Optimal Wasteload Allocation Procedure for Achieving Dissolved Oxygen Water Quality Objectives. II: Optimal Load Control

This paper presents the development of an efficient strategy for achieving in-stream dissolved oxygen (DO) water quality standards (WQSs) via optimized point-load control strategies using the adjoint method. To this end, a least-squares-type objective function is formulated that measures the difference between desired (WQSs) and current DO concentrations at strategically selected monitoring points in the domain. The goal is to minimize the difference between actual DO concentration and the WQS, hence allowing time-variant loadings to utilize the assimilative capacity of the receiving water body at an optimal level. Time-variant discharge rates for a number of discharge locations are considered as control parameters, while different zone-specific critical DO levels are imposed as constraints. The selection of the control is kept flexible and a number of different scenarios are tested. First, only carbonaceous biochemical oxygen demand is used, which allows for a reduction of the number of equations that need to be solved. In the other tests, all constituents are switched on and different variables at each load node are selected as a control by first varying the concentrations individually, and then linking them through control of the volumetric flow rate. Optimization is achieved using a conjugate gradient search method, for which the gradients are computed through the solution of both the direct and adjoint problems. It is shown that the large amount of gradient information (parameter space has a dimension of several thousands) can be computed very efficiently using the adjoint, and that optimized results are achieved after only a few iterations irrespective of the initial guess. Computations are carried out using both two-dimensional model formulation applied to a long rectangular channel with varying width and slope and a model for the upper Potomac River estuary.     

Spatial-Dynamic Modeling of Algal Biomass in Lake Erie: Relative Impacts of Dreissenid Mussels and Nutrient Loads

Over the past several decades, reductions in phytoplankton stocks and increased water clarity in Lake Erie have resulted from phosphorus load abatement and the introduction of zebra (Dreissena polymorpha) and quagga mussels (D. bugensis). The relative impacts of these developments and their implications for lake management have remained difficult to delineate. To address this issue, we numerically model the complex biophysical interactions occurring in Lake Erie using a two-dimensional hydrodynamic and water quality model that is extended to include dreissenid mussel and zooplankton algorithms. The model reasonably simulates longitudinal trends in water quality as well as the dynamics of central basin hypoxia. Phosphorus is the limiting nutrient through the euphotic zone and its control decreases the algal growth rate and biomass ( ～ 55–60%). Filter feeding by dreissenid mussels also decreases algal biomass ( ～ 25–30%), simultaneously stimulating increased net algae growth through enhanced algal consumption and subsequent phosphorus recycling. Effective recycling implies that algae stocks are ultimately regulated by external phosphorus loads. Returning phosphorus loads to pre-abatement 1960s levels, in the presence of dreissenid mussels, results in a western basin algae concentration of ～ 0.7?mg?dry?weight?L?1 with a potential for nuisance algae growth.     

Eutrophication and Pathogen Abatement in the San Juan Bay Estuary

The San Juan Bay Estuary is a tropical lagoon system severely impacted by eutrophication and by elevated pathogen concentrations. This investigation examined alternatives for pollution abatement primarily through physical modifications to the system. The investigation included field surveys, computation of pollutant loads, and application of hydrodynamic and eutrophication models. A eutrophication model developed for temperate estuaries was successfully transferred to San Juan Bay Estuary. Results indicate two primary modifications reduce eutrophication. The first clears a constricted channel to the interior of the system and promotes flushing. The second fills deep holes in which anoxic conditions promote sediment nutrient release to the water column. Major reductions in pathogen concentration require regional controls on sources.     

Dissolved Oxygen Demand at the Sediment-Water Interface of a Stream: Near-Bed Turbulence and Pore Water Flow Effects

