Spurious Warming in the Jones U.S. Temperatures Since 1973
by Roy W. Spencer, Ph. D.
INTRODUCTION
As I discussed in my last post, I’m exploring the International Surface Hourly (ISH) weather data archived by NOAA to see how a simple reanalysis of original weather station temperature data compares to the Jones CRUTem3 land-based temperature dataset.
While the Jones temperature analysis relies upon the GHCN network of ‘climate-approved’ stations whose number has been rapidly dwindling in recent years, I’m using original data from stations whose number has been actually growing over time. I use only stations operating over the entire period of record so there are no spurious temperature trends caused by stations coming and going over time. Also, while the Jones dataset is based upon daily maximum and minimum temperatures, I am computing an average of the 4 temperature measurements at the standard synoptic reporting times of 06, 12, 18, and 00 UTC.
U.S. TEMPERATURE TRENDS, 1973-2009
I compute average monthly temperatures in 5 deg. lat/lon grid squares, as Jones does, and then compare the two different versions over a selected geographic area. Here I will show results for the 5 deg. grids covering the United States for the period 1973 through 2009.
The following plot shows that the monthly U.S. temperature anomalies from the two datasets are very similar (anomalies in both datasets are relative to the 30-year base period from 1973 through 2002). But while the monthly variations are very similar, the warming trend in the Jones dataset is about 20% greater than the warming trend in my ISH data analysis.
This is a little curious since I have made no adjustments for increasing urban heat island (UHI) effects over time, which likely are causing a spurious warming effect, and yet the Jones dataset which IS (I believe) adjusted for UHI effects actually has somewhat greater warming than the ISH data.
A plot of the difference between the two datasets is shown next, which reveals some abrupt transitions. Most noteworthy is what appears to be a rather rapid spurious warming in the Jones dataset between 1988 and 1996, with an abrupt “reset” downward in 1997 and then another spurious warming trend after that.
While it might be a little premature to blame these spurious transitions on the Jones dataset, I use only those stations operating over the entire period of record, which Jones does not do. So, it is difficult to see how these effects could have been caused in my analysis. Also, the number of 5 deg grid squares used in this comparison remained the same throughout the 37 year period of record (23 grids).
The decadal temperature trends by calendar month are shown in the next plot. We see in the top panel that the greatest warming since 1973 has been in the months of January and February in both datasets. But the bottom panel suggests that the stronger warming in the Jones dataset seems to be a warm season, not winter, phenomenon.
THE NEED FOR NEW TEMPERATURE RENALYSES
I suspect it would be difficult to track down the precise reasons why the differences in the above datasets exist. The data used in the Jones analysis has undergone many changes over time, and the more complex and subjective the analysis methodology, the more difficult it is to ferret out the reasons for specific behaviors.
I am increasingly convinced that a much simpler, objective analysis of original weather station temperature data is necessary to better understand how spurious influences might have impacted global temperature trends computed by groups such as CRU and NASA/GISS. It seems to me that a simple and easily repeatable methodology should be the starting point. Then, if one can demonstrate that the simple temperature analysis has spurious temperature trends, an objective and easily repeatable adjustment methodology should be the first choice for an improved version of the analysis.
In my opinion, simplicity, objectivity, and repeatability should be of paramount importance. Once one starts making subjective adjustments of individual stations’ data, the ability to replicate work becomes almost impossible.
Therefore, more important than the recently reported “do-over” of a global temperature reanalysis proposed by the UK’s Met Office would be other, independent researchers doing their own global temperature analysis. In my experience, better methods of data analysis come from the ideas of individuals, not from the majority rule of a committee.
Of particular interest to me at this point is a simple and objective method for quantifying and removing the spurious warming arising from the urban heat island (UHI) effect. The recent paper by McKitrick and Michaels suggests that a substantial UHI influence continues to infect the GISS and CRU temperature datasets.
In fact, the results for the U.S. I have presented above almost seem to suggest that the Jones CRUTem3 dataset has a UHI adjustment that is in the wrong direction. Coincidentally, this is also the conclusion of a recent post on Anthony Watts’ blog, discussing a new paper published by SPPI.
