This R&D item consists of three topics: (1) elucidation of mathematical structures in which small inputs can produce large control effects, (2) derivation of optimal perturbations for control based on advanced applications of adjoint operators, and (3) controllability of large-scale motions based on cross-scale interactions.
Topic (1) aims to apply cutting-edge knowledge from mathematical sciences to simple systems in order to understand mechanisms by which small external forces can induce significant changes in finite-time. In FY2025, we investigated the properties of perturbations that most efficiently drive the system toward a target state, using a convection model. As a result, we found that as the perturbation amplitude increases, the optimal spatial pattern spontaneously transitions from a simple and ordered structure to a complex and intricate one (Fig. 1). Furthermore, we clarified that this transition can be understood as a shift from a regime dominated by linear behavior to one in which nonlinearity plays an essential role. These findings provide a new theoretical foundation not merely for maximizing growth, but for designing interventions that safely guide a system toward a desired state.
In Topic (2), we solve the optimization for developing perturbations for a TC reproduced in realistic models. In this work, we define targets such as TC intensity and rainfall associated with rainbands, and then identify the physical variables that have the greatest influence. In FY2025, assuming cloud seeding from aircraft and ships, we performed an optimization to determine where phase changes should be induced to contribute to TC weakening. The results showed that condensation within certain regions outside the eyewall can weaken a tropical cyclone 2–3 days later. Furthermore, when considering interventions with somewhat larger energy, nonlinear optimal perturbations can influence more efficiently. This finding is also consistent with the results obtained from the fundamental research in Topic (1).
In Topic (3), we analyzed numerical experiment data on the impact of TC intensity modification on the large-scale atmospheric circulation, using the global nonhydrostatic model NICAM provided by meteorological approach. The influence of the intervention was found to expand progressively in stages: from the vicinity of the TC (within 1–2 days), to synoptic-scale wave trains (3–6 days), and then to waves propagating along the westerly jet (>7 days). Significant changes proportional to the intervention magnitude appear to persist until approximately day 6. To quantify this phenomenology, we applied so-called DMD analysis to the experimental data and detected temporal modes of pressure-pattern evolution corresponding to synoptic wave trains and confirmed a linear relationship between the intervention magnitude and the mode amplitude (Fig. 2). Although the large-scale field is inherently chaotic and therefore exhibits orbital instability, focusing on particular modes revealed that the effects of the intervention decay over a characteristic timescale.

Based on advanced mathematical methods, we have been able to analyze perturbations that produce much larger changes than conventional methods. It also leads to a deeper understanding of the phenomena. In addition, progress has been made in analyzing results derived from realistic meteorological data. Going forward, in order to effectively apply the outcomes of mathematical research to tropical cyclone control, we will further strengthen collaboration with other R&D items. Also, we will work on higher-resolution modeling, appropriate model reduction, and the introduction of new computational methods.