The surface seiches of Lake of Lugano

A computational analysis of the periods and structure of surface seiches of the southern basin of Lake of Lugano and its experimental verification from three simultaneous water gauge recordings, mounted along the shores in Agno, Morcote and Riva S. Vitale, is given. The first five theoretical modes are calculated with a finite element code of the tidal equations; it yields the eigenperiods and co-range and co-tidal lines, which are graphically displayed and discussed in detail. Experimental verification is from recordings taken during February/March 1982. Inspection by eye allows identification of the five lowest order modes, partly including interstation phase shift. Power spectral analysis of three-time series and interstation phase difference and coherence spectra allow identification of higher order modes, probably up to order 13. Agreement between the theoretically predicted and the experimentally determined periods is excellent for all calculated modes. Computational results for the four lowest modes and their structure of the northern basin of Lake of Lugano are also presented and experimentally verified with records taken from an event in August 1979. Agreement is again excellent.     

Die Eigenschwingungen der durch den Kanal im Damm von Melide gekoppelten Becken des Luganersees

The northern and the southern basin of Lake Lugano, Switzerland, are separated by an artificial dam. The flow of the water is not only influenced by the outflow of the northern basin but also by gravitational oscillations (seiches) of both basins. A longperiodic peak around 100 minutes can be explained by a mathematical model. The interaction of the internal waves is a coupled oscillation with a period of 74 hours.      

Strömungsdynamische Untersuchungen im Zürich- und im Luganersee Ein Vergleich von Feldmessungen mit Resultaten theoretischer Modelle

Density distribution and temperature and current data which were measured in Lake of Zürich and Lake of Lugano in two summer field programs are scrutinized and interpreted by means of hydrodynamic models. Barotropic surface seiches and baroclinic internal seiches are studied using a one-and two-layer model and measured data permit identification of the respective resonant periods. Wind induced barotropic and baroclinic circulation dynamics is also studied by means of three-dimensional finite difference models of the hydrodynamic viscous equations on the rotating earth. In general the predictions of these models agree favorably with observed data.     

On the feasibility of using a lake water balance model to infer rainfall: an example from Lake Victoria

Abstract

A water balance model of Lake Victoria that can be used to assess rainfall from lake level, is derived. The model utilizes satellite estimates of rainfall directly over the lake. The model, initially derived and calibrated for the period 1956–1978, is reformulated here in such a way that all water balance terms except evaporation can be calculated from a combination of catchment rainfall and level of the lake. The reformulated model is validated and used to predict lake level fluctuations during the period 1931–1994. An error analysis is also performed. The model is then “inverted” to solve for mean rainfall conditions during various intervals of changing lake levels. For modern periods with known rainfall conditions, the error in model estimates is of the order of 1%.     

ON THE CALCULATION OF THE MEAN RESIDENCE TIME IN MONOMICTIC LAKES / Sur le calcul du temps moyen de résidence dans les lacs monomictiques

Abstract

A general method for the calculation of the mean residence time of water in monomictic lakes of simple morphometry is worked out on the same physical assumptions as those made by Piontelli and Tonolli (1964). After a short outline of the mathematical foundation of the method, the numerical procedure is presented, on which the computer code for the determination of the mean residence time is based. Finally some examples of the application of the method to Lake Maggiore and to a lake of complex morphometry (Lake of Lugano) are presented and discussed.     

Past and present state of the ichthyofauna of Lake Lugano

The evolution of the ichthyofauna of Lake Lugano (Lago di Lugano) during the past 120 years is characterized by the introduction of eight new fish species and by the possibly natural addition of the blenny (Blennius fluviatilis) in recent years. Introduced Salmonids such as charr (Salvelinus alpinus) and whitefish (Coregonus sp.) have established strong populations during the first half of this century, but have declined drastically thereafter. Likewise, the population of the native shad (Alosa fallax lacustris) has diminished significantly. A hydroacoustic survey of the pelagic fish stock of Lake Lugano in 1989 revealed the presence of a dense bleak (Alburnus albidus) population at 0 to 14 m depth. No other fish were found to be present in the pelagic zone. Oxygen and temperature distributions seem to confine the bleak to the uppermost layer in summer. In winter, very few fish were located by echosounding. Growth of bleak and roach (Rutilus rubilio) was difficult to interpret since data for comparison are lacking. Growth of perch (Perca fluviatilis) in the littoral zone was found to be slower than in other eutrophic lakes, for no obvious reason. Possible ways of restructuring the pelagic fish community are discussed.     

