  This paper describes the inversion procedure being used operationally at the
Norwegian Meteorological Institute for estimating ash emission rates from
retrieved satellite ash column amounts and a priori knowledge.
  The overall procedure consists of five stages:
  (1) generate a priori emission estimates;
  (2) run forward simulations with unit emissions;
  (3) collocate/match observations with emission simulations;
  (4) build system of linear equations; and
  (5) solve overdetermined system.
  We go through the mathematical foundations for the inversion procedure,
performance for synthetic cases, and performance for real-world cases. The
novelties of this paper includes pruning of the linear system of equations used
in the inversion and inclusion of observations of ash cloud top altitude.
  The source code used in this work is freely available under an open source
license, and is possible to use for other similar applications.
