Guest essay by Pat Frank
This essay expands on a point made in a previous post here at WUWT, that climate models do not produce a unique solution to the energy state of the climate. Unique solutions are the source of physical meaning in science, and make a physical theory both predictive and falsifiable.
Predictive because a unique solution is a derived and highly specific statement about how physical reality behaves. It allows that only one possibility, among an infinite number of possibilities, will occur. A unique solution asserts an extreme improbability; making it vulnerable to disproof by observation.
Falsifiable because if the prediction is wrong, the physical theory is refuted.
Figure 1 in the previous post showed that the huge uncertainty limits in projections of future global air temperatures make them predictively useless. In other words, they have no physical meaning. See also here (528 kB pdf), and see Figure 1 here, a paper just now out in Energy & Environment on the pervasive negligence that infects consensus climatology. 
This post will show that hindcasts of historically recent global air temperature trends also have no physical meaning.
The Figure below shows data from Figure SPM.5 of the IPCC 4AR.  The dark red line in the top panel shows the multi-model average simulation of the 20th century global surface air temperature. The blue points are the 1999 version of the GISS land+sea global average air temperature record.  The correspondence between the simulated and observed temperatures is good (correlation R = 0.85; p<0.0001). The inset at the top of the panel shows the SPM.5 multi-model average as published in the 4AR. The grey IPCC uncertainty envelope about the 20th century simulation is ± one standard deviation about the multi-model mean.
The IPCC’s relatively narrow uncertainty envelope implies that the hindcast simulation merits considerable confidence. The good correspondence between the observed and simulated 20th century temperatures is well within the correlation = causation norm of consensus climatology.
The bottom panel of Figure 1 also shows uncertainty bars about the 20th century multi-model hindcast. These represent the CMIP5 average ±4 Wm-2 systematic cloud forcing error propagated through the simulation. The propagation is carried out by inserting the cloud error into the previously published linear equation that accurately emulates GCM air temperature projections; also see here (2.9 MB pdf). Systematic error propagates as the root-sum-square.
Figure 1. Top panel (red line), the multi-model simulation of the 20th century global air temperature (IPCC AR4 Figure SPM.5). Inset: SPM.5 multi-model average 20th century hindcast, as published. Blue points: the GISS 1999 land+sea global surface air temperature record. Bottom panel: the SPM.5 multi-model 20th century simulation with uncertainty bars propagated from the root-sum-square CMIP5 average ±4 Wm-2 cloud forcing error.
The consensus sensibility will now ask: how is it possible for the lower panel uncertainty bars to be so large, when the simulated temperatures are so obviously close to the observed temperatures?
Here’s how: the multi-model average simulated 20th century hindcast is physically meaningless. Uncertainty bars are an ignorance width. Systematic error ensures that the further out in time the climate is projected, the less is known about the correspondence between the simulation and the true physical state of the future climate. The next part of this post demonstrates the truth of that diagnosis.
Figure 1 from Rowlands , below, shows “perturbed physics” projections from the HadCM3L climate model. In perturbed physics projections, “a single model structure is used and perturbations are made to uncertain physical parameters within that structure…”  That is, a perturbed physics experiment shows the variation in climate projections as model parameters are varied step-wise across their physical uncertainty.
Figure 2. Original Legend: “Evolution of uncertainties in reconstructed global-mean temperature projections under SRES A1B in the HadCM3L ensemble.” The embedded black line is the observed surface air temperature record. The horizontal black lines at 1 C and 3 C, and the vertical red line at year 2055, are PF-added.
The HADCML model is representative of the behavior of all climate models, including the advanced CMIP3 and CMIP5 versions. Different sets of parameters produce a spread of projections of increasing deviation with simulation time.
Under the SRES A1B scenario, atmospheric CO2 increases annually. This means the energy state of the simulated climate increases systematically across the years.
The horizontal black lines show that the HADCM3L will produce the same temperature change for multiple (thousands of) climate energy states. That is, different sets of parameters project a constant 1 C temperature increase for every single annual climate energy state between 1995-2050. The scientific question is, which of the thousands of 1 C projections is the physically correct one?
Likewise, depending on parameter sets, a constant 3 C increase in temperature can result from every single annual climate energy state between 2030-2080. Which one of those is correct?
None of the different sets of parameters is known to be any more physically correct than any other. There is no way, therefore, to choose which temperature projection is physically preferable among all the alternatives.
Which one is correct? No one knows.
The identical logic applies to the vertical red line. This line shows that the HADCM3L will produce multiple (thousands of) temperature changes for a single climate energy state (the 2055 state). Every single Rowlands, et al., annual climate energy state between 1976-2080 has dozens of simulated air temperatures associated with it.
Again, none of the different parameter sets producing these simulated temperatures is known to be any more physically correct than any other set. There is again no way to decide which, among all the different choices of projected annual air temperature, is physically correct.
