Benestad at realclimate here, against Cohn and Lins, argues that their use of time series methods more advanced than Benestad’s IID, somehow offended against the laws of physics, "pitching statistics against physics" – plus other gems. It has to be read to be believed. Now white noise (equivalent to Benestad’s IID, independent identically distributed residuals) has a distinctive horizontal spectrum, while red noise has spectra sloping down and to the right. Before proclaiming that it is against the "laws of physics" for temperature data to have autocorrelation properties, one thinks that Benestad might have examined some actual spectra of temperature and temperature proxy series (rather than exclusively relying on GCM output), to determine whether his IID assumption applies.
As I mentioned before, the redness of geophysical series was remarked upon as long by Mandelbrot. The references in Cohn and Lins  are clear and Benestad would profit from reading these articles. Another interesting recent discussion is Pelletier [PNAS, 2002], who not only shows redness in both temperature and temperature proxy data, but proposes a physical mechanism which could account for the power law properties of the series. I don’t have any views on whether Pelletier’s theory is right or wrong, but it is interesting. Equally important is the mere fact that the series have distinctive power law properties – since the measurements have power law properties, such power law behavior is obviously not against the "laws of physics" (contra realclimate), but a valid topic of inquiry. If GCMs do not capture this power law behavior, as they seem not to do, based on Benestad’s account, then possibly the GCMs are at fault, rather than the data.
Pelletier’s Figure 1 and Figure 2 below show the spectra from Vostok and from 94 GHCN stations. While one can quibble with how Pelletier divides up the diagram, it is indisputable that the spectra are downsloping to the right – characteristic of autocorrelation of the type contemplated by Cohn and Lins .
Original Caption: Left: Fig. 1. Power-spectral density estimated with the Lomb periodogram of the temperature inferred from the deuterium concentrations in the Vostok (East Antarctica) ice core. The power-spectral density S is given as a function of frequency for time scales of 500 yr to 200 kyr. Right Fig. 2. Average power-spectral density of 94 complete monthly temperature time series from the data set of Vose et al. (8) plotted as a function of frequency in yr^-1. The power-spectral density S is given as a function of frequency for time scales of 2 months to 100 yr.
Pelletier’s Figures 3 and 4 show what appear to be different spectra for land and maritime stations – with the maritime stations being considerably redder.
Original Caption: Fig. 3. Average power-spectral density of 50 continental daily temperature time series from the data set of the National Climatic Data Center (9) as a function of frequency in yr^-1. The power-spectral density S is given as a function of frequency for time scales of 2 days to 10 yr. Fig. 4. Average power-spectral density of 50 maritime daily temperature time series from the data set of the National Climatic Data Center (9) as a function of frequency in yr^-11. The power-spectral density S is given as a function of frequency for time scales of 2 days to 10 yr.
Pelletier then combines the spectra for different scales into one composite spectrum as follows:
Original Caption: Fig. 5. Power-spectral density of local atmospheric temperature from instrumental data and inferred from ice cores from time scales of 200 kyr to 2 days. The high frequency data are for continental stations. Piecewise powerlaw trends are indicated.
Pelletier provides an interesting physical hypothesis as to how such power-law behavior could arise in terms of very different heat transfer properties between land and atmosphere as compared with ocean and atmosphere:
We can interpret these results in terms of the vertical turbulent transport of heat energy in the atmosphere in addition to its radiation into space and its exchange with the ocean. The ocean acts as a thermal reservoir, buffering changes in atmospheric temperature. In our model, vertical turbulent transport is modeled as a stochastic diffusion process. Convective instabilities diffuse heat energy within the atmosphere by turbulent mixing. Deterministic diffusion is not adequate to model atmospheric heat transport, however, because the stochastic nature of turbulent flow in the atmosphere gives rise to fluctuations in the transport of heat through time….
In the introduction, we presented evidence that continental stations exhibit an f^-3/2 high-frequency region, and maritime stations exhibit f^-1/2 scaling up to the highest frequency considered. This observation can be interpreted in terms of the diffusion model presented above. The power spectrum of temperature variations in an air mass exchanging heat by one-dimensional stochastic diffusion is proportional to f^-1/2 if the air mass is bounded by two diffusing regions and is proportional to f^-3/2 if it interacts only with one. The boundary conditions appropriate to maritime and continental stations are a layer interacting with two (upper atmosphere and ocean) and one (upper atmosphere only) thermal reservoirs, respectively.The layer considered is taken to have an upper boundary embedded in the atmosphere and a lower boundary at the earth’s surface. For maritime stations, heat is transferred across this lower boundary into the oceans … and therefore the power spectrum of temperature variations is S(f) = f^-1/2. For continental stations, the lower boundary is insulating so…S(f) = f^-3/2. At low frequencies, horizontal heat exchange between continental and maritime air masses limits the variance of the continental stations This crossover occurs at the time scale when the air masses above continents and oceans become mixed. The time scale for one complete Hadley or Walker circulation which mixes the air masses…
The second term is the time scale for transport of the heat energy of the ocean to the top of the atmosphere where it can be radiated from clouds. If the time scale for one of these processes is much larger than the time scale for the other, the crossover time scale will be determined by that rate-limiting step. For the Earth’s climate system, the transport of the oceans’ heat through the atmosphere seems to be the rate-limiting step. This process takes a long time because the atmosphere has a low heat capacity compared to the oceans and is therefore a poor heat conductor. The time scale of radiative damping is estimated to be 600 yr from the well known constants listed in Fig. 6
Elsewhere Pelletier makes an interesting comparison between the stochastic properties of turbulent eddies and Brownian movement. Pelletier has a number of interesting articles at two websites amd they are worth reading. Whether right or wrong, considering the possibility of power law behavior in the spectra of temperature series is not an obvious offence against the "laws of physics", as Benestad would have us believe.
Reference: Jon D. Pelletier Natural variability of atmospheric temperatures and geomagnetic intensity over a wide range of time scales, 2002, PNAS, 99, 2546-2553. URL