Primitive Equation Model Research Articles

Quantifying the Incoherent M2 Internal Tide in the Philippine Sea

AbstractThe baroclinic tides are a crucial source of mixing energy into the deep ocean; however, the incoherent portion of the spectrum is not well examined because it is difficult to observe. This study estimates the coherent and incoherent M2 internal tide energy fluxes in the Philippine Sea using a primitive equation model that resolves the M2 barotropic and baroclinic tides and the time-evolving atmospherically forced eddying circulation. A time-mean, incoherent, internal tide energy flux of 25% of the coherent energy flux is found to emanate eastward into the Philippine Sea from the Luzon Strait and a time-mean incoherent portion of 30% of the coherent energy flux propagates westward into the South China Sea (SCS). The incoherent internal tide energy results from baroclinic tide generation and propagation variability. Quantifying the incoherent portion estimates the energy missing from altimeter-derived or line-integral acoustic measurements and places short-lived, in situ observations in the context of variability.

Near-inertial motions in the DeSoto Canyon during Hurricane Georges

Hurricane Georges passed directly over an array of 13 moorings deployed in the DeSoto Canyon in the northern Gulf of Mexico on 27–28 September 1998. Current velocity data from the mooring array were analyzed together with a primitive-equation model simulation with realistic hurricane forcing, to characterize the generation and propagation of the hurricane-generated near-inertial waves. The model successfully reproduces the observed mean (sub-inertial) and near-inertial motions. The upper ocean response is strongly impacted by the canyon ‘wall’: a strong jet is formed along the slope, and the near-inertial motions on the shelf are rapidly suppressed. The model results moreover suggest that strong near-inertial waves in the mixed layer are mostly trapped in an energy flux recirculating gyre around the canyon. This gyre retains the near-inertial energy in the canyon region and enhances the transfer of near-inertial energy below the mixed layer. Additional simulations with idealized topographies show that the presence of a steep slope rather than the canyon is fundamental for the generation of this recirculating gyre. The near-inertial wave energy budget shows that during the study period the wind generated an input of 6.79×10–2Wm–2 of which about 1/3, or 2.43×10–2Wm–2, was transferred below the mixed layer. The horizontal energy flux into and out of the canyon region, in contrast, was relatively weak.

DATA ASSIMILATION BY ENSEMBLE KALMAN FILTER WITH THE LORENZ EQUATIONS

Data Assimilation is a procedure to get the initial condition as accurately as possible, through the statistical combination of collected observations and a background field, usually a short-range forecast. In this research a complete assimilation system for the Lorenz equations based on Ensemble Kalman Filter is presented and examined. The Lorenz model is chosen for its simplicity in structure and the dynamic similarities with primitive equations models, such as modern numerical weather forecasting. Based on results, was concluded that, in this implementation, 10 members is the best setting, because there is an overfitting for ensembles with 50 and 100 members. It was also examined if the EnKF is effective to track the control for 20% and 40% of error in the initial conditions. The results show a disagreement between the “truth” and the estimation, especially in the end of integration period, due the chaotic nature of the system. It was also concluded that EnKF have to be performed sufficiently frequently in order to produce desirable results.

Pathways and mechanisms of offshore water intrusions on the Espírito Santo Basin shelf (18°S–22°S, Brazil)

AbstractThe pathways and physical mechanisms associated with intrusions of cold, nutrient‐rich South Atlantic Central Water (SACW) on the continental shelf of the Espírito Santo Basin (ESB), off southeast Brazil (18°S–22°S), are investigated. To this end, a set of process‐oriented, Primitive‐Equation (PE) numerical models are used, together with an independent and more complete PE model, available observations and simple theoretical ideas. SACW enters the model ESB shelf mostly through two preferential pathways along the Tubarão Bight (TB, 19.5°S–22°S). These pathways are found to be locations where an equatorward along‐isobath pressure gradient force (PGFy*) of m s−2) develops in response to steady wind forcing. This equatorward PGFy* is essentially in geostrophic balance, inducing onshore flow across the shelf edge, and most of the shelf proper. The Brazil Current (BC) imparts an additional periodic (in the along‐shelf direction) PGFy* on the shelf. The intrinsic pycnocline uplifting effect of the BC in making colder water available at the shelf edge is quantified. The BC also induces local intrusions by inertially overshooting the shelf edge, consistent with estimated Rossby numbers of 0.3–0.5. In addition, the planetary β‐effect is related to a background equatorward PGFy*. A modified Arrested Topographic Wave model is shown to be a plausible rationalization for the shelf‐wide spreading of the pressure field imparted by the BC at the shelf edge. The deep‐ocean processes examined here are found to enhance the onshore transport of SACW, while wind forcing is found to dominate it at leading order.

