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Flow Matching for Convective-Scale Precipitation Downscaling

This paper demonstrates that a flow matching model outperforms a score-based diffusion model in capturing the spatial structure of convective-scale precipitation when downscaling from 8 km to 2 km over Singapore, although it exhibits a dry bias in the upper tail of the precipitation distribution.

Original authors: Tom Wetherell

Published 2026-06-02

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Tom Wetherell

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to recreate a highly detailed, chaotic painting of a rainstorm, but you only have a blurry, low-resolution sketch to start with. This is the challenge scientists face when trying to predict local weather from global climate models. Global models are like looking at the world from a satellite: they see the big picture but miss the tiny, violent details of individual thunderstorms.

This paper introduces a new AI tool called Flow Matching to solve this problem. Here is how it works, using simple analogies:

The Problem: Blurry Maps vs. Sharp Details

Think of a Global Climate Model (GCM) as a low-resolution photo of a rainstorm. It tells you it's raining, but it's too blurry to see where the heaviest downpours are happening. Scientists usually use "Regional Climate Models" (RCMs) to zoom in and sharpen the image, but this is like hiring a team of artists to manually redraw every single drop of rain—it takes a massive amount of time and computer power.

Recently, AI has stepped in to do this "zooming" much faster. The current champion of these AI tools is a method called Diffusion Models. You can think of a Diffusion Model like a sculptor who starts with a block of marble (pure noise) and slowly chips away pieces until a perfect statue (the rain map) emerges. It's very good, but it can be slow.

The New Contender: Flow Matching

The author, Tom Wetherell, tested a newer AI method called Flow Matching.

If Diffusion is a sculptor chipping away at stone, Flow Matching is like a river. Imagine you have a drop of water at the start of a river (random noise) and you want it to flow to a specific destination (the detailed rain map). Flow Matching learns the exact current and speed needed to guide that drop of water smoothly and directly to its destination. It doesn't chip away; it flows.

The Experiment: Singapore's Rain

The team trained this "river" AI to take daily rain data from an 8-kilometer grid (the blurry sketch) and turn it into a 2-kilometer grid (the sharp picture) over Singapore. They pitted their Flow Matching river against the current champion, the Diffusion Model (CPMGEM).

The Results: A Tale of Two Strengths

1. The Winner: Spatial Structure (The Shape of the Storm)
When it came to getting the shape and location of the rainstorms right, Flow Matching was the clear winner.

The Analogy: Imagine two artists trying to draw a storm cloud. The Diffusion artist drew a cloud that was in the right place but looked a bit fuzzy and spread out. The Flow Matching artist drew a cloud that had the exact same jagged edges, size, and shape as the real storm.
The Proof: The paper shows that Flow Matching was better at predicting exactly where the rain would hit and how big the "objects" of rain were. It captured the complex, patchy nature of tropical rainstorms better than the Diffusion model.

2. The Loser: The Extreme Tail (The Heavy Downpours)
However, Flow Matching had one major flaw: it was a bit too conservative.

The Analogy: If the real storm dropped 100 buckets of water, Flow Matching only dropped about 80. It missed the absolute heaviest, most extreme downpours. The Diffusion model, on the other hand, managed to capture those extreme "100-bucket" moments more accurately.
The Result: Because Flow Matching missed the heaviest rains, the total amount of rain it predicted over a long period was slightly too low (a "dry bias").

The Bottom Line

The paper concludes that Flow Matching is a very competitive new tool for weather downscaling.

Best for: Capturing the intricate, patchy structure of where rain falls. It is also much faster to run (it took only 1/3rd of the computer time to generate a result compared to the Diffusion model).
Needs work: It needs to be tweaked to stop underestimating the most extreme, heavy rain events.

In short, Flow Matching is like a new artist who is incredibly fast and brilliant at drawing the shape of the storm, but currently draws the intensity of the rain a little too lightly. For now, it's a powerful new addition to the weather prediction toolkit, especially for understanding the complex layout of tropical rain.

