Phytoplankton

The unit models the photosynthesis, respiration and mortality of algae.

Description

Algae is a general name used to cover a wide range of phytoplankton. Phytoplanktons are microscopic organisms (plants and certain types of bacteria) that are in suspension and are liable to movement by currents. Algae are modelled in the 1D Water Quality Solver by a single representative species. The variable which is actually modelled is algal carbon, the part of the algal biomass (by dry weight) that is carbon. Algae concentration is often measured in terms of the amount of the chlorophyll present. The ratio of carbon to chlorophyll can vary from species to species.

Algae are able to create their own food by photosynthesis. They take up carbon dioxide from the surrounding water and, in the presence of sunlight, produce carbohydrates and release oxygen. Other nutrients such as nitrates and phosphates are required to synthesise amino acids and proteins. The rate of growth of algae therefore depends on the presence of adequate sunlight and sufficient nutrients in the water. It is known that there is an optimum light intensity at which maximum primary productivity occurs for a particular species. Lower or higher intensity gives a lower productivity. By combining this optimum intensity with the actual light intensity (see SOLAR RADIATION) a light induced growth limitation factor can be calculated.

Algal growth is also limited by the availability of nutrients. A Michaelis-Menten equation, using a half saturation constant, determines the limitation factor (see Equation 3 below) for each nutrient. A low half-saturation constant would mean that the nutrient is only limiting at very low concentrations. A high value means that production will only be unlimited at very high concentrations.

In the 1D Water Quality Solver, two nutrients are considered to be most important. These are nitrates and phosphates. In general these are the two nutrients that are most likely to limit growth. The PHYTOPLANKTON module only considers these two nutrients when calculating nutrient limitation. In the case of diatoms, silicates are an important nutrient because their cell walls are impregnated with silica. In cases where silicates may be a limiting nutrient then the SILICATE module must be used. The supply of phosphate may be limited by adsorption of phosphorus on to sediment particles. This process may be simulated using the ADSORBED Phosphorus module.

Production occurs at the rate determined by the limiting nutrient. Thus, for example, if the amount of nitrate would allow 70% of the maximum production, but the phosphate limits it to only 45% then the actual production would be 45% of the maximum. The amount of nutrient taken up by the algae depends on the proportion of the nutrient in the plant cells. This is expressed as the ratio of the nutrient to carbon in the cell. These ratios vary from species to species. Thus the total amount of nutrient taken up is equal to the algal carbon produced multiplied by the ratio of nutrient to carbon in the cell. The increase in algal carbon is given directly by the net production rate.

The amount of oxygen released by photosynthesis is also calculated as a proportion of the mass of carbon produced. 2.67g of oxygen are released for each gram of algal carbon produced. Algal carbon and oxygen are consumed by respiration. The respiration rate is a function of temperature (see below).

Algae are also depleted by death. They can either die naturally due to the cell ceasing to function or due to grazing by zooplankton. All such loss processes are combined into a single mortality process, described by a first order decay (see below). This is a broad assumption because algal mortality is not a constant process. Mortality will vary with the nutrient supply and the concentration of predators such as zooplankton. To model such losses accurately would require a more complex model including most of the food chain.

On death, the algal carbon becomes detrital carbon. This decays further, by a first order process, to return the nutrients back into the dissolved phase. Carbon is released to slow dissolved BOD, nitrogen to slow organic nitrogen and phosphorus to phosphates. As well as decaying, the detritus settles on to the bed and can release nutrients into the pore water. When simulating PHYTOPLANKTON, the 1D Water Quality Solver does not keep track of the total amounts of detrital nitrogen and phosphorus. The reason for this is that the amounts are related to the detrital carbon concentrations by the ratio of the relevant nutrients to carbon in the plant cells.

Equations

The maximum algal growth or rate of production per day (P_max) is expressed as a function of temperature:

        (1)

Where:

T = temperature (°C)

m, c = constants which depend on the species being modelled

Two sets of the constants, m and c, are given to the 1D Water Quality Solver. These represent growth above and below a critical temperature.

