Tidal Coefficients Research Articles

Simplified 1-D Hydrodynamic and Salinity Transport Modeling of the Sacramento–San Joaquin Delta: Sea Level Rise and Water Diversion Effects

Long-term hydrodynamic and salinity transport modeling of the Sacramento–San Joaquin Delta is needed to evaluate the future Delta in terms of the California co-equal goals of ecosystem health and reliable water supply. While 2-D and 3-D hydrodynamic and water quality models are by definition better suited to modeling a complex network of tidally influenced flows under future conditions, a 1-D model is more computationally efficient in narrowing the large variety of multiple-year simulations required into a more manageable task. Still, a 1-D model of sea level rise in an estuary must account for the three-dimensional effects where increased depths will affect density driven (baroclinic) circulation and tidal dispersion of salt. In this paper, we use a simplified Delta network model with a tidally averaged computational approach to quickly perform multi-year simulations for sea level rise. The 1-D model uses tidal dispersion coefficients developed from 3-D hydrodynamic models. The resulting model is capable of performing very fast simulations over a wide range of conditions, providing guidance on what should be explored in depth with more detailed, but slower models. Comparisons of unimpaired Delta inflow with the historical case show that the south Delta and San Joaquin River would be much fresher without exports, while the Sacramento River would be fresher in spring and more saline in the fall. Sea level rise will increase salinity throughout the Delta over time. With peripheral conveyance of export, water salinity will intrude upstream in the Sacramento River, be slightly lower up the San Joaquin River and increase in the south Delta. With sea level rise, peripheral conveyance will have similar trends to changes to the historical case, but export salinity will be improved by the peripheral conveyance component. A larger peripheral conveyance can benefit both the ecosystem and exports if managed properly.

The Accidental Tide Gauge: A GPS Reflection Case Study From Kachemak Bay, Alaska

For the last decade, it has been known that reflected GPS signals observed with specialized instruments could be used to measure sea level. In this letter, data from an existing geodetic-quality GPS site near Kachemak Bay, Alaska, are analyzed for a one-year time period. Daily sea-level variations are more than 7 m. Tidal coefficients have been estimated and compared with coefficients estimated from records from a traditional tide gauge at Seldovia Harbor, <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\sim$</tex></formula> 30 km away. The GPS and Seldovia estimates of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$M_{2}$</tex></formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$S_{2}$</tex> </formula> coefficients agree to better than 2%; much of this residual can be attributed to true differences in the tide over 30 km as it propagates up Kachemak Bay. For daily mean sea levels the agreement is 2.3 cm. Because a standard geodetic GPS receiver/antenna is used, this GPS instrument can measure long-term sea-level changes in a stable terrestrial reference frame.

River flow controls on tides and tide‐mean water level profiles in a tidal freshwater river

Tidal rivers feature oscillatory and steady gradients in the water surface, controlled by interactions between river flow and tides. The river discharge attenuates the tidal motion, and tidal motion increases tidal‐mean friction in the river, which may act as a barrier to the river discharge. Time series of tidal water level amplitudes at five gauge stations along the River Mahakam in Indonesia, and tidal flow velocity amplitudes at a discharge monitoring station were obtained applying wavelet analysis. Temporal variations in tidal damping coefficients for quaterdiurnal, semidiurnal, and diurnal tidal species were quantified from the observed amplitude profiles. The analysis shows that tidal damping during the rising limb of a discharge wave differs from damping during the falling limb. Wavelet cross‐correlations between surface levels yielded empirical estimates of wave numbers. An empirical relation between tidal damping and river flow is derived to describe subtidal bottom friction along an idealized tidal river resembling the Mahakam. The subtidal friction is decomposed into contributions from the river flow only, from river‐tide interaction, and from tidal asymmetry. Even for high river flow and low tidal velocity, river flow enhances friction attributed to river‐tide interaction, causing subtidal water level setup. A simple multilinear regression model using subtidal bottom friction is employed to predict subtidal water levels at locations upstream, with a relatively good agreement between predictions and observations. The explicit expression shows the nonlinear dependence of subtidal friction on river flow velocity, explaining the complex behavior of tidal‐mean surface level profiles.