A microbial dissolved oxygen (DO) uptake model was developed for a stream bed, including the effect of turbulence in the flow over the bed and pore water flow in the porous bed. The fine-grained sediment bed has hydraulic conductivities 0.01 ≤ k ≤ 1??cm/s, i.e., sediment particle diameter 0.006 ≤ ds ≤ 0.06??cm. The pore water flow is driven by pressure fluctuations at the sediment-water interface, mostly attributable to near-bed coherent motions in the turbulent boundary layer above the sediment bed. An effective mass transfer coefficient (De) coupled to a pore water flow model was used in the DO transport and DO uptake model. DO flux across the sediment-water interface and into the sediment, i.e., sedimentary oxygen demand (SOD), was related to hydraulic conductivity and microbial oxygen uptake rate in the sediment and shear velocity at the sediment-water interface. Simulated SOD values were validated against experimental data. For hydraulic conductivities of the sediment bed up to k ≈ 0.01??cm/s, the pore water flow effect on SOD was found negligible. Above this threshold, the effective mass (DO) transfer coefficient in the sediment bed (De) becomes larger as the hydraulic conductivity (k) becomes larger as the interstitial flow velocities increase; consequently, DO penetration depth increases with larger hydraulic conductivity of the sediment bed (k), and SOD increases as well. The enhancement of vertical DO transport into the sediment bed is strongest near the sediment-water interface, and rapidly diminishes with depth into the sediment layer. An increase in shear velocity at the sediment-water interface also enhances DO transfer. Shear velocity increases at the sediment-water interface will raise SOD regardless of the maximum oxidation rate if the hydraulic conductivity is above the threshold of k ≈ 1??cm/s. The relationship is nearly linear when U*<0.8??cm/s. At shear velocity U* = 1.6??cm/s, SOD for oxidation rates μ = 1000 and 2000??mg?l-1?d-1 are almost five times larger than those with no pore water flow. When pore water transport of DO is not limiting, SOD is a linear function of oxygen demand rate μ in the sediment when 0 ≤ μ ≤ 200??mg?l-1?d-1.     

Parameter Sensitivity and Predictive Uncertainty in a New Water Quality Model, Q2

A new dynamic model of water quality, Q2, has recently been developed, capable of simulating large branched river systems. This paper describes the application of a generalized sensitivity analysis (GSA) to Q2 for single reaches of the River Thames in southern England. Focusing on the simulation of dissolved oxygen (DO) (since this may be regarded as a proxy for the overall health of a river); the GSA is used to identify key parameters controlling model behavior and provide a probabilistic procedure for model calibration. It is shown that, in the River Thames at least, it is more important to obtain high quality forcing functions than to obtain improved parameter estimates once approximate values have been estimated. Furthermore, there is a need to ensure reasonable simulation of a range of water quality determinands, since a focus only on DO increases predictive uncertainty in the DO simulations. The Q2 model has been applied here to the River Thames, but it has a broad utility for evaluating other systems in Europe and around the world.     

Cost-Effective Approach for Continuous Major Ion and Nutrient Concentration Estimation in a River

Major ion and nutrient concentration monitoring and estimation are important factors in management and interpretations on river health, particularly in the context of total maximum daily load limits. Spatial and temporal (daily, seasonally, yearly, etc.) variations commonly complicate investigations and can produce unrepresentative results, particularly in systems with large seasonal or daily variation in river parameters or concentrations as a result of physical loading or biogeochemical activity (e.g., photosynthesis and respiration). This study combines an observed relationship between electrical conductivity and major ions, including nitrate, and continuous colorimetric estimation of ammonium and phosphate to permit cost-effective real-time estimation of river concentrations for major ions and nutrients for surface water quality monitoring. Data collected from sites both up- and downstream of a major city were used to evaluate the method. Constant total dissolved solids (TDS) to electrical conductivity (EC) relationships were observed at both the upgradient (TDS = 696EC; r2 = 0.93) and downgradient (TDS = 684EC; r2 = 0.90) sites. The resulting predicted estimations of major ion and nutrient concentrations for each site had average errors of less than 5%. Combining this method with a modified continuous colorimetric method for ammonia and phosphate allows for the continuous estimation of major ion and nutrient concentrations in a river system.     

Robotic Monitoring to Assess Impacts of Zebra Mussels and Assimilative Capacity for a River

Water quality impacts of zebra mussel metabolism over an infested 15?km reach of the Seneca River, N.Y., are documented, based on vertically and temporally detailed robotic monitoring at the reach boundaries during the summer through early fall intervals of 2?years. Substantial reductions over the study reach are documented for dissolved oxygen (DO), pH, fluorometric chlorophyll a, and turbidity, associated with the metabolism of this invader. Violations of New York State water quality standards for DO that would not be resolved by traditional manual monitoring programs were observed. The loss of assimilative capacity caused by the zebra mussel invasion is confounding rehabilitation efforts for a downstream polluted lake that had considered diversion of municipal effluent to the river. The critical role robotic monitoring units would play in an automated control system for an innovative strategy of time-variable river discharge of the effluent is described. Near-real time robotic monitoring provides a more detailed understanding of the impacts of zebra mussels on water quality than traditional less intensive manual measurements.     

