**Answer:** It is generally safe to use both nitrate and phosphate
in OMP analysis, and in most cases using both parameters rather than only
one of them results in information gain. There are a number of reasons
for this:

- Observations are invariably afflicted with instrumental error. This error may already be enough to produce linear independence of the data sets for the two parameters. If the errors are only small, the OMP algorithm recognises this by placing very low weights on the two parameters.
- The Redfield ratio is not constant throughout the world ocean. It varies with depth, and more importantly for OMP analysis it varies between water masses. This guarantees linear indepence of all parameters. (It makes the use of a constant Redfield ratio in the expanded OMP analysis questionable; but the method is still developing, and this question will no doubt be addressed by future users. First experience shows that nutrient weights are usually low, so the method is not very sensitive to the choice of the Redfield ratio.)
- The method used in the OMP algorithm for finding the least square minimization tests for linear independence of all equations. It eliminates line duplicates automatically and will therefore exclude either nitrate or phosphate from the solution if by chance the two equations are in fact linearly dependent.

**Answer:** OMP analysis nearly always returns a result, but it can
only be as good as the information which goes into it.

- The first thing to check is the distribution of the mass residual. Most users place a large weight on mass conservation and therefore can expect small mass residuals. If the mass residual is small for most of the data points, the occurrence of larger mass residuals for some data points can indicate a problem with these data. For example: Your analysis uses 5 water types; all mass residuals are small except those associated with data points which contain a very large contribution from water type 3. This may indicate a problem with the definition of water type 3.
- You can follow this up by checking the residuals for individual parameters. If you then find that (say) oxygen shows a large residual for those data with a very large contribution from water type 3 and the other parameters behave normally, this indicates a problem with your oxygen definition of water type 3.
- If you find that ALL parameters display large residuals in a particular area of the region under investigation, this probably indicates the presence of another water mass which you did not include in your water mass matrix.

**Answer:** OMP analysis is surprisingly robust, but it is generally
good practice to test the result against small variations in the water
type matrix and in the data. A good procedure is to generate a new synthetic
data set from the original observations by adding white noise with an amplitude
equal to one or two standard deviations and run OMP analysis again. This
will show how much the mixing contributions change if the observations
are randomly changed by the observed (and therefore realistic) data
variability.
A similar test should be done by adding white noise with an amplitude of
the appropriate one or two standard deviations to the water type matrix.
See (4
) for examples.

**Answer:** The additional constraint that only positive solutions
are accepted (non-negativity constraint) gives an additional degree of
freedom, so using n parameters for n+1 water types still produces an optimised
solution - but you are really pushing the system to its limits.

**Answer:** This is a question of personal choice. On one hand, mass
conservation is an elementary physical principle and should be satisfied by
any model. On the other hand, OMP analysis is based on the assumption that
oceanic mixing is a linear process. (In other words, oceanic diffusion of
properties is achieved by turbulence). Mixing products from two water
masses therefore can only produce temperature-salinity combinations which
are located on the straight line connecting the temperature-salinity
combinations of the sources.

In case of double-diffusion, linear mixing of all properties is not warranted. Salinity and nutrients may have the same mixing behaviour (McDougall and Ruddick, 1992, DSR #39) but temperature will not follow them. If there is a suspicion that double diffuive processes may occur, one has to be careful by using OMP analysis. One way around the problem is to put different weights on temperature and salinity within this regions, insted of using the same (as usually in OMP analysis).

In any case, there are ways to enforce mass conservation, or at least come
close to it. The easiest way is to give mass conservation a much larger
weight than any other parameter. This will reduce the mass residuals but
not enforce strict mass conservation. The obvious way to enforce mass
conservation is to exclude mass conservation from the source water type
matrix and replace the unknown x_{1} by 1 - Sx_{j}, where j = 2, ... n.