対流のメソ構造における形態-機能関係性に向けて

Abstract

Mesoscale patterns in atmospheric convection (between the inner scale of convecting-layer depth and the outer scales of domain constraints) are fascinating and ubiquitous. This review asks whether some aspects of that form (normalized for a given amount of convective activity) play a meaningful role or function in the total flow, especially in its more-predictable larger scales. Do some mesoscale features deserve to be called organization in its strong sense, acting like multi-cellular organs in an organism? After enumerating hypotheses from null (mesoscale arrangement doesn't matter) to various detailed ideas (rectification of nonlinear processes with spatial agglomeration, size-dependent top-heaviness of heating, vertical momentum flux effects, adjustment roles, and the character of stochastic noise), a tabular framework for categorizing form-function research is offered. Function measures are divided into micro (mere quantification of budget terms averaged over mesoscale patches) vs. macro (roles played through time in larger-scale phenomena). Tools and approaches are arrayed from literal and explicit (case observations) to conceptualized (models, ranging from theory to numerical to statistical depictions), on timelines both historical (contacting case observations in some way) and synthetic (theory, simulation, and composites). Efforts are further distinguished by whether their inferences are associative (derived from conditional sampling of either form or function) or causal (involving controlled experimentation). Literature examples are surveyed, albeit incompletely, and future research strategies are suggested across this tabular landscape or framework. One spotlighted result is an apparent internal optimum in the horizontal geometry continuum between isotropic horizontal two-dimensionality and horizontally one-dimensional squall lines. Form-function questions could help justify, orient, and capitalize scientifically on the field's costly multiscale activities (requiring both coverage and resolution) in both observational and modeling realms. Data assimilation is a motivating application, and also a potentially powerful research tool for achieving greater synthesis. An observant human sensibility remains crucial for discovering and interpreting form-function relationships, at the very least to design more salient algorithms in the age of big data and computing.

1. Introduction

1.1 Mesoscales and form-function relationships in other disciplines

The prefix meso- means middle: defined not by what it is, but rather by at least two things it is not. Patterns on meso scales occur between inner scales, the realm of more fundamental or indivisible processes, and outer scales set by larger domain-level constraints and drivers. Beyond their direct impacts, mesoscales pose fascinating challenges of interpretation. What aspects have meaning or importance in the evolution and predictability of the outer scales? What aspects are mere baubles, arbitrary and inconvenient distractions to be ignored or averaged over? A grand aspiration across many disciplines is to relate cared-about function to observable pattern or form, whether positively as organization or negatively (or neutrally) as noise.

Chemistry transcended alchemy with the brilliant deduction that the functional properties of substances are rooted in a secret, invisibly small realm of form (molecular shapes, of which some aspects are more important than others). Today the quantum laws of atomic (Greek for indivisible) inner scales are known, a great triumph of physics, but re-assembling those fundamental laws into a working understanding of the macroscopic world is intractable, even in principle, exploding the simplistic promise of reductionism (Anderson 1972; Laughlin and Pines 2000). Faced with that impasse, and spurred by the prospects of powerful biomedical and electronic technology, a new branch of physics seeks “as-yet-undiscovered organizing principles … at the mesoscopic scale” (Laughlin et al. 2000). Those principles reside in “protectorates”: regimes of behavior that are insensitive to (protected from the fickle details of; but also containing literally no information about) the details of the inner-scale underpinnings. The idea of such emergent laws of nature has a long history (Ablowitz 1939), and a long future: there is no theoretical short-cut to bypass observation and measurement, and utility is measured by “multiscale modeling [, which] relies on physical insight” (Schieber and Hütter 2020). The mesoscale ceiling of physics tractability becomes the approximate but protected floor of chemistry, allowing models to build up toward molecular biology's inner scale, culminating in the triumph of drug design from first (or perhaps second) principles.

In organismic biology, mesoscale form has long been accessible to gross anatomy, and it functions crucially in the scales between cells and organisms. Essentially every form that exists has a function, even the long-doubted appendix which may function as a microbiome refuge for risk-taking omnivores. The word organ, from the Greek for implement or instrument, fits snugly into organism – but also into the less well-defined term organization. In ecosystem biology and social sciences, much looser mesoscale patterns fill the vast scale gap between individuals and populations. Transient groups with limited or garbled communication are at least as common as efficient formal organizations, so not all patterns can be assumed to have a functional purpose (positive or negative), nor even salience.

1.2 Meteorology's mesoscale convection problem

In meteorology, wet weather and cloudy climate define cared-about Grand Challenge domains of function, where we desire better understanding and predictive power (Bony et al. 2015). Myriad mesoscale patterns of convection fill the gap between our outer scales (geographical, or at least deformation radii set by Earth's rotation rate) and some inner scale we try to draw a line at: “cells” about as wide as the depth of the convecting layer, or perhaps the (groups of) bubbles or thermals that comprise them (Morrison et al. 2020). Meteorology's challenge, most obvious in the tropics, is to formulate a moist dynamics for largescale flows that somehow takes the full reality of the mesoscale-patterned convection process into account. Parameterization (in its broadest intellectual framing; see lucid reviews by Arakawa 2004 and Rio et al. 2019) is our analogue of the drug-design problem, but we still don't know what aspects of mesoscales require consideration, or what facets of observations bear on these grand challenges.

This article's overarching question is: Can we relate some aspects of mesoscale form — that is, the easily seen but hard to quantify non-randomness of cloud scene patterns — to their function in larger-scale moist dynamics? Progress will require careful definitions, in part to set aside the many questions we are not asking. As a Review, the goal initially is to classify existing research, but hopefully it may serve as a useful spring-board for proposing or prioritizing future research.

One challenge is how to bound or define “the convection process” at all, since the correlation of buoyancy with ascent is the ultimate driver of all atmospheric motion, and occurs on many scales, both vertical and slantwise. The related computational problem of numerical model resolution (whether spectral or grid) ends up drawing its main cut by horizontal wavelength. If convective drafts were very wide and laminar there would be no problem, so convection is (partly) a high-wavenumber or “small scale” problem. If drafts were infinitely narrow and utterly random like the molecular motions subsumed in continuum mechanics, the problem would simply reduce to tallying their sum, in a smoothly varying way whose key closure step is a “dispatcher function” (from Section 4 of the seminal Ooyama 1971). Middle scales seem to be the nexus of difficulties, both practical and conceptual.

When in doubt, consider observations. Early hints of cloud mesoscales, far larger than the visibility limit as seen from any one point, could be inferred from time sequences. Later, aircraft and RADAR gave better glimpses of the breadth of convective clouds and precipitation. But satellites really blew the lid off the sky. Mesoscales were revealed to be “less a reincarnation of creatures from dreams than from nightmares”, impelling a “Fourth School of Thought” (Zipser 1970). Mesoscales cover about 3 orders of magnitude (labeled meso-α, β, γ by Orlanski 1975, or maso-, meso-, miso- by Fujita 1981). Boundary-forced mesoscales may be distinguished from those internally generated, which may be further divided into upscale processes (self-organization) vs. downscale size-reduction processes such as tracer filamentation by confluence in large-scale flows. By now satellite observations of clouds and cloud systems are so routine that the descriptive stage of our topic is arguably complete, well enough encapsulated in textbooks (e.g., Cotton et al. 2011; Trapp 2013; Houze 2014). But how can we understand the implications of those forms and patterns for scales other than the directly observed opaque patches?

Equally bewildering is meteorology's diversity of function-defining larger-than-cloud scale phenomena. Rotational disturbances span a few Rossby deformation radii, meaning the entire equatorial waveguide (out to perhaps 15° for deep disturbances) although sometimes collapsing to just a few troposphere depths in tropical cyclones. Divergent or wavelike convectively-coupled motions exhibit a continuum from planetary (around the equatorial waveguide) down to cloud connectivity scales, where they join nongeostrophic swirling flows in the messy mesoscales that make up Zipser's “nightmares”. It becomes rather arbitrary (but thus a tool in our hands!) where to draw the line between the convective process and the definition of function. Physical regimes (based on the relative sizes of mathematical terms) offer one useful domain for categorization (e.g., Craig and Selz 2018). One sometimes incisive decomposition is balanced vs. imbalanced, based on some measure of how small a local or Lagrangian time rate of change is in relation to physical tendencies (e.g., Raymond et al. 2015). Balance may thus have implications for the temporal persistence of structures, certainly a predictability function we care about, although not uniquely: “imbalanced” propagating wave packets can also exhibit time-extended (albeit nonlocal) identity and predictability (e.g., Straub et al. 2006), competitive with tracer-defined balanced circulations (Adames et al. 2019).

Such physical regime decompositions are not straightforward to discern in data: by any definitions, observed weather scenes co-mingle multiple scales and mechanisms and phenomena. If these are merely superposed (additively decomposable; that is, non-interacting), then simple linear filters (like Fourier analysis) might suffice to also discern physical regimes. But if different wavenumbers are strongly interacting, whole sets may need to be viewed as indivisible elements of some higher-level family of multiscale structures obeying Laughlin and Pines' “as-yet-undiscovered organizing principles … at the mesoscopic scale”. Our challenge may be analogous to biology's epic journey to systematics from its merely-descriptive taxonomy phase, with cosmetic similarities but cosmic differences in meaning.

One contemporary challenge motivating this review is how to better justify the cost, and best utilize the results, of special targeted observational campaigns in a maturing post-exploratory science. As the novelty of discovery and description tapers off, sample size requirements rise steeply and representativeness questions come to the fore (Hirose et al. 2017). A parallel challenge is how to justify the cost and best utilize the results of high-resolution numerical simulation. Prioritizing between these two parallel approaches is a delicate subject, but seems unnecessary as their distinct technology stacks sustain a basement level of support for each. Towering above that basement is a third motivating goal, the hope of robust observation-model synergies. We could call that synergy assimilation in its broadest sense, noting that its pinnacle is not merely another gridded data product but some deeper synthetic understanding of scale and process relationships, deduced from efforts requiring both types of activity. An exploding new toolkit for all this data-intensive multiscale work is machine learning, which offers agnostic ways to get a handle on patterns and features, even as their meaning remains to be interpreted and labeled by humans–a huge improvement on hand-crafted morphometric algorithms measuring only the connectivity of threshold-exceeding pixels.

