Most inland waters in Germany did not meet the good ecological status requirements stipulated in the EU Water Framework Directive for 2015. It was previously assumed that phosphorus is the primary determinant of water quality. In the BMBF funded project NITROLIMIT (www.nitrolimit.de) it has been proved that nitrogen is also a crucial control variable for many surface waters and its reduction ecologically meaningful. This has led to demands for procedures to ensure the reduction of nitrogen input.
Scientists from different disciplines and seven scientific institutions worked together on interrelated research modules to clarify whether nitrogen reduction is ecologically meaningful and economically feasible. Modelling was part of research module 2 that aimed to fill knowledge gaps about N and Pturnover processes.
The "toymodel" found at these pages aims to demonstrate some of the main scientific questions:
Please note: this model is an extremely simplified representation of a natural lake. It aims to support understanding of main processes, and especially their dynamics and complexity. However, the model presented here is not able to make ultimate predictions.
Langer See (Brandenburg, Germany), one of the research objects of the project.
The model describes nutrient turnover, growth of phytoplankton and zooplankton, and its sedimentation and remineralization in a shallow lake. Main ideas were borrowed from a simplified version of the BELAMO lake model (Reichert, Mieleitner and Schuwirth 2016), while we added some more emphasis on processes in shallow lakes.The present version contains the following state variables.
Three functional groups of phytoplankton and one zooplankton group:
Sedimentation and remineralization were of special interest, so we distinguish different fractions of particulate organic matter. The model considers a degradable and a nondegradable (inert) fraction and keeps track from which living compartment (algae group or zooplankton) this material originates:
External forcing variables include water inflow, import of nutrients, organisms and organic matter; temperature, solar radiation (light), and light absorption by ice covering during the winter.
Figure 1 shows a simplified schematic representation of the model, and Figure 2 the socalled stoichiometry matrix. This matrix indicates which variables influence each other and in which direction.
Fig 1: Simplified representation of the most important model compartments and their connections.
Process  HPO_{4}^{2}  ALG_F1  ALG_F2  ALG_F3  ZOO  O_{2}  NH_{4}^{+}  NO_{3}^{}  POMD_{ALG_F1}  POMI_{ALG_F1}  POMD_{ALG_F2}  POMI_{ALG_F2}  POMD_{ALG_F3}  POMI_{ALG_F3}  POMD_{ZOO}  POMI_{ZOO}  SPOMD  SPOMI 

