  The Note presents an alternative derivation and interpretation of the Germano
identity and its error, showing that the Germano identity error directly
estimates the residual of the LES equation, i.e., the misfit when evaluating
the inexact equation for the exact solution, and therefore represents the
source of errors in LES. This has many applications, including for optimal
output-based grid/filter-adaptation and uncertainty quantification in LES.