Incremental Improvements in Chesapeake Bay Environmental Model Package

The performance of the Chesapeake Bay Environmental Model Package is examined in four steps of model development. The steps include initial application, grid refinements, addition of living resources, and grid refinements with recalibration. Performance statistics are presented for the mainstem bay and for the James River, a major tributary. Computed salinity has the lowest relative error. Computed total phosphorus and surface chlorophyll have the greatest relative error. Errors in the bay are lower than in the James River. The capacity of the model has increased substantially over more than a decade but quantitative performance, measured by the summary statistics, has reached a plateau. Limited spatial sampling, uncertainty in loading, and difficulty in assigning boundary conditions are among the factors that limit the accuracy that can be attained with the model.     

Jackson River Modeling: 50‐Year Perspective

The development of water quality models, and also the nature of water quality impairment, is uniquely presented in the point source dissolved oxygen (DO) modeling completed in the Jackson River (Virginia) over the past 50?years. Various water quality modeling studies have been completed in the Jackson River over the years starting with the earliest of modeling frameworks, the Streeter–Phelps equation (1950s and 1960s); progressing to a biochemical oxygen demand–DO model (1970s and 1990s) including diurnal photosynthetic effects (DIURNAL); a Monte Carlo DO analysis using the DIURNAL model (1990s); to the most recent modeling that is currently developing a periphyton model to assess the impact of nutrient loadings on the periphyton community and ultimately DO levels (2000). These early modeling studies were completed by such modeling forefathers as Clarence J. Velz and Donald J. O'Connor, both completing their work at academic institutions (Manhattan College and the University of Michigan) and private consulting firms (Hydroscience and HydroQual, Inc.). Interesting to note is that Earle B. Phelps taught Clarence J. Velz, Donald J. O’Connor’s eventual professor at Manhattan College. Other work completed on the river by early environmental engineers included reaeration studies by Ernest C. Tsivoglou (1966) and the first activated sludge wastewater treatment design for a pulp and paper mill by Wesley Eckenfelder (1950s). The studies investigated: how to improve existing DO conditions in the river; the effects of color reductions on diurnal DO swings; proposed upstream flow regulation effects on water quality and river temperature; and the impact of instream oxygen addition.     

Optimal Wasteload Allocation Procedure for Achieving Dissolved Oxygen Water Quality Objectives. I: Sensitivity Analysis

A method is presented to compute sensitivities of in-stream dissolved oxygen (DO) with respect to perturbations in the load vector and the reaction coefficients that make up the eutrophication cycle. It is shown that the direct sensitivity method, i.e., the repetitive solution of the direct problem, produces the desired information, however at a large computational cost. The utilization of the adjoint sensitivity method proves to be a much more efficient way to compute these sensitivities as large subsets of the sensitivity information domain can be easily extracted with just a few runs. It is found that for the given problem setup, in-stream DO is most sensitive to ammonia, effluent DO, algae, and carbonaceous biochemical oxygen demand (CBOD) loads. Additionally, the computed sensitivities vary considerably in their general trend over the simulation time. Sensitivities also are computed with respect to the reaction coefficients (26 total) that govern the interdependency of all constituents. Sediment oxygen demand proves to be the coefficient with the highest influence that is three orders of magnitude higher than the next set of coefficients comprised of reaeration, CBOD degradation, nitrification, and denitrification. All other coefficients have a negligible influence on DO concentrations. Computations are carried out using a two-dimensional model formulation applied to a long rectangular channel with varying width and slope and periodic but unsteady flow conditions.     

