Nonlinear and Linear Evolution of Initial Forecast Errors

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  • 1 National Center for Atmospheric Research, Boulder, Colorado
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Abstract

The hypothesis that the short-time evolution of forecast errors originating from initial data uncertainties can be approximated by linear model solutions is investigated using a realistic prognostic model. A tangent linear limited-area model based on a state of the art mesoscale numerical forecast model is developed. The linearization is performed with respect to a temporally and spatially varying basic state. The basic state fields are produced by the nonlinear model using observed data.

The tangent model solutions and the error fields based on the nonlinear integrations are compared. The results demonstrate that the initial error evolution is well represented by the tangent model for periods of 1–1.5 days duration. The linear model solutions based on the time-independent basic state are also good approximations of the real-error evolutions, providing the prognostic fields are not changing rapidly in time.

The application of the linear model for estimating appropriate initial perturbation for the initial error sensitivity study is illustrated using a simple method. Comparison between the nonlinear integrations based on the unstable initial perturbation and an arbitrarily selected initial perturbation shows that the latter initialization can produce misleading results.

Abstract

The hypothesis that the short-time evolution of forecast errors originating from initial data uncertainties can be approximated by linear model solutions is investigated using a realistic prognostic model. A tangent linear limited-area model based on a state of the art mesoscale numerical forecast model is developed. The linearization is performed with respect to a temporally and spatially varying basic state. The basic state fields are produced by the nonlinear model using observed data.

The tangent model solutions and the error fields based on the nonlinear integrations are compared. The results demonstrate that the initial error evolution is well represented by the tangent model for periods of 1–1.5 days duration. The linear model solutions based on the time-independent basic state are also good approximations of the real-error evolutions, providing the prognostic fields are not changing rapidly in time.

The application of the linear model for estimating appropriate initial perturbation for the initial error sensitivity study is illustrated using a simple method. Comparison between the nonlinear integrations based on the unstable initial perturbation and an arbitrarily selected initial perturbation shows that the latter initialization can produce misleading results.

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