Edward Norton Lorenz: Chaos, Predictability, and the Limits of Weather Forecasting

Research notes for an NWP-history blog post. Sources flagged inline; disagreements are explicitly called out.

1. Setting: Lorenz at MIT, 1948-1961

Career timeline (from Kerry Emanuel’s NAS Biographical Memoir and Wikipedia)

Born 23 May 1917, West Hartford, Connecticut. Dartmouth BA in mathematics 1938. Harvard MA in mathematics 1940.
WWII pulled him out of mathematics into weather forecasting for the Army Air Corps in the Pacific theatre (Saipan, then Guam/Okinawa); the experience converted him to meteorology.
MIT meteorology PhD 1948 under Henry Houghton, then research scientist; Assistant Professor 1955; Full Professor 1962; Department Head 1977-1981.
Married Jane Loban 1948; she died 2001. Lorenz died 16 April 2008 in Cambridge MA, age 90, of cancer. He was working on the proofs of his last paper (on the Henon map) days before he died.

The Statistical Research Project at MIT (1955-1961)

This is the crucial context the popular accounts skip: Lorenz did not set out to discover chaos. He set out to disprove statistical forecasting.

Emanuel: “By this time a number of statistical forecasters had come to believe that linear regression models would perform at least as well as numerical methods ever could, apparently bolstered by a theorem developed by Norbert Weiner. Ed was deeply skeptical of this idea and determined to test it using a simple set of equations, which he would numerically integrate and then see how well the result could be reproduced using linear regression methods.”

The MIT Statistical Forecasting Project had been founded by Thomas Malone; Houghton invited Lorenz to lead it in 1948 (Emanuel says Henry Houghton wrote inviting him, and Emanuel suggests in a footnote that Jule Charney may have negotiated this hire as a condition of Charney’s own arrival at MIT). The whole point of the project was to test whether linear regression on past weather could match the new numerical-dynamical forecasts coming out of the Princeton ENIAC group. Lorenz did not believe it could. He needed irregular, nonperiodic test data – the kind a linear model could not trivially fit. So he sat down to build a small dynamical system that would produce aperiodic output.

The irony, restated: he discovered chaos in 1961 while running the very model he had built as a strawman to defeat statistical forecasting. Statistical forecasting did poorly on his nonperiodic output, exactly as he had predicted. But the same nonperiodicity also meant that any small input error would amplify – so dynamical forecasting was also doomed at long ranges. He killed both regimes in the same gesture.

2. The Royal McBee LGP-30: hardware that made it possible

The Librascope General Precision LGP-30 was the workhorse. It arrived in Lorenz’s MIT office in 1958 and “sat in Ed’s office for many years thereafter” (Emanuel).

Specifications (Wikipedia LGP-30 entry, masswerk.at, ed-thelen.org)

Year: Introduced 1956 by Librascope, sold by Royal Precision (a Royal McBee subsidiary).
Memory: Magnetic drum, 4096 words. Each word 31 bits + 1 unused bit (so the popular “32-bit word” claim is technically true but only 31 bits were data). 64 tracks of 64 sectors each.
Drum speed: 3700 rpm; one revolution = 17 ms. Word access time on the order of 0.26 ms; inter-instruction access about 2.34 ms (every instruction had to wait for the next address to come round under the read head).
Arithmetic: Bit-serial, fixed-point fractional. About 60 multiplications per second (Gleick: “the Royal McBee could carry out sixty multiplications each second”). This is the authoritative figure; the looser “about 1 multiplication per second” from popular sources is wrong by roughly two orders of magnitude.
Construction: ~113 vacuum tubes plus ~1450 diodes. Weight about 800 lb (~360 kg). Footprint of a refrigerator/desk.
Programming: Paper tape input. Hexadecimal, plus the LGP-30’s idiosyncratic 16-character alphabet (0123456789fgjkqw).
Cost: ~$47,000 in 1956 dollars.

Gleick’s description: “made a surprising and irritating noise” – it was loud enough that the Quanta Magazine piece reports it had its own office. The LGP-30 was the size of a desk and “sounded like a passing propeller plane” (Quanta).

