Nitrogen-phosphorus model cons

A schematic of the modelled nitrogen and phosphorus cycles. The unlabelled arrows leading into the phytoplankton (O and NF) indicate the biological uptake of nitrate and phosphate.

A schematic of the modelled nitrogen and phosphorus cycles. The unlabelled arrows leading into the phytoplankton (O and NF) indicate the biological uptake of nitrate and phosphate.

As with any model, simplification has both advantages and disadvantages. This article describes some of the nitrogen-phosphorus model cons.

Types of Models

In computer modelling there is a continuum between two caricature classes of models:

  1. conceptual-type models that aim to simplify a system down to include only its most important elements, in particular those that govern its behaviour
  2. simulation-type models that are highly detailed and try whenever possible to avoid making assumptions about what is important; instead they try to include as much detail as possible in the expectation that nothing important will be omitted

By simplifying to only the most important fluxes and state variables, this model is very much a conceptual-type model. 


Potential weaknesses of a conceptual approach include the likelihood of omitting something important. Every assumption runs the risk of being incorrect in an important way and thereby divorcing the model results from reality. It only takes one unreasonable assumption or omission, if it relates to a key part of the system, to invalidate the model's results.

Some of the major simplifications made in the nitrogen-phosphorus (NP) model are as follows:

  1. The representation of biology is extremely simplified. Limitation of growth rate due to light, temperature and other nutrients (for instance, silicate and iron) are not included at all in the model. The omission of iron, in particular, is a potentially critical deficiency of the model, because observational evidence suggests that abundant nitrogen-fixers are found in those parts of the ocean that receive large amounts of (iron-containing) dust. Accurately characterising the competition between N2-fixing and other phytoplankton is critical for this model, and getting this wrong could lead the model to produce erroneous results. A more detailed consideration of the importance of omitting iron is given below, but in brief the omission is likely to make this model unrealistic over shorter timescales (e.g. <1000 years).
  2. There is no day-night cycle and no seasonal cycle in the model.
  3. Horizontal variations are completely ignored. The model is unable to simulate differences between different ocean basins, between high and low latitudes, or between deep and shallow water environments. The model is therefore suitable only for calculating average global responses.
  4. Vertical variations can only be captured in an approximate way due to only two boxes in the vertical.
  5. Only the major fluxes are included. Fluxes deemed to be of lesser importance, such as the delivery of phosphorus to the surface ocean within dust, are not included.
  6. Only two different types of phytoplankton are simulated in the model.
  7. Only inorganic phosphate and nitrate are modelled. Dissolved organic nitrogen (DON) and phosphate (DOP) are not modelled. Nitrate (i.e. fixed nitrogen) is modelled, but is not broken down into its constituents (e.g. nitrate, nitrite, ammonium). The concentration of dinitrogen (N2) is not explicitly modelled as a state variable. However, this will not make any difference to the model results because dinitrogen would in any case never run out. The amounts used by nitrogen-fixers are so small relative to the very large concentrations in seawater (e.g. 1000 mol kg-1), that there is no point in modeling it explicitly.
  8. The N2-fixers are assumed to have no choice in their nitrogen source. They are unable to access fixed nitrogen in the model, even though they can and do in reality.

The motivation for all of these omissions is the expectation that their addition would not fundamentally change the behaviour of the model. It is predicted that adding these features would not greatly alter the model's general response to, for instance, changes in the amount of phosphorus in the ocean, or changes in the input rate of phosphate down rivers.

For many of the cases above we carried out sensitivity analyses to test this assumption. The large majority found that our main results were obtained regardless of whether or not we made the assumptions listed above. Click here to read more about the sensitivity analyses.

Iron limitation and nitrogen fixation

Although it seems likely that iron availability is influential in determining where in the oceans that nitrogen-fixers can live, it is less clear that the rate of iron supply to the ocean controls the amount of nitrogen-fixation taking place. In-situ measurements suggest that N2-fixation is co-limited by both phosphate and iron in one of the areas where N2-fixation is most intense. There are also other areas where phosphate is relatively abundant but iron scarce, and in which nitrogen-fixers do not thrive. It is likely that a temporary increase in the amount of dust falling into the ocean surface would open up new areas to nitrogen-fixers (which iron scarcity has previously prevented them colonising) and lead to a temporary increase in global nitrogen-fixation.

However, such an increase could most likely not be sustained indefinitely. Eventually the increased phosphate use would impoverish ocean stocks of phosphate, and global nitrogen-fixation would become increasingly controlled by phosphate rather than iron scarcity. Because there are parts of the ocean (such as over continental shelves and downwind of deserts) that are probably never iron-limited, we consider that, in the extreme case of low iron supply, global nitrogen fixation would become restricted to those areas only, but be more concentrated there. We suggest that the same amount of nitrogen-fixation would take place, but concentrated in a smaller area. The lack of N2-fixation in other areas would lead to an accumulation of phosphate in the ocean circulation until the point at which the circulation impinges on a high-iron supply, at which point intense N2-fixation would ensue until all of the accumulated phosphate is used up.

If this contention is correct then the results of this NP model should be treated with caution over timescales shorter than about 1000 years (the approximate average transit time of the ocean circulation) but will give more realistic results over longer timescales.


Lenton, T.M. and Klausmeier, C.A. (2007). Biotic stoichiometric controls on deep ocean N:P ratio. Biogeosciences 4, 353-367.
Mills, M.M., Ridame, C., Davey, M., La Roche, J. and Geider, R.J. (2004). Iron and phosphorus co-limit nitrogen fixation in the eastern tropical North Atlantic. Nature 429, 292-294.
Tyrrell, T. (1999). The relative influences of nitrogen and phosphorus on oceanic primary production. Nature 400, 525–531.