  The Wasserstein metric is introduced as a probabilistic method to enable
quantitative evaluations of LES combustion models. The Wasserstein metric can
directly be evaluated from scatter data or statistical results using
probabilistic reconstruction against experimental data. The method is derived
and generalized for turbulent reacting flows, and applied to validation tests
involving the Sydney piloted jet flame. It is shown that the Wasserstein metric
is an effective validation tool that extends to multiple scalar quantities,
providing an objective and quantitative evaluation of model deficiencies and
boundary conditions on the simulation accuracy. Several test cases are
considered, beginning with a comparison of mixture-fraction results, and the
subsequent extension to reactive scalars, including temperature and species
mass fractions of \ce{CO} and \ce{CO2}. To demonstrate the versatility of the
proposed method in application to multiple datasets, the Wasserstein metric is
applied to a series of different simulations that were contributed to the
TNF-workshop. Analysis of the results allowed to identify competing
contributions to model deviations, arising from uncertainties in the boundary
conditions and model deficiencies. These applications demonstrate that the
Wasserstein metric constitutes an easily applicable mathematical tool that
reduce multiscalar combustion data and large datasets into a scalar-valued
quantitative measure.
