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A three-dimensional, time-dependent, baroclinic, hydrodynamic and salinity model, UnTRIM, was performed and applied to the Danshuei River estuarine system and adjacent coastal sea in northern Taiwan. The model forcing functions consist of tidal elevations along the open boundaries and freshwater inflows from the main stream and major tributaries in the Danshuei River estuarine system. The bottom friction coefficient was adjusted to achieve model calibration and verification in model simulations of barotropic and baroclinic flows. The turbulent diffusivities were ascertained through comparison of simulated salinity time series with observations. The model simulation results are in qualitative agreement with the available field data. The validated model was then used to investigate the influence of wind stress and freshwater discharge on Dasnhuei River plume. As the absence of wind stress, the anticyclonic circulation is prevailed along the north to west coast. The model results reveal when winds are downwelling-favorable, the surface low-salinity waters are flushed out and move to southwest coast. Conversely, large amounts of low-salinity water flushed out the Danshuei River mouth during upwelling-favorable winds, as the buoyancy-driven circulation is reversed. Wind stress and freshwater discharge are shown to control the plume structure.

A 3-D, time-dependent, baroclinic, hydrodynamic and salinity model was implemented and applied to the Danshuei River estuarine system and the adjacent coastal sea in Taiwan. The model forcing functions consist of tidal elevations along the open boundaries and freshwater inflows from the main stream and major tributaries in the Danshuei River estuarine system. The bottom friction coefficient was adjusted to achieve model calibration and verification in model simulations of barotropic and baroclinic flows. The turbulent diffusivities were ascertained through comparison of simulated salinity time series with observations. The model simulation results are in qualitative agreement with the available field data. The validated model was then used to investigate the influence of freshwater discharge on residual current and salinity intrusion under different freshwater inflow condition in the Danshuei River estuarine system. The model results reveal that the characteristic two-layered estuarine circulation prevails most of the time at Kuan-Du station near the river mouth. Comparing the estuarine circulation under low- and mean flow conditions, the circulation strengthens during low-flow period and its strength decreases at moderate river discharge. The river discharge is a dominating factor affecting the salinity intrusion in the estuarine system. A correlation between the distance of salt intrusion and freshwater discharge has been established allowing prediction of salt intrusion for different inflow conditions.

Advances in technology have resulted in a new instrument that is designed for in-situ determination of particle size spectra. Such an instrument that can measure undisturbed particle size distributions is much needed for sediment transport studies. The LISST-100 (Laser In-Situ Scattering and Transmissometry) uses the principle of laser diffraction to obtain the size distribution and volume concentration of suspended material in 32 size classes logarithmically spaced between 1.25 and 250 μm. This paper describes a laboratory evaluation of the ability of LISST-100 to determine particle sizes using suspensions of single size, artificial particles. Findings show the instrument is able to determine particle size to within about 10% with increasing error as particle size increases. The instrument determines volume (or mass) concentration using a volume conversion factor Cv. This volume conversion factor is theoretically a constant. In the laboratory evaluation Cv is found to vary by a factor of about three over the particle size range between 5 and 200 μm. Results from field studies in South San Francisco Bay show that values of mass concentration of suspended marine sediments estimated by LISST-100 agree favorably with estimates from optical backscatterance sensors if an appropriate value of Cv, according to mean size, is used and the assumed average particle (aggregate) density is carefully chosen. Analyses of size distribution of suspended materials in South San Francisco Bay over multiple tide cycles suggest the likelihood of different sources of sediment because of different size characteristics during flood and ebb cycles.

This report describes an experiment to make a completely non-contact open-channel discharge measurement. A van-mounted, pulsed doppler (10GHz) radar collected surface-velocity data across the 183-m wide Skagit River, Washington at a USGS streamgaging station using Bragg scattering from short waves produced by turbulent boils on the surface of the river. Surface velocities were converted to mean velocities for 25 sub-sections by assuming a normal open-channel velocity profile (surface velocity times 0.85). Channel cross-sectional area was measured using a 100 MHz ground-penetrating radar antenna suspended from a cableway car over the river. Seven acoustic doppler current profiler discharge measurements and a conventional current-meter discharge measurement were also made. Three non-contact discharge measurements completed in about a 1-hour period were within 1% of the gaging station rating curve discharge values. With further refinements, it is thought that open-channel flow can be measured reliably by non-contact methods.

