Square Root Analysis schemes

The perturbation of measurements used in the EnKF standard analysis is an additional source of sampling error. The works by Anderson (2001), Whitaker and Hamill (2002), Bishop et al. (2001), the review by Tippett et al. (2003), and the paper by Evensen (2004), have developed “square root” implementations of the analysis scheme where the perturbation of measurements is avoided. The square root methods are intuitively very appealing but there are also some pitfalls as pointed out by Lawson and Hansen (2004) and Leeuwenburgh et al. (2005). See also the papers by Sakov and Oke (2008) and Livings et al. (2008) for a revised interpretation and mathematical analysis of the square root schemes.