Before you open this blog entry, you should make sure that all the nuclear power plants in your country are operational. You may need them because the text below contains a really long table (with 415 lines or so) which will be processed as \(\rm\LaTeX\) using MathJax. ;-)



About two years ago, Kevin Trenberth and others promoted a paper (Ben Santer and 16 co-authors, 2011) that claimed that one needs 17 years – what a precision – to determine the existence of a global warming trend. The purpose of the paper was to inject some patience to the minds of the alarmists and the undecided – 15 years of "no warming" isn't enough to notice the absence of any warming because you need 17 and not 15 years. Your humble correspondent wrote a tirade explaining that people like Santer and Trenberth were numerologists because there can obviously be nothing special about the 17-year-long interval. The whole continuum of the frequencies contributes to the temperature change and all the confidence levels etc. are depending on the duration continuously. There's no sharp "magic deadline" after which a hypothetical trend "must" show up.







At any rate, my preferred temperature record – the satellite-based RSS AMSU dataset – has approached a point in which the global warming trend in the recent 17 years is statistically insignificant and negligible. In fact, if you include the latest 200 months i.e. 16 years and 8 months (from December 1996 through July 2013 included) into your calculation of linear regression, you get a negative warming trend!









Yes, a particular episode that helps the trend to be negative is the (globally warmer) El Niño of the century in 1997-1998 that occurred 15+ years ago.



In shorter recent intervals, the negative warming trends are about as widespread as the positive ones. In other words, the data from the 17 recent years show no noticeable temperature trend, in one way or another. Chances are high that by the end of 2013, the recent interval in which the temperature trend will be tiny and negative (i.e. a negligible global cooling) will actually extend to the full 17 years. With some sensible conventions for statistical significance, one would conclude that the record in the last 20 years or so shows no statistically significant trend in the global temperature. Compare this absence of a trend in the real world with the hysterical hype about "global warming" in the very same 20-year-long interval.









The table below contains the temperature trends in Celsius degrees per century (rounded to one hundredth) calculated by linear regression applied to the RSS AMSU dataset for all intervals whose length is between 415 and 2 months. The minus signs in the middle column indicate that we're returning a certain number of months into the past. For your convenience, I emphasize the multiples of twelve as whole years – see the number in the first column.



Because the laymen and occasional thinkers about these linear regression results are often horrified by the following observation, let me clarify it again. If you look at the table, it becomes clear that the absolute value of the temperature trend is severely increasing as you go towards shorter, more recent intervals (near the bottom of the table).



This fact does not mean that something is getting crazy about the climate. The larger absolute values of the trend are a consequence of evaluating shorter periods of time, not a consequence of evaluating more recent intervals. When the period of time is shorter, then the calculated trend is clearly dominated by high-frequency, fast, nearly random changes of the weather – i.e. by noise of a sort – while the role of a hypothetical underlying trend – if one exists at all – gets suppressed.



For example, the last line says that the temperature trend between June 2013 and July 2013 is –83 Celsius degrees per century. This doesn't mean that all of us will freeze soon and the Earth will drop below the absolute zero in several centuries from now. ;-) Such an extrapolation is of course completely illegitimate because the temperature doesn't change uniformly and linearly by any stretch of imagination. It's chaotically oscillating up and down and the shorter intervals of time you consider, the more inappropriate it becomes to extrapolate the trend from the short interval to a very long one! However, I would kindly point out that it's wrong to extrapolate the temperature trend even from 30-year or 100-year – or any other – intervals in the future, too.



A way to think about the behavior is to approximate the temperature by a random walk (or, using equivalent words, Brownian motion or red noise) which is a qualitatively realistic model to describe the behavior of the temperatures at certain timescales. Such a random walk has no underlying trend whatsoever but after \(t\) months, the temperature changes by something comparable to \(\pm C\sqrt{t}\) in average. The longer time you allow the climate to change, the more its temperature will change although the change will be far smaller than the change expected from proportionality.



If you divide this change by the length of the interval, \(t\), you obtain a temperature trend of order \(\pm C / \sqrt{t}\) which goes to infinity for really short intervals of time. And that's what you will see in the table below, too.



