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

Technical Summary: Event-Level Probabilistic Prediction of Extreme Rainfall Over India Using Physics-Gated Latent Dynamics

Problem Statement
Predicting daily extreme rainfall over the Indian Summer Monsoon (ISM) region remains a critical challenge for disaster mitigation. While large-scale atmospheric physics provides essential context, deterministic prediction of localized extremes is hindered by strong temporal persistence, stochastic convective triggering, and multiscale interactions between synoptic forcing and mesoscale dynamics. Standard Numerical Weather Prediction (NWP) models struggle with the precise timing and intensity of these events due to parameterization uncertainties. Furthermore, evaluating predictive models at daily time scales is complicated by the "double-penalty" problem, where standard deterministic metrics (e.g., RMSE) unfairly penalize models for minor spatiotemporal displacements of high-intensity events. Additionally, naive persistence forecasts often outperform complex models in pixel-wise verification due to the strong temporal memory of large-scale systems.

Methodology
The study proposes a novel framework called Physics-Gated Latent Ordinary Differential Equations (PG-LODE) to address these limitations, comparing it against an adaptive ConvLSTM baseline.

• Data: The model utilizes ERA5 reanalysis variables (Total Column Water Vapor, CAPE, vertical velocity at 500 hPa, 850 hPa winds, and Surface Pressure) as predictors and high-resolution IMD gridded rainfall data as targets for the JJAS (June–September) seasons from 2000–2020.
• Extreme Definition: Extreme events are defined locally as rainfall exceeding the 95th percentile of the local JJAS climatology.
• Baseline (ConvLSTM): A standard ConvLSTM models temporal evolution through discrete-time recurrent updates. The authors note that this formulation implicitly assumes uniform temporal dynamics, forcing rapid convective intensification to be compressed into single update steps, often leading to conservative forecasts that regress toward the climatological mean.
• Proposed Model (PG-LODE):
  • Continuous-Time Latent Dynamics: Unlike the discrete updates of ConvLSTM, PG-LODE models the atmospheric state evolution as a continuous-time trajectory in a learned latent space using a Neural ODE.
  • Physics-Gating Mechanism: The core innovation is a gating function, $G(X_{phys})$, which explicitly modulates the rate of latent evolution based on physically meaningful indicators of atmospheric instability (specifically CAPE and mid-tropospheric vertical velocity, $\omega_{500}$).
  • Dynamics: The evolution is governed by $\frac{dz(t)}{dt} = f_\theta(z(t), t) \odot G(X_{phys})$. Under quiescent conditions, the gate remains near unity, yielding near-inertial dynamics. Under convectively unstable conditions, the gate activates ($G > 1$), accelerating the latent evolution to reflect rapid state transitions associated with convective initiation.
  • Loss Function: An extreme-weighted loss function is employed to penalize the underestimation of extreme events (where rainfall $\ge P_{95}$) more heavily than standard errors.
• Evaluation Strategy: To mitigate the double-penalty problem, the study employs a two-tiered verification strategy:
  1. Pixel-Level: Standard categorical metrics (POD, FAR, CSI) at native resolution.
  2. Event-Level (Tile-Based): The domain is partitioned into $32 \times 32$ pixel tiles. A tile is considered a "hit" if the model predicts a probability of exceedance $> 0.5$ and the observed maximum rainfall in the tile exceeds the $P_{95}$ threshold.

Key Results

• Pixel-Level Performance: Both models struggle in pixel-wise deterministic verification, with the persistence baseline outperforming both ConvLSTM and PG-LODE in Critical Success Index (CSI). This confirms that at daily lead times, pixel-level skill is dominated by large-scale persistence rather than the accurate localization of convective initiation. PG-LODE shows improved detection over ConvLSTM but still suffers from spatial displacement penalties.
• Event-Level (Tile-Based) Performance: A clear separation in performance emerges when evaluating hazard detection rather than exact grid-point localization:
  • ConvLSTM: Remains highly conservative, detecting only 27% of extreme events (TILE-POD $\approx 0.27$) with a very low false alarm ratio (TILE-FAR $\approx 0.019$).
  • PG-LODE: Achieves near-complete detection of extreme events (TILE-POD $\approx 0.996$) with a moderate false alarm ratio (TILE-FAR $\approx 0.215$).
  • Skill Score: Consequently, PG-LODE achieves a substantially higher event-level skill (TILE-CSI $\approx 0.78$) compared to both the ConvLSTM (0.269) and the persistence baseline (0.495).
• Case Studies: Visual analysis of specific events (e.g., June 4, 2000) demonstrates that while ConvLSTM fails to deviate from the climatological mean during peak events, PG-LODE successfully captures rapid intensification driven by the activation of the physics gate.

Significance and Claims
The paper claims that the primary contribution of PG-LODE is not the deterministic prediction of exact rainfall locations, but rather the effective translation of large-scale environmental predictability into reliable probabilistic assessments of extreme rainfall risk.

The authors argue that by reframing the problem from exact spatial localization to event-level probabilistic detection, physics-gated continuous-time latent dynamics offer a superior approach for hazard-relevant monsoon forecasting. The physics gate allows the model to remain inertial during stable conditions while rapidly adapting to convectively unstable regimes, aligning the learned dynamics with the known physical behavior of the monsoon system. This approach successfully overcomes the conservatism of purely data-driven recurrent architectures, providing a tool that is better suited for early warning systems where missing an extreme event is more costly than a false alarm.

Limitations
The authors acknowledge that PG-LODE is physics-guided rather than physics-constrained; it does not explicitly resolve convective processes or enforce conservation laws, which limits its ability to provide deterministic grid-point localization. The study also notes that experiments were conducted at a small model scale to ensure fair comparison, and broader generalization and probabilistic calibration are left for future work.