Spencer: Spurious warming demonstrated in CRU surface data

‘mike roddy (09:14:21)
Even according to Spencer, it’s still warming, so what’s the point? Glaciers are melting, antarctic ice is calving, and birds and plants are migrating north. Humans are the cause.
Deal with it, wattsupwiththat readers, or risk becoming increasingly ridiculous’
I’m assuming that you are assuming that “CO2 Drives the Climate”?

Stephen Wilde (08:13:07) :
“Or would satellite sensors do the job well enough ?”
Hey Stephen, should have mention you in there (on oceans). I agree, satellites would be the last choice.
I included satellites just to give a hypothetical system an alternate view if someone didn’t understand the one described on the ground. I wanted everyone to think of the theory, not a specific implementation. How is it best to measure this globes temperature? Is it even possible? If so, how. How with the least error so no adjustments needed.
I had to jump out of the box. Whole point of that was to have everyone stop and say, wait, what in the world are doing? We are going in circles! Or another way to say it is performing adjustments on top of adjustments. Crazy! This whole process has bothered me of late and I just had to come up with a possible alternative.
It’s not meant to be perfect. Add to it. Change it. It’s just a start so we don’t keep thinking of the same broken system with layers on layers of adjustments!
telecorder (09:04:23) :
Thanks. Appreciate that at least someone stopped and read it. Didn’t know if it was just a hair-brain idea or not, well, yes, I think its close. I enjoy theoretical physics, it is a design created this morning for the public to modify, and most of all, stop and think. It may never be physical but in theory it’s what we need to approach.

Quite simply.
Temperature alone has NO relevance
Never has & never will!
My tuppence.
DaveE.

Remember, sensor GPS address can attenuate or accentuate weather pattern variation drivers (such as greenhouse gases, humidity, clouds, El Nino/La Nina, Jet stream influences, pressure cells, topography, etc). So you must randomize through the climate zones and microclimates.

Hello Everyone,
This is my first time posting at WUWT. I live in Montreal, and have been an “avid lurker” on WUWT for a long time (since the NorCal days, actually). I’ve sometimes had the urge to submit a comment, but someone else has always said more or less what I would have, and without much delay, so there was generally no need. I greatly appreciate the existence of this blog and the work that it does. In some sense, I feel that I already “know” some of you, and I find myself looking forward to posts from various individuals. That would make a fairly long list. In particular, though, I have liked almost everything written by Willis Eschenbach, including his recent semi-rants regarding Drs. Ravetz and Curry, and I religiously “click” all of Smokey’s links. 🙂 I am greatly impressed by the thought processes exhibited by many of the contributors, to say nothing of their concern for the integrity of Science. The only mild criticism I might make is that people sometimes spend way too much time feeding trolls, but I suppose that’s rooted in good intentions. (It would also be nice if we could search the site for more than the words contained in post titles, but I seem to remember that Anthony is somewhat at the mercy of other parties in that regard, so I won’t enter a full-blown complaint.)
OK then, introductions done, I am responding to the request by Carsten Arnholm, Norway (04:36:34) regarding the proper way of finding an average temperature. Before doing that, I would like to say that I’m a physicist, and I am thus not entirely comfortable with the notion of finding an average temperature for anything beyond one thermometer at one location. Everybody seems to be doing it anyway, however, and I’ve been known to say things like “It’s been hot today.”, which is tantamount to making a comment on the temperature across a non-infinitesimal region, so if you want to define such a thing and calculate it, here is my take on how it should be done (for that one thermometer).
::
The Lagrange Approach:
To calculate the mean value of any quantity over some interval, the ideal situation is to have a continuous function, which would be integrated over the full interval and divided by its “length”. For daily temperatures, that would mean integrating over 24 hours and dividing by 24. In practice, if only a finite number of equally-spaced readings are available, the integration then becomes a weighted sum of the individual values, a form of numerical quadrature, as it is called.
– The weights are determined by the number of points available and the function used to represent the entire set of values for that day. If we use a polynomial fit, the order of the polynomial can be anything up to one less than the number of measurements used. We can fit a straight line to two points, a parabola to three, and so on. This leads to well-known results such as the Trapezoidal Rule, Simpson’s Rule, etc.
– In Dr. Spencer’s case, there are readings every six hours, starting at Midnight, which effectively gives 5 points per day (or 4 intervals) since the two Midnights would define the start and end of the data set for an individual day. In this case, a quartic (4th order) polynomial can be used. The procedure for doing this is to find the coefficients of the Lagrange Polynomial that exactly reproduces the original five values. There are many ways to do this, some more efficient than others.
– This polynomial is then used in place of the actual continuous function that would give the temperature at any instant, but because it (the polynomial) is an explicit function, it can be integrated over the whole day, and the weights that should be assigned to each of the five readings can be found. If we use Dr. Spencer’s every-six-hours approach, the weighting formula (starting at 00hrs and going to 24hrs in steps of 6hrs) works out to:
T(avg) = {7T(00) + 32T(06) + 12T(12) + 32T(18) + 7T(24)}/90
::
The Chebyshev Approach:
The Lagrange procedure described above is perfectly workable and sound. There is, however, another method that allows for simple arithmetical averaging of the temperature values, and which gives equally valid results. In this case, however, the weighting is accomplished by taking the readings at non-equally-spaced times within the 24-hour period. In other words, instead of unequal weights, we use unequal intervals, but it accomplishes the same thing.
– The time-values at which the readings should be taken are found from the roots of a group of functions called Chebyshev Polynomials (or variant spellings). With four readings, the 4th-order polynomial is appropriate, and is given by f(x) = x^4 – (2/3)x^2 + (1/45). Note that this function is not intended to represent the temperature itself, but rather its roots are used to determine the times at which measurements should be made. As given, it is defined on an interval from x = -1 to +1, so adapting it to a 24-hour time-period would put t = 0 at Noon, and the end-points at -12 and +12hrs, thus covering a “self-contained” day centered on Noon. Note that there would be no reading at Midnight. All four readings would be made “inside of the day”.
– The roots of this polynomial are approximately: +/- 0.18759 and +/- 0.79465, which when translated into time-values would result in the following optimal choices for observation times:
(2:28AM, 9:45AM, 2:15PM, and 9:32PM) or (02:28, 09:45, 14:15, and 21:32)
Readings taken at these times can simply be averaged (just add them up and divide by 4), and would give the best accuracy available with four readings per day. Whether it might be practical to obtain readings on such a precise schedule is, of course, another matter.
::
Try It At Home:
If you want to check the accuracy of these procedures, you can make up functions yourself and try them out. Both will give exact results if the actual function is a polynomial of order lower than five. They can also be used as approximations for any funtion you like, including non-symmetric transcendental ones, as long they aren’t “pathologically wiggly” or contain singularities. If you pick something that can be integrated exactly by some analytical method, you can compare the three outcomes, and you will find that they give very similar results.
Example: Find the average value of f(x) = exp(x) + cos(x) on the interval (-1,1).
2.0166706 – Chebyshev Method
2.0166722 – Analytical Result
2.0166745 – Lagrange Method
::
Final Comment:
I would not personally consider such calculations to be valid with fewer than four readings per day because of the Nyquist sampling/aliasing issues that have been previously pointed out by E.M. Smith, “jordan”, and others. And, of course, “if I were God”, I would ban the “two-readings max/min thing” to oblivion. But that’s just me. 🙂
dr.bill
PS: To 10 decimals, the roots of the Chebyshev 4th order polynomial are: +/- 0.1875924741 and +/- 0.7946544723. Any standard textbook on Numerical Analysis intended for physicists, engineers, chemists, or geologists will have full explanations of these methods. Look in the Interpolation and Numerical Quadrature sections. Several other sets of special polynomials (Legendre, Hermite, Laguerre, …) can also be used for such purposes, and they are sometimes collectively referred to as Gaussian Quadrature methods.

