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## Abstract

We know that long-period (>1 day) and long-wavelength (>100 km) topographical Rossby waves can be generated by a wind acting directly on a continental shelf (Adams and Buchwald, 1969). Here we examine the characteristics of them waves which can also be produced off the shelf by wind and current eddies and can propagate up to and onto the shelf. We use a shelf model which varies in depth in one direction only and assume that a shelf can be approximated by at most two breaks with the depth varying exponentially. We assume velocity-dependent bottom friction to determine the effect of frictional dissipation. The following results are derived by our analysis. The regression angle of scatter plots for topography-dominated waves should be small and the preponderant direction of the waves determined by the sign. The group velocity directed up the slope possesses an absolute maximum which occurs at a relatively short period. The ability of a wave moving up a slope to overcome friction correlates with this group velocity. The energy flux transmission across one and two breaks can be determined. It is suggested that the product of this flux transmission coefficient and the group velocity component up the shelf be the criterion to determine which wavelengths and frequencies penetrate nearest to shore. It is found, however, that the energy from off the shelf is likely to he decayed completely in bottom depths ≲25 m. A comparison of some results with data for the New England and west Florida shelf shows a general agreement.

## Abstract

We know that long-period (>1 day) and long-wavelength (>100 km) topographical Rossby waves can be generated by a wind acting directly on a continental shelf (Adams and Buchwald, 1969). Here we examine the characteristics of them waves which can also be produced off the shelf by wind and current eddies and can propagate up to and onto the shelf. We use a shelf model which varies in depth in one direction only and assume that a shelf can be approximated by at most two breaks with the depth varying exponentially. We assume velocity-dependent bottom friction to determine the effect of frictional dissipation. The following results are derived by our analysis. The regression angle of scatter plots for topography-dominated waves should be small and the preponderant direction of the waves determined by the sign. The group velocity directed up the slope possesses an absolute maximum which occurs at a relatively short period. The ability of a wave moving up a slope to overcome friction correlates with this group velocity. The energy flux transmission across one and two breaks can be determined. It is suggested that the product of this flux transmission coefficient and the group velocity component up the shelf be the criterion to determine which wavelengths and frequencies penetrate nearest to shore. It is found, however, that the energy from off the shelf is likely to he decayed completely in bottom depths ≲25 m. A comparison of some results with data for the New England and west Florida shelf shows a general agreement.

## Abstract

In October 1987, 49 Lagrangian surface drifters (TRISTAR-II) were released in a 200-km × 200-km square area southeast of Ocean Station Papa as part of the OCEAN STORMS Experiment. The drifters measured temperature at the drogue level and reported their position through ARGOS approximately 11 times per day. Thirty-one of the drifters retained drogues for longer than three months, and data from those instruments are used to describe the evolving fall 1987 pattern of current and temperature structures at 15 m in the area between 46° and 49°N, 142°W and 132°W. Time variable currents were dominated by mesoscale eddies of anticyclonic rotation with horizontal radii of 53–86 km and rotational speeds of 10–20 cm s^{−1}. These eddies persisted for at least 90 days as evidenced by successive drifter trajectories through the eddies. Currents with periods longer than 1 day had a mean to the east of 4.4 cm s^{−1} and a mean to the north of 0.7 cm s^{−1}. Background eddy kinetic energy levels were 40 cm s^{−2}. Thus, eddy kinetic energy was four times larger than mean kinetic energy. The eastward single particle diffusivity was 1100 m^{2} s^{−1} and northward diffusivity was 1600 m^{2} s^{−1}. The local change of thermal energy at 15-m depth was −2.9 W m^{−3}, while on average, flow advected cold water to the east at a rate of 0.8 W m^{−3}. Therefore, large-scale advective processes accounted for 28% of the thermal energy balance at 15 m. This horizontal heat convergence in the open ocean is comparable in magnitude to that produced by powerful equatorial currents in the eastern Pacific cold tongue.

