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Representation of Topography in Spectral Climate Models and Its Effect on Simulated Precipitation

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  • 1 Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, New Jersey
  • | 2 Geophysical Fluid Dynamics Laboratory/N0AA, Princeton University, Princeton, New Jersey
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Abstract

Spectral climate models are distinguished by their representation of variables as finite sums of spherical harmonics, with coefficients computed by an orthogonal projection of the variables onto the spherical harmonics. Representing the surface elevation in this manner results in its contamination by Gibbs-like truncation artifacts, which appear as spurious valleys and mountain chains in the topography. These “Gibbs ripples” are present in the surface topographies of spectral climate models from a number of research institutions. Integrations of the Geophysical Fluid Dynamics Laboratory (GFDL) climate model over a range of horizontal resolutions indicate that the Gibbs ripples lead to spurious, small-scale extrema in the spatial distribution of precipitation. This “cellular precipitation pathology” becomes more pronounced with increasing horizontal resolution, causing a deterioration in the fidelity of simulated precipitation in higher resolution models.

A method is described for reducing the Gibbs ripples that occur when making an incomplete spherical harmonic expansion of the topography. The new spherical harmonic representations of topography are formed by fitting a nonuniform spherical smoothing spline to geodetic data and found by solving a fixed-point problem. This regularization technique results in less distortion of features such as mountain height and continental boundaries than previous smoothing methods. These new expansions of the topography, when used as a lower boundary surface in the GFDL climate model, substantially diminish the cellular precipitation pathology and produce markedly more realistic simulations of precipitation. These developments make the prospect of using higher resolution spectral models for studies of regional hydrologic climate more attractive.

Abstract

Spectral climate models are distinguished by their representation of variables as finite sums of spherical harmonics, with coefficients computed by an orthogonal projection of the variables onto the spherical harmonics. Representing the surface elevation in this manner results in its contamination by Gibbs-like truncation artifacts, which appear as spurious valleys and mountain chains in the topography. These “Gibbs ripples” are present in the surface topographies of spectral climate models from a number of research institutions. Integrations of the Geophysical Fluid Dynamics Laboratory (GFDL) climate model over a range of horizontal resolutions indicate that the Gibbs ripples lead to spurious, small-scale extrema in the spatial distribution of precipitation. This “cellular precipitation pathology” becomes more pronounced with increasing horizontal resolution, causing a deterioration in the fidelity of simulated precipitation in higher resolution models.

A method is described for reducing the Gibbs ripples that occur when making an incomplete spherical harmonic expansion of the topography. The new spherical harmonic representations of topography are formed by fitting a nonuniform spherical smoothing spline to geodetic data and found by solving a fixed-point problem. This regularization technique results in less distortion of features such as mountain height and continental boundaries than previous smoothing methods. These new expansions of the topography, when used as a lower boundary surface in the GFDL climate model, substantially diminish the cellular precipitation pathology and produce markedly more realistic simulations of precipitation. These developments make the prospect of using higher resolution spectral models for studies of regional hydrologic climate more attractive.

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