Mountain Wave Simulations Research Articles

An Intercomparison of T-REX Mountain-Wave Simulations and Implications for Mesoscale Predictability

Numerical simulations of flow over steep terrain using 11 different nonhydrostatic numerical models are compared and analyzed. A basic benchmark and five other test cases are simulated in a two-dimensional framework using the same initial state, which is based on conditions during Intensive Observation Period (IOP) 6 of the Terrain-Induced Rotor Experiment (T-REX), in which intense mountain-wave activity was observed. All of the models use an identical horizontal resolution of 1 km and the same vertical resolution. The six simulated test cases use various terrain heights: a 100-m bell-shaped hill, a 1000-m idealized ridge that is steeper on the lee slope, a 2500-m ridge with the same terrain shape, and a cross-Sierra terrain profile. The models are tested with both free-slip and no-slip lower boundary conditions. The results indicate a surprisingly diverse spectrum of simulated mountain-wave characteristics including lee waves, hydraulic-like jump features, and gravity wave breaking. The vertical velocity standard deviation is twice as large in the free-slip experiments relative to the no-slip simulations. Nevertheless, the no-slip simulations also exhibit considerable variations in the wave characteristics. The results imply relatively low predictability of key characteristics of topographically forced flows such as the strength of downslope winds and stratospheric wave breaking. The vertical flux of horizontal momentum, which is a domain-integrated quantity, exhibits considerable spread among the models, particularly for the experiments with the 2500-m ridge and Sierra terrain. The differences among the various model simulations, all initialized with identical initial states, suggest that model dynamical cores may be an important component of diversity for the design of mesoscale ensemble systems for topographically forced flows. The intermodel differences are significantly larger than sensitivity experiments within a single modeling system.

A coupled mesoscale-model Fourier-method for idealized mountain-wave simulations over Hawaii

Mesoscale model simulations of representative trade winds impinging upon the Big Island of Hawaii are diagnosed for their mountain-wave characteristics by coupling a mesoscale model to a Fourier method. Localized phase-averaged wave momentum fluxes are calculated, which facilitates the study of wave generation from fine-scale topographic features. We find that the wave momentum fluxes are dominated by forcing from subsidiary topographic peaks, with the broader island topography controlling flow splitting and lee vortex generation. Waves also arise at the far northern and southern extremities of the island by acceleration of split flow. The strength of the local momentum fluxes proves to be sensitive to a small change in the incident flow direction. Areally integrated fluxes (wave drag) align closely with the incident flow direction and are an order of magnitude smaller than linear predictions and an order of magnitude larger than corresponding dividing streamline predictions. We briefly discuss the relevance of these results to the parameterization of subgrid-scale mountain-wave drag in climate and weather models.

A Conservative Discontinuous Galerkin Semi-Implicit Formulation for the Navier–Stokes Equations in Nonhydrostatic Mesoscale Modeling

A discontinuous Galerkin (DG) finite element formulation is proposed for the solution of the compressible Navier-Stokes equations for a vertically stratified fluid, which are of interest in mesoscale nonhydrostatic atmospheric modeling. The resulting scheme naturally ensures conservation of mass, momentum, and energy. A semi-implicit time-integration approach is adopted to improve the efficiency of the scheme with respect to the explicit Runge-Kutta time integration strategies usually employed in the context of DG formulations. A method is also presented to reformulate the resulting linear system as a pseudo-Helmholtz problem. In doing this, we obtain a DG discretization closely related to those proposed for the solution of elliptic problems, and we show how to take advantage of the numerical integration rules (required in all DG methods for the area and flux integrals) to increase the efficiency of the solution algorithm. The resulting numerical formulation is then validated on a collection of classical two-dimensional test cases, including density driven flows and mountain wave simulations. The performance analysis shows that the semi-implicit method is, indeed, superior to explicit methods and that the pseudo-Helmholtz formulation yields further efficiency improvements.

