ENSO forecast based on tidal forcing with an Artificial Neural Network
Investigation submitted by Per Strandberg
Here on this page, you are going to find evidence that tidal forcing is one of the most important, if not the most important driver for ENSO variations. That tidal forcing could be the main explanation for ENSO variations was something I stumbled upon when I examined possible ENSO drivers.
After the previous results which I got when I was using an Artificial Neural Network ANN and where I did an analysis of the correlations between the global mean temperature and possible forcing drivers, which can be viewed here, I turned my attention to the ENSO index by looking into the Multivariate ENSO Index (MEI).
One thing I found when I analyzed the result from correlations to ENSO was that there is a strong correlation between variations in Earth’s rotations both to the global mean temperature and to the ENSO index. What we are talking about here are small variations in Earth’s rotations, which are in the order of milliseconds.
One other factor with correlation to the ENSO is of course SOI, but I also found correlations to SST, PDO, and the Kp and Ap indexes.
From this, I concluded that either it is ENSO which is driving changes in Earth’s rotation or it changes in Earth’s rotation, which is causing variations in ENSO or more likely it is some combination of both.
Proof that ENSO and variations of Earth’s rotation are proportionally correlated to each other has been known for some time. This can be seen here.
The mechanisms which tie ENSO and variations in Earth’s rotation together are caused by sea current changes, changes in trade winds or by displacements of water between the equator and slightly higher latitudes. This all makes sense.
The water currents in the northern hemisphere follow a clockwise pattern, and in the Southern hemisphere they follow a counterclockwise pattern because of the Coriolis effect. The trade wind and the currents near the equator are moving to the west. However the Current closest to the equator called the equatorial counter current move to the east. Still deeper at depth down to 200 meters at the equator an ever stronger current is moving to the east.
The behavior of this current of the Equatorial Pacific is shown on this page by Bob Tisdale.
The only mechanism by which ENSO can be driven by changes in Earth’s rotation is by variations in the tidal force.
My next step was to try to include tidal forcing in my ANN.
I then got three problems, which I had to overcome.
Firstly: I had to find data over the position and distance to the Moon and to the Sun. Eventually, I found software from which I could get this data, although it gave limited information and I was only able to print out time and position when the Sun and the Moon were closest and farthest from the Earth and with the Moon I could also calculate the time and position of the new moon, the full moon and the moon nodes. The Moon nodes are the location where the Moon cross over the ecliptic plane.
Secondly: I had to find the formula for the tidal force vector and implement this into my software.
Thirdly: I had to figure out what features in the tidal forcing which could affect ENSO. I had to experiment with different configurations based in my limited and rather crude data. To do this, I had to make complicated trigonometrically calculations in order to get the right value of the tidal force. Eventually, I got good correlations between ENSO and the tidal forcing. By this time, I had figured out which features in the tidal forcing that were causing this correlation. However it was not a direct correlation with ENSO, rather it was a correlation with the derivate signal of ENSO, i.e. it was affecting the rate of change of ENSO. The correlation to the change of rate in Earth’s rotation, on the other hand, is direct. This means that tidal forcing is causing the rate of Earth’s rotation to either speed up or speed down. The rate of rotation is then responsible for changes of the ENSO index. One reason was that it was difficult to identify, which features, which cause correlations. This was because each tidal forcing point I use the sum of monthly calculations. The size of the tidal forcing changes each and every day and how to summarize this data the right way into useful functions, which can be used to construct values that could create good correlations were difficult.
Of course, the tidal force is not the only factor which drives ENSO, but it is the most influential factor.
To test if that would be the case I ran my network with the right tidal forcing data. I also included feedback loops back in the network from the output ENSO values to some of the input nodes. After some testing and individual adjustments of the internal components in the artificial network, I got good results. Following on my earlier experiment of the ANN on the mean global temperature I trained the ANN from late 1978 up to the end of 2004. I used the time from 2005 up to the late 2011 for test the calculations, in order to find the minimal error function.
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This is the result I got. The exciting thing with this result is that it is possible to make forecasts for much longer times into the future. Today’s predictions use computer models and are only able to make credible predictions 4 to 5 months into the future. While in my case, using my ANN calculations based on tidal forcing can be made for forecasts for an almost unlimited time because the Moon and Sun’s positions into the future are known in advance. Although, I have to stress that with the predication so far it is not possible to get the last figure right. Currently, it is only possible to make an estimate with a relative high likelihood at any date if ENSO are going to be positive, negative or neutral. However, as can be seen here the predictions are not always correct. The main large El Niño events of 1982 and 1998 can clearly be seen, but the large magnitude of these events can not be predicted.
