A large number and wide variety of lake ecosystem models have been developed and published during the past four decades. We identify two challenges for making further progress in this field. One such challenge is to avoid developing more models largely following the concept of others ('reinventing the wheel'). The other challenge is to avoid focusing on only one type of model, while ignoring new and diverse approaches that have become available ('having tunnel vision'). In this paper, we aim at improving the awareness of existing models and knowledge of concurrent approaches in lake ecosystem modelling, without covering all possible model tools and avenues. First, we present a broad variety of modelling approaches. To illustrate these approaches, we give brief descriptions of rather arbitrarily selected sets of specific models. We deal with static models (steady state and regression models), complex dynamic models (CAEDYM, CE-QUAL-W2, Delft 3D-ECO, LakeMab, LakeWeb, MyLake, PCLake, PROTECH, SALMO), structurally dynamic models and minimal dynamic models. We also discuss a group of approaches that could all be classified as individual based: superindividual models (Piscator, Charisma), physiologically structured models, stage-structured models and traitbased models. We briefly mention genetic algorithms, neural networks, Kalman filters and fuzzy logic. Thereafter, we zoom in, as an in-depth example, on the multi-decadal development and application of the lake ecosystem model PCLake and related models (PCLake Metamodel, Lake Shira Model, IPH-TRIM3D-PCLake). In the discussion, we argue that while the historical development of each approach and model is understandable given its 'leading principle', there are many opportunities for combining approaches. We take the point of view that a single 'right' approach does not exist and should not be strived for. Instead, multiple modelling approaches, applied concurrently to a given problem, can help develop an integrative view on the functioning of lake ecosystems. We end with a set of specific recommendations that may be of help in the further development of lake ecosystem models.

In 2012, the Convergent Cross Mapping method for finding a causal relationship between system variables from their time series was published. This method is widely used in the study of systems of various nature - from assessing the effect of cosmic radiation on the climate, to the study of cerebral activity. The relevance and prospects of using this method prompted us to master it and to apply it to identifying causal relationships between the variables of the “biosphere-climate” system. The obtained results seemed suspicious and forced us to check carefully the adequacy of the CCM conclusions in relation to various model systems. This paper presents examples of model situations when the method gives false estimates of the presence of causal relationships and offers a possible explanation for the causes of false estimates appearance.

A one-dimensional numerical model and a two-dimensional numerical model of the hydrodynamic and thermal structure of Lake Shira during summer have been developed, with several original physical and numerical features. These models are well suited to simulate the formation and dynamics of vertical stratification and provide a basis for an ecological water-quality model of the lake. They allow for the quantification of the vertical mixing processes that govern not only the thermal structure but also the nutrient exchange, and more generally, the exchange of dissolved and particulate matter between different parts of the lake. The outcome of the calculations has been compared with the field data on vertical temperature and salinity distributions in Lake Shira. Lake Shira is meromictic and exhibits very stable annual stratification. The stratification is so stable because of the high salinity of the water. If the water in Lake Shira were fresh and other parameters (depth, volume, and meteorology) were the same, as now, the lake would be mixed in autumn. Using the newly developed models and using common meteorological parameters, we conclude that Lake Shira will remain stratified in autumn as long as the average salinity is higher than 3%.

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