Search

This paper is an outcome of a Lake Modelling Workshop held at Griffith University from 18 to 19 October 2017 and funded through an 'Area of Strategic Investment' in Water Science at Griffith University. We thank the reviewers for constructive comments. M.F. and D.H. conceived the study; M.F. wrote the first draft of the paper. All authors contributed in further writing, reviewing and editing the manuscript. Except from the lead-author and last author, authors are listed in alphabetic order.

A key phenological event in the annual cycle of many pelagic ecosystems is the onset of the spring algal bloom (OAB). Descriptions of the factors controlling the OAB in temperate to polar lakes have been limited to isolated studies of single systems and conceptual models. Here we present a validated modelling approach that, for the first time, enables a quantitative prediction of the OAB and a systematic assessment of the processes controlling its timing on a continental scale. We used a weather-driven, 1-dimensional lake model to simulate the seasonal dynamics of the underwater light climate in 16 lake types characterized by the factorial combination of 4 lake depths with 4 levels of water transparency. We did so at 1,962 locations across western Europe and over 31 years (1979-2009). Assuming that phytoplankton production is light-limited in winter, we identified four patterns of OAB control across lake types and climate zones. OAB timing is controlled by (i) the timing of ice-off in ice-covered clear or shallow lakes, (ii) the onset of thermal stratification in sufficiently deep and turbid lakes, and (iii) the seasonal increase in incident radiation in all other lakes, except for (iv) ice-free, shallow and clear lakes in the south, where phytoplankton is not light-limited. The model predicts that OAB timing should respond to two pervasive environmental changes, global warming and browning, in opposite ways. OAB timing should be highly sensitive to warming in lakes where it is controlled by either ice-off or the onset of stratification, but resilient to warming in lakes where it is controlled by incident radiation. Conversely, OAB timing should be most sensitive to browning where it is controlled by incident radiation, but resilient to browning where it is controlled by ice-off or the onset of stratification. Available lake data are consistent with our findings. published

© The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adap- tation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statu- tory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons. org/licenses/by/4.0/. ake surfaces are warming worldwide, raising concerns about lake organism responses to thermal habitat changes. Species may cope with temperature increases by shifting their seasonality or their depth to track suitable thermal habitats, but these responses may be constrained by ecological interactions, life histories or limiting resources. Here we use 32 million temperature measurements from 139 lakes to quantify thermal habitat change (percentage of non-overlap) and assess how this change is exacerbated by potential habitat constraints. Long-term temperature change resulted in an average 6.2% non-overlap between thermal habitats in baseline (1978–1995) and recent (1996–2013) time periods, with non-overlap increasing to 19.4% on aver- age when habitats were restricted by season and depth. Tropical lakes exhibited substantially higher thermal non-overlap com- pared with lakes at other latitudes. Lakes with high thermal habitat change coincided with those having numerous endemic species, suggesting that conservation actions should consider thermal habitat change to preserve lake biodiversity. Faculty yes

Boom-bust dynamics - the rise of a population to outbreak levels, followed by a dramatic decline - have been associated with biological invasions and offered as a reason not to manage troublesome invaders. However, boom-bust dynamics rarely have been critically defined, analyzed, or interpreted. Here, we define boom-bust dynamics and provide specific suggestions for improving the application of the boom-bust concept. Boom-bust dynamics can arise from many causes, some closely associated with invasions, but others occurring across a wide range of ecological settings, especially when environmental conditions are changing rapidly. As a result, it is difficult to infer cause or predict future trajectories merely by observing the dynamic. We use tests with simulated data to show that a common metric for detecting and describing boom-bust dynamics, decline from an observed peak to a subsequent trough, tends to severely overestimate the frequency and severity of busts, and should be used cautiously if at all. We review and test other metrics that are better suited to describe boom-bust dynamics. Understanding the frequency and importance of boom-bust dynamics requires empirical studies of large, representative, long-term data sets that use clear definitions of boom-bust, appropriate analytical methods, and careful interpretations.

