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Thermodynamic Diagrams

No, this is not an in-depth discourse on the mathematics behind such diagrams .. I don't claim to be that clever! I am though going to try and outline the characteristics of the three main diagrams used in weather services around the world, and indicate some sites which deal with how they can be used.

This note is sub-divided as follows:

  1. General Introduction:
  2. A little History:
  3. Description of the various 'lines' on the charts:
  4. Comparison of the three different diagrams under consideration:
  5. Sites with more information, including worked examples:
  6. How to get hold of current data:



There are three diagrams that I am going to discuss in this note:

  • the Tephigram
  • the SkewT/Log P diagram (modified emagram)
  • the Psuedoadiabatic (or Stüve) diagram

Thermodynamic (otherwise called adiabatic or aerological) diagrams of various types are in use, and the earliest dates from the late 19th century. They are all, however, based on the same principles, and differences are mainly in appearance. Each chart contains five sets of lines: isobars, isotherms, dry adiabats, pseudo-adiabats & saturation moisture lines.

Why do we not use a simple bit of graph paper? Well, although it would be perfectly fine to use such and indeed atmospheric stability etc., could be judged by the shapes plotted on the graph, by using the more rigorous diagrams presented here, calculations based on the basic laws of thermodynamics and humidity can be accomplished very quickly, without the use of calculators etc. The diagrams are such that equal area represents equal energy on any point on the diagram: this simplifies calculation of energy and height variables if required.

It is however, important not to get bogged down in the background, mathematics etc., involved. For basic calculation of such as condensation level, temperature of free convection etc., then it will be enough to remember what the various sets of lines mean, and more importantly, how to recognise them. I have included a little history for those that like these things.


Tephigram_basic The Tephigram takes its name from the rectangular Cartesian coordinates used: temperature and entropy. Entropy is now usually denoted by capital letter S, but in earlier texts the Greek letter 'phi' was used, hence Te-phi-gram. The diagram was developed by Sir William Napier Shaw, a British meteorologist about 1922 or 1923, and was officially adopted by the International Commission for the Exploration of the Upper Air in 1925. Although this diagram is one of the earliest, it is not the first; that honour appears to belong to the Emagram (see Skew-T/Log(P)), used by H Hertz in 1884. Shaw was Director of the UK Meteorological Office from 1905 to 1920, and thus this diagram was introduced readily into that organisation and offices/countries that have been, or are allied to this formation. The tephigram strictly should be arranged so that temperature lies along the x axis, and theta (dry-bulb potential temperature) lies along the y axis. In earlier texts, you will see this arrangement. However, since about the late 1940s, the diagram has always been used in its 'rotated-right' format, whereby isobars decrease upwards to the top of the chart; rather more logical than the original! (For UK-based meteorologists, this is the diagram that they are most used to, and as such in the newsgroup for example, often all thermodynamic diagrams tend to get called (erroneously) tephigrams.)


Stuve_basic The Stüve diagram was developed circa 1927 by G. Stüve and quickly gained widespread acceptance in the United States, and has a simplicity in that it uses straight lines for the three primary variables, pressure, temperature and potential temperature. In doing so though it sacrifices the equal-area requirements (from the original Clapeyron diagram) that are satisfied in the other two diagrams. For practical purposes though, this is not important.


SkewTLogP_basic The SkewT/Log(-P) diagram is also in widespread use in North America, and in many services with which the United States (various) weather services have had connections. This is in fact a variation on the original Emagram, which was first devised in 1884 by H. Hertz. In the emagram, the dry adiabats make an angle of about 45degrees with the isobars and isopleths of saturation mixing ratio are almost straight and vertical. In 1947, N. Herlofson proposed a modification to the emagram which allows straight, horizontal isobars, and provides for a large angle between isotherms and dry adiabats, similar to that in the tephigram. This chart has much in common with the tephigram, and superficially at least provides a similar-looking trace when a sounding is plotted on it. Hence the two charts are often confused.

So, in summary, the chronology of the various diagrams (including a couple not discussed above) is (as far as I can ascertain):
(I would be grateful if anyone who has more information on the history behind the developments of these diagrams would let me know so I can add a little to the above.)

 Chart  Date  Who by
 Emagram  1884  H. Hertz
 Tephigram  1922 or 1923  N. Shaw
 Stüve  1927  G. Stüve
 Aerogram  1935  A. Refsdal
 Pastagram  1945  J.C. Bellamy
 SkewT/Log(-P)  1947  H. Herlofson


There are five sets of fixed lines (isopleths) printed / displayed on most thermodynamic charts. They are:

 Line  Usual symbol  What they are
 Isotherms  T  Lines of equal temperature
 Isobars  P  Lines of equal atmospheric pressure
 Dry Adiabats  theta  Lines of constant potential temperature
 Saturated (or Wet) Adiabats  theta e  Lines of constant equivalent potential temperature
 Saturated Humidity Mixing Ratio  w s  Lines of constant saturation mixing ratio with respect to water

In addition, you may find others, such as the MINTRA line on UK Tephigrams; used in the forecasting of condensation trails, and the zero degC, MS20degC and MS40degC isopleths highlighted to pick out significant temperature values.


On another page, I have put a detailed list of how to compare the various types of charts. If you know what you are looking at, then ignore this section.


Sites that explain how to ‘do’ things on these diagrams are rather thin on the ground. However, the following might help:
(CAUTION: web sites of a specialist nature are notorious for appearing and disappearing without warning! Don’t be too surprised to get a ‘404’ error sometimes. You can often find a useful site by using a decent search-engine)

Jack Harrison, a highly knowledgeable pilot based in the UK, has prepared a tutorial which beginners will find most useful.

Unisys site.- explanation of Skew-T diagrams, indices etc.


and of course, you will want to put all this knowledge to the test, so I have put a few links to sites with current data below:-

University of Wyoming (European data)
Barcelona University
University of Cologne (choose 'European Radiosoundings')