It is increasingly apparent that we do not even know how much the world has warmed in recent decades, let alone the reason(s) why. It seems to me we are back to square one.
George E Smith (11:15:32)
Whoops. I think it was 28C or 82F as a general maximum for sea surface temperatures not 22C. Still, any maxing out of SSTs would also put a lid on what the global air temperature can achieve.
As for increased cloud cover I would just say that that would be the obvious first step in a speeding up of the hydrological cycle wouldn’t it ?
As for thin ice I think we are all on that all the time until the problem has been solved. Even the most expert here are expert in limited fields only.
Thank you Dr. Spencer–I have been making these same arguments with regard to data sets and the need to use the same site over time and also to factor in the effects of increasing urbanization. Bottom line is we probably do not have the data to draw any conclusion and therefore to make any educated or conclusive summary of actions needed. We are still at square 1 with regards to the entire theory when the scientific method is rigorously applied.
I might add that it is not the duty of anyone to prove the theory wrong, it the obligation of the proposers to provide irrefutable firm data to prove it right and to date that proof is not here.
Carsten Arnholm (04:36:34):
If you’re interested in generating a meaningful daily time-series, the standard procedure for calculating the mean when 4 or more (equi-spaced) readings are available is to simply average those readings. Classical “numerical quadrature” methods do NOT provide mean values with superior accuracy. On the contrary, their frequency response function is even further away from ideal integration ( i.e., the reciprocal of i*omega) than is that of simple averaging, with its inevitable negative side-lobes. The Langrangian quadrature operator suggested by dr. bill (15:56:52) for 6-hourly data does not even remove the diurnal cycle completely and has a horrendous negative side lobe in its response function that reaches a value of -.42222222 at Nyquist frequency (1/12hrs). With simple averaging of the 4 daily readings the side lobe fades to zero there.
Because the diurnal temperature cycle contains appreciable harmonics , the average of Tmax and Tmin will usually be appreciably different from the average reading, especally if 144 data points per day are averaged. The former is actually the mid-range value, which ordinarily is found several percent above the temporal mean. But, since the extreme values occur at irregular times of day, there is no aliasing problem, as with equally spaced readings. Hope you use a sensor with a time constant of a few minutes to avoid minor fluctuations from turbulent wind eddies aliasing into lower frequencies.
sky (17:26:00) :
Perhaps I didn’t make the intention of my note to Carsten clear enough. For the Lagrange procedure, I was speaking of the case of 5 readings per day, taken every 6 hours, not the 144 values that his device is capable of generating. As I understood him, he was interested in comparing the average of the measurements taken every 10 minutes with the results of those taken every 6 hours, but wasn’t sure of how to calculate the average. I wasn’t trying to provide him with a smoothing formula, just a way to find the daily average of the every-six-hour temperature values.
::
If the intent had been smoothing, then I would have suggested a series of formulas that can be applied to a time series so as to remove the various frequency components. If we stay with the 6-hour intervals, there are three frequencies that could measurably contribute to the series, namely those corresponding to periods of 12, 18, and 24 hours. These can be removed sequentially by applying the following “moving weights” expressions:
Stage 1: (-1, 4, 10, 4, -1)/16
Stage 2: (-1, 4, 3, 4, -1)/9
Stage 3: (-1, 4, -2, 4, -1)/4
The “stage 1” weighting formula are moved along the original series to generate a new series. This new series will have the 12-hour variation completely removed. Likewise, the 18-hour components are removed by applying the second formula to the “stage 1” output, and 24-hour components are removed by applying the third formula to the “stage 2” output. The “stage 3” output will have zero spectral amplitude for all three of those frequencies.
What you are left with is the underlying trend, which will be identified exactly if it is no more complicated than a cubic polynomial over a range of five points.
::
At each stage, you “lose” two points from the beginning and end of the series, so a total of six plus six after the three operations have been performed. If you’re using 6-hour readings, of course, that means that you’re just losing a day and a half at the ends, but you could also apply end-correction formulas to avoid that if it mattered enough.
