Craig C. Epifanio

Mesoscale Predictability of Moist Baroclinic Waves: Convection-Permitting Experiments and Multistage Error Growth Dynamics

A recent study examined the predictability of an idealized baroclinic wave amplifying in a conditionally unstable atmosphere through numerical simulations with parameterized moist convection. It was demonstrated that with the effect of moisture included, the error starting from small random noise is characterized by upscale growth in the short-term (0–36 h) forecast of a growing synoptic-scale disturbance. The current study seeks to explore further the mesoscale error-growth dynamics in idealized moist baroclinic waves through convection-permitting experiments with model grid increments down to 3.3 km. These experiments suggest the following three-stage error-growth model: in the initial stage, the errors grow from small-scale convective instability and then quickly [O(1 h)] saturate at the convective scales. In the second stage, the character of the errors changes from that of convective-scale unbalanced motions to one more closely related to large-scale balanced motions. That is, some of the error from convective scales is retained in the balanced motions, while the rest is radiated away in the form of gravity waves. In the final stage, the large-scale (balanced) components of the errors grow with the background baroclinic instability. Through examination of the error-energy budget, it is found that buoyancy production due mostly to moist convection is comparable to shear production (nonlinear velocity advection). It is found that turning off latent heating not only dramatically decreases buoyancy production, but also reduces shear production to less than 20% of its original amplitude.

Three-Dimensional Effects in High-Drag-State Flows over Long Ridges

Abstract Numerical simulations of nonrotating flow with uniform basic wind and stability past long three-dimensional (3D) ridges are compared to the corresponding two-dimensional (2D) limit to reveal the importance of 3D effects. For mountain heights smaller than the threshold for breaking waves, the low-level flow over the interior of the ridge is well described by 2D theory when the horizontal aspect ratio β is roughly 10 or greater. By contrast, in flows with wave breaking significant discrepancies between 2D and 3D results remain apparent even for β = 12. It is found that the onset of wave breaking and the transition to the high-drag state is accompanied in 3D by an abrupt increase in deflection of the low-level flow around the ridge. The increased flow deflection is produced at least in part by upstream-propagating columnar disturbances forced by the transition to the high-drag state. The deflection of the incident flow reduces the amplitude of the mountain wave aloft relative to 2D and acts as a neg...

Lee-Vortex Formation in Free-Slip Stratified Flow over Ridges. Part II: Mechanisms of Vorticity and PV Production in Nonlinear Viscous Wakes

Abstract The formation of orographic wakes and vortices is studied within the context of numerically simulated viscous flow with uniform basic-state wind and stability past elongated free-slip ridges. The viscosity and thermal diffusivity are sufficiently large that the onset of small-scale turbulence is suppressed. It is found in Part I of this study that wake formation in the viscous flow is closely tied to the dynamics of a low-level hydraulic-jump-like feature in the lee of the obstacle. Here the role of the hydraulic jump in producing the vorticity and potential vorticity (PV) of the viscous wake is considered. A method for diagnosing vorticity production is developed based on a propagator analysis of the Lagrangian vorticity equation that generalizes Cauchys formula for the evolution of vorticity in a Lagrangian framework. Application of the method reveals that the vertical vorticity of the wake originates through baroclinic generation and tilting in the mountain wave upstream of the jump. However,...

The Dynamics of Orographic Wake Formation in Flows with Upstream Blocking

The development of orographic wakes and vortices is revisited from the dynamical perspective of a three-dimensional (3D) vorticity-vector potential formulation. Particular emphasis is given to the role of upstream blocking in the formation of the wake. Scaling arguments are first presented to explore the limiting form of the 3D vorticity inversion for the case of flow at small dynamical aspect ratio . It is shown that in the limit of small the inversion is determined completely by the two horizontal vorticity components—that is, the part of the velocity induced by the vertical component of vorticity vanishes in the small- limit. This result leads to an approximate formulation of small- fluid mechanics in which the three governing prognostic variables are the two horizontal vorticity components and the potential temperature. The remainder of the study then revisits the problem of orographic wake formation from the perspective of this small- vorticity dynamics framework. Previous studies have suggested that one of the potential routes to stratified wake formation is through the blocking of flow on the upstream side of the barrier. This apparent link between blocking and wake formation is shown to be relatively straightforward in the small- vorticity context. In particular, it is shown that blocking of the flow inevitably leads to a horizontal vorticity distribution that favors deceleration of the leeside flow at the ground. This process of leeside flow deceleration, as well as the subsequent time evolution of the wake, is illustrated through a series of numerical initial-value problems involving flows past 2D and 3D barriers. It is proposed that the initiation of the wake flow in these stratified problems resembles the flow produced by a retracting piston in shallow-water theory.

Linear Theory Calculations for the Sea Breeze in a Background Wind: The Equatorial Case

The equatorial coastal circulation is modeled in terms of the linear wave response to a diurnally oscillating heat source gradient in a background wind. A diurnal scaling shows that the solution depends on two parameters: a nondimensional coastal width L and a nondimensional wind speed U. The solutions are interpreted by comparing to the U 5 0 theory of Rotunno. For U 6 0 the Fourier integral solution consists of three distinct wave branches. Two of these branches correspond to the prior no-wind solution of Rotunno, except with Doppler shifting and associated wave dispersion. The third branch exists only for U 6 0 and is shown to be broadly similar to flow past a steady heat source or a topographic obstacle. The relative importance of this third branch is determined largely by the parameter combination U/L. For sufficiently large U/L the third branch becomes the dominant part of the solution. The spatial structures of the three branches are described in terms of group velocity arguments combined with a desingularized quadrature method.

