Primitive Equation Model Research Articles

Sub-Mesoscale Frontal Instabilities in the Omani Coastal Current

The Omani Coastal Current (OCC) flowing northward along the southern coast of Oman during the summer monsoon is associated with an upwelling system. The mesoscale circulation of the western Arabian Sea is dominated by energetic mesoscale eddies down to about 1000 m depth. They drive the pathways of the upwelling water masses and the Persian Gulf Outflow water. This paper focuses on the sub-mesoscale frontal dynamics in the OCC by analyzing the results from a regional realistic numerical simulation performed with a primitive equation model. Off the Omani coast, the interaction between the upwelling fronts and the mesoscale eddies triggers the frontogenesis at play in the surface mixed layer during the summer monsoon. In spring, sub-mesoscale eddies are generated at the Cape of Ra’s al Hadd due to the horizontal shear instabilities undergone by the OCC. The OCC also drives and elongates Peddies formed during the Summer monsoon and located below the thermocline. Finally, the interaction between mesoscale eddies and the upwelling system leads to the formation of sub-mesoscale eddies at depth through baroclinic instabilities.

Life cycle of mesoscale eddies in the Gulf of Aden

The Red Sea Water is a warm and salty water produced in the Red Sea by evaporation induced by strong solar radiation. This dense water mass exits the Red Sea through the Strait of Bab El Mandeb, and enters the Gulf of Aden as a density current between 400 and 1000 metre depth. In the Gulf of Aden, in situ and satellites observations have shown the impact of the deeply reaching eddies dominating the mesoscale dynamics, on the spreading of the Red Sea Water. In this paper, we study the life cycle of these mesoscale eddies in the Gulf of Aden by using a regional primitive equation model at mesoscale resolution, and an eddy-tracking algorithm. The mesoscale anticyclonic eddies are formed at the mouth of the Gulf of Aden, and subsequently drift westward into the gulf. Mesoscale anticyclones are long-lived compared to the cyclones. The cyclones result from the interaction of anticyclones with the coast and the sloping topography. The wind stress, the bathymetry and the surrounding eddy field drive the life cycle of eddies. Finally, Kelvin and internal waves are triggered along the northern and southern coasts.

A Budget Equation for the Amplitude of Rossby Wave Packets Based on Finite-Amplitude Local Wave Activity

AbstractRecently, the authors proposed a novel diagnostic to quantify the amplitude of Rossby wave packets. This diagnostic extends the local finite-amplitude wave activity (LWA) of N. Nakamura and collaborators to the primitive-equations framework and combines it with a zonal filter to remove the phase dependence. In the present work, this diagnostic is used to investigate the dynamics of upper-tropospheric Rossby wave packets, with a particular focus on distinguishing between conservative dynamics and nonconservative processes. For this purpose, a budget equation for filtered LWA is derived and its utility is tested in a hierarchy of models. Idealized simulations with a barotropic and a dry primitive-equation model confirm the ability of the LWA diagnostic to identify nonconservative local sources or sinks of wave activity. In addition, the LWA budget is applied to forecast data for an episode in which the amplitude of an upper-tropospheric Rossby wave packet was poorly represented. The analysis attributes deficiencies in the Rossby wave packet amplitude to the misrepresentation of diabatic processes and illuminates the importance of the upper-level divergent outflow as a source for the error in the wave packet amplitude.

Impact of multiple tidal forcing on the simulation of the M2 internal tides in the northern South China Sea

Previous studies have indicated that internal tides (ITs) in the South China Sea (SCS) are dominated by the M2, K1, and O1, among which intense nonlinear interaction occurs. In this study, the impact of multiple tidal forcing on the simulation of the M2 ITs in the northern SCS is investigated based on a primitive equation model. Under the same model settings except the forcing at open boundaries, the run forced by the M2 individually yields larger M2 tidal currents and baroclinic energy fluxes than observations and the run forced by the M2, K1, and O1 together, although the M2 barotropic tidal forcing is the same in the two runs. The M2 barotropic to baroclinic energy conversion in the Luzon Strait (LS) is almost comparable in the two runs, suggesting that it is not the cause for the differences between the two runs. Indeed, the intense nonlinear interaction between the M2 and diurnal ITs should account for the differences. Results show that the nonlinear interaction is more intense in the SCS Basin than the western Pacific. Therefore, more energy is transferred from the M2 to tri-diurnal ITs in the SCS Basin. In addition, the nonlinear interaction enhances the energy loss of the M2 ITs in the LS.

