Numerical weather prediction Study Guide

📖 Core Concepts Numerical Weather Prediction (NWP) – Uses mathematical models of the atmosphere/ocean to turn current observations into forecasts. Primitive equations – Set of PDEs that conserve mass, momentum, energy, plus the ideal‑gas law; they describe how density, pressure, temperature, and wind evolve. Data assimilation – Process of converting irregular, noisy observations into a coherent, gridded initial state for the model. Parameterization – Approximate formulas that represent sub‑grid processes (e.g., convection, radiation, land‑surface fluxes) that the model cannot resolve directly. Ensemble forecasting – Runs many model simulations with slightly different initial conditions or physics to estimate forecast uncertainty. Model Output Statistics (MOS) – Statistical post‑processing that corrects systematic model biases and tailors output to local conditions. --- 📌 Must Remember Forecast horizon: Deterministic skill ≈ 6 days; error doubles about every 5 days → reliable forecasts ≈ 14 days. Time‑step stability: Δt linked to grid spacing (Δx); global models: tens of minutes, regional models: 1–4 min. Ensemble spread vs. skill: Correlation usually < 0.6; spread often under‑estimates error beyond 10 days. Key observation sources: Radiosondes, satellites, surface METAR/SYNOP, aircraft AMDAR, reconnaissance aircraft. Vertical coordinates: Pressure‑based (most models) vs. sigma (terrain‑following, common in mesoscale). Major global models: GFS, ECMWF IFS, UK Unified Model, ICON, NEMS, JMA GSM/GEPS, CMA GAFS, BAPTEC. Parameterization families: Convection, cloud microphysics, radiation, surface fluxes, land‑surface, air‑quality emissions. --- 🔄 Key Processes Observation → Quality Control → Data Assimilation Remove erroneous data → blend with prior model background → produce gridded analysis. Model Integration (Time Stepping) Choose Δt based on Courant‑Friedrichs‑Lewy (CFL) condition → apply finite‑difference or spectral methods → advance primitive equations. Ensemble Generation Perturb initial state (singular vectors, breeding) or perturb physics → run multiple members → diagnose spread (spaghetti maps, meteograms). Post‑Processing (MOS) Fit statistical relationships between model fields and observed surface weather → adjust forecasts for systematic biases. --- 🔍 Key Comparisons Global vs. Regional Models Coverage: Whole Earth vs. limited area. Resolution: Coarser (≈ 50–100 km) vs. finer (≈ 1–3 km). Boundary conditions: None vs. supplied by surrounding global model (adds uncertainty). Finite‑Difference vs. Spectral Horizontal Methods Finite‑Difference: Direct grid‑point calculations, easier to implement on irregular terrain. Spectral: Represent fields as sums of waves → high accuracy for smooth fields, but more complex handling of localized features. Deterministic vs. Ensemble Forecasts Deterministic: Single best‑estimate trajectory, limited skill beyond 6 days. Ensemble: Probabilistic spread, useful for risk assessment and extending useful forecast range. --- ⚠️ Common Misunderstandings “More grid points always mean better forecasts.” – Higher resolution helps but can amplify errors if physics (parameterizations) are not correspondingly refined. “Ensemble mean is the best forecast.” – Mean can smooth out extreme events; specific members may capture rare but important outcomes. “MOS replaces the need for a good model.” – MOS corrects systematic bias but cannot fix fundamental model dynamics errors. --- 🧠 Mental Models / Intuition “Butterfly effect” → Error growth – Small perturbations in initial conditions double roughly every 5 days → limits predictability. Grid‑box as a “parcel” – Think of each model cell as a well‑mixed parcel whose unresolved processes are “averaged” via parameterizations. Ensemble as a “weather forecast lottery” – Each member draws a slightly different ticket; the spread shows the odds of different outcomes. --- 🚩 Exceptions & Edge Cases Spread‑Skill Relationship – Occasionally (e.g., strong synoptic events) ensemble spread correlates > 0.7 with error; otherwise it under‑represents uncertainty. Sea‑ice and SST Initialization – Accurate sea‑ice fields have been used only since 1971; older re‑analyses may misrepresent polar conditions. Tropical Cyclone Intensity – Dynamical models improve track skill but intensity still relies heavily on statistical or hybrid methods. --- 📍 When to Use Which Short‑term, high‑resolution forecasts (≤ 3 h to 2 days) → Regional model with fine grid (e.g., HRRR, NAM) + MOS for local bias correction. Medium‑range deterministic forecasts (3–7 days) → Global model (GFS, IFS) – accept deterministic limitations. Probabilistic risk assessment (≥ 5 days) → Ensemble (GEFS, NAEFS) – examine spread, probability of exceedance. Air‑quality prediction → High‑resolution mesoscale model + detailed land‑surface and emission parameterizations. Climate projection → Coupled atmosphere‑ocean‑land‑ice general circulation model (GCM) with multi‑decadal integrations. --- 👀 Patterns to Recognize “Spaghetti” diagram → high spread → low confidence (often beyond 10 days). Systematic bias in temperature → MOS correction needed (common in mountainous regions). Rapid error growth after a strong upper‑level trough → anticipate forecast divergence among ensemble members. Consistent under‑prediction of precipitation in convective regimes → likely due to convection parameterization limits. --- 🗂️ Exam Traps Mistaking ensemble mean for “the forecast”. Exams may ask which product gives the best probability estimate; the answer is the ensemble distribution, not the mean. Confusing sigma vs. pressure coordinates. Sigma follows terrain; pressure is flat. Mis‑labeling can lead to wrong interpretation of vertical resolution. Assuming deterministic skill extends to 10 days. Remember the 6‑day deterministic limit; beyond that, only ensembles retain useful skill. Over‑emphasizing model resolution without noting parameterization quality. High‑resolution runs can still be biased if convection schemes are inadequate. ---