Making Tunable Parameters State-Dependent in Weather and Climate Models with Reinforcement Learning

Weather and climate models rely on parametrisations to represent unresolved sub-grid processes. Traditional schemes rely on fixed coefficients that are weakly constrained and tuned offline, contributing to persistent biases that limit their ability to adapt to the underlying physics. This study presents a framework that learns components of parametrisation schemes online as a function of the evolving model state using reinforcement learning (RL) and evaluates the resulting RL-driven parameter updates across a hierarchy of idealised testbeds spanning a simple climate bias correction (SCBC), a radiative-convective equilibrium (RCE), and a zonal mean energy balance model (EBM) with both single-agent and federated multi-agent settings. Across nine RL algorithms, Truncated Quantile Critics (TQC), Deep Deterministic Policy Gradient (DDPG), and Twin Delayed DDPG (TD3) achieved the highest skill and the most stable convergence across configurations, with performance assessed against a static baseline using area-weighted RMSE, temperature profile and pressure-level diagnostics. For the EBM, single-agent RL outperformed static parameter tuning with the strongest gains in tropical and mid-latitude bands, while federated RL on multi-agent setups enabled geographically specialised control and faster convergence, with a six-agent DDPG configuration using frequent aggregation yielding the lowest area-weighted RMSE across the tropics and mid-latitudes. The learnt corrections were also physically meaningful as agents modulated EBM radiative parameters to reduce meridional biases, adjusted RCE lapse rates to match vertical temperature errors, and stabilised SCBC heating increments to limit drift. Overall, results highlight RL to deliver skilful state-dependent, and regime-aware parametrisations, offering a scalable pathway for online learning within numerical models.