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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: super-individual 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.
Model-derived relationships between chlorophyll a (Chl-a) and nutrients and temperature have fundamental implications for understanding complex interactions among water quality measures used for lake classification, yet accuracy comparisons of different approaches are scarce. Here, we (1) compared Chl-a model performances across linear and nonlinear statistical approaches; (2) evaluated single and combined effects of nutrients, depth, and temperature as lake surface water temperature (LSWT) or altitude on Chl-a; and (3) investigated the reliability of the best water quality model across 13 lakes from perialpine and central Balkan mountain regions. Chl-a was modelled using in situ water quality data from 157 European lakes; elevation data and LSWT in situ data were complemented by remote sensing measurements. Nonlinear approaches performed better, implying complex relationships between Chl-a and the explanatory variables. Boosted regression trees, as the best performing approach, accommodated interactions among predictor variables. Chl-a-nutrient relationships were characterized by sigmoidal curves, with total phosphorus having the largest explanatory power for our study region. In comparison with LSWT, utilization of altitude, the often-used temperature surrogate, led to different influence directions but similar predictive performances. These results support utilizing altitude in models for Chl-a predictions. Compared to Chl-a observations, Chl-a predictions of the best performing approach for mountain lakes (oligotrophic-eutrophic) led to minor differences in trophic state categorizations. Our findings suggest that both models with LSWT and altitude are appropriate for water quality predictions of lakes in mountain regions and emphasize the importance of incorporating interactions among variables when facing lake management challenges.
Precision agriculture (PA) strongly relies on spatially differentiated sensor information. Handheld instruments based on laser-induced breakdown spectroscopy (LIBS) are a promising sensor technique for the in-field determination of various soil parameters. In this work, the potential of handheld LIBS for the determination of the total mass fractions of the major nutrients Ca, K, Mg, N, P and the trace nutrients Mn, Fe was evaluated. Additionally, other soil parameters, such as humus content, soil pH value and plant available P content, were determined. Since the quantification of nutrients by LIBS depends strongly on the soil matrix, various multivariate regression methods were used for calibration and prediction. These include partial least squares regression (PLSR), least absolute shrinkage and selection operator regression (Lasso), and Gaussian process regression (GPR). The best prediction results were obtained for Ca, K, Mg and Fe. The coefficients of determination obtained for other nutrients were smaller. This is due to much lower concentrations in the case of Mn, while the low number of lines and very weak intensities are the reason for the deviation of N and P. Soil parameters that are not directly related to one element, such as pH, could also be predicted. Lasso and GPR yielded slightly better results than PLSR. Additionally, several methods of data pretreatment were investigated.