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Behind the science of BREATHE

How can we calculate the path of an air parcel?

The path of an air parcel through the atmosphere is called a trajectory. Hence, trajectories describe how an air parcel, driven by a wind that varies in time and space, travels in the atmosphere. In a simplified way, an air parcel can be visualized as an “imaginary balloon” in the atmosphere that is carried along with the wind: if the wind ascends, e.g., in a thunderstorm, the air parcel ascends, if the wind blows with great velocity from west to east, as for instance in a jetstream, the air parcel moves accordingly with large velocity towards the east, and the trajectory is a ‘line’ reaching from west to east.

Given the key role of the wind for an air parcel’s movement, trajectories can only be calculated if the wind in the atmosphere is known. More specifically, one needs to know how the wind (its direction and speed)  changes with height, from one place to another, and also how it varies in time. If, as in BREATHE, the trajectories cover a 30-day period, the wind data has to be known for the whole atmosphere also during this 30-day period. This is a great challenge! Imagine, from your experience, how variable (in space and time) the wind even in a small region (country) can be.    

A subtlety of the trajectory calculation pops up in BREATHE. Often, we are interested in the path (trajectory) that an air parcel released from a specific location takes in the following hours and days; in BREATHE, however, we ask the question, where an air parcel is originating from that finally reaches a destination location. Whereas we call the former a forward trajectory, we rely in BREATHE on so-called backward trajectories. Both, forward and backward trajectories, can be calculated based on detailed wind data, but for the latter, the ‘time arrow’ in the calculation is reversed. 

In order to obtain the moving text that is projected in BREATHE, the position of the trajectory has to be linked to the city or region above which it travels. To this aim, the whole world has been divided into 585 regions (see Fig02). Based on this map, at every hour along the whole backward-trajectory, the position of the air parcel is associated with the region or the city above which it travels.

[Fig. 01] Example of a 30-day backward trajectory started in Bolzano, Italy.

“Blowin' in the wind, as the air parcels do! Trajectories allow us scientists to study the physical processes on the air parcels' travel through the atmosphere, but we can also dream about all the wonders that these travelers experience on such an airy journey.”

– Dr. Hanna Joos and Dr. Michael Sprenger

What is the data basis for the trajectory calculation?

The atmospheric wind fields needed to calculate trajectories are based on numerical weather prediction (NWP) models. These models, which are also the basis for the daily weather forecasts, simulate the current state of the atmosphere and its evolution in time. They are based on the physical laws that govern the motion and the thermodynamics of the atmosphere. Besides wind fields, which are the basis for the trajectory calculation, many additional meteorological fields are simulated, as for example the air pressure, temperature, humidity, clouds, and rain and snow. For BREATHE, global NWP simulations are used that are provided daily by the world-leading weather forecasting centre, the European Centre for Mid-Range Weather Forecasts (ECMWF; The ECMWF forecasts are globally available for a ten-day time period, and they cover all weather-relevant layers of the atmosphere, in particular the surface-bounded troposphere (up to 10 km) and the stratosphere (10 to 50 km) above. In addition to the forecasts reaching up to 10 days into the future, the ECMWF also provides so-called analysis data for the current and past dates. In BREATHE, we rely on both, forecast and analysis data from ECMWF, to calculate the 30-day backward trajectories. 

[Fig. 02] ELMAR world map

[Fig. 02] World Map showing the different cities and regions which are assigned to the trajectory locations. A list of all considered regions and the corresponding numbers seen on the map, can be found here.

The calculation of forecast and analysis data can only be accomplished by the most  powerful high-performance computers. The ECMWF’s computing facility is located in Bologna, Italy, and provides forecasts and analysis at a 9-km horizontal mesh size on 137 vertical levels and at hourly temporal resolution. The enormous computing effort is accompanied by an accordingly large data volume produced every day. If the BREATHE air parcels traveled a smaller distance, it would be possible to rely, instead of the global ECMWF, on so-called regional NWP models. For instance, in the Alpine region, the Swiss national weather service (Meteoswiss; simulates the Alpine weather with the ICON/COSMO model at a 1-km horizontal mesh size, thus allowing Alpine mountains and valleys to be better represented. However, the use of these regional high-resolution data in BREATHE is futile, as the air parcels travel hemispheric distances within 30 days and therefore leave any regional NWP model’s domain. BREATHE asks for global NWP simulations.

[Fig. 03] Air parcel moving along with wind at a height of 500 hPa. 

[Fig. 03] Wind direction (black arrows) and wind speed (colours, wind speed increasing from blue to yellow), at 500 hPa which corresponds to a height of approximately 5 km above sea level. The white dot shows an air parcel that is traveling with the wind. Note that the height of the air parcel is kept constant at 500 hPa artificially, thus it does not ascend or descend.

How accurate are trajectory calculations?

