Machine Learning for Precipitation Nowcasting

Precipitation nowcasting is the problem of predicting rainfall up to ~2 hours ahead. It remains hard because of the chaotic nature of convective systems and the steep decay of predictability.

Formulation

Let $X_t \in \mathbb{R}^{H \times W}$ be a radar reflectivity field at time $t$. Nowcasting asks for the conditional distribution

$$p(X_{t+1}, \ldots, X_{t+\tau} \mid X_{t-k+1}, \ldots, X_{t})$$

over the next $\tau$ frames. Most production systems predict the conditional mean and call it a forecast.

Approaches

1. Optical flow extrapolation — Lagrangian advection of the last observed field.
2. ConvLSTM and successors — recurrent networks with convolutional state transitions.
3. Generative models — GANs and diffusion models that sample realistic nowcasts calibrated on skill scores.

A simple optical flow baseline

import numpy as np

def extrapolate(sequence, velocity, lead_time):
    """Extrapolate radar frames along a constant velocity field."""
    h, w = velocity.shape[:2]
    out = np.empty_like(sequence[0])
    for y in range(h):
        for x in range(w):
            sy = int(np.clip(y - velocity[y, x, 0] * lead_time, 0, h - 1))
            sx = int(np.clip(x - velocity[y, x, 1] * lead_time, 0, w - 1))
            out[y, x] = sequence[-1][sy, sx]
    return out

The mean-squared error between the extrapolation and the observed frame drops sharply after 20–30 minutes, which motivates the current interest in learned, stochastic models.