  This study proposes introducing convex optimization to find initial
perturbations of atmospheric models for realizing specified changes in
subsequent forecasts. In the proposed method, we formulate and solve an inverse
problem to find effective perturbations in atmospheric variables so that
controlled variables satisfy specified changes at a specified time. The
proposed method first constructs a sensitivity matrix of controlled variables,
such as accumulated precipitation, to the initial atmospheric variables, such
as temperature and humidity, through sensitivity analysis using numerical
weather prediction (NWP) models. The sensitivity matrix is used to solve the
inverse problem as convex optimization, in which a global optimal solution can
be found computationally efficiently. The proposed method was validated through
a benchmark warm bubble experiment using an NWP model. The experiments showed
that identified perturbation successfully realized specified spatial
distributions of accumulated precipitation. These results demonstrated the
possibility of controlling the real atmosphere by solving inverse problems and
adding small perturbations to atmospheric states.