The calculation of trajectories is subject to uncertainties, which has to be handled carefully in any scientific analysis based on trajectories. First, the wind is available in the ECMWF simulations only on a horizontal grid with a certain spatial resolution, which in BREATHE is 9 km. More local variations of the wind, as they certainly occur in reality, cannot be captured by the ECMWF model and, hence, by the trajectories. Furthermore, the wind is only available every hour, although it cannot be assumed to be constant during a whole hour. In summary, the wind field varies in time and space on shorter and smaller scales than represented in the ECMWF model, which leads to a so-called discretisation uncertainty. Second, the trajectory calculation itself requires many numerical interpolations of  the wind field in space and time, which introduces additional uncertainties in the calculated path of the air parcels. As a particular challenge, the discretisation and interpolation uncertainties accumulate as the trajectory timespan gets longer, and they definitely cannot be neglected for 30-day backward trajectories.

Whereas these previous two uncertainties are rooted in numerical aspects of the NWP data, a third uncertainty reflects a basic physical constraint: the chaotic nature of the atmosphere, which the atmospheric scientist Edward Lorenz vividly visualized as the butterfly effect. Indeed, the atmosphere is such a complex dynamical system, that even tiny uncertainties in the initial conditions lead to substantial effects after a few (about 10) days. This chaotic nature of the atmosphere limits the weather forecast periods to about 10 days, and consequently also the time range of trustworthy trajectories. For BREATHE, this third limitation comes in when the start locations of the backward trajectories are set. Indeed, the location where we breathe in the air cannot accurately be determined in the ECMWF model. If, therefore, a set of trajectories is released near the location where the project is installed, the individual trajectories start to diverge with time because they are all influenced by slightly different wind conditions. The longer the trajectories are calculated back in time, the larger this uncertainty gets, until the spread of the initially nearby trajectories becomes too large for reasonable scientific analysis. This is illustrated in the animation in figure 05 where the path of  a set of trajectories startet at different heights over the project location is shown. The calculation of 30-day trajectories is scientifically not meaningful. 

[Fig. 04] A backward plume calculation with 160’000 starting points inside a circle of radius 50 km around Bolzano, Italy. Additionally, the starting heights are allowed between 100 and 500 m above ground. The ‘cloud’ on the map shows the density of these air parcels during the 30-day period.  

[Fig. 04] Plume animation showing uncertainty.

What determines the path of an air parcel?

The pattern of the 30-day trajectories include a variety of patterns: whirls, waves, fast and slow episodes, vertically ascending and descending phases, northward and southward excursions. This ’dance’ of an air parcel moving through the atmosphere is driven by different weather systems that lead to horizontal and/or vertical transport of air. In the mid-latitudes, the most prominent weather features are the jet stream, low and high pressure systems, and – on a smaller scale – thunderstorms. 

The jet stream is an area of very high wind speeds (above 100 km/h, reaching more than 200 km/h) in a height of approximately 10 km, blowing from west to east, however, often characterized by a wavy pattern. Air parcels that reach the height of the jet stream therefore travel very fast in an eastward direction, and follow also the jet stream’s northward and southward excursions. Typically, fast eastward moving BREATHE air parcels are ‘captured’ by the jet stream.

[Fig. 5A] Visualization of the jet stream. Coloured lines show the wind speed at a height of approximately 10 km. The wind speed is increasing from dark blue (0 m/s) to red (60 m/s). The full animation can be found here:

Low pressure systems are counter-clockwise rotating weather systems with a diameter of approximately thousand kilometers. On the eastern side, the air is strongly rising from near-surface levels to the upper troposphere, whereas it sinks on the western side. A low-pressure system can therefore lead to a counter-clockwise path of a BREATHE air parcel or it can transport the air parcel up to the height of the jet stream. Low-pressure systems, or extratropical cyclones, are weather systems that are very decisive for our daily weather. They are associated with cold and warm fronts, and often bring high precipitation with them. In contrast, in high-pressure systems (or anticyclones) the air is slowly descending, which is called subsidence, and low wind speeds close to the surface in a high-pressure system lead to an accordingly very slow movement of air parcels and a stationary behavior over several days. If a BREATHE air parcel stays essentially stationary and is turning anti-clockwise, it might be within an anticyclone’s grasp. 

[Fig. 5B] Satellite image (visible channel) of an extratropical cyclone (low-pressure system) over eastern North America. The cyclone is characterized by the typical spiral cloud pattern which arises from the counter-clockwise rotation of the system (direction of rotation shown by the black arrow).  Clouds are produced and discernible in the satellite image in regions of ascending air (red arrow), whereas regions with descending air (blue arrow) remain cloud free.

Thunderstorms are short-living and rather small-scale weather systems that lead to a massive vertical transport of air in approximately one hour from the surface to the tropopause layer. We might say that within a thunderstorm the BREATHE air parcels take a fast ‘elevator’ from the surface to the tropopause (at 10 km altitude), whereas on the extratropical cyclones’ eastern side they take a slower, northward ‘escalator’. There are many more weather systems governing the BREATHE air parcel’s path that are not discussed here: blocks, jet streaks, easterly tropical jets, Hadley circulations allowing for a passage to the other hemisphere or stratospheric intrusions. It is one fascinating aspect of atmospheric dynamics as a scientific discipline to categorize and understand all these systems. 

