ESP

ESP stands for Earth System Predictability and appears to be an initiative released during the remaining months of the Trump administration.

Introduction
From predictions of individual thunderstorms to projections of long-term global change, knowing the degree to which Earth system phenomena across a range of spatial and temporal scales are practicably predictable is vitally important to society. Past research in Earth System Predictability (ESP) led to profound insights that have benefited society by facilitating improved predictions and projections. However, as there is an increasing effort to accelerate progress (e.g., to improve prediction skill over a wider range of temporal and spatial scales and for a broader set of phenomena), it is increasingly important to understand and characterize predictability opportunities and limits. Improved predictions better inform societal resilience to extreme events (e.g., droughts and floods, heat waves wildfires and coastal inundation) resulting in greater safety and socioeconomic benefits. Such prediction needs are currently only partially met and are likely to grow in the future. Yet, given the complexity of the Earth system, in some cases we still do not have a clear understanding of whether or under which conditions underpinning processes and phenomena are predictable and why. A better understanding of ESP opportunities and limits is important to identify what Federal investments can be made and what policies are most effective to harness inherent Earth system predictability for improved predictions.

They outline these primary goals:

  • Goal 1: Advance foundational understanding and theory for an improved knowledge of Earth system predictability of practical utility.
  • Goal 2: Reduce gaps in the observations-based characterization of conditions, processes, and phenomena crucial for understanding and using Earth system predictability.
  • Goal 3: Accelerate the exploration and effective use of inherent Earth system predictability through advanced modeling.
  • Cross-Cutting Goal 1: Leverage emerging new hardware and software technologies for Earth system predictability R&D.
  • Cross-Cutting Goal 2: Optimize coordination of resources and collaboration among agencies and departments to accelerate progress.
  • Cross-Cutting Goal 3: Expand partnerships across disciplines and with entities external to the Federal Government to accelerate progress.
  • Cross-Cutting Goal 4: Include, inspire, and train the next generation of interdisciplinary scientists who can advance knowledge and use of Earth system predictability.

Essentially the idea is to get it done with whatever means are available, including applying machine learning/artificial intelligence. The problem is that they wish to “train the next generation of interdisciplinary scientists who can advance knowledge and use of Earth system predictability”. Yet, interdisciplinary scientists are not normally employed in climate science and earth science research. How many of these scientists have done materials science, condensed-matter physics, electrical, optics, controlled laboratory experimentation, mechanical, fluid, software engineering, statistics, signal processing, virtual simulations, applied math, AI, quantum and statistical mechanics as prerequisites to beginning study? It can be argued that all the tricks of these trades are required to make headway and to produce the next breakthrough.

https://www.nationalacademies.org/event/09-22-2020/earth-system-predictability-r-d-continuing-the-conversation

ESD Ideas article for review

Get a Copernicus login and comment for peer-review

The simple idea is that tidal forces play a bigger role in geophysical behaviors than previously thought, and thus helping to explain phenomena that have frustrated scientists for decades.

The idea is simple but the non-linear math (see figure above for ENSO) requires cracking to discover the underlying patterns.

The rationale for the ESD Ideas section in the EGU Earth System Dynamics journal is to get discussion going on innovative and novel ideas. So even though this model is worked out comprehensively in Mathematical Geoenergy, it hasn’t gotten much publicity.

Complexity vs Simplicity in Geophysics

In our book Mathematical GeoEnergy, several geophysical processes are modeled — from conventional tides to ENSO. Each model fits the data applying a concise physics-derived algorithm — the key being the algorithm’s conciseness but not necessarily subjective intuitiveness.

I’ve followed Gell-Mann’s work on complexity over the years and so will try applying his qualitative effective complexity approach to characterize the simplicity of the geophysics models described in the book and on this blog.

from Deacon_Information_Complexity_Depth.pdf

Here’s a breakdown from least complex to most complex

1. Say we are doing tidal analysis by fitting a model to a historical sea-level height (SLH) tidal gauge time-series. That’s essentially an effective complexity of 1 because it just involves fitting amplitudes and phases from known lunisolar sinusoidal tidal cycles.

