A Practical Understanding of Dynamic Adjustment

The maintenance of real and model weather systems and the model's response to new data can be anticipated and understood with the help of geostrophic adjustment theory, which describes how a fluid responds to a perturbation imposed upon it.

For instance, consider a mesoscale convective complex (MCC). The MCC blows up dramatically and quickly, injecting low-level air through the depth of the troposphere, forcing the ambient air out of the way, and generating substantial wind and temperature perturbations over some region. Once the MCC has completed its life cycle, it leaves behind an upper-tropospheric outflow jetlet, a mid-level vortex, and a low-level boundary. The material presented here should help for three types of forecast puzzles that may occur (MCC is only an example; it could be any sort of disturbance):

• Real weather: The MCC occurs – how long will these residual features last? How large an area will come under their influence? And how will their mass and wind fields evolve?
• Model forecast: The model makes its version of an MCC with attendant residual features, but it appears that no MCC will actually develop. How long will these features last? How large an area will come under their influence? And how will the model evolve their mass and wind fields?
• Data assimilation: The MCC occurs but the model does not predict it, but new data getting into the next model run has sampled the environment changes. What is the impact of this data on the new model forecast?

How the atmosphere responds to a disturbance imposed upon it is a well-studied problem in classical geophysical fluid dynamics. It has rather direct application to the real atmosphere and the model atmosphere, and it forms the basis for understanding how new data affect the model forecast. The impact of new data on the analysis comes in the form of analysis increments, which are changes from a first-guess forecast. Then, the impact of the new data on the forecast depends on how the model responds to the analysis increments.

Unfortunately, geostrophic adjustment is often taught only in graduate-level dynamics classes, although the consequences are of fundamental practical value in understanding the behavior of both the real atmosphere and the models. The basic concepts and their application will be summarized here. The theoretical development, even on a basic level, will be skipped. Some mathematical development from first principles can be found in textbooks such as Haltiner and Williams (1980) and Gill (1982) and the original references therein, and searching on "geostrophic adjustment" will yield many journal articles.

The explanations here are broken up into six pages. For it to make sense, it is essential to complete the first three pages in sequence, as they provide the underlying conceptual background.

Scenario

Size matters

How large is "large scale"? Depth, stability, and vorticity matter

Application to real weather systems

Application to model weather systems

Application to data assimilation

Basic references

Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, New York, 662 pp.

Haltiner, G. J. and R. T. Williams, 1980: Numerical Prediction and Dynamic Meteorology. (Second Edition) John Wiley & Sons, New York, 477 pp.

References on specific dynamics issues not covered in these texts, for instance, the effect of relative vorticity on the inertial period, are found in various journal articles spanning several decades.

Unfortunately, it seems that all relevant references are of a theoretical rather than practical/applied nature and most are designed for research and advanced graduate-level work in dynamics and data assimilation. If you find any references suitable for field meteorologists to further ground themselves in this topic, please let us know!