A field investigation of the hydrodynamics and the resuspension and transport of particulate matter in a bottom boundary layer was carried out in South San Francisco Bay (South Bay), California, during March-April 1995. Using broadband acoustic Doppler current profilers, detailed measurements of turbulent mean velocity distribution within 1.5 m above bed have been obtained. A global method of data analysis was used for estimating bottom roughness length zo and bottom shear stress (or friction velocities u*). Field data have been examined by dividing the time series of velocity profiles into 24-hour periods and independently analyzing the velocity profile time series by flooding and ebbing periods. The global method of solution gives consistent properties of bottom roughness length zo and bottom shear stress values (or friction velocities u*) in South Bay. Estimated mean values of zo and u* for flooding and ebbing cycles are different. The differences in mean zo and u* are shown to be caused by tidal current flood-ebb inequality, rather than the flooding or ebbing of tidal currents. The bed shear stress correlates well with a reference velocity; the slope of the correlation defines a drag coefficient. Forty-three days of field data in South Bay show two regimes of zo (and drag coefficient) as a function of a reference velocity. When the mean velocity is >25–30 cm s−1, the ln zo (and thus the drag coefficient) is inversely proportional to the reference velocity. The cause for the reduction of roughness length is hypothesized as sediment erosion due to intensifying tidal currents thereby reducing bed roughness. When the mean velocity is

In 1983, current data were collected by the National Oceanic and Atmospheric Administration using mechanical current meters. During 1992 through 1996, acoustic Doppler current profilers as well as mechanical current meters and tide gauges were used. These measurements not only document tides and tidal currents in San Diego Bay, but also provide independent data sets for model calibration and verification. A high resolution (100-m grid), depth-averaged, numerical hydrodynamic model has been implemented for San Diego Bay to describe essential tidal hydrodynamic processes in the bay. The model is calibrated using the 1983 data set and verified using the more recent 1992–1996 data. Discrepancies between model predictions and field data in both model calibration and verification are on the order of the magnitude of uncertainties in the field data. The calibrated and verified numerical model has been used to quantify residence time and dilution and flushing of contaminant effluent into San Diego Bay. Furthermore, the numerical model has become an important research tool in ongoing hydrodynamic and water quality studies and in guiding future field data collection programs.

The seasonal response of sea level in San Francisco Bay (SFB) to atmospheric forcing during 1980 is investigated. The relations between sea-level data from the Northern Reach, Central Bay and South Bay, and forcing by local wind stresses, sea-level pressure (SLP), runoff and the large-scale sea-level pressure field are examined in detail. The analyses show that the sea-level elevations and slopes respond to the along-shore wind stress T y at most times of the year, and to the cross-shore wind stress T x during two transition periods in spring and autumn. River runoff raises the sea-level elevation during winter. It is shown that winter precipitation in the SFB area is mainly attributed to the atmospheric circulation associated with the Aleutian Low, which transports the warm, moist air into the Bay area. A multiple linear regression model is employed to estimate the independent contributions of barometric pressure and wind stress to adjusted sea level. These calculations have a simple dynamical interpretation which confirms the importance of along-shore wind to both sea level and north-south slope within the Bay.

