# A novel technique for nonlinear sensitivity analysis : application to moist predictability

## Riviere, O. ; Lapeyre, G. ; Talagrand, O.

A new nonlinear technique is described to compute the sensitivity of synoptic perturbation growth to environmental moisture. The perturbation growth is defined using a nonlinear generalization of singular vectors called Nonlinear Singular Vectors (NLSV). For a given atmospheric state evolving in time, the nonlinear sensitivity method consists in maximizing the growth rate of perturbations by seeking both the optimal NLSV perturbations and the most favorable spatial distribution of the moisture field. This results in a new atmospheric state that differs initially only by the water vapour field. The NLSV computed along this new state has the largest possible growth rate for all possible water vapour fields. We apply this method to a simulation of the moist primitive equations. For the particular case we study, we obtain a moistening of the lower troposphere and an amplification of energy of optimal perturbations three times larger than the amplification of optimal perturbations computed without altering the water vapour field. The optimal perturbations are similar to the perturbations of the unmodified water vapour case. A noteworthy property is that the complete saturation of the atmosphere leads to a smaller increase in amplification rate, which means that the water vapour field is strongly tied to the NLSV structure. Mechanisms explaining these results are discussed. This technique overcomes the limitations (in particular the linearity assumption) of moist singular vector analysis using moist norms or adjoint sensitivity analysis. It can be applied to diagnose sensitivity to other fields as well. Copyright © 2009 Royal Meteorological Society

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