Amino – “There’s a problem with his math—-in 10 minutes from now USA, not Canada, must win the gold today”
Hmmm, looks like The Team may be onto something here eh? Torture, toture, ah, there…
Sorry, we won!

Apparently you have reproduced Menne, Williams and Palecki’s finding that electronic temperature sensors have a slight cooling bias.
REPLY: Josh, knowing you, apparently you’ll just take that wrong impression and shout it from the rooftops. Let me be clear. Menne et al used an incomplete dataset against my wishes, denying my right to publish first. At 88% the network looks a lot different. If the situation was reversed, you are your cronies would be all over me, telling the world how terrible I am for doing such a thing. Yet you and your band of anonymous bunny trolls give Menne a free pass for his actions because you side with the findings. Such integrity. Now back to your hole bunny boy. Watch out for flying cabbages. – Anthony Watts

Pamela Gray (15:45:05) :
Daniel, you would have to control for climate zone affect. This can cause your “random” sample to be not random at all. One of the main pitfalls in data collection is to assure you are taking from a random sample. GPS address would become a key measure of randomness if you selected only rural stations. That would tell you if your data set is randomized for longitude, latitude, altitude, and proximity to local micro-climate parameters such as large bodies of water or mountain shadows. Not to mention proximity to homemade truck sized BBQ’s for roasting quarters on a spit.
Pamela, respectably I must disagree here. You are talking of random samples. I am assuming you are saying cities must be included in the sample because if left out, you would not have a random sample. Exaggerate the example. Think in your mind the UHI is twenty degrees. UHI pictorial much like a big bump over the city. Anthony has a couple of good illustrations of this. Now, when wind is blowing, there is little UHI effect, the heat doesn’t create the bubble. When there is no wind, you have full UHI effect. If your objective is to accurately as possible measure the world’s temperature, why would you include cities in your measurements? The heat from the city will continuously be dispersed to the surrounding rural locations, spread out and smoothed. To leave them in, the displacement of the measurement would never be more than the excess heat you see in the bubble over the city, but it would add large amounts of error, now depending on the wind and its speed. Error and complexity has sneaked in, because the cities were included.
Now the rural, generated-heat-free sites, they must be randomly distributed or at least form an evenly covered grid as close as possible. Am I missing something?
Now about the micro-climates, unlike the UHI effects of the cities where extraneous heat is created, they are part of the world we are measuring and do not create heat of themselves. Every point on this Earth is part of some micro-climate. I don’t see why you are including them as something specially handled.
This is a good example how seemingly most have accepted as real and necessary errors and deviations that can be eliminated if looking at the problem in a new light. I think Daniel is correct. You seem to be in the mind-set of controlling, not thinking of a measurement system that needs no controlling, the system handles itself, and of course, all of the above is only in proper physics and science.

son of mulder (16:37:55) :
“And I ask again, Who is denying access to such raw data, as certainly some seems to be available judging from ”
For per-station daily raw data, I have only found sites (NCDC/NOAA) wanting to purchase the data or order CDs or are only of recent years. If you can find an explicit link to a page or ftp directory, please let us know. Some now have .gov, .edu, .org domain limits for access but can’t recall exactly where.

Wren (13:04:31) :
“I believe Ivan’s question was a about the difference between UAH and rural ground records for the U.S. over the 1979-2009 period. Do you mean UAH “should” warm 1.6 times faster than rural stations in the U.S. over this 30-year period?”
It should have warmed 1.7 times faster. Actually, UAH has even warmed slower, what is another strong indication, that ground based measurements have a strong warming bias.