Finally, here is the long table of temperature trends. It's plausible that you may have to wait for half a minute for your browser and the Javascript in it to convert the table to a nice \(\rm\LaTeX\) output. I found this "export as \(\rm\LaTeX\)" to be the simplest way to reprint the result from Mathematica to the blog's HTML source.\[

\begin{array}{|c|c|c|}

\hline \text{#years}&\text{#months}&{}^\circ {\rm C}/\text{century}\\

\hline

\text{} & -415 & 1.29 \\

\text{} & -414 & 1.28 \\

\text{} & -413 & 1.28 \\

\text{} & -412 & 1.28 \\

\text{} & -411 & 1.27 \\

\text{} & -410 & 1.27 \\

\text{} & -409 & 1.27 \\

34 & -408 & 1.27 \\

\text{} & -407 & 1.27 \\

\text{} & -406 & 1.27 \\

\text{} & -405 & 1.28 \\

\text{} & -404 & 1.29 \\

\text{} & -403 & 1.3 \\

\text{} & -402 & 1.3 \\

\text{} & -401 & 1.31 \\

\text{} & -400 & 1.32 \\

\text{} & -399 & 1.32 \\

\text{} & -398 & 1.33 \\

\text{} & -397 & 1.34 \\

33 & -396 & 1.35 \\

\text{} & -395 & 1.36 \\

\text{} & -394 & 1.36 \\

\text{} & -393 & 1.37 \\

\text{} & -392 & 1.37 \\

\text{} & -391 & 1.37 \\

\text{} & -390 & 1.39 \\

\text{} & -389 & 1.4 \\

\text{} & -388 & 1.41 \\

\text{} & -387 & 1.42 \\

\text{} & -386 & 1.42 \\

\text{} & -385 & 1.43 \\

32 & -384 & 1.43 \\

\text{} & -383 & 1.44 \\

\text{} & -382 & 1.44 \\

\text{} & -381 & 1.44 \\

\text{} & -380 & 1.44 \\

\text{} & -379 & 1.46 \\

\text{} & -378 & 1.45 \\

\text{} & -377 & 1.46 \\

\text{} & -376 & 1.45 \\

\text{} & -375 & 1.45 \\

\text{} & -374 & 1.45 \\

\text{} & -373 & 1.44 \\

31 & -372 & 1.43 \\

\text{} & -371 & 1.43 \\

\text{} & -370 & 1.43 \\

\text{} & -369 & 1.42 \\

\text{} & -368 & 1.42 \\

\text{} & -367 & 1.42 \\

\text{} & -366 & 1.43 \\

\text{} & -365 & 1.44 \\

\text{} & -364 & 1.46 \\

\text{} & -363 & 1.48 \\

\text{} & -362 & 1.49 \\

\text{} & -361 & 1.49 \\

30 & -360 & 1.5 \\

\text{} & -359 & 1.51 \\

\text{} & -358 & 1.52 \\

\text{} & -357 & 1.53 \\

\text{} & -356 & 1.54 \\

\text{} & -355 & 1.53 \\

\text{} & -354 & 1.52 \\

\text{} & -353 & 1.52 \\

\text{} & -352 & 1.52 \\

\text{} & -351 & 1.51 \\

\text{} & -350 & 1.51 \\

\text{} & -349 & 1.5 \\

29 & -348 & 1.5 \\

\text{} & -347 & 1.49 \\

\text{} & -346 & 1.47 \\

\text{} & -345 & 1.47 \\

\text{} & -344 & 1.46 \\

\text{} & -343 & 1.44 \\

\text{} & -342 & 1.43 \\

\text{} & -341 & 1.42 \\

\text{} & -340 & 1.4 \\

\text{} & -339 & 1.39 \\

\text{} & -338 & 1.37 \\

\text{} & -337 & 1.35 \\

28 & -336 & 1.33 \\

\text{} & -335 & 1.32 \\

\text{} & -334 & 1.31 \\

\text{} & -333 & 1.3 \\

\text{} & -332 & 1.29 \\

\text{} & -331 & 1.28 \\

\text{} & -330 & 1.28 \\

\text{} & -329 & 1.27 \\

\text{} & -328 & 1.26 \\

\text{} & -327 & 1.26 \\

\text{} & -326 & 1.25 \\

\text{} & -325 & 1.24 \\

