Four-Dimensional Data Assimilation and Numerical Weather Prediction

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 which have to be determined. Four dimensional variational data assimilation (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 which the model is meant to predict. 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. Although the method of 4D-Var described in this report is not restricted to any particular system, the application described here has a Numerical Weather Prediction (NWP) model at its core, and the parameters to be determined are the initial conditions of the model. The purpose of this report is to give a survey covering assimilation of Doppler radar wind data into a high-resolution NWP model. Some associated problems, such as sensitivity to small variations in the initial conditions or due to small changes in the background variables, and biases due to nonlinearity are also studied.