Margaret Hamilton and Ellen Fetter

Two women did most of the programming. Both have only recently been credited:

Margaret Hamilton (yes, the same Hamilton who later led Apollo flight-software at MIT Draper Lab) arrived at MIT in summer 1959, fresh math degree from Earlham, no programming experience. She wrote and debugged the LGP-30 code, editing binary instructions on paper tape with a pencil when necessary. She trained her replacement in summer 1961.
Ellen Fetter (Mount Holyoke math, 1961) took over and was the one running the program at the moment of the truncated-printout incident; she also produced the hand-plotted trajectories that became the famous strange-attractor figures.

Quanta’s Gabai-Sokoler-Yoder piece (2019) records Lorenz’s own remark that “every one of them would say that if this were going on today … they’d be a co-author!”

3. The 1963 paper: Deterministic Nonperiodic Flow

Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130-141.

(Lorenz originally titled it “Deterministic Turbulence.” The JAS editor made him change it – Physics Today’s Chaos at Fifty (2013) cites this directly.)

From the 12-variable model to the 3-variable model

Two distinct models are conflated in popular accounts.

The 12-variable model (1959-1961): Lorenz’s first toy weather. Twelve ODEs approximating the equations of motion of a rotating stratified fluid. Solutions were nonperiodic. This is the model that ran on the LGP-30 every Monday for the office betting pool that Gleick describes (“the other meteorologists would gather around with the graduate students, making bets on what Lorenz’s weather would do next”). It is also the model in which the truncated- printout incident occurred in winter 1961.

The 3-variable model (1962): After the discovery, Lorenz wanted the simplest possible system that exhibited the same behaviour. Around this time he visited Barry Saltzman (then at the Travelers Research Center in Hartford) and saw Saltzman’s 1962 paper “Finite amplitude free convection as an initial value problem – I” (J. Atmos. Sci. 19, 329-342). Saltzman had truncated a Rayleigh-Benard convection problem into seven coupled ODEs in the Fourier coefficients of the streamfunction and temperature perturbation. In one of his runs Saltzman saw that four of the seven variables decayed to zero while the remaining three behaved aperiodically.

Emanuel: “Ed noticed that in this particular solution, four of the seven variables settled down to zero and stayed that way. Thus he realized that there are chaotic solutions to a three-variable system; this became the celebrated Lorenz (1963,1) model.”

The Lorenz equations

$\dot x = \sigma(y - x)$ $\dot y = rx - y - xz$ $\dot z = xy - bz$

With the canonical parameters $\sigma = 10$ (Prandtl number), $r = 28$ (normalised Rayleigh number; the critical value for the onset of chaos in this system is $r_c \approx 24.74$), and $b = 8/3$ (geometric factor for the convection roll’s aspect ratio). These parameter values appear in the 1963 paper and are universal across the chaos literature.

Physical interpretation: $x$ is the convective overturning rate, $y$ the horizontal temperature contrast, $z$ the deviation of the vertical temperature profile from linearity. Lorenz integrated with a double-approximation Runge-Kutta-like scheme at $\Delta t = 0.01$ non-dimensional units.

The truncated-printout incident: dating and the exact numbers

Date: “One day in the winter of 1961” (Gleick); Emanuel writes “At one point, in 1961.” The often-quoted “January 1961” date appears in the APS This Month in Physics History column (Jan 2003); other sources keep it loose to “winter 1961.” This was on the 12- variable model, not the 3-variable model – this is worth getting right because the 3-variable system did not yet exist in 1961.

The exact numbers (Gleick’s authoritative version, derived from interviews with Lorenz):

In the computer’s memory, six decimal places were stored: .506127. On the printout, to save space, just three appeared: .506.

So the famous pair is 0.506 (printed/typed) vs 0.506127 (stored internally). A difference of “one part in a thousand.” Lorenz had walked away to get a coffee while the rerun was underway, came back an hour later, and found two solutions that had been identical for a few time-steps had diverged so completely that “within just a few months, all resemblance had disappeared.”