A numerical model using a semi-implicit finite-difference method for solving the two-dimensional shallow-water equations is presented. The gradient of the water surface elevation in the momentum equations and the velocity divergence in the continuity equation are finite-differenced implicitly, the remaining terms are finite-differenced explicitly. The convective terms are treated using an Eulerian-Lagrangian method. The combination of the semi-implicit finite-difference solution for the gravity wave propagation, and the Eulerian-Lagrangian treatment of the convective terms renders the numerical model unconditionally stable. When the baroclinic forcing is included, a salt transport equation is coupled to the momentum equations, and the numerical method is subject to a weak stability condition. The method of solution and the properties of the numerical model are given. This numerical model is particularly suitable for applications to coastal plain estuaries and tidal embayments in which tidal currents are dominant, and tidally generated residual currents are important. The model is applied to San Francisco Bay, California where extensive historical tides and current-meter data are available. The model calibration is considered by comparing time-series of the field data and of the model results. Alternatively, and perhaps more meaningfully, the model is calibrated by comparing the harmonic constants of tides and tidal currents derived from field data with those derived from the model. The model is further verified by comparing the model results with an independent data set representing the wet season. The strengths and the weaknesses of the model are assessed based on the results of model calibration and verification. Using the model results, the properties of tides and tidal currents in San Francisco Bay are characterized and discussed. Furthermore, using the numerical model, estimates of San Francisco Bay's volume, surface area, mean water depth, tidal prisms, and tidal excursions at spring and neap tides are computed. Additional applications of the model reveal, qualitatively the spatial distribution of residual variables.

Two-dimensional river flow patterns have been measured using a pair of RiverSondes in two experiments in the Sacramento-San Joaquin River Delta system of central California during April and October 2007. An experiment was conducted at Walnut Grove, California in order to explore the use of dual RiverSondes to measure flow patterns at a location which is important in the study of juvenile fish migration. The data available during the first experiment were limited by low wind, so a second experiment was conducted at Threemile Slough where wind conditions and surface turbulence historically have resulted in abundant data. Both experiments included ADCP near-surface velocity measurements from either manned or unmanned boats. Both experiments showed good comparisons between the RiverSonde and ADCP measurements. The flow conditions at both locations are dominated by tidal effects, with partial flow reversal at Walnut Grove and complete flow reversal at Threemile Slough. Both systems showed complex flow patterns during the flow reversals. Quantitative comparisons between the RiverSondes and an ADCP on a manned boat at Walnut Grove showed mean differences of 4.5 cm/s in the u (eastward) and 7.6 cm/s in the v (northward) components, and RMS differences of 14.7 cm/s in the u component and 21.0 cm/s in the v component. Quantitative comparisons between the RiverSondes and ADCPs on autonomous survey vessels at Threemile Slough showed mean differences of 0.007 cm/s in the u component and 0.5 cm/s in the v component, and RMS differences of 7.9 cm/s in the u component and 13.5 cm/s in the v component after obvious outliers were removed.

A two-dimensional laterally averaged numerical estuarine model is developed to study the vertical variations of tidal hydrodynamic properties in the central/north part of San Francisco Bay, California. Tidal stage data, current meter measurements, and conductivity, temperature, and depth profiling data in San Francisco Bay are used for comparison with model predictions. An extensive review of the literature is conducted to assess the success and failure of previous similar investigations and to establish a strategy for development of the present model. A σ plane transformation is used in the vertical dimension to alleviate problems associated with fixed grid model applications in the bay, where the tidal range can be as much as 20–25% of the total water depth. Model predictions of tidal stage and velocity compare favorably with the available field data, and prototype salinity stratification is qualitatively reproduced. Conclusions from this study as well as future model applications and research needs are discussed.

In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined Eulerian-Lagrangian approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit Eulerian-Lagrangian method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the Eulerian-Lagrangian approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses.

Two RiverSondes were operated simultaneously in close proximity in order to provide a two-dimensional map of river surface velocity. The initial test was carried out at Threemile Slough in central California. The two radars were installed about 135 m apart on the same bank of the channel. Each radar used a 3-yagi antenna array and determined signal directions using direction finding. The slough is approximately 200 m wide, and each radar processed data out to about 300 m, with a range resolution of 15 m and an angular resolution of 1 degree. Overlapping radial vector data from the two radars were combined to produce total current vectors at a grid spacing of 10 m, with updates every 5 minutes. The river flow in the region, which has a maximum velocity of about 0.8 m/s, is tidally driven with flow reversals every 6 hours, and complex flow patterns were seen during flow reversal. The system performed well with minimal mutual interference. The ability to provide continuous, non-contact two-dimensional river surface flow measurements will be useful in several unique settings, such as studies of flow at river junctions where impacts to juvenile fish migration are significant. Additional field experiments are planned this year on the Sacramento River.