A Four-Dimensional Incremental Analysis Update for the Ensemble Kalman Filter

Abstract The analysis produced by the ensemble Kalman filter (EnKF) may be dynamically inconsistent and contain unbalanced gravity waves that are absent in the real atmosphere. These imbalances can be exacerbated by covariance localization and inflation. One strategy to combat the imbalance in the analyses is the incremental analysis update (IAU), which uses the dynamic model to distribute the analyses increments over a time window. The IAU has been widely used in atmospheric and oceanic applications. However, the analysis increment that is gradually introduced during a model integration is often computed once and assumed to be constant for an assimilation window, which can be seen as a three-dimensional IAU (3DIAU). Thus, the propagation of the analysis increment in the assimilation window is neglected, yet this propagation may be important, especially for moving weather systems. To take into account the propagation of the analysis increment during an assimilation window, a four-dimensional IAU (4DIAU) used with the EnKF is presented. It constructs time-varying analysis increments by applying all observations in an assimilation window to state variables at different times during the assimilation window. It then gradually applies these time-varying analysis increments through the assimilation window. Results from a dry two-layer primitive equation model and the NCEP GFS show that EnKF with 4DIAU (EnKF-4DIAU) and 3DIAU (EnKF-3DIAU) reduce imbalances in the analysis compared to EnKF without initialization (EnKF-RAW). EnKF-4DIAU retains the time-varying information in the analysis increments better than EnKF-3DIAU, and produces better analysis and forecast than either EnKF-RAW or EnKF-3DIAU.

On the merger of subsurface isolated vortices

Vortex merger is a phenomenon characterizing the whole class of geophysical vortices, from atmospheric storms and large oceanic eddies up to small scale turbulence. Here we focus on the merger of subsurface oceanic anticyclones in an idealized primitive equations model. This study has been motivated by past and recent observations of colliding lens-like anticyclones off of Gibraltar Strait. The critical conditions for merger (critical merger distance and time needed for merger) are determined. We will show that the predictions of classical two-dimensional merger are not verified for subsurface isolated vortices. For instance, critical merger distances will be reduced because of the vortex potential vorticity (PV) structure. The post-merger characteristics of the vortex (radius, extension and PV), are also determined. Merger-related effects, like production of peripheral filaments and small-scale eddies are also investigated and suggest the contribution of merger in both direct and inverse energy cascades.

Global observations and modeling of nonmigrating diurnal tides generated by tide‐planetary wave interactions

AbstractAdvective processes that couple planetary waves with tides have long been proposed as sources of nonmigrating diurnal tides. This paper reports observations of short‐term variability in global observations of nonmigrating tides predicted to arise from the interaction of the migrating diurnal tide (DW1) with a quasi‐stationary planetary wave number one (PW1). PW1 and tidal definitions are extracted from satellite temperatures and high‐altitude meteorological analyses. During winter months, the evolution of westward traveling diurnal tides with zonal wave number 2 (DW2) generally tracks that of strong‐amplitude stratospheric PW1. DW1 and PW1 spectra are used to compute nonlinear tidal forcing terms arising from advection. We then examine the response of a primitive equation model to the observation‐based nonlinear forcing. The model experiments indicate that meridional advection of PW1 zonal momentum by DW1 is a significant source of lower thermospheric DW2. Modeled DW2 amplitudes are very consistent with observed DW2 amplitudes when stratospheric PW1 penetrates to equatorial latitudes. The model experiments also indicate that the interaction can imprint short‐term variability associated with wintertime PW1 upon DW2 in the summer hemisphere and the lower thermosphere.