1.3 Nomenclature

a. Macrofunction, microfunction, and form

The definition of function is based on practical goals. Our ultimate macro-function goal is to understand the behavior (or the “moist dynamics”) of the comprehensive convecting flow, especially the larger scales for which temporal predictability is longer and practical impacts are greatest. While detailed understanding is impossible for our low-dimensional minds, the aspiration still orients our overall enterprise. More partial or micro-function goals, like quantifying budget terms at an instant, are only as satisfying as the intellectual project of reductionism they are a part of: can one re-assemble the whole with useful accuracy after breaking it down into parts? For such reconstructive reasoning to be useful, the basis set for decomposition should ideally be complete and mutually exclusive. Micro-function's basis set of terms in the governing equations meets this test, and can be integrated over neighborhoods coarse enough to summarize mesoscale patterns yet fine enough to resolve the large scales, thereby discriminating macro-important from unimportant details. It connects directly to our digital modeling frameworks, providing a robust pathway back to synthesis (macro-function). Indeed, the intellectual and engineering problems are closely related, although not identical (Arakawa 2004). But micro-function still does not fully express the interactive role these tendencies play in moist dynamics across time.

Not all sets of micro-function measures are as satisfying. For example, Fourier decomposition is complete and orthogonal, yet its physical relevance is debatable. Consider a physical system in which some large-scale envelope process truly modulates the amplitude of a small-scale oscillation. Fourier decomposition depicts this situation as mere interference (beating) of two high wavenumbers, with no low wavenumbers present at all! Careful thought is needed to devise useful decompositions, whose non-uniqueness requires us to simply commit (albeit provisionally) to a framework.

Defining relevant measures of mesoscale form or pattern is even trickier. Fourier decomposition's patterns live not primarily in power spectra, but rather in relationships among values in the phase spectra, which we have no interpretive or even perceptive or graphical tools to help us decode, other than partial or modified reconstructions into physical space. Morphometric algorithms for connected cloud blobs can easily slip into fussy many-parameter procedures tuned to match preconceptions, belying their putative objectivity. Classification by machine learning offers data-driven and agnostic techniques (e.g., Denby 2020), but interpretation still falls back into human hands and minds and tongues. The poorly-defined and overused word organization spotlights our challenge. Is every non-randomness (such as mere conglomeration) deserving of the term, or only certain facets or aspects? This form-function relationship question can only be addressed after form is somehow characterized, and poor characterization severely limits the prospects.

b. Systems nomenclature

A system is defined by its boundaries. If the boundaries are too arbitrary, or too changeable over time, labeling the contents a “system” can be unhelpful or even counterproductive. Systems can be divided into conceptually-smaller (that is, less inclusive) subsystems, or combined into supersystems. A system has sensitivities and impacts, which together comprise its responses (these are micro-function measures, such as budget impacts and their conditionality). A system's response characteristics are not easy to estimate from observations if it is intimately coupled to other systems, either directly or via mutual coupling to some overarching main supersystem (for more discussion see Mapes et al. 2019). One role a subsystem can play is adjustment, if it is deterministically responsive to larger-system variables with a timescale much shorter than the cared-about evolution timescale of that larger system. Readers will recognize the notion of “convective adjustment” of an air column, or its generalization as “quasi-equilibrium” (Arakawa 2004). Subsystems can also play the role of a forcing, if they have impacts without sensitivities. A fast subsystem, with shorter timescales than the main system in question, may act as stochastic forcing, treatable for instance as white or colored (autocorrelated) noise. Here may lie one macro-functional role for mesoscales (Berner et al. 2017, Section 2.6 below).

For our meteorological mesoscales, is the visible edge of cloudiness or radar echo a useful system boundary? In its defense, hydrologic and radiative effects are intensely concentrated inside contiguous clouds or echoes (e.g., Li et al. 2020). But such a system is intimately coupled to an invisible embedding system — clear air — like a hand in a tight glove. That invisible complementary system is knowable mathematically, if hard to see and unintuitive: its motions consist of internal waves in the stratified environment, obeying constraints known as dispersion relations. Our macro-functional challenge of understanding moist dynamics encompasses this complementary pair of sub-systems, so it is neither wholly observable nor wholly mathematically tractable. One creative new numerical approach to treating this intimate coupling, numerically at least, is multi-fluid modeling (e.g., Thuburn et al. 2018).

In systems terms, our form-function problem is sometimes viewed as being 3 or 4 hierarchical scales deep. For instance, in Fig. 2 of Moncrieff and Klinker 1997, a synoptic-scale weather entity defines macrofunction, and it contains an ensemble of mesoscale convective (sub-)systems (MCSs; Houze 2004, 2018; Schumacher and Rasmussen 2020), comprising in turn two kinds of sub-subsystems: (1) convective cells, and (2) the associated, contingent precipitating stratiform anvils (Houze 1997), fed by the cells which act as “particle fountains” (Yuter and Houze 1995). A cell (from the Latin for an enclosed room) actually comprises a multitude of sub-sub-subsystems, conceptualized as bubbles or thermals (e.g., Morrison et al. 2020), so this “cell” discretization is a rather loose borrowing from the truly walled structures of biology.

c. Probability notation

Probability notation is profound in its simplicity. Let F represent some multivariate (bold face) micro or macro measure of function, normalized by the amount of convection (for instance, per unit mass flux, or per unit rainfall production). Let f denote some multivariate measure of mesoscale form: typically some definable and measurable aspect of the observable cloud or radar echo field. Case studies of pattern (form), if sampled representatively, yield the marginal probability or frequency distribution or density p(f). For instance, Houze et al. (1990) classified radar echoes from storms into a few discrete categories, forming a distribution which could if desired be further decomposed as a probability density over some continuous characteristic like size. The marginal distribution p(F), again if sampled representatively, describes the occurrence frequency of function measure F. These marginals p(f) and p(F) are merely two shadows (strictly, integrals) of the majestic joint distribution p(F, f). Conditional slices of that joint include p(F | f), addressing questions like what are the functional impacts (or at least associations) of squall lines as opposed to nonsquall systems?, and p(f | F), addressing questions like what kinds of convective cloud systems are associated with major forecast busts?

The vertical bar | in this notation, pronounced “given”, has an open-ended right-hand side (RHS) which ideally should be elaborated to include every important conditionality, both structural (framework-related) and narrow (within-framework parameters). In order to combine disparate studies into a growing corpus of knowledge, for our aspirational “form-function understanding”, the list of important dependences should ideally be standardized. A comma-separated list is often used for narrowly explicit variables, like the mean convection amount we wish to normalize by; then, semicolon-separated entries express higher-level conditions or parameters, such as upstream screening and conditional sampling, or essential model domain and boundary condition choices. Many statistical confusions and puzzles (e.g., Simpson's paradox) can be traced to the temptation not to clutter our symbolic expressions with such extended lists of conditions. Even when critically important to the results, these conditions are often left implicit, with the key choices buried in methodology sections, making literature syntheses and meta-analyses very labor intensive.

Finally, it is important to remember that questions of causality's direction, the true heart of scientific knowledge, would not be answered even by a complete and perfect p(f, F) of simultaneous associations. Causality methods require the use of graph theory, the language of network science, a visually oriented yet rigorous mathematics with a real grounding in matrix algebra and its solver technologies. A subset called directed acyclic graphs (DAGs) and a related docalculus underpin the inference of causality, introduced in the recent accessible nofiction Book of Why (Pearl and McKenzie 2019). While predictive sciences like ours can tolerate merely-associative descriptions or garbled causality arguments as part of our knowledge base better than robotics (where infamous fails make good reading), we could still benefit from better tools to spotlight underlying causal pathways (e.g., Samarasinghe et al. 2019; Hirt et al. 2020).

d. Partial derivative notation

Another notation for expressing relationships often translated semi-causally as “dependencies” is partial derivatives, like the Jacobian matrix ∂F_i /∂f_j. These assume local linearity (Calculus' differentiability) of possibly-nonlinear structure in p(f, F), but differential geometry tells us that atlases of such locally-linear maps can suffice to express the structure of a round world or other abstract curved manifolds. As in probability notation, the vertical bar pronounced “given” is available, but often neglected; especially out in the semicolon list of framing assumptions. Derivative with what held constant, and at what values? In our familiar fluid dynamics vector calculus, these are rarely specified, except when an unusual coordinate metric is used in the vertical, but they are encountered more in thermodynamics and are crucial in abstract spaces (Nolte 2010) where orthogonality becomes meaningless. For illustration, Mapes et al. (2017) elaborated the radiative kernels of Soden et al. (2008) and several other “importance” metrics of water vapor as highly-annotated partial derivatives, and Mapes et al. (2019) used such notation to express why simple regressions of field data are not estimates of the quantities needed for convection parameterization, despite having the same physical units and even comparable magnitudes. Definitions of “susceptibility” to aerosols also beg for more clarification (e.g., Sorooshian et al. 2010) in the midst of many possibly co-varying causal factors (confounders). In this view, form-function relations look like [∂F_i /∂f_j ]_{amt;condition1;condition2;…}, where amt means amount of convective activity (e.g., rainfall; 4 mm d⁻¹ < amt < 5 mm d⁻¹) and “condition1, condition2, …” stand for the specification of everything that matters. This derivative's value can differ utterly from unconditional or differently-conditioned derivatives, or even from those merely evaluated at a different value for amt.

1.4 Roadmap to rest of document

Section 2 postulates a set of hypotheses about the functional importance of mesoscale structure. Section 3 introduces a tabular landscape of research approaches. Sections 4–7 survey that landscape, noticing where a (very incomplete) sample of the literature may fit. Section 8 summarizes, and revisits Section 2's hypotheses in that light. Section 9 revisits the article's top goals, spotlighting where study gaps or new capabilities suggest opportunities for future research. A glossary of all acronyms can be found in Table 3.

2. Hypotheses about the functional importance of mesoscale structure

To focus further discussion, consider the following postulates about the larger-scale importance (or function) of mesoscale pattern or form in deep convective cloud fields. As notated above, our goal requires normalizing by the amount of activity. Highly active or disturbed weather scenes are often perceived as more organized purely for that reason, but clarity requires disentangling these aspects carefully, just as biologists compare the function of microbes vs. elephants on a per-unit biomass or energy flow basis, or ecosystem productivity on a per square km basis. Net precipitation or cloud-base mass flux are common bulk measures of convection amount, and in practice the nonuniqueness of such arbitrary definitions should be bracketed for robustness.