An Upper Gravity-Wave Absorbing Layer for NWP Applications

Although the use of a damping layer near the top of a computational model domain has proven effective in absorbing upward-propagating gravity-wave energy in idealized simulations, this technique has been less successful in real atmospheric applications. Here, a new technique is proposed for nonhydrostatic model equations that are solved using split-explicit time-integration techniques. In this method, an implicit Rayleigh damping term is applied only to the vertical velocity, as a final adjustment at the end of each small (acoustic) time step. The adjustment is equivalent to including an implicit Rayleigh damping term in the vertical momentum equation together with an implicit vertical diffusion of w, and could be applied in this manner in other time-integration schemes. This implicit damping for the vertical velocity is unconditionally stable and remains effective even for hydrostatic gravity waves. The good absorption characteristics of this layer across a wide range of horizontal scales are confirmed through analysis of the linear wave equation and numerical mountain-wave simulations, and through simulations of an idealized squall line and of mountain waves over the Colorado Rocky Mountains.

Observations and numerical simulations of mountain waves in the presence of directional wind shear

Three research aircraft observed small-amplitude gravity waves over the south-western French Alps on 13 November 1999 during the Mesoscale Alpine Programme (MAP). Radiosonde ascents and Global Positioning System dropsondes deployed by MAP research aircraft indicate that the upstream flow was characterized by topographic blocking below 2 km and low-level directional wind shear associated with a synoptic-scale depression that extended above the Alpine crest. The in situ vertical velocity data from the three research aircraft, and backscatter from lidar onboard the low-level and upper-level aircraft, exhibit gravity-wave signatures in the lower troposphere that are characterized by relatively short horizontal wavelengths on a scale of 5 km or less. The in situ flight-level and backscatter data also suggest a rapid decrease in the wave amplitude with height, due to a directional critical layer that partially absorbs wave energy in the lower to middle troposphere in concert with a decrease in the Scorer parameter with height that traps the wave energy. Numerical simulation results, obtained from the non-hydrostatic Coupled Ocean–Atmosphere Mesoscale Prediction System model using a horizontal resolution of 556 m, indicate the presence of low-level wave breaking above the highest peaks, and confirm the presence of trapped waves and a directional critical level. Results based on linear theory and nonlinear model simulations suggest that the absorption of wave energy associated with the directional critical layer has an important impact on the wave characteristics including the momentum flux. Copyright © 2006 Royal Meteorological Society

Extension of an orographic‐drag parametrization scheme to incorporate orographic anisotropy and flow blocking

AbstractThe Kim–Arakawa orographic gravity‐wave drag parametrization scheme, which is a component of the US Navy's NOGAPS ALPHA (Navy Operational Global Atmospheric Prediction System, Advanced‐Level Physics and High Altitude), is extended to include the effects of orographic anisotropy and low‐level flow blocking. The algorithms to calculate the orographic statistics needed for the parametrization are also revised. The extended scheme is evaluated against mountain waves explicitly simulated with COAMPS®† (Coupled Ocean/Atmosphere Mesoscale Prediction System) of NRL (Naval Research Laboratory).Mountain‐wave simulations over Boulder, Colorado, USA, are used for representing realistic situations of different wave activity including severe downslope windstorms. The simulations are area‐averaged and interpolated to the vertical grid of NOGAPS, and are used as the input to the extended Kim–Arakawa scheme. The scheme is calibrated by comparing the parametrized vertical distribution of the momentum fluxes with the counterpart obtained from the explicit mesoscale simulations. Overall, the calibrated scheme successfully represents the simulated magnitudes and vertical divergences of the momentum fluxes. A flow regime diagram is constructed utilizing a time series of the simulations to further evaluate the parametrization. The robustness of the orographic statistics, together with an approximate method to improve it, are also addressed. Copyright © 2005 Royal Meteorological Society.

