Weather app with its own forecast model: GPT-5.6 Sol

Build me a visually stunning weather forecasting web app for North America that pulls REAL data and produces its own short-term forecast — not just a wrapper around a "current conditions" widget.

Requirements:

1. Pull real, live weather data from a free public API that needs no paid key — use Open-Meteo (open-meteo.com — free, no API key, covers all of North America with hourly + historical data). If Open-Meteo is unreachable, pick another genuinely free keyless source; do NOT fake the data.
2. Let me search any North American city (or use my location) and show current conditions plus the next 7 days.
3. The actual test: build a SHORT-TERM FORECASTING layer of your own on top of the raw data — e.g. pull the last N days of hourly readings for the location and fit a simple model (moving average / linear trend / simple regression on temperature + pressure) to project the next 24–48 hours, then show YOUR projection next to the API's official forecast so I can compare them. Explain in one line what method you used.
4. DESIGN it beautifully: a clean, modern dashboard — temperature curves, a pressure/humidity panel, an animated sky/condition visual, responsive layout. Real data-viz (labeled charts), not decorative gauges.
5. Handle the unhappy paths: city not found, API down, no data for a location — show a real message, never a blank screen or a crash.

Research the Open-Meteo endpoints first, then build, then QA: search at least 3 different North American cities, confirm real numbers load, confirm your forecast layer actually computes and renders. Deploy live to Vercel.

DONE when: the deployed app loads real live weather for any NA city I type, renders clean charts, and shows its own computed forecast beside the official one. If the data is hardcoded or the forecast is fake, it's not done.