Thermodynamic derivation and use of a nonequilibrium canonical ensemble

A thermodynamic expression for the analog of the canonical ensemble for nonequilibrium systems is described based on a purely information theoretical interpretation of entropy. As an application, it is shown that this nonequilibrium canonical distribution implies some important results from nonequilibrium thermodynamics, specifically, the fluctuation theorem and the Jarzynski-equality.Comment: 4 pages, 0 figure

The chaos machine: analogue computing rediscovered (1)

Analogue computers provide actual rather than virtual representations of model systems. They are powerful and engaging computing machines that are cheap and simple to build. This two-part Retronics article helps you build (and understand!) your own analogue computer to simulate the Lorenz butterfly that's become iconic for Chaos theory

An adiabatic mechanism for the reduction of jet meander amplitude by potential vorticity filamentation

The amplitude of ridges in large-amplitude Rossby waves have been shown to decrease systematically with lead time during the first 1-5 days of operational global numerical weather forecasts. These models also exhibit a rapid reduction in the isentropic gradient of potential vorticity (PV) at the tropopause during the first 1-2 days of forecasts. This paper identifies a mechanism linking the reduction in large-scale meander amplitude on jet streams to declining PV gradients. The mechanism proposed is that a smoother isentropic transition of PV across the tropopause leads to excessive PV filamentation on the jet flanks and a more lossy waveguide. The approach taken is to analyse Rossby wave dynamics in a single-layer quasi-geostrophic model. Numerical simulations show that the amplitude of a Rossby wave propagating along a narrow but smooth PV front do indeed decay transiently with time. This process is explained in terms of the filamentation of PV from the jet core and associated absorption of wave activity by the critical layers on the jet flanks, and a simple method for quantitatively predicting the magnitude of the amplitude reduction without simulation is presented. Explicitly-diffusive simulations are then used to show that the combined impact of diffusion and the adiabatic rearrangement of PV can result in a decay rate of Rossby waves which is 2-4 times faster than could be expected from diffusion acting alone. This predicted decay rate is sufficient to explain the decay observed in operational weather forecasting models

Marginal stability and predator-prey behaviour within storm tracks

A predator-prey relationship between storm track intensity and growth rate is revealed in reanalysis data for the North Atlantic and North Pacific, as well as in an idealised global circulation model with a zonally asymmetric heating dipole. Averaging in the phase space of these two quantities reveals that both quantities oscillate on approximately monthly timescales. These oscillations occur due to quasi-periodic bursts in storm track activity that reduce excess baroclinicity and bring the flow back towards a state that is marginally stable to those bursts. Many detailed properties of these oscillations are reproduced well by a two-dimensional dynamical system, especially in respect of the North Atlantic storm track which is more zonally constrained compared to the North Pacific. It is predicted and observed that on average stronger storm events occur less frequently but grow on a shorter timescale. The results suggest that nonlinearly oscillating behaviour around a state of baroclinic neutrality is a general feature of localised storm tracks, and they offer a new perspective on the study of baroclinic instability

The lifecycle of the North Atlantic storm track

The North Atlantic eddy-driven jet exhibits latitudinal variability, with evidence of three preferred latitudinal locations: south, middle and north. Here we examine the drivers of this variability and the variability of the associated storm track. We investigate the changes in the storm track characteristics for the three jet locations, and propose a mechanism by which enhanced storm track activity, as measured by upstream heat flux, is responsible for cyclical downstream latitudinal shifts in the jet. This mechanism is based on a nonlinear oscillator relationship between the enhanced meridional temperature gradient (and thus baroclinicity) and the meridional high-frequency (periods of shorter than 10 days) eddy heat flux. Such oscillations in baroclinicity and heat flux induce variability in eddy anisotropy which is associated with the changes in the dominant type of wave breaking and a different latitudinal deflection of the jet. Our results suggest that high heat flux is conducive to a northward deflection of the jet, whereas low heat flux is conducive to a more zonal jet. This jet deflecting effect was found to operate most prominently downstream of the storm track maximum, while the storm track and the jet remain anchored at a fixed latitudinal location at the beginning of the storm track. These cyclical changes in storm track characteristics can be viewed as different stages of the storm track’s spatio-temporal lifecycle

Rossby wave propagation on potential vorticity fronts with finite width

The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here an approximate correction is derived for the case of a finite width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models

On the microphysical effects of observed cloud edge charging

Liquid layer clouds are abundant globally. Lacking strong convection, they do not become electrified by the usual thunderstorm mechanisms of collisional electrification between hydrometeors of different phases. Instead, the background global circuit current flow in fair weather is largely unaffected by the layer cloud’s presence, and, if the layer cloud is extensive horizontally, the vertical fair weather conduction current passes through the cloud. A consequence of the vertical current flow is that, at the cloud-air boundary where there is a conductivity transition and droplets form or evaporate, droplet charging occurs. Charge can affect both droplet evaporation and droplet-droplet collisions. Using new radiosonde instrumentation, the charge observed at layer cloud edges is evaluated for both these microphysical droplet processes. This shows that the charging is more likely to affect collision processes than activation, for small droplets. Enhancing the collection efficiency of small droplets modifies their evolution and propagates through the size distribution to shorten the autoconversion timescale to rain drops, and the cloud radiative properties. Because the conduction current density is influenced by both external (e.g. solar modulation of high energy particles) and internal (e.g. ENSO) factors, current flow leading to layer cloud edge charging provides a possible route for expressing solar influences on the climate system and a teleconnection mechanism for communicating internal climate variability

Flow-dependent predictability of the North Atlantic Jet

The North Atlantic eddy-driven jet is a major component of the large-scale flow in the northern hemisphere. Here we present evidence from reanalysis and ensemble forecast data for systematic flow-dependent predictability of the jet during northern hemisphere winter (DJF). It is found that when the jet is weakened or split it is both less persistent and less predictable. The lack of predictability manifests itself as the onset of an anomalously large instantaneous rate of spread of ensemble forecast members as the jet becomes weakened. This suggests that as the jet weakens or splits it enters into a state more sensitive to small differences between ensemble forecast members, rather like the sensitive region between the wings of the Lorenz attractor

The implications of an idealised large-scale circulation for mechanical work done by tropical convection

A thermodynamic analysis is presented of an overturning circulation simulated by two cloud resolving models, coupled by a weak temperature gradient parametrisation. Taken together, they represent two separated regions over different sea surface temperatures, and the coupling represents an idealised large-scale circulation such as the Walker circulation. It is demonstrated that a thermodynamic budget linking net heat input to the generation of mechanical energy can be partitioned into contributions from the large-scale interaction between the two regions, as represented by the weak temperature gradient approximation, and from convective motions in the active warm region and the suppressed cool region. Model results imply that such thermodynamic diagnostics for the aggregate system are barely affected by the strength of the coupling, even its introduction, or by the SST contrast between the regions. This indicates that the weak temperature gradient parametrisation does not introduce anomalous thermodynamic behaviour. We find that the vertical kinetic energy associated with the large-scale circulation is more than three orders of magnitude smaller than the typical vertical kinetic energy in each region. However, even with very weak coupling circulations, the contrast between the thermodynamic budget terms for the suppressed and active regions is strong and is relatively insensitive to the degree of the coupling. Additionally, scaling arguments are developed for the relative values of the terms in the mechanical energy budget