Automatic sensitivity analysis of a finite volume model for two-dimensional shallow water flows

Given a numerical model for solving two-dimensional shallow water equations, we are interested in the robustness of the simulation by identifying the rate of change of the water depths and discharges with respect to a change in the bottom friction coefficients. Such a sensitivity analysis can be carried out by computing the corresponding derivatives. Automatic differentiation (AD) is an efficient numerical method, free of approximation errors, to evaluate derivatives of the objective function specified by the computer program, Rubar20 for example. In this paper AD software tool Tapenade is used to compute forward derivatives. Numerical tests were done to show the robustness of the model and to demonstrate the efficiency of these AD-derivatives.     

Rates of shoreline change along the coast of Bangladesh

Bangladesh, at the confluence of the sediment-laden Ganges and Brahmaputra Rivers, supports an enormous and rapidly growing population (>140 million in 2011), across low-lying alluvial and delta plains that have accumulated over the past few thousand years. It has been identified as one of the most vulnerable places in the world to the impacts of climate change and sea-level rise. Although abundant sediment supply has resulted in accretion on some parts of the coast of Bangladesh, others are experiencing rapid erosion. We report a systematic assessment of rates of shoreline change over a 20-year period from 1989 to 2009, using Landsat satellite images with pixel resolution of 30 m on the ground. A Band ratio approach, using Band-5 divided by Band-2, discriminated the water line on images that were largely cloud-free, adequately registered, and at comparable tidal stages. Rates of shoreline change were calculated for >16,000 transects generated at 50 m intervals along the entire mainland coastline (>1,100 km) and major islands, using the End Point Rate (EPR) method in the Digital Shoreline Analysis System (DSAS) extension in ArcGIS®. Erosion characterises most of the seaward margin of the Sundarbans in western Bangladesh. Retreat rates of up to 20 m/yr are typical, with little evidence that local devastation of the mangrove fringe by Cyclone Sidr in November 2007 had resulted in uncharacteristic long-term rates of retreat where it made landfall. Erosion exceeded accretion in the Barguna Patuakhali coastal zone, most of which eroded at up to 20 m/yr, but with truncation of the southern tip of the Patharghata Upazila at up to 100 m/yr. In Bhola, erosion at rates of up to 120 m/yr were observed along much of the coast, but in the Noakhali Feni coastal zone, similar rates of erosion were balanced by rapid accretion of the main promontory by more than 600 m/yr. Rates of change were more subdued in the Chittagong and Cox’s Bazar coastal zones of southeast Bangladesh. Islands in the Meghna estuary were especially dynamic; Hatiya Island accreted along some of its shoreline by 50 km² between 1989 and 2009, but lost 65 km² through erosion elsewhere, resulting in the island moving south. Similar trends were observed on adjacent islands. The overall area changed relatively little across the entire coastline over the 20-year period with accretion of up to 315 km², countered by erosion of about 307 km².     

Evaluation and application of a three-dimensional water quality model in a shallow lake with complex morphometry

Fundamental hydrodynamic and ecological processes of a lake or reservoir could be adequately depicted by one-dimensional (1D) numerical simulation models. Whereas, lakes with significant horizontal water quality and hydrodynamic gradients due to their complex morphometry, inflow or water level fluctuations require a three-dimensional (3D) hydrodynamics and ecological analyses to accurately simulate their temporal and spatial dynamics. In this study, we applied a 3D hydrodynamic model (ELCOM) coupled with an ecological model (CAEDYM) to simulate water quality parameters in three bays of the morphologically complex Lake Minnetonka. A considerable effort was made in setting up the model and a systematic parameterization approach was adopted to estimate the value of parameters based on their published values. Model calibration covered the entire length of the simulation periods from March 29 to October 20, 2000. Sensitivity analysis identified the top parameters with the largest contributions to the sensitivity of model results. The model was next verified with the same setup and parameter values for the period of April 25 to October 10, 2005 against field data. Spatial and temporal dynamics were well simulated and model output results of water temperature (T), dissolved oxygen (DO), total phosphorus (TP) and one group of algae (Cyanobacteria) represented as chlorophyll a (Chla) compared well with an extensive field data in the bays. The results show that the use of the model along with an accurate bathymetry, a systematic calibration and corroboration (verification) process will help to analyze the hydrodynamics and geochemical processes of the morphologically complex Lake Minnetonka. An example of an ecological application of the model for Lake Minnetonka is presented by examining the effect of spatial heterogeneity on coolwater fish habitat analysis in 3D and under a scenario where horizontal spatial heterogeneity was eliminated (1D). Both analyses captured seasonal fish habitat changes and the total seasonal averages differed moderately. However, the 1D analysis did not capture local and short duration variabilities and missed suitable fish habitat variations of as much as 20%. The experiment highlighted the need for a 3D analysis in depicting ecological hot spots such as unsuitable fish habitats in Lake Minnetonka.     

