Nonlinear Barotropic Model Research Articles

Barotropic tides in the global oceans from a nonlinear tidal model assimilating altimetric tides: 2. Altimetric and geophysical implications

In this second part, we explore the implications of the tides derived from the high‐resolution, data‐assimilative, nonlinear barotropic global ocean tidal model described by Kantha (this issue) in altimetric analysis and geophysical applications. It is shown that when applied to the task of removing tidal sea surface height from TOPEX altimetric records, the model performance is comparable to other global tidal models in the open ocean as measured by the reduction in crossover variances. The performance is slightly better than that of the only other high‐resolution global tidal model from Grenoble (Le Provost et al., 1994). The results are however mixed in regions shallower than 1000 m and in semienclosed seas such as the Bering Sea, with the model performance slightly worse overall than the Grenoble model. Computations of total power input (and hence total tidal dissipation rate) are shown to be in excellent agreement with recent analyses of TOPEX data and geophysical observations. In addition, distributions of the tidal power input, tidal dissipation, and the power fluxes in the global oceans are shown for the two primary constituents, M2 and K1. Load tides in solid Earth due to ocean tidal loading fluctuations are also computed for the major semidiurnal and diurnal constituents. The load tides are shown to be large in the shallow seas adjacent to the coasts with high tides such as the Patagonian shelf, because of the higher resolution of this global tide model. This has potential implications in geophysical applications.

Barotropic tides in the global oceans from a nonlinear tidal model assimilating altimetric tides: 1. Model description and results

In this first part of a two‐part paper we present results from a high‐resolution, data‐assimilative, fully nonlinear barotropic tidal model of the global oceans that excludes the Arctic. The model assimilates, in waters deeper than 1000 m, altimetric tides derived from the analysis of 2 years of TOPEX altimetric data. It also assimilates tide gage data from coastal tide gages. The model domain includes that covered by the altimeter and extends to the Antarctic. In the first part we present tidal results for the primary semidiurnal (M2, S2, N2, and K2) and diurnal (K1, O1, P1, and Q1) constituents. The second part deals with applications (Kantha, et al., this issue). The model results are compared with observational data from pelagic gages. These comparisons show that overall in the open ocean, in deep waters away from the margins of the primary basins, the model performance is comparable to other tidal models derived using TOPEX data, except for M2 and S2. However, one advantage of this model compared with those based solely on the analysis of altimetric data is that the altimetry‐derived tides are subjected to dynamical constraints by the model. This results in reduction of subtidal variability often folded into tidal signals by TOPEX data analysis. It is also shown that in shallow waters along the margins, especially in east Asian marginal seas, the model differs substantially from these other models. In addition to sea surface heights, we also present dynamically consistent barotropic currents in the form of tidal ellipses for M2 and K1 constituents. Since the goal of this research is a global tidal model uniformly valid in both deep and shallow waters, we finally present tidal elevations and currents on two well‐known shallow water areas, the northwest European shelf and the northeast American shelf, and a semienclosed western Pacific marginal sea, the Bering Sea. The model results are compared with independent observations and, where possible, with results from other numerical models. The results highlight the importance of bottom topography; on the northwest European shelf, where accurate bottom topography was included in the model, the results are much better than on the northeast American shelf, where the Digital Bathymetric Data Base 5 (DBDB5) topographic database has significant errors. Results from the Bering Sea, where the topography is more accurate than the DBDB5, compare well with known tides in the region.

Idealized Life Cycles of Planetary-Scale Barotropic Waves in the Middle Atmosphere

Abstract A nonlinear nondivergent barotropic model is used to investigate the mature and decay stages of waves arising from barotropic instability of planetary-scale eastward jets. Two simulations were carried out in weakly diffusive and unforced conditions, corresponding to two types of linear instabilities. One simulation was initialized with a high-latitude polar night jet and the other with a double-peaked jet, which has a maximum at subtropical latitudes and a subsidiary maximum at high latitudes. The polar night jet is chosen to be unstable on its poleward side; an unstable wave 1 (the polar mode) developed into a persistent dipolar vorticity pattern traveling coherently around the globe in slightly more than 3 days. The dipolar feature decays with a timescale of about three weeks, before the anticyclonic anomaly is destroyed in a region of strong cyclonic shear. For the case of an instability associated with the double-peaked jet, which has a region of negative vorticity gradient between the two je...

On circulation in the Tropical Atlantic induced by a meridionally-inhomogeneous wind field

The paper discusses a non-linear barotropic model of large-scale circulation which incorporates a mechanism of lateral friction. Some numerically calculated data on the interaction of two large-scale gyres induced by a meridionally-inhomogeneous wind field are reported which enable modelling of the Equatorial Countercurrent (EC) formation in the Tropical Atlantic Ocean. Consideration of the coastline in the western part of the region leads to the meandering of the EC and the emergene of quasi-stationary eddies in the area of its origin, thereby providing good compatibility with the experimentally documented data.

Transients and the Extratropical Response to El Niño

Abstract A baroclinic stationary wave model linearized about a zonally symmetric flow is used to interpret the extra-tropical atmospheric response to El Nino produced by a general circulation model. When forced by the anomalous diabatic beating and tendency due to transients, the linear model provides a useful simulation of this response. The direct response to anomalous diabatic heating is found to be small in the extratropics; the dominant term is the response to the anomalous transients, particularly the anomalous upper tropospheric transients in the vorticity equation. These results are complementary to those obtained with a nonlinear barotropic model by Held and Kang, and indicate that the anomalous subtropical convergence which plays a key role in that study is itself primarily forced by the anomalous transients. One can distinguish between two distinct parts of the response of the transients to the tropical heating: the movement of the Pacific storm track associated with the anomalous extratropical...

On the forcing of planetary‐scale Rossby waves by Antarctica

AbstractThe propagation of Rossby waves forced at high latitudes into middle and low latitudes is studied using the barotropic vorticity equation on the sphere. Ray tracing theory indicates that fundamental differences exist between the response of an atmosphere initialized with typical northern hemisphere winter flow and typical southern hemisphere winter flow to such a forcing, with a substantial response more likely for the southern hemisphere case. Integrations with a fully nonlinear barotropic model confirm this suggestion and indicate that away from the local forcing region, linear theory provides a good description of the response. The most notable feature in the steady solutions is a split of the mid‐latitude jet close to New Zealand. The location of this split coincides well with a region where blocking is observed to be prevalent in the southern hemisphere.

A Comparison of the Bounded Derivative and the Normal-Mode Initialization Methods Using Real Data

Application of the bounded-derivative and normal-mode methods to a simple linear barotropic model at a typical middle latitude shows that the two methods lead to identical constraints up to a certain degree of approximation. Beyond this accuracy the two methods may differ from each other. When applied to a global nonlinear barotropic model using real data, again the two methods lead to similar balanced initial states. The gravity oscillations in the unbalanced height field, which have amplitudes of up to 60 m with a dominant periodicity of about 5 to 6 h, are practically eliminated by both initialization methods. The rotational wind component is smooth even for the unbalanced initial state. The small-scale spatial features of the irrotational wind component are drastically reduced by initialization. Both the nonlinear normal-mode and the bounded-derivative initialization methods yield similar divergence fields centered around the areas of highest orography. The comparison shows that there is no significant loss of information in the mass and momentum fields, despite the fact that the bounded-derivative method employs only the original, rotational wind component to construct a balanced initial state compared to the normal-mode method, which, in addition, makes use of the unbalanced divergent wind and height fields.

The wind-driven circulation in the South Atlantic-Indian Ocean—I. Numerical experiments in a one-layer model

Abstract In this study another step is taken in the development of a series of increasingly more complex models of the circulation in the subtropical South Atlantic and Indian oceans. A series of mesoscale resolution numerical experiments is carried out in a nonlinear barotropic model ocean that is wind driven and contains the essential geometric features of the South Atlantic-Indian Ocean basin. In the least nonlinear experiment virtually the full transport of the model Agulhas Current flows westward around South Africa into the South Atlantic Ocean. With increasing Rossby number the anticyclonic circulations in the subtropical Atlantic and Indian Ocean parts of the two-ocean domain become more and more isolated from each other. Also, there is a dramatic increase in the basin-wide eddy kinetic energy level and in the associated mixing of vorticity and momentum between the cyclonic and anticyclonic wind-driven gyres. Retroflection of part of the model Agulhas Current is largely due to the net accumulation of β-generated anticyclonic relative vorticity as the current follows an inertially driven southward path after having left the southern tip of the African continent. In a final experiment it is shown that, within the limitations inherent to the model assumptions, the distance between the latitude of zero wind stress curl and the southern tip of the African peninsula is one of the primary factors that determine the degree of isolation of the anticyclonic gyres east and west of the African continent. Given the observed relatively large variation of the wind stress pattern on the seasonal time scale it is suggested that the associated fluctuating inflows of warm Agulhas water into the South Atlantic may have an important impact on the climatic variability over that region.

Non-linear model of the tides in the Gulf of Carpentaria

A non-linear barotropic model was used to evaluate the tidal regime in the Gulf of Carpentaria. The model was forced by open boundary conditions specified on a line joining Wessel Islands to False Cape and a volume flow through Torres Strait estimated from tidal constants on each side of the Strait. The model gives results in agreement with the available observations and in particular predicts mixed tides in the northern half of the Gulf and diurnal tides in the south-east corner of the Gulf. The diurnal tide consists of a Kelvin wave entering the Gulf in the north-west and propagating clockwise around the Gulf with one amphidromic point. The higher frequencies of the semidiurnal tides allow the generation of a first-mqde Poincare wave and the trapping of energy in the northern half of the Gulf. Amphidromes near Mornington Island and Groote Eylandt are also predicted, as is a region of low amplitude and rapid phase variations in the centre of the Gulf.

Tidal exchange through Naruto, Akashi and Kitan Straits

In order to re-evaluate the water volume exchange through Naruto Strait, we have performed a numerical experiment (nonlinear barotropic model including the actual depth of water and the details of shoreline) where trajectories of a number of labeled particles are calculated during a full cycle of the M2 tidal current. The ratio of water volume exchanged through Naruto Strait to that through Akashi Strait is found to be twice as large as the previously estimated value. The calculated water exchange rate is 104 % for Naruto Strait, 52 % for Akashi Strait and 28 % for Kitan Strait. In the case where the tide-induced residual current is excluded from the calculated velocity field (i.e. considering only the M2 current), the calculated exchange rate maintains the level of 68 % for Naruto Strait, 18 % for Akashi Strait and 11 % for Kitan Strait, respectively. The mechanism of tidal exchange through these three straits is discussed, and it is shown that a suitable exchange rate is obtained by starting the calculation of trajectories of labeled particles at the time of either a maximum ebb- or flood-current.