In situ experiments on sediment resuspension were carried out along a depth transect in shallow polytrophic Lake Langer See, northeast Germany (area = 1.27 km2, Zmax = 3.8 m), in winter under ice and in summer 2006, using a hydrodynamically calibrated erosion chamber (diameter 20 cm). Shear velocity U* was incrementally increased 11 times for 10 min each (0–2.57 cm s−1) to initiate resuspension. Entrainment rates (E) of suspended particulate matter (ESPM) and total P (ETP) were determined by a mass balance. Sandy nearshore sediments at 1–2 m depth showed low ESPM (0.01–6.64 g m−2 h−1) and ETP (0.2–2.96 mg m−2 h−1). There was no difference in critical shear velocity (U*crit) of incipient resuspension between winter and summer. Muddy offshore sediments at 2–3.8 m depth showed higher ESPM (0.09–106.1 g m−2 h−1) and ETP (0.06–532.3 mg m−2 h−1). Under ice, U*crit was 0.9–1.1 cm s−1 higher than in summer, indicating that the wave-unaffected sediment had ample time for consolidation and biostabilization. Wind-wave modeling, using measured ESPM and ETP, revealed that resuspension is primarily (90%) restricted to the nearshore sediments (17% lake area). Our scenarios show that annual entrainment of SPM and TP increased linearly with the duration of ice-free period. Since ice coverage increased shear resistance, climate-driven absence or shortening of ice-cover would reduce the period for settling of particles and their integration into sediments, lowering their biostabilization, thus facilitating resuspension and phytoplankton recruitment in spring after ice thaw.

Cyanobacteria of the order Nostocales found in lakes in temperate regions are generally assumed to benefit from climate change. To predict their future development under varying environmental conditions, we developed a mathematical model that simulates their entire life cycle. Cylindrospermopsis raciborskii, a tropical species which spread to the northern temperate zone during the last decades, was used as the model organism. We calibrated and validated the model using a 13-year data set on the species' population dynamics gathered in a shallow lake in northern Germany. The predicted values were consistent with the observed data. We used sensitivity studies and Hasse diagrams based on partial order theory to rank the impact of different model parameters on life cycle dynamics. Our results show that the seasonal dynamics of C. raciborskii are mainly determined by the optimum growth temperature of its vegetative cells. The dynamics of pelagic populations in the water and akinete populations (resting stages) in the sediment is highly dependent on lake water temperature and underwater light intensity and, thus, on climatic conditions. Therefore, any future increase in lake water temperature will presumably lead to an increase in the size of C. raciborskii populations in particular and of Nostocales populations in general.

Some tropical cyanobacteria have spread to temperate freshwaters during the last decades. To evaluate their further development in temperate lakes, we studied the temperature- and light-dependent growth of three invasive (Cylindrospermopsis raciborskii, Anabaena bergii and Aphanizomenon aphanizomenoides) and three native (Aphanizomenon gracile, Aphanizomenon flos-aquae and Anabaena macrospora) cyanobacterial species (Nostocales) from German lakes. We also included one potentially invasive (Aphanizomenon ovalisporum) Nostocales species. We conducted semi-continuous culture experiments and a microcosm experiment along a natural light gradient. Temperature data were used to design a model to simulate the development of selected species according to three temperature scenarios (past, present and future). Native species had significantly higher growth rates than invasive species and the potential invader A. ovalisporum at low temperatures (� 108C), while the opposite was true at high temperatures (� 358C). Maximum growth rates of A. ovalisporum, A. aphanizomenoides and C. raciborskii were clearly higher than those of A. bergii and the native species. Regarding light-dependent growth, significant differences were found between single species but not between all native and invasive species. The model simulation demonstrates a shift in dominance from the native A. gracile in the historic scenario to C. raciborskii populations in the future scenario, in which also the potential invader A. ovalisporum is able to establish populations in temperate lakes. Our findings suggest that any further temperature increase would promote the growth and development of Nostocales species in general, and that of the invasive species in particular, and would enable a more northward expansion of A. ovalisporum.

Modeling studies examining the effect of lakes on regional and global climate, as well as studies on the influence of climate variability and change on aquatic ecosystems, are surveyed. Fully coupled atmosphere–land surface–lake climate models that could be used for both of these types of study simultaneously do not presently exist, though there are many applications that would benefit from such models. It is argued here that current understanding of physical and biogeochemical processes in freshwater systems is sufficient to begin to construct such models, and a path forward is proposed. The largest impediment to fully representing lakes in the climate system lies in the handling of lakes that are too small to be explicitly resolved by the climate model, and that make up the majority of the lake-covered area at the resolutions currently used by global and regional climate models. Ongoing development within the hydrological sciences community and continual improvements in model resolution should help ameliorate this issue.

Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles are coupled through competition between prey species. Here, we investigate predator-prey oscillations in a long-term experiment with a marine plankton community. Wavelet analysis of the species fluctuations reveals two predator-prey cycles that fluctuate largely in anti-phase. The phase angles point at strong competition between the phytoplankton species, but relatively little prey overlap among the zooplankton species. This food web architecture is consistent with the size structure of the plankton community, and generates highly dynamic food webs. Continued alternations in species dominance enable coexistence of the prey species through a non-equilibrium 'killing-the-winner' mechanism, as the system shifts back and forth between the two predator-prey cycles in a chaotic fashion.

