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Course description: Numerical Weather Prediction - 2012




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Numerical methods, adiabatic formulation of models and ocean wave forecasting, 16 - 20 April 2012(course code NWP-NM)

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This five-day module will start Monday 16 April at 09.00h and finish Friday 20 April at 13.00h. Short descriptions of the main lectures are given below.

Governing equations/adiabatic formulation of large-scale models of the atmosphere

These lectures discuss the Euler equations for the atmosphere and various approximations to this equation set used in numerical weather or climate prediction and illustrate how the adiabatic part of the large-scale models of the atmosphere is formulated. Furthermore, an introduction into the physics and dynamics of ocean waves is given.

Numerical methods for weather prediction

This module provides an introduction to various numerical techniques used in NWP to find the solution of the governing equations of the atmosphere. The finite difference, finite element and spectral techniques will be introduced by examining their use for solving the advection, diffusion and gravity wave equations. Stability, accuracy and efficiency of the various schemes will be discussed as well as their relative merits. Other topics addressed include aliasing and non-linear instability, splitting methods, semi-implicit schemes and the semi-Lagrangian technique.

Atmospheric waves

As a complement to the lectures on the adiabatic formulation of models and on numerical prediction, this module investigates the types of wave motions described by the linearized atmospheric prediction equations. Study of the dynamics of these waves and the identification of their mechanisms enables the filtering and isolation of wave types, and an appreciation to be gained of the validity of the various simplifications and approximations made in the study of atmospheric motion at different scales.

Ocean wave modelling

An overview of the state-of-the-art of ocean wave modelling is given. The basic evolution equation of the wave spectrum, the energy balance equation, is derived. The practice of wave modelling is discussed and it is shown that in particular from validation studies using satellite and buoy data that present-day wave models are reliable. From experience it is known that wave results depend in a sensitive manner on the quality of the driving surface winds. For this reason ocean wave forecasting has certain benefits for atmospheric modelling. Examples of these benefits are given.

Optimisation and parallelisation

This lecture will outline how to profile and optimise a numerical weather prediction model written in Fortran for scalar and vector processors. Examples will be given from ECMWF's IFS model.

Data Assimilation and Use of Satellite Data,
23 April - 2 May 2012 (course code NWP-DA) 

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This eight-day module will start on Monday 23 April at 09.00h and finish Wedneday 2 May at 13.00h. Short descriptions of the contents are given below.


An overview of the global observing systems and their properties is given. Their use and impact on numerical weather prediction (NWP) is discussed. The concept of an 'observation operator' is introduced. The role and implementation of such operators in the analysis is presented and examples for both linear and non-linear ones shown. Various operational data monitoring activities, including statistics of information content, adjoint based sensitivity methods and the fit of short range forecast/analysis to the observations are discussed. Some pre-processing and automatic quality control techniques will be described, with special emphasis on the variational quality control method.

Data assimilation concepts and algorithms

The fundamental concepts and notations are introduced and illustrated with some simple examples. The least-squares estimation problem is presented, from a mathematical and from a meteorological perspective, with special emphasis on the modelling of error covariances and some fundamental problems like bias removal, non-Gaussian errors, non-linearities and modelling issues. The numerical solution of the least-squares problems leads to the algorithms of OI (Optimal Interpolation), 3D-Var, 4D-Var and the Kalman filter; the linearization and adjoint techniques are explained. The notions of numerical complexity, minimization methods, preconditioning, incremental method, and estimation of the quality of the analysis are illustrated with some practical applications.

Data assimilation techniques

The detailed implementation of four-dimensional variational (4D-Var) assimilation techniques is described and contrasted to OI, 3D-Var and ensemble Kalman Filters. The meteorological implications of choosing one technique over another are illustrated using ECMWF data. Introductions to oceanographic applications and to atmospheric chemical assimilation will be given. Talks will describe the most recent data assimilation developments at ECMWF: implementation of a weak-constraint 4D-Var system and the introduction of an Ensemble Data Assimilation system.

Land surface analysis

A presentation is given to describe the special issues related to land surface analysis. This covers the analysis of soil moisture, soil temperature, snow and sea surface temperature. This is an area where significant progress has been made recently by moving from simple analysis methods to more advanced Extended Kalman Filter methods. These more advanced methods allow a more realistic representation of surface properties, enabling use of satellite data in the land surface assimilation scheme.

Satellite Data

Satellite observations represent the most important information source in current NWP analysis systems. The lectures provide an overview of the main observation types that are currently in use from polar-orbiting (e.g. ATOVS, SSM/I, AIRS, IASI, GRAS; nadir and limb-sounding instruments) and geostationary orbits (e.g. SEVIRI, GOES-Sounder). Both the forward modelling of radiances, i.e. radiative transfer, from NWP model output as well as the inverse modelling, i.e. the retrieval of information on atmospheric and surface states from radiance observations are introduced and illustrated with numerous examples from every-day applications. Other aspects of satellite data assimilation, namely quality control and bias correction are demonstrated. The wide range of applications illustrates the strong interaction of satellite data processing with data assimilation and model development in global and regional NWP as well as reanalysis and climate research.


Background to reanalysis and results from the past ECMWF reanalysis projects will be reviewed from the perspective of the changing global observing system and the improving data-assimilation system. The impact of the changes on the reanalysis climate will be demonstrated and the potential for future reanalysis projects will be discussed.

Hands-on sessions

Hands-on sessions have been added to cover the topics 'Design and coding of tangent linear and adjoints' and 'Lorenz 95 toy data assimilation system practice'.