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I later made a ENSO forecast from late 2011 up to 2020. I cannot show the result here because of proprietary reasons. This picture shows the test period and some of the forecast which ends in early 2013.
Note, however that the calculations from this graph, the ENSO index uses ENSO feedback values which all are from estimated ones. Those are not the real ENSO values.
Now Look at: the previous graph with the whole time span from 1979 up to 2011! On this graph, look at the beginning at the 3 first years from the start of 1979. These 3 first years have all exceptional good correlation to the real ENSO values. The difference with the start values in this case is that I use real ENSO values for the feedback values in the network calculations which are going into the calculations with values before the graph begins. This is because in my ANN, I use for every calculation point values which goes 3 years back in time and I must use real input values for values before my first calculated value.
If I would make a forecast for the next years using current real ENSO values from 3 years back and up to the current date, my forecast would be greatly improved and would be much better than forecast made with current computer models. There were 2 important events that happened the years just after 1979. The first was the eruption of El Chichon in 1982 in Mexico. The second was the unusually strong el Niño event between 1982-1983.
My calculated values after 1982 of ENSO tend to come out of phase after and around 1982, and the ANN seems not to be able to handle strong El Niño’s very well. After some years, the estimated ENSO value deteriorate somewhat mainly because of errors in the feedback caused by the inertia in Earth’s rotation. In contrast to computer model forecasts, I don’t use data from the Tropical Atmosphere Ocean TAO network which is a NOAA measurement network of buoys in the tropical Pacific that deliver real time data which feeds these ENSO models with real time data.
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Here is a result from the same program, but as input it uses variations in the Earth’s rotation instead of tidal forcing. As you can see, the correlation to the Earth’s rotation makes the result much better. However in contrast to tidal forcing, future changes in Earth’s rotation is unknown.
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Here is another graph from the same program with feedback but this time the input signal is only from SOI Southern Oscillation Index. As expected SOI is closely related to ENSO.
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Here is a repeat with the same program, but this time with a combination of tidal forcing, changes in Earth’s rotation, SOI, Kp and the Ap indexes. As you can see, this result is similar to that of the previous with only SOI.
The next step I plan to take is to use the ANN with real time data and make more accurate ENSO predictions for the next 3 to 4 years in to the future. I also want to test with real ENSO input data for several time periods in order to evaluate statistically how the good predictions can be based on real time ENSO feedback input data for the beginning.
After that, I want to improve on my result by using more precise and accurate tidal calculations. I have found a program from which I can make precise calculations of the Moon and the Sun on a daily basis. Other factors I plan to look into are the mechanism of the Kelvin wave, Walker circulation and MJO which all should influence ENSO to some degree.
So far I have only looked at ENSO. I can easily switch to SOI, NOI and changes in Earth’s rotation and use that as an output for predicting ENSO with the ANN.
Conclusion from my result is that tidal forcing is as a major factor in ENSO forcing. I now have gotten new questions. Compared with other causes how important is the effect from tidal forcing? Is it possible to find an increasing effect from tidal forcing by improving the tidal data I use? Is it, for example, possible to identify tidal forcing as the cause for the strong El Niño of 1982 and 1998?
It may be possible to get better ENSO results by using predictions based on SOI, NOI, Earth’s rotations or by starting from tidal forcing only. I’ll test and see. Also, ENSO and SOI are parameters for which there exists long historical data records. By, using a longer time span for training and testing, the accuracy of predictions based on ANN should be improved.
I acknowledge that it is not easy to find correlations between tidal forcing without testing out the right feature and by using am ANN. However I do find it very strange that no scientist to my knowledge has been looking into a possible connection between tidal forcing and ENSO in any depth.
As can be seen from what the IPCC writes about ENSO predictions, they do not have a clue. The current data models that are in use can only predict with any accuracy 4 to 5 months into the future. When it comes to the ENSO drivers, these researchers think chaos theory and random noise are the mechanisms which explains the causes of ENSO changes.