Figure 1: Conventional tidal analysis by fitting amplitudes and phases of known tidal periods

This image has been resized to fit in the page. Click to enlarge.

2. The same effective complexity of 1 applies for the differential length-of-day (dLOD) time-series, as it involves straightforward additive tidal cycles.

Figure 2 : Long-period tidal cycles map directly to dLOD.
The long-term modulation shown follows the 18.6 year nodal cycle

This image has been resized to fit in the page. Click to enlarge.

3. The Chandler wobble model developed in Chapter 13 has an effective complexity of 2 because it takes a single monthly tidal forcing and it multiplies it by a semi-annual nodal impulse (one for each nodal cycle pass). Just a bit more complex than #1 or #2 but the complexity already may be too great for geophysicists to accept, as the consensus instead argues for a stochastic forcing stimulating a resonance.

Figure 3 : Chandler Wobble model consisting of a lunisolar tidal forcing.
The beat frequency is annual (sun) nodal against lunar nodal cycle.

This image has been resized to fit in the page. Click to enlarge.

4. The QBO model described in Chapter 11 is also estimated at an effective complexity of 2, as it is impulse-modulated by nearly the same mechanism as for the Chandler wobble of #3. But instead of a bandpass filter for the Chandler wobble, the QBO model applies an integrating filter to create more of a square-wave-like time-series. Again, this is too complex for consensus atmospheric physics to accept.

Figure 4 : QBO model has a fundamental cycle of ~2.33 years.
This is an aliasing of lunar nodal cycle against the annual cycle

This image has been resized to fit in the page. Click to enlarge.

5. The ENSO model described in Chapter 12 is an effective complexity of 3 because it adds the nonlinear Laplace’s Tidal Equation (LTE) modulation to the square-wave-like fit of #4 (QBO), tempered by being calibrated by the tidal forcing model for #2 (dLOD). Of course this additional level of physics “complexity” is certain to be above the heads of ocean scientists and climate scientists, who are still scratching their heads over #3 and #4.

Figure 5 : Higher complexity of ENSO model due to nonlinear modulation of the LTE solution

This image has been resized to fit in the page. Click to enlarge.

The ENSO model is complex due to the non-linearity of the solution. The cyclic tidal factors can create harmonics from both the inverse cubic gravitational pull and from the LTE solution, and together with the annual impulse modulation creates an additional nasty aliasing that requires painstaking analysis to reveal.

By comparison, most GCMs of climate behaviors have effective complexities much more than this because — as Gell-Man defined it — the shortest algorithmic description would require pages and pages of text to express. To climate scientists perhaps the massive additional complexity of a GCM is preferred over the intuition required for enabling incremental complexity.

Since this post started with a Gell-Mann citation, may as well stick one here at the end:

“Battles of new ideas against conventional wisdom are common in science, aren’t they?”

“It’s very interesting how these certain negative principles get embedded in science sometimes. Most challenges to scientific orthodoxy are wrong. A lot of them are crank. But it happens from time to time that a challenge to scientific orthodoxy is actually right. And the people who make that challenge face a terrible situation. Getting heard, getting believed, getting taken seriously and so on. And I’ve lived through a lot of those, some of them with my own work, but also with other people’s very important work. Let’s take continental drift, for example. American geologists were absolutely convinced, almost all of them, that continental drift was rubbish. The reason is that the mechanisms that were put forward for it were unsatisfactory. But that’s no reason to disregard a phenomenon. Because the theories people have put forward about the phenomenon are unsatisfactory, that doesn’t mean the phenomenon doesn’t exist. But that’s what most American geologists did until finally their noses were rubbed in continental drift in 1962, ’63 and so on when they found the stripes in the mid-ocean, and so it was perfectly clear that there had to be continental drift, and it was associated then with a model that people could believe, namely plate tectonics. But the phenomenon was still there. It was there before plate tectonics. The fact that they hadn’t found the mechanism didn’t mean the phenomenon wasn’t there. Continental drift was actually real. And evidence was accumulating for it. At Caltech the physicists imported Teddy Bullard to talk about his work and Patrick Blackett to talk about his work, these had to do with paleoclimate evidence for continental drift and paleomagnetism evidence for continental drift. And as that evidence accumulated, the American geologists voted more and more strongly for the idea that continental drift didn’t exist. The more the evidence was there, the less they believed it. Finally in 1962 and 1963 they had to accept it and they accepted it along with a successful model presented by plate tectonics….”

