Formulation of a Lateral Sponge Layer for Limited-Area Shallow-Water Models and an Extension for the vertically Stratified Case

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  • 1 Department of Atmospheric Sciences, University of California, Los Angeles, Los Angeles, California
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Abstract

A lateral sponge layer is designed to minimize the spurious rejections of nondispersive surface gravity waves in a linear, one-dimension shallow-water limited-area model. The formulation selectively damps out the characteristic variables associated with the reflected waves inside the sponge layer. Through normal-mode analyses and subsequent applications to a forced-wave initial-value problem, the effectiveness of the sponge layer is compared to an established formulation of the open boundary condition. It is shown that for moderate thicknesses, the sponge is more effective than the open boundary condition in reducing the reflections of outgoing waves on all spatial scales. Application of the sponge layer to a vertically stratified model atmosphere is accomplished using a matrix procedure that essentially applies the shallow-water formulation to each vertical eigenmode of the model solution. Results of time-integrations using a multilevel quasi-static model of forced gravity waves, once again, demonstrate the relative superiority of the sponge layer over the open boundary condition.

Abstract

A lateral sponge layer is designed to minimize the spurious rejections of nondispersive surface gravity waves in a linear, one-dimension shallow-water limited-area model. The formulation selectively damps out the characteristic variables associated with the reflected waves inside the sponge layer. Through normal-mode analyses and subsequent applications to a forced-wave initial-value problem, the effectiveness of the sponge layer is compared to an established formulation of the open boundary condition. It is shown that for moderate thicknesses, the sponge is more effective than the open boundary condition in reducing the reflections of outgoing waves on all spatial scales. Application of the sponge layer to a vertically stratified model atmosphere is accomplished using a matrix procedure that essentially applies the shallow-water formulation to each vertical eigenmode of the model solution. Results of time-integrations using a multilevel quasi-static model of forced gravity waves, once again, demonstrate the relative superiority of the sponge layer over the open boundary condition.

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