[1] Conventional measurements of river flows are costly, time-consuming, and frequently dangerous. This report evaluates the use of a continuous wave microwave radar, a monostatic UHF Doppler radar, a pulsed Doppler microwave radar, and a ground-penetrating radar to measure river flows continuously over long periods and without touching the water with any instruments. The experiments duplicate the flow records from conventional stream gauging stations on the San Joaquin River in California and the Cowlitz River in Washington. The purpose of the experiments was to directly measure the parameters necessary to compute flow: surface velocity (converted to mean velocity) and cross-sectional area, thereby avoiding the uncertainty, complexity, and cost of maintaining rating curves. River channel cross sections were measured by ground-penetrating radar suspended above the river. River surface water velocity was obtained by Bragg scattering of microwave and UHF Doppler radars, and the surface velocity data were converted to mean velocity on the basis of detailed velocity profiles measured by current meters and hydroacoustic instruments. Experiments using these radars to acquire a continuous record of flow were conducted for 4 weeks on the San Joaquin River and for 16 weeks on the Cowlitz River. At the San Joaquin River the radar noncontact measurements produced discharges more than 20% higher than the other independent measurements in the early part of the experiment. After the first 3 days, the noncontact radar discharge measurements were within 5% of the rating values. On the Cowlitz River at Castle Rock, correlation coefficients between the USGS stream gauging station rating curve discharge and discharge computed from three different Doppler radar systems and GPR data over the 16 week experiment were 0.883, 0.969, and 0.992. Noncontact radar results were within a few percent of discharge values obtained by gauging station, current meter, and hydroacoustic methods. Time series of surface velocity obtained by different radars in the Cowlitz River experiment also show small-amplitude pulsations not found in stage records that reflect tidal energy at the gauging station. Noncontact discharge measurements made during a flood on 30 January 2004 agreed with the rated discharge to within 5%. Measurement at both field sites confirm that lognormal velocity profiles exist for a wide range of flows in these rivers, and mean velocity is approximately 0.85 times measured surface velocity. Noncontact methods of flow measurement appear to (1) be as accurate as conventional methods, (2) obtain data when standard contact methods are dangerous or cannot be obtained, and (3) provide insight into flow dynamics not available from detailed stage records alone.

A UHF RiverSonde system, operating near 350 MHz, has been in operation at Threemile Slough in central California, USA since September 2004. The water in the slough is dominated by tidal effects, with flow reversals four times a day and a peak velocity of about 0.8 m/s in each direction. Water level and water velocity are continually measured by the U. S. Geological Survey at the experiment site. The velocity is measured every 15 minutes by an ultrasonic velocity meter (UVM) which determines the water velocity from two-way acoustic propagation time-difference measurements made across the channel. The RiverSonde also measures surface velocity every 15 minutes using radar resonant backscatter techniques. Velocity and water level data are retrieved through a radio data link and a wideband internet connection. Over a period of several months, the radar-derived mean surface velocity has been very highly correlated with the UVM index velocity several meters below the surface, with a coefficient of determination R 2 of 0.976 and an RMS difference of less than 10 cm/s. The wind has a small but measurable effect on the velocities measured by both instruments. In addition to the mean surface velocity across the channel, the RiverSonde system provides an estimate of the cross-channel variation of the surface velocity.

Long-term, non-contact river velocity measurements have been made using a UHF RiverSonde system for several months at each of two locations having quite different flow characteristics. Observations were made on the Cowlitz River at Castle Rock, Washington from October 2003 to June 2004, where the unidirectional flow of the river ranged from about 1.0 to 3.5 m/s. The radar velocity was highly correlated with the stage height which was continually measured by the U. S. Geological Survey. The profile of the along-channel velocity across the water channel also compared favorably with in-situ measurements performed by the Survey. The RiverSonde was moved to Threemile Slough, in central California, in September 2004 and has been operating there for several months. At Threemile Slough, which connects the Sacramento and San Joaquin Rivers, the flow is dominated by tidal effects and reverses direction four times per day, with a maximum speed of about 0.8 m/s in each direction. Water level and water velocity are continually measured by the Survey at the Threemile Slough site, with velocity recorded every 15 minutes from measurements made by an ultrasonic velocity meter (UVM). Over a period of several months, the radar and UVM velocity measurements have been highly correlated, with a coefficient of determination R/sup 2/ of 0.976.

