Geostrophic Adjustment Process Research Articles

Sensitivity of South Asian summer monsoon simulation to land surface schemes in Weather Research and Forecasting model

AbstractThe land surface scheme is crucial for the performance of regional climate models in dynamic downscaling application. In this study, we explore the sensitivity of the simulation with 10‐km resolution Weather Research and Forecasting (WRF) model to the land surface schemes in simulating South Asian summer monsoon. The WRF simulations for 19 summers from 2000 to 2018 are conducted with four different land surface schemes including Exp‐CLM4, Exp‐Noah‐MP, Exp‐PX, and Exp‐SSiB, with that the initial and boundary conditions for the WRF model simulations are provided from the NCEP‐FNL data. The ERAI reanalysis data, GHCN‐CAMS, and CRU gridded data are used to comprehensively evaluate the WRF simulations. Compared with verification data, the WRF model can reasonably capture the spatial patterns of summer mean large‐scale atmospheric circulation, 2‐m temperature and precipitation. The simulation results, however, are sensitive to the option of land surface scheme. The performance of Exp‐CLM4 and Exp‐SSiB is better than that of Exp‐Noah‐MP and Exp‐PX assessed by multivariable integrated evaluation (MVIE) method. To explore the dynamic and physical mechanisms behind the WRF model sensitivity to land surface schemes, the differences in the surface energy balance between the ensemble means Ens‐CLM4‐SSiB and Ens‐NoanMP‐PX are analysed in detail. The results illustrate that the intensity of the simulated sensible heat flux over South Asia is weaker in Ens‐CLM4‐SSiB than that in Ens‐NoahMP‐PX. The simulated wind fields are influenced due to the geostrophic adjustment process caused by large differences in geopotential height; thus, the simulations of 2‐m temperature and precipitation are all affected.

Simulation of summer climate over Central Asia shows high sensitivity to different land surface schemes in WRF

Land surface processes are vital to the performance of regional climate models in dynamic downscaling application. In this study, we investigate the sensitivity of the simulation by using the weather research and forecasting (WRF) model at 10-km resolution to the land surface schemes over Central Asia. The WRF model was run for 19 summers from 2000 to 2018 configured with four different land surface schemes including CLM4, Noah-MP, Pleim-Xiu and SSiB, hereafter referred as Exp-CLM4, Exp-Noah-MP, Exp-PX and Exp-SSiB respectively. The initial and boundary conditions for the WRF model simulations were provided by the National Centers for Environmental Prediction Final (NCEP-FNL) Operational Global Analysis data. The ERA-Interim reanalysis (ERAI), the GHCN-CAMS and the CRU gridded data were used to comprehensively evaluate the WRF simulations. Compared with the reanalysis and observational data, the WRF model can reasonably reproduce the spatial patterns of summer mean 2-m temperature, precipitation, and large- scale atmospheric circulation. The simulations, however, are sensitive to the option of land surface scheme. The performance of Exp-CLM4 and Exp-SSiB are better than that of Exp-Noah-MP and Exp-PX assessed by Multivariable Integrated Evaluation (MVIE) method. To comprehensively understand the dynamic and physical mechanisms for the WRF model’s sensitivity to land surface schemes, the differences in the surface energy balance between Ave-CLM4-SSiB (the ensemble average of Exp-CLM4 and Exp-SSiB) and Ave-NoanMP-PX (the ensemble average of Exp-Noah-MP and Exp-PX) are analyzed in detail. The results demonstrate that the sensible and latent heat fluxes are respectively lower by 30.42 W·m−2 and higher by 14.86 W·m−2 in Ave-CLM4-SSiB than that in Ave-NoahMP-PX. As a result, large differences in geopotential height occur over the simulation domain. The simulated wind fields are subsequently influenced by the geostrophic adjustment process, thus the simulations of 2-m temperature, surface skin temperature and precipitation are respectively lower by about 2.08 ℃, 2.23 ℃ and 18.56 mm·month−1 in Ave-CLM4-SSiB than that in Ave-NoahMP-PX over Central Asia continent.