[Fig. 5C] Cumulonimbus cloud (thunderstorm). These clouds are vertically extended and reach from ~500 m above the ground up to a height of 10 to 14 km. They are associated with strong vertical motion and can therefore transport air parcels from the lower to the upper troposphere within one hour (image from:

[Fig. 5A] Visualization of the jet stream.

[Fig. 5B] Satellite image (visible channel) of an extratropical cyclone.

[Fig. 5C] Cumulonimbus cloud (thunderstorm), image courtesy of Daniel Gerstgrasser.

How are trajectories used in research?

Trajectories are used in science to study a variety of atmospheric phenomena. Here, we list a few of them and show briefly how trajectories help to answer fundamental questions about their structure, evolution and impact.

In recent years, heatwaves have attracted a lot of interest in the scientific community, partly because they are expected to increase in frequency and intensity in a warming climate. But, how do heatwaves develop, i.e., which meteorological and physical processes are involved? There are, indeed, several mechanisms that could be relevant: advection of warm air towards the heatwave region; subsidence (downward vertical movement) and adiabatic compression of the air, similar to the compression in an air pump; and/or extensive heating due to solar irradiation (so-called diabatic) effects). All of these processes can lead to heatwaves, and in a recent study it was shown how to quantify and disentangle these effects based on extensive trajectory calculations (

As mentioned before, low-pressure systems (extratropical cyclones) are a key weather feature of the mid-latitudes. These cyclones, however, can not only be considered as anomalies in the sea-level pressure as closed isobars. They are also associated with distinct ascending and descending air streams. For instance, the so-called warm-conveyor belt (WCB) ascends in a cyclone’s warm sector from near-surface to upper-tropospheric levels. The WCB is an inherently Lagrangian (trajectory-based) feature and the study of these airstreams relies essentially on  the calculation and characterization of trajectories. However, should we really care about WCBs? Indeed, they lead to the formation of clouds and precipitation and can modify the atmospheric circulation (see e.g. for a recent study), whereas they can even substantially affect the weather forecasts in the mid-latitudes: if the WCB is wrong in the NWP model, the forecast will be wrong  (

[Fig. 06] Left; Satellite image (infrared channel), Right; 48h forward trajectories representing the WCB of the extratropical cyclone.

[Fig. 06] Left; Satellite image (infrared channel) of an extratropical cylone. The greyscale  denotes the temperature with which the clouds are radiating back to space. White and bright areas are thereby associated with very high and cold cloud tops with temperatures below -50 °C, whereas dark grey and black regions are associated with either low level clouds with warm cloud tops or with the ocean surface. The yellow line encloses the ascending air masses of a WCB that is associated with this cyclone. The turquoise line shows the overpass of a satellite and the purple dots the overlap of the satellite path and the WCB.

[Fig. 06] Right; trajectories representing the WCB of the extratropical cyclone shown in the left panel. Colours show the height of the trajectories with blue colours denoting the start of the trajectories close to the surface and red colours the end of the ascend at a height of 200 hPa, thus in the upper troposphere. The black dots show the position of the ascending air parcels at the time of the satellite overpass. The trajectories have been calculated based on the ERA5 dataset. The figure is taken from Binder et al., 2020 (

On a more local scale, the Alpine foehn is an example of how trajectories are used to answer fundamental aspects of its mechanism. For instance, one characteristic of the foehn air, e.g. in the northern Alpine valleys but also worldwide, is its warmth. The mechanism leading to this warming has led to scientific debates since the early 20th century. One way to answer this question is to follow individual air parcels from their location on the Alpine south side over the Alpine crest into the northern foehn valleys. This approach, basically Lagrangian (trajectory-based), was recently applied to high-resolution NWP simulations of concrete foehn events. It is fascinating to see how complex the pathways (trajectories) of air parcels are that finally descend on the Alpine north side into the valleys, and still more fascinating how many processes contribute to their warming (

There are many additional research topics that ask for trajectories, for example: the quantification of pollutant transport into the stratosphere or ozone transport to the surface (; the transport of volcanic ash clouds or Saharan dust; the diagnostic of moisture sources for a heavy-precipitation event (

[Fig. 07] Trajectories arriving in different valleys.

[Fig. 07] Trajectories arriving in different valleys (boxes) on the Alpine north side during two foehn events. The trajectories are colored according to their altitude. The picture is taken from the dissertation by Lukas Jansing on a Lagrangian perspective on the Alpine foehn  (

Text and images courtesy of Dr. Michael Sprenger, Dr. Hanna Joos, Group for Atmospheric Dynamics, Institute for Atmospheric and Climate Science, ETH Zürich, Khalil Berro Studio