Module WaterQuality

Overview

The ecological model described in Module Water Quality is adapted from EPA (1985) and pertain to the category of ecosystem simulations models i.e. sets of conservation equations describing as adequately as possible the working and the interrelationships of real ecosystem components. The nitrogen, oxygen, phosphorus and silica biogeochemical cycles are included.

Many of the equations are written as dependent on a regulating factor, which contains the functional response of the organism to some environmental parameters such as light, nutrients or temperature. When growth is a function of many resources, there is a large range of functional forms that might express the joint dependence. To control the various possibilities, it is common to think of separate resources as limiting factors reducing some theoretical maximum growth rate - factors that can be determined separately and the combined by a small number of ways.

Each growth limitation factor can range from a value of 0 to 1. A value of 1 means the factor does not limit growth (i.e. is at optimum intensity, nutrients are available in excess, etc) and a value of 0 means the factor is so severely limiting that growth is inhibit entirely. The model uses:

• A minimum formulation only for nutrients limitation, in which the most severely limiting factor alone is assumed to limit growth. This formulation is based on “Liebig’s law of the minimum” which states that the factor in shortest supply will control the growth of algae;
• A multiplicative formulation for the three main limiting factors (light, nutrients and temperature) in which all factors are multiplied together. This approach assumes that several factors in short supply will more severely limit growth than a single factor in short supply. The major criticism of this approach is that the computed growth rates may be excessively low when several factors are limiting. Also, the severity of the reduction increases with the number of limiting nutrients considered in the model, making comparison between models difficult.

State variables

Organisms

Phytoplankton - flagellates and diatoms

Flagellates and Diatoms are described in terms of carbon concentration (mgC / l). The model assumes three limitations affecting the organisms maximum growth rate, $\mu^{\max }_x$ : Temperature $\psi (E)_x$, light $\psi (E)_x$ and nutrient limitation $\psi (N)_x$, which is computed as the minimum of $\psi (N)_x$, $\psi (P)_x$ (and $\psi (Si)_x$ when simulating diatoms. These two groups of primary producers share the same formulations for the most part of the processes differing just in terms of parameters used by the model. The model is able to consider either one or the two groups of primary producers. The simulation of the primary producers (Flagellates and/or Dioatoms) is developed with the following considerations (Figure 3):

• Organisms consume inorganic nutrients (ammonia and nitrate from the nitrogen cycle and inorganic phosphorus from the phosphorus cycle, and silicate in the case of diatoms) depending on their availability;
• Organisms’ growth is also influenced by the temperature and availability of light as a source of energy for photosynthesis;
• Dissolved oxygen is produced during respiration process consumes oxygen and produces ammonia;
• By excretion phytoplankton produces dissolved organic material (DONr, DONnr, DOPr and DOPnr);
• By mortality phytoplankton increases the dissolved organic material and the particulate organic material (PON and POP) in the system;
• By zooplankton grazing, the concentration of flagellates and diatoms decreases.
• By ciliates grazing, the concentration of flagellates decreases;
• Settling process is modeled in Module WaterProperties as for any other particulate property in the model.

The rate equation used by the model to compute flagellates and diatoms evolution and the processes formulations are synthetically described in the next tables.

Zooplankton - Micro- and Mesozooplankton

Like in primary producers, the two zooplankton groups have similar formulation differing in terms of specific parameters and grazing possibilities. Globally, zooplankton (micro and mesozooplankton) considers:

• Organisms’ growth is influenced by the temperature and prey concentration;
• Respiration process consumes oxygen and produces ammonia;
• Excretion represents a source of dissolved and particulate organic material (DONr, DONnr, DOPr and DOPnr) in the system;
• By mortality, zooplankton increases the particulate organic material (PON and POP);
• Microzooplankton grazing on bacteria and flagellates;
• Mesozooplankton grazing on diatoms and flagellates.

Bacteria

In terms of simulating bacteria the model considers:

• The specific uptake rate of bacteria is dependent on resource availability (organic substrate), accordingly to a Michaelis-Menten function, and on temperature;
• For ammonia uptake to take place, DOM or POM concentrations must be higher than the bacteria minimum substrate concentration needed for growth, representing the Carbon limitation for bacteria growth;
• For DOM or/and POM uptake to take place, ammonium concentrations must be higher than the bacteria minimum substrate concentration needed for growth, representing the Nitrogen limitation for bacteria growth;
• Total uptake rate of bacteria is the sum of the specific uptake rate for each one of the nutrient sources (DOMnr, ammonium, and POM);
• Nitrogen uptake is converted in carbon units using the N:C ratio of bacteria;
• Excretion represents a source of dissolved organic material (Non-Refractory Dissolved Organic Nitrogen) in the system;
• By mortality, bacteria increases the particulate organic material (Particulate Organic Nitrogen) and ammonia.
• Microzooplankton grazing on bacteria.

References

Bowie G L, Mills W B, Porcella D B, Cambell C L, Pagendorf J R, Rupp G L, Johnson K M, Chan P W, Gherini S A, Chamberlin C E (1985) Rates, Constants and Kinetic Formulations in Surface Water Quality Modelling. U.S. Environmental Protection Agency