Island Rule Research Articles

Diagnosing the mean strength of the Indonesian Throughflow in an ocean general circulation model

We have tested a rigorous version of the Island Rule for the long‐term mean magnitude of the Indonesian Throughflow, in a Bryan‐Cox model of the Pacific and Indian Oceans. We assign specific causes, in definite locations, to departures from the original version of the rule. Some of these causes can be tested observationally. If Australasia's northern tip is taken at the equator, then in the original version of the rule the throughflow magnitude can be calculated as follows. (1) Everywhere along the standard Island Rule path from Chile to Australasia's southern tip, via the equatorial Pacific, the long‐path gradient ∂ P/∂ l of depth‐integrated steric height (DISH) P is given by the long‐path wind stress τl divided by density ρ and gravitational acceleration g. (2) The Indonesian Throughflow is the sum of the geostrophic flow balancing the resulting DISH difference ΔP between Chile and southern Australasia and the northward Ekman transport between Chile and Australasia. (Corrections for the pressure difference across New Zealand; for flows through Bass, Torres, and Bering Straits; for pressure gradients at the sill depth; and for the Pacific‐wide vertical transport W through the sill depth are all treated here as effects omitted from the original version, as are all nonlinear and frictional contributions.) In the model, Torres and Bering Straits were closed and Tasmania was submerged, so the flows through minor straits were all zero. Local balance of wind stress by the DISH gradient worked well along the South American coast and along the western coast of Australasia north of 20°S. In particular, no large frictional components developed near the eastern side of the narrow Indonesian gap. Lateral friction and nonlinearity introduced quite large contributions across the equatorial Pacific, though they largely cancelled one another. However, major departures from the balance assumed in the Island Rule (relative to the sill depth, 629 m in our model) occurred along south western and southern Australia, owing to substantial longshore pressure gradients at the sill depth. These longshore pressure gradients appear to drive the model's Leeuwin Undercurrent. There was also a moderate Coriolis contribution from net outflow near Cape Leeuwin that is supplied by upwelling along Australia's south coast. These effects combined to reduce the model's value of ΔP to 34.6 m2, well below the Island Rule value of 60.4 m2. However, the corresponding depth‐integrated pressure (DIP) difference was very close to the original value, because pressure gradients at sill depth largely compensated for the reductions in DISH. The pressure difference across New Zealand was not small; it took 1.0 Sv away from the original estimate. Pacific‐wide upwelling W through sill depth was −0.5 Sv, and departures from geostrophy across the South Pacific contributed 0.1 Sv. It was also found that the DIP difference calculated around the direct and indirect routes from Chile to Australasia differed by 3.8 m2, an indication of the model's inability to precisely close the pressure integral over long, closed paths that follow complex topography. Several of these correction terms cancelled, so that the full model value of the throughflow (9.5 Sv; 1 Sv = 106 m3 s−1) was not very different from the original value. This was 10.5 Sv for the wind and topography of our model.

Barotropic Circulation around Islands with Friction*

Abstract Godfrey’s Island Rule is generalized to include previously neglected dissipation on the north, south, and east boundaries of the island as well as the eastern basin boundary. The resulting extended island rule predicts the transport ψI between the island and the eastern basin boundary when strong frictional effects alter Godfrey’s original result. The new result is derived for a barotropic ocean with either Munk or Stommel friction and with no bottom topography. The Munk case is marked by the interesting feature that friction enhances the flow over a certain range of widths of the gap separating the island from the western (or eastern) basin boundary. Transport predictions for the Munk case are compared to results based on linear and moderately nonlinear numerical simulations. The original island rule overpredicts ψI by no more than 25% unless the island is within about 3 Munk layer thickness of the east or west boundary, in which case the errors are much larger. For such cases the extended islan...

Seasonal Near-Surface Dynamics and Thermodynamics of the Indian Ocean and Indonesian Throughflow in a Global Ocean General Circulation Model

Abstract The near-surface dynamics and thermodynamics of the Indian Ocean are examined in a global ocean general circulation model (OGCM) with enhanced tropical resolution. The model uses a Seager-type heat flux formulation (weak relaxation toward a fixed SST, flux-corrected toward seasonal observed values). Resulting seasonal patterns of surface heat flux, mixed layer depth, and surface steric height all compare quite well with observations in the Indian Ocean, away from western boundaries. Distribution of flow in the mean Indonesian Throughflow is quite well simulated in the top 700 m. The model Indonesian throughflow transports, on average, 16.3 × 106 m3 s−1 from the Pacific to the Indian Ocean, and its magnitude is fairly well predicted seasonally by the instantaneous Sverdrup version of the “Island Rule.” Model geostrophic transports relative to 700 m are substantially smaller, with a different seasonal cycle. Observed geostrophic transports are smaller than those in the model, though the model repro...

Circulation around islands and ridges

The circulation in an ocean basin containing an island is studied under nearly geostrophic, beta plane dynamics. The model is a fluid of uniform density driven by wind forcing or sources and sinks of mass at the upper boundary of the flow. The circulation is studied analytically, numerically, as well as in the laboratory through the device of the “sliced cylinder” model for the ocean circulation. Of particular interest is the estimate of the transport between the island and the oceanic basin’s boundary. The model is conceived as relevant to both the wind-driven circulation as well as the circulation of abyssal waters around deep topographic features such as mid-ocean ridge segments. Godfrey’s Island Rule for the transport is rederived in general form and the validity of the original approximation of Godfrey (1989) is examined in a variety of circumstances. In particular, the role of dissipative boundary layers and inertial effects such as vortex shedding are scrutinized to determine their role in determining the net transport around the island. Linear theory in many cases predicts a recirculation on the eastern side of the island, provided the meridional extent of the island is large enough. The existence of the recirculation, containing trapped fluid, is confirmed in both laboratory and numerical experiments and the evolution of the structure of the recirculation is examined as a function of the boundary layer Reynolds number. In both the laboratory and numerical studies, the recirculation predicted by linear theory is joined and then superseded by an inertial recirculation springing from boundary layer separation as the Reynolds number increases past a critical value. Even in the linear limit it is shown that the recirculation region, which is closed in quasigeostrophic theory, is subject to a small leak due to planetary geostrophic effects, which prediction is confirmed in the laboratory. The original island rule of Godfrey yields an estimate of the transport which is surprisingly robust and generally within 75% of the values measured in our numerical experiments. Agreement is moderately good when island western boundary layer transport is used as a basis for comparison. Several cases are discussed, however, in which the assumptions made by Godfrey are violated. One occurs when the frictional boundary layers of the island and the basin boundary overlap. We derive a threshold width for the gap for the case where the island is close to a northern or southern boundary of the basin and show how the transport is increasingly blocked as the gap is reduced. A second case occurs when the island is thin and zonally elongated so that the dissipative effects on the northern and southern boundaries of the island become important. Here the vorticity balance assumed in the simple Island Rule is fundamentally altered, and we extend the Island Rule to account for the new dissipation.

Indonesian throughflow in a coupled general circulation model

The Indonesian throughflow is analyzed in an extended simulation with a coupled ocean‐atmosphere model. The model, developed by the Max‐Planck‐Institut für Meteorologie, Hamburg, Germany, combines an atmospheric general circulation model at T42 resolution (2.8° latitude by 2.8° longitude) and a primitive equation ocean model with zonal resolution of 2.8° and a meridional resolution of 0.5° in the tropics and is coupled without flux correction equatorward of a latitude of 60°. The onset and strength of the monsoon in the Indonesian waters agree well with climatology, and many aspects of the observed temperature fields in the eastern Indian Ocean and Timor Seas are found in simulation. Differences between simulation and observations of temperature occur in mean and seasonal cycles in the far western Pacific. The annual cycles of sea level along the coast of Sumatra and Java are simulated satisfactorily. The simulated throughflow transports on average 13.8 Sv (106m3S−1) from the Pacific to the Indian Ocean. The vertically averaged (barotropic) component of the throughflow has a seasonal range of 13.1 Sv and is weakest in February and strongest in July. In contrast, deviations from the vertical average of the throughflow (baroclinic) are strongest in March and September. The average and seasonal cycle of the barotropic component of the throughflow are forced by winds over the Pacific and along the western coasts of Australia and South America, as described by the island rule. For closed Torres Strait, the contribution of the average bottom pressure torque is small, and friction closes the vorticity balance. For annual timescales, baroclinic flows affect the throughflow transport through the bottom pressure torque. The annual cycle of the baroclinic component of the throughflow is forced predominantly by winds over the Indonesian Seas. The throughflow exports 0.9 PW of heat from the Pacific into the Indian Ocean and is an important heat sink for the western Pacific. The throughflow is a major heat source for the Indian Ocean and is associated with reversal of the divergence of the meridional transport of heat south of 10°S that is balanced by heat fluxes from the ocean to the atmosphere.

The Response of the Indo–Pacific Throughflow to Interannual Variations in the Pacific Wind Stress. Part II: Realistic Geometry and ECMWF Wind Stress Anomalies for 1985–89

The effect of interannual variability in wind stress on the transport between the Pacific and Indian Oceans through the Indonesian archipelago is investigated using a multilevel, numerical, general circulation model (GCM). The experiments are conducted in a spinup, anomaly mode: the GCM is initially at rest with a horizontally uniform stratification typical of tropical oceans. The wind stress anomalies are derived from the European Centre for Medium-Range Weather Forecasts 1000-mb winds for 1985–89. The modeled variability is sensitive to the specification of bottom topography and archipelago geometry. Two model configurations are considered: (i) flat-bottomed with the option of sills within a simplified, idealized archipelago and (ii) realistic bottom topography and a complex archipelago. In the first model, there is northward depth-integrated transport anomaly lasting 2½ years with phase 6 months ahead of the collapse of the equatorial easterlies prior to the 1986–87 El Niño. The peak transport is about 5 Sv (Sv ≡ 106 m3 s−1), which is reduced to 3 Sv if shallow sills are present in the archipelago. There follows a southward transport anomaly, peaking at about 6 Sv during the ensuing U Nina. The baroclinic transport is consistent with cold and warm equatorial Rossby waves partially scattered into the archipelago during El Niño and La Nina, respectively. The reduction in depth-integrated throughflow generated by the reduction in southern midlatitude westerlies over 1985–86 results in a distinct signal in the baroclinic transport, and similarly in their increase again over 1988. Contrasting models with open and wholly blocked archipelagos yields heat content differences, measured as the temperature averaged over the upper 300 m, of typically O(0.05°C) in the west equatorial Pacific and O(0.3°C) in the Pacific western boundary layers and Indian Ocean. This suggests that throughflow variations could have implications for the timing of ENSO. In contrast, the second model has a very weak throughflow with peak-to-peak amplitude of only 3 Sv. Its archipelago is a relatively poor transmitter of equatorial waves, and its f/H contours are such that the depth-integrated throughflow is driven in part by the southerly extent of the South Pacific midlatitude wind stress anomalies. However, interestingly, the model still exhibits a decrease in throughflow in excess of 1 Sv prior to the onset of the 1986–87 El Niño due to variations in the southern midlatitude wind stress over the Pacific, which is also accompanied by a signature in the baroclinic transport. Also, contrasting homogeneous and stratified versions of the models demonstrates the importance of JEBAR over direct wind stress forcing of the depth-integrated throughflow. A closed form analytical expression for the transport in terms of an integral over a closed path formed by uniquely defined f/H contours, an island rule, is derived and used to help interpret the results.

Seasonal variations in the equatorial Indian Ocean and their impact on the Lombok throughflow

In order to identify the origin of the nonequilibrated pressure field which introduces semiannual variations to the Lombok throughflow, one of the major components of the Indonesian throughflow, seasonal sea level records along the eastern boundary of the Indian Ocean and subsurface temperature records in the equatorial Indian Ocean are compared with the results from ocean general circulation models forced by climatological winds. It is shown, as discussed by Clarke and Liu [1993] using a simple analytical model, that the annual component of the sea level is excited locally by monsoonal winds, whereas the semiannual component is excited remotely by zonal winds in the central equatorial Indian Ocean during the monsoon transition periods. The eastward semiannual propagation observed both in the model and in the 20°C isotherm depth anomaly along the equatorial Indian Ocean is interpreted in terms of the second mode equatorial Kelvin wave excited by the zonal winds during the monsoon transition periods. The propagation direction is westward in the off‐equatorial region along 4°N, suggesting that the equatorial Kelvin wave reflects as an equatorial Rossby wave twice a year at the coast of Sumatra. Since the seasonal winds responsible for those semiannual oceanic variations suffer short‐term climate variabilities such as El Niño‐Southern Oscillation events, they may introduce interannual modulations to the seasonal cycle of the Lombok throughflow. As a corollary, we suggest an ageostrophic limitation due to a nonequilibrated pressure field on the use of Godfrey's [1989] island rule in estimating the throughflow variations.

Flow of a western boundary current through multiple straits: An electrical circuit analogy for the Indonesian throughflow and archipelago

An analogy is drawn between the flow through multiple, frictional straits and the current through combinations of resistors acting in series and parallel in an electrical circuit. Kirchoff's laws are replaced by continuity of mass and the generalized island rule [Wajsowicz, 1993a]. Expressions are derived for the equivalent resistance of straits acting in series and in parallel. Hence the total “current” can be calculated for a given “voltage” supplied by the wind stress curl over the adjacent ocean basin. The model may be used to help understand how to parameterize the effect of the many islands within the Indonesian archipelago in a numerical general circulation model by combining islands/straits into resolvable groups with the same effective resistance. For example, from the expression for parallel straits it can be deduced that if there is at least one gap at each latitude within the archipelago, which is wide and deep enough not to block the throughflow, then the throughflow achieves its predicted wind‐driven maximum. The transport is not carried by the largest gap, but, instead, is carried by the westernmost gap up to a friction‐determined limit, and so on eastward, until a dynamically wide gap is reached. This gap carries the remainder of the transport; gaps to the east carry no transport. Hence the model explains surprising recent observations that the throughflow is as large as the Sverdrup model prediction of O (15 Sv). It also explains observations that the narrow, shallow Lombok and Savu Straits to the west carry significant transport, even though Timor Strait to the east is much wider and deeper, and similarly for Makassar Strait versus Molucca Strait.

The effect of the Indonesian throughflow on ocean circulation and heat exchange with the atmosphere: A review

A new version of the island rule, which relates transport around an island to wind and pressure forcing, provides a basis for comparing various published theoretical estimates of the long‐term mean Indonesian throughflow magnitude. It is found, among other things, that nonlinear effects near Halmahera and pressure gradients across New Zealand may modify the long‐term throughflow magnitude. Recent theoretical estimates of interannual throughflow variations are in approximate agreement with observation; Indian Ocean Kelvin waves play an important role. On still shorter timescales and for understanding flow details in different channels, consideration of the full details of the Indonesian region via numerical modeling becomes essential. Most of the throughflow enters from the Mindanao Current. The process by which the South Pacific waters eventually reach the Mindanao Current appears to involve some nonlinear retroflection process (particularly in northern summer) and subsequent freshening along long pathways in the North Pacific. Observed water mass transformations in Indonesian waters demand a vertical eddy diffusivity of about 10−4 m2 s−1, large enough to generate turbulent heat fluxes of order 40 W m−2 at the base of the mixed layer. According to numerical models, changes in ocean circulation associated with the throughflow are likely to affect patterns of heat exchange with the atmosphere in widely separated regions of the world ocean. In particular, an increased throughflow will result in more heat loss to the atmosphere in the subtropical Indian Ocean and less in the Pacific Ocean. Simple, physically reasonable mechanisms have been offered for these model results. Observational evidence to support or refute these mechanisms is rather fragmentary but is reviewed here. Our present understanding of the throughflow permits some informed speculations as to the possible role of the throughflow in coupled ocean‐atmosphere phenomena, such as the El Niño‐Southern Oscillation (ENSO). Earlier estimates of western Pacific reflectivity seem largely confirmed by recent observational results. However, it is suggested that tidal mixing in the Indonesian seas may generate ENSO‐related sea surface temperature anomalies there, possibly affecting the development of westerly wind bursts.

The Response of the Indo-Pacific Throughflow to Interannual Variations in the Pacific Wind Stress. Part I: Idealized Geometry and Variations

Abstract The effect of interannual variations in the Pacific wind stress on the barotropic and baroclinic components of the flow between the Pacific and Indian Oceans through the Indonesian Archipelago, the Indo-Pacific Throughflow, is investigated using a numerical ocean general circulation model (GCM) with a simplified geometry. In agreement with the modified Island Rule, variations in the depth-integrated throughflow are generated by zonal wind stress variations over the Pacific at the latitudes of the tips of the Australian continent, assuming the Pacific basin is flat bottomed. Wind stress variations at other latitudes generate variations in the depth-integrated transport only if they produce a depth-integrated pressure drop along the oceanic eastern boundary through the archipelago. From the Island Rule, alongshore wind stress variations on the west coasts of Australia and South America produce direct variations, but the observed signal is weak at interannual periods. Baroclinic variations in the th...

Cope's rule, the island rule and the scaling of mammalian population density.

Cope's rule--the generalization that animal taxa tend to evolve toward larger body size--suggests that there are widespread net selective advantages to being large. Size-abundance relationships within bird and desert rodent guilds show that larger species usually do control more energy locally, and thus maintain larger populations than expected for their body size, implying that larger individuals are relatively better at obtaining and using local resources. But we report here results that show that this is not generally the case among mammal species. Within dietary groups containing only small species, larger species usually do better, but within those that contain the largest mammals, small species tend to control more energy. This suggests that in mammals there is an optimum body size for energy acquisition at about 1 kg. Thus, net adaptive advantages of large individuals for resource control cannot be used as a general explanation for evolutionary size increase in mammals, although other proposed explanations for Cope's rule are unaffected. Instead, these results suggest a partial explanation for another widespread ecotypic pattern, the 'island rule': that on islands, small mammal species evolve to larger size and large species to smaller size. If on an island a species' usual competitors and predators are absent, it should often tend to evolve toward the optimum body size, and the adaptive advantages of doing so would be greatest for populations starting at body-size extremes.

The Circulation of the Depth-integrated Flow around an Island with Application to the Indonesian Throughflow

Abstract Godfrey's Island Rule is rederived in terms of the barotrapic streamfunction for flow in a stratified ocean with a rigid lid. Modifications to include bottom topography and frictional effects along eastern boundaries are derived. The “Island Rule” has an important application in describing the net transport through the Indonesian seas, that is the Indonesian Throughflow. The original rule, derived from a Sverdrup model, yielded an annual mean throughflow of 16±4 Sv (Sv ≡ 106 m3) s−1). Observations of depth-integrated steric height differences indicate that frictional effects within the lndonesian seas will reduce this value by the order of 2 Sv. The reduction estimated from a frictional channel model depends on the parameterization and boundary conditions adopted, and ranges from 5%–20%. Topographic effects could give an increase in transport. For example, if the archipelago is represented as a simple sill, then warmer water on the Pacific slope than on the Indian slope would produce an increase ...

A sverdrup model of the depth-integrated flow for the world ocean allowing for island circulations

Abstract The annual mean depth-integrated steric height P and stream function ψ of the world ocean are calculated from a Sverdrup model with Hellerman and Rosenstein's (1983) annual mean wifids. The parameterization of friction is unspecified, but friction is assumed to be important only along western boundaries. A simple rule, based on Sverdrup interior flow and geostrophy of longshore flow along western boundary currents, is used to calculate P at the inshore edge of the western boundary current. The substantial predicted longshore gradients of P drive the model western boundary currents against friction, independent of frictional parameterization. One corollary is an “Island Rule”–an explicit expression for circulation around an island, in terms of wind stress, again independent of frictional parameterization. The circulations around Australasia, New Zealand and Malagasy are calculated as 16±4 Sv, 29±v, and 4±3 Sverdrups respectively. Inclusion of island effects result in more accurate flow estimates i...

Body Size of Mammals on Islands: The Island Rule Reexamined

On commente le tableau de frequence du nanisme et du gigantisme pour 365 populations insulaires de mammiferes terrestres; comparaison avec les mammiferes continentaux. Presentation d'un modele. Role de la limitation des ressources alimentaires de la reduction de la competition interspecifique et de la predation dans les communautes insulaires