Our mathematical nomenclature is as follows. Capitalized Latin letters denote random variables,122and lowercase versions of the same letter indicate particular values of these variables. Vectors123are boldfaced. We define ̃Yto be a climate sensitivity proxy such as the equilibrium climate124sensitivity or a climate feedback strength, for which the constraints are derived. A single emergent125constraint variable is denoted ̃X. A collection ofnemergent constraints will be labeled ̃Xi,i=1261,...,n. Versions of these random variables which have been normalized to have zero mean and127variance of 1 are similarly denoted, but without the tilde. The PDF of any random variableUis128p(u), and similarly for multivariate distributions.

community

Daubert says, the methods should be judged by the following four criteria

There should be a known rate of error

error is intrinsic to our interaction with nature

force

a list of such pretenders

data analysis and the proper application of research methods

two-thirds of all postdoctoral fellows in biology in American universities believe that they are going to make this step, but in fact, only about a quarter of them succeed

media outlets

inconsistent with human nature

choose what is and is not worth observing

we understand

cleansed of harmful preconceptions

demystify somewhat the business of science

But such processeshave not been well characterized.

Deep learning for multi-year ENSO forecasts

trivium

standard deviation σ/√n. Where σ is the standard deviation of the sample and n is the number of observations in the sample

Identifying Causal Effects from Observations

Concepts You Should Know

Reminders from Basic Probability

Scientists should also make their data and all other relevant materials available to the world once they publish their research

calculated the Jacobian using thenumdifftoolsPython package. The specific268method we used from this package is a second-order forward difference method

he proposed framework uniquely elucidates therelationship between the IT and statistical perspectives on causalit

distributions over the effect rather than values of the effect and(2) are defined with respect to random variables representing a cause rather than specific values

We conclude that there is a need to more accurately quantify entrainment rates, improve the representation of plume radius, and incorporate the effects of column instability in future versions of 1D volcanic plume models.

quasi-geostrophi

verticallypointing lidar.

Morning convection is particularly strong in the Gulfof Panama because of its concave coastline

abatic wi

ractional cloud coveragetends to be highest around sunrise and lowest duringthe afternoon. The thinning (and in some cases thebreakup) of the overcast during the daytime is due tothe absorption of solar radiation just below the cloudtops (see Fig. 4.30

evaporation of the drizzle drops in thesubcloud layer absorbs latent heat. The thermody-namic impact of the downward, gravity-driven flux ofliquid water is an upward transport of sensible heat,thereby stabilizing the layer near cloud base

In contrast, cooling from above drivesclosed cell convection

Heating from below drives open cellconvection

horizontal roll vortices

The area indicated by the hatched region representsthe total amount of heat input into the bottom of the boundarylayer from sunrise until time t1

turbulent sensible heatflux FHacross the mixed layer

evolution during summer over land

nonlocal air-parcel movement

Typical variation of wind speeds with height in thesurface layer for different static stabilities

Karmam

logarithmic wind profile is consistent with aK-theory approach

Kmust increase linearly with height

logarithmic profile

The stable boundarylayer near the ground consumes TKE, resulting inweak and sporadic turbulence there

Bowen ratio over the oceans decreaseswith increasing sea surface temperature. Typical valuesrange from around 1.00.5 along the ice edge to lessthan 0.1 over the tropical oceans where latent heatfluxes dominate

owen ratio6:BFHsFEs

bulk transfer

elongated gyre. Rossby waves of very low frequency are active in setting up this western extension of the circulation

Forcing and β-plumes.

The ECN region is defined as 1128–1228E, 258–358Nandthe SUS region is defined as 958–858W, 288–388N.