However Cerveny, R. S. and J. A. Shaffer (2001) et al. in the report, The Moon and El Niño, Geophys. Res., writes about the Moon cycles and ENSO, where they find correlations between the solar cycles and ENSO.
To me at least, it seems that the solution to long range ENSO prediction has for a long time been right in front of the eyes of these researchers, but nobody has taken up the challenge to figure it out.
I see the same reason why the climate community at large has not studied tidal forcing as an explanation for ENSO variations and why none TSI solar forcing as an additional cause for climate forcing ignored. The primary reason is that they have had their education in meteorology, atmospheric physics, thermodynamics or in computer science. Most of them are specialists in a few narrow disciplines, and as such they prefer only to apply knowledge from the fields they know. They are not generalists and display strong resistance for applying knowledge from other area from which they lack knowledge. Then add to that group thinking, peer pressure and lack of funding for research in alternative causes of climate change and this explains the current one-sided situation. This is one of reason that predictions made with computer simulations are failing.
ANN are seldom used in climate science. There are some exceptions. One is research done by Dr William Hsieh from the University of British Columbia who uses this technique for ENSO predictions, but to my knowledge without using any tidal forcing. To learn more about how ANN works and how I have implemented this technique in climate investigation, Click here
I suppose I should respond to this nonsense, for any who do not have the background to immediately grasp what a ridiculous clown this Bart is–after all, he actually has a paper to back up his junk science.
He quotes me: “And no change in AM certainly does entail no energy transfer.” Does he now accept the validity of this obviously correct claim? Can’t tell–he claims external authority regarding its…what? Whatever he is claiming, he prefers to keep it very vague, maybe recognizing he is wrong but still claiming he is right.
And yes, he actually has a paper claiming nutation affects climate: “Earth nutation influence on the temperature regime of the Barents Sea,” written by one H. Yndestad, 1999. For the information of any who are still tracking this thread, the author is claiming that an 18.6 year wobble of about 17″ of arc–this amount to a radius of about half a kilometer–causally correlates with temperatures in the Barents Sea, and with climate generally!
Be it noted, for what it’s worth, that tides play no role in this fantastic correlation–it remains for Mr. Bart X to dig up a second for this fabulous claim. If I were in Bart’s class I would take up the CO2 cause. He makes astrology look like good science. –AGF
@Agile Aspect: The LOD is measure of the change in the Earth’s spin.
The Earth’s rotational or orbital motion is actually complicated.
(Mods: please delete my 8:00 am and replace it with this one)
@Agile Aspect: The LOD is measure of the change in the Earth’s spin.
The Earth’s rotational or orbital motion is actually complicated.
I’m not saying Wikipedia is an authoritative source. If I’m wrong in using the word “rotation” instead of spin, I’ve got a lot of company.
agfosterjr says:
January 22, 2013 at 7:52 am
“Does he now accept the validity of this obviously correct claim?”
Uh, NO, because it is hopelessly ignorant and wrong. Can you not read, either?
As for that Barents Sea paper, a consideration of the Energy needed might be worthwhile.
From: http://rockpile.phys.virginia.edu/arch17.pdf
Suppose we dissipate all that rotational Kinetic Energy through the Earth’s oceans as a form of heat flux, which completely neglects significant Potential Energy that ought to go into raising the moon’s orbit due to tidal drag. Let’s pick a heat flux that is small compared to hypothetical CO2 forcing, like 0.1 W/m^2.
Area of the earth oceans (A) = 3.60E+14 m^2
Seconds per year = 3.16E+07 sec/yr
Average energy flux lost through surface of oceans (assumption) (Flux) = 0.1 W/m2
Average energy lost through oceans per year (E_rate) = 1.14E+21 J/yr
Rotational Kinetic Energy of the earth (KE) = 2.60E+29 J = W*sec
Millions of years at constant loss rate KE/E_rate = 229 million years.
Or assuming an exponential decay:
t-halflife = t * ln(2)/ln( N(t=0)/N(t=t) ) = 158 million years
How big is 0.1 W/m^2? That’s about like trying to change the temperature of an Olympic size Swimming pool (in surface area) with a 100 watt light bulb.
Clearly, I can change the t-halflife to 1.5 billion years if I reduce the heat flux to 0.01 W/m^2, but then I’m trying to heat an Olympic pool with a 10 watt night-light. And I still have a moon to lift in orbit.