2.1 Null hypothesis: Mesoscales are unimportant

Postulate: For a given amount of convective activity in an area, its mesoscale pattern is unimportant to averaged micro-function measures, and therefore to all resulting macro-function (emergent behaviors).

By treating this as a null hypothesis, the burden of evidence is shifted to more ambitious claims, but some supporting words are appropriate. Convection parameterizations with one or a few entraining plumes embody this null hypothesis. While the shortcomings of such schemes are many and familiar, do any of those failures directly indicate that mesoscale structure needs to be parameterized, beyond a democratic impulse to “represent” things because they exist? This null hypothesis's plausibility is evidenced most strongly by the significant successes of small-domain super-parameterization (SP) methods, with large unrepresented mesoscale bands or spectral notches of permitted scales (Pritchard et al. 2014): every size of eddy motion between the nested-domain span and the coarse-grid spacing is mathematically forbidden, discussed further in later sections.

2.2 Rectification of nonlinearities with conglomeration

Postulate: Nonlinear process dependences produce rectified effects in spatial averages over agglomerated (closer-than-random) mesoscale arrangements of a given amount of convective cloud activity.

Nonlinear terms in the governing equations foreseeably create micro-function (area-averaged time tendencies) impacts of conglomeration, an agnostic word chosen to sidestep the stack of implied assumptions characterizing the recent literature boom on convective “aggregation” (Wing et al. 2017; Wing 2019). Conglomeration or agglomeration of pixels into objects is measured by contiguous touching (e.g., Liu et al. 2015); then further by distances between spatial-domain networks of objects (e.g., Weger et al. 1992), and by various hybrid algorithms (e.g., Tobin et al. 2012). Radar data studies use similar measures and metrics (e.g., Retsch et al. 2020). Such conglomeration measures are quite nonunique or arbitrary (Xu et al. 2019). While standards would be desirable, locking in the historical artifacts of early work may hold back progress. Perhaps a supervised machine learning exercise on a set of cloud scenes labeled by the value of some function measure could discover new measures of form in those scenes that are more salient than these simple tallies of pixel clusters, whose strongest justifications rarely transcend the virtue of algorithm-writing convenience.

Whatever the measure of conglomeration, four major nonlinearities produce rectified impacts:

(1) The same amount of cloud has less radiative impact if it is agglomerated than if it were randomly spread out (and thus exposed to unattenuated radiation), creating a clear radiative dependence on cloud object size (e.g., Noda et al. 2016).

(2) Like photons, falling hydrometeors obey non-linear process equations for collection, re-evaporation, etc. As a result, the overlap and conglomeration of a given amount of cloud water and unsaturated air govern “precipitation efficiencies” and related quantities (e.g., Sui et al. 2020).

(3) The strength of horizontally divergent winds, linked by mass continuity to the vertical drafts of convection, depend on conglomeration of those drafts' kinematic divergence. Windspeed rectifies in the non-linear formula for surface flux (e.g., via a “gustiness” effect, Harrop et al. 2018). Rotational winds spun up by the time integral of such divergent flows further amplify this conglomeration dependence, with tropical cyclones as the extreme case. Cyclones undeniably deserve the moniker of organized, and even deserve human names.

(4) Vertical eddy flux is the integral of the nonlinear product of deviation w with other scalars. All Fourier scales below the filter scale used to define eddies (and thereby their aggregate micro-function) contribute to this flux. Therefore, mesoscale wavenumbers contribute.

2.3 Stratiform precipitation and top-heaviness of heating

Postulate: The area-averaged profile of deep convective heating is more top-heavy when a given amount of convection is more agglomerated.

Stratiform precipitation associated with deep convection makes a distinctive contribution to the net heating rate profile (Houze 1989; Johnson 1984, 1986): a vertical dipole component, delayed by some hours after the vertical monopole component, which makes “the net heating profile of the MCS … top-heavy in proportion to its stratiform rain fraction” (Houze 2018). This hypothesis encompasses an observationally-described coherent bundle of the effects in the previous section. The most obvious physical mechanisms of top-heaviness are evaporative cooling of raindrops in the unsaturated lower troposphere, and anvil cloud base absorption of upwelling longwave radiation. But latent heating in the ascending flow in mesoscale anvils contributes importantly, a flow-dependent or feedback effect that begs the ckicken-and-egg question of why the air is ascending. Whatever the causality, stratiform rain fraction is an easily observable index of this top-heaviness, and is observed to increase with conglomeration size as cited above. That trend may be as much dynamical as microphysical, as the increase continues well beyond the scales of contiguous cloud objects (Inoue et al. 2020).

2.4 Special momentum flux properties of squalls

Postulate: Squalls produce up-shear momentum flux or up-scale kinetic energy (KE) flux.

Another special bundle of nonlinear rectifications is the impact of products ρw′u′ and ρw′v′ in horizontal momentum budgets, a showcase micro-function effect of mesoscale organization. (Density and velocity symbols are customary, and ′ denotes deviations from a filter scale mean). Air parcels on sloping streamlines comprise a vertical flux of horizontal momentum that differs systematically from upright streamlines, giving tilted squalls in shear an up-gradient flux (LeMone et al. 1984). In kinetic energy (KE) terms, this is an up-scale flux to larger scales (e.g., Yang et al. 2019). Its emergent macro-function role can be dramatic in two dimensions (2D): waves and convection and shear conspire to generate slowly vertically-propagating wind layers in both stratosphere and troposphere, coupled to correspondingly differently-tilted 2D convective storms (Nishimoto et al. 2016). It remains unclear how relevant this result is to 3D moist dynamics, as 3D convection tends to be a downgradient flux or drag on large-scale winds (e.g., Mapes and Wu 2001).

2.5 Different local instability to organized vs. scattered storms

Postulate: Different mesoscale forms of convection have different instability conditions for their occurrence, important to subsequent moist flow evolution as well as to local storm meteorology.

Stated another way, an atmosphere with given thermodynamic and wind profiles may be stable with respect to convection of one form, but unstable to another. Stated a third way, if we view convection as a process that adjusts the atmosphere toward a “neutral” state, that neutrality condition may depend on whether and how the convection is organized, not merely on the internal assumptions of a zero-buoyancy plume as used in equilibrium models of tropical climate (Singh et al. 2019). Just as Riehl and Malkus (1958) inferred the existence of “hot towers” from gross aspects of mean sounding profiles, slight features of the mean stratification may encode some information about the organization of convective activity within the “waveshed” feeding into the environmental density profile at a given location (Fig. 14 of Mapes 1998; Mitovski and Folkins 2014). The “entrainment dilemma” of Mapes and Neale (2011) has this mean-state effect of mesoscale organization as one of its horns, raising the question of whether and how we need to parameterize organization (Ahn et al. 2019; Park et al. 2019).

2.6 Temporal effects

Postulate: Mesoscale organized convective patterns or entities have longer temporal persistence than the same amount of more isolated cumulonimbi.

At least three functional consequences (sub-postulates) may be anticipated:

a. Different adjustment timescale, overshoot

Postulate: Convective adjustment time may be organization dependent.

Within the adjustment paradigm, and besides having a different “neutral” target state, organized convection might approach its target at a different rate, or overshoot it due to some form of mesoscale “inertial” or “memory”, mechanical or thermal (Colin et al. 2019). In one recent example, Trapp and Woznicki (2017) examined long-lived supercells as agents of adjustment. A pitfall of this reasoning is that permitting both target and timescale to be organization-dependent may make the adjustment concept itself too ambiguous, an invitation to overfitting and/or overinterpretation, especially in the absence of any independent definition of organization.

b. Effects on predictability

Postulate: If mesoscale storms rather than cells act as the basic unit of convection, their average effects as felt by larger-scale flow may be less deterministic, and/or subject to stochastic noise with a longer decorrelation time.

Predictability is an important macro-function measure of large-scale moist flow that could depend on form, both through how signals evolve and through the character of stochastic noise. One view is embodied by Zhang et al. (2007), where mesoscales are viewed as “stage 2” of a cascade-like or upscale difference growth (error growth, in the case of a prediction), with skill-eroding new information moving from convective to synoptic scales. Taking a maximal version of this view, excluding mesoscales could actually improve large-scale predictive skill, as has been claimed in the ocean where they are called “submesoscales” (Sandery and Sakov 2017). Evidence against this view is that super-parameterization (SP) with missing mesoscales (as in Pritchard et al. 2014) does not outperform full-spectrum explicit convecting-flow modeling (Miyakawa et al. 2014) in intraseasonal forecast skill (Kim et al. 2018). Apparent upscale growth (left to right on a variance vs. wavenumber plot) is tricky to distinguish from up-amplitude error growth at each wavenumber toward a saturation level with a sloping dependence on wavenumber (e.g., Mapes et al. 2008).

When “skill” is measured probabilistically, truly realistic noise actually increases it (Berner et al. 2017; Subramanian and Palmer 2017). Stochastic noise from deep convection can be formulated and estimated in many ways (e.g., Lin and Neelin 2002; Shutts and Palmer 2007; Keane and Plant 2012; Tan et al. 2015; Shin and Park 2020), but its relation to mesoscale form is not clear. Even though mesoscale storms are observed to be longer-lived than their cumulonimbus cells, that is not salient evidence: they could still have smoothly continuous sizes and lifetimes that might be governed by larger scales just as deterministically as isolated cells are, or even more so if their supply or “dispatcher function” is more reliable and steady.

c. Propagation across functionally large scales

Postulate: Storms with long lifetimes can travel distances much larger than their meso body size: that is, distances salient to our definition of function.

Even time-mean climatology on grids that don't resolve mesoscales is discernibly shaped by mesoscale storm form. Examples include the classic nocturnal rain maximum in central North America (Wallace 1975), the width of intertropical convergence zone (ITCZ) rainfall (Nolan et al. 2016), or the climatological stripes in Amazon precipitation attributable to diurnal strengthening of multi-day propagating bands generated along the eastern coast (Garstang et al. 1994; Garreaud and Wallace 1997). If diurnal timing is itself considered macro-function (after all, it is predictable over long times and consequential), its dependence on MCS form (lifetime and size) counts as another example (Sakaeda et al. 2020). Of course these effects would apply to other macro-function behaviors beyond climatology as well.

