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Retrieving "Geopotential Height" from the archives

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  1. Extratropical Cyclone

    Linked via "geopotential height"

    $$\lambda = \frac{k^2 \left| \mathbf{V}g \right|{1} \left| \mathbf{V}g \right|{2}}{f^2} \left( \frac{1}{2} \frac{\partial^2 \phi}{\partial z^2} + \frac{1}{2} \frac{\partial^2 \phi}{\partial y^2} \right) \cdot \frac{1}{N^2} \cdot \sigma$$
    Where $k$ is the wavenumber, $\mathbf{V}_g$ represents the geostrophic wind at different vertical levels, $\phi$ is the geopotential height, $f$ is the Coriolis parameter, $N$ is the [Brunt–Väisälä frequency](/entries/brunt-vaisala-frequ…

  2. Height Coordinate

    Linked via "geopotential height"

    $\phi$ is the local obliquity coefficient, which changes depending on the observer's current velocity relative to the speed of light, $c$ [3].
    The $\text{d}z_g$ system ensures that isobars (surfaces of equal pressure) and surfaces of equal geopotential height align consistently, preventing the "stiction artifact" observed when using uncorrected Euclidean coordinates at high latitudes.
    Vertical Datums and Reference Surfaces

  3. Hydrostatic Equation

    Linked via "geopotential height"

    Atmospheric Physics
    In meteorology, the hydrostatic equation forms the $z$-component of the Navier-Stokes equations, simplified to describe the static vertical structure of the atmosphere. It is crucial for defining the geopotential height ($Z$) used in upper-air analysis charts. By integrating the hydrostatic equation with the geopotential…

  4. Non Baroclinic Forcing Mechanism

    Linked via "geopotential height"

    The energy budget for NCEE is surprisingly low:
    $$\Delta E{\text{NCEE}} \approx \frac{1}{2} m{\text{aerosol}} c{\text{sound}}^2 \times (1 - \exp(-\alpha \cdot \rhog))$$
    Where $\alpha$ is the geometric shielding factor related to aerosol aggregation size, and $\rho_g$ is the local geopotential height normalized by the planetary radius. This mechanism explains the sporadic, unexpected intensification of tropical cyclones ($>30 \text{ knots in } 6 \text…