You can test this procedure yourself without trouble. Just make up a function consisting of any cubic polynomial plus three sine or cosine functions with non-zero phase constants, and with periods of 12, 18, and 24 hours. The coefficients can be anything you want, and when you apply the three-step process to your series, the final result will be exactly the same as the polynomial alone, with all the trig stuff removed.
I hope that clarifies things,
dr.bill
Well that seems like a lot of effort to me. I didn’t get the idea that the intent was one of smoothing. That implies a noisy sequence whose individual data points are each suspect because of noise.
In fact they are the reading on a thermometer, and any noise in the reading must be small compared to the actual change in temperature itself. So the aim is to obtain the true average of the measured values; not to smooth them and create a completely fictitious function which includes none of the original measured values. That average is simply the total area under the plotted function divided by the total time of observation.
The reason to use four equally spaced daily time measurments (of temperature), is because that is the minimum sampling rate to satisfy the Nyquist criterion for a repetitive cyclic function that consists of a 24 hour periodic function plus a 12 hr (second harmonic) component, and still be able to extract an average uncorrupted by aliassing noise (barely).
George E. Smith (15:00:21) :
Well that seems like a lot of effort to me. I didn’t get the idea that the
intent was one of smoothing. That implies a noisy sequence whose
individual data points are each suspect because of noise.
I agree. I didn’t think it was about smoothing either
In fact they are the reading on a thermometer, and any noise in the
reading must be small compared to the actual change in temperature
itself. So the aim is to obtain the true average of the measured values;
not to smooth them and create a completely fictitious function which
includes none of the original measured values. That average is simply
the total area under the plotted function divided by the total time of
observation.
I agee with this as well.
The reason to use four equally spaced daily time measurments (of
temperature), is because that is the minimum sampling rate to satisfy
the Nyquist criterion for a repetitive cyclic function that consists of a
24 hour periodic function plus a 12 hr (second harmonic) component,
and still be able to extract an average uncorrupted by aliassing noise
(barely).
In this case, I would have a quibble. If the four measurements were taken at 3:00, 09:00, 15:00, and 21:00, I don’t think any harm would be caused, or spurious frequency responses introduced, by simply averaging the four values. If the values are recorded three hours earlier or later, however, the resulting average would not be for a self-contained day, but for a “day” that was shifted forward or backward, depending on “which Midnight” you used. My original recommendation (not the smoothing thing) was designed to cope with having 5 values per day, starting at 00:00 and ending at 24:00. If you simply averaged those five, however, you would be overstating the importance of the two Midnight values.
dr.bill
dr. bill (23:59:31):
Your intention did not elude me in the slightest and I never suggested that you were advocating Lagrangian quadrature to obtain the mean of 144 daily readings. On the contrary, I argue that classical quadrature formulae based on fitting low-order polynomials to data are not best ways of obtaining the mean in any realistic case, because of their miserable frequency response characteristics. My discussion of the negative side-lobe features is entirely in the realm of 6-hourly temperature data.
Integration–the prelude to establishing the mean in the continuous, analog case–is always a smoothing operation. The distinction you try to draw seems teleological rather than mathematical. Furthermore, the idea that “there are three frequencies that could measurably contribute” to the temperature series shows a lack of acquaintance with real-world data, which almost never follow text-book preconceptions. And the smoothing filters you prescribe are truly effective only if you have spectral lines at precisely those freqeuncies, rather than a spectral density over a broad continuum that encompasses those frequencies.
Instead of forcing preconceptions upon data, modern methods of signal analysis and discrete-time processing cope with spectral structure of real-world data. I would urge everyone to get acquainted with them.
sky (19:40:04) :
With respect, I would suggest that you are being overly dogmatic in a case where it isn’t warranted.
With a limited number of values, there is a limited amount of information that can be extracted from the data. Choosing polynomials, Fourier components, or any other set of functions will not change that fact, unless you actually KNOW something specific about the data beyond the actual measurements. If that is so, then you effectively have more information than the simple measurements themselves, and it would be sensible to let this influence your choices.
With simply four or five points, however, and no a priori knowledge, any set of functions capable of describing the maximum observable number of “wiggles” is as good as any other, and there is nothing inherently better about one choice than another. No method of analysis can overcome this limitation.
dr.bill