2.7 Representativeness and assimilation challenges

Whatever its contribution to moist dynamics, mesoscale patterning of vigorous entities reduces the representativeness of local observations in large-scale data assimilation. Even if the predictability horizon for imbalanced mesoscale structures is shorter than one's macro-function interests per se, accounting for this consequence of their persistence in assimilation systems could improve analyses (initializations) of the predictable large-scale manifolds of moist dynamics.

3. A literature survey framework: From theory to observations

Studies have addressed the above hypotheses and mechanisms in many ways. In an attempt to categorize and hopefully organize such efforts, this section offers a tabular landscape of research approaches. In this landscape, columns range from pure theory to pure observations, while the rows span the more conceptually vertical questions on the form (bottom) to function (top) axis, with intermediate rows for form-driven vs. function-driven inquiries about their relationship (Fig. 1).

Fig. 1.

A two column by four row conceptual space for categorizing where research studies fall in regard to how they address the form-function relationship. Inside both main columns, a shared sub-axis spans an abstract range from conceptualied to literal instances. See text for details.

The right-most edge on Fig. 1 represents pure observation, but the whole right half involves events on Earth's natural history timeline, meaning that they all necessarily have an ingredient of case-specific observations within them. Numerical weather prediction (NWP) activities are more conceptualized or theory-containing than pure observation, especially at low resolution (LR) where more processes are parameterized, so they are depicted to the left of Case obs. The most conception-entangled research activity in this realm is the single column model (SCM) forced in some way with observational data (e.g., Randall et al. 1996). Meanwhile, on the far left edge of Fig. 1 lies pure theory, timeless in its claims. Free-running numerical simulation lies to its right: time dependent (with instances), but on a Timeless, or arbitrary timeline as indicated. LR and HR again stand for low and high resolution, in a way that parallels the overall left-right axis (from conceptualized to explicit to realistic). Composite or Mean obs approaches yield instances, but on an arbitrary (event-relative) timeline and minimally conceptualized, on the far right of the Timeless half of the space. While many studies use multiple methods from both arbitrary and natural history timelines (e.g., theory and observations), sub-efforts may still be usefully distinguished in this way.

The vertical axis of Fig. 1 has pure Form at the base. In observational studies, form appears through description, or perhaps its categorical generalization, taxonomy. In some model studies, form is subject to control, including unwanted controls such as lateral boundary conditions. At the top is pure Function, distinguished into Macro- representing across-time behaviors vs. Micro-, commonly involving estimates of instantaneous budget tendencies in our temporal differential equations. Sandwiched between these are rows of questions, asked in the bottom or top of their table cells to exhibit their close associations with adjacent rows labeled Form or Function.

3.1 Illustration of categories with early meteorology ideas

To illustrate the use of this conceptual landscape, Fig. 2 shows a numbered list of classical research approaches to questions of convective form and function, prior to radar and satellite data and the easy digital capability to construct composite averages. Instead, Imagination is depicted as mediating between theory and observation. While imagination remains crucial today, it is now covered by formal constructs that lend a thicker gloss of apparent objectivity to Fig. 1's column labels.

Fig. 2.

Early meteorological knowledge placed in the landscape of Fig. 1 for illustration. Without computation, observations, theory, and imaginative synthesis led the way. Numbers indicate the order of mention in the text.

Observations are numbered 1, reflecting the primacy of observers' attempts to categorize visible cloud form and the time course of weather events they experienced. Macro-function interests (like predicting wind for global sea voyages) spurred initially-descriptive work at large scales like climatological wind mapping (2). Meanwhile, laboratory-grounded theory about air and water (3), a micro-function line of inquiry, paved the way for theories of airflow on a differentially heated gravitating sphere (4), and also of the gravitydriven vertical instability (5) of parcels (a crude version of moist convection's form). A macro-functional theory about convection (6) is that it behaves so as to neutralize that instability. More-detailed theory, requiring Imagination, asked questions about multiscale views of convection like turbulence ideas (7). A very imaginative culmination of pre-satellite knowledge is expressed in the fascinating 1958 painting (Fleming 2007; reproduced as Fig. 3) predicting how Earth's clouds would look someday from space (8).

Fig. 3.

A 1954 painting anticipating what weather would someday look like from satellite altitudes. (Fleming 2007; a high resolution version is available at https://www.nesdis.noaa.gov/sites/default/files/wexler3.jpg.)

3.2 Today's landscape of tools

With the new abundance of radar and satellite observations, further developments in theoretical meteorology, and vast growth in digital informatics and display, modern research activities can be distinguished into at least 7 gradations along the left-right subaxis from conceptualized to instances, in both arbitrary and historical timelines (Table 1). Case observations (column n) invariably exhibit mesoscale form in their instances, distorted only by observability biases and selection effects. Leftward of that (columns m to h, expressed as a list in Table 1), historical weather events are increasingly seen through the lens of concepts and mathematics, toward SCMs with nothing but assumption-laden parameterization schemes. Columns a–g parallel columns h–n almost exactly, but freed of the specific time of history.

Rows in Fig. 4 are as in Fig. 1, but formally splitting micro- vs. macro- function and described vs. controlled form. The result is a 7 × 6 table for categorizing research efforts on our title topic. The grand challenge of form-function research is to synthesize the lessons of all these approaches, in order to test and refine and extend the hypotheses of Section 2, toward the goals expressed in Section 1.

Fig. 4.

Fully elaborated conceptual review space or landscape, after Figs. 1, 2 and Table 1.

Figure 5 is a road map to how Sections 4–7 below traverse the landscape of Figs. 1–3 and Table 1. Conditionally sampled studies are discussed in Sections 4 (screening by form) and 5 (screening by function); these lie closer to instances (toward the right of their timeline category). Controlled experimentation is considered in Sections 6 (manipulating form) and 7 (manipulating function), the framing of which necessarily implies a conceptualized framework (more toward the left of their timeline category). The questions about form-function linkage (central rows, empty in Fig. 5) are sometimes not asked explicitly in studies which may be nonetheless salient to them.

Fig. 5.

Road map of Sections 4–7 in the conceptual landscape of Fig. 1.

4. Conditional sampling of form: The pioneers' path

Subsection 4.1 considers form-driven case observations (box (n) of Table 1) where our science necessarily began (Fig. 2). The soon-noticed ubiquity of mesoscale structure spurred thought both upward, toward questions of its averaged micro-function (Houze 1989), and leftward on the long road toward theory. Subsection 4.2 considers observation-like sampling from huge HR simulation outputs, paralleling the pioneering path in observations.

4.1 Conditionally sampled case observations

The impoverished mesoscale imagination in Fig. 3 (except for a tiny hurricane near Puerto Rico and perhaps orographic cloud bands in western Canada) was blown open by satellite meteorology. The term “cloud cluster” (Martin and Suomi 1972) was coined for contiguous high-cloud “shields” up to 1000km in size, marking but hiding the details of mysterious convective events. Expeditions with aircraft culminated in brilliantly-deduced schematics of mesoscale entities too big and cloudy for direct visual experience (Malkus and Riehl 1964; Zipser 1969). In lucky instances, instrumented aircraft have revealed unbroken updrafts > 10 km in width: slabs of cloudy air can themselves ascend as a mesoscale updraft, even as they are internally convecting and turbulent (Zipser and Gautier 1978; Fig. 16 of Mapes and Houze 1992; Bryan and Fritsch 2000).

Larger campaigns with portable research RADAR revealed (Houze and Betts 1981) that cloud clusters contain contiguous echoes or “mesoscale precipitation features” over 100 km in size (Leary and Houze 1979). These MPFs and their dressing of cloudy air were further elevated to convective “systems” (MCSs, Zipser 1982; Houze 2004, 2018), although they are certainly very open systems as discussed in Section 1.3b. The noun “complex” (MCC) of Maddox (1980) refers to a rare subset of MCSs with especially large sizes and close-to-round shapes. Tropical dynamics “must reckon with” MCSs, concluded Houze (1982) based on micro-function (budget) estimates of their impacts. That drumbeat of observation-based experts reminding theorists and parameterization schemers of the ubiquity of mesoscale form, and cautioning against its neglect, seems perpetually necessary.

A full “reckoning” would require a richer basis set of salient quantitative paradigms, along with a corresponding “dispatcher function”, extending Ooyama's size-discriminated bubble launcher in space and time, or a “closure” condition if these systems are ascribed telos, a role it is their defining job to perform. Our main rigorous mathematical paradigm for mesoscale deep convection is a two-dimensional (2D), steady overturning flow (e.g., Moncrieff and Miller 1976). Fully nonlinear equations become tractable under this idealization of space-time structure, culminating in theory's triumph: closed analytical solutions. Bolstered by the numerically demonstrated possibility of such (statistical) steadiness in 2D (Fovell and Ogura 1988), anchored further by partial theory centered on the local gust-front dynamics (Rotunno et al. 1988; Bryan and Rotunno 2014), this rigorous “archetype” (Moncrieff 1992) lacks only a guide to how it may apply in realistic settings. Even retreating from that strict-2D rigor, the Leading Line Trailing Stratiform (LLTS) form of “organization” remains the leading MCS paradigm, for good reasons. It is fairly frequently observed, and very convenient to depict on the 2D pages of our discourse. Indeed, the word nonsquall had to be invented for the many MCSs that are far from 2D or steady (Houze et al. 1990; Parker and Johnson 2000), sometimes labeled as “unorganized” or “disorganized” (e.g., Zhang et al. 2019).

Circular-shaped mesoscale form paradigms also exist, from tropical cyclones to the weaker generality of mesoscale convective vortices (MCVs), with several foreseeable mechanisms for longevity and evolution (Raymond and Jiang 1990). The combination of MCVs with squalls is “bow echoes” with “bookend vortices” (Weisman 1993). Efforts continue to account for such mathematical entities, or at least tilted up-drafts and top-heavy heating augmentations of an entraining plume, in larger-scale model schemes (e.g., Donner 1993; Moncrieff et al. 2017).