Tidal and low-frequency currents along the CK Line (31 deg 45 min N) over the East China Sea shelf

The bottom-mounted and ship-mounted ADCP velocities were analyzed to quantify tidal and low-frequency currents between 124.0deg E and 128.5deg E over the CK line (31deg 45min N) in the East China Sea shelf. The bottom-mounted ADCP, deployed in summer and autumn at station 1 (127deg 25min E) or station 2 (125deg 30min E), reveals relatively large (≃0.2ms−1) mean currents to the north or northwest at station 1 and a small (≤0.03ms−1) eastward current at station 2, as well as large tidal currents whose major axis amplitude amounts to 0.25ms−1 at station 1 and 0.5ms−1 at station 2. The bottom-mounted ADCP velocities were used to correct the tidal harmonic coefficients of the NAO.99Jb model under the assumption of uniform correction coefficients. The corrected coefficients were then used to remove the tidal currents in the ship-mounted ADCP velocity obtained over the whole CK-line. The detided ship-mounted ADCP velocities, which agree well with the bottom-mounted ADCP velocities at stations 1 and 2, show a more detailed spatial structure of the low-frequency current and its seasonal variations. The overall structure is characterized by a large northward/northwestward current in the eastern part and a small eastward current in the western part. The northward/northwestward current is largest (0.24ms−1) and most baroclinic in summer, while it becomes weakest (0.11ms−1) and most barotropic in winter. The zonal position of the boundary between the northward/northwestward current and the eastward current changes seasonally.

Estimation of coseismic deformation, poroelasticity, and fracturing of rocks from the data on water level in a borehole

Variations in the water level in boreholes emerge in response to tidal, baric, and tectonic forcing. We analyze the data on atmospheric pressure and water level recorded in the boreholes located in the mid-latitude Eurasia (45°–55°N) from Western Europe (Belgium, Uccle), Siberia (coastal area of Lake Baikal, Talaya River) to Far Eastern Russia (the Bychikha borehole near Khabarovsk and the boreholes on the Kamchatka Peninsula and Kurils). The response of the water level in a borehole to periodic tidal and baric impacts is investigated. In this case, water level variations reflect areal (lateral) and vertical deformations, which allows estimating the elastic moduli and porosity of the confined aquifer in a static model. Measurements in the boreholes drilled in the fractured solid rock enable determining the geometric parameters of the fractures. The possibility to apply the method for evaluating tectonic deformations is discussed. Application of tidal coefficients of boreholes for determining the coseismic deformation is demonstrated by the example of the Kultuk earthquake (Lake Baikal, August 27, 2008, M = 6.3).

Erratum: Post-Newtonian diagnostic of quasiequilibrium binary configurations of compact objects [Phys. Rev. D69, 104021 (2004)

Using equations of motion accurate to the third post-Newtonian (3PN) order (O(v/c)^6 beyond Newtonian gravity), we derive expressions for the total energy E and angular momentum J of the orbits of compact binary systems (black holes or neutron stars) for arbitrary orbital eccentricity. We also incorporate finite-size contributions such as spin-orbit and spin-spin coupling, and rotational and tidal distortions, calculated to the lowest order of approximation, but we exclude the effects of gravitational radiation damping. We describe how these formulae may be used as an accurate diagnostic of the physical content of quasi-equilibrium configurations of compact binary systems of black holes and neutron stars generated using numerical relativity. As an example, we show that quasi-equilibrium configurations of corotating neutron stars recently reported by Miller et al. can be fit by our diagnostic to better than one per cent with a circular orbit and with physically reasonable tidal coefficients.

