9.2. Primary producer growth
The equations and processes governing primary production in Atlantis have been adopted from the PPBIM model of Murray and Parslow (1997). Primary production processes are executed by Primary_Production() routine in atprocess.c
Growth of a primary producer pp is determined by multiplying the biomass of pp by the maximum specific growth rate (mum) and by three additional potentially limiting factors:
- nutrient limitation factor
- light limitation factor
- space limitation factor for benthic macrophytes
- optional eddy scalar, representing enhancement of primary production by eddies
- optional pH scalar, accounting for possible effects of acidification on primary production
\[G_{pp} = mum \cdot B_{PP} \cdot \delta_{light} \cdot \delta_{nutrient} \cdot \delta_{space} \cdot \delta_{eddy} \cdot pHscalar\]
The mum parameter defines the maximum growth rate per day (mgN day-1).
Multiplicative model for nutrient and light co-limitation (from Murray and Parslow, 1997, page 26):
“Multiplicative models for nutrient and light co-limitation have been widely used (Fasham et al. 1990). A potential problem with multiplicative interactions involving several factors is that predictive growth rates become very low when each factor is moderately limiting. An alternative, Liebig's law of the minimum (ie. multiply mum by the smallest factor) is more often applied to interactions among multiple nutrients.”
Atlantis has different options to design limitation by different nutrients (N, Si and P if phosphorus is tracked), set by the flagnut parameter, with choices of multiplicative or Leibig (minimum nutrient) limitation. However, this does not apply to combined limitation by nutrient, light and space, where simple multiplication is used. The quote above suggests caution when applying multiple limitations on growth, and careful assessment of whether the multiple impacts do not lead to overly constraining limitation.
9.2.1. Primary producer nutrient limitation
The nutrient limitation δnutrient scalar in case of limitation based on N only is calculated as
\[\delta_{nutrient} = \frac{DIN}{KN + DIN}\]
where DIN = NH3+NO3 (ammonia and nitrate concentration) and KN is the half saturation constant of nutrient uptake (KN_XXX) in mgN m-3
Nutrient limitation is calculated by the Nutrient_Lim() routine in atprocess.c
When phytoplankton is limited by multiple nutrients, such as N and Si in the case of diatoms, the choice of limitation equation is set by the flagnut parameter. This parameter calls three types of nutrient limitation options – Leibig, multicative, and the ERSEM WQI based option. Only the first two options have been more widely used, whereas the third version has been implemented only for testing purposes. The nutrient limitation scalar for the three options is calculated as:
\[\delta_{nutrient} = \min\left( \frac{DIN}{KN + DIN},\frac{Si}{KS + Si} \right)\ \ \ \ \ \ \ \ \ \ \ \ \ if\ Leibig\ limitation\ is\ used\ (flagnut = 0)\]
\[\delta_{nutrient} = \sqrt{\frac{DIN}{KN + DIN} \cdot \frac{Si}{KS + Si}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ if\ multicative\ limitation\ is\ used\ (flagnut = 1)\]
\[\delta_{nutrient} = \frac{2}{\left( \frac{DIN}{KN + DIN} + \frac{Si}{KS + Si} \right)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ if\ WQI\ \ limitation\ is\ used\ (flagnut = 2)\]
For illustration, assuming a hypothetical case of DIN and Si concentrations of 100 mg m-3 and half saturation values for N and Si at 50 mg m-3 and 20 mg m-3 the three limitation cases would results in scalars of 0.67, 0.75 and 1.41.
Atlantis has an optional nutrient limitation for one additional tracer of micronutrients (currently used for iron). This option is set when flagmicro=1. If micronutrient limitation is used, half-saturation constants (KF_XXX) should be provided for all primary producer groups. Limitation by additional nutrients will be done according to the flagnut option described above.
In models that track P and C (TrackAtomicRatio =1 in run.prm file) primary production will also be limited by P and C. Further details are available on the wiki.
9.2.2. Primary producer light limitation
Photosynthesis in the model is potentially light-limited and the available suitable light (W m-2) – the photosytenthically active radiation (PAR) - in the water column and at the sediment surface is modelled explicitly. The light limitation δlight factor is calculated in Light_Lim() in atproces.c as:
\[\delta_{light} = \min\left( \frac{IRR}{KI},1 \right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ if\ light\ adaptation\ is\ not\ used\ (flaglight = 0)\]
where IRR is the amount of light available for the photosynthesis and KI is the light saturation coefficient (KI_XXX) in W m-2.
