Comment on “Data Assimilation Using an Ensemble Kalman Filter Technique”

• Published in: Monthly weather review Vol. 127; no. 6; pp. 1374 - 1377
• Main Author: van Leeuwen, Peter Jan
• Format: Journal Article
• Language: English
• Published: 01.06.1999
• ISSN: 0027-0644; 1520-0493
• DOI: 10.1175/1520-0493(1999)127<1374:CODAUA>2.0.CO;2

In an interesting paper Houtekamer and Mitchell (1998; hereafter HM98) introduce a variant of the ensemble Kalman filter (EnKF) as proposed by Evensen (1994). HM98 point to the hitherto unacknowledged problem that the EnKF has an ``inbreeding'' problem: in the analysis step the ensemble is updated with a gain calculated from that same ensemble. In their new approach a double ensemble (DEnKF) is used and the gain of each ensemble is used to update the other ensemble in the analysis step. The new approach is argued to be much less sensitive to this inbreeding. They strengthen their argument by a specific example, in which the EnKF shows a variance that is too low for small ensemble sizes ( less than or equal to 100), but they fail to give a rigorous justification. The purposes of this comment are twofold. First, a theoretical justification of the inbreeding effect is given, and it is shown that the DEnKF has similar, but smaller, problems. Second, a serious concern about the use of small ensemble sizes is expressed, thus bringing into question the use of the DEnKF over the EnKF for real applications. Author reply follows.