  We propose a unifying framework for generalising the Wasserstein-1 metric to
a discrepancy measure between nonnegative measures of different mass. This
generalization inherits the convexity and computational efficiency from the
Wasserstein-1 metric, and it includes several previous approaches from the
literature as special cases. For various specific instances of the generalized
Wasserstein-1 metric we furthermore demonstrate their usefulness in
applications by numerical experiments.
