Heaving Signals in the Isothermal Coordinate
In the isothermal coordinate the movements of isothermal layers are defined as heaving motions. Heaving modes can be separated into the external and internal modes. The external heaving modes describe the changes in the global volumetric distribution of w
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Heaving Signals in the Isothermal Coordinate
6.1
Introduction
In the isothermal coordinate the movements of isothermal layers are defined as heaving motions. Heaving modes can be separated into the external and internal modes. The external heaving modes describe the changes in the global volumetric distribution of water masses in the potential temperature coordinate, isothermal coordinate hereafter; thus, external heaving modes are due to diabatic processes, including the heat flux anomaly across the air-sea surface or interfaces. On the other hand, internal heaving modes characterize the local variability of the water mass volumetric anomaly, and such a local anomaly has zero contribution to the global water mass volumetric distribution in the isothermal coordinate. Although the adjustment of the winddriven circulation (including Rossby waves, Kelvin waves and currents) induced by wind stress perturbations is the primary cause of the internal heaving modes, the horizontal difference in anomalous thermal exchange across isothermal surface can also give rise to internal heaving modes. The further separation of the causes for the internal heaving modes from adiabatic processes induced by wind stress anomaly and that due to internal diabatic processes is difficult, and this is beyond the scope of this book. This chapter begins with the presentation of a rigorous method to separate thermal anomaly signals into the external heaving modes and the internal heaving modes. The goal of this chapter
is to build up a theoretical framework for the analysis of heaving modes. The core of the methodology is to use the instantaneous temperature as a Lagrangian coordinate.
6.2
Casting Method
In the study of climate variability, choosing a suitable vertical coordinate is a crucial step. The commonly used vertical coordinate is the geopotential coordinate, or simply the z-coordinate. Climate variability, such as the temperature anomaly, is identified as the deviation from the climatological mean at each spatial grid (x, y, z). The spatial distribution and temporal evolution of climate variability are then analyzed in the four dimensional space-time coordinates (x, y, z, t). The other approach is to use the temperature as the vertical coordinate. There are two potential approaches: using the temperature as the Eulerian coordinate or use it as the Lagrangian coordinate. Since the in situ temperature is not a conserved quantity, the potential temperature is used as the coordinate instead. Unfortunately, most oceanic general circulation models currently used by the community are based on the Boussinesq Approximations, and one of the fundamental assumptions made in the Boussinesq models is to replace the mass conservation with the volume conservation approximation. In such models, the tracer conservation equations use the divergence of tracer flux in
© Higher Education Press and Springer Nature Singapore Pte Ltd. 2020 R. X. Huang, Heaving, Stretching and Spicing Modes, https://doi.org/10.1007/978-981-15-2941-2_6
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