Mesoscale variability in the Arabian Sea from HYCOM model results and observations: impact on the Persian Gulf Water path

Abstract. The Arabian Sea and Sea of Oman circulation and water masses, subject to monsoon forcing, reveal a strong seasonal variability and intense mesoscale features. We describe and analyze this variability and these features, using both meteorological data (from ECMWF reanalyses), in situ observations (from the ARGO float program and the GDEM – Generalized Digital Environmental mode – climatology), satellite altimetry (from AVISO) and a regional simulation with a primitive equation model (HYCOM – the Hybrid Coordinate Ocean Model). The model and observations display comparable variability, and the model is then used to analyze the three-dimensional structure of eddies and water masses with higher temporal and spatial resolutions than the available observations. The mesoscale features are highly seasonal, with the formation of coastal currents, destabilizing into eddies, or the radiation of Rossby waves from the Indian coast. The mesoscale eddies have a deep dynamical influence and strongly drive the water masses at depth. In particular, in the Sea of Oman, the Persian Gulf Water presents several offshore ejection sites and a complex recirculation, depending on the mesoscale eddies. The associated mechanisms range from coastal ejection via dipoles, alongshore pulses due to a cyclonic eddy, to the formation of lee eddies downstream of Ra's Al Hamra. This water mass is also captured inside the eddies via several mechanisms, keeping high thermohaline characteristics in the Arabian Sea. The variations of the outflow characteristics near the Strait of Hormuz are compared with variations downstream.

Instability and Mixing of Zonal Jets along an Idealized Continental Shelf Break

AbstractThe interaction between an Antarctic Circumpolar Current–like channel flow and a continental shelf break is considered using eddy-permitting simulations of a quasigeostrophic and a primitive equation model. The experimental setup is motivated by the continental shelf of the West Antarctic Peninsula. Numerical experiments are performed to study how the width and slope of an idealized continental shelf topography affect the characteristics of the flow. The main focus is on the regime where the shelfbreak width is slightly greater than the eddy scale. In this regime, a strong baroclinic jet develops on the shelf break because of the locally stabilizing effect of the topographic slope. The velocity of this jet is set at first order by the gradient of the background barotropic geostrophic contours, which is dominated by the slope of the topography. At statistical equilibrium, an aperiodic cycle is observed. Initially, over a long stable period, an upper-layer jet develops over the shelf break. Once the vertical shear reaches the critical condition for baroclinic instability, the jet becomes unstable and drifts away from the shelf break. The cross-shelf mixing is intrinsically linked with the jet drifting, as most of the meridional flux occurs during this instability period. Investigation of the zonal momentum budget reveals that a strong Reynolds stress divergence inversion across the jet is associated with a drifting event, accelerating one flank of the jet and decelerating the other. The hypothesis that jet drifting may be due to one flank of the jet being more baroclinically unstable than the other is tested using topographic profiles with variable curvatures.

Cyclones and Anticyclones in Seismic Imaging

AbstractNearly all the subsurface eddies detected in seismic imaging of sections in the northeast Atlantic have been assumed to be anticyclones containing Mediterranean Water (MW). Fewer MW cyclones have been observed and studied. In this study, the work of previous numerical studies is extended to investigate some characteristics of layering surrounding MW cyclones, using a primitive equation model with equal diffusivities for salinity and temperature to suppress the effects of double diffusion. It is shown that, after a stable state is reached, both anticyclones and cyclones display similar patterns of layering: stacked thin layers of high acoustic reflectivity located above and below the core of each vortex, which do not match isopycnals. The authors conclude that it should not be possible to distinguish between MW cyclones and anticyclones based on their signature in seismic imaging alone. Complementary information is needed to determine the sense of rotation.