Conditional sampling of form is facilitated by now-easy image segmentation software, used to isolate and characterize connected-pixel objects in satellite or model data (reviewed in Li et al. 2019), including in the vertical plane (Riley et al. 2011; Xu et al. 2016), in 3D space (Liu et al. 2015; Houze et al. 2015), and in space-time (e.g., Haberlie and Ashley 2018). Statistics of the most convenient measures of form (morphometrics) such as size tend to show broad unimodal distributions of unsurprising character: Small objects are numerous but short-lived, such that rarer, larger, longer-lived ones are also important to integrated impacts. The quantitative details may be of limited qualitative interest, but can be used in lookup tables for empirical schemes like that envisioned in Ahmed et al. (2016). Despite a 16-year record, Hirose et al. (2017) argue a “need for further sampling” to reduce “significant” ambiguity in the rain fraction arising from infrequent large systems, so tabulation and taxonomy remain active enterprises.

The search for a fundamental physical meso-scale has had mixed success. Perhaps the only true mesoscale peak in cloud object size distributions is over Sahelian Africa (Mathon et al. 2002; Hirose et al. 2017), a region perhaps too dry for smaller convective clouds to compete effectively against MCSs, or even to survive. Apparent mesoscale “characteristic” scales of Ricciardulli and Sardeshmukh (2002) or Mapes et al. (2009) are often artifacts of coarsened input data: in a radically fine-structured field like precipitation, the e-folding decorrelation scale is often a few pixels of the data arrays used, whatever their mesh size. In other studies, apparent mesoscale peaks reflect logarithmic binning effects on the size axis, which splits the numerous small system into many bins while pooling larger systems into few bins. While log-size is arguably fundamental, and is what we often mean by scale (meter-scale, km-scale, etc.), it may not correspond straightforwardly to the usual meaning of a fundamental physical scale. Mesoscale object sizes in deep convection remain a mysterious, broadly-distributed factor of several-to-many times the depth of the convecting layer.

Perhaps this spatial mesoscale factor flows from a timescale of several-to-many times the lifetime of convective cells, via a fundamental quantity with space/time or velocity units. One simplest paradigm envisions the mesoscale as how far winds typically carry condensate from decaying cellular “particle fountains” (Yuter and Houze 1995) during fallout, a ratio of horizontal wind to hydrometeor fallspeed. If that horizontal wind is a divergent flow carrying ice out of deep convective tops (Machado and Laurent 2004; Roca et al. 2017), it is close to other velocity scales shaping cell development in multicellular MCSs, mostly at low levels where they are harder to observe, including internal-wave speeds as well as the more familiar gravity-current spreading “cold pools” of downdraft outflow along the surface (e.g., Schumacher and Johnson 2008). All these speeds are broadly in the 10 m s⁻¹ range, near also to the perhaps-surprisingly relevant fundamental physical fallspeed of raindrops in air (Parodi and Emanuel 2009). Extending their surprising arguments, might the several-to-many factor in mesoscales ultimately be rooted in microphysics, such as the ratio of raindrop to snowflake fallspeeds? Statistics of gross ratios of MCS sizes to lifetimes are too crude to be incisive about such a wide range of candidate mechanistic hypotheses; model experimentation will be required.

Vast amounts of data invite the use of a logarithmic y-axis on size distributions as well, which can flatten what modest peaks there may be, driving graphs into visual near-conformance with theoretically alluring paradigms of statistical dynamics (e.g., Ahmed and Neelin 2019). Theoretical stochastic processes offer paradigms for distributions from log-normal (López 1977) to exponential (Neelin et al. 2010) to scale-free Pareto or power laws (Peters et al. 2009). Because such distributions are notoriously tricky to distinguish empirically (Bee et al. 2011), the implied convective process (in the stochastic sense) remains also ambiguous, and hard to interpret physically in any case. Data's deviations or breaks from such theoretical curves may end up telling us more than which one is being deviated from. Awe-inspiring multiscale universalities (e.g., Lovejoy and Schertzer 2013) gesture at conceptual models of vast sweep, encompassing branches of science far beyond our own. The practical value of grand log-log relationships depends on one's accuracy tolerances in the non-logarthmic space where impacts are tallied, and their implications for predictability or other concerns may require more discipline-specific and scale-by-scale elaboration. The maximal version of such theories seems to militate for null-hypothesis like views, not notions of special organization of organs into organisms or systems deserving of the species-like “MCS” moniker.

Conditional sampling of object morphometrics (like size) can be used to screen events, entering into studies of function-related quantities like composite larger-scale fields and their time evolution (Masunaga 2012, 2013, 2014). Multi-object relationship measures can be used to distinguish scenes with similar convection amounts but different degrees of conglomeration (Tobin et al. 2012; Stein et al. 2017; Kadoya and Masunaga 2018; White et al. 2018; Brueck et al. 2020). The ubiquity of satellite imagery allows us to amass large sample sizes of association with even spotty contextual data, such as balloon soundings (e.g., Sherwood and Warhlich 1999; Mitovski and Folkins 2014). If gridded reanalyses are adequate, composites can be made around millions of cloud or echo objects, or around thousands of highly screened conditional samples (e.g., Chen et al. 2017). While the accuracy of reanalysis products can be questioned, the finding of statistically significant relationships with non-assimilated data like cloud and radar imagery prove that at least some observations have blessed the assimilated data product's information stream (column i in Fig. 4), and more-quantitative checks against field campaign data lend further provisional confidence in even vertically-resolved aspects of reanalysis data.

A form-measure for neighbor-distances among cloud objects in their common domain is sometimes termed “convective organization” (Bony et al. 2020). There, an index Iorg of the entire tropical belt (a method borrowed from the realm of mesoscale scene characterization but with the “advantage of characterizing the spatial organization relative to the reference of random organization at all spatial scales”) was shown to be strongly correlated with important climate function measures of the planetary radiation budget (Bony et al. 2020) and precipitation extremes (Semie and Bony 2020). Interpretation of I_org is subtle, however: a careful look at high-I_org and low-I_org example scenes (Fig. S2 of Bony et al. 2020) reveals that the difference is not in the data's object neighbor-measures, but rather in the slightly different null hypotheses to which they were compared. Developers of new form metrics should clarify and distinguish their dependences on meso vs. large scales in the data, as well as on what is taken to define “random”.

More precise and accurate (albeit model-dependent) quantitative studies of MCSs through carefully crafted numerical “real-data” simulations have a venerable history (e.g., Zhang and Fritsch 1988a, b), usually driven by conditional sampling for extremes. Today computing has become so affordable that simulations can cover long routine periods, and their outputs can (and indeed must be) sub-sampled, as described next.

4.2 Conditionally sampling simulations

The above observational composites of function-relevant fields around morphometrically-sampled objects, even if blurred by compositing or hard to interpret, can serve importantly as validation targets for large, free-running explicit-convection simulations (e.g., Inoue et al. 2008; Yang et al. 2017; Senf et al. 2018). Such simulation data are actually better than observations for form-function studies, since both the details of form and the larger-scale function measures are known to perfect accuracy – but only if simulation realism can be first established with some confidence. Such form-sampled composites of function variables range from the pioneering NICAM effort (Satoh et al. 2008, 2019) to multi-model intercomparisons (Stevens et al. 2019, whose Palmer-Turing test from Section 2 of Palmer 2016 asks: do the newly-resolved mesoscale patterns look right?). Some insights from this newly-global mesoscale-resolving modeling era are rediscovering those of earlier limited-area nonhydrostatic modeling (Dudhia 2014). Specifically, it is clear that mesoscale form or pattern is spontaneously generated, but under-determined by fundamental dynamics: its texture is subtly, intriguingly, inscrutably dependent on the remaining parameterizations (of turbulence and condensed particles). For instance, early NICAM sensitivity tests indicated that the global climate function of tropical convection can be fulfilled by either sporadic mesoscale convection or by a few long-lived super-typhoons (Fig. 6, adapted from Miura et al. 2007b). The favored form depended on PBL scheme: “excessive upward transport of moisture at the subgrid-scale was likely responsible for the exaggerated organization of convection”, according to Miura et al. An ecology-like view (“competition” between different convection categories like more vs. less organized for a resource like moisture or instability) appears fruitful for understanding such results. Such eco-reasoning finds social importance in, for instance, the important question of how climate change will affect tropical cyclones vs. ordinary convection (Zhao et al. 2012; Zhang and Wang 2018), or less dramatically of how it may change the distribution of modest rains vs. heavy events.

Fig. 6.

Different solutions for tropical deep convection, depending on what boundary layer scheme is used (adapted from Fig. 4 of Miura et al. 2007b).

Momentum flux is the showcase form-function relationship (Section 2.6), and Miyakawa et al. (2012) is a classic example of form-sampling (selecting long narrow rain bands, inspired by LeMone et al. 1984) and then assessing this micro-function measure (momentum flux by sub-6-degree eddy motions). Because that conditionally sampled flux is found to have a coherent pattern on the scale of the Madden-Julian Oscillation, a possible macro-function relevance (MJO behavior) is suggested by these micro-function results. Such estimates of p(F | f) or its expectation value are conditional slices of the majestic p(F, f) or p(f, F).

5. Conditional sampling of function

Cross-slices p(f | F) can also be estimated from form-resolving model outputs. Besides local micro-function budget terms, obtained from coarse-graining the output data of micro-function quantities like bulk heating rates (e.g., Shutts and Palmer 2007; Brenowitz and Bretherton 2019), historical-timeline (or perfect-model) hindcasts can access a much more desirable macro-function measure: prediction skill. Subsections 5.1 and 5.2 discuss instance-sampling of micro and macro elements of F (each at the far right of its time-line columns in Fig. 5). These lead inquiry downward into questions about the associated form, which still then remains to be characterized somehow into some set of measures f.

