The assimilation of water vapor information from satellite observations and the choice of the analysis variable

The Naval Research Laboratory's three- and four-dimensional variational data assimilation systems (NAVDAS and NAVDAS-AR , respectively) use pseudo-relative humidity (PRH) as the moisture variable, following Dee and daSilva (2003), where PRH is defined as the mixing ratio scaled by the saturation mixing ratio of the background field. In the troposphere, PRH has advantages over specific humidity (the forecast model variable), such as having a smaller dynamic range and error characteristics that are more gaussian. However, the choice of PRH has unexpected consequences for the assimilation of moisture information that is sensitive to stratospheric levels.

For the assimilation of satellite brightness temperatures, we use the Joint Center for Satellite Data Assimilation (JCSDA) Community Radiative Transfer Model (CRTM) to compute brightness temperatures and Jacobians corresponding to the background field. The CRTM Jacobians are computed with respect to mixing ratio, and then converted to Jacobians with respect to PRH. The assimilation difficulties arise because in the stratosphere, the combination of warm temperatures and low pressures produce extremely small PRH values. These PRH values can also exhibit large vertical and horizontal gradients that are controlled primarily by the non-linear sensitivity of saturation mixing ratio to temperature change, even when the ambient water vapor abundance is nearly constant. In the stratosphere, mixing ratio (or specific humidity), is a better behaved control variable and is commonly used in chemical data assimilation systems.

The result of the unrealistic values of saturation mixing ratio is a tendency to produce sensitivities to moisture (large Jacobian values) in the upper atmosphere, even though the satellite sensor (such as the 183 GHz channels from the Microwave Humidity Sounder (MHS)) has peak sensitivity in the troposphere. The magnitudes of the PRH Jacobians in the upper atmosphere may be as large as those in the troposphere, and can produce unrealistic increments of moisture in the stratosphere.

An additional complication arises when these Jacobians are used to compute the background error covariances corresponding to the radiance observations. The unrealistically large Jacobians in the stratosphere can lead to background errors much greater than appropriate (values up to 100K for MHS were noted), and much larger than the assumed observation errors of 1-2K.

The quick solution, setting the Jacobians to zero above some arbitrary pressure level, reduced the maximum background errors for MHS to around 12K. While this patch allowed MHS assimilation development to continue, it proved unsatisfactory for GPS bending angle assimilation, as the bending angle Jacobians exhibited similar pathological behavior. One promising solution is to modify the PRH variable by replacing the saturation mixing ratio at low pressures with a constant mixing ratio that is larger than the maximum water abundance observed in the stratosphere. This new hybrid-PRH is proportional to mixing ratio in the stratosphere, with a value in the normal PRH range of 0-100%. The hybrid-PRH smoothly transitions from PRH to scaled-mixing ratio in the upper troposphere/lower stratosphere region. The necessary changes to the computer code to implement the hybrid-PRH were relatively trivial, and are used only in conjunction with the satellite observation processing routines. They are not used for the normal saturation adjustment processes, such as large scale precipitation.

The new moisture variable transformation has the following desirable properties; (1) there are no longer unrealistically large brightness temperature and bending angle background error variances, and (2) it is no longer necessary to zero out the MHS Jacobians at the top levels. With the new definitions for the normalizing variable at low pressure, the moisture contribution from the Jacobians is naturally very small.