Energy‐conserving finite‐difference schemes for quasi‐hydrostatic equations

The pressure‐based hydrostatic primitive equations model LMD‐Z is extended to solve the quasi‐hydrostatic deep‐atmosphere as well as the non‐traditional shallow‐atmosphere equations (with a complete Coriolis force representation).The continuous equations are first derived in their curl form using Eulerian horizontal and non‐Eulerian vertical coordinates. The equations are then interpreted as a Hamiltonian system, as they are expressed in terms of functional derivatives of the Hamiltonian. Using a finite‐difference scheme on a longitude/latitude grid and based either on a Lagrangian or mass‐based vertical coordinate, the discrete scheme is obtained by imitating the Hamiltonian formulation at the discrete level. It is shown how this form leads straightforwardly to the conservation of discrete total energy. The relation between the discrete equations and the discrete antisymmetry property of the Poisson bracket is discussed.The computing infrastructure of the dynamical core is kept essentially unchanged but the modification of the hydrostatic balance requires a mass‐based vertical coordinate. Also, absolute angular momentum is used as a prognostic variable instead of relative velocity, which allows time‐dependent metric terms and the non‐traditional Coriolis force to be absorbed into it.The prototype implementation is applied to idealized circulations of an Earth‐like small planet and validates the stability and accuracy of the new dynamical core.

Assimilação de Dados Via Método 3D-Var em Dinâmica Caótica do Modelo de Lorenz

This paper explores some aspects of data assimilation by 3D-Var method implemented in the Lorenz model. This system was chosen because, although simple, has similar structure to the atmosphere under certain parameters. Conceptual models allow difficult judgments to be made in primitive equation models with their various nonlinear interactions at various scales. It is shown the need to apply data assimilation techniques in highly sensitive models to initial conditions. It was also shown that 3D-Var method is very dependent on the number of cycles during the process of minimizing of the cost function. In the experiment performed on this work was found that at least 1,000 interactions are necessary to solve this minimization problem. However the technique fail to 40% noise added to initial conditions, comparing to control. Additional experiments show the difficulty of performing high quality data assimilation in chaotic dynamics for underdetermined systems, such as the Earth's atmosphere.

Formation and Maintenance of the Tropical Cold-Point Tropopause in a Dry Dynamic-Core GCM

Abstract The formation of the tropical cold-point tropopause (CPT) is examined using a dry primitive equation model driven by the Held–Suarez forcing. Without moist and realistic radiative processes, the dry model successfully reproduces the zonal-mean structure of the CPT. The modeled CPT is appreciably colder (~10 K) than the prescribed equilibrium temperature, and it is maintained by upwelling in the tropical upper troposphere and lower stratosphere (UTLS). A transient simulation starting from an axisymmetric steady state without the CPT shows that the evolution and maintenance of the CPT are closely related to the zonal-mean-flow response to wave driving in the stratosphere. The transformed Eulerian-mean analysis indicates that the wave driving is mostly due to convergence of synoptic-scale waves originating from the midlatitude troposphere and propagating into the subtropical UTLS in this model simulation. The modeled CPT also shows a large sensitivity to increased baroclinicity in the equilibrium temperature. Although planetary-scale waves are not considered in this simulation, the result confirms that wave-driven upwelling in the tropical UTLS is a crucial process for the formation and maintenance of the CPT. In addition, it also implies that synoptic-scale waves may play a nonnegligible role in this mechanism, particularly in the seasons when planetary-scale wave activity in the lower stratosphere is weak.

Energy budget-based backscatter in an eddy permitting primitive equation model

Increasing computational resources are starting to allow global ocean simulations at so-called “eddy-permitting” resolutions, at which the largest mesoscale eddies can be resolved explicitly. However, an adequate parameterization of the interactions with the unresolved part of the eddy energy spectrum remains crucial. Hyperviscous closures, which are commonly applied in eddy-permitting ocean models, cause spurious energy dissipation at these resolutions, leading to low levels of eddy kinetic energy (EKE) and weak eddy induced transports. It has recently been proposed to counteract the spurious energy dissipation of hyperviscous closures by an additional forcing term, which represents “backscatter” of energy from the un-resolved scales to the resolved scales. This study proposes a parameterization of energy backscatter based on an explicit sub-grid EKE budget. Energy dissipated by hyperviscosity acting on the resolved flow is added to the sub-grid EKE, while a backscatter term transfers energy back from the sub-grid EKE to the resolved flow. The backscatter term is formulated deterministically via a negative viscosity, which returns energy at somewhat larger scales than the hyperviscous dissipation, thus ensuring dissipation of enstrophy. The parameterization is tested in an idealized configuration of a primitive equation ocean model, and is shown to significantly improve the solutions of simulations at typical eddy-permitting resolutions.