PEER REVIEWED

FIG. 7. The horizontal distribution of (a),(b)v, (c),(d)vD, (e),(f)vQ, and (g),(h)vaqgat 500 hPa on day 0. Thewhite dashed contour lines denote a heavy-rainfall area (day 0 precipitation greater than 20 mm day21in ECN andgreater than 12 mm day21in the SUS

To separate thesesignals, we decompose each meteorological variable intoan EPE-related background component (means fromday213 to day24 and from day14today113) and anEPE-related synoptic-scale component (the differencesbetween the total and the background component)

stronger coupling

The expression for can be cast in various forms that, although mathematically equivalent, are open to markedly different interpretation.

sea ice

MERRA-2 data collections

nst1_2d_int_Nx

TableofContents

Budgets

the nature of turbulence isstrongly modulated by heat fluxes and drag (momen-tum fluxes) at the surface.

vertical profile of horizontal wind speed

profile of the variance ofvertical velocity

t*is of order 15 min,which corresponds to the turnover time for the largestconvective eddy circulations, which extend from theEarth’s surface all the way up to the capping inversion

Obukhov

aero-dynamic roughness length, z0

kinematic momentum fluxes

friction velocity,

Deardorffvelocity

roth-order closure. In thiscase, neither Eqs. (9.10) nor (9.11) is retained. Instead,the mean flow state is parameterized directly. Thisapproach, called similarity theory

gradient-transfer theory, K-theory, eddy-diffusivitytheory, or mixing-length theory.

Reynoldsaveraging—an applied mathematical method thateliminates small linearterms such as those associatedwith nonbreaking waves, but retains the non-

nalogy with radiative fluxes in theexpression for radiative heating rates (4.52)

inematic heat fluxandhas units of (K m s1

imensionless Richardson number,

Laminar flow becomes turbulent when Ridrops below the critical value Ric0.25

Kelvin-Helmholtz (KH) instability

dvectionof TKEby the mean wind,Mismechanical generationof turbulence,Bis buoyantgeneration or consumptionof turbulence,Tris trans-portof turbulence energy by turbulence itself, and is the viscous dissipation rate.

ecific kinetic en

covariance

for any half-hour period, there is a well-definedmean temperature and velocity; the range of temper-ature and velocity fluctuations measured is bounded(i.e., no infinite values); and a statistically robust stan-dard deviation of the signal about the mean can becalculated. That is to say, the turbulence is not com-pletely random; it is quasi-rand

behomogeneous

Turbulence is a natural response to instabilities inthe flow—a response that tends to reduce the insta-bility. This behavior is analogous to LeChatelier’sprinciplein chemistry.

luctuating

KE cas-cades through medium-size eddies to be dissipated bymolecular viscosity at the small-eddy scale

Scales of horizontal motion

Exercis

The Atmospheric BoundaryLayer

Initial Evaluation

nalysis tendency of vertically integrated total water

TOA radiative fluxes

Observational Data Count

ivTABLE OF CONTENTS

DTDTANA

local and non-local energy diffusion across the wavenumbers, with all Fourier modes feeling a sort of thermal bath described by a Gibbs-ensemble

based on the idea that only the mean flux, ϵin<math><msub is="true"><mrow is="true"><mi is="true">ϵ</mi></mrow><mrow is="true"><mi is="true">i</mi><mi is="true">n</mi></mrow></msub></math>, plays a statistical role in the inertial range [2]. In such a case, Kolmogorov derived the celebrated −5∕3<math><mo is="true">−</mo><mn is="true">5</mn><mo is="true">∕</mo><mn is="true">3</mn></math> power law

Up until now, all manipulations leading to the global and to the scale-by-scale energy balances (8) and (15)–(17) are exact. In order to proceed further we need to make some assumptions.

The presence of a cascade requires that there exists a range of scales where all terms on the RHS of (15) are vanishingly small.