Application of a multi-step computation scheme to an intratidal estuarine water quality model

A computation scheme, which involves multi-step computation of the decoupled mass-balance equations in water quality models, was proposed by Park and Kuo (1996. Water Res. 30, 2255–2264). Using a simple hypothetical model, they explained the concept and demonstrated the accuracy and computational efficiency of the multi-step scheme. This paper describes the concept and the implementation of the multi-step computation scheme in a more generalized format for both intratidal and intertidal estuarine water quality models. The scheme is applied to a prototype estuary using a laterally-integrated two-dimensional intratidal model. The computational efficiency of the scheme is demonstrated by comparing the model results using the multi-step scheme with those using the traditional single-step explicit numerical solution of the kinetic processes.     

Modelling nature-like fishway flow around unsubmerged obstacles using a 2D shallow water model

In the scope to create efficient nature like fish ramps using large-scale roughness elements, the present study is an audit of modelling such complex 3D free surface flows using an industrial 2D code solving shallow water equations. Validation procedure is based upon the comparison between numerous experimental measurements and numerical runs around large-scale roughness patterns disposed on the flume bottom in order to determine what 2D reliable numerical results can be expected. In this paper, we focused on cases of unsubmerged obstacles. The results demonstrate that 2D shallow water modelling using an industrial code such as TELEMAC-2D can be a convenient way for the hydraulic engineer to help design a nature-like fishway. This article emphasizes the limitations due to 2D depth integration of velocities and turbulence modelling and gives the domain of validity of the method.     

Self-contamination of aquaculture cages in shallow water

Fish farms, which initially colonized quiet and protected natural coastal areas, are now frequently installed in open flow zones, due to the lack of space along coasts and to the emergence of new environmental constraints. For the past two decades, a salmon fish farm has been located inside the roadstead of Cherbourg (France) to benefit from both sea protection and tide currents which regularly refresh the water. In spite of these favourable environmental conditions, periods of non-negligible fish mortalities have been observed to occur without clear evidence of their origin. This motivated the turbidity measurements and the numerical simulations presented in this paper. Firstly, it is shown that high turbidities in the farm site under study are mainly due to the flow acceleration under the cages, which causes the re-suspension of sediments and bio-deposits. Secondly, particles which enter the fishnet can have different origins (external source, bottom, or the net itself). Numerical simulations, based on the Reynolds equations and on the discrete random walk model for particle dispersion, suggest that the rear area of the net can be reached by particles emerging from below the net. It is observed that turbulent dispersion is a key ingredient for such a behaviour, as it can lead particles towards a large recirculation cell behind the net. Dispersion by realistic unsteady vortices has also been analysed by means of a Lattice-Boltzmann model. Though these computations involve smaller Reynolds numbers, they confirm qualitatively the observations of the random walk model. In addition, they suggest that vortex shedding and unsteady recirculation cells near the bottom can force particles from the sand bed to be lifted up and reach the rear of the net.     

Analyses on phenological and morphological variations of mangrove forests along the southwest coast of Bangladesh

