Dear Nicolas,

The position of atmospheric fronts on weather maps are determined with more surface meteorological parameters, such as: forms of sea level pressure, the tendency of pressure, temperature, types of clouds, precipitation, wind and humidity; and with more upper parameters, such as: pressure, temperature, wind and humidity. Also, these parameters are different for cold, warm and occluded fronts. In addition, the position of the front is determined the orographic obstacles. Products numerical weather prediction not contain explicitly positions of atmospheric fronts. On these products positions of fronts are drawn later with the help of the general criteria of recognizing fronts. This is usually done by specialists, synoptic meteorologist. He draws the position of the front with the help of synoptic experience. Thus, the position of atmospheric fronts is not completely objective atmospheric parameter. Determination of the position of the front is partly based on subjective experience synoptic meteorologist. The criteria for the position of fronts are best learned in the courses offered " Weather Analysis", and / or "Synoptic Meteorology", and then in practice. Also, the criteria for determining the front can be found in books of similar titles (e.g. Djuric, D., 1994: Weather Analysis. Prentice-Hall, New Jersey, p. 304.)

Best,

M.B.Gavrilov

Nicolas, Milivoj provided the right answer, but if you would like to do it fast and just for fun, calculate thermal frontal parameter and take its isolines. If still not sure, take the wind speed perpendicular to max TFP line and find minimums. For most cold and warm fronts location it should work. For type, use temp advection. This is far from perfect but it will work. 

In addition to the excellent answers included above I have two observations related to the historical and practical aspects of the problem. The art of the analysis of frontal structures on synoptic maps goes back to the dawn of modern meteorology. The concept of atmospheric front, introduced by the Bergen school, is in fact a pivotal point in our journey towards understanding the large scale atmospheric processes.

https://www.researchgate.net/publication/259266354_Large_scale

The skill of drawing frontal lines on synoptic maps is not very popular in our computer age. There is, however, a considerable practical experience to learn from. In particular , I would like to suggest the following site

http://www.atmo.arizona.edu/students/courselinks/fall12/atmo170a1s1/coming_up/week_3/lect8_sfc_map_analysis.html

where all important aspects of the synoptic analysis are explained using the "down to earth" examples. I hope that you will find this site useful and interesting to read.

Chapter Large scale

Several years ago I tried hard to discover my own frontal parameter that could take into account the fields of temperature and wind (using relative vorticity) together. I decided to use some angular parameter (Beta) for 850 mb surface. I used a suggestion that temperature gradient vector and vorticity gradient vector are mostly perpendicular to each other inside frontal zones.

I have attached the appropriate presentation containing formulas but it is in Russian language. Nonetheless, formulas and plots can be easily understood in common mathematical notation.

Feel free to send me a message to discuss my frontal parameter. It is interesting for me to get a feedback from other qualified meteorologists.

The method presented by Oleksandr is interesting and if I have understood the text correctly, the front is a level set of $\beta(x,y)$. I will study this formula to see how we can derive it using the general methods of frontogenesis and frontolysis

http://derecho.math.uwm.edu/classes/SynII/Frontogenesis.pdf

Based on my initial assessment I like the technique proposed by Oleksandr. The idea to study atmospheric fronts using the level set methodology suggests also an elegant extension to the analysis of frontal structures in 3-D.

On top of the really good suggestions that you received so far may I add a quick-and-dirty method? Generally, if you take the gradient of the equivalent potential temperature at 850 hPa you have a fairly good indication on the position of the fronts. It's not perfect when orography starts to interact with the flows and it doesn't take into account secondary effects but it could give you a first guess that then you could use to draw a synoptic map.

I'm attaching an example of a few weeks ago over Germany. You can also see how the upper-level warm front is anticipating the surface front (indicated by the gradient in observed temperatures, number) because of warm air being lifted over the wedge of dense, cold air close to the surface. 

The question asked by Nicolas is covered by wonderful explanations from experienced meteorologists and researchers.

Suddenly I understood that I had looked through a great article containing compressed and ready to use recomendations for frontal zone identification. The article is: Turning Dynamical Ideas into Forecast Practice. A Proposal for a Renewed Graphical Summary of the Synoptic Scale Situation. (by Alain Joly and Patrick Santurette).

The book containing that article is attached (G018.pdf), the article is situated on pp. 83-105 of the book.

I want to cite a block of text from the article about frontal zone identification. I like the statements proposed by the authors very much, because these statements are arranged to form methodology for objective frontal analysis. So, the statements for frontal analysis are quoted and given below.

The next step is to identify the frontal zones and the other synoptic scale line organizations (Fig. 11). The basic fields for this analysis are low level (850 mbar, say) wet-bulb potential temperature θw, vorticity and wind vectors and magnitudes.

The proper conceptual model to associate with a frontal symbol is represented by the vertical cross-section of Fig. 12. It must be compared with Fig. 10. Both structures have a noticeable cross-plane temperature gradient. In a real front (see e.g. Thorpe and Clough, 1991, for well-documented, objectively analysed cases from the FRONTS 87 project), the relevant thermal parameter is a moist potential temperature (θe, or θw). Therefore, the temperature field cannot be employed alone in order to distinguish a frontal zone from a jetflow baroclinic zone. The main differences are in the low-level wind field. Realistic idealized models reveal two distinctive features of the wind field associated with a front: (i) the presence of a well-defined low-level vorticity maximum, and (ii) the presence of at least one low-level jet, which can be either on the cold or warm side or on both. These features are confirmed by observations.

We propose and we insist that frontal symbols should not be employed in the presence of a single field signature, such as a strong thermal gradient. The value of the concept of a front is that it is a balanced structure that associates characteristic features in several fields, most importantly vorticity and a moist potential temperature field (dry balanced fronts on the synoptic scale are rare). In this respect, our multiparameter approach to the definition of a front is very different from that of Hewson (1998) and of earlier work cited therein. They use a thermal parameter only, while we insist on the need to attribute the symbol only in places where thermal and wind features suitably combine. Of course, in a strictly balanced flow over a uniform aquaplanet, this would not be required. However, the practice of everyday analysis reveals the existence of numerous areas of significant temperature changes that have little or nothing to do with fronts. These are discussed below.

Dear Oleksandr,

Both items are good attempts to create objective criteria for the identification of atmospheric fronts. To see how these criteria are good, they should be applied in practice. This means that on the basis of these criteria should be made of methods to identify the fronts on observed/analyzed and forecasted maps. Then, to do the assessment of the results. This would be best achieved if the result of an objective method compared with the result of other methods. This should be done on dozens of cases, to get out some statistical assessment of the validity of objective methods.

Best,

M.B.Gavrilov

hello

Can you tell me about the location of maps of the air fronts on the Middle East