A Method to Find Perturbations That Trigger Blocking Onset: Conditional Nonlinear Optimal Perturbations

In this paper the following question is addressed: assuming that some information is available about initial perturbations ( e. g., that they belong to an ensemble, which consists of the perturbations whose magnitudes are less than a given value), how can one determine which perturbations belong to this ensemble and trigger the blocking onset? The applicability of linear singular vectors (LSVs) and conditional nonlinear optimal perturbations (CNOPs) is investigated by a T21L3 quasigeostrophic (QG) model and its tangent linear and adjoint versions. Particular attention is focused on the roles of nonlinear processes and the importance of choosing a proper objective function. LSVs are the fastest-growing perturbations when the evolutions of the initial perturbations are well described by the tangent linear version of the nonlinear model. CNOPs are a natural generalization of LSVs into the nonlinear category, that is, the initial perturbation whose nonlinear evolution attains the maximum of the objective function at a prescribed forecast time under some initial constraint conditions. The results of this research show that in some cases for the given initial ensemble perturbations CNOPs trigger a transition to a blocking regime ( whereas LSVs may not generate such a transition), which shows that nonlinear advection processes are fundamental for studying the weather regime transitions from zonal flow to blocking in the medium range. By choosing two objective functions and investigating the resulting CNOPs, it is found that CNOPs obtained from the objective function of the blocking-index form (type-1 CNOPs) may trigger a transition to a blocking regime under some circumstances, whereas CNOPs related to the streamfunction squared norm (type-2 CNOPs) fail to yield such a transition. This demonstrates the importance of selecting a proper objective function when aiming at finding the perturbations yielding such a transition. The mechanism of blocking onset triggered by perturbations is also explored. It is shown that the approach of type-1 CNOP remains a viable tool to capture the spatial structure of initial perturbations that trigger a blocking onset. The planetary-scale projection of the nonlinear interaction of such initial perturbations contributes to the amplification of the blocking downstream and then triggers a blocking onset.