The hydrodynamics in the Upper Klamath Lake (UKL) plays a significant role in the water quality conditions of the lake. In order to provide a quantitative evaluation of the impacts of hydrodynamics on water quality in UKL, a detailed hydrodynamic model was implemented using an unstructured grid 3-D hydrodynamic model known as the UnTRIM model. The circulation in UKL is driven primarily by wind. Wind speed and direction time-series records were used as input, the numerical model reproduced the wind set-up and set-down at down wind and upwind ends of the lake, respectively. Of the two acoustic Doppler current profiler (ADCP) records, the UnTRIM model reproduced the measured velocity at the deep station. At the shallow station, the model results showed diurnal patterns that correlated well with wind variations, but the measured velocity showed water velocity sustained at 3 to 5 cm/sec or above. Discrepancies between the model results and observations at the shallow ADCP station is discussed on the basis of correct physics. If the field measurements are inconsistent with the known physics, there exists the possibility that the field data are suspect or the field data are revealing some physical processes that are not yet understood.

River derived fresh water discharging into an adjacent continental shelf forms a trapped river plume that propagates in a narrow region along the coast. These river plumes are real and they have been observed in the field. Many previous investigations have reported some aspects of the river plume properties, which are sensitive to stratification. Coriolis acceleration, winds (upwelling or downwelling), coastal currents and river discharge. Numerical modeling of the dynamics of river plumes is very challenging, because the complete problem involves a wide range of vertical and horizontal scales. Proper simulations of river plume dynamics cannot be achieved without a realistic representation of the flow and salinity structure near the river mouth that controls the initial formation and propagation of the plume in the coastal ocean. In this study, an unstructured grid model was used for simulations of river plume dynamics allowing fine grid resolution in the river and in regions near the coast with a coarse grid in the far field of the river plume in the coastal ocean. In the vertical, fine fixed levels were used near the free surface, and coarse vertical levels were used over the continental shelf. Without Coriolis acceleration, no trapped river plume can be formed no matter how favorable the ambient conditions might be. The simulation results show properties of the river plume and the characteristics of flow and salinity within the estuary; they are completely consistent with the physics of estuaries and coastal oceans.

During the summer of 2000, a bistatic UHF radar - the RiverSonde - was designed, built, and tested on rivers and canals in the Central Valley of California. The transmitter and receiver were on opposite banks. They simultaneously transmit to and receive from elliptical time-delay cells that span the river, with the transmit and receive antennas as their focal points. With 30 MHz bandwidth, the cell span up/down-river is /spl sim/10 m. A three-element receive array employs the direction finding music algorithm to determine echo bearing. Velocity along the river channel is measured vs position across the river from the first-order Bragg-echo Doppler shifts. Radiating less than 1 w power, received surface-echo signal-to-noise ratios of 40 dB were received, both across narrow canals and across the American River that was 80 meters wide. Our tests and analyses were sponsored by and conducted along with the U.S. Geological Survey in Menlo Park, CA. "Surface truth" velocity profiles were established by current meters suspended from a boat, from a bridge, and from timing the drifts of tennis balls between two transverse cuts. RMS velocity differences between 6%-13% of the typical average flow velocity were observed. The rms differences between the three "surface truth" measurements themselves also fell within the same span. From the velocity profiles across the river, estimates of total volume flow for the four methods were calculated based on a knowledge of the bottom depth vs position across the river. The flow comparisons for the American River were much closer, within 2% of each other among all of the methods. Sources of positional biases and anomalies in the RiverSonde measurement patterns along the river are identified and discussed.