## Abstract

In October 1987, 49 Lagrangian surface drifters (TRISTAR-II) were released in a 200-km × 200-km square area southeast of Ocean Station Papa as part of the OCEAN STORMS Experiment. The drifters measured temperature at the drogue level and reported their position through ARGOS approximately 11 times per day. Thirty-one of the drifters retained drogues for longer than three months, and data from those instruments are used to describe the evolving fall 1987 pattern of current and temperature structures at 15 m in the area between 46° and 49°N, 142°W and 132°W. Time variable currents were dominated by mesoscale eddies of anticyclonic rotation with horizontal radii of 53–86 km and rotational speeds of 10–20 cm s^{−1}. These eddies persisted for at least 90 days as evidenced by successive drifter trajectories through the eddies. Currents with periods longer than 1 day had a mean to the east of 4.4 cm s^{−1} and a mean to the north of 0.7 cm s^{−1}. Background eddy kinetic energy levels were 40 cm s^{−2}. Thus, eddy kinetic energy was four times larger than mean kinetic energy. The eastward single particle diffusivity was 1100 m^{2} s^{−1} and northward diffusivity was 1600 m^{2} s^{−1}. The local change of thermal energy at 15-m depth was −2.9 W m^{−3}, while on average, flow advected cold water to the east at a rate of 0.8 W m^{−3}. Therefore, large-scale advective processes accounted for 28% of the thermal energy balance at 15 m. This horizontal heat convergence in the open ocean is comparable in magnitude to that produced by powerful equatorial currents in the eastern Pacific cold tongue.

## Abstract

A new estimate of the heat budget for the North Pacific Ocean is presented in this paper. The seasonal net heat flux and heat storage rates were calculated for the North Pacific Ocean from 1950 to 1990 on a spatial resolution of 5° × 5°. Temperature profiles from the National Ocean Data Center were used to calculate the heat storage rates. Satellite remotely sensed solar irradiance and ship marine weather reports from the Comprehensive Ocean–Atmosphere Data Set were used to calculate the net surface heat flux. Heat storage rates were calculated as the time rate of change of the heat content integrated from the surface down to the isotherm that was 1°C less than the coldest locally observed wintertime sea surface temperature, which was defined as the locally observed wintertime ventilation isotherm. The monthly climatology of the 5° × 5° resolution net heat flux was balanced by the heat storage rate for most regions of the North Pacific. To achieve this balance the net heat flux was calculated using the Liu et al. formulations for latent and sensible heat exchange and a modified version of the Reed cloud correction for solar insolation. The root-mean-square error in the difference between the net heat flux and heat storage rate climatologies was calculated at 40 W m^{−2}. When the individual temperature profiles from the northeastern portion of the basin were normalized to the local 300-m mean temperature, thereby removing some of the potential local changes caused by barotropic variability of water motion, the root-mean-square error in this region was further reduced to 20 W m^{−2} and the large-scale semiannual periodicity in the difference observed in the subtropics was removed. This normalization process may have removed some of the basin-scale variability in the horizontal heat advection. An estimate of the northward heat transport was calculated by integrating the annual mean net heat flux over the North Pacific. The resulting heat transport values were closer to actual northward heat transport estimates made at 10°, 24°, 35°, and 47°N, than previous ocean heat flux estimates. The bias in the data was estimated to be less than 7% by comparing the demeaned seasonal cycle of the net heat flux with that of the heat storage rates. The annual mean net heat flux was then used with the 7% bias and the 20 W m^{−2} uncertainty to calculate a more constrained error envelope for the annual mean northward heat transport in the North Pacific.