Predictability, diagnostics and extended-range forecasting
9 - 18 May 2012 (course code NWP-PR)

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This eight-day module will start on Wednesday 9 May at 09.00h and finish Friday 18 May at 13.00h. Short descriptions of the contents of the lectures are given below.


The predictability of the atmosphere in the medium and extended range will be considered. Theoretical aspects associated with ideas in chaos theory, flow regime diagnosis, and singular vector analysis, will be addressed. There will be a discussion of ensemble techniques, especially those used at the Centre, together with an analysis of specific case-studies of ensemble forecasts. Methods to evaluate the skill of ensemble-based probability forecasts will be studied. The potential value of ensemble forecasts for a variety of users will be assessed through some idealised and practical examples.


Despite impressive improvements in our ability to model the atmosphere, forecasts still exhibit systematic and flow-dependent errors as well as random error. Diagnostics software is a crucial component of the forecast system, used to document such errors, and to understand their causes. Lectures will assess the simulation and predictability of a wide range of phenomena such as monsoons, the Madden-Julian oscillation and blocking. Methods of assessment will include the use of equatorial wave diagnostics, "PV thinking" and seamless approaches.

Extended-range Forecasting

Although detailed weather forecasts are not possible beyond a couple of weeks ahead, it is possible to make probabilistic forecasts of large-scale flow anomalies on the seasonal timescale. Predictability on this timescale arises from ocean-atmosphere interaction, typified by El Niño. Lectures will cover the El Niño phenomenon and the ocean circulation. The formulation and performance of the ECMWF coupled ocean-atmosphere monthly and seasonal forecast systems will be described. Methods for initialization and ensemble generation in seasonal forecasting will be discussed. The concept and performance of multi-model ensemble forecasting will also be studied.

Parametrization of subgrid physical processes,
21 - 31 May 2012 (course code NWP-PA)

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This nine-day module will start on Monday 21 May at 09.00h and finish on Thursday 31 May at 13.00h. Short descriptions of the contents are given below.

General aspects of parametrization and their relation to systematic forecast errors

An overview is given of parametrization of sub-grid processes in large-scale models. The basic assumptions and approximations made in the schemes are considered, and emphasis is placed upon the interaction between various processes and their relation to systematic forecast errors and the evolution of synoptic scale weather systems. Diagnostics of physical processes are presented and compared with observations. Current research at ECMWF in the field of parametrization is discussed and a few lectures are devoted to the numerical aspects of parametrization, and the link between data assimilation and parametrization.

Parametrization of subgridscale orographic effects

The theoretical basis for parametrization schemes for subgridscale orographic processes including gravity wave drag and low-level blocking are described. Observational evidence for these processes is presented. The ECMWF scheme is reviewed, with examples to review its impact.

The middle atmosphere and non-orographic gravity waves

The climate and circulation of the middle atmosphere (stratosphere and mesosphere) is discussed together with the frictional force that breaking upward propagating non-orographic gravity waves exert on the flow. A spectral scheme is explained to parametrize gravity waves of non-orographic origin that are unresolved by the model.

Radiation in numerical weather prediction

The role of radiation in the atmospheric circulation is first addressed. The basic concepts of radiation transfer in the Earth's atmosphere are then briefly reviewed. Present and recent radiation schemes used in the ECMWF forecast model, including some simplifications allowing for an efficient computation of radiative fluxes and heating rates are described. Impact of improvements in the representation of the radiation transfer on the quality of operational forecasts at different resolutions, and the validation of the model clear and cloudy sky radiation are finally addressed.

The parametrization of moist processes

Principles behind parametrization of clouds and convective processes in large-scale models are discussed. Basic principles behind the development of convection are reviewed, highlighting those which are important to consider in the context of representing midlatitude and tropical convective systems. Consideration of the practicalities of convective parametrization focuses on the massflux approach. The importance of various types of convection - deep, shallow, mid-level - is examined, together with uncertain areas such as the parametrization of convective momentum transports. Several approaches to cloud parametrization are described both for the representation of microphysics and of cloud cover. Emphasis is put on the conceptual differences between different schemes. The ECMWF cloud scheme is described in detail and evaluation issues are discussed.

The planetary boundary layer

The properties of the planetary boundary layer (PBL) are presented and the need for a parametrization scheme discussed. Two main types of information have to be derived from variables computed in a forecast model - the surface fluxes and the turbulent exchanges at specific levels within the PBL. Both these problems are addressed, including a discussion on the determination of surface conditions, similarity approaches, simple profile and eddy diffusivity approximations, higher order closure schemes and cloud processes.

Land surface processes

Physical mechanisms regulating the interaction of the land surface and the atmosphere are presented and components of the land surface parametrization are detailed; including the representation of the surface energy and water budgets (soil moisture in particular) and parameterization of cold regions, where snow and soil water phase changes dominate. The surface carbon budget is presented, as a physical mechanism to obtain realistic vegetation phenology in the model.

Finally, land surface assimilation is presented, as a way to control long time scales in the land; data assimilation methods are presented, with their advantages and drawbacks.

Diabatic data assimilation

Recent data assimilation systems can include information from parametrized diabatic processes for improving initial conditions of numerical weather prediction models and subsequent forecasts. Such diabatic data assimilation systems allow the use of new types of observations related to the hydrological cycle (clouds, precipitation, soil moisture). We describe various methods developed for including more physical processes in data assimilation systems. Emphasis is put on more recent variational assimilation techniques (3D-Var, 4D-Var,) using the tangent-linear and adjoint concepts. The problems encountered when including linearized diabatic processes in data assimilation and practical applications to cloud and precipitation assimilation will be presented.


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