Stephen Rasey says:
January 22, 2013 at 9:49 am
A very confused analysis. Basically, a determination of the time for slowing down the spin rate to zero needed to release 0.1 W/m^2 on average. And, this proves… what? That it takes a very long time at that meager rate of energy dissipation to come to a stop. No duh?
You guys do not understand nutation dynamics, the storage of energy in the perturbed motion of the spin axis induced by disturbance torques, and its subsequent release through dissipative mechanisms, in particular by the action of viscous friction within the oceans. Such dynamics are old hat. Textbook. I can pull out my undergrad textbook (many moons, and advanced coursework, ago), Kaplan, Modern Spacecraft Dynamics and Control, page 127, Energy Dissipation Effects – it’s all right there, and this book is considered very, very basic.
Mr. Foster complains I haven’t a high school understanding of physics. That is one thing he got right. I do not. You guys apparently do. Congratulations. Now, run along and do your homework.
Thank you Stephen Rasey, and a few comments:
Solid planets also undergo tidal braking, which is why the moon, Mercury and Venus, and many of the moons of the giant planets have locked-in rotation behavior. Thus much of the earth’s tidal braking is dissipated in the lithosphere, but of course the majority of this feeble heat too must work its way out through the ocean. At the current, unusually high, rate of deceleration it would take the earth over a billion years to stop (non-exponentially). George Darwin calculated the age of the earth at 2.2 billion years based on his info on secular rotational (negative) acceleration.
Nutational transformation of rotation energy is a whole lot weaker than total rotational energy (by a factor of somewhere in the ball park of sin 15″, I would suppose). Moreover it is not at all apparent (to me at least) that the torques involved apply to the lithosphere to the exclusion of the ocean. For all I know more torque per mass is applied to the seas than to the solid earth.
And to our fool in residence–Bart: why don’t you specify the problems you perceive with the statement, “And no change in AM certainly does entail no energy transfer.” Do you think you can get energy from nothing? –AGF
By the way, precessional angular displacement is four times as great as that of nutation, and core/mantle coupling would be expected to play a vastly more significant role in energy dissipation than lithosphere/hydrosphere coupling (tides). The core has a whole lot more inertia than the ocean, and is more round. –AGF
I don’t have a dog in this fight but it seems to me if you want to try and relate changes in tidal motions to the ENSO, it might make sense to relate the observed properties of the ENSO to those tidal motions. Per my understanding ENSO changes have particular spatial-temporal characteristics – for instance, an El Nino begins with an anomalous warming in the Eastern Pacific waters along with a reduction/change in wind patterns.
Can the tidal motions reproduce these specific spatio-temporal patterns? Any change in LOD seems like it must affect the Earth as a whole equally and not preferentially favor an effect in the Eastern Pacific ocean and the atmosphere above it. However, I may be mistaken, perhaps there is some geological/hydrological feature of the Earth that might account for this.
Cheers, 🙂
u.k.(us): The man threw a theory out there, if you must disparage something, maybe it should be the theory.
Willis did exactly that in his first post. Almost immediately thereafter I posted a very encouraging note essentially seconding some of Willis’ critiques (especially the secrecy) and inviting more detail. The entire subsequent discussion of Willis’ tone is a total red herring. From the start, Per Strandberg ignored the substance of the critical commentary on his work. That’s what turned the discussion away from the ideas and toward the man.
agfosterjr says:
January 22, 2013 at 10:48 am
‘why don’t you specify the problems you perceive with the statement, “And no change in AM certainly does entail no energy transfer.”’
The magnitude squared of angular momentum is
H^2 = (I1*w1)^2 + (I2*w2)^2 + (I3*w3)^2
where I1 etc. are the inertias and w1 etc. are the rates in a body space coordinate system aligned to the principal axes. In the absence of external torque about the spin axis, the angular momentum stays constant.
Setting H constant defines the momentum ellipsoid in rate space. Energy is
T = 0.5*I1*w1^2 + 0.5*I2*w2^2 + 0.5*I3*w3^2
Setting T constant defines another ellipsoid, the inertia ellipsoid. If T remains constant, the rate trajectory is confined to a connected intersection of the two ellipsoids.
