Ralph T. Cheng

measuring stream discharge by non‐contact methods: A Proof‐of‐Concept Experiment

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.

Estimates of bottom roughness length and bottom shear stress in South San Francisco Bay, California

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 <25–30 cm s−1, the correlation between zo and the reference velocity is less clear. A plausible explanation of scattered values of zo under this condition may be sediment deposition. Measured sediment data were inadequate to support this hypothesis, but the proposed hypothesis warrants further field investigation.

Numerical models of wind-driven circulation in lakes

Abstract 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.

Harmonic analysis of tides and tidal currents in South San Francisco Bay, California

Abstract 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.

Simulation model of Skeletonema costatum population dynamics in northern San Francisco Bay, California

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.

Evaluation of the UnTRIM model for 3-D tidal circulation

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.

Ground penetrating radar methods used in surface-water discharge measurements

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.

Canal and river tests of a RiverSonde streamflow measurement system

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%.

Stability analysis of Eulerian-Lagrangian methods for the one-dimensional shallow-water equations

Abstract 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.

Modeling a Three-Dimensional River Plume over Continental Shelf Using a 3D Unstructured Grid Model

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.