27 & -324 & 1.23 \\

\text{} & -323 & 1.22 \\

\text{} & -322 & 1.21 \\

\text{} & -321 & 1.19 \\

\text{} & -320 & 1.18 \\

\text{} & -319 & 1.18 \\

\text{} & -318 & 1.19 \\

\text{} & -317 & 1.2 \\

\text{} & -316 & 1.19 \\

\text{} & -315 & 1.2 \\

\text{} & -314 & 1.2 \\

\text{} & -313 & 1.21 \\

26 & -312 & 1.22 \\

\text{} & -311 & 1.22 \\

\text{} & -310 & 1.22 \\

\text{} & -309 & 1.23 \\

\text{} & -308 & 1.25 \\

\text{} & -307 & 1.27 \\

\text{} & -306 & 1.29 \\

\text{} & -305 & 1.29 \\

\text{} & -304 & 1.3 \\

\text{} & -303 & 1.31 \\

\text{} & -302 & 1.32 \\

\text{} & -301 & 1.33 \\

25 & -300 & 1.34 \\

\text{} & -299 & 1.35 \\

\text{} & -298 & 1.37 \\

\text{} & -297 & 1.36 \\

\text{} & -296 & 1.36 \\

\text{} & -295 & 1.34 \\

\text{} & -294 & 1.32 \\

\text{} & -293 & 1.3 \\

\text{} & -292 & 1.28 \\

\text{} & -291 & 1.27 \\

\text{} & -290 & 1.25 \\

\text{} & -289 & 1.24 \\

24 & -288 & 1.23 \\

\text{} & -287 & 1.22 \\

\text{} & -286 & 1.22 \\

\text{} & -285 & 1.21 \\

\text{} & -284 & 1.21 \\

\text{} & -283 & 1.2 \\

\text{} & -282 & 1.19 \\

\text{} & -281 & 1.18 \\

\text{} & -280 & 1.19 \\

\text{} & -279 & 1.2 \\

\text{} & -278 & 1.2 \\

\text{} & -277 & 1.21 \\

23 & -276 & 1.2 \\

\text{} & -275 & 1.2 \\

\text{} & -274 & 1.2 \\

\text{} & -273 & 1.2 \\

\text{} & -272 & 1.23 \\

\text{} & -271 & 1.25 \\

\text{} & -270 & 1.26 \\

\text{} & -269 & 1.26 \\

\text{} & -268 & 1.28 \\

\text{} & -267 & 1.29 \\

\text{} & -266 & 1.3 \\

\text{} & -265 & 1.33 \\

22 & -264 & 1.34 \\

\text{} & -263 & 1.35 \\

\text{} & -262 & 1.35 \\

\text{} & -261 & 1.34 \\

\text{} & -260 & 1.33 \\

\text{} & -259 & 1.3 \\

\text{} & -258 & 1.3 \\

\text{} & -257 & 1.28 \\

\text{} & -256 & 1.27 \\

\text{} & -255 & 1.25 \\

\text{} & -254 & 1.23 \\

\text{} & -253 & 1.2 \\

21 & -252 & 1.16 \\

\text{} & -251 & 1.11 \\

\text{} & -250 & 1.06 \\

\text{} & -249 & 1.03 \\

\text{} & -248 & 1.01 \\

\text{} & -247 & 0.97 \\

\text{} & -246 & 0.93 \\

\text{} & -245 & 0.9 \\

\text{} & -244 & 0.85 \\

\text{} & -243 & 0.81 \\

\text{} & -242 & 0.79 \\

\text{} & -241 & 0.77 \\

20 & -240 & 0.75 \\

\text{} & -239 & 0.71 \\

\text{} & -238 & 0.66 \\

\text{} & -237 & 0.64 \\

\text{} & -236 & 0.61 \\

\text{} & -235 & 0.6 \\

\text{} & -234 & 0.58 \\

\text{} & -233 & 0.55 \\

\text{} & -232 & 0.53 \\

\text{} & -231 & 0.49 \\

\text{} & -230 & 0.47 \\

\text{} & -229 & 0.46 \\

19 & -228 & 0.44 \\

\text{} & -227 & 0.43 \\

\text{} & -226 & 0.42 \\

\text{} & -225 & 0.38 \\

\text{} & -224 & 0.37 \\

\text{} & -223 & 0.36 \\

\text{} & -222 & 0.36 \\

\text{} & -221 & 0.35 \\

\text{} & -220 & 0.33 \\

\text{} & -219 & 0.34 \\

\text{} & -218 & 0.33 \\

\text{} & -217 & 0.32 \\

