Comparing the vertical structures of weighting functions and adjoint sensitivity of radiance and verifying mesoscale forecasts using AIRS radiance observations

An adjoint sensitivity analysis is conducted using the adjoint of the hyperspectral radiative transfer model (RTM) that simulates the radiance spectrum from the Advanced Infrared Sounder (AIRS). It is shown, both theoretically and numerically, that the height of the maximum sensitivity of radiance in a channel could be higher or lower than the height of the maximum weighting function of that channel. It is shown that the discrepancy between the two heights is determined by the vertical structures of the atmospheric thermodynamic state. The sensitivity finds the level at which changes in temperature and/or moisture will have the largest influence on the simulated brightness temperature (BT), and the maximum weighting function (WF) height indicates the level where the model atmosphere contributes most significantly to the emission at the top of the atmosphere. Based on the above findings, an adjoint method for forecast verification using AIRS radiances is presented. In this method, model forecasts are first mapped into radiance space by an RTM so that they can be compared directly with the observed radiance values. The adjoint sensitivity analysis results are then used to connect the deviations of the model forecasts from observed radiances to the changes of temperature and moisture variables in model space. This adjoint sensitivity based model verification provides useful information on forecast model performances based on indirect observations from satellites.