This set of examples shows that the HADCM3L cannot produce a unique solution to the problem of the climate energy state. No set of model parameters is known to be any more valid than any other set of model parameters. No projection is known to be any more physically correct (or incorrect) than any other projection.
This means, for any given projection, the internal state of the model is not known to reveal anything about the underlying physical state of the true terrestrial climate. More simply, the model cannot tell us anything at all about the physically real climate, at the level of resolution of greenhouse gas forcing.
The same is necessarily true for any modeled climate energy state, including the modeled energy states of the past climate.
Now let’s look back at the multi-model average 20th century hindcast in the top panel of post Figure 1. Analogize the multiple temperature projections in Rowlands, et al., Figure 1, that represent the ignorance widths of the parameter sets, onto the single hindcast line of SPM.5. Doing so brings the realization that there must be an equally large set of equally valid but divergent hindcasts.
Each of the multiple models that produced that hindcast has a large number of alternative parameter sets. Those alternative sets are not known to be any less physically valid than whatever set produced each individual model hindcast.
There must exist a perturbed physics spread, analogous to Rowlands Figure 1, for the 20th century hindcast projection. The alternative parameter sets, all equally valid, would produce a set of hindcasts that would diverge with time. Starting from 1900, the individual perturbed physics hindcasts would diverge ever further from the known air temperature record through to 2000. But they have all been left out of Figure SPM.5.
The model states that produced the SPM.5 20th century hindcast, then, do not reveal anything at all about the true physical state of the 20th century terrestrial climate, within the resolution of 20th century forcing.
That means the multi-model average hindcast in SPM.5 has no apparent physical meaning. It is the average of hindcast projections that themselves have no physical meaning. This is the reason for the huge uncertainty bars, despite the fact that the average hindcast temperature trend is close to the observed temperature trend. The model states are not telling us anything about what caused the observed temperatures. Therefore the hindcast air temperatures have no physical connection to the observed air temperatures. The divergence of the perturbed physics hindcasts will increase with simulation time, in a manner exactly portrayed by the increasingly wide uncertainty envelope.
This conclusion remains true even if a given climate model happens to produce a projection that tracks the emergent behavior of observed air temperatures. Such correspondences are accidental, in that the parameter set chosen for that model run must have had offsetting errors. They were inadvertently assigned beneficial values from within their uncertainty margins. Whatever those beneficial values, they are not known to be physically correct. Nor can the accidental correlation with observations imply that the underlying model state corresponds to the true physical state of the climate.
The physical meaning of the recently published study of M. England, et al.,  exemplified in Figure 3 below, is now apparent. England, et al., reported that some CMIP5 projections approximated the air temperature “hiatus” since 2000. They then claimed that this correspondence proved the, “robust nature of twenty-first century warming projections” and that it, “increase[s] confidence in the recent synthesized projections reported in the Intergovernmental Panel on Climate Change Fifth Assessment Report.”
Compare Figure 1 of England, et al., 2015, below, with Figure 1 of Rowlands, et al., 2012, above. The horizontal black lines and the vertical green line transmit the same diagnosis as the analogous lines in Rowlands, et al., Figure 1.
The England, et al., set of CMIP5 models produced constant air temperatures for multiple climate energy states, and multiple air temperatures for every single annual climate energy state. This, despite the fact that, “all simulations follow identical historical forcings (, Supplementary Information).” The divergence of the projections, despite identical forcings, clearly reveals a spread in model parameter values.
Figure 3. Figure 1 from England, et al. 2015.  Original Legend: Global average SAT anomalies relative to 1880–1900 in individual and multi-model mean CMIP5 simulations. Blue curves: RCP4.5 scenario; red curves: RCP8.5 scenario. The horizontal black lines at 2 C and 3 C and the vertical green line at 2060, are PF added.
The diagnosis follows directly from Figure 3: CMIP5 climate models are incapable of producing a unique solution to the problem of the climate energy state. They all suffer from internal parameter sets with wide uncertainty bands. The internal states of the models do not reveal anything about the underlying true physical state of the climate, past or future. None of the CMIP5 projections reported by England, et al., has any knowable physical meaning, no matter whether they track over the “hiatus” or not.
This brings us back around to the meaning of the huge uncertainty bars in the bottom panel of the 20th century hindcast in post Figure 1. These arise from the propagated CMIP5 model ±4 Wm-2 average cloud forcing error. [7, 8] Like parameter uncertainty, cloud forcing error also indicates that climate models cannot provide a unique solution to the problem of the climate energy state.
Uncertainty bars are an ignorance width. They indicate how much confidence a prediction merits. Parameter uncertainty means the correct parameter values are not known. Cloud forcing error means the thermal energy flux introduced by cloud feedback into the troposphere is not well-known. Models with internal systematic errors introduce that error into every single step of a climate simulation. The more simulation steps, the less is known about the correspondence between the simulated state and the physically true state.
The more simulation steps, the less knowledge, and the greater the ignorance about the model deviations from the physically true state. This is the message of the increasing width of the uncertainty envelope of propagated error.
