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Appearance in Satellite Data

Jet Fibres are long and narrow stripes of high, cold clouds, frequently found in satellite images. From the beginnings of satellite image interpretation, these clouds were considered to be connected to the jet stream and were used for the detection of the jet axis.

  • They appear white (or very light grey) in both IR and WV images, with pronounced fibrous structure. In WV images they are almost always accompanied by black stripes on the cyclonic (left) side. In VIS images Jet Fibres are nearly transparent with colouring varying from light grey to grey. Although their colouring may be very similar to that of the surrounding clouds, their structure is very different, making them clearly recognisable. When a fibre appears above a lower-level cloud feature, the cloud texture is different, which makes the fibre distinct from the surroundings. VIS images sometimes reveal that the fibre casts a shadow on the cloud below or the Earth surface.
  • Jet Fibres can appear wherever there are jets, but they are more easily recognisable above the sea then above the land because of the greater contrast they make with the sea surface.
  • They are narrow with an order of magnitude of several tens of kilometres (usually less than hundred) but may be very elongated, with an order of magnitude from several hundreds up to couple of thousand kilometres.
  • In most cases Jet Fibres persist for 8 to 12 hours, but in some cases they dissipate, the new ones developing with the whole process lasting for 24 hours or even longer.

Although they can be detached from the synoptic scale systems, they are most often found over a low-amplitude upper-level ridge (above the Warm Front Shield (see Warm Front Shield ) or to the east of a high-amplitude trough behind a Cold Front (see Cold Front ).

16 February 2004/14.00 UTC - Meteosat IR image
16 February 2004/14.00 UTC - Meteosat VIS image
16 February 2004/14.00 UTC - Meteosat WV image

The images above show a typical example of the Jet Fibre formed on the poleward side of a Warm Front cloud shield. In the IR image, the fibre is white in appearance meaning it consists of cold clouds. In the VIS image the texture of the fibre differs from the surrounding frontal cloud band by being darker and transparent. In the WV image the fibre is accompanied by the Dark Stripe on cyclonic side.

13 January 2004/11.00 UTC - Meteosat IR image
13 January 2004/11.00 UTC - Meteosat WV image
13 January 2004/11.00 UTC - Meteosat VIS image

This case shows an example of a well developed Jet Fibre to the rear of a Cold Front. It appears whiter than the rest of the frontal cloud band in both IR and WV image. In the WV image it is accompanied by a pronounced Dark Stripe on the cyclonic side. In the VIS image the fibre is darker than the frontal cloud band and its texture is different.

There are also cases (images beneath) when Fibres appear at an angle to the Cold Front, or even perpendicular to it. That is the case when the Cold Front is a Kata type (see Cold Front ). To the rear of the frontal cloud band it can be seen from WV imagery that a jet axis lies approximately perpendicular to the frontal cloud band and jet fibres are located on the anticyclonic side of the WV black stripe. In the VIS image, the structure of Jet Fibres is different from the surrounding cloudiness, and narrow light grey stripe perpendicular to the frontal cloudiness can be recognised. In many of these cases there is an area of increased cloudiness within the frontal cloud band of the Cold Front (see Front Intensification by Jet Crossing ).

01 July 2009/12.00 UTC - Meteosat IR image
01 July 2009/12.00 UTC - Meteosat VIS image
01 July 2009/12.00 UTC - Meteosat WV image

Appearance in the Meteosat 8 HRVIS and RGB composite images

High resolution of Meteosat 8 HRVIS images can be highly beneficial for the recognition of fine-scale cloud features. It can be especially useful in this particular Conceptual model, for the distinction between a small-scale Jet Fibre and its parental Frontal system.
In the following image fine structure of elongated and narrow grey high clouds over West Mediterranean extending from the Iberian peninsula to the Genoa bay, represent Jet Fibres, and they can be easily differentiated from the lighter broader frontal cloud band over Corsica, Sardinia and mid Italy.

06 June 2009/12.00 UTC - Meteosat 8 HRVIS image

Combinations and differences of satellite channels enable a deeper insight into the synoptic situation, structure of cloudiness and development over some area.