Comparison of Nutrient Limitation in Freshwater and Estuarine Reservoirs in Tropical Urban Singapore

Nutrient limitation was examined for two contrasting tropical reservoirs in Singapore: the semiurban, freshwater Kranji Reservoir and the highly urbanized, estuarine Marina Reservoir. Nutrient enrichment experiments in the laboratory showed that the Kranji Reservoir was phosphorus limited, whereas the Marina Reservoir was nitrogen limited. This was supported by field measurements of nitrogen (N) to phosphorus (P) ratios that showed average values of 16 and 8.3 for the Kranji Reservoir and Marina Reservoir, respectively. In addition to nutrient concentrations, total suspended solids measurements (TSS) showed high levels of turbidity in the Marina Reservoir (average TSS = 74.2??mg/L) compared to the Kranji Reservoir (average TSS = 3.9??mg/L). Thus, light could also be a significant limiting factor for algal growth in the Marina Reservoir. To estimate whether the estuarine system was a source or sink for nutrients, budget models were used to determine fluxes of nitrogen, phosphorus, and carbon. The calculations showed that there was a net loss of nitrogen from the estuarine Marina Reservoir through denitrification and a net loss of carbon. Phosphorus, in contrast, was estimated to be released from the sediments. These results support the earlier findings that the Marina Reservoir is currently nitrogen-limited. The next logical step is to trace the main sources of nutrients into the reservoirs and to deal with nutrient load reduction, bearing in mind that one reservoir is phosphorus limited and the other is nitrogen limited. The implication is that different remediation methods may need to be employed to tackle the eutrophication problems in the two contrasting reservoirs.     

Dissolved Oxygen and pH Modeling of a Periphyton Dominated, Nutrient Enriched River

Nutrient enrichment of the South Umpqua River, Oregon was linked to periphyton growth and large diel fluctuations in dissolved oxygen and hydrogen ion (pH) concentrations using the water quality model QUAL2Kw. The available data provide a good case study for the relatively new water quality model. QUAL2Kw simulates a dynamic diel heat budget and water quality kinetics for a one-dimensional, steady-flow system and is part of a family of models meant to serve as an update to the widely used QUAL2E. The model was used to quantify nonpoint source loading, determine the pollutant of concern, estimate natural conditions, and calculate a phosphorus total maximum daily load during summer, low-flow conditions. Control of both nonpoint and point sources is required to achieve the low instream phosphorus concentrations necessary to meet water quality criteria. To our knowledge, this is the first paper that reports on the application of a model for computing the maximum allowable load necessary to manage the diel variation in pH.     

High-Frequency Diel Dissolved Oxygen Stream Data Modeled for Variable Temperature and Scale

Diel dissolved oxygen (DO) concentrations and temperature were sensed at high-frequency and modeled in an eastern Iowan stream, Clear Creek, in an agricultural setting. The magnitude of the diel changes in DO and temperature were largest at the upstream (headwater) station. Inclusion of temperature change factors increased the accuracy of modeling results and yielded estimates of the reaeration rate constant, primary production rate, and respiration rate. The DO modeling of the high-frequency measurements (15-min intervals) revealed a temperature-driven nonlinear reaeration process that led to increases in nighttime DO concentrations. The DO modeling results from three sensing stations in the watershed revealed decreasing trends in primary productivity, respiration, and the reaeration rate constant with increasing drainage area. Light extinction from suspended solids was the main factor limiting net primary production. As a result, the P/R ratio also decreased with increasing drainage area. High-frequency sensor data and DO modeling revealed the effects of temperature and watershed scale on the primary factors that dictate diel DO dynamics in a stream setting.     

Comparison of the Monod and Droop Methods for Dynamic Water Quality Simulations

The Monod method is widely used to model nutrient limitation and primary productivity in water bodies. It offers a straightforward approach to simulate the main processes governing eutrophication and it allows the proper representation of many aquatic systems. The Monod method is not able to represent the nutrient luxury uptake by algae, which consists of the excess nutrient uptake during times of high nutrient availability in the water column. The Droop method, which is also used to model nutrient limitation and primary productivity, takes into account the luxury uptake of nutrients. Because of the relative complexity of the Droop method, it has not been systematically adopted for the simulation of large stream networks. The Water Quality Analysis Simulation Program (WASP) version 7.1 was updated to include nutrient luxury uptake for periphyton growth. The objective of this paper is to present the new nutrient limitation processes simulated by WASP 7.1 and to compare the performance of the Droop and the Monod methods for a complex stream network where periphyton is the main organism responsible for primary productivity. Two applications of WASP 7.1 with the Droop and Monod methods were developed for the Raritan River Basin in New Jersey. Water quality parameters affecting the transport and fate of nutrients were calibrated based on observed data collected for the Raritan River total maximum daily load. The dissolved oxygen and nutrients simulated with WASP 7.1, obtained with the Droop and Monod methods, were compared at selected monitoring stations under different flows and nutrient availability conditions. The comparison of the WASP 7.1 applications showed the importance of using the Droop method when periphyton was the main organism responsible for primary productivity. The data simulated with the Droop method resulted in good agreement with the observed data for dissolved oxygen, ammonia-nitrogen, nitrate-nitrogen, and dissolved orthophosphate at the selected stations. The Monod method was not able to capture the diel dissolved oxygen variation when nutrients were scarce, and it resulted in unrealistic diel variations of nutrients at times of strong primary productivity at some locations.     