Emanuel’s version is the same in substance: “the new solution was the same as the original for the first few time steps, but then gradually diverged until ultimately the two solutions differed by as much as any two randomly chosen states of the system.”

Lorenz’s own reaction, quoted by Emanuel: “At this point, I became rather excited.” This is the closest thing on record to a Lorenz Eureka moment. Gleick: “Lorenz felt a jolt: something was philosophically out of joint.”

Sensitive dependence on initial conditions

The phrase “sensitive dependence on initial conditions” became the technical name. Gleick attributes the formulation as a general principle explicitly to Lorenz’s 1963 paper; the underlying intuition is older (Poincare 1889, Hadamard 1898; see below).

The butterfly attractor

The hand-plotted phase-space figure of the (x, z) projection of the trajectory – two “wings” of looping trajectories that never close on themselves – was prepared by Ellen Fetter. The resemblance to an owl’s face or a butterfly silhouette was noticed later. The name “strange attractor” came from Ruelle and Takens (1971), not from Lorenz.

Lorenz’s own geometric insight in 1963 was that any finite volume in phase space contracts to zero (because the system is dissipative; $\nabla \cdot \mathbf F = -(\sigma + 1 + b) = -13.667$), and yet trajectories diverge exponentially. He resolved this paradox in the 1963 paper by noting that the attractor must be a set of zero volume but non-trivial dimension – what we now call a fractal. From Emanuel quoting Lorenz directly:

It would seem, then, that the two surfaces merely appear to merge, and remain distinct surfaces. Following these surfaces along a path parallel to a trajectory, we see that each surface is really a pair of surfaces, so that, where they appear to merge, there are really four surfaces. Continuing this process for another circuit, we see that there are really eight surfaces, etc., and we finally conclude that there is an infinite complex of surfaces, each extremely close to one or the other of two merging surfaces.

This is the first concrete description of a fractal attractor in the scientific literature. Mandelbrot’s fractal terminology did not appear until 1975, Ruelle’s “strange attractor” in 1971.

Initial reception (1963-1975)

Citations in the meteorological literature were sparse: Chaos at Fifty (Physics Today, 2013) reports fewer than 20 citations in the first 12 years. The paper sat largely unread by meteorologists until the mathematicians found it.

The mathematical pipeline:

Stephen Smale (Berkeley) and his school worked on hyperbolic dynamical systems and the horseshoe map through the 1960s, building up the geometric theory of differentiable dynamics independently of Lorenz.
David Ruelle and Floris Takens, 1971: “On the nature of turbulence” (Commun. Math. Phys. 20, 167-192) coined the term strange attractor for chaotic invariant sets of dissipative systems. Crucially, Ruelle and Takens did not cite Lorenz in the 1971 paper; they were proposing turbulence emerged via successive bifurcations on Axiom-A systems. Ruelle himself later admitted, per the chaos-history literature, “Lorenz’s work was unfortunately overlooked.” James Yorke is the one usually credited with bringing Lorenz’s equations to Smale’s circle around 1972.
Tien-Yien Li and James Yorke, 1975: “Period three implies chaos” (Amer. Math. Monthly 82, 985-992). This paper coined the word chaos in its modern technical sense.
Otto Rossler, 1976: simpler attractor with only one quadratic nonlinearity.
James Gleick, Chaos: Making a New Science (Viking, 1987): the book that took the story to the general public. Chapter 1 (“The Butterfly Effect”) is essentially built around Lorenz; Gleick’s interviews are now the primary source for many of the quoted recollections.

By the late 1980s the citation count had exploded and chaos was a recognised research field.

4. The 1969 Tellus paper: the real predictability result

Lorenz, E. N., 1969: The predictability of a flow which possesses many scales of motion. Tellus, 21, 289-307.

This is the paper that matters most for NWP, and it is consistently underweighted in popular accounts of Lorenz. The 1963 system has three degrees of freedom; the atmosphere has something like $10^{20}$. The interesting question for forecasters is: how does error behave in a high-dimensional flow with a continuous spectrum of scales?