## Abstract

A new estimate of the heat budget for the North Pacific Ocean is presented in this paper. The seasonal net heat flux and heat storage rates were calculated for the North Pacific Ocean from 1950 to 1990 on a spatial resolution of 5° × 5°. Temperature profiles from the National Ocean Data Center were used to calculate the heat storage rates. Satellite remotely sensed solar irradiance and ship marine weather reports from the Comprehensive Ocean–Atmosphere Data Set were used to calculate the net surface heat flux. Heat storage rates were calculated as the time rate of change of the heat content integrated from the surface down to the isotherm that was 1°C less than the coldest locally observed wintertime sea surface temperature, which was defined as the locally observed wintertime ventilation isotherm. The monthly climatology of the 5° × 5° resolution net heat flux was balanced by the heat storage rate for most regions of the North Pacific. To achieve this balance the net heat flux was calculated using the Liu et al. formulations for latent and sensible heat exchange and a modified version of the Reed cloud correction for solar insolation. The root-mean-square error in the difference between the net heat flux and heat storage rate climatologies was calculated at 40 W m^{−2}. When the individual temperature profiles from the northeastern portion of the basin were normalized to the local 300-m mean temperature, thereby removing some of the potential local changes caused by barotropic variability of water motion, the root-mean-square error in this region was further reduced to 20 W m^{−2} and the large-scale semiannual periodicity in the difference observed in the subtropics was removed. This normalization process may have removed some of the basin-scale variability in the horizontal heat advection. An estimate of the northward heat transport was calculated by integrating the annual mean net heat flux over the North Pacific. The resulting heat transport values were closer to actual northward heat transport estimates made at 10°, 24°, 35°, and 47°N, than previous ocean heat flux estimates. The bias in the data was estimated to be less than 7% by comparing the demeaned seasonal cycle of the net heat flux with that of the heat storage rates. The annual mean net heat flux was then used with the 7% bias and the 20 W m^{−2} uncertainty to calculate a more constrained error envelope for the annual mean northward heat transport in the North Pacific.

## Abstract

Heat flux, CTD and current profile data from the Hawaii-to- Tahiti Shuttle Experiment are used to study the upper ocean heat budget in order to better understand the seasonal evolution of sea surface temperature (SST) in the central tropical Pacific Ocean between February 1979 and June 1980. The surface heat flux is estimated using bulk formulas and the standard meteorological data taken aboard ship. Upper ocean heat storage is computed from CTD data in such a way (using temperature vertically averaged between the sea surface and fixed isotherm depths) as to filter internal waves. It is found that the surface heat flux plays a large role in the seasonal evolution of SST. A time-latitude correlation coefficient of 0.70 is found between the surface heat flux and heat storage. The seasonal evolution of the vertically averaged temperature whose time rate of change determines storage is very closely correlated with the seasonal evolution of SST.

At 155°W, there is no evidence for a relation between changes of main thermocline depths and changes in SST. Also, we see no feedback from the ocean to the atmosphere through SST governed heat flux. Horizontal heat advection is estimated from Firing *et al*. profiling current meter data. The advection of cold water from the east is important in the 15-cruise (16-month) mean but the data are too noisy to estimate the seasonal evolution of heat advection.

## Abstract

Heat flux, CTD and current profile data from the Hawaii-to- Tahiti Shuttle Experiment are used to study the upper ocean heat budget in order to better understand the seasonal evolution of sea surface temperature (SST) in the central tropical Pacific Ocean between February 1979 and June 1980. The surface heat flux is estimated using bulk formulas and the standard meteorological data taken aboard ship. Upper ocean heat storage is computed from CTD data in such a way (using temperature vertically averaged between the sea surface and fixed isotherm depths) as to filter internal waves. It is found that the surface heat flux plays a large role in the seasonal evolution of SST. A time-latitude correlation coefficient of 0.70 is found between the surface heat flux and heat storage. The seasonal evolution of the vertically averaged temperature whose time rate of change determines storage is very closely correlated with the seasonal evolution of SST.

At 155°W, there is no evidence for a relation between changes of main thermocline depths and changes in SST. Also, we see no feedback from the ocean to the atmosphere through SST governed heat flux. Horizontal heat advection is estimated from Firing *et al*. profiling current meter data. The advection of cold water from the east is important in the 15-cruise (16-month) mean but the data are too noisy to estimate the seasonal evolution of heat advection.

