The Cycle that Changed History

Much of the alarm about man’s influence on the climate is due to the observed rapid rise in temperatures over the two decade period starting in the late 1970s. The rise was coincident with a exponential rise in the concentration of CO2 in the atmosphere, which, while still a piddling .04% of the atmospheric volume, was assumed to have an impact greater than its mass through feedback. The clarion call was sounded and 100 of billions of dollars in direct and indirect costs have been spent since trying to ameliorate the perceived environmental threat.

HAdcrut3 Temperature anomaly, box-care averaged (P=12) and decimated (D=12)

Hadcrut3 Temperature anomaly, boxcar averaged (P=12) and decimated (D=12)

Parts 1 and 2 of this series and the original post on WUWT examined the temperature record through two different means of spectral decomposition. Both showed the strong likelihood of a significant periodic signal in the climate record with a repeating period of about 60 years. The phase stability of this cycle and the presence of smaller, harmonically related signals, points to a celestial origin – natural, emergent cycles simply do not exhibit this type of stable behavior. But for this analysis, we are going to assume only that it is a natural phenomenon, unrelated to any human activity.

Singular spectrum analysis (SSA) provides the means to decompose a time series into components which when summed together, reconstruct the original signal with precision. Some of these components correspond to (at least locally) periodic signals present in the data, while some are just noise. There are statistical means to tell one from the other. SSA then allows us to reconstruct the record in various ways, depending on the time frame of interest, and whether we want to filter off the noisy signals.

The 60 year signal is the second strongest mode (after the trend, which may or may not actually be another periodic low-frequency signal harmonically related to the 60 year cycle). As mentioned above, we are going proceed under the assumption that the second mode is a natural (and perhaps temporary) phenomenon, and ask the question, what would the temperature record have looked like had this natural cycle not been present?

SSA allows us to answer this question, because by definition, all of the trend information is contained in the first mode. The other modes represent trendless fluctuations about the main trend. We can adjust the window length (L) to maximize the amplitude difference between the trend and the second mode, and reconstruct the signal, leaving out the contribution of the 60-year (second) mode. The result in shown below (purple line) along with the original timeseries (blue) and a linear fit to the reconstructed record (red dashed).

Hadcrut3 SSA recontruction (L=35,k=1,3,4) without the 60-year mode

The slope of the best-fit line is a benign .5 degreeC per century, remarkably constant over the entire 113-year record. Had the 60-year signal not been present, no discernible acceleration in warming would have been observed, no conclusions as to cause would have been jumped to and the ensuing damage to the world’s economy would have been avoided.

What about all the other modes we’ve filtered out (by using a low k-value). The higher modes correspond to noise at various bandwidths. We can add them back as shown below.

Hadcrut3 SSA  recontruction (L=35,k=1,3-35) without the 60-year mode

Hadcrut3 SSA recontruction (L=35,k=1,3-35) without the 60-year mode

With the high-frequency noise added back in, the slope is virtually unchanged (insignificantly smaller at .49 degsC / century).

This truly is the cycle that changed history. Only time will tell if Climatology will admit they fell victim to the fallacy we all learned in our first day of college – never confuse correlation with causation, and end their global warming hysteria. I’m not holding my breath.

Part IV – Global warming a la mode


SSA of the Hardcrut3 Global Temperature Anomaly , Part 2

One of the nifty things about Singular Spectrum Analysis is it allows you to decompose your data using basis functions (eigenvectors) which are adapted to the data record. Each eigen vecter/value pair is a direction in Hilbert space which minimizes the variance in that direction. You can look at the contribution from each of these modes individually. The top pane below shows the contribution of the 1st mode (called the trend) where the SSA window length (L=42) was adjusted for maximum amplitude difference between the first and second modes. Note the trend is not linear and in fact looks fairly sinusoidal. It has an apparent period (using the term loosely since it might not be periodic) of about 180 years with an inflection point somewhere around 1965.