5.1 Sampling microfunction: Local budget terms

What forms of convection occur in the presence of given (conditionally sampled) heating or momentum flux profiles? Complementary to the Miyakawa et al. (2012) approach above, Cheedela and Mapes (2019) conditionally sampled HR global simulation outputs (Putman and Suarez 2011) for strong upgradient eddy momentum flux events in sufficiently rainy scenes, focusing especially on the more exotic up-gradient events with their implication of up-scale KE transfers (e.g., Majda and Stechmann 2009). For an ensemble of these strongest events, full-detail 4D hyperslabs were examined by eye to characterize form. Instead of the expected squalls (LeMone et al. 1984), the biggest flux events (of both signs, actually) were found to involve deep convective updrafts arrayed asymmetrically around low-level cyclones embedded in shear. While obvious in retrospect, this unexpected finding required applying the human eye to a dataset big enough to contain and to strongly reinforce surprises. The lesson is that these huge computations offer a valuable source of dynamically-consistent artificial imagination. In other words, such expensively-obtained spatial process articulations may have value beyond increasing trust in their gross averages and other parameterization-relevant statistical summary quantities (e.g., Bretherton and Khairoutdinov 2015).

5.2 Sampling macrofunction: Forecast busts, analysis residuals

Forecast centers closely monitor both their skill and assimilation challenges (mismatches between first guess and observations). Time series of skill sometimes exhibit “dropouts” or “forecast busts”. What causes these failures of prediction? Do certain weather situations present special assimilation (initialization) problems, or is their flow regime inherently less predictable, or both? For European busts, Rodwell et al. (2013) suggest that North American “mesoscale convective systems… act to slow the motion of the trough. Hence, convection errors play an active role in the busts”, a result extended in Parsons et al. (2019) and mechanistically elucidated in Clarke et al. (2019).

Such studies (under “NWP” in Fig. 4) embody a powerful new dialogue between principles and empiricism, wringing enormous research as well as practical value from routine observations. Multi-model products like TIGGE (Park et al. 2008) could further refine such conditional sampling to busts common to many NWP centers, likely to point more to big naturalscience truths and less to the mere shortcomings of any one particular forecast system.

Related research on assimilation challenges can be conveniently done with analysis tendencies (ATs), discussed further in Section 7.2, such as those packaged in NASA's MERRA and MERRA-2 reanalyses (as used e.g., in Mapes and Bacmeister 2012). Examination of cloud-field patterns in satellite imagery sampled around AT extremes could expose whether certain types of mesoscale cloud form occur systematically in association with assimilation surprises—a more local-in-time measure of macro-function than forecast skill, but still a deeper view than budget-term microfunction. Again, form should be characterized, or at least checked visually, to avoid cementing preconceptions or missing truths that might be obvious (once seen) but inconvenient to measure with morphometric algorithms. Machine learning (ML), which is so extremely well developed for imagery nowadays, could also assist in keeping needed agnosticism in this effort to characterize form, in a supervised ML exercise with AT used as the macro-function labeling. Such function-driven work could help sustain and revitalize the hearty exploratory and visually observant spirit of mesoscale meteorology without the logistical overhead of special field campaigns.

6. Manipulating form, evaluating function

Manipulating convection's form is only possible in a model context, and only rather light-handedly if the model is to remain free enough to deliver answers not overdetermined by the intervention itself. For questions of micro-function (Section 6.1), small domains may suffice and manipulations can be rather direct. For questions of macro-function (Section 6.2), larger-domain models with multiscale flow are needed, and manipulations are trickier.

6.1 Measuring micro-function effects of manipulated form

These subsections are roughly chronological, paralleling the rise of computing and methodological sophistication.

a. Initial conditions: The pioneers' path

Early modeling studies, when computing was expensive, often triggered storms with an initial warm bubble in an unstable stratification (e.g., Weisman and Klemp 1984). With mesoscale-sized bubbles, clumps or lines of convection can be triggered (e.g., Weisman et al. 1988), and the evolution or impacts of those larger storms characterized, along with their sensitivity to the initial environment (e.g., Takemi and Satomura 2000). More elaborate input signals were devised by Crook and Moncrieff (1988) to spotlight the importance of external mesoscale convergent forces, not just cell-cell interactions, in sustaining multicellular convective events. The resulting storm-scale meteorology insights did not emphasize larger-scale function, but still their bulk measures of domain averages like rainfall have implications (latent heat release), if only within the artifices of the crude initialization.

b. Domain aspect ratio and shear in equilibrated Cyclic Cloud-Permitting Models

A cleaner mathematical treatment of boundaries is lateral cyclicity, a tactic that enforces conservation and permits longer integrations of ensembles of spontaneously- triggered convective cloud entities in statistical equilibrium with their environment. However, cyclicity also imposes symmetries that constrain convection's form: for instance, in two dimensions, every cloud represents a squall line, infinite in the suppressed third dimension. For a given complexity of physical processes (microphysics, radiation, turbulence), such Cyclic Cloud-Permitting Models (CCPM; cells e, l in Table 1) are characterized by a 5-dimensional computational resource tradeoff among area and elongation (a restatement of x-size and y-size), mesh resolution, integration time, and ensemble size. Form can be manipulated with domain geometry, on a continuum from 2D to isotropic 3D, and also with imposed vertical wind shear. Because of cyclicity, ongoing destabilization processes are also needed to keep convection going, but this can be used strategically as another control process to facilitate clean interpretation of experiments.

Destabilization tactics affect (distorting, but allowing experimental manipulations of) both form and function. These include not only surface fluxes and radiative cooling of the air, but also uniformly-applied pseudo-advective tendencies, both vertical and horizontal, described in subsection c below. When the only forcings are radiative and surface flux schemes (typically with a domain-mean surface wind speed added to obtain sufficient flux), the resulting radiative-convective equilibrium (RCE) paradigm has a venerable history as a clean idealization for climate reasoning. In CCPM experiments, mesoscale pattern impacts on that climate reasoning (e.g., Wing 2019) depend strongly on domain size and shape, and on the assumption of unrealistically weak vertical wind shear to allow the very slow development of clear areas for radiative cooling. Still, it serves as a comparison point for the most concept-entangled model of all: SCM RCE modeling (somewhere between columns a and b in Fig. 4). Carelessly prescribing total vertical motion as a forcing to a CCPM tramples the delicate interplays elaborated in subsection c below, a gesture to making some use of observations (e.g., Randall et al. 1996), but one that verbally cements a misinterpretation of the coupled-system observations used to construct that forcing.

More-idealized prescribed forcing can yield more insights. In one early study, the form of simulated convection was altered systematically by sustaining a vertical wind shear (Xu et al. 1992) while multi-day cycles of vertical advection-inspired strong destabilization were imposed. Under such overwhelming forcing, the convection's only freedom to respond to shear's effects on its form was via modest time delays, but that mechanism has a grain of relevance (Section 2.6). Grabowski et al. (1998) used domain geometry (2D vs. square 3D) to impose form, but again the forcing determined most function measures, except eddy momentum flux (Mapes and Wu 2001). Shear's effects on form itself, within a steadily forced RCE, were characterized in an isotropic 3D domain by Robe and Emanuel (2001). The only function-relevant responses they could measure under such unconditional forcing were slight differences in the equilibrated mean profiles (salient to Section 2.5), along with eddy momentum flux, but these offer clues to form-function relationships.

c. Toward macro-function: Parameterized large-scale dynamics

Parameterized large-scale dynamics (PLSD) methods add another interactive term to the uniform-across-the-domain destabilization, designed to mimic advection by the domain-scale ascent that would be induced by increments of domain-mean convective heating or decrements. Because lateral boundary conditions cannot accurately permit the passage of heating-generated subsident internal wavefronts accurately enough (Durran 2001), highly conservative cyclic lateral conditions are used instead. The latent-energy-exporting escape of these wavefronts (the birth of domain-mean ascent) then must be parameterized, based on weak density gradient assumptions (Edman and Romps 2014) or on a more complex time-delayed accounting for the vertical wavelength dependent finite speeds of these wavefronts. This diabatic ascent is a positive feedback mechanism: convective heating drives ascent which destabilizes the domain. Another pseudo-advection term is sometimes added to represent forbidden larger-scale horizontal advection, acting as a negative feedback to “blow away” and thus locally damp whatever anomalies (relative to some reference state) develop in the state variables. For weak-gradient PLSD, several arbitrary parameters of such methods were explored for instance by Raymond and Zeng (2005), and eventually refined into standard protocols for a CCPM intercomparison exercise (as reviewed in Daleu et al. 2015).

To probe the macro-function (larger-scale responsiveness) of a CCPM with PLSD, its destabilization terms can be spiked with input signals, whether in surface flux variables, radiative cooling interventions, or adiabatic ascent signals modeled as pseudo-advection by adiabatic vertical motions that are not driven by prior diabatic heating within the domain. With this configuration, a CCPM can undergo larger-scale interactions salient to macro-function while the form or pattern of its convection is manipulated through domain geometry and shear. Form-manipulation studies have compared 2D vs. square-3D domains (Wang and Sobel 2011) and various aspects of imposed wind shear in 3D (Anber et al. 2014, 2016), in their steady-state precipitation responses to water surface temperature anomalies. An intriguing internal optimum is found in the shear experiments of Anber et al. (2014, see their Figs. 5a, 14).

Transient wave PLSD methods (Kuang 2008), motivated by the phenomenon of large-scale convectively-coupled tropical waves (Kiladis et al. 2009), cleverly enforce the condition that domain-mean CCPM density anomalies are responded to by (or coupled with) a linear wave solution of specified horizontal wavelength in the x-z domain. In this framework, a wide range of CCPM symmetries along the continuum between strict 2D and isotropic 3D (but with the same number of grid points) were explored by Riley (2013). Her chapter 4 and Appendices report many results, including the effects of shear. Again an intriguing internal optimum on the 2D-3D continuum was found, in this case an optimum of this coupled-wave instability for convective forms shaped by 512 × 32 domain geometry (panel d in Fig. 7).

Fig. 7.

Precipitation time series indicating performance characteristics of cloud model simulations, with different sized and shaped cyclic domain configurations that roughly define a 3D-to-2D continuum of geometric “organization” (Fig. 4.5 of Riley 2013). During days 0–20, the model was run to equilibrium with a specified radiation-like cooling. From day 20, the domain-averaged density profile was coupled to a 5000 km plane wave equation as in Kuang (2008), allowing unstable convectively coupled wave solutions to develop spontaneously.