The light induced growth limitation factor is derived using the Steele (1965) formulation:
                                                         (2)

Where:

μ_light = light limitation factor at some depth, z, below the surface

I = intensity of light at some depth, z, below the surface (kJ/cm²)

I_max = light intensity which will produce maximum productivity (kJ/cm²)

The equation is integrated over the depth to give an average value for the whole water column. See SOLAR RADIATION for a full description of the light intensity calculation.

Nutrient limitation factors are calculated according to a Michaelis-Menten equation:

                                                      (3)

Where:

μ_nutrient  = nutrient limitation factor

C_nutrient  = concentration of the nutrient (mg/l)

k_nutrient  = half saturation constant for the nutrient (mg/l)

The actual daily rate of production P is then given by:
                                          (4)

Where:

μ_N, μ_P, μ_SI = nutrient limitation factors due to nitrates, phosphates and silicates respectively. Note that μ is set to one when the SILICATE module is not simulated.

Algal growth requires nutrients - nitrogen, phosphorus and silicon if the SILICATE module is activated. The amounts of these nutrients taken up by the algae are controlled by the nutrient to carbon ratios (rphtn, rphtp, rphts). Nitrogen is taken up from nitrate-nitrogen; phosphorus from orthophosphate; and silicon from silicate. The rate of uptake is given by (taking nitrogen as an example)

                                                          (5)

Where:
AC= concentration of algal carbon. Production can be further limited if effective growth requires more nutrients than are available.

Algal respiration is a function of temperature:

 (6)

Where:

R_T= respiration constant at T°C

R₂₀= respiration constant at 20°C

Q₁₀= parameter which controls the temperature dependency. Its effect is to double the rate for a 10C rise in temperature.

Algal mortality is given by a first order process with a fixed rate constant M. This is also the rate of production of detrital carbon. Thus the nett production of phytoplankton algal carbon, AC, is given by:

                                                             (7)

Detrital carbon is produced on the death of algal carbon at a rate given by the mortality constant M. It is then oxidised releasing nutrients into the water column. The rate constant, K , is given by

                                                                 (8)

Where:

K _dc = rate constant for detrital decay at temperature θ°C

K _{dc 20} = rate constant for detrital decay at temperature 20°C

α _dc = temperature coefficient for decay of detrital carbon

In addition, detrital carbon can settle with a settling velocity v, ultimately depositing onto the bottom of the channel.

So the net change in suspended detrital carbon is given by:

                                              (9)

Where:

d = depth of water

v= settling velocity of detrital carbon.

Detrital carbon on the bottom of the channel is held in the variable ’Bed detrital carbon’, DC. This decays at the same rate as the suspended matter. The nett change in bed detrital carbon is given by:

                                                      (10)

The decay of detritus releases nutrients into the water column (bed detritus releases nutrients into the pore water). Nitrogen is recycled as slow organic nitrogen, phosphorous as orthophosphate and silicon as silica. The proportions of the detritus that are nitrogen, phosphorus or silicon are governed by the nutrient to carbon ratios.

If the MACROPHYTE or BENTHIC ALGAE options are present then additional variables indicating the amount of nitrogen, phosphorus and silicon contained in the detritus are required, reflecting the different nutrient to carbon ratios in the algae and plants.

The production respiration of phytoplankton and the decay of detritus affect the oxygen balance as follows:
                                     (11)

The factor 8/3 represents the equivalent mass of oxygen utilised or produced per gram carbon dioxide produced during respiration and detrital decay or consumed during photosynthesis.

General

The PHYTOPLANKTON module must be run in conjunction with the OXYGEN WITH SEDIMENT and SOLAR RADIATION modules. If the simulation of the MACROPHYTES or BENTHIC ALGAE modules is required, then the PHYTOPLANKTON module must be included in the simulation. If silicon is known to be an important nutrient for the particular type of algae then the SILICATE module should be included. If the adsorption of phosphorus is thought to limit the supply of phosphates available for uptake by the algae then the ADSORBED PHOSPHORUS module should be included in the simulation. The PHYTOPLANKTON module also simulates the following transported variable names:

• Phytoplankton (mg/l)
• Phosphate (mg/l)
• Detrital carbon (mg/l)

The PHYTOPLANKTON module simulates the following variables on the river bed:

• Pore water orthophosphate (mg/l)
• Fluffy detrital carbon (g/m)
• Bed detrital carbon (g/m)