Geostrophic adjustment on the f-plane: Symmetric versus anti-symmetric initial height distributions

We study the fundamental process of geostrophic adjustment in infinitely long zonal and meridional channels of widths Ly and Lx, respectively, by deriving analytic solutions and simulating the linearized rotating shallow water equations (LRSWE). All LRSWE's variables are divided into time-independent (geostrophic) and time-dependent components. The latter includes Kelvin waves, Poincaré waves, and inertial oscillations. Explicit expressions are derived for both components, which are confirmed numerically. Anti-symmetric and symmetric initial height distributions, η0(x), are considered, both of which introduce a length scale, D, into the problem. We show that for an anti-symmetric η0(x), (i) the rate of approach to geostrophy is D-independent; (ii) the decay rate of inertial oscillations is ∝t−1/2; and (iii) for DLy≫1, the energy of the final state in any finite sub-domain of the channel exceeds that of the initial state, while for DLy≪1 the energy in the final state is smaller than in the initial state. In contrast, for a symmetric η0(x): (i) the rate of approach to geostrophy increases with D; (ii) the decay rate of inertial oscillations is ∝t−3/2, and (iii) the energy of the final state is always smaller than that of the initial state. In meridional channels, the effect of boundaries is to (i) block the waves, propagation to infinity; (ii) alter the spatial structure of the geostrophic flow; and (iii) discretize the frequency spectrum, thus eliminating the inertial oscillations. The ratio of wave energy to initial energy decreases with Lx for anti-symmetric η0(x) and increases with Lx for symmetric η0(x).

Geostrophic adjustment on the equatorial beta-plane revisited

The process of geostrophic adjustment of localized large-scale pressure anomalies in the standard adiabatic shallow-water model on the equatorial beta-plane is revisited, and it is shown that the standard scenario of generation of westward-moving Rossby and eastward-moving Kelvin waves, which underlies the classical Gill theory of tropical circulation due to a localized heating, is not unique. Depending on the strength and aspect ratio of the initial perturbation, the response to the initial perturbation in the western sector can be dominated by inertia-gravity waves. The adjustment in the diabatic moist-convective shallow water model can be totally different and produces, depending on parameters, either Gill-like response or eastward-moving coherent dipolar structures of the type of equatorial modons, which do not appear in the “dry” adjustment, or vortices traveling, respectively, northwest in the Northern and southwest in the Southern hemispheres.

Asymmetry of jet streams formed under nonlinear geostrophic adjustment in shallow water

The process of geostrophic adjustment in a rotating layer of shallow water is considered. For initial distributions of the fluid depth in the form of a step and a localized rectangle, this process results in the formation of an isolated jet stream and a system of two counter jet streams, respectively. In this paper, the features of these flows structure, related to the nonlinearity of the adjustment process, are studied. The main feature for an isolated jet stream is the horizontal asymmetry of its velocity profile. For a system of two opposing flows, a mirror asymmetry is characteristic, which is caused by the dependence on the sign of the amplitude of the initial disturbance of depth. The velocity of flows with a negative sign (depression) always exceeds the velocity with a positive sign (elevation).

Generation of oceanic internal gravity waves by a cyclonic surface stress disturbance

Atmospheric cyclones with strong winds significantly impact ocean circulation, regional sea surface temperature, and deep water formation across the global oceans. Thus they are expected to play a key role in a variety of energy transport mechanisms. Even though wind-generated internal gravity waves are thought to contribute significantly to the energy balance of the deep ocean, their excitation mechanisms are only partly understood.The present study investigates the generation of internal gravity waves during a geostrophic adjustment process in a Boussinesq model with axisymmetric geometry. The atmospheric disturbance is set by an idealized pulse of cyclonic wind stress with a Rankine vortex structure. Strength, radius and duration of the forcing are varied. The effect upon wave generation of stratification with variable mixed-layer depth is also examined.Results indicate that internal gravity waves are generated after approximately one inertial period. The outward radial energy flux is dominated by waves having structure close to vertical mode-1 and with frequency close to the inertial frequency. Less energetic higher mode waves are observed to be generated close to the sea floor underneath the storm. The total radiated energy corresponds to approximately 0.02% of the wind input. Deeper mixed-layer conditions as well as weaker stratification reduce this fraction.The low energy transfer rates suggest that other processes that drive vertical motion like surface heat fluxes, turbulent motion, mixed region collapse and storm translation are essential for significant energy extraction by internal gravity waves to occur.

Asymmetry of Jet Streams Formed under Nonlinear Geostrophic Adjustment in Shallow Water

The process of geostrophic adjustment in a rotating layer of shallow water is considered. For initial distributions of the fluid depth in the form of a step and a localized rectangle, this process results in the formation of an isolated jet stream and a system of two counter jet streams, respectively. In this paper, the features of these flows structure, related to the nonlinearity of the adjustment process, are studied. The main feature for an isolated jet stream is the horizontal asymmetry of its velocity profile. For a system of two opposing flows, a mirror asymmetry is characteristic, which is caused by the dependence on the sign of the amplitude of the initial disturbance of depth. The velocity of flows with a negative sign (depression) always exceeds the velocity with a positive sign (elevation).

Analysis of modified Godunov type schemes for the two-dimensional linear wave equation with Coriolis source term on cartesian meshes

The study deals with collocated Godunov type finite volume schemes applied to the two-dimensional linear wave equation with Coriolis source term. The purpose is to explain the wrong behaviour of the classic scheme and to modify it in order to avoid accuracy issues around the geostrophic equilibrium and in geostrophic adjustment processes. To do so, a Hodge-like decomposition is introduced. Then three different well-balanced strategies are introduced. Some properties of the associated modified equations are proven and then extended to the semi-discrete case. Stability of fully discrete schemes under a suitable CFL condition is established thanks to a Von Neumann analysis. Some numerical results reinforce the purpose and exhibit the concrete improvements achieved by the application of these new techniques in both linear and nonlinear cases.

Theoretical aspects of upscale error growth on the mesoscales: Idealized numerical simulations

The mechanism for the upscale growth of small errors through the atmospheric mesoscales has not been conclusively identified, but geostrophic adjustment in response to diabatically generated motions such as cumulus convection is a plausible candidate. In a companion paper, an analytic solution of the linearized, hydrostatic Boussinesq equations to an impulsive, localized heat source that mimics the effect of latent heating within a convective cloud on an unperturbed, rotating environment is found. Three characteristics of the solution are shown to be potentially useful for identifying the geostrophic adjustment process in numerical simulations. The predictions relate to the horizontal gravity wave speed, the Rossby number and the quantitative relationship between a precipitation anomaly and the balanced flow response (i.e. large‐scale vorticity).Here these predictions are tested in the framework of error growth experiments in idealized numerical simulations of a convective cloud field. Three different rotation rates are employed in order to identify the geostrophic adjustment mechanism and allow a quantitative comparison with the predictions of the analytic model. The gravity wave speed estimated from the simulations resembles the theoretical value and is independent of the Coriolis parameter, as predicted. The Rossby number resulting from the proposed scaling of temporal and spatial coordinates features a unique shape and the vorticity diagnostic agrees quantitatively with the analytical predictions. Based on these findings, it is proposed that upscale error growth through the atmospheric mesoscales is governed by the geostrophic adjustment process.

Theoretical aspects of upscale error growth through the mesoscales: an analytical model

Recent numerical studies suggest that convective instability and latent heat release quickly amplify errors in numerical weather predictions and lead to a complete loss of predictability on scales below 100 km within a few hours. These errors then move further upscale, eventually contaminating the balanced flow and projecting on to synoptic‐scale instabilities. According to this picture, the errors have to transition from geostrophically unbalanced to balanced motion while propagating through the mesoscale. Geostrophic adjustment was suggested as the dynamical process of this transition, but so far has not been clearly identified.In the current study, an analytical framework for the geostrophic adjustment of an initial point‐like pulse of heat is developed on the basis of the linearized, hydrostatic Boussinesq equations. The heat pulse is thought to model a convective cloud or an error within the prediction of a cloud. A time‐dependent solution for both transient and balanced flow components is derived from the analytical model. The solution includes the Green's function of the problem, which enables the extension of the model to arbitrary heat sources by linear superposition. Spatial and temporal scales of the geostrophic adjustment mechanism are deduced and diagnostics are proposed that could be used to demonstrate the geostrophic adjustment process in complex numerical simulations of midlatitude convection and upscale error growth.

Monsoon Convection in the Maritime Continent: Interaction of Large-Scale Motion and Complex Terrain