Contribution from first Eigenmode

Contribution from first Eigenmode

The second pane shows the residual between the first mode and the data. I’ve eyeballed two linear trends on the top pane fit to the apparent residual trends over these intervals. Note the residual trend since 1970 is steeper than the earlier trend and is going against the mode 1 trend whose slope is decreasing during this period. Maybe the warmists are right to ring the alarm bells.

But watch what happens when we add in the second mode (k=1,2) This mode is very sinusoidal and has the 60 year period that others have found in many climate records.

Contribution from modes 1 and 2

Contribution from modes 1 and 2

Both trends disappear in the residual and the residual itself shows zero overall trend.

One can argue about the physical source of these modes. Both eigenpairs are in rough quadrature which indicates significance and there is a clear step-wise separation from the noise floor which also is indicative of a noise free measurement(note the mode amplitudes in the bottom panes are in dB). It is also more than passing strange that the two modes are harmonically related as noted in my last post. But in reality, their source, whether internal to the climate system or an external forcing is irrelevant. They are what’s left of the climate signature once we’ve removed the extraneous noise.

These two modes account for about .7 degrees of warming and all of the trend of the past century. But suppose only the second mode is significant (and as I’ve mentioned, there is mounting peer-reviewed evidence that it is). The lack of stationarity in the first mode would only impact our ability to forecast, not the measured trend for the past century. As can be seen from the residual which contains no sign of an AGW signature, any such signature must be contained within the extracted mode(s), because their sum plus the residual recreates the data exactly. But the primary trend has been losing steam since 1965 or so while CO2 has risen exponentially during this interval. The mode 2 trend is nearly sinusoidal over the entire record. There is no anthropomorphic explanation for this characteristic. Therefore those who argue that some natural variation (a fancy term for “we don’t know”) has masked the AGW effect will have find it in the residual left from mode 1+2, because that’s the only garden left for them to dig.

On to part 3…

Singular Spectrum Analysis of Hadcrut3

One of the comments on my post on WattsUp suggested I attempt to do an SSA on the Hadcrut3 data. Here are the results:
(Note: higher resolution plots may be viewed by clicking on the plots below)

The best signal-to noise ratio was obtained with a window-size (L) of 20 and an eigenspan of 4 (2 eigenpairs). Low frequency oscillatory behavior is evident in the spectral plot which show the 2 lowest eigenvectors significantly above the noise floor.

Looking at the FFT of the model, we see again similar harmonically related spectral peaks to those found via harmonic decomposition.


Proceeding as before, we find the frequency of the psd spectral peaks
w1 = ArgMax[psdMod, w];
w2 = ArgMax[{psdMod, w > 1.5 w1}, w];
2*Pi/{w1, w2}
{185.83453775994096, 60.87208526557042}

which are fairly close to the values found via HD. Note the ratio = 3.05. Assuming we have more accuracy on the higher frequency mode, and assuming a harmonic ratio of three we form the model:

AY1 sin(phiY1 + 0.0344065 t) + AY2 sin(phiY2 + 0.103219 t)

where the radian frequencies {0.103219, 0.0344065} are w2 and w2/3 from above, and fit the model to the data to solve for the phase and amplitudes.

fitParmsSSA =
FindFit[yearly, modelSSA, varsSSA, t, Method -> NMinimize]
fitSSA = Table[modelSSA /. %, {t, 1, 113}];
residualSSA = yearly - fitSSA;
DateListPlot[TemporalData[residualSSA, Automatic]["Path"],
Joined -> True]
ListPlot[{yearly, fitSSA}, Joined -> True]

{AY1 -> -0.261994, phiY1 -> 1.38923, AY2 -> -0.160245,
phiY2 -> 0.464517}

The figures below shows the hybrid model (that is an HD model derived from the SSA eigenpairs as described above) versus the monthly Hadcrut3 data, hindcasted 25 and 50 years (to 1875 and 1850), and in the second figure forecasted 50 years to 2063. The hindcast matches the data closely for 23 years or so. One interesting feature that the event of 1878 is co-incident with the data matching the model, and the super-el-nino event of 1997 is co-incident with divergence. One highly speculative explanation (besides mere coincidence, or events like these causing issues in the SSA algorithm)) is the possibility that climate disruptions triggered a new phase state in the climate dynamics.