Drastic changes in river discharge and salinity levels are threatening the phenology and morphology of the coastal mangrove forests of the Sundarbans of Bangladesh. We have used AVHRR GIMMS (1985–2006) and MODIS (2005–2010) satellite Normalized Difference Vegetation Index (NDVI) data to identify the temporal variation of the phenology of the mangroves. Linear interpolation and Fourier-based adjustment were applied to remove noise from the NDVI time series. Then linear regression analysis on a single area (8 km ? 8 km) and a composite of 36 areas for three NDVI statistics the annual minimum, annual average, and annual maximum were performed--over the time periods 1985–1990, 1990–2000, 2000–2006 and 2005–2010 to identify possible functional changes in NDVI time series around the Sundarbans. Furthermore, we used fourteen LANDSAT images spanning the period 1989–2010 to estimate the spatiotemporal rate of shoreline changes over the three time periods 1989–2000, 2000–2006, and 2006–2010. A decreasing trend in the annual minimum NDVI was observed in most of the areas of the Sundarbans for the period 1990–2000. During the years 2000–2006, the trends of the three NDVI statistics became significantly positive, indicating an improvement of the mangrove phenology. In the period 2005–2010, a decreasing trend in all the NDVI variables was again dominant. The coast underwent rapid erosion from 1989–2000 and 2006–2010. However, the rate substantially declined between 2000 and 2006, when accretion was dominant. The advent of the upstream Farakka barrage caused a significant reduction in the Ganges-Gorai River discharge and increased the salinity in and around the Sundarbans. Our study concludes that this may be responsible for the degradation of mangrove phenology and accelerated erosion in the earlier and recent periods. In the interim, 2000–2006, improved river discharge and salinity levels due to the Ganges water sharing agreement (1996) and dredging of the Gorai River bed (1998–1999) enhanced the mangrove phenology and helped the coast to gain land.     

A numerical investigation of the influence time distribution in a shallow coastal lagoon environment of the Gulf of California

Environmental Fluid Mechanics - The influence time distribution in Santa María La Reforma coastal lagoon, which is one of the most productive ecosystems in Mexico, has been numerically...     

Experimental and numerical analysis of flow instabilities in rectangular shallow basins

Free surface flows in several shallow rectangular basins have been analyzed experimentally, numerically and theoretically. Different geometries, characterized by different widths and lengths, are considered as well as different hydraulic conditions. First, the results of a series of experimental tests are briefly depicted. They reveal that, under clearly identified hydraulic and geometrical conditions, the flow pattern is found to become non-symmetric, in spite of the symmetrical inflow conditions, outflow conditions and geometry of the basin. This non-symmetric motion results from the growth of small disturbances actually present in the experimental initial and boundary conditions. Second, numerical simulations are conducted based on a depth-averaged approach and a finite volume scheme. The simulation results reproduce the global pattern of the flow observed experimentally and succeed in predicting the stability or instability of a symmetric flow pattern for all tested configurations. Finally, an analytical study provides mathematical insights into the conditions under which the symmetric flow pattern becomes unstable and clarifies the governing physical processes.     

Assesment of the response of a shallow macrotidal estuary to changes in hydrological and wastewater inputs through numerical modelling

The aim of this study was to investigate the response to short-term changes in river freshwater discharges and in nutrients loadings (mainly from the treatment of urban wastewater), of the shallow macrotidal Urdaibai estuary (north of Spain), by using numerical tools. A two-dimensional hydrodynamic model and a water quality model were applied to the estuary, in order to better use it as a prediction tool in the study of the effects of variations in hydrodynamic conditions and in waste water inputs. The model was calibrated and verified using data measured under different hydrological conditions (spring and summer). A model calibration was carried out with field data measured during the summer, while the model validation was conducted for spring conditions. The calibration process allowed the model parameter definition, while the model validation permitted the verification of the calibrated parameters under different environmental conditions. The model results were in reasonable agreement with field measurements, in both the calibration and the validation phases. The model showed a significant decrease in phytoplankton concentration with river input increase. A study on the effects of nutrient input reduction from the Gernika Waste Water Treatment Plant (WWTP) was conducted. It showed a decrease in phytoplankton concentration with decreasing levels of nutrient discharge. This reduction was more pronounced in conjunction with the highest river discharge. In that case, a 50% decrease for the elimination of the WWTP discharge was observed.     

Lunar influence on distribution of a calanoid copepod in the water column of a shallow,temperate estuary

Moonlight had a significant influence on the distribution of the copepodPseudodiaptomus hessei in the water column. Copepod samples were taken between March 1986 and March 1987 in the Sundays River estuary. South Africa. Late copepodid stages and adults showed vertical differences in abundance on moonlit nights, with more animals in bottom waters, but not on dark nights. Numbers of adults present in the water column were markedly lower on full moon nights compared with new moon nights. The strongest decrease in abundance was displayed by ovigerous females. These observed distribution patterns support published predation hypotheses.     

Biogeochemical properties and potential risk of shallow arsenic-rich sediment layers to groundwater quality in Western Bangladesh

Environmental Geochemistry and Health - The arsenic-contaminated groundwater has attracted attention in much south and southeast Asian deltas, however, mainly on the deep aquifers. Here, arsenic...     

