Use of adjoint sensitivity analysis to diagnose the CMC global analysis performance: A case study

The sensitivity of forecast errors to initial conditions obtained from the adjoint of a numerical weather prediction model provides new insights into the analysis errors responsible for poor short-range to mediumrange forecasts. In recent years, we have developed a sensitivity analysis system based on the tangent linear and adjoint of the Global Environmental Multiscale model, in which an iterative procedure minimizing the shortrange forecast errors leads to the so-called key analysis errors. These errors are dominated by a small number of atmospheric structures, those growing the most rapidly. The algorithm has proven very useful in understanding improvements to the three-dimensional variational data assimilation (3D-Var) system implemented in the Canadian Meteorological Centre operational suite in December 2001. The main difference between the old and the new 3D-Var systems is the assimilation of temperature and surface pressure from surface and upper air stations as opposed to geopotential heights, additional Tiros Operational Vertical Sounder channels, new sources of observations such as temperature observations from aircraft, and wind and temperature from dropsondes. In this paper, we examine key analysis errors of the old 3D-Var analysis, which led to a very poor 3-day forecast of a severe winter storm that struck eastern Canada on 10 February 2001. In this case, the same 3-day forecast from the new 3D-Var analysis is much better. We compare the difference between the two 3D-Var analyses and the key analysis errors. We find that the main key analysis errors, in terms of potential vorticity, is located along the west shore of southern California and is characterized by a strong baroclinic structure that has its maximum amplitude in the upper part of the troposphere. The difference between the two analyses is three times more energetic than the key analysis errors and its structure is much more barotropic in the troposphere. However, we show that the large improvement in the new 3D-Var analysis stems mainly from the reduction of the analysis errors that project onto the key analysis structures.