As with HD, I find it surprising that a fit can be achieved with so few eigenpairs (or in the case of HD, harmonic pairs). The fact that the SSA modes are also harmonically related (there is nothing in the SSA method that requires them to be so), adds credence to the notion that harmonically related periodicities are part of the current climate dynamics.

There are forecasting methods which use only the SSA results. Once I figure them out and code the algorithms I’ll post an update.

Part 2 is available here.

Synthesis – Part 1

Perusing the reader comments section that follows most online political articles these days one cannot help forming a bleak opinion of this nation’s future. The vitriolic volleys bombard from both sides of a chasm wider and deeper than perhaps at any time since the Civil War. Granted, self-selection is at work here- the extremes are probably over represented in such forums which tends to exaggerate the divide, but there is little doubt that this country is deeply polarized and our civil discourse is near an all time low. One wonders how long our Republic can survive when the motivating force animating our political discourse seems to be blind hatred. In this two part essay I intend to explore the outlines of a synthetic theory which concentrates on what I believe to be the shared goals of both sides.

Boiled to it essence, the conflict is over the role of Government, which is not coincidentally the subject matter of these essays. The organizing principle of those advocating a limited role for government is liberty, broadly defined as the absence of government coercion in the lives of its citizens. The other side is organized around the principle of social justice which requires government coercion to execute the policies necessary to achieve what is seen as an equitable redistribution of resources. Obviously there can be very little intersection in these views, which accounts for the polarization we see today. And both sides see themselves as fighting for the soul of our democracy which accounts for the vitriol of the debate.

It should be clear by now that  I agree with Madisonian view that government can not be both a guarantor of our rights and an instrument of charity. The two are mutually exclusive because Collectivism, in all its forms, equates one citizen’s need to a claim on the fruits of the labor of another, an inherently immoral precept. And since men by nature feel entitled to their property, that claim must be enforced under threat of law by a Government powerful enough to make it stick. Coercive “charity” is thus antithetical to the government’s fundamental role as protector of the rights of all of its citizens and to the Founder’s view, enshrined in the Constitution, of a strictly limited federal role which emphatically eschewed any re-distributive function. How then did we arrive at the point we find ourselves today, where charity is now seen as the federal government’s primary role?

It was Woodrow Wilson who first forwarded the notion that the Constitution itself was preventing social progress. Except in academia, his ideas were largely ignored and/or rejected as unconstitutional by the Supreme Court until the Great Depression finally gave Roosevelt the political capital necessary to legitimize a charitable role for the Federal government. Our political history since the New Deal has been an attempt to balance these two conflicting ideals, individual liberty and social justice. In practice this has proven a fool’s errand. As our Civil War demonstrated decisively, we cannot hold as the basis of governance, two foundational principles so fundamentally at odds, one must eventually yield to the other. We’ve avoided war this time and not surprisingly, it has been the Social Democrats who have carried the day, it being much more politically expedient to mollify the mob at the expense of the taxpayers who have become the minority.

 A Democracy cannot exist as a permanent form of Government. It can only exist until the voters discover they can vote themselves largess out of public treasury.  From that moment on the  majority always votes for the candidate promising the most benefits from the public treasury with the result that Democracy always collapses over a loose fiscal policy, always to be followed by a Dictatorship.

While the attribution of the above is uncertain, its logic seems unassailable and its prediction of “loose fiscal policy” surely has come upon us. Our massive accumulated debt, the unfunded liability of the entitlements already in place, the devaluation of our currency (which will rob our eldest of any wealth they may have managed to accumulate) and the constant clamor for more government aid all point to the unsustainability of our current system.  Can the collapse it predicts be avoided? I think so, but only if we can forge a new consensus that will allow our leaders the political space to address the root issues. One that enshrines the common goals of a fair and just society which protects the liberty of all.  Part II will explore the outlines such a consensus might take.

