Video_UK_lambda_sigma

# Supplementary Material: Machine Learning Nowcasting of GNSS-Derived Tropospheric Turbulence Parameters

**Authors:** Gaël Kermarrec, [co-authors]
**Journal:** [Journal name]
**DOI:** [to be added upon publication]

## Overview

This repository contains supplementary animations accompanying the manuscript *"Machine Learning Nowcasting of GNSS-Derived Tropospheric Turbulence Parameters over the United Kingdom."*

The animations show the spatiotemporal evolution of two turbulence parameters — the cutoff frequency λ (s⁻¹) and the fluctuation amplitude σ (mm) — estimated from high-rate Zenith Wet Delay (ZWD) observations at approximately 100 GNSS stations across the United Kingdom. Fields are interpolated using natural neighbor interpolation with Gaussian smoothing for visualization.

## Files

| File | Movie | Event | Parameter | Description |
|------|-------|-------|-----------|-------------|
| `lambda_2021_214_evolution_HD.mp4` | S1 | 2 Aug 2021 (DOY 214) | λ | Organized frontal passage |
| `sigma_2021_214_evolution_HD.mp4` | S2 | 2 Aug 2021 (DOY 214) | σ | Organized frontal passage |
| `lambda_2021_221_evolution_HD.mp4` | S3 | 9 Aug 2021 (DOY 221) | λ | Fragmented air-mass convection |
| `sigma_2021_221_evolution_HD.mp4` | S4 | 9 Aug 2021 (DOY 221) | σ | Fragmented air-mass convection |
| `lambda_2021_304_evolution_HD.mp4` | S5 | 31 Oct 2021 (DOY 304) | λ | Halloween windstorm (organized frontal) |
| `sigma_2021_304_evolution_HD.mp4` | S6 | 31 Oct 2021 (DOY 304) | σ | Halloween windstorm (organized frontal) |

## Event Descriptions

### Movies S1–S2: Organized Frontal Event (2 August 2021)
A frontal system associated with an upper-level trough crosses the UK from southwest to northeast. The λ and σ fields display coherent maxima propagating systematically across the network at approximately 40 km h⁻¹, consistent with the documented frontal speed from ERA5 reanalysis. The southwest-to-northeast progression is clearly visible in both parameters.

### Movies S3–S4: Fragmented Convection (9 August 2021)
Air-mass convection develops in an environment of moderate CAPE with weak synoptic forcing. Multiple isolated cells appear and decay asynchronously across the domain. The λ and σ fields show scattered hotspots without coherent spatial organization or systematic propagation, illustrating the fundamental contrast with organized frontal events.

### Movies S5–S6: Halloween Windstorm (31 October 2021)
An intense frontal system with a secondary mesolow produces the strongest turbulence signals in the dataset. Sharp gradients in both λ and σ propagate rapidly across the domain, with the frontal band clearly visible as a coherent band of elevated values extending from southwestern England to northeastern Scotland.

## Technical Details

- **Temporal resolution:** 25-minute intervals (corresponding to the sliding window step of the Matérn parameter estimation)
- **Spatial resolution:** ~100 GNSS stations across the UK, interpolated to a 0.1° grid
- **Video format:** MP4 (H.264), 1920×1080, 1 fps
- **Parameter estimation:** Von Kármán / Matérn spectral model fitted to ZWD residuals using weighted maximum likelihood estimation (see manuscript Section 2)

## Data Availability

Raw GNSS observations are available from the British Isles continuous GNSS Facility (BIGF; http://www.bigf.ac.uk). The processed turbulence parameter dataset and trained Random Forest models are available from the corresponding author upon reasonable request.

## Citation

If you use these materials, please cite:

```
[Full citation to be added upon publication]
```

## License

This supplementary material is provided under [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).