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First-order and higher-order approximations of observation impact

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In studies by Errico (2007) and Gelaro et al. (2007), it was found that first order approximations of the reduction of forecast error by the analysis were systematically close to twice the correct value, while higher order approximations lead to relatively accurate estimations. We show that this factor of 2 is due to the quadratic nature of the forecast error measure and to the fact that the analysis point is near the minimum of this quadratic measure.

Studien von Errico (2007) und Gelaro et al. (2007) kamen zum Ergebnis, dass Näherungen erster Ordnung der Verringerung des Vorhersagefehlers durch die Analyse systematisch Werte ergeben, die in etwa doppelt so hoch wie der korrekte Wert sind, während Näherungen höherer Ordnung zu recht präzisen Schätzungen führen. Wir zeigen in der vorliegenden Arbeit, dass der Faktor 2 darauf zurückzuführen ist, dass der Vorhersagefehler als Quadratzahl gemessen wird, und darauf, dass der Analysepunkt nahe am Minimum dieses quadratischen Messwertes liegt.
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Document Type: Research Article

Publication date: 2007-12-01

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  • Meteorologische Zeitschrift (originally founded in 1866) is the joint periodical of the meteorological societies of Austria, Germany and Switzerland. It accepts high-quality peer-reviewed manuscripts on all aspects of observational, theoretical and computational research out of the entire field of meteorology, including climatology. Meteorologische Zeitschrift represents a natural forum for the meteorological community of Central Europe and worldwide.
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