Large scale water movements in lakes

By large scale circulation in lakes one means motions whose characteristic length scales extend over most parts or all of the water masses in a lake or the ocean. We present the governing equations and motivate, by means of a scale analysis, the various simplified versions of model equations that are in use in computational lake dynamics. This scale analysis not only permits rational deduction of the reduced equations, it equally provides a means of estimating their limitations. These are discussed as are the difficulties and the peculiarities inherent in the proposed equation sets.Special features of external and internal wave motions are studied. For barotropic oscillations of a lake system (Lake of Lugano) it is shown that substantial water masses are exchanged between the individual basins at the resonating periods. Baroclinic seiches of a three layer model in which each layer is effective within its own domain show (for the North basin of the Lake of Lugano) that mode structures may differ from layer to layer pointing at important modifications of classical interpretations of higher baroclinic wave dynamics. And in large lakes in the equatorial belt the-effect forces modifications of the classical understanding of seiche behavior. Long periodic oscillating features may be attributed to topographic Rossby waves or higher baroclinic internal gravity waves; the observational identification is, however, difficult because lack of spatial resolution of the data makes this identification non-unique. We, finally present results of a full nonlinear numerical baroclinic circulation model and demonstrate that it is able to reproduce the gross features of the immediate response to strong storms during a few days.This paper is an extended version of a lecture with the same title, held by K. Hutter on June 14, 1989, at the Workshop Spatial and temporal scales of water bodies of the Sonderforschungsbereich Stoffhaushalt des Bodens, Universität Konstanz. The character of the paper is that of areview, however, it contains material, theoretical, computational and observational, that has never been presented before to make it sufficiently unique. Some of the new material has been collected and gathered by E. Bäuerle, G. Salvadè, C. Spinedi and F. Zamboni, who should be credited for it, even though none of these people contributed to the layout and drafting of the text, for which K. Hutter is responsible alone.We thank Professor Max Tilzer of the University Konstanz for inviting K. Hutter to the workshop and giving him the opportunity to present the material as of that time.As far as referencing current literature is concerned we are neither exhaustive nor complete and only refer to literature which is directly related to the material presented. For a list with more than 300 relevant references, the reader may consult the article Hydrodynamic Modeling of Lakes by K. Hutter in the Encyclopedia of Fluid Mechanics, Gulf Publ. Company, Houston Texas (1987). I would like to express my sincere thanks to Mrs. Danner for her diligent work in typing the text.     

Mathematische Modelle zur Simulation von Zirkulationsströmungen in einem See

The three-dimensional, finite-difference model of R.L. Street (Stanford University) has been adapted at the simulation of wind-induced currents in the northern basin of the Lake of Lugano. The model makes use of complete Navier-Stokes equations and a dynamical algorithm to calculate the eddy viscosity. The model predictions are compared with data collected in the measure campaign of 1979. A further application of the model is the cold inflow simulation in a stratified basin with inclusion of turbulent vertical exchange processes. A two-dimensional version of the model, which assumes an hydrostatic pressure distribution, is utilized to simulate the thermal sommer development of the Lake of Lugano, during 40 days. The model includes the thermical interactions and the wind influence. The results obtained show the possible application of the three-dimensional model to the currents simulation in lake basins. The two-dimensional model may be utilized to predict the development of a basin subject to a thermal load.      

Hydrodynamics of Lake Lugano

The hydrodynamic processes in the Lake of Lugano (Lago di Lugano) have been the object of three major measuring campaigns. The first during summer 1979 in the North Basin, the second in the autumn of 1984 in the South Basin and the last in 1989 again in the North Basin. It is expected that analysis of the collected data in conjunction with theoretical concepts will yield conclusive findings on the driving forces and hydrodynamics of the lake. Numerical models have been applied to the lake and the results have been compared to the measurements. Some models calculate the periods and distributions of amplitude, as well as surface velocities and internal seiches. Other models calculate wind-induced water circulation. Evidence is given to the peculiarities of the North Basin and the difficulties related with the depth-width ratio and with its deep chemical stratification.     

Internal tides and waves near the continental shelf edge

Abstract

The subject is reviewed from the viewpoints of theory, internal tide and wave structure and their implications.

A wider theoretical context suggests scope for further investigation of natural or nearly-trapped forms above the inertial frequency.

Although internal tides in many locations are observed to have first-mode vertical structure, higher modes are seen offshore from shallow shelf-break forcing and for particular Froude numbers, and may be expected locally near generation. Bottom intensification is often observed where the sea floor matches the characteristic slope. Solitons form from internal tides of large amplitude or at large changes of depth.

Internal tides and solitons are observed also at many sills and in straits, and to intensify in canyons.

Non-linear effects of the waves, especially solitons, include the conveyance of water, nutrients, ‘‘mixing potential'’ etc. away from their source to other locations, and the generation of mean currents. The waves transfer energy and possibly heat between the ocean and shelf, may be a source of medium frequency waves on the shelf (periods of minutes) and can contribute to interior mixing and overturning, bottom stirring and sediment movement.     

