Hey! I found last month’s HadCrut notes!

As I was catching up on some things that I haven’t been able to get to lately because of all the otehr crap I have going on, I decided I had to actually pay my bills.  As much as I’d like to put that job off longer, I realize that certain things need to take place as they – in Covey-speak – shift into “Quadrant 1.”

Lo and behold, as I sifted through all the things that cost me money, and deliberated about the intelligence of some of our spending decisions, I found a piece of paper with a bunch of notes scribbled on it.   I blurted out something about HadCrut and it was one of those moments where the wife sees excitement in me where none should reasonably exist.  At these moments, she gets this look on her face, as if to pat me on the top of the head and say “Dear boy, is this truly what you’ve become? ”

Bah!  How can one NOT appreciate a bunch of numbers on a page summarizing temperature trending?   Seriously.   No…  really.

 

May 2009 Sunspot Update – Fun Facts / Cool Outlook

We continue to see a quiet sun. I know there is a lot of debate about whether it’s truly “unusual” activity, or whether it means anything at all to temperature and climate. I honestly don’t know the answer to the second. From what I understand, the theory is that a quiet sun means that solar flares and other wild activity are not there to hamper cosmic rays from pelting the earth. (As an aside, whenever I hear things like “Cosmic Rays” it takes me back to my youth, where different space ray exposure meant you would be turned int a Super Hero. So, maybe one byproduct of a quiet sun will be people who can fly, or are really flexible, or who can turn invisible. Let’s just pray they don’t turn into orange, rock-like monstrosities strong enough to lift tanker-trucks into the air).

What was I saying? Oh, yeah… Cosmic Rays. Anyway, unimpeded rays apparently stir up more evaporation, elevating the level of water vapor, elevating cloud cover, elevating rain… eventually, between clouds blocking the sun and the rains cooling the land, we get cooler temperatures.

There have been some correlation analysis done that linked the length of solar cycles to changes in temperature. These, as far as I can tell, have been fairly simple and, while compelling, have limited data points. So, it’s interesting as far as it goes.

I’ve done a similar exercise, but by looking at the full set of data as it relates to lags, using a minimization of least squares simultaneous approach. I have updated that study and will present it here. In addition, I’ll throw out the latest observations on how current data trends in sunspot counts stack up to history.

Before I begin with that, I need to throw out a caveat that was rightly pointed out to me in a previous post I made regarding the sunspot numbers: if you go to the NOAA Sunspot data, which is the source I am using (linked to the right), you will see a statement at the bottom of the page that tells you that the data after such and such a month (about 6 months ago, depending on when you’re checking) is preliminary. That is because the traditional way of counting sunspots incorporates formulas that, today, don’t seem to make a whole lot of sense. You might think that the count is the count, but it’s not quite that simple. The count itself is a formula, based on number of days of observation adjusted for a formula to account for the other side of the sun, clusters, etc. Then, after that, the monthly average count is adjusted for an annual average. It can all be pretty confusing, and at one time I could rattle off all the details, but it’s been a while since I refreshed my memory on it, and quite honestly I’m admitting to laziness by not digging into it at the moment. The important thing to realize is that the last few months could see adjustments to the numbers over the coming months, but I will treat them for presentation purposes as “the number.” The reasons for these adjustments, I believe, have more to do with maintaining consistency in the method so that we can compare a reading today to a reading 200 years ago. We can argue about differences in technology affecting that, but at least the determination of the count number is consistent.

OK, so on to some data tidbits:

In each of the last five months, the sunspot count is preliminarily showing values of 1.5 or less in each month. The last time we saw a consecutive 5-month stretch like that was the period ending September 1913. Yes, that’s over 95 years ago.

The latest count = 1.2. The two-month average = 1.0, and the three month average = 1.1. While very low by historical levels, we did see similar 2-3 month averages in 2008.

Sunspot counts since 1850.

I took a look at the following averages, all of which are the lowest averages since similar periods ending in 1914-1915: 6-month (1.6), 12-month (1.8), 24-month (3.9), 36-month (7.0). So, any way you slice it, the sun in the last three years is unlike anything most of us have seen in our lifetimes. Does it mean anything? I don’t know for sure, but it’s still an interesting phenomenon.

Here are a couple of those charts, for your entertainment:

Deconstructing the HadCrut Data

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.

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.

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:

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

Observations:

• 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:

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:

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

Observations:

• 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:

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.

Eighth Warmest November in Human History! (aka: December 2008 Update on Global Temperature – HadCrut)

The alarming rise in global temperatures continues unabated. Our planet is in peril, and for the last eight years, nothing has been done to stop this train wreck. Only now does it appear that someone is about to step in and take things seriously.

