The data assimilation method to improve sea fog forecast over the Yellow Sea is usually three-dimensional variational assimilation (3DVAR), whereas ensemble Kalman filter (EnKF) has not yet been applied on this weather phenomenon. In this paper, two sea fog cases over the Yellow sea, one spread widely and the other spread narrowly along the coastal area, are studied in detail by a series of numerical experiments with 3DVAR and EnKF based on the Grid-point Statistical Interpolation (GSI) system and the Weather Research and Forecasting (WRF) model. The results show that the assimilation effect of EnKF outperforms that of 3DVAR: for the widespread-fog case, the probability of detection and equitable threat scores of the forecasted sea fog area get improved respectively by ~57.9% and ~55.5%; the sea fog of the other case completely mis-forecasted by 3DVAR is produced successfully by EnKF. These improvements of EnKF relative to 3DVAR are benefited from its flow-dependent background error, resulting in more realistic depiction of sea surface wind for the widespread-fog case and better moisture distribution for the other case in the initial conditions. More importantly, the correlation between temperature and humidity in the background error of EnKF plays a vital role in the response of moisture to the assimilation of temperature, which leads to a great improvement on the initial moisture conditions for sea fog forecast.

Three Dimensional Variational data assimilation or analysis (3DVAR) is one of most classical methods for providing the initial values for numerical models. In this method, the dimensions of the background error covariance and the observational error covariance matrices are large. Therefore, it is difficult to get the inverse of the covariance matrices and to reduce the orders of these matrices without information loss. With the use of the Sylvester Equation, on the basis of a new linear regression, a new cost function for 3DVAR was given. For the first-guess m×n field, there is an approximate 1−(m²+n²)/(mn×mn) reduction with m>1 & n>1 by using the cost function. The results of the numerical experiments show that the effect of this algorithm is no worse than that of the old cost function for 3DVAR.