve. One may feel inclined to get all puffy and declare that the case has been solved.

But looks can be deceiving. The best fit with three waves – a reduction to 45.47 – uses parameters that are not sensible. And this becomes a case study in trying to be “too accurate” with model forecasting.

When the third wave is introduced, I was able to generate a number of “best fit” scenarios all around the same value of 45. One such scenario shows that we will go into dramatic cooling by 2051, and the anomaly will be -2 at that time. The next scenario had a best fit of 46.43, with dramatically different parameters. That model shows no downturn whatever in temperature after the current period, and suggests unabated warming through 2050, where the anomaly will be around 1.

This is common when adding multiple parameters to models. In the quest to get more accurate, you actually introduce so much additional uncertainty that the range of reasonable projections becomes meaningless.

My conclusion is that the best representation using a sine wave analysis is a simpler 2-wave representation.

The conclusions are basically in line with the PDO/AMO analysis, as well. These drive the longer-term cycles about a trend. Whether it is a linear trend or something else is worth looking into. Also, is the trend related to the sun or carbon dioxide, or other things? The cycles still do not explain the overall trend, but they do help explain why the recent linear trends cannot simply be extrapolated into the future.

Posted in Atlantic Multidecadal Oscillation (AMO), Climate Change, Cycles, Earth, ENSO, Global Warming, HadCrut, PDO, Science, Temperature Analysis | Tagged: , , , , , , , , | 11 Comments »

A Closer Look At Oceanic Oscillation Cycles

Posted by The Diatribe Guy on February 2, 2009

In the past, I’ve presented some charts on the different Oceanic Oscillations for PDO, AMO, and ENSO. I’ve started to take a look at these again with an eye towards running a correlation analysis. The initial work I’ve done today is something I considered somewhat interesting, so I thought I’d share it.

The first thing I’ll present is the chart for Arctic Ocean Oscillation Indices since 1950, smoothed at one year, 5 years, and 10 years. These are presented below:

1-year smoothed Arctic Oscillation Data since 1950

The overall Arctic Oscillation index data since 1950 - 1 year smoothing.

5-year smoothed Arctic Oscillation Data since 1950

The overall Arctic Oscillation index data since 1950 - 5 year smoothing.

10-year smoothed Arctic Oscillation Data since 1950

The overall Arctic Oscillation index data since 1950 - 10 year smoothing.

Unlike the AMO, PDO, and ENSO charts, there is no apparent cyclicality showing up in the Arctic Oscillation chart. There does appear to be a trend upward overall, and there are certainly ups and downs within that. The 1-year chart looks much like an ENSO chart would be. Unlike ENSO, though, I’m not picking up a longer cycle.

Well, I wanted to show that chart to start, since the Arctic seems to be the focus of a lot of attention. I guess it bears musing whether or not the Oscillation has a root cause from the Ocean itself, or the sun, or melting ice, or freezing ice, or other factors that override any cyclical nature that would otherwise be apparent.

That’s all I really did on that piece. But I’d like to move on to some work I did with the AMO, PDO, and ENSO (as well as a look at those Arctic Oscillations).
Read the rest of this entry »

Posted in Arctic, Arctic Oscillation Index, Atlantic Multidecadal Oscillation (AMO), Climate Change, Cycles, Earth, ENSO, Global Warming, Oceans, Pacific Ocean, PDO, Science, Temperature Analysis | Tagged: , , , , , | 17 Comments »

January 2009 Update on Global Temperature – UAH

Posted by The Diatribe Guy on January 21, 2009

Note: I realized I screwed up my naming convention. I already had a December update on UAH. This one is January…


Sorry it took so long to get this up. I had a couple things I wanted to look at here and since this isn’t my day job, every now and then other priorities get in the way.

The December anomaly from the UAH data is 0.183. This was 0.069 degrees warmer than December 2007, but was 0.068 below the November anomaly. According to UAH, it is the 11th warmest December out of the 30 Decembers in the data. It is ranked 102nd out of 361 overall monthly anomalies. It is the second consecutive warmer anomaly year-over-year after the streak of 14 consecutive cooler anomalies.


The longest we can go back in the UAH data without showing a warming trend line is May 1997. Based on the way January seems to be coming in, it would be surprising if this moved forward after this month. It may even move back to April 1997, but we’ll see on that.

I’m not going to show the different trend charts here, because I actually want to point out something else this month. But here’s a quick recap of what is going on with the trend lines:

60-month: -0.309158 represents the third consecutive increase. So, there has been a bit of a moderation in the rate of cooling we have seen lately. Read the rest of this entry »

Posted in Climate Change, Cycles, Earth, El Nino, ENSO, Global Warming, Science, Temperature Analysis | Tagged: , , , , , , | 14 Comments »