Nino’s Razor

I am not a lawyer. I don’t even play one on television. Nevertheless, I am steadfast in my belief that one should not need a law degree to understand our individual rights and protections as guaranteed by the Constitution. Yet for the past few months here we sat, bait upon our breath, waiting for yet another edict from On High validating or rejecting yet another expansive power grab by the federal government.  How has it come to this? Two hundred and ten years since Marbury v. Madison and We the People still don’t know “what the Law is”???

Of course the law can never be complete. There will always be new cases with new circumstances, completing rights to be weighed and prioritized. But the Law, the Lex Suprema, the Constitution which was meant to be the bedrock foundation of all law, should long ago have been so established in its meaning and application that every citizen could predict with near certainty the outcome of any case resting upon the mere constitutionality of a statute. The Brits have their Magna Carta, a rambling, incohesive collection of banalities. We, on the other hand, have a Constitution, a binding contract between the States and the Union whereby the former surrendered specific, enumerated portions of their Sovereignty in exchange for the protections extended by the latter. It is written in plain English; and even if the meaning of some of the words have changed over the years, the Founders left us a wealth of exposition that we might understand the meaning they ascribed to the terms. After all, it was that meaning upon which they voted to ratify.

Which brings us to the subject at hand. In ARIZONA ET AL. v. UNITED STATES, the Supreme Court determined that certain provisions of an Arizona anti-illegal immigration law ran a foul of the Supremacy Clause of the Constitution. In Justice Scalia’s brilliant dissent we find this gem,

Are the sovereign States at the mercy of the Federal Executive’s refusal to enforce the Nation’s immigration laws? A good way of answering that question is to ask: Would the States conceivably have entered into the Union if the Constitution itself contained the Court’s holding?

which I have affectionately dubbed Nino’s Razor. Here then is a Rosseta Stone, by which the average citizen can judge the legitimacy not just of this particular ruling but all such rulings. In the case at hand, remembering that the primary contention of the anti-Federalists opposed to ratification was that the Constitution ceded too much power to the federal government, Scalia’s question becomes clearly rhetorical. Hamilton stood alone at the convention; his proposal for a more powerful federal government failed to attract even a single vote, yet somehow here we are, with a national government so expansive in size and scope that even Hamilton would surely blush at his shortsightedness.

We can apply this principle to this week’s other landmark ruling on the so called Affordable Care Act. If the ratifiers had thought that the General Welfare Clause granted Congress an unfettered right to tax and spend on anything  deemed to be “for the general welfare” does anyone seriously believe they would have voted for ratification? They had just fought and won a bloody war to reject that very notion. Nino’s Razor works for amendments as well. Fast forward to July of 1868. How would the vote for adoption of the 14th Amendment gone had it been known at the time that hidden within its clear language lay a snare that would later be used to establish a right to practice sodomy (Lawrence v. Texas) or same-sex marriage?

Regardless of where one stands on these issues, we should all stand firm for the notion that our Constitution cannot be changed by extra-constitutional means. If We the People need to change the Constitution, the Founders provided the means to do so. But among those means one will not find a provision whereby the Court can simply redefine the terms. The Supreme Court’s task is to say what the Law is, not what they think it ought to be.

Government and Society



Last time we responded to a recent article in Commentary by Peter Wehner  forwarding the notion that a just government is one which cares for people who can’t take care of themselves. This sounds reasonable but as we’ve seen, empowering government to redistribute wealth destroys the delicate balance of force required to render Government a safe repository of our civil rights.

How then to deal with the second part of his argument?

A society ought to be judged on whether the weak and disadvantaged are cared for or exploited. And a just society is incompatible with one where government doesn’t care for people who can’t care for themselves.

Hopefully all men of goodwill would agree with his premise as expressed in the first sentence. His conclusion however is a non sequitur and demonstrably false. One can easily imagine a society where the helpless are well cared for and the government isn’t involved at all. Wouldn’t that society deserved to be called just? Besides, the subject at hand is government  not society, and a government that it is empowered to take from the rich to give to the poor can in no way be called just.  Robin Hood’s heart was in the right place, but he was a still a thief.