## Abstract

Simultaneous moored temperature, salinity, velocity, and wind measurements from the equator at 157.5°E, during 10 May–21 December 1992, are combined with a no-stress-level boundary condition in the Equatorial Undercurrent core to estimate the total zonal pressure gradient force and subgrid-scale residuals of the momentum balance. Estimates are made of the depth of wind stress penetration, momentum depth, distribution of subgrid-scale stresses, and balance of forcing terms in the surface layer and pycnocline. Westerly winds of greater than 5 m s^{−1} in September 1992 coincided with the appearance of an eastward surface Yoshida jet and subsurface westward (Hisard) jet on the equator. The momentum depth increased with successive wind events, eroding the shallow halocline until it merged with the permanent thermocline. Wind-induced stresses were not restricted to the depth of density homogenization. The record-length-averaged pressure gradient force was westward and was balanced by downstream accelerations and stress drag. However, time-dependent accelerations were balanced by vertical divergence of the stresses. The pressure gradient dominated decelerations of the surface flows and played a lesser role in accelerating subsurface currents. The force balance was consistent with the concept of wind-driven surface flow above the momentum depth; in the pycnocline it implied forcing of the mean zonal currents via the eddy and turbulent momentum flux divergences. The results indicate that steady-state theories do not explain the existence of subsurface zonal currents on the equator. Time-dependent forcing in the equatorial pycnocline includes significant transfers of zonal momentum by submesoscale processes.

## Abstract

Simultaneous moored temperature, salinity, velocity, and wind measurements from the equator at 157.5°E, during 10 May–21 December 1992, are combined with a no-stress-level boundary condition in the Equatorial Undercurrent core to estimate the total zonal pressure gradient force and subgrid-scale residuals of the momentum balance. Estimates are made of the depth of wind stress penetration, momentum depth, distribution of subgrid-scale stresses, and balance of forcing terms in the surface layer and pycnocline. Westerly winds of greater than 5 m s^{−1} in September 1992 coincided with the appearance of an eastward surface Yoshida jet and subsurface westward (Hisard) jet on the equator. The momentum depth increased with successive wind events, eroding the shallow halocline until it merged with the permanent thermocline. Wind-induced stresses were not restricted to the depth of density homogenization. The record-length-averaged pressure gradient force was westward and was balanced by downstream accelerations and stress drag. However, time-dependent accelerations were balanced by vertical divergence of the stresses. The pressure gradient dominated decelerations of the surface flows and played a lesser role in accelerating subsurface currents. The force balance was consistent with the concept of wind-driven surface flow above the momentum depth; in the pycnocline it implied forcing of the mean zonal currents via the eddy and turbulent momentum flux divergences. The results indicate that steady-state theories do not explain the existence of subsurface zonal currents on the equator. Time-dependent forcing in the equatorial pycnocline includes significant transfers of zonal momentum by submesoscale processes.

## Abstract

A current meter mooring maintained for over three years at 28°N, 152°W, in the eastern North Pacific has yielded velocity and temperature data throughout the water column, with particularly good thermocline resolution The flow is characterized by weak primarily westward mean velocities, with a superimposed eddy field having rms velocities ranging from 10 cm s^{−1} in the upper thermocline to 3 cm s^{−1} at 1000 m depth. The eddy energy is divided into two main bands: the low frequency eddies have spatial scales of 250–300 km and periods of 100–200 days, propagate southwestward, and have slightly more zonal than meridional energy. The high frequency eddies also propagate southwestward, have spatial scales of 150–175 km and periods of 40–80 days, and are strongly meridionally oriented. Vertical EOF structure calculated in the frequency domain suggests that the low frequency eddies are more wavelike (linear) in nature than are the high frequency. The entire band appears to derive energy baroclinically from a secularly varying background flow; as a function of time, the eddy heat flux tends to be down the very low frequency varying temperature gradient. Some interesting points of comparison are found with eddies in a three-layer nonlinear model of the eastern North Pacific recently described by Lee.

