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Removal of Systematic Biases in S-Mode Principal Components Arising from Unequal Grid Spacing

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  • 1 Departamento de Ciencias de la Atmósfera y los Océanos, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
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Abstract

Frequently, physical variables are analyzed using gridded fields, on regular latitude–longitude frameworks. Such networks often concentrate a disproportionate number of observations over polar regions. If these types of grids are used for an S-mode principal component analysis, they produce a bias of the component patterns toward the temporal patterns observed at higher latitudes. A method to potentially eliminate this effect, while employing the covariance similarity matrix, is to weight the variables by the square root of the cosine of the latitude of the point at which the datum was observed. However, this processing is not useful when using the correlation similarity matrix. In this case, a spatially uniform or equal density grid can be designed by means of the criteria of a constant density of points in each circle of latitude. Then, the variable values are linearly interpolated into this new equal-density grid. This technique is easy to program and to adapt to any regular latitude–longitude network.

As an example, an application of the technique is presented for monthly anomalies of 70-hPa temperature data collected by the Microwave Sounding Unit (MSU) flown on board the NOAA Television Infrared Observation Satellites (TIROS-N). A regular latitude–longitude network generates an overestimation of the polar area significance with respect to those obtained by the equal-density criterion. By comparing two sets of point distributions, it is shown that the representative patterns of the temporal evolution of the variables at low or midlatitudes are modified little, if any, by creating a network of equal density points. Nevertheless, changes may be observed in the explained variances because the eigenvalues are impacted directly to the change in the number of points in the networks caused by processing a non-equal-density grid to the equal-density one.

Corresponding author address: Dr. Diego C. Araneo, Departamento de Ciencias de la Atmósfera y los Océanos, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria—Pabellon 2—2do piso, Cuidad de Buenos Aires 1428, Argentina. Email: araneo@at.fcen.uba.ar

Abstract

Frequently, physical variables are analyzed using gridded fields, on regular latitude–longitude frameworks. Such networks often concentrate a disproportionate number of observations over polar regions. If these types of grids are used for an S-mode principal component analysis, they produce a bias of the component patterns toward the temporal patterns observed at higher latitudes. A method to potentially eliminate this effect, while employing the covariance similarity matrix, is to weight the variables by the square root of the cosine of the latitude of the point at which the datum was observed. However, this processing is not useful when using the correlation similarity matrix. In this case, a spatially uniform or equal density grid can be designed by means of the criteria of a constant density of points in each circle of latitude. Then, the variable values are linearly interpolated into this new equal-density grid. This technique is easy to program and to adapt to any regular latitude–longitude network.

As an example, an application of the technique is presented for monthly anomalies of 70-hPa temperature data collected by the Microwave Sounding Unit (MSU) flown on board the NOAA Television Infrared Observation Satellites (TIROS-N). A regular latitude–longitude network generates an overestimation of the polar area significance with respect to those obtained by the equal-density criterion. By comparing two sets of point distributions, it is shown that the representative patterns of the temporal evolution of the variables at low or midlatitudes are modified little, if any, by creating a network of equal density points. Nevertheless, changes may be observed in the explained variances because the eigenvalues are impacted directly to the change in the number of points in the networks caused by processing a non-equal-density grid to the equal-density one.

Corresponding author address: Dr. Diego C. Araneo, Departamento de Ciencias de la Atmósfera y los Océanos, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria—Pabellon 2—2do piso, Cuidad de Buenos Aires 1428, Argentina. Email: araneo@at.fcen.uba.ar

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