Technical Summary: Flow Matching for Convective-Scale Precipitation Downscaling

Problem Statement
High-resolution climate information is essential for assessing local impacts and extreme events, yet Global Climate Models (GCMs) lack the resolution to resolve complex topography and mesoscale convective processes. While Regional Climate Models (RCMs) dynamically downscale GCM output to finer resolutions (2–12 km), they are computationally expensive, limiting the generation of large ensembles and the exploration of diverse climate scenarios. Machine learning (ML) offers a computationally efficient alternative. However, deterministic ML architectures (e.g., CNNs, U-Nets) often produce overly smooth outputs that fail to capture the spatial heterogeneity and heavy-tailed nature of precipitation. While diffusion models have emerged as the state-of-the-art generative approach for downscaling, this work investigates Flow Matching as a competitive alternative framework.

Methodology
The study trains a Flow Matching model to perform daily precipitation downscaling from 8 km to 2 km resolution over a convective-scale domain centered on Singapore.

Data: The model utilizes data from Singapore's Third National Climate Change Study (V3), specifically the SINGV-RCM simulations. The task emulates the second stage of the V3 downscaling (8 km to 2 km) using an imperfect model framework. The input (predictor) consists of 8 km atmospheric fields (temperature, specific humidity, wind components at 200–850 hPa, and sea-level pressure) alongside static fields (orography, land-sea mask). The target is daily-mean precipitation at 2 km resolution. The dataset is split temporally, with training on 1995–2014 and 2080–2099, validation on 2040–2049, and testing on 2050–2059.
Model Architecture: The Flow Matching model learns to transport samples from a source distribution (standard Gaussian) to the target distribution (high-resolution precipitation) conditioned on coarse inputs.
- Interpolant: A linear interpolant is used: $x_t = (1-t)x_0 + tx_1$ , where $x_0$ is the source and $x_1$ is the target.
- Network: A 23-million-parameter ADM U-Net parameterizes the velocity field. Conditioning is achieved by concatenating upsampled coarse predictors, static fields, and the interpolant $x_t$ . The network also utilizes sinusoidal positional embeddings and Fourier time embeddings.
- Training: The model minimizes the Conditional Flow Matching (CFM) loss, regressing the network output against the conditional velocity field derived from paired source-target samples.
- Inference: Samples are generated by drawing from the source distribution and numerically integrating the learned ODE using Heun's method with 50 steps (100 network evaluations).
Baseline: The Flow Matching model is benchmarked against CPMGEM [1], a state-of-the-art score-based diffusion model. The baseline uses 300 Euler sampling steps (300 network evaluations).

Key Results
The evaluation focuses on probabilistic skill (CRPS), spatial structure (FSS, SAL), and intensity calibration.

Overall Probabilistic Skill: Flow Matching achieves a lower Continuous Ranked Probability Score (CRPS) of 4.59 compared to CPMGEM's 4.70, despite requiring only one-third of the sampling cost (100 vs. 300 network evaluations).
Spatial Skill:
- Fractions Skill Score (FSS): Flow Matching consistently outperforms CPMGEM across all tested precipitation thresholds (1, 10, 50, and 100 mm/day) and all neighborhood scales (6–130 km).
- SAL Score: Flow Matching demonstrates tighter distributions for the Structure (S) and Amplitude (A) components, indicating superior consistency in object shape/size and total precipitation amounts. The Location (L) skill is comparable between the two models, suggesting Flow Matching does not suffer from significant displacement errors.
Intensity Calibration: A critical limitation of the Flow Matching model is identified in the upper tail of the precipitation distribution. While both models track the target well at low-to-moderate intensities, Flow Matching underestimates heavy precipitation events (the upper tail) more frequently than CPMGEM. This results in a systematic dry bias in the climatological mean, particularly over marine areas, whereas CPMGEM remains closer to the target mean with a slight positive bias.

Significance and Claims
The paper concludes that Flow Matching is a competitive generative framework for convective-scale precipitation downscaling. Its primary significance lies in its ability to capture spatial structure more effectively than the diffusion baseline, achieving higher spatial skill scores with significantly lower computational cost during inference.

The authors position this work as a "first step" toward a patch-based approach for downscaling the full 960 × 960 grid of the Western Maritime Continent. They suggest that Flow Matching is particularly well-suited for applications requiring the generation of large ensembles to characterize uncertainty, provided that the under-representation of extreme precipitation tails is addressed. The study does not claim to solve the intensity calibration issue but highlights it as a specific area for future improvement while affirming the framework's overall viability for high-resolution climate projection.