Abstract The Asian monsoon is a planetary-scale circulation system powered by the release of latent heat, but important features of deep convection and rainfall distribution cannot be adequately represented by the large-scale patterns. This is mainly due to the strong influences of terrain that are important across a wide range of horizontal scales, especially over the Maritime Continent where the complex terrain has a dominant effect on the behavior of convective rainfall during the boreal winter monsoon. This chapter is a review and summary of published results on the effects on monsoon convection due to interactions between the Maritime Continent terrain and large-scale transient systems. The Maritime Continent topographic features strongly affect both the demarcation of the boreal summer and winter monsoon regimes and the asymmetric seasonal marches during the transition seasons. In the western part of the region, the complex interactions that lead to variability in deep convection are primarily controlled by the cold surges and the synoptic-scale Borneo vortex. The Madden–Julian oscillation (MJO) reduces the frequency of weaker surges through an interference with their structure. It also influences convection, particularly on the diurnal cycle and when synoptic activities are weak. When both surges and the Borneo vortex are present, interactions between these circulations with the terrain can cause the strongest convection, which has included Typhoon Vamei (2001), which is the only observed tropical cyclone that developed within 1.5° of the equator. The cold surges are driven by midlatitude pressure rises associated with the movement of the Siberian high. Rapid strengthening of surge northeasterly winds can be explained as the tropical response via a geostrophic adjustment process to the pressure forcing in the form of an equatorial Rossby wave group. Dispersion of meridional modes leads to a northeast–southwest orientation that allows the surge to stream downstream through the similarly oriented South China Sea. This evolution leads to a cross-equatorial return flow and a cyclonic circulation at the equator, and thus a mechanism for equatorial cyclogenesis. Although the narrow width of the southern South China Sea facilitates strengthening of the cold surge, it also severely restricts the likelihood of cyclone development so that Vamei remains to be the only typhoon observed in the equatorial South China Sea. Climate variations from El Niño–Southern Oscillation to climate change may impact the interactions between the large-scale motion and Maritime Continent terrain because they lead to changes in the mean flow. The thermodynamic effects on the interaction between MJO and the monsoon surges and Borneo vortex over the complex terrain also need to be addressed. These and other questions such as any possible changes in the likelihood of equatorial tropical cyclogenesis as a result of climate change are all important areas for future research.

Synoptic and mesoscale processes supporting vertical superposition of the polar and subtropical jets in two contrasting cases

Observational studies have shown that the tropopause characteristically exhibits a three‐step Pole‐to‐Equator structure, with each break between steps in the tropopause height associated with a jet stream. While the two jet streams, the polar and subtropical jets, typically occupy different latitude bands, their separation can occasionally vanish, resulting in a relatively rare vertical superposition of the two jets. A cursory examination of several historical and recent high‐impact weather events over North America and the North Atlantic suggests that superposed jets are a component of their evolution. This study examines the processes that support the production of a polar/subtropical jet superposition during two such events; the 18–20 December 2009 Mid‐Atlantic Blizzard and the 1–3 May 2010 Nashville Flood.Given that ageostrophic transverse circulations and convection have both been shown to be capable of restructuring the tropopause within a single jet environment, the analysis focuses on the role these same processes play within the more complex double‐jet environment. The results demonstrate that ageostrophic transverse circulations play a primary role in the production of a superposition during the December 2009 case by placing subsidence, and a downward protrusion of high potential vorticity (PV) air, between the two jet cores, thereby contributing to the production of the single, steep tropopause wall characteristic of the superposed jet environment. Furthermore, convection fundamentally influences the existence and structure of the subtropical jet stream in both cases, through its associated latent heat release and irrotational outflow as well as the geostrophic adjustment process that responds to upper‐tropospheric mass deposition from convection on the anticyclonic shear side of the jet.

An Initialization Method for Idealized Channel Simulations

Abstract Idealized model simulations have long been established as valuable tools to gain insight into atmospheric phenomena by providing a simplified, easier to comprehend version of the complex atmospheric system. A specific subgroup of idealized simulations, such as baroclinic channel models, requires the initialization of the model with balanced atmospheric fields to investigate the evolution of an introduced perturbation. The quality of these simulations depends on the degree of balance of the initial state, as imbalances result in geostrophic and hydrostatic adjustment processes that potentially skew the results. In this paper, a general method to create geostrophically and hydrostatically balanced initial conditions is introduced. The major benefit of this method is the possibility to directly define a basic state wind field with the pertinent atmospheric fields being derived given appropriate boundary conditions. Application of the method is exemplified by constructing initial conditions for a baroclinic test case with WRF and analyzing a perturbed and unperturbed numerical simulation. The unperturbed simulation exhibits weak inertia–gravity wave activity and minimal adjustment of the initial state during a 5-day simulation, which confirms the high degree of initial balance provided by the initialization technique. In the perturbed simulation, baroclinic instability is initiated, resulting in a cyclogenesis event similar to previous idealized baroclinic channel simulations. The proposed method is compared with initial conditions formulated in a Boussinesq framework, illustrating the difference in imbalances and their effect on perturbation growth.

