Of weather prediction without models II
Lorenz had already expressed  the existence of what he termed the empirical approach, as opposed to the dynamical. Also called "prediction without laws" , such a forecasting would be based on an analogue method, where two states of the atmosphere would be deemed alike. Naturally this was long before we knew  how to reconstruct  the state space of a dynamical system from a set of observations. Yet this modern embedding approach, void of model usage, could very well be an example of what Lorenz considered but had to relinquish.
Though recognized as the father of the butterfly effect, Lorenz called into question the real limits of predictability. In one of his last papers , he propounded that, in order to tackle the veridical forecasting limits, the error growth should result solely from the amplification of already present errors. We formerly mentioned the work of Robert  on the dubiety of this sensitive dependency in the prediction of atmospheric flows, we now echo the work of Orrell  in stating that the main thing stopping us from getting longer-term accurate weather forecasts is not the butterfly effect but the errors in the models.
Our scheme thence advocates the prediction of weather from the lone knowledge of past raw data values, in the voluntary absence of models. But where in the data can predictability information be found? What evidence do we have for holographic boundaries inside the time-series of atmospheric variability? This is in reality at the heart of Hurst's work  on the Nile river records, that of statistical persistence or long-range dependency. The so-called  "second law of self-organization" is at play, with the inherent ability of a time-series to store information  about bubbles of its own future. How does one draw [e.g., 12, 13] on this information reserve? One example is the aforementioned reconstruction as instanced by Farmer & Sidorowich . Alike methods [e.g., 15, 15bis, 15ter] are left to the discretion of the author who devised and used self-similarity analysis techniques for the past fifteen years. As phrased by Lorenz: "existence of predictability may be established by demonstrating a forecasting procedure which exhibits skill" .
Moreover, this utmost approach (a systems approach  in its philosophy of counter-reductionism) finds justification  in a recent mathematical result , a non-constructive proof of the existence of ampliative inference from past events. Hence with no pretension on the how-to, this proof set up by others indicates that inductive extrapolations could exist and thus provides the grounds for the statistical inference we ourselves suggest. The heuristics of this reasoning will be explained by way of a prisoners' game and analogy; a working example will also be given and put in perspective with the proof.
A mathematical seer conceivably interprets dreams of the past, foretelling the weather.
 Lafitte MJ. et al., Of weather prediction without models, 17B.1, 23rd Conference on Weather Analysis and Forecasting/19th Conference on Numerical Weather Prediction, 2009
 Lorenz EN., Three approaches to atmospheric predictability, Bulletin of the American Meteorological Society, Vol. 50 (1969), pp. 345--351
 Lorenz EN., How much better can weather prediction become?, Technology Review, July/August (1969), pp. 39--49
 Takens F., Detecting strange attractors in turbulence, in Rand DA. & Yound L-S, Dynamical Systems and Turbulence, Lecture Notes in Mathematics, Vol. 898 (1981), pp. 230--242
 Packard N. et al., Geometry from a time series, Physical Review Letters, Vol. 45 (1980), pp. 712--716
 Lorenz EN., Predictability --- a problem partly solved, in Palmer T. & Hagedorn R., Predictability of Weather and Climate, Cambridge University Press (2006), pp. 40--58
 Robert R. et al., Long range predictability of atmospheric flows, Non Linear Processes in Geophysics, Vol. 8 (2001), pp. 55--67
 Orrell D. et al., Model error in weather forecasting, Nonlinear Processes in Geophysics, Vol. 8 (2001), pp. 357--371
 Hurst H., Long term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers Vol. 116 (1951), pp. 770--799
 Farmer JD., The second law of organization, Chap. 22 in Brockman J., The Third Culture: Beyond the Scientific Revolution, Simon&Schuster (1995)
 Farmer JD., Cool is not enough, Nature, Vol. 436 (2005), pp. 627--628
 Smith LA, Local optimal prediction: exploiting strangeness and the variation of sensitivity to initial condition, Philosophical Transactions of the Royal Society A, Vol. 348 (1994), pp. 371-381
 Sugihara G. et al., Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts, Proceedings of the National Academy of Sciences, Vol. 96 (1999), pp. 210--215
 Farmer JD., Sidorowich JJ., Predicting chaotic time series, Physical Review Letters, Vol. 59 (1987), pp. 845--848; Los Alamos National Laboratory Report No. LA-UR-88-901
 Gluzman S, Yukalov VI, Resummation methods for analysing time series, Modern Physics Letters B, Vol. 12 (1998), pp. 61-74
[15bis] Yukalov VI, Gluzman S, Weighted fixed points in self-similar analysis of time series, International Journal of Modern Physics B, Vol. 13 (1999), pp. 1463--1476
[15ter] Yukalov VI, Self-similar extrapolation of asymptotic series and forecasting for time series, Modern Physics Letters B, Vol. 14 (2000), pp. 791--800
 Lorenz EN., On the existence of extended range predictability, Journal of Applied Meteorology, Vol. 12 (1973), pp. 543--546
 Orrell D. et al., A systems approach to forecasting, Foresight, Issue 14 (Summer 2009), pp. 25--30
 George A., A proof of induction?, Philosopher's Imprint, Vol. 7 No. 2 (March 2007), pp. 1--5
 Hardin CS. et al., A peculiar connection between the axiom of choice and predicting the future, American Mathematical Monthly, Vol. 115 (February 2008), pp. 91--96