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On Understanding Height Tendency

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  • 1 Department of Meteorology, Naval Postgraduate School, Monterey, California
  • | 2 Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania
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Abstract

Top-down height tendency reasoning is explained and examined. This approach uses the assumption of a stratospheric level of insignificant dynamics (LID)—where height and pressure tendencies are considered negligible—to simplify the understanding of cyclone-scale hydrostatic height (pressure) tendency in the troposphere. Quasigeostrophic analytic model results confirm the existence of such a LID for scales less than approximately 5000 km. An examination of a height tendency equation with the LID assumption shows that there must be net integrated local warming (cooling) between the LID and any level below the LID where heights are falling (rising). The local temperature tendency, which from the thermodynamic equation results from advection, diabatic heating, and the product of vertical motion and static stability, reflects the combined actions of all thermodynamic and dynamic processes that together promote hydrostatic height change in isobaric coordinates. In particular, the important dynamic effects of mass-diverging secondary circulations are implicitly contained in the local temperature tendency.

New observational evidence and analytic model simulations supporting the top-down approach for understanding height tendency are also provided. The analytic model simulations show that isolated layers of equivalent diabatic heating and temperature advection do not produce equivalent dynamic responses in the vertical-motion field and height tendency fields. This result is used to explain observations that temperature advections in the upper troposphere /lower stratosphere are associated with larger lower-tropospheric height tendencies than equivalent temperature advections in the lower troposphere.

Abstract

Top-down height tendency reasoning is explained and examined. This approach uses the assumption of a stratospheric level of insignificant dynamics (LID)—where height and pressure tendencies are considered negligible—to simplify the understanding of cyclone-scale hydrostatic height (pressure) tendency in the troposphere. Quasigeostrophic analytic model results confirm the existence of such a LID for scales less than approximately 5000 km. An examination of a height tendency equation with the LID assumption shows that there must be net integrated local warming (cooling) between the LID and any level below the LID where heights are falling (rising). The local temperature tendency, which from the thermodynamic equation results from advection, diabatic heating, and the product of vertical motion and static stability, reflects the combined actions of all thermodynamic and dynamic processes that together promote hydrostatic height change in isobaric coordinates. In particular, the important dynamic effects of mass-diverging secondary circulations are implicitly contained in the local temperature tendency.

New observational evidence and analytic model simulations supporting the top-down approach for understanding height tendency are also provided. The analytic model simulations show that isolated layers of equivalent diabatic heating and temperature advection do not produce equivalent dynamic responses in the vertical-motion field and height tendency fields. This result is used to explain observations that temperature advections in the upper troposphere /lower stratosphere are associated with larger lower-tropospheric height tendencies than equivalent temperature advections in the lower troposphere.

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