  We consider the problem of an ensemble Kalman filter when only partial
observations are available. In particular we consider the situation where the
observational space consists of variables which are directly observable with
known observational error, and of variables of which only their climatic
variance and mean are given. To limit the variance of the latter poorly
resolved variables we derive a variance limiting Kalman filter (VLKF) in a
variational setting. We analyze the variance limiting Kalman filter for a
simple linear toy model and determine its range of optimal performance. We
explore the variance limiting Kalman filter in an ensemble transform setting
for the Lorenz-96 system, and show that incorporating the information of the
variance of some un-observable variables can improve the skill and also
increase the stability of the data assimilation procedure.

Data Analysis, Statistics and Probability;Chaotic Dynamics;Atmospheric and Oceanic Physics