Uncertainties in Numerical Weather Prediction

Front-Matter_2021_Uncertainties-in-Numerical-Weather-Prediction
Front matter
Copyright_2021_Uncertainties-in-Numerical-Weather-Prediction
Copyright
Contributors_2021_Uncertainties-in-Numerical-Weather-Prediction
Contributors
Preface_2021_Uncertainties-in-Numerical-Weather-Prediction
Preface
Chapter-1---Dynamical-cores-for-NWP--An-_2021_Uncertainties-in-Numerical-Wea
Dynamical cores for NWP: An uncertain landscape
Introduction
Governing equations
Some physical properties
Discretizing in time
Some different approaches
Single-stage, single-step schemes
Single-stage, multistep schemes
Multistage single-step schemes
Some numerical properties
Single-stage, single-step schemes
Single-stage, multistep schemes
Multistage single-step schemes
Discretizing in space
Some different approaches
Finite-difference method
Finite-volume method
Finite-element method
Some numerical properties
Finite difference
Finite volume
Finite element
(Semi-)Lagrangian approach
Multidimensional aspects
Extending the discretization to two dimensions
Grids
An outlook
Acknowledgments
References
Chapter-2---Numerical-uncertainties-in-discretizati_2021_Uncertainties-in-Nu
Numerical uncertainties in discretization of the shallow-water equations for weather predication models
Introduction
Discretization of the governing equation I
Temporal differential operator
Euler and Crank-Nicholson methods
Multistep methods
Multistage methods
Spatial differential operators
Grid staggering and operator discretization
Nonzero null space of discrete operators
Extension to two dimensions
Discretization of the governing equation II
Flux-corrected transport (FCT) schemes
Flux limiter transport schemes
Multidimensional positive definite advection transport algorithm (MPDATA)
Filtering, damping, and limiting techniques
Horizontal diffusion
Divergence damping (2D)
Smagorinsky horizontal diffusion
Shapiro filters
Polar spectral filtering
Robert-Asselin time filtering
Lax-Wendroff advection method
Shape preserving advection methods
Global models on unstructured grids
Icosahedral-hexagonal grid
MPAS: A community global model
Cubed-sphere grid
FV3: NGGPS model at NCEP
Some remarks on unstructured grid
Summary
Acknowledgments
References
Chapter-3---Probabilistic-view-of-numerical-we_2021_Uncertainties-in-Numeric
Probabilistic view of numerical weather prediction and ensemble prediction
The numerical weather prediction problem
What are the key processes of numerical weather prediction?
An integrated suite of analysis and forecasts
Observations
The model equations
The definition of the initial conditions
Sources of forecast errors and the chaotic nature of the atmospheric flow
Ensemble-based probabilistic prediction
How can a forecast PDF be generated?
Ensemble methods: How should one design an ensemble?
