The Initial Formulation of A Technique To Employ Gradient Information In A Simple Variational Minimization Scheme

Abstract

In 1989, when the first version of the Local Analysis and Prediction System (LAPS) emerged from the drawing boards, it was equipped with a gradient analysis component to utilize satellite data structure. At that time, satellite data were not well calibrated and ancillary data were used to “anchor” the data field, while satellite gradients were then applied between these points to fill in structure. Since the launch of GOES-8, better blackbody calibration on the spacecraft and improved ground comparison (and moonlook) techniques were implemented to reduce, in theory, the overall error of the satellite data. The LAPS system then dropped its gradient approach for satellite data in favor of direct assimilation as FSL began incorporating 3DVAR techniques in its analyses, based on the assumption that observation errors were well defined and bias was negligible. Then in 2002, a landmark water vapor experiment, the International H2O Project (IHOP), allowed the Forecast Systems Laboratory (FSL) the opportunity to compare GOES retrieved integrated water vapor with the equivalent measurement made from a set of ground-based, satellite independent measurements from the radio signal delay data using Global Positioning System (GPS) data. The results revealed a significant moist bias in the satellite measurements at asynoptic times. It became apparent that the GOES retrievals were optimized for synoptic times and these corrections were not working well for the majority of the GOES products at intervening time periods. There are two independent paths to address this problem. One is to correct the GOES product itself, and that is being pursued and is not the subject of this paper. The second approach, and the theme of this paper, is to modify the assimilation system to a form that only utilizes satellite gradients, much like the initial approach in LAPS years ago. To initiate this change, some preliminary work had to be undertaken to ascertain the weights to be applied to gradient terms in the revised analysis functional. That is the main topic of the experiment described in this document. To do this, an analytical function was used to describe “truth,” and a gradient version of this function was used for “satellite gradient observations;” then a degraded version of the function was used for a “background field.” Numerical experiments were undertaken to measure the effectiveness in the gradient information in minimizing the error by using variational analysis to improve the background field to fit truth. Once the relative coefficient weights were determined in the foregoing analytic test, the new numerical analysis equations were incorporated into the existing LAPS software and compared to real data cases. One comparison (randomly selected) is presented in this memo. In all cases examined, the impact was significant; bias error was remarkably reduced and analyzed structural detail was vastly improved in moist areas. This report 2/22 includes Appendix B that documents the actual changes to the LAPS FORTRAN software that is now being used operationally.