The setup

Lorenz uses the 2D barotropic vorticity equation on a doubly-periodic domain. He decomposes the spectrum into discrete “scale bands” (each a factor-of-two range in wavenumber). He then derives a closed system of evolution equations for the ensemble-mean error energy in each band. The closure depends on the assumed background energy spectrum.

The key result: spectrum slope controls predictability

Two cases are studied:

$k^{-5/3}$ spectrum (the Kolmogorov inertial-range spectrum). Lorenz shows that with this spectrum, the predictability time is finite even in the limit of vanishing initial error. Reducing the initial error by an arbitrary factor does not buy any arbitrary amount of extra forecast skill; the time-to-saturation only grows logarithmically with the inverse error.
$k^{-3}$ spectrum (which more closely matches the atmospheric synoptic-scale spectrum observed in radiosonde data). In this case the predictability limit is asymptotically infinite as initial error tends to zero – but only logarithmically slowly.

Both cases produce an upscale error cascade: errors that are initially localised at small scales saturate quickly in those small scales (doubling in hours) and then bleed up into the next-larger band, saturating that band after a longer time, and so on. The total time for an error to propagate from the smallest resolved scale up to synoptic scales is the predictability horizon for synoptic-scale forecasting.

The “two-week” number

With Lorenz’s chosen parameters and the $k^{-5/3}$ closure, the cascade-saturation time for synoptic-scale errors comes out to roughly two weeks. This is the origin of the “two-week limit” folklore in operational meteorology. It is not a hard theorem; it depends on the assumed spectrum slope and on the doubling time for small-scale errors. Recent papers (Zhang et al. 2019; Shen, Pielke et al. MDPI Atmosphere 2024 “On the Two-Week Predictability Limit Hypothesis”) have argued the original estimate combined Lorenz’s 1969 cascade model with a doubling time of ~5 days from the Mintz-Arakawa GCM circulating at UCLA at the time. The Smagorinsky model at GFDL gave a doubling time closer to 10 days for the first 30 days, dropping to 6-7 days for the second 30 days as the model output became more aperiodic (this is documented in the same revisit paper).

Lorenz himself gives the predictability times per scale in 1969 as approximately:

Cumulus-scale (~1 km): one hour
Synoptic-scale (~1000 km): a few days
Planetary-scale: a few weeks

Why 1969 matters more than 1963 for NWP

The 1963 paper shows that some deterministic systems are chaotic. The 1969 paper shows that the atmosphere is chaotic in a way that imposes an intrinsic upper bound on deterministic forecast skill that you cannot beat by buying a bigger computer or a denser observing network – because the error-source population at the smallest scales is inexhaustible and the upscale cascade is irreducible. This is the theoretical foundation on which all of ensemble forecasting was eventually built.

The 1982 follow-up

Lorenz, E. N., 1982: Atmospheric predictability experiments with a large numerical model. Tellus, 34, 505-513.

By 1982 Lorenz had access to operational ECMWF forecasts. He compared, over a 100-day period, the operational forecasts at different lead times with each other and with the verifying analyses. The methodology: take the day-$D$ analysis, compare it to the (D-1)-day forecast valid for day $D$, the (D-2)-day forecast, etc. This gives both an upper bound on predictability (perfect model, small initial error) and a lower bound (operational skill of the day).

Key finding (from Emanuel’s summary): “errors in the pressure field roughly 5 km above the surface doubled in about 2.5 days.” Lorenz warned, presciently, that as resolution improved, the doubling time would shrink, because higher-resolution models would resolve faster-growing small-scale errors. This implied an asymptotic plateau in forecast skill – the very thing Bauer, Thorpe and Brunet would later (2015, “The quiet revolution of NWP”, Nature) show had emerged in the 2010s as the curve of forecast skill flattened around day 9-10.

The 1982 paper also estimated: “predictions at least ten days ahead as skilful as predictions made seven days ahead appear to be possible” – this was the theoretical headroom that ECMWF eventually realised in the 2000s-2010s.