Analogies of Ocean/Atmosphere Rotating Fluid Dynamics with Gyroscopes: Teaching Opportunities

The dynamics of the rotating shallow-water (RSW) system include geostrophic f low and inertial oscillation. These classes of motion are ubiquitous in the ocean and atmosphere. They are often surprising to people at first because intuition about rotating f luids is uncommon, especially the counterintuitive effects of the Coriolis force. The gyroscope, or toy top, is a simple device whose dynamics are also surprising. It seems to defy gravity by not falling over, as long as it spins fast enough. The links and similarities between rotating rigid bodies, like gyroscopes, and rotating fluids are rarely considered or emphasized. In fact, the dynamics of the RSW system and the gyroscope are related in specific ways and they exhibit analogous motions. As such, gyroscopes provide important pedagogical opportunities for instruction, comparison, contrast, and demonstration. Gyroscopic precession is analogous to geostrophic flow and nutation is analogous to inertial oscillation. The geostrophic adjustment process in rotating fluids can be illustrated using a gyroscope that undergoes transient adjustment to steady precession from rest. The controlling role of the Rossby number on RSW dynamics is reflected in a corresponding nondimensional number for the gyroscope. The gyroscope can thus be used to illustrate RSW dynamics by providing a tangible system that behaves like rotating fluids do, such as the large-scale ocean and atmosphere. These relationships are explored for their potential use in educational settings to highlight the instruction, comparison, contrast, and demonstration of important fluid dynamics principles.

On several mechanisms of the formation of the compensated thermohaline inhomogeneities in the ocean

The process of the geostrophic adjustment in the stably stratified two-component medium is studied in the framework of a linear approximation. We demonstrate that, at the final stage of that process, a stationary trace is generated by the distribution of the temperature and salinity, whose horizontal inhomogeneities mutually compensate in the field of the density. The compensation level for the stationary thermohaline distributions forming during the geostrophic adjustment is estimated. The origination mechanism of compensated thermohaline inhomogeneities in hydrodynamically stable shear flows is examined. We show that, in such flows, the disturbances of the fields of buoyancy (density), pressure, and velocity damp with time, whereas the compensated disturbances of the fields of the temperature and salinity are carried off by the flow without damping. Based on the explicit solutions of the dynamic equations, it is shown that the evolution of the compensated distribution of the temperature and salinity in the shear flows usually results in the sharpening of the spatial gradients. This feature may be, among others, related to one of the factors of the origination of the fine structure of the ocean: the small-scale thermohaline inhomogeneities, which exist against the background of the smooth vertical distribution of the density.

Vertical propagation of a mesoscale gravity wave from the lower to the upper atmosphere

To investigate the vertical propagation of gravity waves from the lower to the upper atmosphere, combined measurements with an airglow imager and lidars were carried out at the Arctic Lidar Observatory for Middle Atmosphere Research (ALOMAR) station (69.3°N, 16.0°E) in northern Norway. Airglow imaging reveals the two-dimensional structure of gravity waves in the mesopause region, while the ALOMAR Rayleigh/Mie/Raman (RMR) lidar and sodium lidar provide the vertical structures between the stratosphere and the lower thermosphere. On 26 November 2010, the imager identified a mesoscale gravity wave structure in the sodium airglow that had a horizontal wavelength of 277km, a wave period of 59min, and propagated northeastward at a phase speed of 78m s−1. Simultaneous lidar measurements also showed upward wave signatures with a similar wave period in the temperature perturbations; the vertical wavelength of the upward wave seen in the temperature data is consistent with the dispersion relation for gravity waves. Based on the combined measurements with the imager and sodium lidar, the momentum flux of this gravity wave was estimated to be 1.0m2 s−2 at the sodium airglow height. Ray-tracing analysis suggested that the observed gravity wave was generated by a distortion of the polar jet at the tropopause via a geostrophic adjustment process.

MST radar observation of inertia-gravity waves generated from tropical cyclones

Using a Mesosphere Stratosphere Troposphere (MST) radar, operating at 53 MHz at Gadanki (13.5°N, 79.2°E), India, the present study reports on the temporal and spatial characteristics of inertia-gravity waves (IGWs) generated from four tropical cyclones that formed over the Bay of Bengal. IGWs are observed with intrinsic frequencies, vertical and horizontal wavelengths in the ranges of 1.2 f–3.0 f, 2.5–5, and 300–1600 km, respectively, where f is the Coriolis frequency at the Gadanki site. It is found that both the convective and geostrophic adjustment processes in the troposphere play a major role in the generation of IGWs. Also it is found that the horizontal propagation direction of IGWs is aligned along the motion of convective rain bands.