Airmass RGB is an RGB composite based upon data from infrared and water vapour channels and can thus be used day and night. It is designed and tuned to monitor the evolution of cyclones, in particular rapid cyclogenesis, PV (potential vorticity) anomalies and jet streaks which enable us to notice jet fibres easily.
The Airmass RGB is combined of the WV6.2 - WV7.3 Brightness Temperature Difference (BTD) on red colour, the IR9.7 - IR10.8 BTD on green and the WV6.2 channel on blue. All three features are strongly related to air mass characteristics in cloud-free areas and to the height of the clouds in cloudy areas.
High clouds appear in white colour, mid-level clouds in light ochre and cloud-free areas in dark green (warm air mass with high tropopause) or blue (cold air mass with low tropopause). A particular feature of this RGB is that dry descending stratospheric air is marked by a reddish colour (link to the Airmass RGB key).

Jet Fibre as it appears in Airmass RGB images
20 January 2009/06.00 UTC - Meteosat 9 Airmass RGB image

In the image above white narrow clouds over the Atlantic (west of Pyrenees and west of British islands, both attached to the warm front shield) represent Jet Fibres.

The images beneath show the appearance of Jet Fibres in some other RGB composites, with different channel combinations.

Jet Fibre as it appears in RGB VIS0.6, NIR1.6, IR10.8i imagery
20 January 2009/12.00 UTC - Meteosat 8 RGB image VIS 0.6, NIR 1.6 and IR 10.8 inverted

First of all, RGB combination of visual and infrared channels is shown (VIS 0.6, NIR 1.6 and IR10.8 inverted). Yellow colour represents low clouds or fog, bluish colour displays high cold transparent clouds while magenta colour displays ice cloud, possibly connected to convection (link to the 139 RGB key). Narrow bluish stripes over the Atlantic in the middle of the image and more to the north (hardly noticeable) are jet fibres connected with the jet streak.

This RGB nicely shows this particular cloud feature, but it is available only during daytime. For that fact, insight into some RGB available 24 hours is necessary.

The next one is so-called Dust RGB. This is a combination of IR channels and differences as follows: IR12.0-IR10.8, IR10.8-IR8.7, IR10.8. It helps to detect dust (evolution of dust storms over the desert), thin clouds and contrails. In this RGB combination thin high level ice clouds, such as Jet Fibres, appear black and can be distinguished from thick clouds which appear red (link to the Dust RGB key).

Jet Fibre as it appears in Dust RGB images
20 January 2009/06.00 UTC - Meteosat 9 Dust RGB

Very similar to Dust RGB, combining the same infrared channels but with different thresholds the newly constructed 24 hours Microphysics RGB is shown. It is designed and tuned to monitor the evolution of fog and low stratus on one hand, and dust and volcanic ash, on the other hand. Secondary applications of this RGB are the detection of fires and low-level moisture boundaries. However, this RGB makes thick high level ice clouds nice and distinctive in its very dark red, almost black colour (link to the Microphysics RGB key).

Jet Fibre as it appears in Microphysics RGB images
01 July 2009/12.00 UTC - Meteosat 9 Microphysics RGB

The above image shows a nice case of a Jet Fibre perpendicular to the Cold Front approaching Portugal from the west. The fibre was originally connected to the Warm front shield far away over the Atlantic. Since it has been transported ahead of the primal cloud system it can be easily recognized by its elongated structure, as well as the dark red colour separating it from the purplish environment of the sea below, or the orange to red colouring of the frontal cloudiness.

Meteorological Physical Background

Jet Fibres,also mentioned in the literature as cirrus streaks, are elongated patches of cirrus clouds, which move rapidly near the jet axis and are usually associated with jet streaks.

In general, bands of cirrus clouds tend to form or persist on the anticyclonic side of the jet. The reason for this is that jet streams are associated with the strong thermal contrast across frontal zones and the layered clouds form in the warm moist air of the Warm Conveyor Belt with cloud edge lying along the jet core.

jet_fibres

In most cases clouds do not cross the limiting streamline of the conveyor belt and they only reach the jet stream axis in straight or anticyclonically curved sections of the jet stream.

About 50 cases were examined in this investigation. It has been observed that Jet Fibres are mostly found over the Warm Front Shield or behind a Cold Front.

There is no single theory explaining the formation of the Jet Fibres, but there are several mechanisms probably acting in combination.