Results of field tests of a RiverSonde streamflow radar are compared with in-situ current measurements at a canal and a river in central California during June, 2000. Typical water velocity in the middle of the canal was about 0.45 m s/sup -1/ and 0.30 ms/sup -1/ at the edges. Velocity in the river was about 20% lower with similar cross-channel variation. Differences between the RiverSonde and in-situ velocities were 6-18% of the mean flow, with similar differences among the various in-situ velocities. In addition to the surface velocities, the total volume flow was estimated based on the in-situ depth measurements. Volume flow for the canal was about 37 m/sup 3/ s/sup -1/ and for the river was about 64 m/sup 3/ s/sup -1/, with differences between the various radar and in-situ techniques of less than 10%.

A family of numerical models, known as the TRIM models, shares the same modeling philosophy for solving the shallow water equations. A characteristic analysis of the shallow water equations points out that the numerical instability is controlled by the gravity wave terms in the momentum equations and by the transport terms in the continuity equation. A semiimplicit finite-difference scheme has been formulated so that these terms and the vertical diffusion terms are treated implicitly and the remaining terms explicitly to control the numerical stability and the computations are carried out over a uniform finite-difference computational mesh without invoking horizontal or vertical coordinate transformations. An unstructured grid version of TRIM model is introduced, or UnTRIM (pronounces as “you trim”), which preserves these basic numerical properties and modeling philosophy, only the computations are carried out over an unstructured orthogonal grid. The unstructured grid offers the flexibilities in representing complex study areas so that fine grid resolution can be placed in regions of interest, and coarse grids are used to cover the remaining domain. Thus, the computational efforts are concentrated in areas of importance, and an overall computational saving can be achieved because the total number of grid-points is dramatically reduced. To use this modeling approach, an unstructured grid mesh must be generated to properly reflect the properties of the domain of the investigation. The new modeling flexibility in grid structure is accompanied by new challenges associated with issues of grid generation. To take full advantage of this new model flexibility, the model grid generation should be guided by insights into the physics of the problems; and the insights needed may require a higher degree of modeling skill.

The U.S. Geological Survey (USGS) operates a network of about 7,000 streamflow-gaging stations that monitor open-channel water discharge at locations throughout the United States. The expense, technical difficulties, and concern for the safety of operational personnel under some field conditions have led to the search for alternate measurement methods. Ground- penetrating radar (GPR) has been used by the USGS in hydrologic, geologic, environmental, and bridge-scour studies by floating antennas on water or mounting antennas in boats. GPR methods were developed to measure and monitor remotely the cross-sectional area of rivers by suspending a 100-megahertz (MHz) radar antenna from a cableway car or bridge at four unstable streams that drained the slopes of Mount St. Helens in Washington. Based on the success of these initial efforts, an experiment was conducted in 1999 to see if a combination of complementary radar methods could be used to calculate the discharge of a river without having any of the measuring equipment in the water. The cross-sectional area of the 183- meter (m) wide Skagit River in Washington State was measured using a GPR system with a single 100-MHz antenna suspended 0.5 to 3 m above the water surface from a cableway car. A van- mounted, side-looking pulsed-Doppler (10 gigahertz) radar system was used to collect water-surface velocity data across the same section of the river. The combined radar data sets were used to calculate the river discharge and the results compared closely to the discharge measurement made by using the standard in-water measurement techniques. The depth to the river bottom, which was determined from the GPR data by using a radar velocity of 0.04 meters per nanosecond in water, was about 3 m, which was within 0.25 m of the manually measured values.

Estuaries, bays and contiguous coastal seas are the world's most valuable, and yet most vulnerable marine ecosystems. Fundamental to the protection and management of these important resources is an understanding of the physical processes involved which affect the circulation, mixing and transport of salt, nutrients and sediment. This book explores the processes that appear to have direct control over freshwater inflows, contaminant loadings, dispersion and transport of sediments and nutrients, and causes of declining living resources. It provides a comprehensive summary of the research results on these processes in estuaries and bays. Contributions include results based on theoretical formulations, analyses of field data, numerical models and case studies.

