Validity of the Tangent Linear Approximation in a Moist Convective Cloud Model

Seon Ki Park Center for Analysis and Prediction of Storms and School of Meteorology, University of Oklahoma, Norman, Oklahoma

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Kelvin K. Droegemeier Center for Analysis and Prediction of Storms and School of Meteorology, University of Oklahoma, Norman, Oklahoma

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Abstract

The validity of the moist tangent linear model (TLM) derived from a time-dependent 1D Eulerian cloud model is investigated by comparing TLM solutions to differences between results from a nonlinear model identically perturbed. The TLM solutions are found to be highly sensitive to the amplitude of the applied perturbation, and thus the linear approximation is valid only for a specific range of perturbations. The TLM fails to describe the evolution of perturbations when the initial variation is given on a parameter in the vicinity of a nonlinear regime change, a result that has important implications for many cloud-scale processes. Uncertainty imposed on certain aspects of microphysical processes can have a significant influence on the behavior of the TLM solutions, and in some cases this behavior can be explained by the particular discretizations used to solve the equations. The frequency at which the nonlinear basic state is updated in the TLM can also have a profound effect on the TLM validity, though this sensitivity is in some cases modulated by the numerical scheme and model configuration used.

Corresponding author address: Dr. Seon Ki Park, Center for Analysis and Prediction of Storms, University of Oklahoma, Sarkeys Energy Center Room 1110, 100 East Boyd, Norman, OK 73019-0470.

Email: spark@ou.edu

Abstract

The validity of the moist tangent linear model (TLM) derived from a time-dependent 1D Eulerian cloud model is investigated by comparing TLM solutions to differences between results from a nonlinear model identically perturbed. The TLM solutions are found to be highly sensitive to the amplitude of the applied perturbation, and thus the linear approximation is valid only for a specific range of perturbations. The TLM fails to describe the evolution of perturbations when the initial variation is given on a parameter in the vicinity of a nonlinear regime change, a result that has important implications for many cloud-scale processes. Uncertainty imposed on certain aspects of microphysical processes can have a significant influence on the behavior of the TLM solutions, and in some cases this behavior can be explained by the particular discretizations used to solve the equations. The frequency at which the nonlinear basic state is updated in the TLM can also have a profound effect on the TLM validity, though this sensitivity is in some cases modulated by the numerical scheme and model configuration used.

Corresponding author address: Dr. Seon Ki Park, Center for Analysis and Prediction of Storms, University of Oklahoma, Sarkeys Energy Center Room 1110, 100 East Boyd, Norman, OK 73019-0470.

Email: spark@ou.edu

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