To conflate Society with Government is to confuse master with slave. In our constitutional republic it is society which controls the government; the objects and limit of that control proscribed by the Constitution. Society may use the instrument of government to limit the liberty of its citizens only to the extent that such limitations do not impinge on the rights the majority has agreed all citizens possess. Entitlement programs funded from the public purse are violative of this foundational principle. As we showed in Part 1, expenditures for this purpose are not constitutionally authorized precisely because they are counter to the purpose for which our government was instituted in the first place. Society may not use government for this noble cause even if the majority wishes to do so anymore than society can use the government to curtail political speech the majority finds offensive. This is not abstract political philosophy. We’ve been running the counter-experiment for 75 years and the results are in.
Since 1937, when the three branches of the federal government colluded to break out of their constitutional straight jacket, using the General Welfare clause as a pretext to provide our representatives with the power to pander, we’ve seen the slow demise of our democratic processes.  Half the population now receives federal assistance of some sort and nearly half pay no federal income tax. We are nearing the tipping point Cicero warned would be the death of democracy, when the majority realizes they can vote themselves benefits from the public treasure with no incentive towards restraint. Massive, unsustainable debt has been the predictable result. A government which has placed a 200 trillion dollar burden on the generations yet to come (who had no say in the matter)  in no way deserves to be called just, nor the society which allowed this to occur. The irony is that those who advocate for an ever expanding safety net (as if life itself were some sort of high wire act) think they are on the side of the angels.

What role does Government have in caring for the indigent? Absolutely none. Edmund Burke put this question to rest long ago.

Whenever it happens that a man can claim nothing according to the rules of commerce, and the principles of justice, he passes out of that department, and comes within the jurisdiction of mercy. In that province the magistrate has nothing at all to do: his interference is a violation of the property which it is his office to protect. Without all doubt, charity to the poor is a direct and obligatory duty upon all Christians, next in order after the payment of debts, full as strong, and by nature made infinitely more delightful to us. […] But the manner, mode, time, choice of objects, and proportion, are left to private discretion; and perhaps, for that very reason it is performed with the greater satisfaction, because the discharge of it has more the appearance of freedom;

Edmund Burke, Thoughts and Details on Scarcity, 1795

Charity is a private affair. So must it ever remain if our republic is to survive.

Justice is not Fair



In a recent article in Commentary, Peter Wehner examines the proper role of the federal government in caring for “people who can’t take care of themselves”. Along the way, he invokes Madison:

The end of government, we’re told in Federalist #51, is justice. Justice is defined as the quality of being impartial and fair and bestowing equal treatment. But it also means caring for the defenseless, the disadvantaged, and the oppressed. This is a public as well as a private concern. A society ought to be judged on whether the weak and disadvantaged are cared for or exploited. And a just society is incompatible with one where government doesn’t care for people who can’t care for themselves.

Here Mr. Wehner begs the question by providing a self-serving definition of Justice, one clearly at odds with meaning Madison ascribes to the term. Justice is not to be conflated with fairness, as is so often seen in left-leaning screed. The Universe is inherently and unalterably unfair though many a tyrant has paved their way to power by deluding a naive public into believing this can be rectified if only the individual will surrender his sovereignty to the State.  But we need not debate what Madison had in mind when he used the term Justice, he spells it out clearly in his Gazette.

Government is instituted to protect property of every sort; as well that which lies in the various rights of individuals, as that which the term particularly expresses. This being the end of government, that alone is a just government, which impartially secures to every man, whatever is his own.

By equating his definition here of “the end of government” with that quoted by Mr. Wehner from Federalist 51 (“The end of government is Justice”) we see that Justice, as Madison uses the term, lies in the impartial and equitable protection of our possessions, most precious among them our constitutionally enumerated rights and those unenumerated rights vested in the sovereign will of the majority. A just government is one where the weak and the strong, the majority and the minority are all given equal power to protect their property.

Here we must be careful to understand property in the way Madison intended.

