Consequently, the ensemble update can be computed by evaluating the observation function formula_71 on each ensemble member once and the matrix formula_11 does not need to be known explicitly. This formula holds also for an observation function formula_80 with a fixed offset formula_81, which also does not need to be known explicitly. The above formula has been commonly used for a nonlinear observation function formula_71, such as the position of a hurricane vortex. In that case, the observation function is essentially approximated by a linear function from its values at ensemble members.