5. The 1972 AAAS talk: the butterfly metaphor

Where, when, was it actually delivered?

Date: 29 December 1972. (Confirmed by the Gymportalen reprint, which puts “Presented before the American Association for the Advancement of Science, December 29, 1972” at the head of the talk text.)
Venue: 139th meeting of the AAAS, Washington DC. Session was Section on Environmental Sciences (per Pielke’s substack); the session convener was meteorologist Philip Merilees (at NCAR at the time).
Was it actually delivered, or only an abstract? It was delivered. The MIT Technology Review piece (2011, “When the Butterfly Effect Took Flight”) and Pielke’s substack both treat it as a delivered talk. The full text – about 1100 words – circulated in photocopies for decades and was reprinted as Appendix 1 of Lorenz’s 1993 The Essence of Chaos.

How the title got that title

The Wikipedia Butterfly effect entry quotes Lorenz himself: “when he failed to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merilees concocted ‘Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?’ as a title.” Merilees needed a title to print in the program; he could not reach Lorenz; he made one up.

So the title is Merilees, not Lorenz. The concept is Lorenz. The earlier-and-more-modest metaphor in Lorenz’s 1963 paper was the seagull:

One meteorologist remarked that if the theory were correct, one flap of a sea gull’s wings would be enough to alter the course of the weather forever. The controversy has not yet been settled, but the most recent evidence seems to favor the gulls.

(Lorenz 1963, p. 141, as quoted in Emanuel footnote 6.)

There is an even older lineage. Emanuel’s footnote 6 traces it further back to William S. Franklin’s 1898 grasshopper:

Long range detailed weather prediction is therefore impossible, and the only detailed prediction which is possible is the inference of the ultimate trend and character of a storm from observations of its early stages; and the accuracy of this prediction is subject to the condition that the flight of a grasshopper in Montana may turn a storm aside from Philadelphia to New York!

(Franklin, Phys. Rev. 6, 170-175.) So the “small-creature-changes-the-weather” trope predates Lorenz by 65 years.

Emanuel also credits Joseph Smagorinsky with first using the butterfly metaphor specifically (Smagorinsky 1969, “Problems and promises of deterministic extended range forecasting,” Bull. Amer. Meteorol. Soc. 50, 286-311) – so the butterfly may have travelled from Smagorinsky to Merilees to the talk title before Lorenz delivered it. This is a tangled provenance and worth noting in the post.

The talk’s actual content

The full text is brief. Two propositions open it:

If a single flap of a butterfly’s wing can be instrumental in generating a tornado, so also can all the previous and subsequent flaps of its wings, as can the flaps of the wings of millions of other butterflies, not to mention the activities of innumerable more powerful creatures, including our own species.

If the flap of a butterfly’s wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado.

The technical reformulation: “is the behavior of the atmosphere unstable with respect to perturbations of small amplitude?”

The talk’s four numbered findings are essentially a summary of Lorenz 1969:

Coarse-structure errors double in about three days; halving observation error buys roughly three more days of useful forecast.
Fine-structure errors (cloud-position scale) double in hours or less.
Fine-structure errors cascade upscale into coarse structure, capping useful prediction regardless of fine-scale observation density. “The hopes for predicting two weeks or more in advance are thus greatly diminished.”
Certain temporally-averaged quantities (weekly average temperature, weekly total rainfall) may still be predictable beyond the deterministic limit – foreshadowing modern S2S (sub-seasonal to seasonal) prediction.

Closing line, with a nod to the Global Atmospheric Research Programme (GARP):

It is to the ultimate purpose of making not exact forecasts but the best forecasts which the atmosphere is willing to have us make that the Global Atmospheric Research Program is dedicated.

This is the only place in Lorenz’s published work where the operational implication is spelled out for a general audience: the project of weather forecasting is not the project of perfect prediction, but of “the best forecasts the atmosphere is willing to have us make.” A useful phrase to quote.