[1] The United States Geological Survey and the University of Washington collaborated on a series of initial experiments on the Lewis, Toutle, and Cowlitz Rivers during September 2000 and a detailed experiment on the Cowlitz River during May 2001 to determine the feasibility of using helicopter-mounted radar to measure river discharge. Surface velocities were measured using a pulsed Doppler radar, and river depth was measured using ground-penetrating radar. Surface velocities were converted to mean velocities, and horizontal registration of both velocity and depth measurements enabled the calculation of river discharge. The magnitude of the uncertainty in velocity and depth indicate that the method error is in the range of 5 percent. The results of this experiment indicate that helicopter-mounted radar can make the rapid, accurate discharge measurements that are needed in remote locations and during regional floods.

A finite element model which uses triangular, isoparametric elements with quadratic basis functions for the two velocity components and linear basis functions for water surface elevation is used in the computation of shallow water wave motions. Specifically addressed are two common uncertainties in this class of two-dimensional hydrodynamic models: the treatment of the boundary conditions at open boundaries and the treatment of lateral boundary conditions. The accuracy of the models is tested with a set of numerical experiments in rectangular and curvilinear channels with constant and variable depth. The results indicate that errors in velocity at the open boundary can be significant when boundary conditions for water surface elevation are specified. Methods are suggested for minimizing these errors. The results also show that continuity is better maintained within the spatial domain of interest when ‘smooth’ curve-sided elements are used at shoreline boundaries than when piecewise linear boundaries are used. Finally, a method for network development is described which is based upon a continuity criterion to gauge accuracy. A finite element network for San Francisco Bay, California, is used as an example.

The Lagrangian residual circulation has often been introduced as the sum of the Eulerian residual circulation and the Stokes' drift. Unfortunately, this definition of the Lagrangian residual circulation is conceptually incorrect because both the Eulerian residual circulation and the Stokes' drift are Eulerian variables. In this paper a classification of various residual variables are reviewed and properly defined. The Lagrangian residual circulation is then studied by means of a two-stage formulation of a computer model. The tidal circulation is first computed in a conventional Eulerian way, and then the Lagrangian residual circulation is determined by a method patterned after the method of markers and cells. To demonstrate properties of the Lagrangian residual circulation, application of this approach in South San Francisco Bay, California, is considered. With the aid of the model results, properties of the Eulerian and Lagrangian residual circulation are examined. It can be concluded that estimation of the Lagrangian residual circulation from Eulerian data may lead to unacceptable error, particularly in a tidal estuary where the tidal excursion is of the same order of magnitude as the length scale of the basin. A direction calculation of the Lagrangian residual circulation must be made and has been shown to be feasible.

Availability of extensive field data permitted realistic calibration and validation of a hydrodynamic model of tidal circulation and salt transport for Suisun Bay, California. Suisun Bay is a partially mixed embayment of northern San Francisco Bay located just seaward of the Sacramento-San Joaquin Delta. The model employs a variant of an alternating direction implicit finite-difference method to solve the hydrodynamic equations and an Eulerian-Lagrangian method to solve the salt transport equation. An upwind formulation of the advective acceleration terms of the momentum equations was employed to avoid oscillations in the tidally averaged velocity field produced by central spatial differencing of these terms. Simulation results of tidal circulation and salt transport demonstrate that tides and the complex bathymetry determine the patterns of tidal velocities and that net changes in the salinity distribution over a few tidal cycles are small despite large changes during each tidal cycle. Computations of tidally averaged circulation suggest that baroclinic and wind effects are important influences on tidally averaged circulation during low freshwater-inflow conditions. Exclusion of baroclinic effects would lead to overestimation of freshwater inflow by several hundred m3/s for a fixed set of model boundary conditions. Likewise, exclusion of wind would cause an underestimation of flux rates between shoals and channels by 70–100%.

A mixed analytical and numerical model to study the wind-driven, transient, three-dimensional circulation in lakes is presented. Emphasis is placed on the formulation and development of the model, which consists of a formal analytical solution together with a system of depth-averaged conservation equations. After solving the depth-averaged system numerically by the finite element technique, the three-dimensional velocity profiles are calculated from the formal solution. Simulation of an idealized lake shows good agreement on the general circulation pattern and wave characteristics with the works of others. The limitation of this model is examined, and a solution is proposed to accommodate it.