The prescribed radiative cooling rate is at the default value (−1.5 K/day) in the first control simulation (BASE). It is reduced by half to −0.75 K/day throughout the troposphere in HEAT

96 × 96 grid points with a horizontal spacing of 2 km. There are 50 vertical levels

Equation (6) illustrates that the magnitude of effective buoyancy depends on the local second derivative of B, rather than the simple sign and magnitude of B

It cannot penetrate when something is taking its place

defense of its members,

long-enduring disintegration of science into specialties,we need to re-integratescientific reasoninginto a new holistic worldview.

it is a profoundly human activity,

will be free from this struggle

problems of science are not so much in Nature itself but in our own thoughtsabout Nature

the dispositionof contemporary science itsel

ebulousness of modern science

he nature and necessity of explanations, and, above all, the fundamental,but often unrecognized,obstacles toobtaining them

Edmund Husserl

enaissance magic

odern science has convinced us that nothing that is obvious is true and that everything that is magical, improbable, extraordinary, gigantic, mi-croscopic, heartless, or outrageous is scientific

the true nature of causality outside of my range

not random but teleological,yet without a presetgoal

Everything is evolving

Given that todaythatfundamental scientific questions about time, space, matter, life, and consciousness remain unanswered, more precise measurements willnot help. Instead, weneed tounearth and reexaminethose of our beliefsfrom which the questions stem.

the worldview

Mathematics is the language of expressing natural laws, but a correct syntax, as such,is noguaranteeofthe truth of a script

Thequantumis understood as the elemental constituent of everything that exists. It is postulatedthat thiscould be the underlying reason why all processes are essentially alik

guides us through an examination

Current problems of physics may well imply thatwe areon the verge ofrevealingeye-opening new insights

he theories themselves influence

I do not pretend to master modern science in all of its complexity

nature this

the book draws oncommon sense, onpractical wisdom, and oneveryday experience

Thermodynamics is considered a uni-versal theory

this theory of nonequilibrium thermodynamics

understanding and insight. In fact, this newly revealednatural law of time makes sense

Why is evolutionary theory notformulated as a law of physics?

thoseprinciples of physicsthat

probing and

Can we discern the whole?

explained by the fact that everything that exists is comprised of the same elemental constituents, quanta of light

As surprising as it maybe, common patterns are ubiquitous

the principle of least action does not, in itself, describe the trajectory of a planet or the course of a river, the free-energy principle will need to be unpacked carefully in each sphere of its application

the time-average of free energy, which is called “action” in physics

“reduce surprise,” you “live longer.”

the aim of philosophy “is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term.”

we harvest sensory signals that we can predict

Dark-Room agents can only exist if they can exist. The tautology here is deliberate, it appeals to exactly the same tautology in natural selection (Why am I here? – because I have adaptive fitness: Why do I have adaptive fitness? – because I am here).

surprise is also the negative log-evidence for the model entailed by the agent

the intriguing link between informational uncertainty and physical disorder. Mathematically, they are identica

Shannon set out this framework, with its beautifully simple, core idea of equating generation of information with reduction of uncertainty (i.e., “surprise”).

see Potochnik2017on the role of “rampant andunchecked” idealizations in science

productively argue about theaptness of modeling tools for their intended purposes

the boom of researchrelying on FEP just highlights there is room for deductive systematization and physics-first approaches in life science theorizing

FEP is like all other scientific principles in being truth-apt

whatevertautologies do, they don’t explain

free-energy theorists attempt an enormous vari-ety of derivations from FEP. In that sense, FEP may be said to play the role of a firstprinciple

just a characterization

The tautology here is deliberate

the whole point of[FEP]istounifyalladaptiveautopoieticandself-organizingbehaviorunderonesimpleimperative; avoid surprises and you will last longer [...]

atautology,astipulative definition

Free-energy theorists may simply reject the idea that adequate scientific repre-sentation of life science phenomena must target the component parts and operationsand internal organization of mechanisms.

