Equations
for toy and real huge systems
These statements are important because they hold true for data assimilation systems in very large multidimensional problems (e.g., NWP).
We have to
replace scalars (obs, forecasts) by vectors
Instead of model, analysis and observational scalars, we have 3-dimensional vectors of sizes of the order of 107-108
and their error variances
by error covariances: