Machine Learning Methods for Multiscale Physics and Urban Engineering Problems.

We present an overview of four challenging research areas in multiscale physics and engineering as well as four data science topics that may be developed for addressing these challenges. We focus on multiscale spatiotemporal problems in light of the importance of understanding the accompanying scientific processes and engineering ideas, where "multiscale" refers to concurrent, non-trivial and coupled models over scales separated by orders of magnitude in either space, time, energy, momenta, or any other relevant parameter. Specifically, we consider problems where the data may be obtained at various resolutions; analyzing such data and constructing coupled models led to open research questions in various applications of data science. Numeric studies are reported for one of the data science techniques discussed here for illustration, namely, on approximate Bayesian computations.

Self-aggregation of clouds in conditionally unstable moist convection.

The behavior of moist Rayleigh-Bénard convection is investigated using a Boussinesq model with a simplified thermodynamics for phase transitions. This idealized configuration makes the problem accessible to high-resolution three-dimensional direct numerical simulations without small-scale parameterizations of the turbulence for extended layers with aspect ratios up to 64. Our study is focused on the frequently observed conditionally unstable environment that is stably stratified for unsaturated air, but is unstable for cloudy air. We find that no sharp threshold for the transition to convective turbulence exists, a situation similar to wall-bounded shear flows. Rather, the transition depends on the amplitude of the initial perturbation of the quiescent equilibrium and on the aspect ratio of the convective domain. In contrast to the classical dry Rayleigh-Bénard case, convection is highly asymmetric with respect to the vertical direction. Moist upwelling air inside turbulent cloud aggregates is surrounded by ambient regions of slowly descending unsaturated air. It is also found that conditionally unstable moist convection is inefficient at transporting energy. Our study suggests that there is an upper bound on the Nusselt number in moist convection that is lower than that of the classical dry case.

Satellite estimates of precipitation-induced dissipation in the atmosphere.

A substantial amount of frictional dissipation in the atmosphere occurs in the microphysical shear zones surrounding falling precipitation. The dissipation rate is computed here from recently available satellite retrieval from the Tropical Rainfall Measurement Missions and is found to average 1.8 watts per square meter between 30°S and 30°N. The geographical distribution of the precipitation-induced dissipation is closely tied to that of precipitation but also reveals a stronger dissipation rate for continental convection than for maritime convection. Because the precipitation-induced dissipation is of the same magnitude as the turbulent dissipation of the kinetic energy in the atmosphere, changes in the hydrological cycle could potentially have a direct impact on the amount of kinetic energy generated and dissipated by the atmospheric circulation.

Rayleigh-Bénard convection with phase changes in a Galerkin model.

The transition to turbulence in Rayleigh-Bénard convection with phase changes and the resulting convective patterns are studied in a three-dimensional Galerkin model. Our study is focused on the conditionally unstable regime of moist convection in which the stratification is stable for unsaturated air parcels and unstable for saturated parcels. We perform a comprehensive statistical analysis of the transition to convection that samples the dependence of attractors (or fixed points) in the phase space of the model on the dimensionless parameters. Conditionally unstable convection can be initiated either from a fully unsaturated linearly stable equilibrium or a fully saturated linearly unstable equilibrium. Highly localized moist convection can be found in a steady state, in an oscillating recharge-discharge regime, or turbulent in dependence of the aspect ratio and the degree of stable stratification of the unsaturated air. Our phase-space analysis predicts parameter ranges for which self-sustained convective regimes in the case of subcritical conditional instability can be observed. The observed regime transitions for moist convection bear some similarities to transitions to turbulence in simple shear flows.

It is not the entropy you produce, rather, how you produce it.

The principle of maximum entropy production (MEP) seeks to better understand a large variety of the Earth's environmental and ecological systems by postulating that processes far from thermodynamic equilibrium will 'adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate'. Our aim in this 'outside view', invited by Axel Kleidon, is to focus on what we think is an outstanding challenge for MEP and for irreversible thermodynamics in general: making specific predictions about the relative contribution of individual processes to entropy production. Using studies that compared entropy production in the atmosphere of a dry versus humid Earth, we show that two systems might have the same entropy production rate but very different internal dynamics of dissipation. Using the results of several of the papers in this special issue and a thought experiment, we show that components of life-containing systems can evolve to either lower or raise the entropy production rate. Our analysis makes explicit fundamental questions for MEP that should be brought into focus: can MEP predict not just the overall state of entropy production of a system but also the details of the sub-systems of dissipaters within the system? Which fluxes of the system are those that are most likely to be maximized? How it is possible for MEP theory to be so domain-neutral that it can claim to apply equally to both purely physical-chemical systems and also systems governed by the 'laws' of biological evolution? We conclude that the principle of MEP needs to take on the issue of exactly how entropy is produced.

The global atmospheric circulation on moist isentropes.

The global atmospheric circulation transports energy from the equatorial regions to higher latitudes through a poleward flow of high-energy and -entropy parcels and an equatorward flow of air with lower energy and entropy content. Because of its turbulent nature, this circulation can only be described in some averaged sense. Here, we show that the total mass transport by the circulation is twice as large when averaged on moist isentropes than when averaged on dry isentropes. The additional mass transport on moist isentropes corresponds to a poleward flow of warm moist air near Earth's surface that rises into the upper troposphere within mid-latitudes and accounts for up to half of the air in the upper troposphere in polar regions.