Targeting observations in data assimilation for a model problem of front propagation

We apply the local ensemble transform Kalman filter (LETKF) data assimilation methodology to forecast a traveling front solution of Burgers' equation, using random data to initialize our ensembles. One goal in numerical weather prediction is to optimally target satellite observations for improved forecasting, and we parallel this aim by targeting observations of this front solution. We compare the LETKF methodology for observations randomly located in time with the LETKF methodology for targeted observations located at the point of largest ensemble variance. We numerically demonstrate that LETKF with randomly located observations outperforms model error over a sufficient time interval, and that targeted observations based on ensemble variance are optimal to randomly located observations.