Aircraft measurements and numerical simulations of mountain waves over the central Alps: A pre‐MAP test case

AbstractIn preparation for the field phase of the Mesoscale Alpine Project (MAP), in situ research‐aircraft observations from the DLR Falcon, and three‐dimensional high‐resolution numerical simulations are used to investigate mountain waves generated during a south föhn event on 10 October 1987. The model simulation qualitatively compares favourably with the aircraft observations in terms of identifying the horizontal and vertical locations of maximum gravity‐wave amplitude and rapid decay of wave amplitudes in the lower stratosphere. However, even with reasonably specified large‐scale conditions, the vertical velocity and temperature perturbations are not in quantitative agreement with the aircraft measurements. The results highlight some deficiencies that still exist in our predictive capability to simulate gravity‐wave generation and propagation explicitly over three‐dimensional topography for non‐steady conditions. The complexity of the gravity‐wave response points toward the necessity of a straightforward aircraft observing strategy that features linear flight segments oriented along the cross‐mountain wind direction, a rapid repetition of these segments in order to assess the significance of transients, and a combination of in situ measurements with remote‐sensing data (e.g. from lidar systems and dropsondes), an approach that was successfully applied during the MAP. Copyright © 2002 Royal Meteorological Society

VHF radar measurements and model simulations of mountain waves over Wales

AbstractVery high frequency (VHF) radar measurements of mountain waves over Aberystwyth, Wales, during 29 November 1997 are presented and compared with the predictions made by a three‐dimensional numerical model which is based on the linearized equations of motion. The radar height–time plot of vertical velocity reveals a wave field in the troposphere and lower stratosphere which changes significantly throughout the day. Four separate radiosonde soundings taken during the day are used to represent the steady background flow in the numerical model. In this case the steady‐state model wave fields are shown to compare qualitatively well with the radar measurements and the three‐dimensional information provided by the model is used to help explain the changes in the wave field observed by the radar throughout the day.The radiosonde profiles are interpolated in time to provide approximate basic‐state data at two‐hour intervals. Model steady‐state vertical‐velocity fields, based on each of these 13 approximate basic‐state profiles are used to generate a model time–height vertical‐velocity plot which is qualitatively similar to that obtained from the radar measurements, indicating that, to a reasonable approximation, the evolving wave field can be regarded as a sequence of independent steady states. This is generally true if the basic‐state flow remains steady over the time taken for wave packets to propagate over several wavelengths. Group‐velocity arguments are used to show that, for typical mountain waves in the troposphere, such time‐scales are generally less than one hour.Model simulations in which the basic‐state flow is allowed to vary in time continually (based on either the interpolated radiosonde soundings or the radar horizontal‐wind measurements) are conducted. In this case the simulated wave fields are always unsteady; the waves show a tendency to drift in response to changes in the basic‐state wind field. For example, during instances when the wind speed at a given level decreases (whilst the wind direction remains the same) the waves show an upwind phase propagation with a typical phase speed of the order of 1 m s−1. The consequence of this unsteadiness for the propagation of the waves is discussed. Copyright © 2002 Royal Meteorological Society.

A time-split, forward-backward numerical model for solving a nonhydrostatic and compressible system of equations

In this paper, we present a numerical procedure for solving a 2-dimensional, compressible, andnonhydrostatic system of equations. A forward-backward integration scheme is applied to treathigh-frequency and internal gravity waves explicitly. The numerical procedure is shown to beneutral in time as long as a Courant–Friedrichs–Lewy criterion is met. Compared to the leapfrog-scheme most models use, this method involves only two time steps, which requires lessmemory and is also free from unstable computational modes. Hence, a time-filter is not needed.Advection and diffusion terms are calculated with a time step longer than sound-wave relatedterms, so that extensive computer time can be saved. In addition, a new numerical procedurefor the free-slip bottom boundary condition is developed to avoid using inaccurate one-sidedfinite difference of pressure in the surface horizontal momentum equation when the terraineffect is considered. We have demonstrated the accuracy and stability of this new model in bothlinear and nonlinear situations. In linear mountain wave simulations, the model results matchthe corresponding analytical solution very closely for all three cases presented in this paper.The analytical streamlines for uniform flow over a narrow mountain range were obtainedthrough numerical integration of Queney’s mathematical solution. It was found that Queney’soriginal diagram is not very accurate. The diagram had to be redrawn before it was used toverify our model results. For nonlinear tests, we simulated the famous 1972 Boulder windstormand a bubble convection in an isentropic enviroment. Although there are no analytical solutionsfor the two nonlinear tests, the model results are shown to be very robust in terms of spatialresolution, lateral boundary conditions, and the use of the time-split scheme.