6. The other key Lorenz papers (less famous, equally important)

1955: Available potential energy

Lorenz, E. N., 1955: Available potential energy and the maintenance of the general circulation. Tellus, 7, 157-167.

Defined APE as the difference between the total potential energy of an atmospheric state and the minimum total potential energy attainable under any adiabatic redistribution of mass. Margules (1903) had introduced the idea for an isolated mass; Lorenz generalised it to a planetary fluid. APE vanishes when the density stratification is horizontal and stable everywhere; otherwise it is positive and approximately equal to a weighted vertical average of the horizontal variance of potential temperature.

Why this matters: APE is the energy reservoir that baroclinic instability taps to spin up extratropical cyclones. The Lorenz cycle (APE -> eddy APE -> eddy kinetic energy -> mean-flow KE) became the standard diagnostic framework for general-circulation studies and for evaluating GCMs. Smagorinsky, Manabe, and the whole GFDL group adopted it.

This is the paper that made Lorenz’s reputation in the 1950s. By 1963 he was a tenured full professor primarily on the strength of APE, not chaos.

1967: The Nature and Theory of the General Circulation of the Atmosphere

WMO publication No. 218. A 161-page monograph, written as a commissioned overview. The book became the standard graduate-school text on the general circulation through the 1970s. Lorenz lays out the energy cycle, the angular momentum budget, the role of the Hadley and Ferrel cells, eddy transports, and the maintenance of the zonal mean flow. The 1967 monograph and the APE paper together earned Lorenz the Carl-Gustaf Rossby Research Medal (AMS) in 1969.

1993: The Essence of Chaos

University of Washington Press. A general-audience book based on Lorenz’s 1990 Jessie and John Danz Lectures at U Washington. Three appendices reprint:

Appendix 1: the 1972 AAAS talk text (this is the principal modern archival source for that talk).
Appendix 2: an updated, more accessible derivation of the 3-variable system from the Saltzman convection model.
Appendix 3: technical details of the slow manifold.

In Chapter 4, “Our Chaotic Weather,” Lorenz tells the discovery story in his own words.

1996: “The Bulletin Interviews”

WMO Bulletin 45, 111-120. Lorenz interviewed at length about his career. Used heavily by Emanuel as a primary source.

Other key papers worth knowing about

1960: “Maximum simplification of the dynamic equations.” Tellus 12, 243-254. Spectral truncation theory; foundation for the 1962 collaboration with Saltzman.
1969 (b): “Atmospheric predictability as revealed by naturally occurring analogues.” J. Atmos. Sci. 26, 636-646. The “analog method” – searching for past atmospheric states resembling the current one and using them as a forecast. Lorenz showed analogs are useless because the atmosphere is too high-dimensional to ever sample its own state space, but the technique reappeared decades later in machine-learning weather models.
1986: “On the existence of a slow manifold.” J. Atmos. Sci. 43, 1547-1557. Demonstrates that no exact slow manifold exists for stratified rotating flow; relevant to initialisation and to the GCM data-assimilation problem.
1996: The “Lorenz-96” model: a one-dimensional chain of $K$ ODEs with nearest-neighbour quadratic coupling and constant forcing. Designed as a generic chaos testbed for data-assimilation experiments. Universally used in ensemble-DA research; it is to predictability research what the Ising model is to statistical mechanics.

7. Intellectual ancestry (and why meteorologists didn’t know it)

Poincare 1889

Henri Poincare’s prize essay on the three-body problem (Acta Mathematica, 1890; awarded King Oscar II’s prize 1889) showed that bounded gravitational systems of three bodies generically exhibit infinitely complicated orbits. The published version contained the famous passage about how “it may happen that small differences in the initial conditions produce very great ones in the final phenomena … prediction becomes impossible” (this quote is most often cited from Science et Methode, 1908). Poincare’s homoclinic-tangle diagrams contain everything we now call “chaos.” But this was Hamiltonian chaos (conservative, no attractor), in celestial mechanics, published in French, written for mathematicians. The body of work was foundational for Birkhoff’s ergodic theory but had essentially no readership in meteorology.

