Adjoint-Based Forecast Sensitivity to Quasigeostrophic Potential Vorticity

Abstract A novel approach to deriving an analytical expression to diagnose the sensitivity to quasigeostrophic potential vorticity (QGPV) from adjoint model sensitivities to the horizontal wind and potential temperature is presented. The approach involves making use of the results of an often-used technique to derive adjoint-informed, optimal initial perturbations which minimize initial-time energy and elicit a specified change in a final time response function. The approach, applied to other forms of potential vorticity, is verified against previously published results for sensitivity to vorticity and sensitivity to shallow-water potential vorticity. The sensitivity to QGPV is shown to be proportional to the result of inverting QGPV calculated using the adjoint sensitivities to the horizontal wind field and potential temperature in place of the horizontal winds and potential temperature of the prognostic model. Given the sensitivity to QGPV, the sensitivities to the geostrophic wind and hydrostatic temperature fields are readily diagnosed. The initialization and subsequent integration of an adjoint model with these balanced sensitivities suppresses high-frequency oscillations associated with adjoint adjustment while preserving the salient characteristics of low-frequency adjoint sensitivity fields. Application of these results is demonstrated in a case study of North Pacific cyclogenesis.