DATA
The information is found here, in column 2.. I encourage you to do your own analysis. The numbers are simply staggering.

The November 2008 anomaly is 0.387. This is a full 0.120 degrees Celsius warmer than November 2007. The implications of this is horrifying. At this rate, we will warm a full 12 degrees in 100 years. Swimming in the Arctic on New Years Day is a possibility with such an extreme rise in temperature. While the anomaly is 0.051 degrees cooler than October 2008, if we compare it to January 2008, we will see that the current anomaly is 0.338 degrees higher now than it was then. This is less than one year! It doesn’t take a rocket scientist to tell you that 35 degrees of warming per Century is a disastrous scenario.

RANK
*8th warmest November anomaly out of 159 data points since 1850. Since we have no temperature records before 1850, we can conclude that this is the 8th warmest November in all of human history.
*87th warmest anomaly out of the total 1,907 monthly observations. 87th might not sound too scary, but consider that it is in the top 5% of all anomalies in all of human history! There is no hiding from the fact that temperatures are simply out of control. Also consider that a rank of 87 means that only 86 months in all of human history had higher anomalies. This is the Top 100! In the music world, if you hit the Top 100, it’s a big deal. In the temperature world, it’s not? Why aren’t we making a bigger deal of this?

AVERAGES
*The latest 12-month average is now 31.5, which is a full 0.01 degrees Celsius increase from last month’s value.

STREAK
*Four of the last 5 monthly anomalies are warmer year-over-year. That’s 80% of all anomalies in that time period.

CHARTS

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. We can ignore the slope of this line as irrelevant, because Carbon Dioxide didn

The current period for which we show no warming can be taken back to April 1997, or 11 years and 8 months. The new month did not extend the line back any further, but added one point at the end. The last time we had a stretch this long in the data with no warming was the period from January 1966 to August 1977. This cooling period actually demonstrates how significant the warming trend has been.

The most recent 60-month trend is only presented to point out how silly it is to try and talk about trends on such a short-term basis. Clearly, this is driven from La Nina and a PDO shift which should be discounted when talking about climate change. Only El Nino and a positive PDO are relevant. Again, if anything, this cooling only acts to serve as an indicator of how grave our situation is, when the hopeful ostriches cling to such flimsy hope as trends such as these.

I could present numerous charts with changes in slopes of all the trend lines, but this would confuse many of you simpletons who would be likely to read into the negative trends something that is simply not there. So, instead, I have decided only to present the one chart that I believe is most credible and menaingful, the 300-month trend. By pure coincidence, this chart happens to have the steepest trend line. I think it is clear the future this portends for us if we do not soon implement carbon taxes and credit swaps. We simply cannot act too soon.

IMPORTANT: Here are some common sense things you can do to help save the planet:

• Boycott all stores that sell goods in boxes or plastic.  Only buy from stores that sell goods packaged in natural fibers or glass.
• If you insist on celebrating Christmas, remove the star from your manger scene, if you have one of these silly displays.  These days, the wise men can use a GPS system to find their way.
• Christmas lights should be put up, but not turned on unless you expect company.  Then, once your company is inside the house, turn them back off.
• When you shower, save the water in the tub, so you can bath in it the next day.  It should be at room temperature, which is warm enough.
• We all breathe out lethal carbon dioxide.  This is a flaw in our design, and there is little we can do about that.  However, we can reduce our emissions by moving as little as possible and keeping our heart rate low.  This also has the benefit of a lower life span, which will further reduce carbon emissions.

November 2008 Update on Global Temperature – HadCrut

Just to clarify, this is the update using October month-end information. HadCrut has not released the November anomaly yet, and probably won’t for a couple weeks. I just fell behind last month and wasn’t able to get to this as timely as I would have liked. So, here is the update with some randomly selected charts. (I really did choose them randomly. I’m such a geek)

DATA
The information is found here, in column 2..

The October anomaly is 0.440.

HISTORICAL COMPARISON OF THE SINGLE DATA POINT
*It is 0.073 degrees warmer than October 2007
*It is 0.069 degrees warmer than September 2008

RANK
*6th warmest (154th coolest) October anomaly out of 159 data points since 1850
*63rd warmest (1,844th coolest) anomaly out of the total 1,906 monthly observations

AVERAGES
*The latest 12-month average is now 30.3, which is a slight increase from last month’s recent low point. The 12-month average has been in the range of 29.7 to 30.4 for six months running.

STREAK
*There are no current streaks of consecutive cooler or warmer anomalies over previous year of any significance.

CHARTS

The overall trend since January 1850 has a slope of 0.000365, which corresponds to warming of 0.437 degrees Celsius per Century. Light blue lines are raw anomalies, and the black line is a 12-month smoothed number.