The dynamic model Seemod applied to the Southern Basin of Lake Lugano

The dynamic model Seemod developed at the EAWAG (Imboden and Gächter, 1978) and modified by Bührer (Ambühl and Bührer, 1984), was adapted to the South Basin of the Lake of Lugano (Lago di Lugano). The model can predict the evolution of the state of the lake, described by the concentrations of dissolved phosphorus, dissolved oxygen particulate phosphorus and organic particulate carbon, in function of phosphorus load and taking into account physical and biochemical initial- and boundary conditions. The model parameters were chosen through measurements and calibrations by short runs. A 10-year-long simulation was done, starting from the data of 1980, and its results agree quite well with the measurements. Then some 15-year-long simulations were done, which corresponded to different scenarios related to a progressive linking up of sewage systems to water treatment plants. The model predicts that a satisfactory water quality level can only be reached by reducing the total phosphorus input to less than 25 t/a.     

Seasonal changes of microbial populations in the sediments of the basins of Lugano and Agno

This research was carried out with the aim to explore the heterotrophic microbial population of two sediments in different oxic conditions of the Lake of Lugano (Lago di Lugano). The values of the viable bacterial counts found in our sediment samples were typical for an eutrophic lake.The increase in the proportion of anaerobic to aerobic bacteria at 30 °C observed in the sediment samples of Agno may reflect the depletion of oxygen concentrations in the water column.The generaAeromonas, Pseudomonas, Bacillus andClostridium, as well as strains belonging to the Coryneform-group, represented the major taxonomic groups of heterotrophic bacterial communities in the water-sediment interface.     

The Fate of Chernobyl137Cs in Lake Lugano

A rapid removal of Chernobyl¹³⁷Cs from a number of large lakes has been previously reported. Our measurements of¹³⁷Cs in water, sediments and pore water in the mono- and meromictic basins of Lake Lugano (Lago di Lugano) reveal generally slower half-removal times of 1.2 and 6.7 yrs, respectively. In the seasonally anoxic southern basin, this is most probably related to an intensive recycling of¹³⁷Cs between water and sediments. In the permanently stratified northern basin the removal rate is much slower due to an important inventory build up in the deep anoxic part of the basin.     

Empirical statistical characterization and regionalization of amplitude–duration–frequency curves for extreme peak flows in the Lake Victoria Basin,East Africa

Abstract

This paper focuses on a regionalization attempt to partly solve data limitation problems in statistical analysis of high flows to derive discharge–duration–frequency (QDF) relationships. The analysis is based on 24 selected catchments in the Lake Victoria Basin (LVB) in East Africa. Characteristics of the theoretical QDF relationships were parameterized to capture their slopes of extreme value distributions (evd), tail behaviour and scaling measures. To enable QDF estimates to be obtained for ungauged catchments, interdependence relationships between the QDF parameters were identified, and regional regression models were developed to explain the regional difference in these parameters from physiographic characteristics. In validation of the regression models, from the lowest (5 years) to the highest (25 years) return periods considered, the percentage bias in the QDF estimates ranged from –2% for the 5-year return period to 27% for 25-year return period.

Editor D. Koutsoyiannis     

Nonlinear internal waves in ideal rotating basins

Abstract

Starting from Euler's equations of motion a nonlinear model for internal waves in fluids is developed by an appropriate scaling and a vertical integration over two layers of different but constant density. The model allows the barotropic and the first baroclinic mode to be calculated. In addition to the nonlinear advective terms dispersion and Coriolis force due to the Earth's rotation are taken into account. The model equations are solved numerically by an implicit finite difference scheme. In this paper we discuss the results for ideal basins: the effects of nonlinear terms, dispersion and Coriolis force, the mechanism of wind forcing, the evolution of Kelvin waves and the corresponding transport of particles and, finally, wave propagation over variable topography. First applications to Lake Constance are shown, but a detailed analysis is deferred to a second paper [Bauer et al. (1994)].     

Eutrophication of lake lugano ‘read’ by means of planktonic remains in the sediment

The trophic evolution of Lake Lugano has been studied by examination of Cladoceran remains and P, N and C in the sediment. The frequency ofBosmina remains has increased in recent years andSida has gradually decreased; today it is completely eliminated.Acroperus harpac is influenced by man's activities in the littoral zone. A clear relationship between P concentration in the sediment and the ratios between the Cladoceran species is evident.     

