An exact solution for the analysis and forecast error covariances of a Kalman filter is used to investigate how the locations of fixed observing platforms such as radiosonde stations affect global distributions of analysis and forecast error variance. The solution pertains to an autonomous system with no model error. The atmospherically relevant autonomous dynamical system used in this study is the forward tangent propagator derived from a low-resolution (T21L3) quasi-geostrophic global model. The simplified setting allows for an examination of the sensitivity of the error variances to many different observing configurations. It is also feasible to determine the optimal location of one additional observation given a fixed observing network, which, through repetition, can be used to build effective observing networks.

Effective observing networks result in error variances several times smaller than other types of networks with the same number of column observations, such as equally-spaced or land-based networks. The impact of the observing network configuration on global error variance is greater when the observing network is less dense. The impact of observations at different pressure levels is also examined. It is found that upper level observations are more effective at reducing globally averaged error variance, but mid-level observations are more effective at reducing error variance in the baroclinic regions associated with mid-latitude jets.