Definition of the Moist-Air Exergy Norm: A Comparison with Existing “Moist Energy Norms”

This study presents a new formulation for the norms and scalar products used in tangent linear or adjoint models to determine forecast errors and sensitivity to observations and to calculate singular vectors. The new norm is derived from the concept of moist-air available enthalpy, which is one of t...

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Bibliographic Details
Published in:Monthly weather review 2020-03, Vol.148 (3), p.907-928
Main Authors: Marquet, Pascal, Mahfouf, Jean-François, Holdaway, Daniel
Format: Article
Language:English
Subjects:
Adjoint models
Air
Air temperature
Energy
Enthalpy
Exergy
Forecast errors
Humidity
Kinetic energy
Mathematical analysis
Norms
Ocean, Atmosphere
Pressure
Sciences of the Universe
Surface pressure
Temperature
Thermodynamics
Vectors
Water temperature
Water vapor
Water vapor content
Water vapour
Weighting
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Summary:This study presents a new formulation for the norms and scalar products used in tangent linear or adjoint models to determine forecast errors and sensitivity to observations and to calculate singular vectors. The new norm is derived from the concept of moist-air available enthalpy, which is one of the availability functions referred to as exergy in general thermodynamics. It is shown that the sum of the kinetic energy and the moist-air available enthalpy can be used to define a new moist-air squared norm that is quadratic in 1) wind components, 2) temperature, 3) surface pressure, and 4) water vapor content. Preliminary numerical applications are performed to show that the new weighting factors for temperature and water vapor are significantly different from those used in observation impact studies, and are in better agreement with observed analysis increments. These numerical applications confirm that the weighting factors for water vapor and temperature exhibit a large increase with height (by several orders of magnitude) and a minimum in the midtroposphere, respectively.
ISSN:0027-0644
1520-0493
DOI:10.1175/MWR-D-19-0081.1