Weather and Climate Prediction

Weather and climate prediction represents one of humanity's most successful forecasting endeavors, blending physics-based numerical models, ensemble methods, machine learning, and massive observational networks. Modern weather forecasts are accurate up to 10-15 days, while climate projections extend decades. This skill covers numerical weather prediction (NWP) basics, ensemble weather models, climate modeling fundamentals, extreme event forecasting, uncertainty quantification, and skill scores for evaluating prediction quality.

## Key Points

- Sensitive to initial conditions
- Predictable for ~10-15 days
- Question: "Will it rain next Tuesday?"
- Sensitive to boundary conditions (CO2, solar, land use)
- Predictable for decades (statistical properties)
- Question: "Will summers be hotter in 2050?"
1. Numerical Weather Prediction solves fundamental physics equations on a 3D grid; accuracy depends critically on initial conditions (data assimilation)
2. Ensemble forecasting is essential because weather is chaotic; running 50+ perturbed forecasts quantifies forecast uncertainty
3. Weather is an initial value problem (sensitive to starting conditions), while climate is a boundary value problem (sensitive to forcings like CO2)
4. The Anomaly Correlation Coefficient (ACC) is the standard NWP skill metric; forecasts are useful when ACC > 0.6 (typically out to 10-15 days)
5. CRPS is the proper scoring rule for probabilistic continuous forecasts, generalizing the Brier Score beyond binary outcomes
6. Extreme value analysis (GEV distributions) estimates return periods for unprecedented events by fitting distributions to historical extremes