Role of heavy polar organic compounds for water repellency of sandy soils

Separation and chemical characterisation of specific compounds responsible for soil water repellency has not previously been achieved. Here we describe the extraction, separation and analysis by gas chromatography-mass spectrometry of organic compounds found in wettable and water repellent sandy soils from the Netherlands and United Kingdom. Fatty acids (C₁₆–C₂₄), amides (C₁₄–C₂₄), alkanes (C₂₅–C₃₃), aldehydes/ketones (C₂₃–C₃₁) and complex ring-containing structures were detected in all samples. We found a greater abundance of high molecular mass polar compounds in the water repellent samples.     

A two-dimensional numerical model for eutrophication in Baiyangdian Lake

Hydrodynamic, physical, and biochemical processes in the Baiyangdian Lake water environment were analyzed comprehensively. An eutrophication ecodynamics model including the effects of reed resistance on flow was coupled with the hydrodynamics governing equations. An improvement on the Water Quality Analysis Simulation Program (WASP, a modeling system introduced by the US Environmental Protection Agency) is established, which uses the zooplankton kinetic equation. The model simulates water quality constituents associated with eutrophication in the lake, including phytoplankton, zooplankton, nitrogen, phosphorus, dissolved oxygen, and others. Various kinetic coefficients were calibrated using measured data or information from relevant literature, to study eutrophication in the lake. The values calculated by the calibrated model agree well with field data, including ammonia nitrogen, total nitrogen, total phosphorus and dissolved oxygen. Changes related to nutrition and dissolved oxygen during the processes were simulated. The present model describes the temporal variation of water quality in Baiyangdian Lake with reasonable accuracy. Deviations between model-simulated and observed values are discussed. As an ideal tool for environmental management of the lake, this model can be used to predict its water quality, and be used in research to examine the eutrophication process.     

Investigation of severe water problem in urban areas of a developing country: the case of Dhaka,Bangladesh

The present study evaluated water supply geochemistry in Dhaka City, Bangladesh, to provide detailed trace level (subppb) water quality data that include major ions, low dissolved oxygen (DO) and toxic trace metals for sustainable development. Dhaka Groundwater, which almost uniformly meets the World Health Organization guideline, has become the preferred source. Due to groundwater depletion and an ever-increasing need to meet water demands by city residents, Dhaka water supply and sewerage authority has initiated the treatment of river water, despite the fact that very little is known about the geochemical structure, and trace metal content in the Dhaka water supply. Major ion composition of water samples was determined, and the results used to generate Stiff diagrams. The diagrams served to visually compare water from different sources based on units of mass/volume. Hydrochemical facies analysis showed supply ground and surface waters are comprised predominately of Ca–Na–Mg–HCO₃ and Ca–Na–Mg–HCO₃–Cl types. Spatial distribution of ions, and Na/Cl and Na/SiO₂ molar ratio indicated that silicate weathering is the dominant geochemical process. Chemical data revealed that toxic Cr metal mobilization is associated with chemical hazards from the leather industry. The vulnerability of deep wells to contamination by As is governed by the geometry of induced groundwater flow paths and the geochemical conditions encountered between the shallow and deep regions of the aquifer. Quantifying total arsenic (As) and As from interlocking geochemical cycles (Fe, Mn) may assist in interpreting As dynamics in Dhaka well water. The surface source water was hypoxic to anoxic low DO associated with very high concentrations of biological oxygen demands, and electrical conductivity compared to industrial and non-industrial urban processes and standard activity guidelines. The results of this study should be applied to future research focused on the potential to improve water quality in urban and surrounding areas.     

Higher oil biodegradation potential at the Arabian Gulf coast than in the water body

Littoral materials collected from the intertidal zone along the coast of Kuwait City were associated with much higher numbers of oil-utilizing microorganisms than inshore and offshore water samples. Animate materials viz. epilithic biomass, cyanobacterial mats and roots of higher plants were richer in such microorganisms than inanimate materials, e.g. littoral sand, rock pieces, shells and others. Those numbers remained highest during the autumn, winter and spring and decreased dramatically during the hot summer. By far, the predominant indigenous oil-utilizing bacterium in the marine environment of Kuwait was Acinetobacter calcoaceticus. Less dominant organisms included Micrococcus sp., nocardioforms and others. Coast-immobilized strains of A. calcoaceticus and Micrococcus sp. had a higher hydrocarbon degradation potential than planktonic strains of the same organisms. It was concluded that marine coasts have a much higher potential for oil biodegradation than the water body. Received: 28 April 1999 / Accepted: 23 September 1999     