The requirement that H remain constant, however, does not dictate that T remain constant. As energy dissipates, and T shirnks, the rate trajectory is confined to the evolving intersection of the two ellipsoids, the static momentum ellipsoid, and the diminishing inertia ellipsoid. Only when the intersection shrinks locally to a single point, and the inertia ellipsoid is fully contained within the momentum ellipsoid, does T become constrained, and energy dissipation cease.
It is not difficult to find information on this if you trouble yourself to do a search, e.g., here and here.
agfosterjr says:
January 22, 2013 at 11:01 am
“By the way, precessional angular displacement is four times as great as that of nutation…”
Nomenclature varies. In spacecraft engineering (see last sentence, first paragraph), any off-nominal spin condition which creates time varying stresses is generically referred to as nutation. Having a small nutation angle does not necessarily mean the rate of energy dissipation is small, as the energy dissipation is a result of movement of the dissipating medium. Efficient dissipation of energy is what keeps the nutation angle small. On spacecraft, dissipating elements often consist of fluid filled vessels or conduits. Engineers trade off dimensions, along with fluid viscosity and density, to optimize the rate of dissipation which damps out vehicle nutation induced by disturbance torques.
I thought Anthony’s website was a place of discussions about new ideas on subjects related to the climate.
In my work I have always followed where the data takes me, rather than followed some preconcived ideas on how things work.
So when I found that specific tidal data correlate well to the derivate value of ENSO, I followed that path.
The difficult part then was to introduce feedback and then to get the Neural Network to became stable and to respond to the tidal data input.
So I simply raise my hand here and say I found something.
Because, I think that the fact that the tide play an impartant part in ENSO forcing is a discovery of some importance.
My work is an ongoing prosess and I do want to publish the result with full explaination and transparency by working togheter with others.
Those other must however behave in a civil manner and have integrity. Altough I don’t mind frank discussions.
Per Strandberg (@LittleIceAge) says:
January 22, 2013 at 3:52 pm
Your correlation certainly appears solid. But, of course, correlation is not causation, and the variation in LOD is very small. The energy dissipation effects I have been attempting to explain would also be correlated with the LOD, but could be large enough to be a driver of ENSO. If there are data sets of polar motion available somewhere, you might try looking at those correlations.
Here is info and data.
Bart says:
January 22, 2013 at 1:18 pm
In the discussion above, I referred to the “inertia ellipsoid”. This seemed an odd bit of nomenclature to me, but it was what they chose at the wikipedia link and I didn’t want to muddy the waters. Looking back at the link, I think the writer just got sloppy, so I would advise any readers following the discussion not to adopt that convention and call it the “energy ellipsoid” instead.
Bart, the equation you’re looking for is T = dL/dt, where T is torque and L is angular momentum. Wiki says: “Angular momentum is conserved in a system where there is no net external torque…” and Likins (your source, p.3) says: “As no further change in angular momentum can occur [after the perturbation is removed], energy cannot be dissipated without limit…” which of course corresponds to my statement: “And no change in AM certainly does entail no energy transfer,” which you curiously seem to think you have disproved. The trivial difference between my version and the other is that I use the general term “energy” whereas torque is a specific kind of energy: mechanical and rotational.
I like the way Likins writes and thinks. He goes so far as to consider the etymology of the terms while sorting through inconsistent usage. He defines precession as a response to external torque, and nutation as an internal response independent of (external) torque. Yet he relates how with spacecraft problems the distinction can depend on the frame of reference. He continues the above quote: “…consequently the body must in time approach again a state in which no relative motions occur.” Relating this to earth science this amounts to removing the earth from outside gravitational influences, which if done, precession and nutation immediately stop, but a few million years are required for the earth to dissipate accumulated tidal heat. The mantle would cool to a stable temperature determined by radioactive decay, and the core might shrink a little.
Rasey has the right approach to both problems–tidal effects on ENSO and nutation effects on SST–he quantifies! This immediately constrains the possibilities to the level of the insignificant. I added to that the thermodynamic objection that only irreversible tidal processes entail conversion to heat which leaves on the table only that energy that corresponds to the translation of the moons orbit. And this is according to basic principles of conservation of energy which I correctly stated, and which you continue to deny. Accordingly the LOD data, which almost entirely deal with reversible processes, i.e., changes in rotational inertia, can have nothing to do with tidal heating, nor with ENSO.