Post-Newtonian diagnostic of quasiequilibrium binary configurations of compact objects

Using equations of motion accurate to the third post-Newtonian (3PN) order $[{O(v/c)}^{6}$ beyond Newtonian gravity], we derive expressions for the total energy E and angular momentum J of the orbits of compact binary systems (black holes or neutron stars) for arbitrary orbital eccentricity. We also incorporate finite-size contributions such as spin-orbit and spin-spin coupling, and rotational and tidal distortions, calculated to the lowest order of approximation, but we exclude the effects of gravitational radiation damping. We describe how these formulas may be used as an accurate diagnostic of the physical content of quasiequilibrium configurations of compact binary systems of black holes and neutron stars generated using numerical relativity. As an example, we show that quasiequilibrium configurations of corotating neutron stars recently reported by Miller et al. can be fit by our diagnostic to better than one percent with a circular orbit and with physically reasonable tidal coefficients.

Paralytic shellfish poison outbreaks in the Penzé estuary: Environmental factors affecting toxin uptake in the oyster,Crassostrea gigas

Several experiments using a self-regulated system were conducted to define the factors likely to influence the uptake of paralytic shellfish poison (PSP) by oysters in the Penzé estuary (France, Brittany). Each 4-day experiment was carried out in a recirculated sea water system using 15 Pacific oysters (Crassostrea gigas) separated from each other and supplied with unfiltered natural seawater containing alternatively toxic (Alexandrium minutum) or non-toxic (Skeletonema costatum) algal diets. The food supply and exposure times to toxic diets were determined according to field studies of the upstream and downstream movement of patches containing A. minutum. The experimental parameters corresponded roughly to the hydrological conditions generally observed in June when tidal coefficients are lowest and blooms occur: (i) A. minutum concentrations in sea water of 200, 5000 and 10 000 cell ml−1; (ii) inorganic matter consisting of 5 and 15 mg L−1 of calcinated muddy sediments; and (iii) low and high tide salinities of 25 and 35‰, respectively. Significant experimental contamination (greater than the 80 µg STX equiv. 100 g-1 sanitary threshold) occurred after 4 days of exposure for the monospecific A. minutum diet (20-200 cell ml−1) and alternated A. minutum and S. costatum diets (5000 and 20 000 cell ml−1, respectively). Contamination levels were less than the sanitary threshold for alternated A. minutum/S. costatum diets of 200 and 20 000 cell ml−1, respectively, and for a monospecific A. minutum diet (1000−10 000 cell ml−1). In the last case, the accumulation rate was quite low, possibly because of inhibition of the filtration rate related to a lower biodeposit production rate and decreased feeding time activity. The addition of inorganic matter appeared to play a significant role in the observed increase of toxin uptake, whereas salinity was not a determining factor for toxin accumulation rates. These last observations were corroborated by statistical analysis and stepwise multiple linear regressions integrating all or some of the experimental parameters.

High‐frequency variations in Earth rotation from Global Positioning System data

Using the data of the global, dense Global Positioning System (GPS) network established by the International GPS Service a continuous, uninterrupted series of subdaily Earth rotation parameters (ERPs) with a time resolution of 2 hours has been generated at the Center for Orbit Determination in Europe. The series starts in January 1995 and has a length of more than 3 years. Starting from the 2‐hour ERP values of this, to our knowledge, unique time series, the high‐frequency variations in Universal Time (UT1) and polar motion (PM) due to ocean tides are studied and a set of sine and cosine coefficients is estimated for all the major tidal terms at nearly diurnal and semidiurnal frequencies. The GPS series is not very homogeneous (various processing changes during the 3 years) and still short compared to the length of very long baseline interferometry (VLBI) and satellite laser ranging (SLR) data sets. However, the results derived from this series are already of the same quality as the results from VLBI and SLR. A comparison of the tidal coefficients stemming from all three space‐geodetic techniques shows an agreement on the 1 μs level for UT1 and 10 microarc seconds (μas) for PM, respectively. The RMS difference between the ocean tide amplitudes estimated from GPS data and from TOPEX/Poseidon altimeter data amounts to 0.7–0.9 μs in UT1 and 9–13 μas in PM. The residual spectrum that remains after the removal of all tidal terms has a noise level of ∼5–10 μas in PM and 0.5–1 μs in UT1 and contains nontidal signals (up to 55 μas in PM and 3 μs in UT1) that might be due to the impact of the satellite orbit modeling (12‐hour revolution period of the satellites) or, alternatively, due to atmospheric or oceanic normal modes.