In the present study, a numerical model of the hydrodynamic and thermal structure of artificial shallow lakes in eastern India has been developed as a tool to assess the ecological water quality, driven by the meteorological forcings. It allows quantification of the vertical mixing processes that govern not only the thermal structure but also nutrient exchanges and the distribution of dissolved and particulate matter among water layers. Vertical temperature profiles were calculated by solving coupled partial differential equations for temperature (heat energy balance equation), one-dimensional momentum equation and a second order closure scheme for small-scale turbulence effects, i.e. turbulent kinetic energy and turbulent dissipation rates numerically using an implicit time integration method. The effect of advection due to the inflow and outflow is not taken into consideration as these shallow waterbodies are assumed to behave as a closed lake. The oxygen level measured at different layers during the simulation period in these waterbodies reflects hypolimnetic oxygen depletion due to the thermal stratification in the aquatic environment. The changes in the stratification regime in these waterbodies are expected to affect the water quality and the health of the ecosystem, primarily based on temperature and dissolved oxygen parameter and in particular, the certain features of the oxygen resources of the hypolimnion.

Dense surface blooms of toxic cyanobacteria in eutrophic lakes may lead to mass mortalities of fish and birds, and provide a serious health threat for cattle, pets, and humans. It has been argued that global warming may increase the incidence of harmful algal blooms. Here, we report on a lake experiment where intermittent artificial mixing failed to control blooms of the harmful cyanobacterium Microcystis during the summer of 2003, one of the hottest summers ever recorded in Europe. To understand this failure, we develop a coupled biological-physical model investigating how competition for light between buoyant cyanobacteria, diatoms and green algae in eutrophic lakes is affected by the meteorological conditions of this extreme summer heatwave. The model consists of a phytoplankton competition model coupled to a one-dimensional hydrodynamic model, driven by meteorological data. The model predicts that high temperatures favour cyanobacteria directly, through increased growth rates. Moreover, high temperatures also increase the stability of the water column, thereby reducing vertical turbulent mixing, which shifts the competitive balance in favour of buoyant cyanobacteria. Through these direct and indirect temperature effects, in combination with reduced wind speed and reduced cloudiness, summer heatwaves boost the development of harmful cyanobacterial blooms. These findings warn that climate change is likely to yield an increased threat of harmful cyanobacteria in eutrophic freshwater ecosystems.

Here, we present a community perspective on how to explore, exploit and evolve the diversity in aquatic ecosystem models. These models play an important role in understanding the functioning of aquatic ecosystems, filling in observation gaps and developing effective strategies for water quality management. In this spirit, numerous models have been developed since the 1970s. We set off to explore model diversity by making an inventory among 42 aquatic ecosystem modellers, by categorizing the resulting set of models and by analysing them for diversity. We then focus on how to exploit model diversity by comparing and combining different aspects of existing models. Finally, we discuss how model diversity came about in the past and could evolve in the future. Throughout our study, we use analogies from biodiversity research to analyse and interpret model diversity. We recommend to make models publicly available through open-source policies, to standardize documentation and technical implementation of models, and to compare models through ensemble modelling and interdisciplinary approaches. We end with our perspective on how the field of aquatic ecosystem modelling might develop in the next 5-10 years. To strive for clarity and to improve readability for non-modellers, we include a glossary.

Microcystis is one of the most notorious phytoplankton species, because it can form harmful toxic blooms that cause problems in freshwaters all over the world. Since Microcystis colonies are buoyant, high concentrations of toxic Microcystis accumulate at the water surface in scums during calm, warm conditions. The aim of this study was to investigate the physiology and population dynamics of benthic and pelagic Microcystis, and to use this knowledge to predict which lake management strategies could be effective in the battle against Microcystis blooms in Lake Volkerak-Zoommeer, The Netherlands. Changes in benthic and pelagic populations of Microcystis were monitored in the water and sediments of the lake. Sedimentation and recruitment rates were measured using traps, and the physiology of benthic colonies was investigated. In addition, the response of Microcystis to light, temperature, salinity and the aggregation of Microcystis to clay was determined in the laboratory. Large amounts of Microcystis sink from the water column in summer due to attachment of sediment particles. The attachment of clay particles to colonies depends on the concentration and type of clay and on the composition of the mucus that surrounds Microcystis. Colonies that have sunk overwinter in the sediments. A small amount of colonies overwinter in the water column. During autumn and winter, benthic colonies from shallow sediments are gradually transported to the deeper parts of the lake. The concentration of benthic Microcystis therefore increases with lake depth. Although all benthic colonies remain vital during winter, colonies in shallow euphotic sediments have a higher vitality then colonies in deep anoxic sediments. The overwintering benthic population inoculates the water column in spring. Since the density of benthic colonies does not change in spring, colonies do not actively recruit by using their buoyancy, but are probably passively resuspended by wind-induced mixing or bioturbation. Since colonies from shallow sediments have the highest vitality and are more frequently resuspended then deeper parts, most recruitment originates from the shallow sediments. Model simulations indicate that benthic recruitment contributes for 50-75% to the size of the summer bloom. To suppress harmful blooms of Microcystis in Lake Volkerak-Zoommeer, two management strategies have been suggested: flushing the lake with freshwater or reintroducing saline water. A mechanistic model of the population dynamics of Microcystis predicts that flushing with freshwater will suppress Microcystis blooms when the current flushing rate is sufficiently increased. Furthermore, the inlet of saline water will suppress Microcystis blooms for salinities exceeding 14 g/l. Both management strategies are technically feasible.