Study of the stability of a large realistic cyclonic eddy

We investigate the stability of a composite cyclone representative of Arabian Sea eddies using a high resolution primitive equation model. We observe that the eddy is unstable with respect to a mixed barotropic/baroclinic instability, leading to the growth of an azimuthal mode 2 perturbation. The latter deforms the eddy, which eventually evolves into a tripole after about 4 months of simulation. The presence of a critical level for the most unstable mode generates sharp fronts in the surface mixed layer where the Rossby number is large. These fronts then become unstable, and this generates submesoscale cyclones and filaments. Near these fronts, diapycnal mixing occurs, causing the potential vorticity to change sign locally, and symmetric instability to develop in the core of the cyclonic eddy. Despite the instabilities, the eddy is not destroyed and remains a large-scale coherent structure for the last 6 months of the simulation. Looking at Sea Surface Height only, the composite eddy evolves little, and fairly represents the eddy observed in the altimetry which can live for several months. The study of this simulation thus illustrates the numerous kinds of instabilities which may occur in large cyclonic eddies but cannot be captured directly by altimetric data.

Eddy Saturation of the Southern Ocean: A Baroclinic Versus Barotropic Perspective

Abstract“Eddy saturation” is the regime in which the total time‐mean volume transport of an oceanic current is relatively insensitive to the wind stress forcing and is often invoked as a dynamical description of Southern Ocean circulation. We revisit the problem of eddy saturation using a primitive equations model in an idealized channel setup with bathymetry. We apply only mechanical wind stress forcing; there is no diapycnal mixing or surface buoyancy forcing. Our main aim is to assess the relative importance of two mechanisms for producing eddy‐saturated states: (i) the commonly invoked baroclinic mechanism that involves the competition of sloping isopycnals and restratification by production of baroclinic eddies and (ii) the barotropic mechanism that involves production of eddies through lateral shear instabilities or through the interaction of the barotropic current with bathymetric features. Our results suggest that the barotropic flow component plays a crucial role in determining the total volume transport.

The Effect of Measurement Limitations on High-Frequency Radar-Derived Spectral Energy Fluxes

AbstractThe ocean’s inverse cascade of energy from small to large scales has been confirmed from satellite altimetry for scales larger than 100 km. However, measurements of the direct energy cascade to smaller scales have remained difficult to obtain. Here, the possibility of estimating these energy transfers to smaller scales from observations by high-frequency radars is investigated using numerical simulations. Synthetic measurements are first extracted from a quasigeostrophic simulation of freely decaying turbulence for which the reference energy flux is characterized by the transition from positive to negative values. Fluxes obtained from synthetic data are compared to this reference flux in order to assess the robustness to various measurement limitations. The geometry of the observational domain (nonperiodicity, domain size, and aspect ratio) affects mostly large scales, while the spatial resolution of the instruments affects mostly small scales. In contrast, measurement noise and missing data affect both large and small scales. Despite resulting in significant biases in the amplitude of the fluxes, the transition scale between the positive and negative fluxes is relatively robust to measurement limitations. These results are also confirmed using a simulation from a primitive-equations model in a realistic coastal geometry.

Three-Dimensional Baroclinic Eddies in the Ocean: Evolution, Propagation, Overall Structures, and Angular Models

AbstractThe evolution and dynamics of an initially Gaussian baroclinic vortex embedded in a resting stratification environment are investigated with a three-dimensional primitive equation model. The vortex evolution process strongly depends on multiple parameters. Particularly, the effects of the gradient of planetary vorticity, nonlinearity, and friction have been studied to evaluate their roles. Comparisons with previous results from a simplified model are made. We particularly focus on interactions between vortices at different levels to understand their evolution. Additionally, a set of numerical simulations has been performed to examine the role of parameter space (Froude–Rossby number) on the evolution of eddies. The evolution and propagation of the vortex is affected by the planetary vorticity gradient; nonlinearity accelerates the transfer of energy from low to high angular mode and speeds up the propagation of eddies. A new finding is that a “double dipole” structure is observed with the development of a vortex, which is located in the core and edge regions, respectively. Only eddies in a finite depth range can maintain synchronous motion, and the dispersive translation paths in all levels imply that initially aligned eddies finally develop into misaligned structures and lead the tilted axis. In contrast to the results in a previous study, eddies have a southward drift irrespective of the vortex polarity. The eddies in the upper level maintain strong stability; in the middle depths, eddies decay rapidly where they form mixed barotropic and baroclinic instabilities. The energy budget analysis demonstrates the complex energy conversion between eddy and angular modes. The Burger number is the most important factor affecting the pattern of eddy evolution.