## Abstract

A current meter mooring maintained for over three years at 28°N, 152°W, in the eastern North Pacific has yielded velocity and temperature data throughout the water column, with particularly good thermocline resolution The flow is characterized by weak primarily westward mean velocities, with a superimposed eddy field having rms velocities ranging from 10 cm s^{−1} in the upper thermocline to 3 cm s^{−1} at 1000 m depth. The eddy energy is divided into two main bands: the low frequency eddies have spatial scales of 250–300 km and periods of 100–200 days, propagate southwestward, and have slightly more zonal than meridional energy. The high frequency eddies also propagate southwestward, have spatial scales of 150–175 km and periods of 40–80 days, and are strongly meridionally oriented. Vertical EOF structure calculated in the frequency domain suggests that the low frequency eddies are more wavelike (linear) in nature than are the high frequency. The entire band appears to derive energy baroclinically from a secularly varying background flow; as a function of time, the eddy heat flux tends to be down the very low frequency varying temperature gradient. Some interesting points of comparison are found with eddies in a three-layer nonlinear model of the eastern North Pacific recently described by Lee.

## Abstract

A kinematic description of the surface circulation in the southern California current System is presented using the statistics of the 7–11 month long trajectories of 29 satellite-tracked mixed layer drifters. The drifters were released north of 30°N and traveled southward at an average speed of 3–4 cm s^{−1} along Baja California through an inhomogeneous field of mesoscale eddies of 15 cm s^{−1} rms variability. Lagrangian and Eulerian statistics of the variations about this mean southward drift are computed. The drifter ensemble mean Lagrangian decorrelation time scale is 4–5 days and the Lagrangian decorrelation space scale is 40–50 km. The computation of dispersion of single particles about the mean drift shows that the theory of diffusion by homogeneous random motion (Taylor's theory) describes these dispersive motions well. Ensemble mean diffusivities of about 4 × 10^{7} cm^{2} s^{−1} are found. On a 200 × 200 km^{2} spatial average, single-partial diffusivities are found to be proportional to the kinetic energy of the locally inhomogeneous fluctuations. Particle-pair statistics are used to study the relative dispersion of particles. The relative diffusivities depend on the initial separation and on the duration of drift. The results are compared to Richardson's 4/3 power law. The Eulerian spatial and temporal correlation of the velocity field indicates that the eddy field is isotropic for scales less than 200 km. The zero time lag correlation indicates an Eulerian length scale of 80 km. The 25-day lagged correlation function indicates that a 2 cm S^{−1} northwestward propagation of features exists roughly perpendicular to the mean flow.

## Abstract

A kinematic description of the surface circulation in the southern California current System is presented using the statistics of the 7–11 month long trajectories of 29 satellite-tracked mixed layer drifters. The drifters were released north of 30°N and traveled southward at an average speed of 3–4 cm s^{−1} along Baja California through an inhomogeneous field of mesoscale eddies of 15 cm s^{−1} rms variability. Lagrangian and Eulerian statistics of the variations about this mean southward drift are computed. The drifter ensemble mean Lagrangian decorrelation time scale is 4–5 days and the Lagrangian decorrelation space scale is 40–50 km. The computation of dispersion of single particles about the mean drift shows that the theory of diffusion by homogeneous random motion (Taylor's theory) describes these dispersive motions well. Ensemble mean diffusivities of about 4 × 10^{7} cm^{2} s^{−1} are found. On a 200 × 200 km^{2} spatial average, single-partial diffusivities are found to be proportional to the kinetic energy of the locally inhomogeneous fluctuations. Particle-pair statistics are used to study the relative dispersion of particles. The relative diffusivities depend on the initial separation and on the duration of drift. The results are compared to Richardson's 4/3 power law. The Eulerian spatial and temporal correlation of the velocity field indicates that the eddy field is isotropic for scales less than 200 km. The zero time lag correlation indicates an Eulerian length scale of 80 km. The 25-day lagged correlation function indicates that a 2 cm S^{−1} northwestward propagation of features exists roughly perpendicular to the mean flow.

