Overview
The first third of the course, focusing on numerical model formulation and configuration, follows the first three chapters of Numerical Weather and Climate Prediction by T. Warner. The second third of the course, focusing on physical parameterizations, is drawn equally from the Warner text, Parameterization Schemes by D. Stensrud, and peer-reviewed articles describing individual parameterizations. The final third of the course, focusing on data assimilation, is drawn equally from the Warner text and the NCAR Data Assimilation Research Testbed’s laboratory exercises and accompanying slides.
This courses emphasizes dynamical weather prediction; i.e., using numerical methods to solve the dynamical equations governing atmospheric motions. Artificial-intelligence–based methods for weather prediction have recently begun to demonstrate skill competitive with that of the best dynamically based numerical weather prediction models, however, and continue to rapidly develop. Please refer to published preprints describing individual artificial-intelligence models for further details on these models.
Lecture Notes
All course materials are in Adobe PDF format. A free reader for PDF files is available from Adobe’s website, and recent versions of most major web browsers can natively render PDF files in the browser.
- Introduction to Numerical Weather Prediction
- Model Formulation and Resolved vs. Unresolved Scales
- Horizontal Grids and Map Projections
- Vertical Coordinates and Upper Boundary Conditions
- Lateral Boundary Conditions
- Temporal and Spatial Finite Differencing Methods
- Thinking in Waves
- Truncation Error
- Linear Numerical Stability and Implicit Damping
- Diffusion
- Numerical Dispersion
- Aliasing
- Microphysical Parameterization
- Cumulus Parameterization
- Boundary-Layer/Turbulence Parameterization
- Land-Surface Models
- Radiation Parameterization
- Model Initialization
- Introduction to Data Assimilation
- Variational and Kalman Filter Data Assimilation Methods
- Introduction to the Ensemble Adjustment Kalman Filter
- Multivariate/Non-Identity Observation Data Assimilation
- Sampling Error and Observation Localization
- Other Ensemble Data Assimilation Methods
Class Resources
Additional resources can be found at the outset of many of the lecture notes provided above, particularly those related to physical parameterizations.
- NWP Essentials: MetEd: NWP Essentials (free MetEd account required)
- Numerical Methods: An Introduction to Numerical Modeling of the Atmosphere
- Numerical Modeling: ECMWF Lecture Notes (more available from left sidebar at this page)
- Parameterization Topics: An Introduction to Global Atmospheric Modeling
- Data Assimilation: NCAR DART Lab Tutorial
- Data Assimilation: NCAR DART Tutorial (full version)
- WRF Workshop Presentations (generally at the top of each linked page)
General Reading
- Ancell et al. (2018) article entitlted, “Seeding Chaos: The Dire Consequences of Numerical Noise in NWP Perturbation Experiments”
- ECMWF Newsletter article on spectral transform grids
- New York Times article on weather forecasting
- Warner (2011) article on designing effective numerical weather prediction model simulations
- Davis (2012) presentation applying Warner (2011)’s concepts in a WRF-ARW context
- Lynch (2008) article on the history of numerical weather prediction