Elimination of spectral blocking by ensuring rotation‐free property of discretized pressure gradient within a spectral semi‐implicit semi‐Lagrangian global atmospheric model

AbstractThe widely‐adopted discretization of the horizontal pressure gradient term formulated by Simmons and Burridge for atmospheric models on σ‐p hybrid vertical coordinate is found to incur spectral blocking for rotational wind components at high vertical levels when used in a spectral semi‐Lagrangian model run on a linear grid. A remedy to this issue is proposed and tested using a spectral semi‐implicit semi‐Lagrangian hydrostatic primitive equations model. The proposed method removes aliasing errors at high wave‐numbers by ensuring that the rotation‐free property of the pressure gradient term on the isobaric surface, a feature possessed by the continuous system, is preserved in the discretized system, which highlights the significance of mimetic discretization within the context of numerical weather prediction models.

Mechanisms for a remote response to Asian anthropogenic aerosol in boreal winter

Abstract. Asian emissions of anthropogenic aerosols and their precursors have increased rapidly since 1980, with half of the increase since the pre-industrial era occurring in this period. Transient experiments with the HadGEM3-GC2 coupled model were designed to isolate the impact of Asian anthropogenic aerosols on global climate in boreal winter. It is found that this increase has resulted in local circulation changes, which in turn have driven decreases in precipitation over China, alongside an intensification of the offshore monsoon flow. No large temperature changes are seen over China. Over India, the opposite response is found, with decreasing temperatures and increasing precipitation. The dominant feature of the local circulation changes is an increase in low-level convergence, ascent, and precipitation over the Maritime Continent, which forms part of a tropical Pacific-wide La Niña-like response. HadGEM3-GC2 also simulates pronounced far-field responses. A decreased meridional temperature gradient in the North Pacific leads to a positive Pacific–North American circulation pattern, with associated temperature anomalies over the North Pacific and North America. Anomalous northeasterly flow over northeast Europe drives advection of cold air into central and western Europe, causing cooling in this region. An anomalous anticyclonic circulation over the North Atlantic causes drying over western Europe. Using a steady-state primitive equation model, LUMA, we demonstrate that these far-field midlatitude responses arise primarily as a result of Rossby waves generated over China, rather than in the equatorial Pacific.

Noninstantaneous Wave-CISK for the Interaction between Convective Heating and Low-Level Moisture Convergence in the Tropics

Abstract The interaction between tropical convective heating and thermally forced circulation is investigated using a global dry primitive-equation model with the parameterization of wave-conditional instability of the second kind (CISK). It is demonstrated that deep convective heating can hardly sustain itself through the moisture convergence at low levels regardless of the fraction of immediate consumption of converged moisture. In contrast, when the fraction is large, shallow convective heating and its forced circulation exhibit preferred growth of small scales. As the “CISK catastrophe” mainly comes from the instantaneous characters of moisture–convection feedback in the conventional wave-CISK, a noninstantaneous wave-CISK is proposed, which highlights the accumulation–consumption (AC) time scale for the convective heating accumulation and/or the converged moisture consumption. In the new wave-CISK, once moisture is converged, the release of latent heat takes place gradually within an AC time scale. In this sense, convective heating is not only related to the instantaneous moisture convergence at the current time, but also to that which occurred in the past period of the AC time scale. The noninstantaneous wave-CISK could guarantee the occurrence of convective heating and/or moisture convergence at larger scales, and then favor the growth of long waves, and thus solve the problem of CISK catastrophe. With the new wave-CISK and AC time scale of 2 days, the simulated convective heating-driven system bears a large similarity to that of the observed convectively coupled Kelvin wave.