The New York Bight Jet: Climatology and Dynamical Evolution

Abstract This paper describes the southerly New York Bight (NYB) jet (11–17 m s−1) that develops primarily during the warm season just above the surface offshore (east) of the northern New Jersey coast and south of Long Island (the NYB). Observations from two offshore buoys are used to develop a 9-yr climatology of 134 jet events from 1997 to 2006. There is a seasonal maximum (2.5 events per month) during June and July, with a skew toward the spring months. The wind directions for the jet trace out a nearly elliptical orbit for the 24-h period around the time of jet maximum at ~2300 UTC [1900 eastern daylight time (EDT)] on average. Composites reveal that the NYB jet occurs on days with southwesterly synoptic flow, and the jet is part of a larger-scale (200–300 km) wind enhancement offshore of the mid-Atlantic and northeast U.S. coasts during the early evening hours. High-resolution observations (surface mesonet, aircraft soundings, and a terminal Doppler weather radar) and Weather Research and Forecasting (WRF) model simulations down to 1.33-km grid spacing are used to diagnose the evolution of the NYB jet on 2 June 2007. The NYB jet at ~150 m MSL occurs within the sloping marine inversion near the coast. Low-level trajectories illustrate low-level diffluence and weak subsidence within the jet. A WRF momentum budget highlights the evolving pressure gradient and accelerations during jet formation. The maximum jet winds occur 1–2 h after the peak meridional pressure gradient is established through a geostrophic adjustment process. Sensitivity experiments show that jet occurrence is dependent on diurnal heating and that the concave bend in the southern New Jersey coast limits the southern extent of the jet.

Poincaré oscillations and geostrophic adjustment in a rotating paraboloid

Free liquid oscillations (Poincare oscillations) in a rotating paraboloid are investigated theoretically and experimentally. Within the framework of shallow-water theory, with account for the centrifugal force, expressions for the free oscillation frequencies are obtained and corrections to the frequencies related with the finiteness of the liquid depth are found. It is shown that in the rotating liquid, apart from the wave modes of free oscillations, a stationary vortex mode is also generated, that is, a process of geostrophic adjustment takes place. Solutions of the shallow-water equations which describe the wave dynamics of the adjustment process are presented. In the experiments performed the wave and vortex modes were excited by removing a previously immersed hemisphere from the central part of the paraboloid. Good agreement between theory and experiment was obtained.

Impact of the fourth‐order compact difference scheme on computational properties of 3D grids in a nonhydrostatic model

AbstractTo investigate the potential of the fourth‐order compact difference scheme within the specific context of numerical atmospheric models, a linear baroclinic adjustment system is discretized, using a variety of candidates for practically meaningful staggered 3D grids. A unified method is introduced to derive the dispersion relationship of the baroclinic geostrophic adjustment process. Eight popular 3D grids are obtained by combining contemporary horizontal staggered grids, such as the Arakawa C and Eliassen grids, with optimal vertical grids, such as the Lorenz and Charney‐Phillip (CP) grids, and their time‐staggered versions. The errors produced on the 3D grids in describing the baroclinic geostrophic adjustment process relative to the differential case are compared in terms of frequency and group velocity components with the elimination of implementation error. The results show that by utilizing the fourth‐order compact difference scheme with high precision, instead of the conventional second‐order centered difference scheme, the errors in describing baroclinic geostrophic adjustment process decrease but only when using the combinations of the horizontally staggered Arakawa C grid and the vertically staggered CP or the C/CP grid, the time‐horizontally staggered Eliassen (EL) grid and vertically staggered CP or the EL/CP grid, the C grid and the vertically time‐staggered versions of Lorenz (LTS) grid or C/LTS grid, EL grid and LTS grid or EL/LTS grid. The errors were found to increase for specific waves on the rest grids. It can be concluded that errors produced on the chosen 3D grids do not universally decrease when using the fourth‐order compact difference scheme; hence, care should be taken when implementing the fourth‐order compact difference scheme, otherwise, the expected benefits may be offset by increased errors. Copyright © 2008 John Wiley & Sons, Ltd.