Atlantis allows for light adaptation of primary producers to be represented, which is intended to capture their ability to rapidly adapt to different light conditions. It is used when flaglight = 1 and requires four additional parameters (KIOP_min, KIOP_shift, KI_avail, K_addepth), used to calculate optIRR in Box_Light_Process() in atbiophysics.c
If light adaptation is used the light limitation is calculated as
\[\delta_{light} = \min\left( \frac{IRR}{KI + optIRR},1 \right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ if\ light\ adaptation\ is\ used\ (flaglight = 1)\]
The amount of light falling on the surface of the top layer is either provided through external time series or calculated in Atlantis depending on the lim_sun_hours setting (described in chapter 5, Physics).
The light attenuation Kd through the water column (described in Fulton 2001) defines the availability of light to primary producers at different depths and is calculated as
\[Kd = k_{w} + k_{IS} + k_{PN} \cdot \sum_{i = phytopl}^{}{B_{i} + k_{DON} \cdot B_{DON} + k_{DL} \cdot \left( B_{DL} + B_{DR} \right) + k_{SED} \cdot B_{SED}}\]
The equation shows that light attenuation is simply defined by the background blue water light absorption coefficient (kw), additional light absorption due to tanins and other non-biological particulate matter that is important in coastal areas (set in kIS), and concentration or biomass of light attenuating organisms (plankton) or substances (DON, detrituts, sediments) multiplied by the corresponding light attenuation coefficient. The attenuation is caused by:
- background light absorption by water itself (kw) – used in the PPBIM model.
- additional background light absorption by water due to tanins and other non-biological particulate matter that is important in coastal areas (set in kIS). Different coefficients (k_w_shallow and k_w_deep) are used for coastal and oceanic water. This second term of light absorption was not used in PPBIM but was taken from ERSEM
- phytoplankton, with k_PN defining coefficient of light absorption by particulate matter, such as phytoplankton
- dissolved organic nitrogen and the relevant coefficient k_DON
- labile and refractory detritus and the coefficient k_DL
- light absorption by suspended sediment k_SED, used only if the model is estuary (flagIsEstuary=1)
9.2.3. Primary macrophyte producer space limitation
Space limitation is only applied to epibenthic primary producers, defined by PHYTOBEN or SEAGRASS
The space limitation δspace factor is calculated as
\[\delta_{space} = \frac{B_{PP}}{SPmax \cdot P_{area}}\]
where SPmax is the coefficient setting maximum biomass of the epibenthic primary producer (XXmax) in mgN m-2 and Parea is the proportion of the cell covered with suitable habitat scaled by the habitat degradation scalar (if used). Space limitation is activated using flagXXXlim.
9.2.4 Effect of eddies on primary production
The effect of eddies, or the eddy scalar δeddy, on primary production is modelled by simple scaling (multiplication) using the user defined eddy_scale parameter. This dimensionless parameters is multiplied by the eddy strength in a given box to obtain δeddy
\[\delta_{eddy} = {eddy}_{scale} \cdot {eddy}_{strength}\]
Eddy strengths for each box and each quarter are set in the physics.prm file (see Chapter 5.2, section III).
Effect of eddies on primary production
There is good evidence to suggest that the presence of eddies significantly enhances primary production through vertical water column mixing creating spatial and seasonal variation. There are two ways to add this variation in Atlantis and users are encouraged to make use of these parameters.
First, the effects of eddies on vertical mixing alone can be included through the parameters in the physics.prm (eddy_vertmix, eddy_S1 to eddy_S2, eddy_mixscale – see chapter 5.2, section III). This should increase vertical mixing in the water column and bring extra nutrients to the surface.
Second, the user can add an extra scalar δeddy on primary production through the eddy_scale parameter in the biology.prm file. This scalar will take the eddy values and re-scale the primary production calculated for the available amount of light and nutrients based on eddy strength. The second approach assumes that additional nutrients are implicitly supplied through eddies, increasing primary production (these nutrients do not appear in the tracer values but represent just an assumed increase). This ad hoc approach can be taken if the model fails to accurately reflect spatial and seasonal variation in primary production, but the explicit dynamics of nutrient turnover is not resolved accurately enough to enhance primary production sufficiently through nutrient mixing alone. It is not recommended for models that focus on nutrient dynamics and lower trophic levels, but might be useful for models that focus on the dynamics at higher trophic levels and socio-economic aspects.