Long-Period Tides in an Atmospherically Driven, Stratified Ocean

AbstractLong-period tides (LPT) are studied using a stratified, primitive equation model on a global domain and in the presence of a fully developed, atmospherically forced ocean general circulation. The major LPT constituents, from termensual to nodal (18.6 yr) periods, are examined. Ocean circulation variability can overwhelm the longest tide signals and make inferring LPT from data difficult, but model results suggest that bottom pressure offers cleaner signal-to-noise ratios than sea level, particularly at low latitudes where atmospherically driven variability is substantially stronger at the surface than at the bottom. Most tides exhibit a significant large-scale dynamic response, with the tendency for weaker nonequilibrium signals in the Atlantic compared to the Pacific as seen in previous studies. However, across most tidal lines, the largest dynamic signals tend to occur in the Arctic and Nordic Seas and also in Hudson Bay. Bathymetry and coastal geometry contribute to the modeled nonequilibrium behavior. Baroclinic effects tend to increase with the tidal period. Apart from short spatial-scale modulations associated with topographic interactions, the excitation of various propagating baroclinic wave modes is clearly part of the modeled LPT, particularly at tropical latitudes, for fortnightly and longer-period tides.

Ensemble assimilation of ARGO temperature profile, sea surface temperature, and altimetric satellite data into an eddy permitting primitive equation model of the North Atlantic Ocean

Sea surface height, sea surface temperature, and temperature profiles at depth collected between January and December 2005 are assimilated into a realistic eddy permitting primitive equation model of the North Atlantic Ocean using the Ensemble Kalman Filter. Sixty ensemble members are generated by adding realistic noise to the forcing parameters related to the temperature. The ensemble is diagnosed and validated by comparison between the ensemble spread and the model/observation difference, as well as by rank histogram before the assimilation experiments. An incremental analysis update scheme is applied in order to reduce spurious oscillations due to the model state correction. The results of the assimilation are assessed according to both deterministic and probabilistic metrics with independent/semiindependent observations. For deterministic validation, the ensemble means, together with the ensemble spreads are compared to the observations, in order to diagnose the ensemble distribution properties in a deterministic way. For probabilistic validation, the continuous ranked probability score (CRPS) is used to evaluate the ensemble forecast system according to reliability and resolution. The reliability is further decomposed into bias and dispersion by the reduced centered random variable (RCRV) score in order to investigate the reliability properties of the ensemble forecast system. The improvement of the assimilation is demonstrated using these validation metrics. Finally, the deterministic validation and the probabilistic validation are analyzed jointly. The consistency and complementarity between both validations are highlighted.

Surface seiches in Flathead Lake

Abstract. Standing surface waves or seiches are inherent hydrodynamic features of enclosed water bodies. Their two-dimensional structure is important for estimating flood risk, coastal erosion, and bottom sediment transport, and for understanding shoreline habitats and lake ecology in general. In this work, we present analysis of two-dimensional seiche characteristics in Flathead Lake, Montana, USA, a large intermountain lake known to have high seiche amplitudes. To examine spatial characteristics of different seiche modes, we used the original procedure of determining the seiche frequencies from the primitive equation model output with subsequent derivation of the spatial seiche structure at fixed frequencies akin to the tidal harmonic analysis. The proposed procedure revealed specific seiche oscillation features in Flathead Lake, including maximum surface level amplitudes of the first fundamental mode in straights around the largest island; several higher modes appearing locally in the vicinity of the river inflow; the "Helmholtz" open harbor mode, with the period approximately twice that of the longest seiche mode, generated by a large shallow bay connected to the main lake basin; and several rotating seiche modes potentially affecting the lake-wide circulation. We discuss lake management problems related to the spatial seiche distribution, such as shoreline erosion, floods, and transport of sediments and invasive species in Flathead Lake.