Measurements of fog water interception by shrubs on the California central coast

Fog water deposition may be an important component of the water budget of herbaceous-shrub ecosystems on the central and southern coastal regions of California. This paper presents the first analysis of measured fog water drip rates and meteorological controls in shrublands of Big Sur, California. Seasonal totals of 1255 mm and 306 mm of fog water drip were recorded in 2014 and 2015 (respectively), for averaged fog deposition rates of 0.02–0.08 l m² hr.^?1 to the soil under shrub canopy cover. The diurnal patterns of fog water drip showed that the majority of all trough water collected under shrubs on no-rain days occurred between the hours of 11 PM and 9 AM. During the study period from June 1 to October 31 of both 2014 and 2015, soil water content decreased significantly from average levels of 4–6 % at the shrub canopy center and middle locations, through 2–3 % VWC at the shrub edge locations, to levels at or below 2 % at 2-m distance locations from the shrub edge in open grass cover. Based on these results, we conclude that detectable rates of shrub canopy fog interception help sustain elevated soil water levels under shrubs and aid woody vegetation survival through periods of low rainfall.     

A numerical model of periodically forced circulation near the shore of a lake

Numerical calculations for a model of the near-shore circulation in a lake subject to two diurnal forcing mechanisms are presented. The first mechanism is a heating/cooling term in the heat equation representing the daytime heating and nighttime cooling of the diurnal cycle. The second is a periodic surface stress modelling a sea-breeze/gully wind system typical of some coastal regions. The two forcing mechanisms can either act together or against each other depending on their relative phase. The numerical solutions are compared with previously published analytical solutions and used to explore the extra dynamics associated with non-linear effects (specifically advection). The latter dynamics include the formation of gravity currents and unstable density profiles leading to secondary circulation.     

Modeling the buoyant flow of heated water discharged from surface and submerged side outfalls in shallow and deep water with a cross flow

In this study, a three-dimensional model was used to numerically study the buoyant flow, along with its mixing characteristics, of heated water discharged from the surface and submerged side outfalls in shallow and deep water with a cross flow. Hydraulic experimental data were used to evaluate the applicability of the model. The simulation results agree well with the experimental results, particularly, the jet trajectories, the dimensions of the recirculating zone, and the distribution of the dimensionless excess temperature. The level of accuracy of the simulation results of the present study is nearly identical to that of the results conducted by McGuirk and Rodi (1978). If the heated water is discharged into shallow water where the momentum flux ratio and the discharge densimetric Froude number are high, the submerged discharge method is better than the surface discharge method in terms of the scale of the recirculating zone and the minimum dilution. In deep water, where the momentum flux ratio and discharge densimetric Froude number are low, however, the submerged discharge method had few advantages. In shallow water, the discharge jet is deflected by the ambient cross flow, while forcing the ambient flow to bend towards the far bank for the full depth. For a submerged discharge in shallow water, the recirculating zone is the largest in the lowest layer but becomes smaller in the upper layer. As the water depth increases, the ambient flow goes over the jet and diminishes the blocking effect, thereby decreasing the bending of the jet.     

Predicting arsenic concentration in groundwater of Bangladesh using Bayesian geostatistical model

The pattern of the spatial variation in arsenic concentration in groundwater of Bangladesh is usually needed for the planning of safe drinking water. Often a model-based prediction is required for this purpose. In this paper, we fit a Bayesian hierarchical geostatistical model by utilizing data from the project, ‘Groundwater studies of arsenic concentration in Bangladesh’ conducted by the British Geological Survey and the Department of Public Health Engineering of Bangladesh. We also develop a predictive model for arsenic concentration at different levels of well-depth using the same approach. The resulting predictive model has been cross-validated by appropriate statistical tools. Finally, we obtained reliable spatially continuous predictive maps and predictive probability maps showing the areas with high probability of arsenic concentration for different levels of well-depth. Results indicate that our model fits the data well and captures a substantial amount of spatial variation. Moreover, well-depth is found to have a significant contribution in explaining the observed variation in arsenic concentration. The predictive maps that have been produced are observed to be different for various levels of well-depths and are expected to be helpful to the policy makers in preparing proper regional planning for safe drinking water.