## Abstract

Analysis is presented of the time-dependent motion of 47 surface drifters in the northeast Pacific during fall 1987 and 16 drifters in fall and winter 1989/90. The drifters were designed at 15-m depth and were designed to have wind-produced slips less than 2 cm s^{−1} for wind speeds up to 20 m s^{−1}. The coherence of velocity and local wind is presented for motions with periods between 1 day and 40 days. For periods between 5 and 20 days, drogue motion at 15-m depth is found to be highly coherent with local wind with an average phase of 70° to the right of the rotating wind vector. These results differ from analyses of FGGE-type drifters as reported by McNally et al. and Niiler in the same area. A model of wind-produced slip as a function of drifter design is used to provide a possible explanation of the differences. A linear regression, which accounts for 20%–40% of the current variance, gives water motion al 0.5% of wind speed and 68° to the right of the wind vector. Assuming an Ekman-type balance, this regression with 15-m currents yields an apparent mixing depth of 34–38 m. which is much less than the observed 60-m depth of the mixed layer. New three-parameter models for turbulent stress are presented based on these observed depth scales and regression coefficients. The model stresses rotate from downwind to crosswind at the base of the mixed layer. The model currents rotate from approximately 60° to the right of the wind vector at the surface to 180° to the right of the wind vector at the mixed layer base.

## Abstract

Analysis is presented of the time-dependent motion of 47 surface drifters in the northeast Pacific during fall 1987 and 16 drifters in fall and winter 1989/90. The drifters were designed at 15-m depth and were designed to have wind-produced slips less than 2 cm s^{−1} for wind speeds up to 20 m s^{−1}. The coherence of velocity and local wind is presented for motions with periods between 1 day and 40 days. For periods between 5 and 20 days, drogue motion at 15-m depth is found to be highly coherent with local wind with an average phase of 70° to the right of the rotating wind vector. These results differ from analyses of FGGE-type drifters as reported by McNally et al. and Niiler in the same area. A model of wind-produced slip as a function of drifter design is used to provide a possible explanation of the differences. A linear regression, which accounts for 20%–40% of the current variance, gives water motion al 0.5% of wind speed and 68° to the right of the wind vector. Assuming an Ekman-type balance, this regression with 15-m currents yields an apparent mixing depth of 34–38 m. which is much less than the observed 60-m depth of the mixed layer. New three-parameter models for turbulent stress are presented based on these observed depth scales and regression coefficients. The model stresses rotate from downwind to crosswind at the base of the mixed layer. The model currents rotate from approximately 60° to the right of the wind vector at the surface to 180° to the right of the wind vector at the mixed layer base.

## Abstract

An analysis is made of the ensemble mean ageostrophic near-surface circulation measured by 1503 Lagrangian drifters drogued to 15-m depth in the tropical Pacific between 1987 and 1994. It was found that the physical model of the wind-driven currents in a weakly stratified upper layer, in which the Richardson number remains near unity, accounts for 40% of the vector variance of the observations. In such a model, the amplitude of the current is proportional to *u*∗(*N*/*f*)^{1/2} and the depth scale of the wind-driven layer is proportional to *u*∗(*N*/*f*)^{−1/2}. When the ageostrophic currents at 15-m depth are binned by the scaled Ekman depth, a net rotation of 0.87 radians was observed through the layer depth. These measurements suggest that the vertical *austausch* coefficient of the upper ocean is proportional to *u*^{2}_{∗}*N.* Ekman proposed such a model based on two reports of wind-driven currents in 1905 at widely separated latitudes.

## Abstract

An analysis is made of the ensemble mean ageostrophic near-surface circulation measured by 1503 Lagrangian drifters drogued to 15-m depth in the tropical Pacific between 1987 and 1994. It was found that the physical model of the wind-driven currents in a weakly stratified upper layer, in which the Richardson number remains near unity, accounts for 40% of the vector variance of the observations. In such a model, the amplitude of the current is proportional to *u*∗(*N*/*f*)^{1/2} and the depth scale of the wind-driven layer is proportional to *u*∗(*N*/*f*)^{−1/2}. When the ageostrophic currents at 15-m depth are binned by the scaled Ekman depth, a net rotation of 0.87 radians was observed through the layer depth. These measurements suggest that the vertical *austausch* coefficient of the upper ocean is proportional to *u*^{2}_{∗}*N.* Ekman proposed such a model based on two reports of wind-driven currents in 1905 at widely separated latitudes.