In its larger and juster meaning, [property] embraces every thing to which a man may attach a value and have a right; and which leaves to every one else the like advantage. . . . [A] man has a property in his opinions and the free communication of them. He has a property of peculiar value in his religious opinions, and in the profession and practice dictated by them. He has a property very dear to him in the safety and liberty of his person. He has an equal property in the free use of his faculties and free choice of the objects on which to employ them. In a word, as a man is said to have a right to his property, he may equally be said to have property in his rights.

Source: James Madison, “Property,” National Gazette, March 29, 1792; reprinted in The Papers of James Madison, vol. 14, 6 April 1791-16 March 1793; ed. Robert A. Rutland et al. Charlottesville: University Press of Virginia (1983).

If the proper end of a just government is protection of our possessions, the question naturally arises, protection from whom or what? Madison is clear throughout the Federalist that the paramount threat to our rights and property is the Government itself. Ironically, Federalist #51 quoted by Mr. Wehner in defense of the notion that Government is justified in its charitable endeavors, is in fact a treatise on how to best structure government to neutralize the threat such a broadly empowered government would pose!

So if Justice can not be employed as a rationale for government charity (and in fact argues against it), wherein lies the constitutional underpinnings authorizing the nearly $1 trillion the federal government spends each year on direct aid to the poor? Up until the FDR’s court packing scheme in 1937, such spending by the government was in fact unconstitutional. When threatened with dilution the Supreme Court acquiesced in the  infamous “switch in time that saved nine”. Thenceforth the justification for such expenditures was found by redefining the General Welfare clause of the Constitution. This despite 150 years of precedent and ample historical evidence that shows this clause does not confer any additional power on Congress but rather provided the rationale for the specific powers enumerated (in this case, taxation and expenditure) in the dependent clause following. Thomas Jefferson puts it succinctly:

Congress has not unlimited powers to provide for the general welfare, but only those specifically enumerated.

Madison warned forcefully against the modern (post 1937) interpretation in a letter to Edmund Pendleton in 1792;

If Congress can do whatever in their discretion can be done by money, [to] promote the General Welfare, the Government is no longer a limited one, possessing enumerated powers, but an indefinite one, subject to particular exceptions. (James Madison, Letter to Edmund Pendleton, January 21, 1792 Madison 1865, I, page 546)

and again in a letter to Jame Robertson

With respect to the two words ‘general welfare,’ I have always regarded them as qualified by the detail of powers connected with them. To take them in a literal and unlimited sense would be a metamorphosis of the Constitution into a character which there is a host of proofs was not contemplated by its creators.

As usual, Madison proved himself prescient. The end he feared most has come upon us and we have indeed become a Government  “no longer a limited one, possessing enumerated powers, but an indefinite one, subject to particular exceptions.”

Is all of this merely historical nitpicking pressed into the service of selfishness and greed? Actually quite the opposite. Conservatives rail against these usurpations precisely because they threaten the Common Good, another Madisonian concept that has as its ultimate expression the creation of a governmental regime that can be entrusted to hold and protect its Citizen’s most prized possession, their liberty and their civil rights.

I use the word regime above purposefully. Our Founders crafted an exquisite monstrosity, not unlike the archway which when properly constructed uses the law of gravity to defeat the law of gravity. Madison’s ingenious design of our system of governance conquered the inexhaustible, centripetal force of tyranny by dividing that force in three and pitting each branch against the other. Granting that Congress has a plenary power to tax and spend on anything it deems to be “in the general welfare” reduced that once mighty edifice to a house of cards. History proves that the temptation to pander, to buy the votes of constituents from the public purse, is too great a temptation to be resisted by mere mortal men. The result has been spending beyond comprehension and a society weakened by dependency and factionalism.

The Government is supposed to be pitted against itself, leaving us free to manage our affairs. Instead, the Government has turned the tables, pitting us against each other, leaving them free to manage our affairs. Though the temptation be great, Government can not be both an instrument of charity and the guarantor of our civil rights. We must choose and choose wisely.