The humidity field is an important dynamical field, which drives the precipitation process. Since water vapor is a tracer gas with sources and sinks, it should provide additional information about the wind fields as well. However, due to the special characteristics of the observed humidity field, it is difficult to get the accurate humidity analysis field that is consistent with the other dynamical variables. There are basically two ways to represent observed humidity fields within data assimilation: as relative humidity or as mixing ratio. Relative humidity (RH) has the advantage of being smoothly varying, but its errors are correlated with temperature errors, whereas mixing ratio has errors uncorrelated with temperature errors but has a very strong dependence on space and time, and thus has a very non-Gaussian behavior (Dee and DaSilva, 2003). The observation error covariance between different variables and the non-Gaussian distribution error are not considered in most data assimilation schemes.

Here, we follow the idea of Dee and DaSilva (2003), and define a scaled humidity variable, pseudo RH (PRH), defined as (mixing ratio)/(saturated mixing ratio of the background). It has the advantage of being Gaussian like RH, and that, like mixing ratio, its errors are independent of temperature errors. In the implementation in the Local Ensemble Transform Kalman Fitler (LETKF, Hunt, 2005), an accurate and efficient square root ensemble Kalman filter, we transform the forecast and observed variables used for each ensemble member from mixing ratio to PRH, carry out the KF for PRH, and change the analysis back to mixing ratio by multiplying PRH by the background saturated mixing ratio. We will test the idea in the SPEEDY model with simulated observations to see the impact of using PRH compared with using specific humidity analysis, as well as the impact on other dynamical fields, especially winds.