The thermal phase curve offset on tidally- and non-tidally-locked exoplanets: A shallow water model

Using a shallow water model with time-dependent forcing we show that the peak of an exoplanet thermal phase curve is, in general, offset from secondary eclipse when the planet is rotating. That is, the planetary hot-spot is offset from the point of maximal heating (the substellar point) and may lead or lag the forcing; the extent and sign of the offset is a function of both the rotation rate and orbital period of the planet. We also find that the system reaches a steady-state in the reference frame of the moving forcing. The model is an extension of the well studied Matsuno-Gill model into a full spherical geometry and with a planetary-scale translating forcing representing the insolation received on an exoplanet from a host star. The speed of the gravity waves in the model is shown to be a key metric in evaluating the phase curve offset. If the velocity of the substellar point (relative to the planet's surface) exceeds that of the gravity waves then the hotspot will lag the substellar point, as might be expected by consideration of forced gravity wave dynamics. However, when the substellar point is moving slower than the internal wavespeed of the system the hottest point can lead the passage of the forcing. We provide an interpretation of this result by consideration of the Rossby and Kelvin wave dynamics as well as, in the very slowly rotating case, a one-dimensional model that yields an analytic solution. Finally, we consider the inverse problem of constraining planetary rotation rate from an observed phase curve

The catalytic role of beta effect in barotropization processes

The vertical structure of freely evolving, continuously stratified, quasi-geostrophic flow is investigated. We predict the final state organization, and in particular its vertical structure, using statistical mechanics and these predictions are tested against numerical simulations. The key role played by conservation laws in each layer, including the fine-grained enstrophy, is discussed. In general, the conservation laws, and in particular that enstrophy is conserved layer-wise, prevent complete barotropization, i.e., the tendency to reach the gravest vertical mode. The peculiar role of the $\beta$-effect, i.e. of the existence of planetary vorticity gradients, is discussed. In particular, it is shown that increasing $\beta$ increases the tendency toward barotropization through turbulent stirring. The effectiveness of barotropisation may be partly parameterized using the Rhines scale $2\pi E_{0}^{1/4}/\beta^{1/2}$. As this parameter decreases (beta increases) then barotropization can progress further, because the beta term provides enstrophy to each layer

Cloud/climate sensitivity experiments

A study of the relationships between large-scale cloud fields and large scale circulation patterns is presented. The basic tool is a multi-level numerical model comprising conservation equations for temperature, water vapor and cloud water and appropriate parameterizations for evaporation, condensation, precipitation and radiative feedbacks. Incorporating an equation for cloud water in a large-scale model is somewhat novel and allows the formation and advection of clouds to be treated explicitly. The model is run on a two-dimensional, vertical-horizontal grid with constant winds. It is shown that cloud cover increases with decreased eddy vertical velocity, decreased horizontal advection, decreased atmospheric temperature, increased surface temperature, and decreased precipitation efficiency. The cloud field is found to be well correlated with the relative humidity field except at the highest levels. When radiative feedbacks are incorporated and the temperature increased by increasing CO2 content, cloud amounts decrease at upper-levels or equivalently cloud top height falls. This reduces the temperature response, especially at upper levels, compared with an experiment in which cloud cover is fixed

Meridional Rossby Wave Generation and Propagation in the Maintenance of the Wintertime Tropospheric Double Jet

This is the final version of the article. Available from American Meteorological Society via the DOI in this record.The eddy-driven and subtropical jet are two dynamically distinct features of the midlatitude upper troposphere circulation that are often merged into a single zonal wind maxima. Nonetheless, the potential for a distinct double jet state in the atmosphere exists, particularly in the winter hemi-sphere, and presents a unique zonal mean flow with two waveguides and an interjet region with a weakened potential vorticity gradient upon which Rossby waves may be generated, propagate,reflect, and break. We investigate the interaction of two groups of atmospheric waves, those longer or shorter than the deformation radius, with a double jet mean flow in an idealized atmospheric model. Patterns of eddy momentum flux convergence for long and short waves differ greatly. Short waves behave following classic baroclinic instability theory such that their eddy momentum flux convergence is centered at the eddy-driven jet core. Long waves, on the other hand, reveal strong eddy momentum flux convergence along the poleward flank of the eddy-driven jet and within the interjet region. This pattern is enhanced when two jets are present in the zonal mean zonal wind.National Science Foundatio

The role of criticality on the horizontal and vertical scales of extratropical eddies in a dry GCM

This paper discusses the sensitivity of the horizontal and vertical scales of extratropical eddies when criticality is varied in a dry, primitive-equation, general circulation model. Criticality is a measure of extratropical isentropic slope and when defined appropriately its value is often close to 1 for Earth's climate. The model is forced by a Newtonian relaxation of temperature to a prescribed temperature profile, and criticality is increased by increasing the thermal relaxation rate on the mean flow. When criticality varies near 1, it is shown that there exists a weakly nonlinear regime in which the eddy scale increases with criticality without involving an inverse cascade, while at the same time the Rossby radius may in fact decrease. The quasigeostrophic instability of the Charney problem is revisited. It is demonstrated that both the horizontal and vertical scales of the most unstable wave depend on criticality, and simple estimates for the two scales are obtained. The authors reconcile the opposite trends of the eddy scale and Rossby radius and obtain an estimate for the eddy scale in terms of the Rossby radius and criticality that is broadly consistent with simulations.NSFNOA

Emergence of Fofonoff states in inviscid and viscous ocean circulation models

Numerical experiments are performed to directly test the emergence of the Fofonoff solution in an inviscid closed barotropic domain, and to explore its significance to the weakly dissipative system. The Fofonoff solution, characterized by a linear relationship between absolute vorticity and streamfunction, is generally realized as the time mean state of inviscid simulations over a fairly broad parameter range of varying (β-plane) Rossby number and resolution, in different geometrical domains, and with and without topography. The relevance of the Fofonoff solution to the viscous, decaying system is examined by numerical experiments with two different forms of viscosity, namely, biharmonic and harmonic, as well as with various boundary conditions. It is found that the boundary condition is generally more important than the order of the viscosity in determining the time mean fields. All of the frictional forms and boundary conditions prevented the complete realization of the Fofonoff state to a greater or lesser extent. Of the various boundary conditions used, the super-slip condition is most conducive to realizing a Fofonoff state. In this case, at high enough resolution the timescale of energy variability is much longer than a dynamical timescale, and the Fofonoff flow may be considered a ‘minimum enstrophy’ state. At high Reynolds number and high Rossby number an almost linear q — ψ relationship can be achieved. For lower Rossby numbers, absolute vorticity tends to become homogenized, preventing the Fofonoff solution from arising. In the case of a free slip condition, it is still harder to reach a quasi-equilibrium. The time mean fields, after spin-up, generally show a two-gyre structure with homogenization in the absolute vorticity fields. In the no slip case, neither a quasi-equilibrium nor any well formed time mean field can be reached. As a slight generalization of the flow on β-plane, the inviscid topographic experiments also ultimately yield a linear relationship between absolute vorticity and streamfunction