g_ALG_F1_NH4  ∇  Δ  


Δ  ∇  










g_ALG_F2_NH4  ∇  
Δ  

Δ  ∇  










g_ALG_F3_NH4  ∇  

Δ  
Δ  ∇  










g_ALG_F1_NO3  ∇  Δ  


Δ  
∇  









g_ALG_F2_NO3  ∇  
Δ  

Δ  
∇  









g_ALG_F3_NO3  ∇  

Δ  
Δ  
∇  









g_ALG_F1_N2  ∇  Δ  


Δ  











r_ALG_F1  Δ  ∇  


∇  Δ  










r_ALG_F2  Δ  
∇  

∇  Δ  










r_ALG_F3  Δ  

∇  
∇  Δ  










d_ALG_F1  
∇  





Δ  Δ  







d_ALG_F2  

∇  






Δ  Δ  





d_ALG_F3  


∇  







Δ  Δ  



g_ZOO_ALG_F1  
∇  

Δ  


Δ  Δ  







g_ZOO_ALG_F2  

∇  
Δ  




Δ  Δ  





g_ZOO_ALG_F3  


∇  Δ  






Δ  Δ  



r_ZOO  Δ  


∇  ∇  Δ  










d_ZOO  



∇  








Δ  Δ  

nitri  




∇  ∇  Δ  









miner_POMD_ALG_F1  Δ  



∇  Δ  
∇  








miner_POMD_ALG_F2  Δ  



∇  Δ  


∇  






miner_POMD_ALG_F3  Δ  



∇  Δ  




∇  




miner_SPOMD  Δ  



∇  Δ  








∇  
sed_POMD_ALG_F1  







∇  






Δ  
sed_POMD_ALG_F2  









∇  




Δ  
sed_POMD_ALG_F3  











∇  


Δ  
sed_POMI_ALG_F1  








∇  






Δ 
sed_POMI_ALG_F2  










∇  




Δ 
sed_POMI_ALG_F3  












∇  


Δ 
ex_O2  




Δ  











inflow  ∇  ∇  Δ  ∇  ∇  
Δ  Δ  ∇  
∇  
∇  
∇  


miner_POMD_ZOO  Δ  



∇  Δ  






∇  


sed_POMD_ZOO  













∇  
Δ  
sed_POMI_ZOO  














∇  
Δ 
sed_ALG_F1  
∇  













Δ  Δ 
sed_ALG_F2  

∇  












Δ  Δ 
sed_ALG_F3  


∇  











Δ  Δ 
denitri_1  






∇  









zin  



Δ  












Fig2: Schematic representation of the model stoichiometry. Triangle up: positive dependency, triangle down: inverse dependency.
Reset to defaults
This is a derived work from the NITROLIMIT project, funded by the German Ministry of Education and Research (BMBF) under grant no. 033W015EN. The model is based on a teaching version of the BELAMO lake model (cf. publications of Reichert, Omlin, Mieleitner, Dietzel and Schuwirth below), with some own modifications from our group: Hannes Feldbauer, David Kneis, Thomas Petzoldt, Yue Zhao. Please consult the papers and web pages of our colleagues from EAWAG and ETH Zurich for more background information about the model.
Data were kindly provided by BTU CottbusSenftenberg, Department of Freshwater Conservation. Many thanks to Jacqueline Rücker, Björn Grüneberg, Andrew Dolman, Claudia Wiedner and Brigitte Nixdorf.
Note: The current version of model is intended for demonstration purposes only, not for predictions. It exemplifies a specific state of the discussion process and we are sill continuing to make the process descriptions more realistic. Our main contribution to modelling and process understanding in Nitrolimit part 2 was a 1D model of the sediment water interface, that needs more computer power. Its description and results can be found in written form in the final project report and in scientific publications, listed at the NITROLIMIT project page.
Please contact us in case of comments and questions.
Dietzel, A., Reichert, P. (2012) Calibration of computationally
demanding and structurally uncertain models with an application to a
lake water quality model Environmental Modelling and Software 38,
129146.
Kneis, D. (2016) rodeo: A Code Generator for ODEBased Models. R package
version 0.6. https://github.com/dkneis/rodeo
Mieleitner, J., Reichert, P. (2008) Modelling functional groups of
phytoplankton in three lakes of different trophic state. Ecological
Modelling 211, 279291.
Nixdorf, B., Grüneberg, B. & Rücker, J. (2016) Bilanzierung der
saisonalen Stickstoffein und austräge sowie deren Umsetzungen in einem
eutrophen Flachsee. Erweiterte Zusammenfassungen der Jahrestagung 2015
in Essen. Hardegsen: 6976.
Omlin, M.; Reichert, P., Forster, R. (2001) Biogeochemical model of Lake
Zürich: model equations and results. Ecological Modelling 141, 77103
Omlin, M.; Brun, R., Reichert, P. (2001) Biogeochemical Model of Lake
Zürich: Sensitivity, Identifiability and Uncertainty Analysis.
Ecological Modelling 141, 105123
Reichert, P., Schuwirth, N. (2010) A generic framework for deriving
process stoichiometry in environmental models. Environmental Modelling
and Software 25, 12411251
Reichert, P., Mieleitner, J. and Schuwirth, N. (2016) Modelling Aquatic
Ecosystems. Course 701042600 ETH Zürich. http://www.eawag.ch/en/department/siam/teaching/modellingaquaticecosystems/
Rücker, J., Knie, M., Voss, M., Martienssen, M., Grüneberg, B.,
Kolzau, S., Nixdorf, B. (2016) Abschätzung des Stickstoffeintrages durch
planktische Cyanobakterien (Nostocales). Erweiterte Zusammenfassungen
der Jahrestagung 2015 in Essen. Hardegsen: 170177.
Soetaert, K.; Petzoldt, T., Setzer, R. W. (2010) Solving Differential
Equations in R: Package deSolve. Journal of Statistical Software 33(9),
125. http://dx.doi.org/10.18637/jss.v033.i09

