An online course for PhD students and early stage researchers created by Bethan Perkins, Javier Amezcua, Ross Bannister and David Livings as part of the European Space Agency Data Assimilation projects.
Introduction to 4d-Var
All forecast models, whether they represent the state of the weather, the spread of a disease, or levels of economic activity, contain unknown parameters. These parameters may be the model’s initial conditions, its boundary conditions, or other tunable parameters that have to be found for a realistic result.
Four dimensional variational data assimilation, or “4d-Var”, is a method of estimating this set of parameters by optimizing the fit between the solution of the model and a set of observations that the model is meant to predict. In this context the procedure of adjusting the parameters until the model ‘best predicts’ the observables is known as optimization. The “four dimensional” nature of 4d-Var reflects the fact that the observation set spans not only three dimensional space, but also a time domain.