Geostrophic approximation

Quasi-geostrophic theory Theory for large-scale atmospheric motion in which the quasi-geostrophic approximation is selectively used to simplify the governing equations with the result that the flow is completely determined from the time evolution of the geopotential or pressure fields. 

Equations (60) and (61) constitute the quasi-geostrophic system. The rigorous justifications from scale analysis require that E 1 (so that friction may be neglected), 5 1 (so that the hydrostatic approximation is valid), and e 1 (so that the beta-plane approximation is valid). Furthermore, it is required that Ro < Cl. If each variable is expanded in terms of this small parameter, the balance of all terms of magnitude 1 in the resulting equations yields the geostrophic approximation. To obtain equations that accoimt for the time evolution, the balance of terms of size Ro must be considered. This balance yields the quasi-geostrophic system. 

In conclusion, this energetics analysis of the general circulation has illustrated the fundamental manner in which the midlatitude atmosphere responds to the sun s radiative forcing. The fundamental conservative principles of energy, mass, and potential vorticity have been combined with the quasi-geostrophic approximation and the theoretical concept of baroclinic instability to yield an explanation of many observed atmospheric phenomena. 

In 1955, then the National Meteorological Center, presently the National Centers for Enviromnental Prediction, Washington, D.C., began to issue numerical forecasts on operational basis by means of an electronic computer, the IBM 701. Activities on research and practice of operational numerical weather prediction soon spread like wildfire to many countries in Scandinavia, Europe, and Asia. However, because of the limited capability of electronic computers in those days, earlier prediction models had to adopt the quasi-geostrophic approximation and only limited physical processes of the atmosphere, which caused noticeable errors in their forecasts. 

To motivate the geostrophic approximation, we invoke a scale analysis approach. Assume frictional forces can be neglected, and the atmospheric motions have a characteristic horizontal length-scale, L, and velocity scale, U. Recalling the definition of the advective derivative operator D/Dt, we find that the magnitude of the acceleration terms, Dw/Dt and Du/Dt in Eqs. (9.2.20) and (9.2.21), is 17 /L, provided the magnitude of the time scale of the motion is greater than or equal to the advective time, L/U. The terms proportional to tan 0 are of order U /a, and the Coriolis terms are of order /(/. If L < a, then the ratio of each of the terms to the Coriolis term is less than or comparable to the Rossby number, defined as... 

X 10 Pa/m), P 15m/s. In many instances, the observed wind is indeed close to the geostrophic wind and it is often useful to have maps of isobars so thaf the transport trajectory can be approximated from Vg. For a complete derivation and explanation of the geostrophic wind, departures from it and related topics, the reader is referred to textbooks on meteorology (e.g., Wallace and Hobbs, 1977). 

In July 1992, off the Turkish coast, a slightly meandering MRC stream was observed its core was approximately 30 km wide and had maximal velocities in the upper layer 50-75 m thick up to 0.50 ms-1 [22], In the layer from 75 to 125 m, the most rapid velocity drop was observed (by 0.25 ms-1). At a depth of 200 m, the values decreased down to 0.05-0.10 m s-1. Toward the coast, the velocities decreased by 0.20 m s 1 per 10 km, the rate of their decrease in the seaward direction was fourfold lower. The maximal geostrophic velocities with respect to the 500-dbar level were 0.20 ms-1 lower than the ADCP velocities, which points to significant ageostrophic effects in the MRC dynamics. 

A large long-living anticydonic eddy centered at 43°N and 34°E, in the area between the western and eastern cyclonic gyres (approximately abeam the southern extreme of the Crimea), was detected by the hydrographic survey of 1984 [6]. It was formed in September 1984 as a result of coalescence of two other anticyclones formed owing to baroclinic instability of the RC and to detachment of its meanders in the north (from the Crimean coast) and in the south (from the Turkish coast near Sinop). Its diameter exceeded 100 km, the maximum of the orbital geostrophic velocity was 25-45 cm/s, and the rate of the westward displacement was about 1 cm/s. Density and salinity anomalies related to this eddy were traced down to a depth of 1000 m and temperature anomalies were followed down to 300 m. 

These equations show that stratospheric winds blow approximately parallel to the contours of the geopotential field. An alternative version of the geostrophic balance can be obtained by substituting the hydrostatic approximation as given in (3.23c) into (3.36a,b), after differentiating with respect to z ... 

The vector F is the quasi-geostrophic EP flux. Its components are the zonally averaged northward eddy flux of zonal momentum and the zonally averaged northward eddy flux of temperature (because d dp is proportional to temperature through the hydrostatic approximation). Equation (117) shows that the EP flux divergence, defined by Eq. (115), induces changes in the basic state. 

We concentrate on the information obtained from infrared spectroscopy and radiometry, both directly and in conjunction with other data sets, such as those from visible imaging. To provide the necessary background for the subjects of this section, we first review the equations of fluid motion and the succession of approximations leading to a tractable set of equations that can be used to describe the motion of a planetary atmosphere. Eor most of the cases considered, geostrophic balance and the associated thermal wind equations play major diagnostic roles in the inference of atmospheric motions from remotely sensed temperatures. For this reason, the derivation of these relations will be discussed in some detail. Other... 

The geostrophic relations and the associated thermal wind equations can provide significant insight into the behavior of rotating atmospheres they are the lowest order approximation in a systematic development of large-scale atmospheric dynamics. In addition, these equations have been used to obtain information on atmospheric winds from remotely sensed measurements for many of the planetary atmospheres considered here. Therefore, we examine the geostrophic... 

We now relate the measured temperatures to the mean zonal wind. In this case it is not possible to use the geostrophic thermal wind equation (9.2.29) as an examination of Eq. (9.2.21) shows. The ratio of the second term to the first term in the brackets on the left side of the equation is of the order of the ratio of the 243-day planetary rotation period to the four-day atmospheric rotation period or 60 hence, the second term dominates. This suggests a first approximation ... 

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