Every single projection in England, et al.’s Figure 1 is subject to the ±4 Wm-2 CMIP5 average cloud forcing error. A proper display of their physical meaning should include an uncertainty envelope like that in post Figure 1, bottom. Moreover, the systematic error in the projections of individual models enters a multi-model average as the root-mean-square.  England, et al.’s multi-model mean projections — the dark red and blue lines — have even greater uncertainty than any of the individual projections. This is an irony that regularly escapes consensus climatologists.
So, when you see a figure such as Figure 4 top, below, supplied by the US National Academy of Sciences , realize that a presentation that fully conformed to scientific standards would look like Figure 4 bottom.
Figure 4. Top: Figure 4 from ; original legend: Model simulations of 20th century climate variations more closely match observed temperature when both natural and human influences are included. Black line shows observed temperatures. Bottom, the top left US NAS panel showing the global 20th century air temperature hindcast, but now with uncertainty bars from propagated ±4 Wm-2 CMIP5 average cloud forcing error.
It makes no sense at all to claim that an explanation of later 20th century warming is not possible without including “human influences,” when in fact an explanation of later 20th century warming is not possible, period.
Climate modelers choose parameter sets with offsetting errors in order to successfully hindcast the 20th century air temperature.  That means any correspondence between hindcast temperatures and observed temperatures is tendentious — the correspondence is deliberately built-in.
The previous post made the case that their own statements reveal that climate modelers are not trained as physical scientists. It showed that climate modeling itself is a liberal art in the manner of cultural studies, but elaborated with mathematics. In cultural studies, theory just intellectualizes the prejudices of the theorist. This post presents the other side of that coin: the lack of understanding that follows from the lack of professional training.
The fact that England, et al., can claim the “robust nature of twenty-first century warming projections” and ‘increased confidence‘ in IPCC projections, when their models are obviously incapable of resolving the climate energy state, merely shows that they can have no understanding whatever of the source of physical meaning. This is why they exhibit no recognition that their models projections have no physical meaning. Likewise the editors and reviewers of Nature Climate Change, the management of the US National Academy of Sciences, and the entire IPCC top to bottom.
The evidence shows that these people do not know how physical meaning emerges from physical theory. They do not know how to recognize physical meaning, how to present physical meaning, nor how to evaluate physical meaning.
In short, they understand neither prediction nor falsification; conjointly the very foundation of science.
Climate modelers are not scientists. They are not doing science. Their climate model projections have no physical meaning. Their climate model projections have never had any physical meaning.
To this date, there hasn’t been a single GHG emissions climate projection, ever, that had physical meaning. So, all those contentious debates about whether some model, some set of models, or some multi-model mean, tracks the global air temperature record, or not, are completely pointless. It doesn’t matter whether a physically meaningless projection happens to match some observable, or not. The projection is physically meaningless. It has no scientific content. The debate has no substantive content. The debaters may as well be contesting theology.
So, when someone says about AGW that, “The science is settled!,” one can truthfully respond that it is indeed settled: there is no science in AGW.
1. Frank, P., Negligence, Non-Science, and Consensus Climatology. Energy & Environment, 2015. 26(3): p. 391-416.
2. IPCC, Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, S. Solomon, et al., Editors. 2007, Cambridge University: Cambridge.
3. Hansen, J., et al., GISS analysis of surface temperature change. J. Geophys. Res., 1999. 104(D24): p. 30997–31022.
4. Rowlands, D.J., et al., Broad range of 2050 warming from an observationally constrained large climate model ensemble. Nature Geosci, 2012. 5(4): p. 256-260.
5. Collins, M., et al., Climate model errors, feedbacks and forcings: a comparison of perturbed physics and multi-model ensembles. Climate Dynamics, 2011. 36(9-10): p. 1737-1766.
6. England, M.H., J.B. Kajtar, and N. Maher, Robust warming projections despite the recent hiatus. Nature Clim. Change, 2015. 5(5): p. 394-396.
7. Lauer, A. and K. Hamilton, Simulating Clouds with Global Climate Models: A Comparison of CMIP5 Results with CMIP3 and Satellite Data. J. Climate, 2013. 26(11): p. 3823-3845.
8. Frank, P., Propagation of Error and the Reliability of Global Air Temperature Projections; Invited Poster, in American Geophysical Union Fall Meeting. 2013: San Francisco, CA; Available from: http://meteo.lcd.lu/globalwarming/Frank/propagation_of_error_poster_AGU2013.pdf (2.9 MB pdf).
9. Taylor, B.N. and C.E. Kuyatt., Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results. 1994, National Institute of Standards and Technology: Washington, DC. p. 20.
10. Staudt, A., N. Huddleston, and I. Kraucunas, Understanding and Responding to Climate Change 2008, The National Academy of Sciences USA: Washington, D.C.
11. Kiehl, J.T., Twentieth century climate model response and climate sensitivity. Geophys. Res. Lett., 2007. 34(22): p. L22710.