Effect of residence times on River Mondego estuary eutrophication vulnerability

The south arm of the Mondego estuary, located in the central western Atlantic coast of Portugal, is almost silted up in the upstream area. So, the water circulation is mostly driven by tides and the tributary river Pranto discharges. Eutrophication has been taking place in this ecosystem during last twelve years, where macroalgae reach a luxuriant development covering a significant area of the intertidal muddy flat. A sampling program was carried out from June 1993 to June 1994. Available data on salinity profiles and on nutrients loading into the south arm were used in order to get a better understanding of the ongoing changes. River Pranto flow discharges, controlled by a sluice, were also monitored. Integral formulations are typically based on assumptions of steady state and well-mixed systems and thus cannot take into account the space and time variability of estuarine residence times, due to river discharge flow, tidal coefficients, discharge(s) location and time of release during the tidal cycle. This work presents the hydrodynamics modelling (2D-H) of this system in order to estimate the residence times variability and to assess their effect on the estuarine eutrophication vulnerability, contributing to better environmental management strategies selection.

Tidal shocking and destruction of globular clusters

Abstract Dynamical evolution of globular clusters is strongly influenced and often driven by tidal interactions with the Galaxy. Passing through the Galactic disk or near the bulge, globular clusters experience fast gravitational perturbations, the compressive tidal shocks. A succession of tidal shocks leads to kinematic heating of the clusters and their ultimate destruction. I present the latest Fokker-Planck models including the first and second order tidal diffusion coefficients. In the limit of strong shocks, the typical value of the core collapse time t cc decreases from 10 to 3 half-mass relaxation times, while the destruction time is just 2, t cc. The effects of tidal shocks are rapidly self-limiting: as clusters lose mass and become more compact, the importance of the shocks diminishes. This implies that tidal shocks were more important in the past.

Effects of Tidal Shocks on the Evolution of Globular Clusters

We present new Fokker-Planck models of the evolution of globular clusters, including gravitational tidal shocks. We extend our calculations beyond the core collapse by adopting three-body binary heating. EUects of the shocks are included by adding the tidal shock diUusion coefficients to the ordinary Fokker-Planck equation: the —rst-order heating term, S*ET, and the second-order energy dispersion term, S*E2T. As an example, we investigate the evolution of models for the globular cluster NGC 6254. Using the Hipparcos proper motions, we are now able to construct orbits of this cluster in the Galaxy. Tidal shocks accelerate signi—cantly both core collapse and the evaporation of the cluster and shorten the destruction time from 24 to 18 Gyr. We examine various types of adiabatic corrections and —nd that they are critical for accurate calculation of the evolution. Without adiabatic corrections, the destruction time of the cluster is twice as short. We examine cluster evolution for a wide range of the concentration and tidal shock parameters and determine the region of the parameter space where tidal shocks domi- nate the evolution. We present —tting formulae for the core collapse time and the destruction time, covering all reasonable initial conditions. In the limit of strong shocks, the typical value of the core collapse time decreases from to or less, while the destruction time is just twice that number. 10t rh 3t rh The eUects of tidal shocks are rapidly self-limiting: as clusters lose mass and become more compact, the importance of the shocks diminishes. This implies that tidal shocks were more important in the past. Subject headings: celestial mechanics, stellar dynamicsglobular clusters: general ¨ globular clusters: individual (NGC 6254)

