is... 
The output of the salinity model is a time series of salinity for each cell in the lake.
This is input into a rule based model of ecosystem health. The rule based model outputs a time series of biomass index for each cell and for each species.
As 7 species and 5 cells are used, 35 time series are produced. Thus clearly there is a need for reducing this vast quantity of data to something more useful.
The most basic idea in this index is that biodiversity is an aim in managing the system. Ie. All species identified as important should be found somewhere in the system. Why? The ecosystem is more stable when many alternative food chains exist.
The following basic principles were applied in the design of the health index...
The primary mathematical idea used in this index is that of a P norm. The P norm of an
N vector is...
See figure 8 for a graph of the behaviour of 
with
respect to P.
If P=2, then this is the usual 
, Euclidean, or root mean square norm. In the case
illustrated in figure 8,
If P=1, then this is the taxi-cab metric. (Think of a taxi traveling through a city
with regular square city blocks. The 
norm gives the point to point distance traveled by
the taxi. For nonnegative values, this is simply the average or mean.
If P=
then this is the minimax norm. Ie. it equals the maximum of all the absolute
values of the components.
Taking the limit of P tending to zero from the right, gives you the geometric mean of
the absolute values.
Let 
represent the biomass of species i, in cell j, at time step k. Then an index
of health for any one species i at time k is :-
Where P is an arbitrary constant. Setting P very large makes 
large when any one
cell has a lot of species i.
An index of health for the ecosystem at time k is
Where Q is an arbitrary constant. Setting Q to a smaller value makes 
large when all the species were present at time k. When Q is very small the P norm behaves
as a geometric mean.
An index of health for the ecosystem over full time period...
Where R is an arbitrary constant. Making R small would make H large only if biodiversity was high at all times.
w.r.t. P