A Modeling Study of Nonstationary Trapped Mountain Lee Waves. Part II: Nonlinearity

The generation of nonstationary trapped mountain lee waves through nonlinear wave dynamics without any concomitant change in the background flow is investigated by conducting two-dimensional mountain wave simulations. These simulations demonstrate that finite-amplitude lee-wave patterns can exhibit temporal variations in local wavelength and amplitude, even when the background flow is perfectly steady. For moderate amplitudes, a nonlinear wave interaction involving the stationary trapped wave and a pair of nonstationary waves appears to be responsible for the development of nonstationary perturbations on the stationary trapped wave. This pair of nonstationary waves consists of a trapped wave and a vertically propagating wave, both having horizontal wavelengths approximately twice that of the stationary trapped wave. As the flow becomes more nonlinear, the nonstationary perturbations involve a wider spectrum of horizontal wavelengths and may dominate the overall wave pattern at wave amplitudes significantly below the threshold required to produce wave breaking. Sensitivity tests in which the wave propagation characteristics of the basic state are modified without changing the horizontal wavelength of the stationary trapped wave indicate these nonstationary perturbations are absent when the background flow does not support nonstationary trapped waves with horizontal wavelengths approximately twice that of the stationary trapped mode. These sensitivity tests also show that a second nonstationary trapped wave can assume the role of the nonstationary vertically propagating wave when the Scorer parameter in the upper layer is reduced below the threshold that will support the vertically propagating wave. In this case, a resonant triad composed of three trapped waves appears to be responsible for the development of nonstationary perturbations. The simulations suggest that strongly nonlinear wave dynamics can generate a wider range of nonstationary trapped modes than that produced by temporal variations in the background flow. It is suggested that the irregular variations in lee-wave wavelength and amplitude observed in real atmospheric flows and the complex fluctuations above a fixed point that are occasionally found in wind profiler observations of trapped lee waves are more likely to be generated by nonlinear wave dynamics than changes in the background flow.

A Modeling Study of Nonstationary Trapped Mountain Lee Waves. Part I: Mean-Flow Variability

Abstract The impact of mean-flow variability on finite-amplitude trapped mountain lee waves is investigated by conducting two-dimensional mountain wave simulations for a set of idealized, time-dependent background flows. The lee-wave patterns generated by these time-dependent flows depend on two factors: 1) the degree to which the transition in the background flow changes the amplitude of the stationary trapped lee wave and 2) the difference between the group velocities of the trapped waves generated before and after the transition. When the transition in the background flow significantly reduces the amplitude of the stationary lee wave, the lee-wave pattern generated prior to the transition gradually drifts downstream away from the mountain or back over the mountain, depending on the sign of this wave packet’s group velocity after the transition. When the transition in the background flow changes the resonant wavelength while leaving the lee-wave amplitude relatively unchanged, the lee-wave train develop...

Two-Dimensional Simulations of Mountain Waves Observed during the PYREX Experiment

Abstract Two-dimensional numerical simulations of mountain waves observed during the Pyrenees Experiment have been performed. Two intensive observing periods (IOP) have been simulated, IOP 3, which lasted less than one day, and IOP 9, which lasted two and one-half days. The time evolution of the large-scale flow was incorporated in the model through time-dependent boundary conditions that were updated using the closet upwind sounding. The numerically simulated mountain waves agree well with the available aircraft observations. Good agreement is also obtained between the simulated and observed vertical momentum flux profiles. In addition, the model-generated cross-mountain pressure drag accurately follows the time evolution of the observed drag. To get such a good agreement between observations and computations, it has been necessary to take into account in the model surface layer the effects of subgrid-scale orographic elements.