Sediment Oxygen Demand and Nutrient Fluxes for a Tropical Reservoir in Singapore

Sediment oxygen demand (SOD) and nutrient flux studies were conducted for a tropical reservoir in Singapore in order to determine the approximate SOD and nutrient release rates from the sediments. SOD values obtained from laboratory experiments ranged from 1.4 to 3.3?g?O2/m2-day. Similar results were also obtained by calculating SOD values from in situ DO measurements taken in the field. The nutrient flux study was performed in the laboratory at a constant temperature of 25°C in oxic and anoxic columns. Except for nitrate+nitrite, higher nutrient release rates were generally observed under anoxic conditions. The ammonium release rate was 0.06?g?O2/m2-day under oxic conditions and 0.117?g?O2/m2-day under anoxic conditions. The nitrate flux rate was 0.17?g?O2/m2-day under oxic conditions but was negligible under anoxic conditions. Orthophosphate flux results were negative throughout the oxic incubation implying that sediments acted as a sink. The release rate of orthophosphate was 0.007?6?g?O2/m2-day under anoxic conditions.     

Velocity Pulse Model for Turbulent Diffusion from Flowing Water into a Sediment Bed

The “velocity pulse model” simulates the transfer of turbulence from flowing water into a sediment bed, and its effect on the diffusional mass transfer of a solute (e.g., oxygen, sulfate, or nitrate) in the sediment bed. In the “pulse model,” turbulence above the sediment surface is described by sinusoidal variations of vertical velocity in time. It is shown that vertical velocity components dampen quickly inside the sediment when the frequency of velocity fluctuations is high and viscous dissipation is strong. Viscous dissipation (ν) inside the sediment is related to the apparent viscosity depending on the structure of the sediment pore space, i.e., the porosity and grain diameter, as well as inertial effects when the flow is turbulent. A value ν/ν0 between 1 and 20 (ν0 is kinematic viscosity of water) has been considered. Turbulence penetration into the sediment is parametrized by the Reynolds number Re = UL/ν and the relative penetration velocity W/U, where U=amplitude of the velocity pulse; and W=penetration velocity; L = WT=wave length of the velocity pulse; and T is its period. Amplitudes of vertical velocity components inside the sediment and their autocorrelation functions are computed, and the results are used to estimate eddy viscosity inside the sediment pore system as a function of depth. Diffusivity in the sediment pore system is inferred by using turbulent or molecular Schmidt numbers. Turbulence penetration from flowing water can enhance the vertical diffusion coefficient in a sediment bed by an order of magnitude or more. Penetration depth of turbulence is higher for low frequency velocity pulses. Vertical diffusivity inside the pore system is shown to decrease more or less exponentially with depth below the sediment/water interface. Vertical diffusivities in a sediment bed estimated by the “velocity pulse model” can be used in pore water quality models to describe vertical transport from or into flowing surface water. The analysis has been conducted for a conservative material, but source and sink terms can be added to the vertical transport equation.     