As long as the sun and moon are out there precession and nutation will continue, and angular momentum will continue to be transferred measurably to the moon. The little bit of corresponding kinetic energy will continue to heat the mantle directly, the seas indirectly and even directly a tiny bit, but this is just nothing compared to the energy the sun shines on the globe. The bottom of the ocean is warmer than polar seas not because of radioactive decay but because of warm, salty water from the Red Sea, Persian Gulf, Mediterranean, etc., and it’s still pretty cold down there.
Those in the know are able to deduce from nutation rates a thing or two about mantle viscosity, but I’ll leave it to Velikovsky and Von Daniken to explain how nutation warms the Arctic. Or how fossil CO2 caused Sandy. –AGF
This sentence: ” Accordingly the LOD data, which almost entirely deal with reversible processes, i.e., changes in rotational inertia, can have nothing to do with tidal heating, nor with ENSO,” needs obvious qualification to: “…nor with ENSO by way of tidal heating.” ENSO and LOD certainly are correlated by way of atmospheric coupling, and by way of sea currents. Also LOD shows AM transfer between the lithosphere and fluid spheres (which involve no change in inertia). Atmospheric coupling has been extensively analyzed and effects attributed to LOD accounted for. Tidal effects are fairly modeled as well. The IERS provides data with noisy tidal effects removed.
Other mistakes on my part: nutation energy is not in the ballpark of sin 15″, and Pacific tidal currents can measure several mm per second–bores are another story. –AGF
agfosterjr says:
January 23, 2013 at 8:11 am
No, torque is not energy, either. The change in energy due to torque is found by integrating the dot product of torque with angular rate over time.
Your charade grows tiresome. I have tried to lend a helping hand. You refuse to learn. Be that way.
“…the equation you’re looking for is T = dL/dt…”
No, T is the traditional symbol for kinetic energy in Lagrangian dynamics.
The Greek letter “tau” is commonly used for torque. The equation tau = dL/dt only holds in an inertial (non-accelerating, hence non-rotating) coordinate system, in which the inertia tensor is not constant. Within the body fixed frame, where the inertia tensor is constant, the equation is tau = dL/dt + cross(w,L), where w is the angular rate vector, L is the angular momentum vector, tau is the torque vector, and “cross()” denotes the vector cross product.
This is Euler’s equation. When you add dissipating elements to the equations of motion, they have the effect of bleeding off energy while leaving angular momentum constant in the absence of external torque. With the addition of external torque disturbances, they have the effect of limiting the accumulation of energy from the torque by dissipating the input energy. You are wrong, and way, way, way out of your depth. Good-bye.
OK, you’re right for once, but if dL/dt = 0 so does torque and so does the dot product. If dL/dt does not equal zero then neither does torque nor the dot product, which is to say the energy transfer is not zero. Which is to say what I’ve been saying all along, and which you have been denying all along. I challenge you to attach your name to this idiocy. Come on, don’t be a coward. –AGF
And now I’m out of my depth for using a capital Roman T in place of (Byzantine) lower case Greek t. You should quit after scoring a point. Come on, tell us your name! –AGF
Do you have a perpetual motion machine for sale? Where does all this energy come from that you have to bleed off? With no change in AM? All you are doing is changing the axis of rotation, which for a spacecraft involves very little energy. You are only dissipating the most minimal energy, that due to hysteresis or whatever, extraneous motion induced by your craft’s rotation. You may know a little about preventing it, but you have never understood the most elementary basics of the theory behind it. You are not at all applying remedies to such continual external torques as the earth undergoes. That’s why your experience has no application to geodynamics. Your name please? –AGF
“if dL/dt = 0 so does torque and so does the dot product. If dL/dt does not equal zero then neither does torque nor the dot product, which is to say the energy transfer is not zero…”
Fail, again. The magnitude of the vector L, which I will denote mag(L), has derivative
d/dt(mag(L)) = dot(L/mag(L),tau)
This is zero if tau is zero, OR if tau is orthogonal to L.
The derivative of energy is
dT/dt = dot(w,tau)
So, if tau has a component along w, but is orthogonal to L, then the energy will change while the magnitude of the angular momentum stays constant. Dissipating elements impart precisely such a torque.
If you want to learn any more, then you will address me respectfully. If not, you can go take a flying leap.
Sorry, Professor X, but I’d rather study physics with a tutor who doesn’t blame Global Warming on nutation. Cheers. –AGF