Klaus Jöhnk

Chaos in a long-term experiment with a plankton community

Mathematical models predict that species interactions such as competition and predation can generate chaos. However, experimental demonstrations of chaos in ecology are scarce, and have been limited to simple laboratory systems with a short duration and artificial species combinations. Here, we present the first experimental demonstration of chaos in a long-term experiment with a complex food web. Our food web was isolated from the Baltic Sea, and consisted of bacteria, several phytoplankton species, herbivorous and predatory zooplankton species, and detritivores. The food web was cultured in a laboratory mesocosm, and sampled twice a week for more than 2,300 days. Despite constant external conditions, the species abundances showed striking fluctuations over several orders of magnitude. These fluctuations displayed a variety of different periodicities, which could be attributed to different species interactions in the food web. The population dynamics were characterized by positive Lyapunov exponents of similar magnitude for each species. Predictability was limited to a time horizon of 15–30 days, only slightly longer than the local weather forecast. Hence, our results demonstrate that species interactions in food webs can generate chaos. This implies that stability is not required for the persistence of complex food webs, and that the long-term prediction of species abundances can be fundamentally impossible.

Water Management Strategies Against Toxic Microcystis Blooms In The Dutch Delta

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.

Water level variability and trends in Lake Constance in the light of the 1999 centennial flood

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.

LakeMIP Kivu: evaluating the representation of a large, deep tropical lake by a set of one-dimensional lake models

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 models 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.

On interfacial transition conditions in two phase gravity flow

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.We show that the posed physical problem admits a mathematical solution only in the case that the interface momentum production is non-zero.

Simulation of surface energy fluxes and stratification of a small boreal lake by a set of one-dimensional models

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 lakes 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.

On the Role of Mechanical Interactions in the Steady-State Gravity Flow of a Two-Constituent Mixture down an Inclined Plane

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. δp, where δ 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 δ=1, yield only pure constituent-1 or pure constituent-2 ‘mixtures’. On the other hand, numerical solution of these momentum balances for δ = 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 δ > 0.95, i.e. in this case the sediment remains concentrated at the bottom of the layer.

Assessment of ecosystem health of tropical shallow waterbodies in eastern India using turbulence model

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.

Boom-bust dynamics in biological invasions: towards an improved application of the concept

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.

Meromixis in mining lake Waldsee, Germany: hydrological and geochemical aspects of stratification

Since meromixis was first described by FrNDENEGG (1932), several natural meromictic lakes have been described (HoNGVE 2002, HAKALA et al. 2004). Meromixis can also be a common feature in mining lakes. A certain morphometry (high depth, small surface area) and the inflow of highly mineralised groundwater promote the formation of permanent density stratification. A well-known example for artificial meromixis is the Island Copper Mine (Vancouver Island, BC/Canada; FrsHER & LAWRENCE 2000). In the Lusatian mining district, where lignite mining has lasted for more than 200 years, several meromictic mining lakes are known. Some have shown a permanent density stratification, such as Lake Lugteich (NrxDORF et al. 2001); others for a certain period, such as Lake Plessa ll1 (KARAKAS et al. 2003). The meromixis ofthe Lusatian mining lakes originates mainly from interna! geochemical and biological reactions with the transformation of iron as the predominant process (BoEHRER & ScHULTZE 2005). We studied the influence of groundwater inflow and internai geochemical processes that contribute to the development of meromixis in a small meromictic lake of the Lusatian mining district.