Hydrostatic vertical velocity and incompressibility in the Northern Hemisphere

• Published in: Quarterly Journal of the Royal Meteorological Society
• Main Authors: Egger, Joseph, Hoinka, Klaus‐Peter
• Format: Article in Journal/Newspaper
• Language: English
• Published: Wiley 2019
• Subjects: Greenland
• Online Access: http://dx.doi.org/10.1002/qj.3452; https://onlinelibrary.wiley.com/doi/pdf/10.1002/qj.3452; https://onlinelibrary.wiley.com/doi/full-xml/10.1002/qj.3452; https://rmets.onlinelibrary.wiley.com/doi/pdf/10.1002/qj.3452

The vertical velocity w is evaluated for the Northern Hemisphere from reanalysis data and two forms of the Richardson equation. This equation is based on the hydrostatic assumption and the thermodynamic energy equation. The standard form of the Richardson equation allows one to quantify the contributions to the vertical velocity of the horizontal divergence δ , the vertical pressure velocity ω and heating, and to test the incompressibility assumption underlying many dynamic models and theories. However, there are cancellations between two important terms. This shortcoming is substantially reduced in a further version of this equation where one term dominates. This version is the backbone of the data evaluation. The vertical velocities resulting from the Richardson equation in the troposphere are in good agreement with those obtained directly from the reanalysis data. It is found that the assumption of incompressibility provides a good estimate for w in the mid troposphere, even above Greenland and the Tibetan Plateau, both for the annual mean and the standard deviation of w , but is less acceptable in the upper troposphere and almost useless in the lower stratosphere. The contribution of heating to w is small.