Pumping Test Analysis for a Tidally Forced Aquifer

AbstractThe analysis of pumping test data for a shallow riverbank aquifer afforded the opportunity to compare standard methods for determining hydraulic conductivity (K) and storativity (S) with techniques based on the propagation of periodic fluctuations of head in the aquifer. Tidal fluctuations in water level at the riverbank were found to propagate approximately nondispersively for 200 m in the aquifer, allowing tidal phase lags and amplitude attenuations in the aquifer to be estimated from river levels by least‐squares techniques. The least‐squares attenuations and phases were used to correct measured pumping test drawdowns for tidal influences. Standard transient analyses of the corrected drawdowns were performed, yielding values of approximately 8 to 10 m/d for K and 0.002 for S. The low S value was taken to indicate semi‐confined conditions. The tidal attenuation coefficients were used to determine the hydraulic diffusivity T/S, providing values that were integrated over the distance from the riverbank to the relevant monitoring wells. S values from the drawdown analyses then yielded K estimates ranging from 3 to 7 m/d. A three‐dimensional finite‐element simulation of the pumping tests showed that the estimated K and S values yielded simulated drawdowns in reasonable agreement with field observations.

Caractérisation biologique et variation des captures de la grande alose (Alosa alosa) par unité d'effort sur le fleuve Adour (Pyrénées Atlantiques, France)

Resume The study of logbooks from commercial fishermen on the Adour River and commercial samples allowed characterization of the allis shad population (Alosa alosa L.) caught during the period 1988-91. A better knowledge of the influence of hydroclimatic factors (rate of river flow and intensity of tidal coefficient) on the catchability of the species in that river was also obtained. Allis shad are mainly recruited to this fishery from the beginning of April to the end of May: between 78 and 89 % depending on year. Males in the population were on average younger than females. However, at the same age, males were significantly smaller in size and in weight than females. These results reinforce the knowledge already obtained on French stocks in the Loire and Gironde river networks. During the main exploitation period of allis shad, we noted the influence of the rate of flow and tidal coefficients on catch per unit effort (kg per trip) variations. Analysis performed either with Correspondence Analysis or with Generalized Linear Mode1 indicated that an increase of catch per unit effort (CPUE) is associated with the increase in the tidal coefficient. The rate of flow was considered to be a secondary factor of variation.

The Internal Tide off the West Coast of Vancouver Island

Using data from the Coastal Ocean Dynamics Experiment (CODE) and the Island Coastal Current Experiment, the internal tide off the west coast of the Vancouver Island was studied. Although the semidiurnal barotropic velocity field in the area was weak, the baroclinic field was found to be relatively strong with speeds up to five times greater. The intermittent nature of the baroclinic field was resolved by estimating the M2 tidal harmonic coefficients every 24 hours in 15-day overlaping intervals. These time-evolving coefficients were then analysed using spectral analysis methods. For most of the area under investigation, the internal tide was generated mainly at the shelf break and was found to propagate cross-shore. Off Estevan point, where the bottom contour is regular, the beam structure was identified and traced to distances 40 km from the generation region on the slope. The downward-propagating beam was found to follow the seasonal variation of the characteristic propagation paths. An empirical orthogonal function analysis revealed a highly coherent baroclinic field (78% of the M2 variance). The predictions of an internal tide model were found to he in good agreement with the experimental results on the slope. The interaction of a cyclonic eddy, present in the area during August 1980, with the internal tide was also addressed.

Long‐period perturbations in starlette orbit and tide solution

Continuous and dynamically consistent orbits have been computed using satellite laser ranging (SLR) data to Starlette for a one‐year period during 1976 and 1977 and the three‐year period from 1983 through 1985. A low degree and order ocean tide solution, consisting of a total of 66 tidal parameters from 14 tidal constituents, was obtained in a combined solution using both the one‐ and three‐year Starlette orbits. An enhanced model of the Schwiderski [1980] tide solution was used both as the a priori and the background tide model. The model contains 368 tidal coefficients from 21 tidal constituents. Yearly values for the second‐degree annual tides, Sa, which produce seasonal variations on the Starlette node, were obtained also. These variations were found to have year‐to‐year fluctuations of more than 25% about the mean value and produced significant long‐period perturbations in the Starlette orbit. The Starlette tide solution is in good agreement with the Schwiderski tide solutions and with other satellite solutions, including multi‐satellite tide solutions. The average uncertainties are approximately 0.1 cm for the estimated semidiurnal and diurnal tides and 0.4 cm for the long‐period tides. The discrepancies of effective k2 inferred from the Starlette tide solution and other tide solutions are less than 0.01. The tide solutions were evaluated using orbit fits of a three‐year LAGEOS and a one‐year Starlette long arc. The results indicate that the Starlette tide solution produces significantly improved orbit fits for both LAGEOS and Starlette. The uncertainties for the estimated tide model coefficients were used to predict tidal errors for the LAGEOS orbit and were found to be consistent with the apparent tidal errors present in this orbit. The computed secular change in the Moon's mean motion due to tidal dissipation is −24.8±0.8 arc second/century2, which is in good agreement with the results obtained from other investigations.

