This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low. This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach.

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[1] In many regions the strength of El Niño-Southern Oscillation (ENSO) teleconnections has varied over the last century. It is an active area of research to investigate how such changes can be related to long-term climate variability or climate change. However, fluctuations due to the limited observational record and low signal-to-noise ratio also contribute to variations in the apparent strength of the teleconnections. These contributions are considered at 658 precipitation stations around the globe. For each station the probability is estimated that the observed decadal variations in the effect of ENSO on precipitation are explainable by random statistical fluctuations of a constant teleconnection. The number of stations with statistically significant decadal variations is much lower than the number with statistically significant ENSO teleconnections. It is close to the number expected from chance alone. The observed period is too short to reliably detect multiplicative decadal variability in ENSO precipitation teleconnections. Citation: van Oldenborgh, G.