Simulation of initial condition uncertainties
Simulation of model uncertainties
Ensemble of analyses to estimate initial condition uncertainties
Ensemble of forecasts (and reforecasts) to estimate uncertainty
Examples of ensemble-based probabilistic products
A look into the future
Key learning points
Acknowledgments
References
Chapter-4---Predictability_2021_Uncertainties-in-Numerical-Weather-Predictio
Predictability
Predictability, error growth and uncertainty
Error growth, and scale-dependent predictability
Metrics to measure forecast error and forecast skill
An error growth model
Predictability estimates
Sources of predictability
Conclusions
List of acronyms
References
Further reading
Chapter-5---Modeling-moist-dynamics-_2021_Uncertainties-in-Numerical-Weather
Modeling moist dynamics on subgrid
Introduction
Large-scale vs convective precipitation
Convection, waves, and the large-scale circulation
Assimilation of convective features, microphysics, and heating
Convectively coupled waves and the MJO
Gravity waves and the stratosphere
Mesoscale convective systems and the diurnal cycle
Diurnal cycle
Mesoscale convective systems over the Sahel
Boundary-layer clouds and the radiation budget
Conclusions
Acknowledgments
References
Chapter-6---Ensemble-data-assimilation-for-e_2021_Uncertainties-in-Numerical
Ensemble data assimilation for estimating analysis uncertainty
State estimation and state uncertainty
Basic setup for data assimilation
3D-VAR and the Kalman filter
Determining a statistical covariance matrix B
Two-dimensional example
Analysis uncertainty and its propagation
F4D-VAR
Ensembles of states for uncertainty estimation
Ensemble Kalman filters
Square root filter
Ensembles of 4D state estimation
Particle filters in high dimensions
The localized adaptive particle filter (LAPF)
Localized mixture coefficient particle filter (LMCPF)
References
Chapter-7---Subgrid-turbulence-m_2021_Uncertainties-in-Numerical-Weather-Pre
Subgrid turbulence mixing
Introduction
Nonlocal flux
Mixing length
Subgrid horizontal mixing parameterizations
Discussions
Acknowledgments
References
Chapter-8---Uncertainties-in-the-surface-lay_2021_Uncertainties-in-Numerical
Uncertainties in the surface layer physics parameterizations
Introduction
Atmosphere-ocean interaction
Air-sea fluxes uncertainties
Oceanic and atmospheric parameterization uncertainties
Atmosphere-land interaction
Land surface characteristics
Atmospheric forcing and LSM physics parameterization uncertainties
Summary
References
Chapter-9---Radiation_2021_Uncertainties-in-Numerical-Weather-Prediction
Radiation
Introduction
External uncertainties
Clouds
Aerosols
Aerosol-cloud interactions
Gases
Surface
Internal uncertainties
Top-of-atmosphere solar irradiance
Cloud inherent optical properties
Liquid water clouds
Ice clouds
Aerosol optical properties
Gas optical properties
Surface-radiation coupling
Radiative transfer approximations
Subgrid assumptions
Discretization
Cloud overlap models
3D cloud effects
Topographical 3D effects
Acknowledgment
References
Chapter-10---Uncertainties-in-the-parameterizatio_2021_Uncertainties-in-Nume
Uncertainties in the parameterization of cloud microphysics: An illustration of the problem
Introduction
A brief history of the development of cloud microphysics schemes within the community WRF model
Theoretical basis for cloud microphysics parameterization: A perspective of cloud particle population balance
Uncertainties in the parameterization complexity required for applications
Uncertainties in the parameterized warm rain processes
Uncertainties in the simulated liquid hydrometeor particle size distributions
Uncertainties in the parameterized cold rain processes
Uncertainties in the simulated frozen hydrometeor particle properties and size distributions
Uncertainties in the interaction of aerosols and clouds
Summary
References
Chapter-11---Mesoscale-orographic_2021_Uncertainties-in-Numerical-Weather-Pr
Mesoscale orographic flows
Introduction
Patterns of mountain flows
Forecasting the orographic flows
Future improvements
References
Chapter-12---Numerical-methods-to-identi_2021_Uncertainties-in-Numerical-Wea
Numerical methods to identify model uncertainty
Numerical tracers
Numerical requirements
Passive tracers
Airmass tracers
Water vapor tracers
Water vapor isotope tracers
Challenges and developments
Active tracers
Natural and anthropogenic aerosols
Reactive chemical tracers
Tendency diagnostics
Purpose
Direct tendency framework
Potential vorticity framework
Application examples
Challenges and developments
References
Chapter-13---Dynamic-identification-and-tracking-_2021_Uncertainties-in-Nume
Dynamic identification and tracking of errors in numerical simulations of the atmosphere
Introduction
Variables and functions, useful for error tracing in atmospheric flow
Precipitation and vertical velocity
The method of error tracking
Wrong prediction of the surface pressure field
Wrong prediction of heavy precipitation
Wrong prediction of a rapidly deepening cyclone
Wrong prediction of the surface pressure field and mesoscale orographic impacts
References
Index_2021_Uncertainties-in-Numerical-Weather-Prediction
Index