Ocean tides and tectonic plate motions in high precision orbit determination

A study of the influence of solid earth, ocean and atmospheric tides on the orbits of earth satellites has been carried out, allowing the computation of the spectrum of tidal perturbations on the orbital elements. Some 170,000 laser ranging normal points from over 3 years of tracking were combined in a simultaneous solution for the positions and tectonic motions of the stations of the laser network, earth rotation parameters, and a set of tidal and gravity coefficients. Tectonic plate motion estimates show a reasonable agreement with a recent geophysical model (Minster and Jordan). The principal objective of the work was the development of an improved tidal model from Lageos for use in satellite orbit determination.

A new gravitational model for the Earth from satellite tracking data: GEM‐T1

A major new computation of a terrestrial gravitational field model has been performed by the Geodynamics Branch of Goddard Space Flight Center (GSFC). In the development of this new model, designated Goddard Earth Model GEM‐T1, the design decisions of the past have been reassessed in light of the present state of the art in satellite geodesy. With GEM‐T1 a level of internal consistency has been achieved which is superior to any earlier Goddard Earth Model. For the first time a simultaneous solution has been made for spherical harmonic parameters of both invariant and tidal parts of the gravitational field. The solution of this satellite model to degree 36 is a major factor accounting for its improved accuracy. The addition of more precise and previously unused laser data and the introduction of consistent models were also accomplished with GEM‐T1. Another major factor allowing the creation of this model was the redesign and vectorization of our main software tools (GEODYN II and SOLVE) for the GSFC Cyber 205 computer. In particular, the high‐speed advantage (50:1), gained with the new SOLVE program, made possible an optimization of the weighting and parameter estimation scheme used in previous GEM models resulting in significant improvement in GEM‐T1. The solution for the GEM‐T1 model made use of the latest International Association of Geodesy reference constants, including the J2000 Reference System. It provided a simultaneous solution for (1) a gravity model in spherical harmonics complete to degree and order 36; (2) a subset of 66 ocean tidal coefficients for the long‐wavelength components of 12 major tides. This adjustment was made in the presence of 550 other fixed ocean tidal terms representing 32 major and minor tides and the Wahr frequency dependent solid earth tidal model; and (3) 5‐day averaged Earth rotation and polar motion parameters for the 1980 period onward. GEM‐T1 was derived exclusively from satellite tracking data acquired on 17 different satellites whose inclinations ranged from 15° to polar. In all, almost 800,000 observations were used, half of which were from third generation (&lt;5 cm) laser systems. A calibration of the model accuracies has been performed showing GEM‐T1 to be a significant improvement over earlier GSFC “satellite‐only” models based purely on tracking data for both orbital and geoidal modeling applications. For the longest wavelength portion of the geoid (to 8×8), GEM‐T1 is a major advancement over all GEM models, even those containing altimetry and surface gravimetry. The radial accuracy for the anticipated TOPEX/POSEIDON orbit was estimated using the covariances of the GEM‐T1 model. The radial errors were found to be at the 25‐cm rms level as compared to 65 cm found using GEM‐L2. This simulation evaluated only errors arising from geopotential sources. GEM‐L2 was the best available model for TOPEX prior to the work described herein. A major step toward reaching the accuracy of gravity modeling necessary for the TOPEX/POSEIDON mission has been achieved.

