Variance of the Hydrostatically Integrated Height

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  • a Cooperative Institute for Environmental Sciences (CIRES), University of Colorado/ESG/ERL/NOAA Boulder, Colorado
  • | b National Center for Atmospheric Research, Boulder, Colorado
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Abstract

In radiosonde applications the sonde height is required for assignment of winds and meteorological parameters. Usually, this height is obtained using the classical hydrostatic integration involving measurements of pressure (P) and virtual temperature (T). In this paper we consider the accuracy aspects of this integration. The accuracy obviously depends on the quality of measurements of P and T which can b contaminated by two types of errors—(i) zero mean random errors, characterized by the error variances σP2 and σT2, and (ii) bias errors bP and bT. The random errors combine to yield an error-variance of the hydrostatically integrated height. An approximate expression for this variance is derived in terms of σP2 and σT2. A simplified version of this expression shows that the error-variance of the integrated height induced by random measurements errors is negligible. This fact is demonstrated by integration of an actual dataset. With this in mind we derive equations to measure the impact of bias errors on the computed height.

Abstract

In radiosonde applications the sonde height is required for assignment of winds and meteorological parameters. Usually, this height is obtained using the classical hydrostatic integration involving measurements of pressure (P) and virtual temperature (T). In this paper we consider the accuracy aspects of this integration. The accuracy obviously depends on the quality of measurements of P and T which can b contaminated by two types of errors—(i) zero mean random errors, characterized by the error variances σP2 and σT2, and (ii) bias errors bP and bT. The random errors combine to yield an error-variance of the hydrostatically integrated height. An approximate expression for this variance is derived in terms of σP2 and σT2. A simplified version of this expression shows that the error-variance of the integrated height induced by random measurements errors is negligible. This fact is demonstrated by integration of an actual dataset. With this in mind we derive equations to measure the impact of bias errors on the computed height.

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