Seasonal Variation of the Pacific South Equatorial Current Bifurcation

AbstractThe seasonal variation of the South Equatorial Current (SEC) bifurcation off the Australian coast in the South Pacific (SP) is investigated with observations and a nonlinear, reduced-gravity, primitive equation model of the upper ocean. The mean SEC bifurcation latitude (SBL) integrated over the upper thermocline is around 17.5°S, almost 2° south of the position predicted by Sverdrup theory. For its seasonal variation, the SBL reaches its southernmost position in June/July and its northernmost position in November/December. The south–north migration of 2.7° is twice as large as its counterpart in the North Pacific. It is found that the large seasonal amplitude of the SBL results from the combined effect of Low-Lat-SP and Non-Low-Lat-SP processes. The Low-Lat-SP process (referred to as the Rossby wave dynamics forced by the wind stress curl over the low-latitude SP) accounts for almost ⅔ of the SBL seasonal variability, and the Non-Low-Lat-SP processes account for ⅓. Both of these processes are responsible for its south–north migration but in different ways. The Low-Lat-SP wind forcing determines the offshore upper-layer thickness (ULT) via Rossby wave propagation, while the Non-Low-Lat-SP wind forcing determines the alongshore ULT via coastal Kelvin wave propagation. A simple bifurcation model is proposed under the framework of linear Rossby wave dynamics. It is found that the seasonal bifurcation latitude is predominantly determined by the spatial pattern of the wind and baroclinic Rossby wave propagation. This model explains the roles of local/remote wind forcing and baroclinic adjustment in the south–north migration and peak seasons of the bifurcation latitude.

The Role of Closed Gyres in Setting the Zonal Transport of the Antarctic Circumpolar Current

AbstractEddy-permitting simulations are used to show that basinlike gyres can be observed in the large-scale barotropic flow of a wind-driven channel with a meridional topographic ridge. This is confirmed using both two-layer quasigeostrophic and 25-level primitive equation models at high horizontal resolution. Comparing results from simulations with and without the topographic ridge, it is shown that the zonal baroclinic transport in the channel increases with increasing wind stress when the bottom topography is flat but not when there is a meridional ridge. The saturation of transport for increasing wind occurs in conjunction with the development of recirculating gyres in the large-scale barotropic streamfunction. This suggests that the total circulation can be thought of as a superposition of a gyre mode (which has zero circumpolar transport) and a free circumpolar mode (which contains all of the transport). Basinlike gyres arise in the channel because the topography steers the barotropic streamlines and supports a frictional boundary layer similar to the more familiar ones observed along western boundaries. The gyre mode is thus closely linked with the bottom form stress exerted by the along-ridge flow and provides the sink for the wind momentum input. In this framework, any increase in wind forcing spins a stronger gyre as opposed to feeding the circumpolar transport. This hypothesis is supported with a suite of experiments where key parameters are carried over a wide range: wind stress, wind stress curl, ridge height, channel length, and bottom friction.

Adaptive Localization for the Ensemble-Based Observation Impact Estimate Using Regression Confidence Factors

Abstract The goal of this study is to improve an ensemble-based estimation for forecast sensitivity to observations that is straightforward to apply using existing products of any ensemble data assimilation system. Because of limited ensemble sizes compared to the large degrees of freedom in typical models, it is necessary to apply localization techniques to obtain accurate estimates. Fixed localization techniques do not guarantee accurate impact estimates, because as forecast time increases the error correlation structures evolve with the flow. Here a dynamical localization method is applied to improve the observation impact estimate. The authors employ a Monte Carlo “group filter” technique to limit the effects of sampling error via regression confidence factor (RCF). Experiments make use of the local ensemble transform Kalman filter (LETKF) with a simple two-layer primitive equation model and simulated observations. Results show that the shape, location, time dependency, and variable dependency of RCF localization functions are consistent with underlying dynamical processes of the model. Application of RCF localization to ensemble-estimated impact showed marked improvement especially for longer forecasts and at midlatitudes, when systematically verified against actual impact in RMSE and skill scores. The impact estimates near the equator were not as effective because of large discrepancies between the RCF function and the localization used at assimilation time. These latter results indicate that there exists an inherent relationship between the localization applied during the assimilation time and the proper localization choice for observation impact estimates. Application of RCF for automatically tuned localization is introduced and tested for a single observation experiment.