Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.Comment: 19 pages, 7 figure

Data Descriptor : A European Multi Lake Survey dataset of environmental variables, phytoplankton pigments and cyanotoxins

Under ongoing climate change and increasing anthropogenic activity, which continuously challenge ecosystem resilience, an in-depth understanding of ecological processes is urgently needed. Lakes, as providers of numerous ecosystem services, face multiple stressors that threaten their functioning. Harmful cyanobacterial blooms are a persistent problem resulting from nutrient pollution and climate-change induced stressors, like poor transparency, increased water temperature and enhanced stratification. Consistency in data collection and analysis methods is necessary to achieve fully comparable datasets and for statistical validity, avoiding issues linked to disparate data sources. The European Multi Lake Survey (EMLS) in summer 2015 was an initiative among scientists from 27 countries to collect and analyse lake physical, chemical and biological variables in a fully standardized manner. This database includes in-situ lake variables along with nutrient, pigment and cyanotoxin data of 369 lakes in Europe, which were centrally analysed in dedicated laboratories. Publishing the EMLS methods and dataset might inspire similar initiatives to study across large geographic areas that will contribute to better understanding lake responses in a changing environment.Peer reviewe

Stratification strength and light climate explain variation in chlorophyll a at the continental scale in a European multilake survey in a heatwave summer

To determine the drivers of phytoplankton biomass, we collected standardized morphometric, physical, and biological data in 230 lakes across the Mediterranean, Continental, and Boreal climatic zones of the European continent. Multilinear regression models tested on this snapshot of mostly eutrophic lakes (median total phosphorus [TP] = 0.06 and total nitrogen [TN] = 0.7 mg L−1), and its subsets (2 depth types and 3 climatic zones), show that light climate and stratification strength were the most significant explanatory variables for chlorophyll a (Chl a) variance. TN was a significant predictor for phytoplankton biomass for shallow and continental lakes, while TP never appeared as an explanatory variable, suggesting that under high TP, light, which partially controls stratification strength, becomes limiting for phytoplankton development. Mediterranean lakes were the warmest yet most weakly stratified and had significantly less Chl a than Boreal lakes, where the temperature anomaly from the long-term average, during a summer heatwave was the highest (+4°C) and showed a significant, exponential relationship with stratification strength. This European survey represents a summer snapshot of phytoplankton biomass and its drivers, and lends support that light and stratification metrics, which are both affected by climate change, are better predictors for phytoplankton biomass in nutrient-rich lakes than nutrient concentrations and surface temperature