The generation and maintenance of hollow PV towers in a forced primitive equation model

The generation and maintenance of hollow PV towers in a forced primitive equation model

On Material Transport by Shelfbreak Eddies

AbstractThe Lagrangian motion in the eddy field produced from an unstable retrograde jet along the shelf break is studied from idealized numerical experiments with a primitive equation model. The jet is initially in thermal wind balance with a cross-isobath density gradient and is not subjected to any atmospheric forcing. Over the course of the model integration, the jet becomes unstable and produces a quasi-stationary eddy field over a 2-month period. During this period, the cross-slope flow at the shelf break is characterized by along-slope correlation scales of O(10) km and temporal correlation scales of a few days. The relative dispersion of parcels across isobaths is found to increase with time as tb, where 1 < b < 2. This mixed diffusive–ballistic regime appears to reflect the combined effects of (i) the short length scales of velocity correlation at the shelf break and (ii) the seaward excursion of monopolar and dipolar vortices. Cross-slope dispersion is greater offshore of the front than inshore of the front, as offshore parcels are both subducted onshore below density surfaces and translated offshore with eddies. Nonetheless, the exchange of parcels across the jet remains very limited on the monthly time scale. Particles originating from the bottom experience upward displacements of a few tens of meters and seaward displacements of O(100) km, suggesting that the eddy activity engendered by an unstable along-slope jet provides another mechanism for bottom boundary layer detachment near the shelf edge.

Laplace transform integration of a baroclinic model

A time integration scheme based on the Laplace transform (LT) has been implemented in a baroclinic primitive equation model. The LT scheme provides an attractive alternative to the popular semi‐implicit (SI) scheme. Analysis shows that it is more accurate than SI for both linear and nonlinear terms of the equations. Numerical experiments confirm the superior performance of the LT scheme. The algorithmic complexity of the LT scheme is comparable with SI, with just an additional transformation to vertical eigenmodes each time step, and it provides the possibility of improving weather forecasts at comparable computational cost.

Transient contributions to the forcing of the atmospheric annual cycle

The forcing of the global circulation is examined using a primitive equation model and a 38-year reanalysis dataset. One-timestep integrations are initialised with selected sets of initial conditions, and the forcing budget for the mean annual cycle is deduced. This budget consists of sources and sinks of momentum, temperature and humidity which are balanced by dynamical terms. The associated timescale interactions are examined in detail. The time-mean forcing is balanced by time-mean fluxes, annual cycle interactions and transient fluxes. The annual cycle of the forcing is balanced by the interaction of annual cycle anomalies with the time-mean flow and with themselves (this latter cycle-cycle interaction term is found to be important for the moisture supply over West Africa). Transient interactions on other timescales also contribute to the forcing of the annual cycle, but the interaction term between the annual cycle and other timescales is small, as is the storage term associated with seasonal tendencies. This objectively derived empirical forcing is then used to drive the dynamical model. The resulting simple GCM is called DREAM (Dynamical Research Empirical Atmospheric Model). This is the first time this approach has been used with an annual cycle. The systematic errors of DREAM compared to the reanalysis chiefly concern the momentum balance in the southern hemisphere jet. Perpetual season simulations are similar to individual seasons from the annual cycle run, consistent with the small seasonal tendency term in the forcing.

The Finite-Amplitude Evolution of Mixed Kelvin–Rossby Wave Instability and Equatorial Superrotation in a Shallow-Water Model and an Idealized GCM

Abstract An instability involving the resonant interaction of a Rossby wave and a Kelvin wave has been proposed to drive equatorial superrotation in planetary atmospheres with a substantially smaller radius or a smaller rotation rate than Earth, that is, with a large thermal Rossby number. To pursue this idea, this paper investigates the equilibration mechanism of Kelvin–Rossby instability by simulating the unforced initial-value problem in a shallow-water model and in a multilevel primitive equation model. Although the instability produces equatorward momentum fluxes in both models, only the multilevel model is found to superrotate. It is argued that the shortcoming of the shallow-water model is due to its difficulty in representing Kelvin wave breaking and dissipation, which is crucial for accelerating the flow in the tropics. In the absence of dissipation, the zonal momentum fluxed into the tropics is contained in the eddy contribution to the mass-weighted zonal wind rather than the zonal-mean zonal flow itself. In the shallow-water model, the zonal-mean zonal flow is only changed by the eddy potential vorticity flux, which is very small in our flow in the tropics and can only decelerate the flow in the absence of external vorticity stirring.

Destabilization of an Oceanic Meddy-Like Vortex: Energy Transfers and Significance of Numerical Settings

Abstract The increase of computational capabilities led recent studies to implement very high-resolution simulations that gave access to new scale interaction processes, particularly those associated with the transfer of energy from the oceanic mesoscales to smaller scales through an interior route to dissipation, which is still underexplored. In this context, we study spindown simulations of a mesoscale interior vortex, unstable to a mixed baroclinic–barotropic instability. Even though the global energy is almost conserved, some energy is transferred down to dissipation scales during the development of instabilities. However, in our parameter regime, there is no substantial forward energy cascade sustained by unbalanced dynamics. Rather than exploring the physical parameter range, we clarify numerical discretization issues that can be detrimental to the physical solutions and our interpretation of finescale dynamics. Special care is given to determining the effective resolution of the different simulations. We improve it by a factor of 2 in our primitive equation (PE) finite-difference Coastal and Regional Ocean Community (CROCO) model by implementing a fifth-order accurate horizontal advection scheme. We also explore a range of grid aspect ratios dx/dz and find that energy spectra converge for aspect ratios that are close to N/f, the ratio of the stratification N over the Coriolis parameter f. However, convergence is not reached in the PE model when using a fourth-order centered scheme for vertical tracer advection (standard in ROMS-family codes). The scheme produces dispersion errors that trigger baroclinic instabilities and generate spurious submesoscale horizontal features. This spurious instability shows great impact on submesoscale production and energy cascade, emphasizing the significance of numerical settings in oceanic turbulence studies.

Regime Change Behavior during Asian Monsoon Onset

Abstract As the ITCZ moves off the equator on an aquaplanet, the Hadley circulation transitions from an equinoctial regime with two near-symmetric, significantly eddy-driven cells to a monsoon-like regime with a strong, thermally direct cross-equatorial cell, intense low-latitude precipitation, and a weak summer hemisphere cell. Dynamical feedbacks appear to accelerate the transition. This study investigates the relevance of this behavior to monsoon onset by using primitive equation model simulations ranging from aquaplanets to more realistic configurations with Earth’s continents and topography. A change in the relationship between ITCZ latitude and overturning strength is identified once the ITCZ moves poleward of approximately 7°. Monsoon onset is associated with off-equatorial ascent in regions of nonnegligible planetary vorticity, and this is found to generate a vortex stretching tendency that reduces upper-level absolute vorticity. In an aquaplanet, this causes a transition to the cross-equatorial, thermally direct regime, intensifying the overturning circulation. Analysis of the zonal momentum budget suggests that a stationary wave, driven by topography and land–sea contrast, can trigger a similar transition in the more realistic model configuration, with the wave extending the ascent region of the Southern Hemisphere Hadley cell northward, and enhanced overturning then developing to the south. These two elements of the circulation resemble the East and South Asian monsoons.

The Initial Perturbation for Mesoscale Predictability

The initial conditions and the effective models are important for weather prediction. The efficiency of the forecast depends on the initial conditions. There are many processes that are used to generate the initial conditions, in this research will be generate the initial conditions by the regular perturbation method because it can be used to the big data for weather prediction. The weathers prediction by the single level primitive equation model (SILEPE). The data used in this study from Intergovernmental Panel on Climate Change (IPCC). The forecast error between observed data and forecast data used to the Mean Absolute Deviation (MAD). The results to show that the regular perturbation method can be used to generate the initial conditions for the northeast monsoon prediction on 4 days forecast.

Internal wave generation by tidal flow over a two-dimensional ridge: energy flux asymmetries induced by a steady surface trapped current

The effects of a surface trapped steady background current on internal waves generated by tidal currents oscillating over a small symmetric ridge are investigated using a two-dimensional primitive equation model. A rigid lid is used with a linearly stratified fluid and the effects of rotation are not considered. We consider uni-directional background currents $\bar{U}(z)\geqslant 0$ confined to a surface layer lying well above the ridge. The current introduces asymmetries in the generated wave field. For sufficiently narrow ridges the upstream energy flux is larger than the downstream flux while the opposite is the case for sufficiently wide ridges. The total energy flux radiating away from the ridge is not significantly affected by the current. Mean second-order currents and pressure fields are shown to make important contributions to the total energy flux. A first-order linear theory, valid for a general stratification and surface current, which accurately predicts the wave field is also developed.