Observability for optimal sensor locations in data assimilation

Abstract

In this paper we will discuss the application of observability to the planning of sensor configurations in numerical weather prediction (NWP). The dimensions used in NWP make conventional definitions of observability impractical. For this reason we will rely partial observability which is obtained using dynamic optimization to approximate the observability. Using this metric we will form an optimization problem to select sensor configurations that maximize the partial observability of the dynamical system. This leads to a max–min problem which using an empirical gramian matrix we reduce to an eigenvalue optimization problem. Atmospheric data assimilation is the process of combining prior knowledge with observations to form an estimate of the system state required to produce a forecast of future weather conditions. Optimal sensor configurations leading to improved forecast quality are of interest. Due to the potential size of our intended application we will focus on computational methods that are both efficient and scalable. We will also leverage existing tools used in data assimilation and introduce tools used in nonsmooth optimization.