Aquatic system response to climatic and human changes: Productivity,bottom water oxygen status,and sapropel formation in Lake Lugano over the last 10 000 years

The Holocene record of Lake Lugano (southern basin: surface area 20.3 km², maximum depth 87 m) comprising organic carbon-rich sediments (sapropels), is divided into eight intervals based on radiocarbon- and varve-dating. The content of organic carbon, inorganic carbon, and biogenic silica, as well as the benthic remains of ostracods and oligochaetes, are converted into accumulation rates and benthic abundances in order to assess past production rates and bottom water oxygen status, respectively. The results suggest three periods of distinct palaeolimnological character: (i) low primary production combined with shifts between aerobic and anaerobic profundal conditions (prior to ca. 3000 BC), (ii) moderate rates of production combined with a relatively high profundal oxygen content (after ca. 1500 BC), and (iii), high production rates (460 g C m^–2 a^–1) combined with anaerobic profundal conditions (present eutrophic state). Corresponding organic carbon contents in the sediments are: up to 5% (i), 4% (ii), and 8% (iii). Until the beginning of this century, the flux of autochthonous sediments to the lake floor correlated with the fluctuations in the allochthonous sediment accumulation rate, indicating that catchment erosion largely controlled lacustrine production during the Holocene history of Lake Lugano. Pollen data show catchment-vegetational transformations at ca. 3500 BC (change from fir to beech forests), at 1400 BC (onset of cereal vegetation) and at ca. A.D. 450 (strong increase in various cultural plants). The first two changes had a relatively large imprint on lacustrine sedimentation. At ca. 3500 BP, erosion increase in the catchment was triggered by vegetation changes in the mountain zone above ca. 1000 m a. s. l., which may have been induced by climatic and human alteration (drop in the treeline altitude). Maximum catchment erosion occurred at ca. 1400 BC which was clearly dominated by human cultivation during the Bronze Age. More oxygenated profundal conditions in the lake after ca. 3000 BC are possibly related to a better mixing of the lake waters during the winter season by increased wind activity.     

A stochastic optimization framework for the restoration of an over-exploited aquifer

ABSTRACT

This study investigates the impact of hydraulic conductivity uncertainty on the sustainable management of the aquifer of Lake Karla, Greece, using the stochastic optimization approach. The lack of surface water resources in combination with the sharp increase in irrigation needs in the basin over the last 30 years have led to an unprecedented degradation of the aquifer. In addition, the lack of data regarding hydraulic conductivity in a heterogeneous aquifer leads to hydrogeologic uncertainty. This uncertainty has to be taken into consideration when developing the optimization procedure in order to achieve the aquifer’s sustainable management. Multiple Monte Carlo realizations of this spatially-distributed parameter are generated and groundwater flow is simulated for each one of them. The main goal of the sustainable management of the ‘depleted’ aquifer of Lake Karla is two-fold: to determine the optimum volume of renewable groundwater that can be extracted, while, at the same time, restoring its water table to a historic high level. A stochastic optimization problem is therefore formulated, based on the application of the optimization method for each of the aquifer’s multiple stochastic realizations in a future period. In order to carry out this stochastic optimization procedure, a modelling system consisting of a series of interlinked models was developed. The results show that the proposed stochastic optimization framework can be a very useful tool for estimating the impact of hydraulic conductivity uncertainty on the management strategies of a depleted aquifer restoration. They also prove that the optimization process is affected more by hydraulic conductivity uncertainty than the simulation process.

Editor Z.W. Kundzewicz; Guest editor S. Weijs     

A local time-domain transmitting boundary for simulating cylindrical elastic wave propagation in infinite media

Finite element simulation of the time-dependent wave propagation in infinite media requires enforcing the transmitting boundary to replace the truncated far-field infinite domain so as to model the effect of the wave radiation towards infinity. This paper proposed a novel local time-domain transmitting boundary for simulating the cylindrical elastic wave radiation problem. This boundary is a mechanical model consisting of the spring, dashpot and mass elements, with the auxiliary degrees of freedom introduced, which is dynamically stable and easily implemented into the commercial finite element codes. Numerical analysis of the cylindrical elastic wave radiation problem indicates that the proposed transmitting boundaries with the order N=3 for cylindrical P and SV waves and with the order N=4 for cylindrical SH wave have very high accuracy, even when the artificial boundary at wave source. The proposed transmitting boundary with order N=0 can be applied approximately to the general two-dimensional infinite elastic wave problems that contain the more complex outgoing wave fields at artificial boundary than the cylindrical waves. The plane-strain Lamb problem is analyzed with the acceptable engineering accuracy achieved. On the other hand, the proposed transmitting boundary with higher order can be a tool to localize the temporal convolution that appears in an exact time-domain transmitting boundary for the general infinite wave problems. This potential applicability is mentioned.