Observed tidal braking in the Earth/Moon/Sun system

The low degree and order terms in the spherical harmonic model of the tidal potential have been observed through the perturbations which are induced on near‐Earth satellite orbital motions. This recovery, which is the most complete dynamic model ever obtained, has been achieved through evaluating tracking observations on 17 different, mostly laser, satellites. A new improved GEM‐Tl geopotential model, complete to degree and order 36, was estimated simultaneously with the 66 adjusted tidal coefficients. The gravitational and tidal models were developed using the J2000 Reference System with the adopted nutations of Wahr and the precession model of Lieske. The tidal recovery was made in the presence of an extended oceanographic model containing over 600 long‐wavelength coefficients from 32 major and minor tides. Since solid Earth tides have perturbing frequencies identical to those of the ocean tides, the solid Earth tidal model of Wahr was used as a basis for the recovery of the ocean tidal terms. This provided a complete description of the combined tidal potential sensed by these well‐tracked satellites. This tidal model (for all 32 adjusted and unadjusted tides) has then been used to calculate the secular change in the Moon's mean motion due to tidal dissipation and the tidal braking of the Earth's rotation. The secular change in the Moon's mean motion due to tidal dissipation is found to be −25.27±0.61 arc sec century−2. Our estimate of the lunar acceleration agrees well with that observed from lunar laser ranging techniques, which most recently found −24.9±1.0 arc sec century−2 (Newhall et al., 1986). The corresponding tidal braking of the Earth's rotation is −5.98 ± 0.22 × 10−22 rad s−2. If the nontidal braking of the Earth due to the observed secular change in the Earth's second zonal harmonic (Yoder et al., 1983) is considered, modern satellite techniques yield a total value of the secular change in the Earth's rotation rate of −4.69 ± 0.36 × 10−22rad s−2.

On tide‐induced Lagrangian residual current and residual transport: 2. Residual transport with application in south San Francisco Bay, California

The transports of solutes and other tracers are fundamental to estuarine processes. The apparent transport mechanisms are convection by tidal current and current‐induced shear effect dispersion for processes which take place in a time period of the order of a tidal cycle. However, as emphasis is shifted toward the effects of intertidal processes, the net transport is mainly determined by tide‐induced residual circulation and by residual circulation due to other processes. The commonly used intertidal conservation equation takes the form of a convection‐dispersion equation in which the convective velocity is the Eulerian residual current, and the dispersion terms are often referred to as the phase effect dispersion or, sometimes, as the “tidal dispersion.” The presence of these dispersion terms is merely the result of a Fickian type hypothesis. Since the actual processes are not Fickian, thus a Fickian hypothesis obscures the physical significance of this equation. Recent research results on residual circulation have suggested that long‐term transport phenomena are closely related to the Lagrangian residual current or the Lagrangian residual transport. In this paper a new formulation of an intertidal conservation equation is presented and examined in detail. In a weakly nonlinear tidal estuary the resultant intertidal transport equation also takes the form of a convection‐dispersion equation without the ad hoc introduction of phase effect dispersion in a form of dispersion tensor. The convective velocity in the resultant equation is the first‐order Lagrangian residual current (the sum of the Eulerian residual current and the Stokes drift). The remaining dispersion terms are important only in higher‐order solutions; they are due to shear effect dispersion and turbulent mixing. There exists a dispersion boundary layer adjacent to shoreline boundaries. An order of magnitude estimate of the properties in the dispersion boundary layer is given. The present treatment of intertidal transport processes is illustrated by an analytical solution for an amphidromic system and by a numerical application in South San Francisco Bay, California. The present formulation reveals that the mechanism for long‐term transport of solutes is mainly convection due to the Lagrangian residual current in the interior of a tidal estuary. This result also points out the weakness in the tidal dispersion formulation, and explains the large variability of the observed values for tidal dispersion coefficients. Further research on properties of the dispersion boundary layer is needed.