Article ID: 2025-032
Four-dimensional variational data assimilation (4DVar) has been used as widely as ensemble Kalman filters (EnKFs) in meteorology and oceanography. Unlike EnKFs, 4DVar can be applied to strongly nonlinear regimes in data assimilation. A problem with 4DVar is that the cost function may have multiple minima, and that it can be difficult to find the global minimum using a gradient descent method. Quantum annealing can find the global minimum via quadratic unconstrained binary optimization (QUBO). This study proposes a method of searching for the global minimum of the 4DVar cost function by combining a second-order incremental approach and quantum annealing, in which the latter provides guidance on where to explore in state space by minimizing an approximated cost function. This approximated cost function is constructed in low-dimensional space by expanding state variables up to the second order around a basic state. If the global minimum cannot be reached after a couple of updates of the basic state, the 4DVar analysis is replaced by an EnKF analysis in assimilation cycles. Data assimilation experiments using the Lorenz-63 model were conducted as a proof of concept of the proposed method. The results revealed that the proposed method significantly reduced the frequency of falling into local minima, and that the benefit of extending the length of the assimilation window was realized even in strongly nonlinear regimes. Data assimilation experiments in which simulated annealing was adopted instead of quantum annealing showed that quantum annealing exhibited comparable or better performance compared to simulated annealing.
