Convex Optimization of Initial Perturbations toward Quantitative Weather Control

Abstract

This study proposes introducing convex optimization to find initial perturbations of atmospheric states to realize specified changes in subsequent weather. In the proposed method, we formulate and solve an inverse problem to find effective perturbations to 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 a numerical weather prediction (NWP) model. Then a convex optimization problem is formulated to achieve various control specifications involving not only quadratic functions but also absolute values and maximum values of the controlled variables and initial atmospheric variables in the cost function and constraints. The proposed method was validated through a benchmark warm bubble experiment using the NWP model. The experiments showed that the identified perturbations successfully realized specified spatial distributions of accumulated precipitation.