Integrated Hydrodynamic and Water Quality Modeling System to Support Nutrient Total Maximum Daily Load Development for Wissahickon Creek, Pennsylvania

This paper presents a hydrodynamic and water quality modeling system for Wissahickon Creek, Pa. Past data show that high nutrient levels in Wissahickon Creek were linked to large diurnal fluctuations in oxygen concentration, which combining with the deoxygenation effect of carbonaceous biological oxygen demand (CBOD) causes violations of dissolved oxygen (DO) standards. To obtain quantitative knowledge about the cause of the DO impairment, an integrated modeling system was developed based on a linked environmental fluid dynamics code (EFDC) and water quality simulation program for eutrophication (WASP/EUTRO5) modeling framework. The EFDC was used to simulate hydrodynamic and temperature in the stream, and the resulting flow information were incorporated into the WASP/EUTRO5 to simulate the fate and transport of nutrients, CBOD, algae, and DO. The standard WASP/EUTRO5 model was enhanced to include a periphyton dynamics module and a diurnal DO simulation module to better represent the prototype. The integrated modeling framework was applied to simulate the creek for a low flow period when monitoring data are available, and the results indicate that the model is a reasonable numerical representation of the prototype.     

Upland Erosion Modeling in a Semihumid Environment via the Water Erosion Prediction Project Model

The major water quality impairment in the midwest United States is sediment eroded from agricultural lands. Yet, few understand the spatial and temporal variability of erosion, or soil erosion dynamics, in relation to precipitation, topography, land management, and severe events. The objectives of this paper are to (1) develop a methodology for estimating long-term spatial soil erosion and water runoff losses and (2) explore issues in applying an established physical-based process model, Water Erosion Prediction Project (WEPP), to a large area by establishing a prototype system for the state of Iowa. This study for the first time provides a comparison of the model predictions against long-term measurements of the sediment delivery ratio (SDR) in the South Amana Catchment of the Clear Creek Watershed (CCW), a heavily instrumented watershed that is roughly 10 times the maximum WEPP fold size. To further examine the performance of WEPP in a semihumid environment, such as the CCW, where runoff and raindrop impact to erosion may be significant, the SDR was plotted as a function of the runoff coefficient, defined as the runoff/rainfall ratio. In addition, the WEPP predictions are compared against the statistical relation of SDR vs. runoff coefficient developed by Piest et al. in 1975) for watersheds in Iowa. It is shown that WEPP follows the trend shown by Piest et al. quite closely and performs well for continuous simulations extended up to 300?years.     

Case Study: Particle Velocimetry in a Model of Lake Ogallala

In a case study of Lake Ogallala, a reservoir in central Nebraska, large scale particle tracking velocimetry (LSPTV) is used to measure surface velocities in a physical model of the lake. Knowledge of flow patterns in the lake is essential for predicting the transport of dissolved oxygen (DO). A preliminary comparison with acoustic Doppler velocimetery (ADV) measurements shows that both LSPTV and large scale particle image velocimetry (LSPIV) accurately measure surface velocities. In the present study, LSPTV works better near flow boundaries and in regions with high velocity gradients since smaller sampling areas are possible, and unlike LSPIV measurements, LSPTV measurements are unbiased. Discharges measured at eight different transects using LSPTV were within 6% of the discharge measured with an orifice, the worst correlation occurring where the bathymetry was slightly nonuniform (making application of the 1/7-power law suspect). In the prototype, DO content periodically drops to unacceptable levels throughout most of the Keystone Basin (a subbasin of Lake Ogallala). Predicted flow patterns suggest that low DO problems are exacerbated in regions with low velocities since oxygen consumed by macrophytes during nighttime hours is not quickly replenished.     

Evaluation of the Micromodel: An Extremely Small-Scale Movable Bed Model

The micromodel is an extremely small physical river model having a movable bed, varying discharge, and numerous innovations to achieve quick answers to river engineering problems. In addition to its size being as small as 4?cm in channel width, the vertical scale distortion up to 20, Froude number exaggeration up to 3.7, and no correspondence of stage in model and prototype, place the micromodel in a category by itself. The writer was assigned to evaluate the micromodel’s capabilities and limitations to ensure proper application. A portion of this evaluation documents the deviation of the micromodel from similarity considerations used in previous movable bed models. The primary basis for this evaluation is the comparison of the micromodel to the prototype. The writer looked for comparisons that had (1) a reasonable calibration of the micromodel and (2) about the same river engineering structures constructed in the prototype that were tested in the micromodel and (3) a prediction by the micromodel of the approximate trends in the prototype. Evaluation of these comparisons shows a lack of predictive capability by the micromodel. Differences in micromodel and prototype likely result from uncertainty in prototype data and the large relaxations in similitude. Based on the lack of predictive evidence, the micromodel should be limited to demonstration, education, and communication for which it has been useful and should be of value to the profession.