Generally, there are two necessary conditions needed for clouds to develop: sufficient humidity content and upward motion.

As already mentioned one of the large-scale mechanisms causing upward motion is a Warm Conveyor Belt, bringing warm and humid air to upper levels (see Warm Front Shield - Meteorological Physical Background ). The other one, in case of the Fibres connected to a Cold Front, would be slantwise ascent of the air above the slope of the Cold Front (see Cold Front - Meteorological Physical Background ).

This synoptic scale upward motion would bring a lot of humid air to upper levels and form a broad band of clouds (frontal clouds or broad cirrus bands). So, in order to produce a cloud structure of relatively small dimensions, such as Jet Fibres, there must be an additional smaller scale mechanism.

Since a jet is necessarily involved in the formation of Jet Fibres, ascent may also occur because of the circulation in the cells around the entrance and the exit regions of the jet streak.

jet_fibres

There is upward motion in the right entrance and left exit regions of the jet streak.

Taking into account the vertical wind shear, directly above the jet core there is also upward motion on a smaller (turbulence) scale.

jet_fibres

Whether clouds develop or not is therefore a result of sufficient humidity in the air mass and enough upward motion from one (or a combination) of the effects mentioned above. However, this would mainly explain the formation of broader cloud bands. In some sources it is emphasised that when humidity content in the upper levels is not sufficient to allow the formation of broader cloud shield, the jet axis is still marked by a brighter shade in WV images on the anticyclonic side of the jet, and by narrow cirrus streak in IR. That would mean that these small-scale mechanisms are sometimes strong enough to lift the air sufficiently to allow ice crystals to form. Since Jet Fibres are usually rather long, the jet stream obviously acts as a means for transporting the ice particles along great distances.

In some special cases, a Jet Fibre can get an interesting ornament. Namely, ribbons of cirrus, perpendicular to the Jet Fibre (image beneath), may be seen. This phenomenon occurs in the synoptic environment of an upper level trough and is usually associated with a cold front. The deep frontal cloud dissolves, but cirrus ribbons may persist for days if wind speeds in a subtropical jet are not exceeding 40 m/s and there is a large horizontal wind shear.

17 October 2006/18.00 UTC - GOES 10 IR image over South America (Courtesy NOAA/NESDIS, Source: GALVIN J.F.P., 2007, The Weather and climate of the tropics)

Jet Fibres behind the Cold Front

In the case of the Cold Front, besides the large scale ascending motion there is the impact of the upward motion in the right entrance region of the jet streak and small-scale upward motion caused by wind shear. Therefore, fibres form to the rear of the frontal cloud band, parallel to the jet axis, adjacent to or in the right entrance region of the jet streak, usually on the anticyclonic side of the jet.

jet_fibres

Development of fibres behind the Cold Front: Fibres occur along the jet axis or along the anticyclonic side, in the region of the jet streak or in the right entrance region.

06 November 2003/06.00 UTC - Meteosat IR image; yellow: isotachs, violet: zero line of shear vorticity 300 hPa

The above image shows the example of Jet Fibres developed behind a Cold Front overlaid with isotachs greater than 30 m/s and the zero line of shear vorticity at 300 hPa. The fibres occur along the zero-line of shear vorticity in the entrance region of the jet streak.

Besides the cases when Jet Fibres form parallel to the frontal zone, there are also numerous cases in which jet stream comes from behind the front at a certain angle. This is typically the case when the Cold Front is Kata type. In that case fibres are also located along the jet axis or slightly on the anticyclonic side.

jet_fibres

An example of such case can be found in the following image.

07 November 2003/06.00 UTC - Meteosat IR image; SatRep overlay: names of conceptual models

A special case is when a jet streak crosses or is going to cross the frontal cloud band, with the possible consequence of front intensification in the left exit region. In this case cloud fibres can be completely detached from the frontal systems and they usually form at large angles with the cloud band of the Cold Front ahead of them. Therefore a Jet Fibre can also be considered as an indication of the development of Front Intensification (see Front Intensification by Jet Crossing ).

11 November 2003/18.00 UTC - Meteosat IR image; yellow: isotachs, violet: zero line of shear vorticity 300 hPa

The above image shows Jet Fibres formed in the region of jet streak, along the jet axis, perpendicular to the Cold Front. One can observe the loop to see the propagation of the Fibres and the intensification that occurs at the Cold Front in the left exit region of the jet streak.

