  In this work we present a data driven method, used to improve mode-based
model order reduction of transport fields with sharp fronts. We assume that the
original flow field $q(\mathbf{x},t)=f(\phi(\mathbf{x},t))$ can be
reconstructed by a front shape function $f$ and a level set function $\phi$.
The level set function is used to generate a local coordinate, which
parametrizes the distance to the front. In this way, we are able to embed the
local 1D description of the front for complex 2D front dynamics with merging or
splitting fronts, while seeking a low rank description of $\phi$. Here, the
freedom of choosing $\phi$ far away from the front can be used to find a low
rank description of $\phi$ which accelerates the convergence of $\Vert q-
f(\phi_n)\Vert$, when truncating $\phi$ after the $n$th mode. We demonstrate
the ability of this new ansatz for a 2D propagating flame with a moving front.