From a continuum–mechanical point of view, the heat balance or the thermodynamics of a lake, reservoir, or ocean is governed by three different types of processes: surface fluxes, those through the water surface and the sediment boundary of a water body; internal heat production; and external heat supply. Whereas surface fluxes are accounted for in boundary conditions, supply and production take place in the water volume and are described as additional production terms in the equation of heat (1). Turbulent diffusion and, to a much lesser degree, molecular diffusion lead to a certain temperature stratification, usually dividing a lake into a well-mixed, upper warm layer, the epilimnion, separated from it by a transition zone a colder hypolimnion. The temperature–depth distribution can be determined from the heat balance equation and boundary conditions describing the surface fluxes into the water. In contrast to this, in a well-mixed waterbody with a homogeneous temperature distribution, for example, a polymictic lake, all heat production and flux terms are lumped together in a net thermal energy flux. In this case, the heat production terms are treated as fluxes across the surface. Using such a simple system, one can determine the equilibrium temperature of the waterbody for a certain set of meteorologic conditions, that temperature to which the mixed waterbody is driven under the same prevailing meteorologic conditions. For a stratified lake or ocean, such an approach is only of limited use because it does not account for vertical transport of heat in the waterbody. But it can be a good approximation for the surface temperature when the stratification is strong, thus separating the hypolimnion from the well-mixed epilimnion. Keywords: heat balance; heat flux; air–water interface; short-wave radiation; long-wave radiation; sensible heat flux; evaporation; latent heat flux

Recent winter warming over Central Europe associated with a positive phase of the North Atlantic Oscillation (NAO) strongly influenced the thermal and water column stability properties of deep Lake Constance (zmean = 101 m).Volumet- rically weighted average water temperatures have increased since the 1960s by an average of 0.017 degree C yr-1, and its interannual variability was strongly related to the variability in winter air temperature and the NAO winter index (NAOW). The influence of NAOw on water temperature was more persistent than its influence on air temperature. The seasonal persistence of the NAOw signal increased with water depth. Deep-water temperatures were related to the NAOw from one spring mixing period to the next. This caused a time lag of 1 yr in the response of deep-water winter temperatures to the NAOw. Reduced winter cooling during high-NAOw years resulted in the persistence of small temperature gradients that possibly resisted complete mixing. This, in turn, resulted in less upward mixing of nutrients (total phosphorus and total silica), which accumulated in the hypolimnion during the previous stratification period. A second effect of incomplete mixing was the lack of the replenishment of deepwater oxygen during high-NAOw years. Hence, besides its strong impact on the thermal regime, climate variability influenced both the causes (nutrient supply for phytoplankton growth) and symptoms (the degree of hypolimnetic oxygen deficiency) of trophic changes in Lake Constance.