## Abstract

A new method for diagnosing the zonal gradient of sea level on the equator from in situ data is proposed and validated using satellite altimetry. A no-turbulent-stress-level boundary condition in the Pacific Equatorial Undercurrent core constrains the average flux of zonal momentum above, uniquely determining the zonal sea level gradient. The method is applied to simultaneous data from Tropical Atmosphere–Ocean Array moorings spanning 154°–165°E and ADCP moorings in the vicinity of 157.5°E from 6 October 1992 to 21 December 1993. An independent estimate of sea level slope is obtained from contemporaneous daily equatorial crossings of the first *European Remote Sensing Satellite* (*ERS-1*) and Ocean Topography Experiment (TOPEX)/Poseidon altimeters. The slope is also estimated by assuming no pressure gradient at 500-m depth. When accelerations and the pressure gradient can be estimated at the same location, 5-day averages of the no-stress-level estimate explain 59% of the variance in the altimetry data (correlation 0.77) with an rms difference of 2 × 10^{−8} and no significant mean offset. The variance explained improves to 66% with 7-day averages. In the absence of velocity and salinity gradient observations, 58%–75% of the signal can be captured with a bias of 0.5 × 10^{−8} on timescales greater than 10 days. Assuming no pressure gradient at 500 m cannot explain more than one-half of the variance on any timescale and is biased by −3 × 10^{−8} to 2 × 10^{−8}, depending on the time period and timescale. Estimating the salinity gradient using temperature–salinity relations worsens the results. Error analyses of the observed data indicate that the daily sea level slope can be accurately determined to within less than 1.5 × 10^{−8} when comprehensive in situ data are available. Daily altimetry estimates from equatorial crossings determine the slope to within 2 × 10^{−8}. Both methods are superior to assuming no pressure gradient at depth and improve upon previous comparisons between remotely sensed and in situ observations of sea level that have succeeded only for monthly and longer timescales.

## Abstract

A new method for diagnosing the zonal gradient of sea level on the equator from in situ data is proposed and validated using satellite altimetry. A no-turbulent-stress-level boundary condition in the Pacific Equatorial Undercurrent core constrains the average flux of zonal momentum above, uniquely determining the zonal sea level gradient. The method is applied to simultaneous data from Tropical Atmosphere–Ocean Array moorings spanning 154°–165°E and ADCP moorings in the vicinity of 157.5°E from 6 October 1992 to 21 December 1993. An independent estimate of sea level slope is obtained from contemporaneous daily equatorial crossings of the first *European Remote Sensing Satellite* (*ERS-1*) and Ocean Topography Experiment (TOPEX)/Poseidon altimeters. The slope is also estimated by assuming no pressure gradient at 500-m depth. When accelerations and the pressure gradient can be estimated at the same location, 5-day averages of the no-stress-level estimate explain 59% of the variance in the altimetry data (correlation 0.77) with an rms difference of 2 × 10^{−8} and no significant mean offset. The variance explained improves to 66% with 7-day averages. In the absence of velocity and salinity gradient observations, 58%–75% of the signal can be captured with a bias of 0.5 × 10^{−8} on timescales greater than 10 days. Assuming no pressure gradient at 500 m cannot explain more than one-half of the variance on any timescale and is biased by −3 × 10^{−8} to 2 × 10^{−8}, depending on the time period and timescale. Estimating the salinity gradient using temperature–salinity relations worsens the results. Error analyses of the observed data indicate that the daily sea level slope can be accurately determined to within less than 1.5 × 10^{−8} when comprehensive in situ data are available. Daily altimetry estimates from equatorial crossings determine the slope to within 2 × 10^{−8}. Both methods are superior to assuming no pressure gradient at depth and improve upon previous comparisons between remotely sensed and in situ observations of sea level that have succeeded only for monthly and longer timescales.