Mechanists wouldtherefore conclude that FEP lacks explanatory power

constrain the possible structures and configurations that might perform those oper-ations; but they are equally keen to emphasize that structural decompositions intomodeled components within a mechanism can also constrain the possible functionsand configurations performed

By redescribing systems’capacities in terms of their functional properties and dispositions, functional analysisoffers scientists a way to tackle the target phenomenon. But it also offers the potentialfor prediction and explanation

individuated

whether and when functional accounts of bio-logical phenomena suffice

explanatory power

apparently at odds with mechanists’ emphasisthat life science phenomena should be explained by appeal to mechanisms, and thatadequate strategies for explanation in the life sciences should involve decomposingthese mechanisms into component parts and operations

Stipulative definitions, likelivingsystemasanattractingsetinaphasespaceoradaptivebehaviorasbehaviorthatreducesaverage surprise, provide the bridge principles that connect theoretical predicates fromdifferent disciplines, and that allow free-energy theorists to attempt the deductionsneeded to claim reductions of other principles to FEP

free-energy

phylogenetic and ontogenetic trajectories

Since attracting sets are subsets of classically predefined phase spaces,organicists deny the assumption that all living systems’ characteristic behavior isaptly represented with an attracting set

historicallygrounded

recognition) densityq(Ψ,μ)

nternal parametersμ

likelihoodp(D=dt+1|Ψψt+1,Aat,M) and prior densityp(Ψψt+1|M), which jointly specify the generativemodel “entailed by” the system’s phenotype

unsurprising

the surprise of sampling some sensory outcome (or experiencing somesensory state) can be represented with the negative log probability:−logp(D=dt+1|at,M). This measure quantifies the improbability

“are confined to a bounded subset of states and remain thereindefinitely”

its epistemic status is unclear

As a necessary condition for the reaction to occur at constant temperature and pressure, ΔG must be smaller than the non-PV (e.g. electrical) work, which is often equal to zero (hence ΔG must be negative

Raymond Hide, whom I had met by chance during the last year of my PhD, told me of recent work by climatologist Paltridge [12] showing that the properties of Earth’s climate could be derived using the Principle of Maximum Entropy Production!

tropical convection induces a stationary equilibrium distribution.

In addition, this transition condition for the cellular automaton adds a stochastic component in its evolution, compared with a strictly Boolean ruleset

onditioning for the common history byreplacing time delayed mutual information by a variantof Eq.(4) resolves this aparent paradox.

xample, take a bi-variate time series (seeFig. 3) of the breath rate and instantaneous heart rate ofa sleeping human suffering from sleep apne

much of the common informa-tion is due to the common history

Either one can study transfer entropy as a function of theresolution, or one can fix a resolution for the scope of astudy.

transfer entropy behaves like mutual information.If computationally feasible, the influence of a known com-mon driving forceZmay be excluded by conditioning theprobabilities under the logarithm toznas well

This is the central concept of this paper

preferred path forward for advancing physics in EMC models is one in which innovations from the community are socialized and introduced through strong collaborative working relationships between developers/scientists at EMC and thosein the broader community

In the numerical modeling community it is not uncommon for developers to be confounded when model innovations that look better “on paper” -or seem to perform betterin different modeling frameworks –do not increase overall skill when implemented in complex, highly nonlinear modeling systems

their report and recommendations

MEG provided their analysis

GCM) is nudged towards 6-h reanalyses. The nudging is applied either in the whole tropical band or in a regional summer monsoon domain

using the nudging/relaxation methodology first outlined in Klinker and Sardeshmukh (1992) and used subsequently by others including Douville et al. (2011) and Hall et al. (2013)

To better understand the role of the vertical pressure gradient force, we rewrite Eq. (2) without approximation as

shallow CAPE measures the integrated buoyancy for undiluted parcels only up to the midtroposphere

sensitivities have been examined

standard deviation equal to current uncertainty estimates for radiosonde vertical profiles

Changes to MP produce a similar order-of-magnitude response in convective hydrologic cycle, dynamics, and latent heating as changes to IC

Modes of vertical thermodynamic and wind variabilityover the Maritime Continent

Non-rotated PCs (left panels) and rotated components(right panels) for all variables at the Ranai upper-air sounding site.

Real or Artifact?