Ensemble-on-demand Kalman filter for large-scale systems with time-sparse measurements

The ensemble Kalman filter for data assimilation involves the propagation of a collection of ensemble members. Under the assumption of time-sparse measurements, we avoid propagating the ensemble members for all of the time steps by creating an ensemble of models only when a new measurement is made available. We call this algorithm the ensemble-on-demand Kalman filter (EnODKF). We use guidelines for ensemble size within the context of EnODKF, and demonstrate the performance of EnODKF for a representative example, specifically, a heat flow problem.