The apparent geometric optima of Anber et al. and Riley are among the strongest clear indications we have for a true positive importance (deserving the name “organization”) of non-random mesoscale form or patterning. Additional work to map out the accessible parameter spaces of manipulated form is ripe for doing, although the subtle roles of the myriad underlying PLSD configuration assumptions also need to be pinned down (e.g., in an affordable SCM context). Another simplified approach, at least for shear-induced mesoscale patterns or forms, is to use explicit rather than parameterized larger-scale dynamics. With shear confined to one belt of a CCPM, and surface fluxes fixed, clean dynamical competition between unsheared (isotropic) vs. shear-patterned convecting regions can be measured across a single seamless CCPM domain. Early results suggest that modestly sheared convection may win this competition, earning the moniker of “organized”, but an intermediate step of characterizing the mesoscale patterns or features induced by shear will be required to translate the findings into a true form-function relationship.

6.2 Measuring macro-function effects of manipulated form

Such PLSD experiments are all shortcuts to measuring mesoscale form's macro-function on the Earth, the moist dynamics we seek to understand. But in a global domain, how can one manipulate mesoscale form? One extreme intervention is to structurally forbid a mesoscale range of scales, using super-parameterization (SP; Randall 2013; Randall et al. 2016, sometimes called multiscale modeling frameworks MMF), falling in columns d and k in Table 1. Spatial wavelengths between the CCPM domain size and twice the coarse-grid model's mesh spacing are literally nonexistent in such a model, embodying our null hypothesis (Section 2.1), as the title of Pritchard et al. (2014) expresses crisply. A systematic examination of how small-CCPM SP simulations or hindcasts differ from high-resolution reference solutions, ideally with identical numerics on all scales like in SP-WRF (Tulich 2015), could place a useful outer bound around the form-function hypotheses of Section 2. SP models can simulate surprisingly subtle phenomena such as the nocturnal precipitation peak in central US climatology ascribed to propagating mesoscale storms (Carbone et al. 2002), a version of which somehow emerges from SP-permitted scales alone (Pritchard et al. 2011; Kooperman et al. 2013; Elliott et al. 2016). Other emergent effects in SP-CAM are described by Chen and Kirtman (2018). A new frontier of SP dubbed ultra-parameterization (Grabowski 2016) has only 4 km CCPM domains, with a 250 m grid (Parishani et al. 2018)! The impact of eliminating mesoscales so totally might give a distorted measure of their importance, so a gentler approach could be spectral nudging to constrain or damp meso wavelengths, but models with spectral methods are becoming rarer due to parallelization challenges.

7. Manipulating function

This section illustrates approaches based on controlling larger-scale function, and then seeking to interpret the form or pattern of the underlying mesoscale cloud scene.

7.1 Manipulating micro-function & form, inferring macro-function

Micro-function or budget measures include the domain-mean heating and drying profiles produced by convection in CCPMs. Since CCPMs are stable systems, exhibiting statistically steady behavior under maintained steady forcings, those micro-function budget profiles can be controlled by prescribing their negative as the profile of destabilization or forcing. Tweaks on such forcing profiles can be used to probe the responses (in state variables) of that stable system, expressible as a matrix (Kuang 2010), because (perhaps surprisingly) the mean response of a CCPM's internal convective process is highly linear, even though it is vertically nonlocal and not very deterministic (Tulich and Mapes 2010). Ever-longer steady integrations pin down an ever-more-accurate mean state measurement, the input to the elegant matrix inversion (Kuang 2010) that yields the steadily convecting CCPM's linear response function (LRF).

That LRF is linearized about a particular equilibrated convecting state, containing whatever ensemble of convective entities or features or patterns the configuration generates. The LRF's specificity and precision makes it not only a micro-function description (predicting instantaneous local budget terms), but a gateway to macro-function too: the LRF can be used to compute predictions of time-varying behavior or performance, in either a PLSD setting (Kuang 2008, 2010), a long norotating domain (Kuang 2012), or coupled with an actual global dynamical core (Kelly et al. 2017).

Since the LRF is derived from CCPM behaviors, the form of convection can be manipulated as in Section 6 through cyclic domain geometry (the 2D-3D continuum) and imposed shear. Comparing LRFs for “unorganized” convection confined in small 2D and 3D domains, with different background forcing intensities and profiles, Kuang (2008) has shown that the biggest differences are a simple linear proportionality to the background amount of convection (measured for instance by rain rate). A useful heuristic for this result is to imagine a convective cloud family as being universal in its responses, so that the domain-mean response is proportional to how many cloud families exist per unit area. That dependence on amount must therefore be normalized away to more incisively isolate form-function relationships, as discussed in Section 2.

The LRF is quite different for a very long narrow domain, big enough to host a squall-like MCS and its entire subsiding branch, as displayed in Fig. 8 of Kuang 2012. The vertical integral of that LRF (that is, the profile of sensitivity of surface rainfall response to unit perturbations of temperature and moisture perturbations at various altitudes) is displayed in the “organized” panels of Fig. 5 of Mapes et al. (2017). Discussion there notes the subtleties of interpretation, including the stretching of scale-separation assumptions that motivated the method, and the substantially different mean state the LRF ends up being linearized around. Still, some aspects of the profile differences can be appreciated using the heuristic that, unlike ordinary convection based on lifted-parcel buoyancy (making it most sensitive to the near-surface layer), Moncrieff-style layer overturning in a squall is sensitive to properties in a deep inflow layer. These deepinflow ideas can be reverse-engineered (Ahmed and Neelin 2018) into the plume-buoyancy paradigm as an entrainment rate profile (Schiro et al. 2018), which — if form could be predicted — could be one partial pathway to parameterize its function within existing global model schemes.

7.2 Manipulating macro-function: Assimilation of large scales

Coarse-scales data assimilation, in box (i) in Table 1, manipulates (by shifting toward observations) a co-varying suite of larger-scale state variables in the global model that defines the moist dynamics we wish to understand. This step implies, in part, a manipulation of micro-function variables such as advective tendencies. An informative measure of the assimilation's manipulation is analysis minus first guess (A–F), which is on the model's grid and thus represents only its resolved (function relevant) scales. A–F or the related Analysis Tendency (AT) measure the errors of a model's version of moist dynamics (e.g., Mapes and Bacmeister 2012), especially of the physics schemes. If the first-guess model's convection scheme embodies assumptions of un-organized convection, these errors reflect (among other things) the missing form-function information we seek. That mesoscale form-related component could be teased out by examining A–F or ATs of mesoscale-forbidding super-parameterized data-assimilating models like SP-CFS (Goswami et al. 2013, 2015), SP-WRF (Tulich 2015) or ECMWF's SP-IFS (Subramanian and Palmer 2017). The evaluation of form would seek systematic relationships between values of A–F and patterns or textures in satellite or RADAR data, in hopes that important facets (deserving the name organization) might stand out. Such an activity is an interpretation of conditional samples p(f | F), as previewed in Section 5, but the measures F are being imposed (by the assimilation) rather than extracted from a free-running model simulation.

8. Summary, discussion, conclusions

As a summary, Table 2's rows reiterate the hypotheses of Section 2. While Sections 3–7 have not confronted all of these directly or systematically, a revisitation can be offered in light of that journey. The null hypothesis (2.1) – that mesoscale form is irrelevant, making “organization” an empty term – may seem easy to reject, if only by the undeniably physical effects of conglomeration (2.2). But the considerable success of super-parameterized (SP) models, even with small-domain CCPMs that forbid eddies of a broad meso- range of lengths by construction (Pritchard et al. 2014), reserve some respect for the null view. At the same time, global models with only mesoscales in their patterns of overturning, lacking or barely “permitting” convective scales, also exhibit many successes (Kajikawa et al. 2016; Satoh et al. 2019). For instance, explicit convection on a 14 km mesh makes reasonable intraseasonal simulations (Miura et al. 2007a; Kikuchi et al. 2017) and forecasts (Nasuno et al. 2017). Evidently, many of the bulk macro-functions or jobs of convection, especially those with fundamental drivers, can be adequately performed by drafts of any scale, compensating for scale truncations or gaps with only modest errors (Miyakawa and Miura 2019). Certainly the classical turbulence notion that a seamless spectrum of mesoscales is crucial because of an energy “cascade”, with interactions occurring only between adjacent wavenumbers, is of questionable relevance to the role of patterned convection in moist dynamics (e.g., Mapes et al. 2008; Judt 2020). To seek truly essential contributions by mesoscale patterning, deserving of the term “organization”, one must look closer.

Top-heaviness of heating (hypothesis 2.3) is the most often cited micro-function measure of mesoscale cloud feature importance. It has distinctive impacts on mean flows when prescribed as a forcing (Hartmann et al. 1984; Schumacher et al. 2004; Mapes 1998), and appears essential to macro-function (moist flow behavior) in the form of convectively coupled waves (Mapes 2000; Kiladis 2009; Deng et al. 2016). The ultimate source of this top-heaviness of MCS heating lies partly in the top-heavy profile of clear-air radiative cooling, which total convective heating must balance in a climatic average. Widespread lower-tropospheric heating by precipitating cumuli of middle depth also helps make the remaining climatic heating job of convection top-heavy (Section 3e of Mapes 2001). With these upstream causes in mind, top-heaviness's cloud cluster size dependence should perhaps be viewed as more of an empirical outcome than one fundamentally driven by inside-the-cloud processes. This climatic relationship between convective objects of different depth as well as horizontal size poses subtle holistic challenges for moist dynamics, and even for observational estimation (Hagos et al. 2010), and perhaps explains why models with parameterized moist processes can be so diversely wrong despite the outerscales constraint of radiative driving. Top-heaviness's proportionality to stratiform rain fraction SF, another observable form aspect that varies with the size of mesoscale conglomerations (e.g., Ahmed et al. 2016), needs to be pinned down more causally. Houze (2018) cites only the rather old Pandya and Durran (1996) for mechanisms like hypothesis 2.2c, perhaps amplified by other nonlinear rectifications in 2.2, so this association remains merely empirical to a large degree.

Adjustment ideas are a staple of convection conceptualization (Arakawa 2004). Neutral or target states may be mesoscale form-dependent (hypothesis 2.4), in ways that bias climate averages (2.5). Adjustment timescale may also be form dependent (2.7a), although allowing both target and timescale to vary stretches the adjustment concept beyond any incisive utility, especially if phenomena like overshooting of the target are allowed as well. Form-function questions are simply more nuanced than gross adjustment concepts can contain and constrain.