Hadamard 1898

Jacques Hadamard’s “Les surfaces a courbures opposees et leurs lignes geodesiques,” J. Math. Pures Appl. (1898), proved that geodesic flow on a surface of negative curvature is ergodic and exponentially sensitive to initial conditions. This is the first rigorous proof of what we now call hyperbolic chaos. Again: pure mathematics, French, totally disconnected from atmospheric science.

Birkhoff 1931

George David Birkhoff’s ergodic theorem (Proc. Nat. Acad. Sci., 1931) proved that for ergodic systems, time averages equal space averages. Foundational for statistical mechanics. Birkhoff’s son Garrett Birkhoff taught at Harvard alongside MIT meteorology for decades. There is no record of any meteorologist using Birkhoff’s results before the 1960s.

Why none of this was on meteorologists’ radar

Several reasons:

Different language. Poincare-Hadamard-Birkhoff lived in measure theory and dynamical systems theory; meteorologists in 1960 thought in PDEs and finite-difference grids. The mathematics-meteorology interface was thin.
Different problem. Three-body celestial mechanics is Hamiltonian (volume-preserving). The atmosphere is dissipative (volume-contracting in phase space). Strange attractors are a phenomenon of dissipative systems and had no analogue in Hamiltonian dynamics. Even Poincare’s homoclinic tangle is not the same object as Lorenz’s strange attractor.
The optimism of NWP. From Richardson’s 1922 Weather Prediction by Numerical Process through von Neumann’s ENIAC experiments (1950) and Charney’s first operational forecasts (1955), the prevailing view was that better physics and faster computers would buy unlimited forecast skill. Von Neumann actively believed weather control was feasible (Gleick: he gave “breathtaking talks about his plans” for cloud-seeding and weather modification). Nothing in this optimistic project pointed researchers toward ergodic theory.
Lorenz himself rediscovered chaos. Emanuel and the Chaos at Fifty essay are both clear that Lorenz was not reading Poincare in 1961. He stumbled onto sensitive dependence empirically and then derived its mathematical character on his own.

8. Reception within the NWP community

Charney

Jule Charney joined MIT meteorology in 1957 (Emanuel suggests the move was negotiated when Houghton hired Lorenz). They were colleagues for thirty years. Charney was famously sympathetic to Lorenz’s predictability arguments – he chaired the 1966 WMO conference in Boulder, Colorado, that first formalised the “perfect-model predictability experiment” methodology, which is fundamentally a Lorenzian construction. Tim Palmer, in his 2009 biographical memoir of Lorenz for the Royal Society, writes that Charney’s and Lorenz’s research goals were largely opposing – Charney believed in extending deterministic skill, Lorenz in establishing its limits – and yet “their work is now seamlessly intertwined for the benefit of science and society.”

It is unclear whether Charney engaged in print with the 1963 paper specifically; his published response to Lorenzian predictability concepts came later, through the 1966 GARP predictability conference and his subsequent reports.

Smagorinsky

Joseph Smagorinsky at GFDL was a different matter. Smagorinsky used the butterfly metaphor in print in 1969 (“Problems and promises of deterministic extended range forecasting,” BAMS 50, 286-311) – before Lorenz’s AAAS talk. Smagorinsky’s own GCM (the GFDL spectral model) was used to test predictability empirically; the Smagorinsky-model results gave doubling times of 10 days falling to 6-7 days. So GFDL was running its own Lorenzian predictability experiments in parallel with Lorenz’s analytic work, with broadly compatible results. The “two-week limit” became conventional wisdom at GFDL, ECMWF, and NMC by the late 1970s.

The ECMWF / Palmer line

ECMWF was founded in 1975, became operational in 1979, with a remit to make medium-range (3-10 day) forecasts – right at the predictability boundary Lorenz had identified. Tim Palmer joined ECMWF in 1986 with the explicit project of building an operational ensemble system, motivated by Lorenz. Palmer’s 1992 paper (Palmer, Molteni, and others, ECMWF Tech. Memo 1992) and the operational launch of the Ensemble Prediction System (EPS) in November 1992 are the direct institutional descendants of Lorenz 1969. The EPS uses singular-vector perturbations to sample the initial-condition uncertainty along the fastest-growing error directions, which is exactly the high-dimensional generalisation of Lorenz’s small-error growth analysis. NCEP launched its parallel ensemble system around the same time (Toth and Kalnay’s breeding method).