https://scienceblogs.com/pontiff/2009/09/16/gell-mann-on-conventional-wisd

With all that, progress is being made in earth geophysics by looking at other planets. My high-school & college classmate Dr. Alex Konopliv of NASA JPL has lead the first research team to detect the Chandler wobble on another planet (this case for Mars), see “Detection of the Chandler Wobble of Mars From Orbiting Spacecraft” Geophysical Research Letters(2020).

In the body of the article, a suggestion is made as to the source of the forcing for the Martian Chandler wobble. The Martian moon Phobos is quite small and cycles the planet in ~7 hours, so this may not have the impact that the Earth’s moon has on our Chandler Wobble.

The wobble is small, about 10 cm on average.

Since a Mars year is 687 Earth days, only the 3rd harmonic (229 days) is close to the measured wobble of 206.9 days. With the Earth, it’s quite simple how the nodal lunar cycle interferes with the annual cycle to line up exactly with the Earth’s 433 day Chandler wobble (see Figure 3 up-thread in this post) , creating that wobble as a forced response, but nothing like that on Mars, which may be a natural response wobble.

Gravitational Pull

In Chapter 12 of the book, we provide an empirical gravitational forcing term that can be applied to the Laplace’s Tidal Equation (LTE) solution for modeling ENSO. The inverse squared law is modified to a cubic law to take into account the differential pull from opposite sides of the earth.

excerpt from Mathematical Geoenergy (Wiley/2018)

The two main terms are the monthly anomalistic (Mm) cycle and the fortnightly tropical/draconic pair (Mf, Mf’ w/ a 18.6 year nodal modulation). Due to the inverse cube gravitational pull found in the denominator of F(t), faster harmonic periods are also created — with the 9-day (Mt) created from the monthly/fortnightly cross-term and the weekly (Mq) from the fortnightly crossed against itself. It’s amazing how few terms are needed to create a canonical fit to a tidally-forced ENSO model.

The recipe for the model is shown in the chart below (click to magnify), following sequentially steps (A) through (G) :

(A) Long-period fortnightly and anomalistic tidal terms as F(t) forcing
(B) The Fourier spectrum of F(t) revealing higher frequency cross terms
(C) An annual impulse modulates the forcing, reinforcing the amplitude
(D) The impulse is integrated producing a lagged quasi-periodic input
(E) Resulting Fourier spectrum is complex due to annual cycle aliasing
(F) Oceanic response is a Laplace’s Tidal Equation (LTE) modulation
(G) Final step is fit the LTE modulation to match the ENSO time-series

The tidal forcing is constrained by the known effects of the lunisolar gravitational torque on the earth’s length-of-day (LOD) variations. An essentially identical set of monthly, fortnightly, 9-day, and weekly terms are required for both a solid-body LOD model fit and a fluid-volume ENSO model fit.

Fitting tidal terms to the dLOD/dt data is only complicated by the aliasing of the annual cycle, making factors such as the weekly 7.095 and 6.83-day cycles difficult to distinguish.

If we apply the same tidal terms as forcing for matching dLOD data, we can use the fit below as a perturbed ENSO tidal forcing. Not a lot of difference here — the weekly harmonics are higher in magnitude.

Modified initial calibration of lunar terms for fitting ENSO

So the only real unknown in this process is guessing the LTE modulation of steps (F) and (G). That’s what differentiates the inertial response of a spinning solid such as the earth’s core and mantle from the response of a rotating liquid volume such as the equatorial Pacific ocean. The former is essentially linear, but the latter is non-linear, making it an infinitely harder problem to solve — as there are infinitely many non-linear transformations one can choose to apply. The only reason that I stumbled across this particular LTE modulation is that it comes directly from a clever solution of Laplace’s tidal equations.

for full derivation see Mathematical Geoenergy (Wiley/2018)