The African great lakes are of utmost importance for the local economy (fishing), as well as being essential to the survival of the local people. During the past decades, these lakes experienced fast changes in ecosystem structure and functioning, and their future evolution is a major concern. In this study, for the first time a set of one-dimensional lake models are evaluated for Lake Kivu (2.28°S; 28.98°E), East Africa. The unique limnology of this meromictic lake, with the importance of salinity and subsurface springs in a tropical high-altitude climate, presents a worthy challenge to the seven models involved in the Lake Model Intercomparison Project (LakeMIP). Meteorological observations from two automatic weather stations are used to drive the models, whereas a unique dataset, containing over 150 temperature profiles recorded since 2002, is used to assess the model’s performance. Simulations are performed over the freshwater layer only (60 m) and over the average lake depth (240 m), since salinity increases with depth below 60 m in Lake Kivu and some lake models do not account for the influence of salinity upon lake stratification. All models are able to reproduce the mixing seasonality in Lake Kivu, as well as the magnitude and seasonal cycle of the lake enthalpy change. Differences between the models can be ascribed to variations in the treatment of the radiative forcing and the computation of the turbulent heat fluxes. Fluctuations in wind velocity and solar radiation explain inter-annual variability of observed water column temperatures. The good agreement between the deep simulations and the observed meromictic stratification also shows that a subset of models is able to account for the salinity- and geothermal-induced effects upon deep-water stratification. Finally, based on the strengths and weaknesses discerned in this study, an informed choice of a one-dimensional lake model for a given research purpose becomes possible. Keywords: lake modelling, model intercomparison, surface–atmosphere interactions, tropical lakes, Lake Kivu (Published: 5 February 2014) Citation: Tellus A 2014, 66 , 21390, http://dx.doi.org/10.3402/tellusa.v66.21390 This publication is part of a Thematic Cluster entitled "Parameterization of lakes in numerical weather prediction and climate models". Read the other papers from this thematic cluster here

Daphnids with higher density than the surrounding water body have to push water downwards to hold their position in the water column. This swimming current is mainly the result of the movement of the second antennae and only to a small extent due to the filter current. The water structures under the Daphnia are very variable depending on the swimming behavior. We focused on the hop and sink behavior, where the downward-pushed water masses form a wake which can be described as a mushroom-shaped vortex. The volume of this structure increases linearly with time. The wake volume is much larger than the zooplankton itself which can be important for the percep- tibility by mechanically sensing carnivorous predators. In water with a density gradient of 10 kg m -4 the wake length WL can be described by WL = 1.64 (± 0.096) 3 L 1.58 (± 0.14) with the length of the Daphnia L in millimeters. The wake length, measured after 5 s, remained constant for gradients up to 1 kg m-4. Above this value, the wake length declines in good agreement with the value expected from theory with WL = 10.66 (± 0.21) 3 (dr/dz)-0.265 (± 0.010). Since the intra- and inter-specific 'communication' (e.g. mate seeking, nutrient partition between phytoplankton and bacteria, predator avoidance) can be expected to be bound to the hydrodynamic properties of the wakes, different wake forms and sizes most likely have an important impact on the information sent out.

In this work, we investigate the isothermal gravity-driven Stokes flow of a mixture of two constant true density viscous fluids which are overlain by a (single-constituent) constant density viscous fluid down an inclined plane. The continuum thermodynamical theory for such a system implies that, in the simplest case, the constituents of such a mixture interact mechanically with each other because of (1) friction or drag between the constituents, and (2) the non-uniform (volume) distribution of constituents, in the mixture. The former interaction is proportional to the relative velocity of the two constituents, and the latter to the gradient of the volume fraction. The coefficient of the volume fraction gradient in this latter interaction has the dimensions of pressure, and is usually interpreted as the fluid pressure p in the case of a fluid-solid mixture. More generally, however, this pressure represents that maintaining saturation in the mixture. In this work, we formulate a model for a saturated mixture in which this coefficient takes a slightly more general form, i.e. $\delta $p, where $\delta $ is a dimensionless constant varying between 0 and 1. In particular, in the context of the thin-layer approximation, analytical solutions of the lowest-order non-dimensionalized constituent momentum balances, under the usual assumption $\delta $ = 1, yield only pure constituent-1 or pure constituent-2 `mixtures'. On the other hand, numerical solution of these momentum balances for $\delta \neq $ 1 yield non-trivial volume fraction variations with depth in the layer, and hence represent true mixture solutions. Applying this model to the case of a sediment-ice mixture, such as that found in a glacier or ice sheet, one obtains good qualitative agreement with observations on the variation of sediment in these bodies with depth for $\delta \geq $ 0.95, i.e. in this case the sediment remains concentrated at the bottom of the layer.

This work presents a precise formulation of the balance and constitutive relations appropriate to the modeling of the motion of the fluid outer core, including a full thermodynamic analysis and derivation of the buoyancy frequency, its role in the equations of motion for the fluid outer core, and the dependence of this equation on the thermodynamic state of the outer core. It is shown that the equation of motion is controlled by a single parameter, the buoyancy frequency. Its definition is general, so as to include also thermodynamic effects in various forms. The dependence on concentration or entropy-gradients is of importance for motions on longer time scales but also influences core undertones, the oscillations of the Earth's outer core, in regions of strong concentration gradients. By appropriate scaling a variety of different approximations arise from this formulation using the thermodynamic definiton of the buoyancy frequency. Special interest is put on the scaling for the outer core eigenmodes yielding consistent formulations for the Boussinesq- and the subseismic approximation.

Results of a lake model intercomparison study conducted within the framework of Lake Model Intercomparison Project are presented. The investigated lake was Großer Kossenblatter See (Germany) as a representative of shallow, (2 m mean depth) turbid midlatitude lakes. Meteorological measurements, including turbulent fluxes and water temperature, were carried out by the Lindenberg Meteorological Observatory of the German Meteorological Service (Deutscher Wetterdienst, DWD). Eight lake models of different complexity were run, forced by identical meteorological variables and model parameters unified as far as possible given different formulations of processes. All models generally captured diurnal and seasonal variability of lake surface temperature reasonably well. However, some models were incapable of realistically reproducing temperature stratification in summer. Total heat turbulent fluxes, computed by the surface flux schemes of the compared lake models, deviated on average from those measured by eddy covariance by 17–28 W m−2. There are a number of possible reasons for these deviations, and the conclusion is drawn that underestimation of real fluxes by the eddy covariance technique is the most probable reason. It is supported by the fact that the eddy covariance fluxes do not allow to close the heat balance of the water column, the residual for the whole period considered being ≈–28 W m−2. The effect of heat flux to bottom sediments can become significant for bottom temperatures. It also has profound influence on the surface temperatures in autumn due to convective mixing but not in summer when the lake stratification is stable. Thus, neglecting sediments shifts the summer–autumn temperature difference in models lacking explicit treatment of sediments considerably. As a practical recommendation based on results of the present study, we also infer that in order to realistically represent lakes in numerical weather prediction and climate models, it is advisable to use depth-resolving turbulence models (or equivalent) in favor of models with a completely mixed temperature profile.

A layer of ice and sediment is modelled as a mixture of two nonlinear, very viscous, constant density fluids interacting mechanically via Darcy- and Pick-type forces. An inclined layer of this mixture overlain by a layer of ice modelled as a viscous fluid is considered with boundary conditions of no-slip or viscous sliding at the base and no stress at the free surface. The interface is treated as a singular surface across which the jump conditions of mass and momentum for the constituents are assumed to hold. Furthermore, because the components are viscous fluids, a kinematic condition for the continuity of the tangential velocity is formulated. The momentum jump conditions involve surface production terms requiring additional surfacial constitutive relations.

[1] From a small meromictic lake, we present observations of a circulation pattern that has not been documented in the limnological literature before. While surface cooling drives a vertical circulation of the upper water layer (mixolimnion), the deeper water layer (monimolimnion) is not included because of its higher salt concentration. However, double diffusion (higher diffusivity of heat than of dissolved substances) facilitates the faster escape of heat from the monimolimnion compared to dissolved substances during cold periods. As a consequence, interfacial cooling drives a vertical circulation within the monimolimnion without breaking the stratification toward the mixolimnion. In the presented case, the geochemical setting does not permit dissolved substances to accumulate in the mixolimnion. As a consequence, the system approaches the case of two immiscible layers in thermal contact. Below the interface, a convection layer is formed that exceeds the staircase layer thickness of double diffusion when conservative salts are involved. Finally, the entire lake circulates as two separate convection layers. This has a decisive impact on the formation of gradients and the redistribution of dissolved substances in lakes.

The formation and break-up or erosion of stratification is a major process in all natural and man-made lakes, which controls to a large extent the functioning of their ecosystems. The key challenge here is the specific role of shear generated and convective turbulence in the formation/destruction of stratification and their interactions with internal waves. Three aspects of hydrodynamics, i.e. the dynamical state, the physical mechanism and the energy level are very important elements in understanding problems of turbulent mixing and the formation of vertical thermal stratification. The result of the stratification is the formation of the seasonal thermocline.

A coupled model is presented for simulating physical and biological dynamics in fresh water lakes. The physical model rests upon the assumption that the turbulent kinetic energy in a water column of the lake is fully contained in a mixed layer of variable depth. Below this layer the mechanical energy content is assumed to vanish. Additionally, the horizontal currents are ignored. This one-dimensional two-layered model describes the internal conversion of the mechanical and thermal energy input from the atmosphere into an evolution of the mixed layer depth by entrainment and detrainment mechanisms. It is supposed to form the physical domain in which the simulation of the biological processes takes place. The biological model describes mathematically the typical properties of phyto- and zooplankton, their interactions and their response to the physical environment. This description then allows the study of the behaviour of Lagrangian clusters of virtual plankton that are subjected to such environments. The essence of the model is the dynamical simulation of an arbitrary number of nutrient limited phytoplankton species and one species of zooplankton. The members of the food web above and below affect the model only statically. The model is able to reproduce the typical progression of a predator-prey interaction between phyto- and zooplankton as well as the exploitative competition for nutrients between two phytoplankton species under grazing pressure of Daphnia. It suggests that the influence of the biological system on the physical system results in a weak increase of the surface temperature for coupled simulations, but a considerably higher seasonal thermocline in spring and a lower one in autumn.

