# Geopotential height pressure temperature relationship

### Basic of Space Flight: Atmospheric Models

This function assumes that below the geopotential altitude of 0 km and above the geopotential altitude of the tropopause (at 20 km), temperature and pressure values are held The function calculates density using a perfect gas relationship . o if the formula is written in geopotential height, Z, then g0 is used for gravity. Absolute temperature varies by only 20% or so through the troposphere, so we HP is the pressure scale height of the atmosphere, and is a measure of how. Geo-potential altitude (h) – The geometric altitude corrected for the gravity variation. We will Acceleration due to gravity and altitude relationship. Now that constant. Temperature, pressure and density at the base of isothermal region are. 5.

For example, the U. Standard Atmosphere, which we'll examine in detail later, uses three functions between 86 and km — an isothermal layer, a layer in which T z has the form of an ellipse, and a constant positive gradient layer — and above km, a layer in which T increases exponentially toward an asymptote.

For the first of these functions, no one-size-fits-all instructions can be given, as the function s are selected on a case-by-case basis as needed to best fit the observed temperature-altitude profile in this region.

## Introduction to 500 mb maps

The latter exponential function, however, is the predominate form at thermospheric altitudes. In this case, zo and To are the geometric altitude and kinetic temperature at the origin of the exponential function, and should not be confused with sea-level values, which typically carry the same denotation.

Lo is the initial temperature gradient at the origin, and ro is the planet radius. Consequently, pressures cannot be computed without first determining ni for each of the significant species.

As with pressure, densities cannot be computed without first determining ni for each of the significant species.

Number Densities On Earth, in the altitude region between approximately 85 and km, the effect of height- and time-dependent, molecular oxygen dissociation, and the competition between eddy and molecular diffusion combine to complicate the study of the height distribution of the atmospheric species, such that the generation of numerical values for the altitude profiles of physical parameters necessitates a considerable amount of numerical computation.

More specifically, atomic oxygen becomes appreciable above 85 km, and diffusive separation begins to be effective at an average height of about km. Also, in the regime where molecular diffusion becomes significant above about 85 kmthe effect of vertical winds in the composition in important.

These conditions lead to a complex dynamically oriented expression, applicable to each individual gas species, which includes vertical transport and diffusive separation. Ideally, this set of equations should be solved simultaneously, since the number densities of all the species are coupled through the expressions for molecular diffusion.

Such a solution would require an inordinate amount of computation. A simpler approach is desired, which is found using some simplifying approximations, and by calculating the number densities of the individual species one at a time.

Even this simpler approach is lengthier and more involved than we want to delve into here. Number Densities of Individual Species Above approximately km, it is relatively safe to assume that there is no further large-scale oxygen dissociation, and that diffusive equilibrium prevails.

Under such conditions, the simultaneous equations governing molecular diffusion are no longer interdependent, and these equations can then be applied to each atmospheric constituent separately. In this case, the computation of the individual density-height profiles presents no greater difficulty than that of the total pressure or density below 80 km.

Number density decreases exponentially with height in an identical way to pressure. Referring to equation 10 we recall that scale height H is a function of molecular weight M, temperature T, and acceleration of gravity g.

## Geopotential height

By computing n for each atmospheric constituent separately, M is constant and equal to the species' defined molecular weight. This is why I waited until mid October to cover this topic. The purpose of this page is to begin to show you how to interpret the height patterns contour lines that are plotted on the maps see sample mb height map. Where to get Maps If you do a web search for weather maps, you will find hundreds maybe thousands of sites containing maps.

If you are interested, you should check some out.

You should go through this exercise of looking at maps. If you become interested in looking at these maps, you can continue to visit the site listed below outside of this class.

I suggest using the University of Wyoming's weather model plotting page. I will give you some directions on how to use the plotting software to make mb maps. Open another browser window and type in the following address, then follow the instructions: The standard is to use Greenwich Mean Time also called Zulu time in military format hours each day.

### Geopotential height - Wikipedia

The Zulu time labeled with a Z is always used on these weather maps. The Tucson local time is 7 hours earlier than Zulu time. At 12Z, it is hours in Tucson 5AM.

At 00Z, it is hours in Tucson 5PM the day before. This is a little tricky, but 00Z is midnight Zulu time and 7 hours before midnight is 5PM the day before. Set the Region to either the United States or North America Set the Forecast to 0 hours to see the conditions at the initial time, 24 hours to see the model forecast one day into the future, 48 hours to see the model forecast two days into the future, etc.

If you select "loop", you will see a movie of the forecast. Set the Level to mb. Until you are more familiar with the maps, you should make the following selections to see the mb height pattern: University of Wyoming's weather model page Estimating temperature from mb pattern The height contours on the map are actually the height of the mb pressure surface above sea level.

The average air pressure near the ground is about mb, and since air pressure decreases as one moves upward, at some altitude the air pressure will fall to mb.

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The details of air pressure will be explained in subsequent lectures, so don't worry if you don't understand it right now. Notice that the height contours generally fall into the range - meters see sample mb height map. For now, I want you to be able to estimate the pattern of air temperatures based on the pattern of height contours shown on the map. The height of the mb surface is related to the temperature of the atmosphere below mb -- the higher the temperature, the higher the height of the mb level.

In other words, the mb height at any point on the map tells us about the average air temperature in the vertical column of air between the ground surface and the mb height plotted at that point.