Total vertical energy flux plays an essential macro-functional role (balancing radiative flux in mean climate). For this reason, forbidding or distorting some spatial scales of w will force other permitted scales to compensate in ways that are also erroneous. Since this compensation must occur in response to a signal of the original lack, in the form of some subtle erroneous feature of mean-state profiles, some information about horizontal form-function relations may surprisingly reside in the vertical domain. Unfortunately, other unrealistic aspects of modeled convection (microphysics, etc.) also bias time-mean profiles, and are often highly tuned since thermal wind balance makes them important to much-scrutinized mean jet streams. Any subtle vertical-profile signals attributable to missing or distorted horizontal mesoscale patterning of convection are probably lost in the noise of those other inaccuracies and compensating tunings of modeled convection.

Temporal variability gives a richer view of moist dynamics and its potential dependences on mesoscale patterning, although again it must be decoded in the presence of other dependences on uncertain subprocesses. Forward modeling of convection's microfunction impacts and sensitivities can help to inform this decoding or deduction process, for instance using (somehow) the linear response functions of isolated vs. agglomerated convection (Kuang 2012; Mapes et al. 2017).

Vertical momentum flux (hypothesis 2.6) remains the showcase of form-dependent micro-function, combining hypotheses 2.2c and 2.2d. Most theorizing about it has focused on the effects of quasi-linear horizontal geometry, with its exotic possibility of up-gradient momentum (up-scale KE flux) effects. Such near-two-dimensionality could perhaps best deserve the word “organization”, perhaps worthy of the literature's outsized attention to squall line theories. One surprise in a function-driven form-evaluation study is that upshear momentum flux events are predominated by asymmetric updrafts around low-level mesocyclones in shear, not squalls (Cheedela and Mapes 2019). These two situations reflect divergent vs. rotational convectively-coupled manifolds (Yasunaga and Mapes 2012), which may itself be a model bias; in the WRF model, “convection … coupl[ed] too strongly to rotational circulation anomalies” for instance (Tulich et al. 2011). Whatever its mesoscale configuration, vertical momentum flux's effect is hard to trace from mere micro-function (a budget term) to macro-function (importance in phenomena): where and when is it manifest, with what consequences, and how deterministically? Diagnostically, momentum flux varies systematically across the MJO (Miyakawa et al. 2012) in ways that may be heuristically understandable (Houze et al. 2000), but so do heating and its top-heaviness. Theories invoking a hierarchy of systematic upscale impacts in intraseasonal oscillations (reviewed in Zhang et al. 2020) may be overblown, if “the MJO does not favor any particular scale or type of organization” (Dias et al. 2017). Still, parameterized momentum flux makes discernable general circulation differences (e.g., Moncrieff et al. 2017) so continuing research effort is called for. Momentum flux's lack of a priori climatic constraints makes it a truly emergent result, an excellent motivation for the expensive enterprise of high-resolution simulation, whose models should output coarse-grained product terms like [ ρwu ], since they are extremely costly to compute later.

Beyond those deterministic impacts, there may be stochastic impacts from the chunky nature of MCSs (perhaps with fewer statistical degrees of freedom per square degree per hour than their sub-parts if those varied independently; hypotheses 2.7b, c). This question calls for more statistical study with a modern causal orientation (Pearl and McKenzie 2019), spurred by associated questions of stochastic parameterization and observation representativity for data assimilation (2.8). Now that ensembles of explicit convection on large domains are affordable, the macro-function of such effects can begin to be enumerated (Subramanian and Palmer 2017; Jones et al. 2019), but the relationship of stochastic effects to specific mesoscale storm forms remains under-explored. Can mesoscale cloud objects really be viewed as “systems”, with causal agency beyond their component sub-systems and parts (e.g., Klein and Hoel 2020)? Do observed associations among MCS growth rate, maximum size, and total lifetime (e.g., Machado and Laurent 2004) imply evidence for a low-order quantization, or might they merely be instances along a smoothly continuous range of perhaps accidental and mostly inconsequential conglomerations? How could we tell?

This review has endeavored to sharpen questions of how the ubiquitously observed, highly variable mesoscale form of convective storms may relate to its function. What we most care about is macro-function, defined as key difference-making participation in the moist dynamics of larger-scale flows, asking whether the nonrandom aspects of form act (at least a little) like organs in organisms, truly deserving of the over-used moniker of organization. Micro-function offers halfway budget tools toward those grander questions. All of this is distinct from the intrinsic interest and impacts of storms with various structures, the subject of most of the vast mesoscale meteorology literature. Both those local impacts and the functional coupling are facets of a deeper understanding the field should seek, since truly extreme events occur when largerscale moist dynamics also focuses and concentrates storm-scale impacts.

Tropical cyclones straddle our scale framing, as they may be dynamically large (with highly balanced flow) despite their spatially-mesoscale cloud and condensate structures. One useful heuristic for interpreting tropical cyclone climate variablity is as an ecology-like competition for scarce resources (instability) against ordinary MCSs and scattered convection or its parameterized representation (Zhao et al. 2012; Zhang and Wang 2018).

As the Space (satellite), Silicon, and Software Ages progress, both observational and simulated data sets are becoming ever larger and finer, while algorithms for measuring various aspects of convection (both morphometric and functional) become more refined, or at least more ornate. With more data, diagnostic science can hold more things constant in conditional sampling, evaluating thinner slices p(F | f) or p(f | F) for ever-higher dimensional measures of form f and function F. If such efforts could be somewhat standardized, they could be pooled toward ever-better estimates of the joint p(f, F). Even in that happy eventuality, we would still lack the causal information that defines a complete understanding, so controlled experimentation remains essential. But experiments are best when motivated from observations, and in turn can inform us about what facets of observations are most discriminating. Postulates of a more teleological relationship - for instance, that mesoscale form aspects f have not merely impacts on F, but organ-ized roles in service of macro-function behaviors — will require strong evidence, or even be hard to falsify philosophically (like Biology's long struggle with vitalism). Still, causal hypotheses can formalize these ideas, formerly viewed as merely loose verbal analogies of storms to beasts.

Going forward, ways to foster needed research in these areas include:

• ・To facilitate small-investigator diagnosis of big datasets (both observational and simulated), dataset forms and formats matter. A suite of precomputed facets (f and F measures) help facilitate conditional sampling driven works. Coarse-grained data on costly fields like full-resolution products [ρwu], or error fields from assimilation or hindcast exercises, are especially valuable. Data lakes in small-effort-accessible cloud computing environments can greatly empower efforts formerly requiring daunting file handling.
• ・More easily replicable and extensible workflows of all kinds could help facilite meta-analyses of initially-disparate efforts toward overarching goals. Sometimes very modest modifications can make a published result much more useful or generalizable.
• ・Data assimilation confronts models with observations in scientifically powerful ways. Modest research projects barely access these powers (Anderson et al. 2009), but output of by-products from more serious NWP efforts are more compelling. Easy access to assimilation-related outputs like NASA's AT fields (Bosilovich et al. 2016) or TIGGE's multi-model forecast errors (Park et al. 2003) open doors for studies of pure observations (such as radar or satellite data about mesoscale form) to be powerfully related to these global model-defined macro-function measures..

Conceptual frontiers also remain. Discrete entity or system reasoning, based only on the spatial touching of cloudy pixels, is convenient but not especially physically sound. In high-resolution simulation data, where invisible clear air is sampled equally well as the visible and radar-reflective parts of the atmosphere, more physically based boundaries could be drawn to define larger “systems” that might be more coherent and causal than clouds, such as bodies of vapor (Mapes et al. 2018). The “life cycle” of convective entities is so familiar that the reasons for their senescence remain under-questioned, as emphasized in the Summary of Rio et al. (2019). Our land-animal brains may analogize propagation too much to walking (via easily-observed but shallow near-surface mechanisms such as gust fronts), rather than swimming (the locomotion of fluid-immersed objects of near-neutral buoyancy). In such immersed-entity reasoning, velocity scales tied to invisible internal waves may be the real guiding influence (Tulich and Kiladis 2012), but are tricky to disambiguate from others such as gravity currents and advection (e.g., Oouchi 1999; Shige and Satomura 2001). Might pilot wave theory (Bush 2015), discarded by quantum mechanics, be relevant to wave-convection interaction?

Once discretized entity definitions are firmed up, statistical treatments and ideas from other fields can be brought to bear. Natural selection of the fittest parcels is at the heart of buoyant convection, yet few studies have exploited reasoning tools like evolutionary game theory (Newton 2018), with its growing set of competition paradigms including single vs. plural agents (a potential framework for unorganized and organized convection). What should we expect to observe, in a competitive arena where the energetically fittest structures survive preferentially? Chaos and predictability limits mercifully draw a line under the complication level for all such efforts.

Machine learning and artificial intelligence are opening new pathways for once-subjective activities like categorizing form, whether supervised (Rasp et al. 2020) or unsupervised (Denby 2020). In either case, its characterization finally requires human judgement, based on eyes and brains and tongues (or pens). It is hoped that this incomplete review's framing may help spur readers to invent new threads for the tapestry of form-function knowledge, keeping vital the art of human observancy and sense-making in the increasingly computer-centered science of mesoscale meteorology.

Acknowledgments

The 2011 invitation of this article by JMSJ editors, and the subsequent years of patience and encouragement, are humbly and heartily appreciated. Financial support over the years of this article's development is gratefully acknowledged, from U.S Department of Energy grants DE-SC000823 and DE-SC0006739, Office of Naval Research grant N000141310704, NOAA grant NA13OAR4310156, NASA grants NNX15AD11G and NNX14AR75G, and NSF grants 1639722 and 1917328, as well as from the Max Planck Institute for Meteorology during a fruitful sabbatical visit there. Patient reviews of much-worse drafts by David Raymond and Mitch Moncrieff, and the feedback of many presentation audiences and draft readers since 2011, helped enormously in shaping this review; special thanks are owed to Fiaz Ahmed, Chris Bretherton, Suvarchal Cheedela, Bob Houze, Hirohiko Masunaga, Masaki Satoh, and Bjorn Stevens. We acknowledge the use of imagery from the NOAA Satellite Maps application: https://www.nesdis.noaa.gov/sites/default/files/wexler3.jpg.

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