To prevent flooding of the Dutch delta, former estuaries have been impounded by the building of dams and sluices. Some of these water bodies, however, experience major ecological problems. One of the problem areas is the former Volkerak estuary that was turned into a freshwater lake in 1987. From the early 1990s onward, toxic Microcystis blooms dominate the phytoplankton of the lake every summer. Two management strategies have been suggested to suppress these harmful algal blooms: flushing the lake with fresh water or reintroducing saline water into the lake. This study aims at an advance assessment of these strategies through the development of a mechanistic model of the population dynamics of Microcystis. To calibrate the model, we monitored the benthic and pelagic Microcystis populations in the lake during two years. Field samples of Microcystis were incubated in the laboratory to estimate growth and mortality rates as functions of light, temperature, and salinity. Recruitment and sedimentation rates were measured in the lake, using traps, to quantify benthic–pelagic coupling of the Microcystis populations. The model predicts that flushing with fresh water will suppress Microcystis blooms when the current flushing rate is sufficiently increased. Furthermore, the inlet of saline water will suppress Microcystis blooms for salinities exceeding 14 g/L. Both management options are technically feasible. Our study illustrates that quantitative ecological knowledge can be a helpful tool guiding large-scale water management. [KEYWORDS: benthic–pelagic coupling ; cyanobacteria ; harmful algal blooms ; population dynamics ; recruitment ; residence time ; salinity ; sedimentation ; water management]

Physical problems are described by relationships, which are dominated by quantities having a certain dimension, such as length, time, mass, force, temperature etc. These relations must be so structured that dependent and independent quantities are combined so as to yield dimensionally correct formulas. For instance, a physically correctly written formula must possess on each of its sides, left and right, the same physical dimension. Similarly, in an equation which describes a physical fact, quantities with different dimensions cannot be added. Such properties are connected with what is called dimensional homogeneity. It holds for all mathematical expressions describing physical facts. In other applied sciences, for instance mathematical economy, dimensional homogeneity is not requested to hold, a fact that allows equations with more general structure.

Somewhat unprecise and stretching the correct definition, a physical model is a mapping of Nature or at least of a subprocess that occurs in Nature or in our world of experience to smaller scale. “Projection” instead of “mapping” would be the better denotation, since some information is lost in the mapping. It is not necessary that the processes describe a physical incidence, however in this chapter we shall limit ourselves to physical systems. Naturally, every theory that describes processes of any kind, already represents a model; the theory would better be called a model, and it is imputed that the theory describes the processes in a certain sense and is able to also predict them adequately. The restriction that is imposed by such a theory is the fact, that it only adequately describes partial facts of the reality, those which are important, and that it ignores unimportant facets or even may describe these erroneously. In this sense, every theory or model is a projection of Nature, which enjoys only some similarity with the latter. Its intention is the determination and possibly the forecast of those physical quantities which are thought to be important as derivatives on the basis of the presentation of external sources and of initial conditions. The problems are generally formulated as initial boundary value problems.

In the last chapters a great mathematical stride was taken to deduce several different models for the description of turbulent processes in fluid flow situations. These models find their application in many hydrodynamical problems of mechanical and civil engineering, but equally also meteorology, oceanography and physical limnology (lake hydrodynamics). In the latter applications the intention may be to compute the evolution of the vertical temperature profiles in a large body of water. One can easily imagine that the temperature distribution in a lake is, apart from light, one of the most important quantities that affects the seasonal development of the biological processes. Phyto- and zooplankta grow according to the temperature and light environment they encounter. Let us touch upon some of the phenomena related to this fascinating biological-physical coupling problem.

In Chap. 2 it was assumed that balance equations were referred to an observer at rest in an inertial system. In this chapter our intention is not to concentrate on the issues like existence of such a reference system or on the ideas of constructing such a system, rather we presume that there exists such a reference system relative to which the quantities like momentum density, momentum supply and flux of momentum, as shown in Chap. 2, are uniquely defined. In the following, we shall demonstrate that the balance equations can also be formulated relative to an observer, which moves himself relative to a fixed observer, i.e., the observer performs a translatory and/or rotatory motion. In geophysical applications this situation arises quite frequently, because for a number of processes the Earth can not be identified with an inertial system. This implies that one must take the Earth’s motion in the respective equations into account and modify them accordingly. Theoretically, this can be done by introducing additional terms of the relative motion — Coriolis, centripetal and Euler accelerations. A change of the reference system, however, will also play an important role for the material equations as will be seen in Chap. 5.

