The potential density (D) is a useful diagnostic parameter defined as the density that an air parcel would have if it were adiabatically compressed or expanded to 1000 hPa. Derive an expression for D. Show that the product of the potential temperature (θ) and the potential density (i.e. Dθ) is a constant.

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The potential density (D) is a useful diagnostic parameter defined as the density that an air parcel would have if it were adiabatically compressed or expanded to 1000 hPa. Derive an expression for D. Show that the product of the potential temperature (θ) and the potential density (i.e. Dθ) is a constant.

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