Event-Level Probabilistic Prediction of Extreme Rainfall over India Using Physics-Gated Latent Dynamics

TL;DR

This study tackles daily extreme rainfall prediction over India by reframing the problem as probabilistic event detection using Physics-Gated Latent Ordinary Differential Equations (PG-LODE). PG-LODE models continuous-time latent dynamics that are explicitly modulated by a physics-based gate tied to atmospheric instability, improving sensitivity to convective extremes. Compared to a ConvLSTM baseline and persistence, PG-LODE achieves near-complete event-level detection with a favorable balance of false alarms (Tile-level CSI ≈ 0.78), while pixel-level localization remains challenging due to inherent spatial uncertainty. The approach demonstrates that physics-aware, continuous-time latent representations can translate large-scale atmospheric predictability into reliable hazard assessments, potentially informing early warning systems for monsoon extremes.

Abstract

Extreme rainfall over the Indian monsoon region poses severe societal and infrastructural risks but remains difficult to predict at daily time scales due to stochastic convective triggering and multiscale atmospheric interactions. While large-scale atmospheric fields provide important environmental context, their ability to localize extreme rainfall events is fundamentally limited. In this study, we examine how large-scale atmospheric information from ERA5 reanalysis can be leveraged for event-level probabilistic prediction of daily rainfall extremes over India. We compare an adaptive ConvLSTM baseline with a proposed Physics-Gated Latent Ordinary Differential Equation (PG-LODE) framework, which models atmospheric evolution as a continuous-time latent process whose dynamics are explicitly modulated by a physics-based gating mechanism under convectively unstable conditions. Extreme events are defined using the local 95th percentile of the India Meteorological Department gridded rainfall dataset during the June to September monsoon season. Pixel-wise evaluation shows limited skill for both models due to spatial displacement errors, whereas event-level tile-based verification reveals a clear performance contrast. The ConvLSTM remains highly conservative, detecting only 27 percent of extreme events, while PG-LODE achieves near-complete detection with a substantially higher critical success index and a moderate false alarm rate. These results demonstrate that physics-gated continuous-time latent dynamics offer a robust pathway for translating large-scale atmospheric predictability into reliable assessments of extreme rainfall risk.

Figures (5)

• Figure 1: Compact Architecture of PG-LODE. (a) Encoder compresses ERA5 inputs. (b) Physics-gated ODE evolves the latent state, where $\mathcal{G}$ modulates dynamics based on instability regimes (Quiescent vs Rapid Growth). (c) Decoder maps the trajectory to rainfall probability.
• Figure 2: Comparison of Model Architectures.Left: ConvLSTM evolves hidden states using fixed discrete time steps, treating all temporal transitions uniformly. Right: PG-LODE models atmospheric evolution as a continuous latent process, where a physics-based gating mechanism modulates the rate of state evolution based on thermodynamic instability.
• Figure 3: Extreme Event Detection Skill. Comparison of Hit Rates (Probability of Detection) for extreme rainfall events exceeding the 95th (P95) and 99th (P99) percentiles. The ConvLSTM baseline (left) exhibits severe conservatism ($<20\%$ detection), whereas PG-LODE (right) captures the majority of extreme instances ($>80\%$), validating the effectiveness of physics-gated dynamics.
• Figure 4: Daily Rainfall Case Study. A representative 12-day time series (4 June 2000) showing observed rainfall (IMD, black), ConvLSTM forecast (blue dashed), and PG-LODE forecast (red) on 31 $\times$31 tile. Note that the ConvLSTM fails to deviate from the climatological mean during peak events (Days 3 and 11), while PG-LODE successfully captures the rapid intensification, driven by the activation of the physics gate.
• Figure 5: Intuition behind Physics-Gated Latent Dynamics. High instability (orange trajectory) accelerates state evolution compared to the quiescent regime (blue trajectory).