In this chapter a simple turbulence model of first order — called the k-e model — will be developed, which merely uses evolution equations for the specific turbulent kinetic energy, k and the specific turbulent dissipation rate, e. In the derivation concepts will become known, which illustrate how also higher order models might be handled. This so-called k-e model shall in the subsequent paragraphs be developed for a density preserving fluid and is then extended for a Boussinesq fluid i.e., a fluid in which density variations are only accounted for in the body (gravity) force. In particular the Coriolis acceleration and the buoyancy effects play often a role in combination in such geophysical applications, e.g. in a stratified atmosphere or in the ocean which are typical configurations in meteorology, oceanography and limnology.

In the last two Chaps. 10 and 11, some of the elements of the foundations of turbulence theory and turbulent closure procedures were laid down. It was shown, how the Reynolds averaged field equations could be derived from the full balance laws of physics by applying to them a filter operation 〈•〉. The properties of the filter were so assigned to include the ergodic hypothesis, which, in the averaging process, means that multiple averaging is an invariant operation2, i.e., does not lead to new results, viz. 〈f〉 = 〈〈• • 〈f〉 • •〉〉 for any physical quantity f. As for the physical balance laws of mass, momenta and energy this procedure led to the so-called Reynolds averaged balance equations (of Navier-Stokes and Fourier).

In the preceding chapters our focus was on the study of continuum theories of simple constituent media; mixtures, i. e., materials, which are composed of several different constituents or phases, were not considered. However, the latter play a central role in continuum physics and will briefly be touched upon in this chapter.

As will become apparent in later chapters a large number of physical processes is so conditioned that phase change phenomena play an important role in them. As an example we might mention the water content in a glacier or the melting and freezing processes that take place at the lower boundary of an ice shelf between the shelf and the ocean. The permafrost in arctic regions or at high altitudes in the mountains often thaws in summer and forms a phase change surface between the frozen and thawed soil. If the temperature in an ice sheet is close to or at the melting point then the heat due to internal dissipation will not be used to adjust the ice temperature to the new conditions but to melt ice. For these and many other reasons it is important that the phase change processes are well understood.

Five one-dimensional (1D) lake models were run for the open water season in 2006 for Lake Valkea-Kotinen (Finland) using on-lake measured meteorological forcing. The model results were validated using measurements of water temperature and of eddy covariance (EC) fluxes. The surface temperature is satisfactorily simulated by all models showing slight overestimation (by 0.1–1.1°C). Both sensible and latent heat fluxes are positively biased in respect to EC data, consistent with earlier studies. However, correlation coefficients between EC-fluxes and those simulated are relatively high ranging from 0.55 to 0.74. The skill to simulate vertical temperature profiles by different models is assessed as well. It is found that the lake models underestimate the EC-derived surface drag coefficient, however providing realistic temperature profiles. It is argued that the real momentum flux from the atmosphere is larger than simulated, however it is split up between the wave development and the acceleration of lake currents. Adopting the simple parameterisation for momentum flux partitioning in one of the models showed that this mechanism can be significant. Finally, the effect of including the lake bathymetry data in k-ɛ models was the drastic overheating of water below the thermocline. This is likely to be caused by omitting the heat flux at the lake margins. Thus, the parameterisation of heat flux at the lake’s margins should be included in the models; otherwise it is recommended to neglect bathymetry effects for such small water bodies as the Lake Valkea-Kotinen. Keywords: lakes, numerical modelling, stratification, surface fluxes (Published: 16 January 2014) Citation: Tellus A 2014, 66 , 21389, http://dx.doi.org/10.3402/tellusa.v66.21389 This publication is part of a Thematic Cluster entitled "Parameterization of lakes in numerical weather prediction and climate models". Read the other papers from this thematic cluster here

The extreme flood of Lake Constance in 1999 focused attention on the variability of annual lake levels. The year 1999 not only brought one of the highest floods of the last 180 years but also one of the earliest in the season. The 1999 extreme event was caused by heavy rainfall in the alpine and pre-alpine regions. The influence of precipitation in the two distinct regional catchments on lake level variations can be quantified by correlation analysis. The long-term variations in lake level and precipitation show similar patterns. This is seen through the use of spectral analysis, which gives similar bands of spectral densities for precipitation and lake level time series. It can be concluded from the comparison of these results with the analysis of climate change patterns in northern Europe, i.e. the index of the North Atlantic Oscillation, that the regional effects on lake level variations are more pronounced than those of global climate change.