PCLake is a dynamic,

mathematical model A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...

used to study

eutrophication Eutrophication is the process by which an entire body of water, or parts of it, becomes progressively enriched with minerals and nutrients, particularly nitrogen and phosphorus. It has also been defined as "nutrient-induced increase in phytopla ...

effects in shallow

lake A lake is an area filled with water, localized in a basin, surrounded by land, and distinct from any river or other outlet that serves to feed or drain the lake. Lakes lie on land and are not part of the ocean, although, like the much large ...

s and ponds. PCLake models explicitly the most important biotic groups and their interrelations, within the general framework of

nutrient cycle A nutrient cycle (or ecological recycling) is the movement and exchange of inorganic and organic matter back into the production of matter. Energy flow is a unidirectional and noncyclic pathway, whereas the movement of mineral nutrients is cycli ...

s. PCLake is used both by scientist and water managers. PCLake is in 2019 extended to PCLake+, which can be applied to stratifying lakes.

Background

Typically, shallow lakes are in one of two contrasting

alternative stable state In ecology, the theory of alternative stable states (sometimes termed alternate stable states or alternative stable equilibria) predicts that ecosystems can exist under multiple "states" (sets of unique biotic and abiotic conditions). These alterna ...

s: a clear state with submerged macrophytes and piscivorous fish, or a turbid state dominated by phytoplankton and benthivorous fish. A switch from one state to the other is largely driven by the input of nutrients (

phosphorus Phosphorus is a chemical element with the symbol P and atomic number 15. Elemental phosphorus exists in two major forms, white phosphorus and red phosphorus, but because it is highly reactive, phosphorus is never found as a free element on Ear ...

and

nitrogen Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at se ...

) to the ecosystem. If the nutrient loading exceeds a critical value, eutrophication causes a switch from the clear to the turbid state. As a result of urban water pollution and/or

intensive agriculture Intensive agriculture, also known as intensive farming (as opposed to extensive farming), conventional, or industrial agriculture, is a type of agriculture, both of crop plants and of animals, with higher levels of input and output per unit of ag ...

in catchment areas, many of the world’s shallow lakes and ponds are in a eutrophic state with turbid waters and poor ecological quality. In this turbid state, the lake also becomes subject to algal blooms of toxic

cyanobacteria Cyanobacteria (), also known as Cyanophyta, are a phylum of gram-negative bacteria that obtain energy via photosynthesis. The name ''cyanobacteria'' refers to their color (), which similarly forms the basis of cyanobacteria's common name, blu ...

(also called blue-green algae). Recovery of the clear state however is difficult as the critical nutrient loading for the switch back is often found to be lower than the critical loading towards the turbid state. Lowering the nutrient input thus does not automatically lead to a switch back to the clear water phase. Hence, the system shows

hysteresis Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of ...

Application

PCLake is designed to study the effects of eutrophication on shallow lakes and ponds. On one hand, the model is used by scientists to study the general behavior of these ecosystems. For example, PCLake is used to understand the phenomena of alternative stable states and hysteresis, and in that light, the relative importance of lake features such as water depth or fetch length. Also the potential effects of climate warming for shallow lakes have been studied. On the other hand, PCLake is applied by lake water resource managers that consider the turbid state as undesirable. They can use the model to define the critical loadings for their specific lakes and evaluate the effectiveness of restoration measures. For this purpose also a meta-model has been developed. The meta-model can be used by water managers to derive an estimate of the critical loading values for a certain lake based on only a few important parameters, without the need of running the full dynamical model.

Model content

Mathematically, PCLake is composed of a set of coupled

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

s. With a large number of

state variables A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of a ...

(>100) and

parameters A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...

(>300), the model may be characterized as relatively complex. The main biotic variables are

phytoplankton Phytoplankton () are the autotrophic (self-feeding) components of the plankton community and a key part of ocean and freshwater ecosystems. The name comes from the Greek words (), meaning 'plant', and (), meaning 'wanderer' or 'drifter'. Ph ...

and submerged aquatic vegetation, describing

primary production In ecology, primary production is the synthesis of organic compounds from atmospheric or aqueous carbon dioxide. It principally occurs through the process of photosynthesis, which uses light as its source of energy, but it also occurs through c ...

. A simplified

food web A food web is the natural interconnection of food chains and a graphical representation of what-eats-what in an ecological community. Another name for food web is consumer-resource system. Ecologists can broadly lump all life forms into one ...

is made up of

zooplankton Zooplankton are the animal component of the planktonic community ("zoo" comes from the Greek word for ''animal''). Plankton are aquatic organisms that are unable to swim effectively against currents, and consequently drift or are carried along by ...

, zoo

benthos Benthos (), also known as benthon, is the community of organisms that live on, in, or near the bottom of a sea, river, lake, or stream, also known as the benthic zone.denitrification Denitrification is a microbially facilitated process where nitrate (NO3−) is reduced and ultimately produces molecular nitrogen (N2) through a series of intermediate gaseous nitrogen oxide products. Facultative anaerobic bacteria perform denitr ...

). Inputs to the model are: lake hydrology, nutrient loading, dimensions and sediment characteristics. The model calculates

chlorophyll Chlorophyll (also chlorophyl) is any of several related green pigments found in cyanobacteria and in the chloroplasts of algae and plants. Its name is derived from the Greek words , ("pale green") and , ("leaf"). Chlorophyll allow plants to a ...

-a, transparency, cyanobacteria, vegetation cover and fish biomass, as well as the concentrations and fluxes of nutrients N, P and Si, and oxygen. Optionally, a wetland zone with marsh vegetation and water exchange with the lake can be included. PCLake is calibrated against nutrient, transparency, chlorophyll and vegetation data on more than 40 European (but mainly Dutch) lakes, and systematic sensitivity and uncertainty analysis have been performed.Janse JH and others, 2010. Estimating the critical phosphorus loading of shallow lakes with the ecosystem model PCLake: sensitivity, calibration and uncertainty. Ecological Modelling 221: 654–665 Although PCLake is primarily used for Dutch lakes, it is likely that the model is also applicable to comparable non- stratifying lakes in other regions, if parameters are adjusted or some small changes to the model are made.

Model development

The first version of PCLake (by then called PCLoos) was built in the early 1990s at the

Netherlands National Institute for Public Health and the Environment The National Institute for Public Health and the Environment ( nl, Rijksinstituut voor Volksgezondheid en Milieu or simply RIVM) is a Dutch research institute that is an independent agency of the Ministry of Health, Welfare and Sport. RIVM perfo ...

(RIVM), within the framework of a research and restoration project on Lake Loosdrecht. It has been extended and improved since then. Parallel to PCLake, PCDitch was created, which is an ecosystem model for ditches and other linear water bodies. The models were further developed by dr. Jan H. Janse and colleagues at the

Netherlands Environmental Assessment Agency The Netherlands Environmental Assessment Agency ( nl, Planbureau voor de Leefomgeving - abbr. ''PBL'') is a Dutch research institute that advises the Dutch government on environmental policy and regional planning issues. The research fields includ ...

(PBL), formerly part of the RIVM. Since 2009, the model is jointly owned by PBL and the Netherlands Institute of Ecology, where further development and application of PCLake is taking place, related to aquatic-ecological research.

References

{{Reflist, 2 Mathematical modeling Environmental chemistry

Background

Application

Model content

Model development

See also

References