This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter (EnKF). 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. The EnKF is attractive since it avoids many of the problems associated with the traditional extended Kalman filter; for example, there is no closure problem as is introduced in the extended Kalman filter by neglecting contributions from higher-order statistical moments in the error covariance evolution equation. It can also be computed at a much lower numerical cost, since usually a rather limited number of model states is sufficient for reasonable statistical convergence. For sufficient ensemble sizes, the errors will be dominated by statistical noise, not by closure problems or unbounded error variance growth. The EnKF has been further discussed and applied with success in a twin experiment in Evensen (1994a) and in a realistic application for the Agulhas Current using Geosat altimeter data in Evensen and van Leeuwen (1996). A serious point that will be discussed here and was not known during the previous applications of the EnKF is that for the analysis scheme to be consistent one must treat the observations as random variables. This assumption was applied implicitly in the derivation of the analysis scheme in Evensen (1994b) but has not been used in the following applications of the EnKF. It will be shown that unless a new ensemble of observations is generated at each analysis time, by adding perturbations drawn from a distribution with zero mean and covariance equal to the measurement error covariance matrix, the updated ensemble will have a variance that is too low, although the ensemble mean is not affected. A similar problem is present in the ensemble smoother proposed by van Leeuwen and Evensen (1996), although there only the posterior error variance estimate is influenced since the solution is calculated simultaneously in space and time. There was also another issue pointed out in Evensen (1994b): the error covariance matrices for the forecasted and the analyzed estimate, P^f and P^a, are in the Kalman filter defined in terms of the true state as P^fThis paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter (EnKF). 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. The EnKF is attractive since it avoids many of the problems associated with the traditional extended Kalman filter; for example, there is no closure problem as is introduced in the extended Kalman filter by neglecting contributions from higher-order statistical moments in the error covariance evolution equation. It can also be computed at a much lower numerical cost, since usually a rather limited number of model states is sufficient for reasonable statistical convergence. For sufficient ensemble sizes, the errors will be dominated by statistical noise, not by closure problems or unbounded error variance growth. The EnKF has been further discussed and applied with success in a twin experiment in Evensen (1994a) and in a realistic application for the Agulhas Current using Geosat altimeter data in Evensen and van Leeuwen (1996). A serious point that will be discussed here and was not known during the previous applications of the EnKF is that for the analysis scheme to be consistent one must treat the observations as random variables. This assumption was applied implicitly in the derivation of the analysis scheme in Evensen (1994b) but has not been used in the following applications of the EnKF. It will be shown that unless a new ensemble of observations is generated at each analysis time, by adding perturbations drawn from a distribution with zero mean and covariance equal to the measurement error covariance matrix, the updated ensemble will have a variance that is too low, although the ensemble mean is not affected. A similar problem is present in the ensemble smoother proposed by van Leeuwen and Evensen (1996), although there only the posterior error variance estimate is influenced since the solution is calculated simultaneously in space and time. There was also another issue pointed out in Evensen (1994b): the error covariance matrices for the forecasted and the analyzed estimate, P^f and P^a, are in the Kalman filter defined in terms of the true state as P^f