The scope of the Kalman filter for spatio-temporal applications in environmental science

The Kalman filter is a workhorse of dynamical modeling. But there are challenges when using the Kalman filter in environmental science: the complexity of environmental processes, the complicated and irregular nature of many environmental datasets, and the scale of environmental datasets, which may comprise many thousands of observations per time-step. We show how these challenges can be met within the Kalman filter, identifying some situations which are relatively easy to handle, such as datasets which are high-resolution in time, and some which are hard, like areal observations on small contiguous polygons. Overall, we conclude that many applications in environmental science are within the scope of the Kalman filter, or its generalizations.