Development of a Three-Dimensional Meso-γ Primitive Equation Model: Katabatic Winds Simulation in the Area of Terra Nova Bay, Antarctica

The spatial evolution of Antarctic katabatic winds in the area of Terra Nova Bay is examined using the three-dimensional version of the Universite Catholique de Louvain-Modele Atmospherique Regional (UCL-MAR) mesoscale primitive equation models. The ability of the model to replicate classical linear mountain wave simulations is verified. Then, three-dimensional experiments are performed for the terrain configuration of Terra Nova (Ross Sea coastal zone) using different horizontal resolutions (5, 10, and 20 km). The model converges for resolutions lower than 10 km. Results are in qualitative agreement with available observations and previous modeling work. Strong katabatic winds are simulated with a jet over Terra Nova Bay. The model seems able to initiate the mesocyclonic activity in the Ross Sea due to the katabatic circulation.

Another Look at Downslope Winds. Part II: Nonlinear Amplification beneath Wave-Overturning Layers

Abstract Numerical mountain wave simulations have documented that intense lee-slope winds frequently arise when wave-overturning occurs above the mountain. Explanations for this amplification process have been proposed by Clark and Peltier in terms of a resonance produced by linear-wave reflections from a self-induced critical layer, and by Smith in terms of solutions to Long's equation for flow beneath a stagnant well-mixed layer. In this paper, we evaluate the predictions of these theories through numerical mountain-wave simulations in which the level of wave-overturning is fixed by a critical layer in the mean flow. The response of the simulated flow to changes in the critical-layer height and the mountain height is in good agreement with Smith's theory. A comparison of Smith's solution with shallow-water theory suggests that the strong lee-slope winds associated with wave-overturning are caused by a continuously stratified analog to the transition from subcritical to supercritical flow in conventional...

Numerical modelling of Bora winds

The Bora winds are produced by cold stable air which pours over the Dinaric Alps, often producing intense winds along the Adriatic Coast. Although the flow appears qualitatively similar to the hydraulic flow described by the shallow-water equations, there are certain significant differences: the cold low-level air is continuously stratified and a critical layer in the winds typically occurs near the inversion which caps the cold pool of air. Through two-dimensional numerical mountain wave simulations, we investigate the extent to which hydraulic theory can be used to describe the Bora winds. We analyze the structure of the Bora flow derived from aircraft observations collected during the ALPEX field phase on 15 April 1982 and compare it with a numerical simulation initialized from upstream sounding data. By varying the environmental sounding in our simulations, we find that for this case, neither the critical layer nor the inversion layer play a fundamental dynamical role in generating the strong winds along the lee slope. Instead, the wave overturning which occurs beneath the inversion appears to be the most important factor in producing the strong response. This overturning produces shooting flow over the lee slope and strongly resembles the hydraulic flow which occurs both in shallow water theory and in simulations in which over-turning is suppressed. We believe the hydraulic jump-like mechanism producing the strong Bora slope winds is fundamentally similar to the underlying mechanism which produces the intense winds along the lee slope of the Rocky Mountains. This occurs despite significant differences in the character of the larger scale flow in these two situations.

The Numerical Simulation of Clouds, Rains and Airflow over the Vosges and Black Forest Mountains: A Meso-β Model with Parameterized Microphysics

A three-dimensional meso-β model with parameterized microphysics is presented. The model is capable of simulating orographically forced clouds, rain, and airflow. Tests using a two-dimensional version confirm the ability of the model to replicate the linear and nonlinear mountain wave simulations of previous authors. The model is applied to the Rhine valley and surrounding mountainous areas, the Vosges in France and the Black Forest in Germany. Model-predicted rainfall over the mountainous areas is in good agreement with observations in both magnitude and location; however, an absence of model-predicted cloud cover over the Rhine valley suggests the need for an improved mesoscale initialization procedure.