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In this session we will sort out general house keeping for the course, such as computing accounts as well as introducing ourselves to one another. 

The aim of this session lecture is to understand how data assimilation can improve our knowledge of past weather over long time-scales. We will present recent advances that help capture changes over time in observing system networks, and project this variation in information content into uncertainty estimates of the reanalysis products. We will also discuss the applications of reanalysis, which generally put weather events into the climate context.

By the end of the session you should be able to:

• explain what are the goals of data assimilation in a reanalysis data assimilation system
• list the key aspects that require particular attention in reanalysis, as compared to numerical weather prediction
• describe the most common problems in reanalysis products

By the end of the lecture the participants should be able to:

In this lecture the variational bias correction scheme (VarBC) as used at ECMWF is explained. VarBC replaced the tedious job of estimating observation bias off-line for each satellite instrument or in-situ network by an automatic self-adaptive system. This is achieved by making the bias estimation an integral part of the ECMWF variational data assimilation system, where now both the initial model state and observation bias estimates are updated simultaneously.

By the end of the session you should be able to realize that:

• many observations are biased, and that the characteristics of bias varies widely between types of instruments
• separation between model bias and observation bias is often difficult
• the success of an adaptive system implicitly relies on a redundancy in the underlying observing system.

The aim of these sessions is to understand the role of land surface data assimilation on medium range weather forecasts.

We will give an overview of the different approaches used to assimilate land surface data and to initialise model variables in NWP.  We will  present the current observing systems and describe the land data assimilation structure within ECMWF system.

By the end of the session you should be able to:

• identify the different observations used for snow and soil moisture data assimilation
• define land surface data assimilation approaches used for NWP
• describe the role of land surface data assimilation on medium-range weather forecasts

The goal of the ECMWF Earth System data assimilation is to provide an accurate and physically coherent description of the state of the atmosphere, ocean, sea ice and land surface as an initial point for our forecasts.

This requires blending in a statistically optimal way information from a huge variety of observations and our prior knowledge about the physical laws of the Earth system, which is encapsulated in our models.

In this lecture we will lay the general conceptual framework on how to achieve this from a Bayesian perspective. We will then highlight the approximations and hypotheses which are required to make the assimilation problem computationally tractable and which underlie the practical data assimilation algorithms which will be described in detail in this training course.

By the end of lecture you should be able to:

• understand the basics of how a geophysical data assimilation system works;
• understand the main approximations and hypotheses which are required to build practical data assimilation algorithms for large geophysical systems

The primary purpose of this lecture is explore the implications of the fact that satellites can only measure radiation at the top of the atmosphere and do not measure the geophysical variables we require for NWP (e.g. temperature, humidity and wind). The link between the atmospheric variables and the measured radiances is the radiative transfer equation - the key elements of which are discussed. It is shown how - with careful frequency selection - satellite measurements can be made for which the relationship to geophysical variables is greatly simplified. Despite these simplifications, it is shown that the extraction of detailed profile information from downward looking radiance measurements is a formally ill posed inverse problem.

Data assimilation is introduced as the solution to this inverse problem, where background information and satellite observations are combined to produce a best or optimal estimate of the atmospheric state. The main elements of the assimilation scheme (such as the chain of observation operators for radiances) and its key statistical inputs are examined. In particular it is shown that incorrect specification of observation errors (R) and background errors (B) can severely limit the successful exploitation of satellite data.

By the end of this lecture you will:

• understand exactly what a satellite actually measures (radiance)
• appreciate the complex relationship between what is measured and what we wish to know for NWP
• how information is extracted from satellite measurements in data assimilation

The aim of this session is to understand how data assimilation can improve our knowledge of past weather over long time-scales. We will present recent advances that help capture changes over time in observing system networks, and project this variation in information content into uncertainty estimates of the reanalysis products. We will also discuss the applications of reanalysis, which generally put weather events into the climate context.

By the end of the session you should be able to:

• explain what are the goals of data assimilation in a reanalysis data assimilation system
• list the key aspects that require particular attention in reanalysis, as compared to numerical weather prediction
• describe the most common problems in reanalysis products

A single observation can under some conditions undermine the quality of a global analyses. The lecture will go through methods used to make the analysis more robust against oulier or wrong observations, with focus on variational quality control.

The goal of this lecture is to familiarise the student with the notion of tangent linear and adjoint models, and their use in variational data assimilation.  A general overview of the current use of tangent linear and adjoint models in the ECMWF system will also be provided. Theoretical definitions and practical examples of tangent liner and adjoint models will be given. The student will be invited to work some simple tangent linear and adjoint derivations together with the instructor. A brief introduction to automatic differentiation software will also be given./

By the end of the session you should be able to:

• define what tangent linear and adjoint models are
• derive tangent linear and adjoint equations for a simple nonlinear equation
• describe the use of tangent linear and adjoint codes within the ECMWF's 4D-VAR system.

This lecture will explain the basic concepts of the assimilation algorithms. The terminology used in the next lectures will be introduced.  Simple examples will conduce towards the formulation of the optimal minimum-variance analysis. The optimal interpolation method will finally be presented.

By the end of the lecture the participants should be able to:

• Recognize the notations used for the rest of the week
• Solve the optimal minimum-variance analysis problem
• Apply the optimal interpolation method

The aim of this lecture is to introduce the concept of the EnKF in the context of atmospheric data assimilation. Strengths and weaknesses of the algorithm will be discussed and results of the ECMWF implementation will This lecture will explain the basic concepts of the assimilation algorithms. The terminology used in the next lectures will be introduced.  Simple examples will conduce towards the formulation of the optimal minimum-variance analysis. The optimal interpolation method will finally be presented.

By the end of the lecture the participants should be able to:

• Recognize the notations used for the rest of the week
• Solve the optimal minimum-variance analysis problem
• Apply the optimal interpolation method