Assimilation of current measurements into a circulation model of Lake Michigan

We present a method for assimilating current observations into a two-dimensional circulation model of Lake Michigan, based on the Princeton Ocean Model ( POM) and driven by observed winds. Because measurements of surface level are not available, we require that the point-wise update to the forecast horizontal current does not change the forecast surface level. This requirement makes it possible to represent the current updates by a stream function. Given an appropriate covariance model of this stream function, the current updates are calculated by kriging interpolation using the observations and the corresponding model forecast. It is further required that the current updates do not create cross-shore flows; this is represented by the stream function being constant along the coastline and is enforced by incorporating pseudo coastal data into the interpolation. This eliminates the need to construct complex spatial covariance models for the stream function. The method also accommodates observational errors. Results show that the method successfully melds observations into the model, and the influence of data assimilation propagates in space and time.