Uncertainties in Numerical Weather Prediction

Description

Uncertainties in Numerical Weather Prediction is a comprehensive work on the most current understandings of uncertainties and predictability in numerical simulations of the atmosphere. It provides general knowledge on all aspects of uncertainties in the weather prediction models in a single, easy to use reference. The book illustrates particular uncertainties in observations and data assimilation, as well as the errors associated with numerical integration methods. Stochastic methods in parameterization of subgrid processes are also assessed, as are uncertainties associated with surface-atmosphere exchange, orographic flows and processes in the atmospheric boundary layer. Through a better understanding of the uncertainties to watch for, readers will be able to produce more precise and accurate forecasts. This is an essential work for anyone who wants to improve the accuracy of weather and climate forecasting and interested parties developing tools to enhance the quality of such forecasts. 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