18 & -216 & 0.3 \\

\text{} & -215 & 0.31 \\

\text{} & -214 & 0.33 \\

\text{} & -213 & 0.33 \\

\text{} & -212 & 0.33 \\

\text{} & -211 & 0.29 \\

\text{} & -210 & 0.25 \\

\text{} & -209 & 0.24 \\

\text{} & -208 & 0.22 \\

\text{} & -207 & 0.17 \\

\text{} & -206 & 0.13 \\

\text{} & -205 & 0.09 \\

17 & -204 & 0.07 \\

\text{} & -203 & 0.04 \\

\text{} & -202 & 0.03 \\

\text{} & -201 & 0.01 \\

\text{} & -200 & -0.02 \\

\text{} & -199 & -0.07 \\

\text{} & -198 & -0.13 \\

\text{} & -197 & -0.16 \\

\text{} & -196 & -0.21 \\

\text{} & -195 & -0.27 \\

\text{} & -194 & -0.32 \\

\text{} & -193 & -0.37 \\

16 & -192 & -0.39 \\

\text{} & -191 & -0.41 \\

\text{} & -190 & -0.43 \\

\text{} & -189 & -0.44 \\

\text{} & -188 & -0.46 \\

\text{} & -187 & -0.46 \\

\text{} & -186 & -0.41 \\

\text{} & -185 & -0.31 \\

\text{} & -184 & -0.24 \\

\text{} & -183 & -0.11 \\

\text{} & -182 & -0.02 \\

\text{} & -181 & 0.05 \\

15 & -180 & 0.14 \\

\text{} & -179 & 0.22 \\

\text{} & -178 & 0.28 \\

\text{} & -177 & 0.34 \\

\text{} & -176 & 0.34 \\

\text{} & -175 & 0.36 \\

\text{} & -174 & 0.36 \\

\text{} & -173 & 0.38 \\

\text{} & -172 & 0.33 \\

\text{} & -171 & 0.33 \\

\text{} & -170 & 0.3 \\

\text{} & -169 & 0.23 \\

14 & -168 & 0.2 \\

\text{} & -167 & 0.15 \\

\text{} & -166 & 0.13 \\

\text{} & -165 & 0.1 \\

\text{} & -164 & 0.05 \\

\text{} & -163 & 0.02 \\

\text{} & -162 & -0.06 \\

\text{} & -161 & -0.09 \\

\text{} & -160 & -0.12 \\

\text{} & -159 & -0.12 \\

\text{} & -158 & -0.14 \\

\text{} & -157 & -0.18 \\

13 & -156 & -0.23 \\

\text{} & -155 & -0.31 \\

\text{} & -154 & -0.35 \\

\text{} & -153 & -0.4 \\

\text{} & -152 & -0.48 \\

\text{} & -151 & -0.56 \\

\text{} & -150 & -0.62 \\

\text{} & -149 & -0.67 \\

\text{} & -148 & -0.71 \\

\text{} & -147 & -0.69 \\

\text{} & -146 & -0.68 \\

\text{} & -145 & -0.74 \\

12 & -144 & -0.78 \\

\text{} & -143 & -0.73 \\

\text{} & -142 & -0.76 \\

\text{} & -141 & -0.75 \\

\text{} & -140 & -0.74 \\

\text{} & -139 & -0.74 \\

\text{} & -138 & -0.71 \\

\text{} & -137 & -0.65 \\

\text{} & -136 & -0.63 \\

\text{} & -135 & -0.59 \\

\text{} & -134 & -0.57 \\

\text{} & -133 & -0.52 \\

11 & -132 & -0.48 \\

\text{} & -131 & -0.47 \\

\text{} & -130 & -0.46 \\

\text{} & -129 & -0.53 \\

\text{} & -128 & -0.53 \\

\text{} & -127 & -0.56 \\

\text{} & -126 & -0.48 \\

\text{} & -125 & -0.46 \\

\text{} & -124 & -0.47 \\

\text{} & -123 & -0.46 \\

\text{} & -122 & -0.42 \\

\text{} & -121 & -0.48 \\

10 & -120 & -0.47 \\

\text{} & -119 & -0.47 \\

\text{} & -118 & -0.44 \\

\text{} & -117 & -0.35 \\

\text{} & -116 & -0.3 \\

\text{} & -115 & -0.19 \\

\text{} & -114 & -0.15 \\

\text{} & -113 & -0.11 \\

\text{} & -112 & 0. \\

\text{} & -111 & 0.02 \\