The state-of-the-art of numerical modelling of large-scale wind-driven circulation in lakes is presented. The governing equations which describe this motion are discussed along with the appropriate numerical techniques necessary to solve them in lakes. The numerical models are categorized into three large primary groups: the layered models, the Ekman-type models, and the other three-dimensional models. Discussions and comparison of models are given and future research directions are suggested.

A pseudo-two-dimensional model is developed to simulate population dynamics of one dominant phytoplankton species (Skeletonema costatum) in northern San Francisco Bay. The model is formulated around a conceptualization of this estuary as two distinct but coupled subsystems—a deep (10–20 m) central channel and lateral areas with shallow ( Model output is consistent with the hypothesis that, because planktonic algae are light-limited, shallow areas are the sites of active population growth. Seasonal variation in the location of the null zone (a response to variable river discharge) is responsible for maintaining the spring bloom of neritic diatoms in the seaward reaches of the estuary (San Pablo Bay) and the summer bloom upstream (Suisun Bay). Model output suggests that these spring and summer blooms result from the same general process—establishment of populations over the shoals, where growth rates are rapid, coupled with reduced particulate transport due to estuarine gravitational circulation. It also suggests, however, that the relative importance of physical and biological processes to phytoplankton dynamics is different in San Pablo and Suisun Bays. Finally, the model has helped us determine those processes having sufficient importance to merit further refinement in the next generation of models, and it has given new direction to field studies.

Water level observations from tide stations and current observations from current-meter moorings in South San Francisco Bay (South Bay), California have been harmonically analysed. At each tide station, 13 harmonic constituents have been computed by a least-squares regression without inference. Tides in South Bay are typically mixed; there is a phase lag of approximately 1 h and an amplification of 1·5 from north to south for a mean semi-diurnal tide. Because most of the current-meter records are between 14 and 29 days, only the five most important harmonics have been solved for east-west and north-south velocity components. The eccentricity of tidal-current ellipse is generally very small, which indicates that the tidal current in South Bay is strongly bidirectional. The analyses further show that the principal direction and the magnitude of tidal current are well correlated with the basin bathymetry. Patterns of Eulerian residual circulation deduced from the current-meter data show an anticlockwise gyre to the west and a clockwise gyre to the east of the main channel in the summer months due to the prevailing westerly wind. Opposite trends have been observed during winter when the wind was variable.

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.

Residual currents in tidal estuaries and coastal embayments have been recognized as fundamental factors which affect the long-term transport processes. It has been pointed out by previous studies that it is more relevant to use a Lagrangian mean velocity than an Eulerian mean velocity to determine the movements of water masses. Under weakly nonlinear approximation, the parameter k, which is the ratio of the net displacement of a labeled water mass in one tidal cycle to the tidal excursion, is assumed to be small. Solutions for tides, tidal current, and residual current have been considered for two-dimensional, barotropic estuaries and coastal seas. Particular attention has been paid to the distinction between the Lagrangian and Eulerian residual currents. When k is small, the first-order Lagrangian residual is shown to be the sum of the Eulerian residual current and the Stokes drift. The Lagrangian residual drift velocity or the second-order Lagrangian residual current has been shown to be dependent on the phase of tidal current. The Lagrangian drift velocity is induced by nonlinear interactions between tides, tidal currents, and the first-order residual currents, and it takes the form of an ellipse on a hodograph plane. Several examples are given to further demonstrate the unique properties of the Lagrangian residual current.

The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system. The values of the dependent variable off the grid are calculated by interpolation. When a linear interpolation is used, the method is a slight improvement over the upwind difference method. At this level of approximation both the ELM and the upwind difference method suffer from large numerical dispersion. However, if second-order Lagrangian polynomials are used in the interpolation, the ELM is proven to be free of artificial numerical dispersion for the convection-dispersion equation. The concept of the ELM is extended for treatment of anisotropic dispersion in natural coordinates. In this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field. Several numerical examples are given to further substantiate the results of the present analysis.