Structure, Growth Rates, and Tangent Linear Accuracy of Adjoint Sensitivities with Respect to Horizontal and Vertical Resolution

Abstract

Abstract In this paper, the variation of adjoint sensitivities as horizontal and vertical resolutions are changed is investigated. The fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) and its adjoint are used with consistent physics to generate adjoint sensitivities over a 24-h period. The sensitivities are generated with respect to a response function defined as the lowest sigma level perturbation pressure over a region of northwestern Oregon. It is found that the scale, magnitude, and structure of sensitivity with respect to initial temperature varies significantly as grid spacing is decreased from 216 to 24 km. As found in other adjoint studies at relatively coarse resolution, low-level, upshear-tilted, subsynoptic-scale sensitivities were apparent, with the wavelike sensitivity pattern decreasing significantly in scale and spatial extent with increased horizontal resolution. It is also found that perturbation growth rates depend on horizontal resolution, with the adjoint sensitivities predicting larger changes in the response function with increased horizontal resolution. Relatively little change in sensitivity structure and growth rates occurred when the vertical resolution was varied from 10 to 50 vertical levels. It is shown that a majority of the predicted change in the response function comes from the very small proportion of the domain occupied by sensitive regions. Last, the accuracy of the tangent linear approximation is examined, and it is found that for perturbations made in sensitive regions, the tangent linear approximation degrades at finer grid spacing. The implications of these results are discussed for methodologies utilizing adjoint sensitivities, such as four-dimensional variational data assimilation and targeted observations strategies.