\text{} & -110 & -0.02 \\

\text{} & -109 & -0.11 \\

9 & -108 & -0.26 \\

\text{} & -107 & -0.37 \\

\text{} & -106 & -0.4 \\

\text{} & -105 & -0.39 \\

\text{} & -104 & -0.42 \\

\text{} & -103 & -0.52 \\

\text{} & -102 & -0.4 \\

\text{} & -101 & -0.34 \\

\text{} & -100 & -0.29 \\

\text{} & -99 & -0.12 \\

\text{} & -98 & -0.09 \\

\text{} & -97 & -0.07 \\

8 & -96 & 0.03 \\

\text{} & -95 & 0.05 \\

\text{} & -94 & 0.19 \\

\text{} & -93 & 0.33 \\

\text{} & -92 & 0.42 \\

\text{} & -91 & 0.37 \\

\text{} & -90 & 0.39 \\

\text{} & -89 & 0.42 \\

\text{} & -88 & 0.47 \\

\text{} & -87 & 0.49 \\

\text{} & -86 & 0.36 \\

\text{} & -85 & 0.31 \\

7 & -84 & 0.32 \\

\text{} & -83 & 0.34 \\

\text{} & -82 & 0.44 \\

\text{} & -81 & 0.56 \\

\text{} & -80 & 0.54 \\

\text{} & -79 & 0.63 \\

\text{} & -78 & 1.04 \\

\text{} & -77 & 1.22 \\

\text{} & -76 & 1.43 \\

\text{} & -75 & 1.58 \\

\text{} & -74 & 1.6 \\

\text{} & -73 & 1.63 \\

6 & -72 & 1.75 \\

\text{} & -71 & 1.97 \\

\text{} & -70 & 2.09 \\

\text{} & -69 & 2.17 \\

\text{} & -68 & 2.12 \\

\text{} & -67 & 1.96 \\

\text{} & -66 & 1.5 \\

\text{} & -65 & 1.08 \\

\text{} & -64 & 0.79 \\

\text{} & -63 & 0.44 \\

\text{} & -62 & -0.23 \\

\text{} & -61 & -0.78 \\

5 & -60 & -1.16 \\

\text{} & -59 & -1.61 \\

\text{} & -58 & -1.85 \\

\text{} & -57 & -2.13 \\

\text{} & -56 & -2.34 \\

\text{} & -55 & -2.73 \\

\text{} & -54 & -2.9 \\

\text{} & -53 & -3.24 \\

\text{} & -52 & -3.72 \\

\text{} & -51 & -4.2 \\

\text{} & -50 & -5.07 \\

\text{} & -49 & -6.15 \\

4 & -48 & -6.36 \\

\text{} & -47 & -6.87 \\

\text{} & -46 & -6.65 \\

\text{} & -45 & -6.99 \\

\text{} & -44 & -7.25 \\

\text{} & -43 & -8.02 \\

\text{} & -42 & -7.22 \\

\text{} & -41 & -6.6 \\

\text{} & -40 & -5.52 \\

\text{} & -39 & -4.69 \\

\text{} & -38 & -3.57 \\

\text{} & -37 & -2.44 \\

3 & -36 & -0.7 \\

\text{} & -35 & 1.3 \\

\text{} & -34 & 3.37 \\

\text{} & -33 & 4.41 \\

\text{} & -32 & 5.73 \\

\text{} & -31 & 6.55 \\

\text{} & -30 & 6.39 \\

\text{} & -29 & 5.86 \\

\text{} & -28 & 4.39 \\

\text{} & -27 & 3.9 \\

\text{} & -26 & 3.46 \\

\text{} & -25 & 4.92 \\

2 & -24 & 7.15 \\

\text{} & -23 & 9.34 \\

\text{} & -22 & 12.06 \\

\text{} & -21 & 12.06 \\

\text{} & -20 & 10.79 \\

\text{} & -19 & 10.65 \\

\text{} & -18 & 6.15 \\

\text{} & -17 & -1.91 \\

\text{} & -16 & -7.49 \\

\text{} & -15 & -6.54 \\

\text{} & -14 & -8.89 \\

\text{} & -13 & -7.27 \\

1 & -12 & -8.63 \\

\text{} & -11 & -10.59 \\

\text{} & -10 & -3.05 \\

\text{} & -9 & 2.12 \\

\text{} & -8 & -0.67 \\

\text{} & -7 & -22.67 \\

\text{} & -6 & 10.9 \\

\text{} & -5 & 12.72 \\

\text{} & -4 & 19.32 \\

\text{} & -3 & 49.8 \\

\text{} & -2 & -82.8 \\ \hline

\end{array}



\]