Topographic Effects on the Tropical Land and Sea Breeze

AbstractThe effect of an inland plateau on the tropical sea breeze is considered in terms of idealized numerical experiments, with a particular emphasis on offshore effects. The sea breeze is modeled as the response to an oscillating interior heat source over land. The parameter space for the calculations is defined by a nondimensional wind speed, a scaled plateau height, and the nondimensional heating amplitude.The experiments show that the inland plateau tends to significantly strengthen the land-breeze part of the circulation, as compared to the case without terrain. The strengthening of the land breeze is tied to blocking of the sea-breeze density current during the warm phase of the cycle. The blocked sea breeze produces a pool of relatively cold, stagnant air at the base of the plateau, which in turn produces a stronger land-breeze density current the following morning. Experiments show that the strength of the land breeze increases with the terrain height, at least for moderate values of the height...

Lee-Vortex Formation in Free-Slip Stratified Flow over Ridges. Part I: Comparison of Weakly Nonlinear Inviscid Theory and Fully Nonlinear Viscous Simulations

Abstract The formation of lee wakes and vortices is explored in the context of stratified flow with uniform basic-state wind and stability past elongated free-slip ridges. The theory of inviscid flow past a ridge of small nondimensional height ϵ is revisited using a weakly nonlinear semianalytic model to compute flow fields through O(ϵ2). Consistent with previous work, the weakly nonlinear solutions show an O(ϵ2) couplet of vertical vorticity above the lee slope of the appropriate sense to describe the observed circulation in lee vortices. Nonetheless, the actual O(ϵ2) flow fields are found to be inconsistent with the developing lee-vortex structures observed in previous nonlinear numerical experiments. Lee-vortex formation must therefore depend significantly on finite-amplitude and/or dissipative effects not described by the weakly nonlinear inviscid model. The weakly nonlinear results are compared to fully nonlinear numerical simulations of wake formation in viscous and thermally diffusive laminar flow....

Wave–Turbulence Interactions in a Breaking Mountain Wave

Abstract The mean and turbulent structures in a breaking mountain wave are considered through an ensemble of high-resolution (essentially large-eddy simulation) wave-breaking calculations. Of particular interest are the turbulent heat and momentum fluxes in the breaking wave and their roles in shaping the wave-scale and larger-scale flows. The evolution of the breaking wave in the ensemble mean is found to be broadly consistent with prior low-resolution calculations. A turbulent kinetic energy budget for the wave shows that the turbulence production is almost entirely due to the mean shear. Most of the production is at the top of the leeside shooting flow, where the mean-flow Richardson number is persistently less than 0.25. The turbulent dissipation of mean-flow wave energy is shown to result mainly from the turbulent momentum fluxes—specifically, from the tendency of these fluxes to act counter to the mean-flow disturbance wind. Of particular importance is the eddy deceleration of the leeside shooting f...

Ensemble-based data assimilation for thermally forced circulations

[1] The effectiveness of the ensemble Kalman filter (EnKF) for thermally forced circulations is investigated with simulated observations. A two-dimensional, nonlinear, hydrostatic, non-rotating, and incompressible sea breeze model is developed for this purpose with buoyancy and vorticity as the prognostic variables. Model resolution is 4 km horizontally and 50 m vertically. Forcing is maintained through an explicit heating function with additive stochastic noise. Pure forecast experiments reveal that the model exhibits moderate nonlinearity. The strongest nonlinearity occurs along the sea breeze front at the time of peak sea breeze phase. Considerable small-scale error growth occurs at this phase for vorticity, while buoyancy is dominated by large-scale error as the direct result of the initial condition uncertainty. In the EnKF experiments, simulated buoyancy observations (with assumed error of 10 � 3 ms � 2 ) on land surface with 40-km spacing are assimilated every 3 hours. As a result of their resolution, the observations naturally sample the larger-scale flow structure. At the first analysis step, the filter is found to remove most of the large-scale error resulting from the initial conditions and the domainaveraged error of buoyancy and vorticity is reduced by about 83% and 42%, respectively. Subsequent analyses continue to remove error at a progressively slower rate and the error ultimately stabilizes within about 24 hours for both variables. At later model times, while mostly large-scale buoyancy errors due to the stochastic heating uncertainty are effectively removed, the filter also performs well at reducing smaller-scale vorticity errors associated with the sea breeze front. This is an indication that observations also contain useful small-scale information relevant at the scales of frontal convergence.

A Method for Imposing Surface Stress and Heat Flux Conditions in Finite-Difference Models with Steep Terrain

A numerical implementation of the surface stress boundary condition is presented for finite-difference models in which the terrain slope and curvature cannot necessarily be considered small. The method involves reducing the discretized stress condition in terrain-following coordinates to a pair of coupled linear systems for the two horizontal velocity components at the boundary. The linear systems are then solved iteratively at each model time step to provide the unique boundary values of velocity consistent with the specified values of the stress. Similar methods are used to prescribe the normal flux of heat across the boundary. A related method for imposing stress conditions in two-dimensional vorticity–streamfunction models is also discussed. The effectiveness of the boundary conditions is demonstrated through a series of test problems involving topographic wake flows and thermally driven flows on steep slopes. It is shown that the use of the conventional flat-boundary approximation can lead to substantial errors when the resolved topography is sufficiently steep.