By the late 1990s, Lorenz’s 1969 paper had become the foundational citation for every operational ensemble system in the world. Palmer’s writings (notably his ECMWF Newsletter columns and his 2017 book with Hardin, The Primacy of Doubt) make this lineage explicit.

The folk wisdom

“No useful forecast skill beyond two weeks” entered the meteorological folk-canon sometime in the 1970s and has been there ever since. Modern operational practice (2020s ECMWF deterministic skill curves) shows useful skill (anomaly correlation of 500-hPa height above 0.6) to about day 10, with skilful ensemble means to about day 14-15 in winter – which is exactly the Lorenz horizon and not beyond it. Recent papers (Zhang, Sun, Magnusson et al. 2019, J. Atmos. Sci.) have argued that with sufficiently good initial conditions the limit may be closer to 2-3 weeks rather than 2 weeks, but nobody has shown anything that breaks the qualitative Lorenz result.

The AI weather-model revolution of 2022-2024 (GraphCast, Pangu-Weather, FourCastNet, FuXi) does not violate Lorenz: those models are emulating a deterministic forward operator, and their useful skill horizon is the same 10-14 day window. What they do better is exploit observational analogs more efficiently and reduce systematic model error; the predictability barrier remains.

9. Disputed/uncertain points to flag in the post

Exact date of the truncated-printout discovery. Most sources say “winter 1961” (Gleick). APS This Month in Physics History puts it in January 1961 specifically; this is not independently confirmed elsewhere and may be APS-editor inference. Stay with “winter 1961” unless a primary source can be located.
The 0.506 vs 0.506127 numbers. These are Gleick’s, derived from Lorenz interviews. They are widely quoted but I have not located them in Lorenz’s own written account in The Essence of Chaos. The qualitative description (3 digits printed vs 6 stored) appears in Lorenz’s autobiographical note “A Scientist by Choice” (Kyoto Prize 1991) and in Emanuel. The specific digit string 0.506127 should be attributed to Gleick.
LGP-30 multiplication rate. Gleick’s “sixty multiplications per second” is the widely-cited figure and is consistent with the documented drum-access time and bit-serial multiplier. The prompt’s suggestion of “about 1 multiplication per second” is a factor of 60 too slow.
Was the 1972 AAAS talk delivered or merely abstracted? Tech Review (2011) and Pielke (substack) both state it was delivered. The talk text is dated 29 December 1972 with “Presented before the AAAS” in its header, and was later reprinted as Appendix 1 of The Essence of Chaos (1993). It was delivered. The claim that it was “never delivered” appears occasionally on the internet but is not supported by any of the authoritative sources I located.
Who coined “butterfly effect.” The title of the 1972 talk was Philip Merilees, not Lorenz. The butterfly (as opposed to seagull) metaphor may have originated with Smagorinsky in 1969. The concept of sensitive dependence is Lorenz 1963 (with ancestry back to Poincare). The colloquial phrase “butterfly effect” took off after Gleick 1987. So: Merilees named it, Smagorinsky may have bug-swapped it from the seagull, Lorenz discovered the underlying phenomenon, and Gleick made it pop culture.
Saltzman’s prior knowledge. Saltzman (1962) did not point out the nonperiodic solutions in his published paper; Lorenz saw them on Saltzman’s office floor when he visited. Whether Saltzman would have eventually published the chaos result is an open counterfactual. Lorenz is unfailingly generous in citing Saltzman; Saltzman is gracious in retrospective accounts.

10. Useful quotes for a blog post

From Lorenz himself, via Emanuel:

At this point, I became rather excited.

(On seeing the divergent trajectories, winter 1961.)

From Lorenz’s 1972 AAAS talk: