Steric Sea Level Research Articles

Sea level variations induced by heating and cooling: An evaluation of the Boussinesq approximation in ocean models

In this paper a sigma coordinate ocean model is modified to remove the commonly used Boussinesq approximation so that the effect of thermal expansion is exactly included in the basic equations in order to cope with the seasonal heating cycle and the detection of climate change through variation in sea level height. Tests are performed to evaluate the differences between Boussinesq and non‐Boussinesq calculations under different heating and cooling conditions and different model domains. For an idealized case of a flat bottom, shallow ocean basin without wind forcing, simulations of a warm eddy show that the non‐Boussinesq dynamics have only a minor effect on the baroclinic current field. However, vertically averaged velocities, though small compared with the baroclinic velocities, are cyclonic for the Boussinesq calculation and anticyclonic for the non‐Boussinesq calculation. The results indicate that global or closed basin Boussinesq models should be able to simulate most of the observed steric sea level changes on seasonal or climate timescales, when corrected by a spatially uniform, time‐dependent factor calculated from the volume‐averaged density change. The seasonal variation of the globally averaged sea level calculated from climatological data is small, about 1 cm. Variations in steric sea level in regional models, both Boussinesq and non‐Boussinesq, may differ from those of global models owing to the unknown transport across their boundaries associated with the local heating and cooling. A spatially uniform, time‐dependent correction, similar to that associated with thermal expansion, is proposed to account for transport across open boundaries of regional models. Variations of sea level obtained from a Boussinesq model of the Atlantic Ocean approximate the seasonal signal due to the heating/cooling cycle of each hemisphere as observed by satellite altimeter data.

A note on the representation of steric sea level in models that conserve volume rather than mass

This note discusses the representation of steric sea level in ocean circulation models. Changes in steric sea level are caused when changes in the density of the water column imply an expansion or contraction of the column. Models usually make the Boussinesq approximation and conserve volume, rather than mass, and so do not properly represent expansion or contraction. This means that although expansion/contraction is included in the equation of state, it is not accounted for by the model dynamics. In this note, we examine the equation governing the time evolution of the sea level displacement. It is shown that requiring conservation of mass, rather than volume, introduces a new term to this equation. A simple example is used to show the relationship of the new term to the surface buoyancy flux. The equilibrium response to the new term has two parts. One part consists of the Goldsbrough and Stommel gyres, for which, in the ocean interior, vortex stretching due to the local expansion/contraction of the water column is balanced by changes in planetary vorticity. The other part corresponds to the “inverse barometer.” The effect is to adjust sea level by a globally uniform but timevarying factor, determined by the net expansion/contraction of the global ocean. Since this correction is globally uniform, it has no dynamical significance. Both the Goldsbrough/Stommel gyres and the inverse barometer solution are missing from models as currently formulated. This does not represent a serious error. However, if comparison is made with observations of sea level, model‐calculated sea level should be adjusted by a globally uniform, time‐varying factor, determined by the net expansion/contraction of the global ocean. This would be important for assessing the likely rise in sea level in response to global warming.

Sea level response to the 1986–1987 El Niño‐Southern Oscillation Event in the western Pacific in the vicinity of Papua New Guinea

Sea levels at the Papua New Guinea coast responded to the 1986–87 El Niño‐Southern Oscillation (ENSO) event much as would be expected for points on the inshore edge of a western boundary current driven by remote sea level disturbances. The first empirical orthogonal function of sea level in the region accounts for 60% of the variance, and shows a clear western boundary current signal. Sea level observations from tide gauges and estimates from adjacent expendable bathythermographs (XBTs) are in good agreement, so XBT data are used to supplement sea level results; specifically, we obtain an estimate of the western boundary current as a function of depth. The anomalous transport through Vitiaz Strait varied by about 15 Sv during the event, with possibly more following the eastern New Ireland coast. The western boundary current response appears to be located entirely equatorward of the inflow feeding it, as expected from linear theory. The boundary current followed the Trobriand Island ridge, rather than the main Papua New Guinea coastline, and appears to bifurcate along southern New Britain. A maximum response to the ENSO occurred south of New Ireland, where steric sea level appeared to vary by up to 45 cm due to the ENSO event; this may be an inertial feature.

The structure of the transition zone between coastal waters and the open ocean off northern California, winter and spring 1987

Physical and biological fields in the coastal transition zone off northern California were measured during February, March, May and June 1987 in an extended alongshore region between 60 km and 150 km offshore. The spring transition, as seen in coastal sea level and winds, occurred in mid‐March. Surface variability during the two spring cruises was stronger and of larger scale than that seen during the two winter cruises. An equatorward‐tending current, flowing along the boundary between low steric sea level inshore and high steric sea level offshore, dominated both the directly‐measured (acoustic Doppler current profiler) and geostrophic current fields during spring. Current jets of comparable strength directed both offshore and onshore were seen off Cape Mendocino and Point Arena; these evolved significantly in the 3 weeks between cruises. Inshore of the current, properties associated with upwelled water were found near the surface, including low temperature and high salinity, nutrients and chlorophyll; offshore of the current, waters were warmer, less saline, lower in nutrients and more oligotrophic. Geostrophic and directly measured volume transports in the current were about 2–3 Sv. Isopycnals inshore of the spring upwelling front were displaced vertically by O(40–80 m) from their depths during the winter survey; these displacements extended deep into the water column and were largely independent of depth between 100 and 400 m. Surface mixed layers tended to be deep in winter and shallower inshore of the upwelling front in spring. A connection between the equatorward‐tending frontal jet off northern California and the more well‐studied California Current further south is suggested by the similarity of their transports and of their dynamic height values.

Interpentadal variability of steric sea level and geopotential thickness of the north Atlantic Ocean, 1970–1974 versus 1955–1959

We have composited and objectively analyzed historical hydrographic observations for the North Atlantic Ocean for two periods, 1955–1959 and 1970–1974. Difference fields of steric sea level and geopotential thickness for the North Atlantic Ocean in the 0‐ to 1500‐m depth range between the 1955–1959 and 1970–1974 pentads were computed. We find that in the central portion of the subtropical gyre, steric sea level decreased by up to 17.5 dyn cm, whereas in the western subarctic gyre (north of the Gulf Stream) steric sea level increased by an amount up to 7.5 dyn cm from the earlier to the later pentad. A decrease in steric sea level (∼5 dyn cm) occurred along the eastern boundary of the North Atlantic.

Temporal variability of currents in the eastern Ligurian Sea

Surface and intermediate waters enter the Ligurian Sea from the Tyrrhenian and Algero‐Provencal basins via northward flows along the east and west coasts of Corsica. The temporal variability of these flows is examined by means of a 1‐year time series of current data (October 1986 to September 1987) and hydrographic data from December, March, and May cruises. The flow through the Corsica Channel increases suddenly during December and then gradually decreases after March, reaching its lowest values in late summer. The seasonal variability in the channel seems associated mainly with the steric sea level differences between the Tyrrhenian Sea and Ligurian Sea. The West Corsican Current appears more stable throughout the one year of data. The two flows converge just north of Corsica into the Ligurian Current. Because of the water‐masses differences between the two currents, in the area of convergence considerable smaller‐scaled structure is observed. During winter, the less dense Tyrrhenian water provides available potential energy to the Ligurian shelf area and thereby helps sustain the large‐scale cyclonic circulation in the Ligurian basin. During the other seasons the spatial structures over the Ligurian shelf are less organized and the spatial scale of the flow is a few tens of kilometers.

Steric Sea Level Trends in the Northeast Pacific Ocean: Possible Evidence of Global Sea Level Rise

Abstract Thirty-year time series of hydrographic observations from Ocean Station PAPA and Line ‘P’ are used to estimate secular trends in monthly mean steric sea level heights relative to depths of 100 and 1000 decibars in the northeast Pacific Ocean. Linear trends at station ‘P’ (50°N, 145°W) indicate that steric heights relative to the 1000 db (approx. 1000 m) level are rising at a rate of 1.1 mm yr−1, comparable with the Order 1 mm yr−1 global trends suggested by analysis of selected long-term coastal tide gauge records. Approximately 67% of the increase in steric levels is due to thermosteric change at depths below 100 m, the smaller 33% contribution from the halosteric component apeasrs to be confined to the upper 100 m. Steric height trends at fine ‘P’ locations are also of order 1 mm yr−1 but, in contrast to station ‘P’ trends, arise mainly through the halosteric component. Confidence levels for the linear trends an calculated in two ways. (i) using the Student-t test assuming that cub monthly obse...

Steric height trends at Ocean Station Papa in the Northeast Pacific Ocean

Abstract We estimate secular changes in steric sea level in the northeast Pacific Ocean using the 27‐year time series of monthly hydrographic observations for Station PAPA (50°N, 145°W). Linear trends based on the entire data record suggest that steric heights relative to 1000 db are increasing at a rate of 0.93 mm/yr and that 67% of this increase is due to thermosteric changes at depths below 100 m; the smaller halosteric contribution to the steric trend appears to be confined to the upper 100 m. A trend of 0(1 mm/yr) is consistent with estimates of sea level rise based on coastal tide gauge records. However, a critical examination of the results indicates that sea level changes of such small magnitude would be masked by the large (1–10 cm) interannual variability of open ocean steric height. This is verified by recalculation of trends using abridged versions of the data set. We conclude that our trend estimates are still open to question and that the present 27‐year time series is too short to permit accurate resolution of possible climate‐induced changes in global sea level.

Seasonal cycles of steric sea level off Western Australia with error analysis

Seasonal cycles of steric sea level off Western Australia with error analysis

Australia: An Unstable Platform for Tide-Gauge Measurements of Changing Sea Levels

Twenty-five tide-gauge records non-uniformly distributed along the coast of Australia were used to evaluate the stability of Australia as a platform from which to measure changes in sea levels. The spatial and temporal variabilities of relative sea levels were defined using a multivariate analytical tool (eigenanalysis) on 13 of these stations. Low-frequency (period 20 years and greater) relative sea levels are believed to reflect the combined effects of subsistence due to sediment and water loading, subsidence due to thermal cooling of oceanic crust, and emergence along a convergent plate boundary. Global eustatic sea-level rise cannot be identified unambiguously from these data, but clearly it is not responsible for the observed patterns of relative sea level. The straight average rate-of-rise of relative sea level around Australia is 1.3 mm/yr. (submergence), with general submergence in the south (at an average rate of 1.8 mm/yr.) and emergence in the north (0.5 mm/yr., the latter an average of two stations). Australian tide-gauge data cannot define unambiguously past eustatic sea-level history because of this considerable spatial non-homogeneity in relative sea-level rise, but they may be useful for monitoring possible future increases in rate of global sea-level rise. Higher-frequency fluctuations in relative sea levels show relative peaks at 20, 12, and 6 years, with significant energy at higher frequencies as well. Higher frequency fluctuations correlate with patterns of El Niño/Southern Oscillation. During El Niño events, yearly-averaged sea levels of Australia fall, although not all local minima in relative sea levels correspond with El Niños. The resultant drop in relative sea levels represents a balance between lower sea levels due to raised atmospheric pressure with coincident lowered water temperatures, and higher steric sea levels due to increased precipitation and runoff (for those stations located in estuaries).

Annual and Interannual Variability of Steric Sea Level along Line P in the Northeast Pacific Ocean

Abstract Twenty-five and 22 years of hydrographic-STD casts from Station P and Line P, respectively, have been utilized to describe the annual and interannual variability of thermosteric, halosteric and total steric heights. In the offshore region beyond the continental slope thermosteric effect dominates the annual cycle of total steric height, whereas near the coast over the continental shelf halosteric effect controls the height. In between, over the slope, both temperature and salinity effect contribute almost equally to the annual cycle of height. Offshore, the annual change of steric height relative to 1000 db resembles that relative to 100 db, but as the coast is approached, the change due to the deeper water becomes more important. The heat budget within the upper 100 db of water determines most of the annual range of steric height offshore, but near the coast both dilution due to precipitation and runoff in winter and concentration due to upwelling of cool, saline water in summer govern the annua...

Mean heat and momentum budgets during upwelling for the coastal waters off northwest Africa

Mean heat and momentum budgets for the upwelling region off northwest Africa during March and April 1974 are estimated at midshelf, 32 km from the coast, using current and temperature measurements at six depths in 73 m of water. In the heat budget, the mean cross‐shelf circulation transports 1.14×107 W m−1 offshore, while fluctuations in the cross‐shelf circulation transport an additional 1.9×106 W m−1 offshore. This offshore heat flux is compensated by the net radiative heat gain in the region of 4.8×106 W m−1 and an alongshore heat flux due to the mean circulation of 5.1×106 W m−1 as indicated by southward cooling of the surface mixed layer of 0.5°C per 100 km. In the cross‐shelf momentum budget, the alongshore flow is nearly geostrophic with the Coriolis force being approximately balanced by the steric sea level slope. For the alongshore momentum budget, the surface wind stress is balanced by the bottom stress, alongshore pressure gradient, and Coriolis force associated with the net onshore mass transport. A three‐dimensional momentum balance with significant alongshore pressure gradients results even if the coordinate system is rotated 6° counterclockwise so that no net cross‐shelf mass transport occurs.

A pacific equatorial temperature section from 172°E to 110°W during winter and spring 1979

A composite zonal-depth temperature section was occupied along the equator between 172°E and 110°W, nearly 8.6 × 10 3 km, by combining temperature profiles recorded at about 1- degree intervals on 28 February 1979 between 172°E and 158°W with profiles recorded at 1 4 - degree interval from 23 April to 2 May 1979 between 153°W and 110°W. Coincident with the zonal temperature section, which combined with salinity data produced dynamic height anomalies, were moored current measurements in the upper ocean at three equator sites (166°E, 152°W, and 110°W). The thickness of the mixed layer decreased from about 100 m near 180° to 10 m near 110°W. The depth of the thermocline was about 125 m near 180° and approximately 50 m east of 120°W. At 166°E the velocity core of the Cromwell Current was near the bottom of the thermocline; at 152°W and 110°W it was within the central region of the thermocline. East of about 140°W a 100-m-thick 13°C thermostad occurred below about 175 m. At 110°W the bulk Richardson number encompassing the 150- to 200-m interval was virtually always less than unity from 20 January to 2 May, suggesting that the thermostad was formed by shear-induced dynamic instabilities below the velocity core of the Cromwell Current. The surface dynamic height anomaly relative to 27 dbar tilted upward toward the west between 172°E and 120°W, with the maximum inclination from 153°W to 133°W. East of 120°W the zonal gradient of the 0/270 dbar steric sea level was indistinguishable from a horizontal surface. East of 132°W the directions of the 270/400 dbar pressure force and of the zonal wind field were both westward, indicating that the influence of the prevailing westward wind stress was confined to the region above the thermocline.

Large-Scale Secular Trend in Steric Sea Level over the Western North Pacific from 1954-1974

Large-Scale Secular Trend in Steric Sea Level over the Western North Pacific from 1954-1974

Seasonal variation in temperature, salinity, and density over the continental shelf off Oregon1

Seasonal variations in the hydrography of the waters over the continental shelf off Oregon were observed in a set of hydrographic data collected along 44°39′N at intervals of a few weeks to a few months from 1961 through 1970. The temperature is determined only partly by the local heating and cooling cycle: at the surface it is low (9°C) in winter, increasing in spring, lowest in summer, highest in early fall, and decreasing in winter; near the bottom, it is highest in winter and lowest in summer. The summer minimum is associated with coastal upwelling and a strong southward geostrophic current. Variations in salinity are governed by runoff, both locally and through the Columbia River effluent, as well as by coastal upwelling and advection. Neither temperature nor salinity is negligible in determining sigma‐t. In summer, sigma‐t decreases with distance offshore, and isopyenals slope downward from shore; in winter, sigma‐t increases with distance offshore, and isopyenals slope upward from shore. Steric sea level also slopes downward from the coast in winter, and upward in summer. Alongshore geostrophic flow is southward in summer and northward in winter. The variations in temperature, salinity, and sigma‐t are caused by seasonal cycles in the surface heat balance, precipitation and runoff, the local wind, and the alongshore flow.

Steric Contribution to the Seasonal Oscillation of Sea Level off Oregon

Abstract Thermal, haline and total steric departures of sea level were calculated in a zone up to 165 n mi off Newport, Ore. The thermal and haline components were about equal in magnitudes and in phase, giving low steric sea levels nearshore and high sea levels offshore in summer and the reverse pattern in winter. These results are produced by local oceanographic conditions and reflect seasonal changes in upwelling and the position of the Columbia River plume. In the region close to shore the combined effects of steric and atmospheric-pressure-caused departures do not fully account for the observed variations of sea level. Wind stress variations are likely to be the most important cause but other factors may well contribute.