11 November 2003/10.00 UTC - Meteosat IR image; 11 November 10.00 UTC - 12 November 06.00 UTC hourly image loop

Jet fibres on top of the Warm Front Shield

The upward motion within a Warm Front is associated with the rising Warm Conveyor Belt with the limiting streamline on the jet axis. If the air mass in the warm conveyor belt (or a similar relative stream) is very humid, a broader band of high cloud fibres develops (see Warm Front Shield and Warm Conveyor Belt ).

Besides the smaller scale mechanisms responsible for the formation of Jet Fibres already mentioned in the case of the Cold Front, there is also an influence of the sharply curving jet stream. When the jet is curved, shear caused by the change of the wind speed is increased by the shear resulting from the change in wind direction.

Fibres also form on the cyclonic side of the Warm Front within the frontal cloud band, and there are numerous cases when the jet extends the Fibres beyond the cloud band.

jet_fibres

Sometimes the Fibre is transported so far ahead of the Warm Front Shield that it becomes a feature unconnected to the synoptic scale systems, but only to the jet stream itself.

07 October 2003/12.00 UTC - Meteosat IR image

According to theory, a jet stream flows around the Warm Front Shield, with the frontal cloud band lying on the anticyclonic side of the jet axis. Supporting the theory, there are also observations from WV images in which there is a Dark Stripe along the pole ward edge of the frontal cloud band. Jet fibres develop on the anticyclonic side of the jet.

17 June 2003/12.00 UTC - Meteosat IR image; yellow: isotachs, violet: zero line of shear vorticity 300 hPa

Discussion

Although theory states that the jet flows around the Warm Front cloud band and that the fibres should therefore develop above the frontal cloud band, on the anticyclonic side of the jet, there are numerous cases in which the situation is quite different. Namely, the jet flows through the Warm Front cloud band, fibres are still along the edge of the Warm Front cloud band, but on the cyclonic side of the jet. Here is one such case:

16 January 2004/18.00 UTC - Meteosat IR image; yellow: isotachs, blue: shear vorticity 300 hPa

Or another, even more pronounced example:

25 September 2003/06.00 UTC - Meteosat IR image; yellow: isotachs, blue: shear vorticity 300 hPa

Such cases are not so rare. In the literature it is stated that in two out of nine cases (22 %) cirrus clouds were found on the cyclonic side of the jet axis.

There are several possible explanations but the most probable one is that this effect is a result of the combination of the following causes:

  • The model is not perfectly reliable: parameter fields can be shifted, especially the forecast parameters.
  • The Jet axis is tilted vertically: at higher levels the jet is inclined more northwards compared to its location in lower levels, looking in the direction of the jet. Therefore, if the strongest winds are at level higher than 300 hPa (which is often the highest level in the global model or at least the one representing the jet stream) it is possible that the position of the fibre is determined by a higher jet axis. In that case, the jet axis at 300 hPa would be located more southward and could therefore appear to be on the anticyclonic side of the Jet Fibre.

Finally, if we consider that the model is correct, and the fibre is exactly at the level of maximum wind, and if we still find it on the cyclonic side, the explanation could be:

  • The circulation around the jet axis: small-scale circulation makes the air rise on the anticyclonic and sink on the cyclonic side. Therefore, there is necessarily also part of that circulation cell which transports the air from anticyclonic to cyclonic side at upper layers. Taking into account that air cannot dry instantly, it is possible that humid air also persists for some time on the cyclonic side of the jet.

Since this effect of Fibres forming on the cyclonic side of the jet has only been observed in the case of Fibres seen above the Warm Front Shield, another possible reason could be:

  • Sharply curving jet axis: Because of the shear caused by curvature, there could also be some ascent on the cyclonic side of the jet allowing the cirrus to persist on that side.

Key Parameters

  • Isotachs (at 300 hPa, 250 and 200 hPa can all be considered)
    • Indications of jet intensity and the location of entrance and exit regions
    • Jet Fibres form very near to the jet maximum
  • Shear vorticity (zero-line of shear vorticity at 300 hPa)
    • Indication of jet axis
    • Zero-line of shear vorticity is parallel to both Jet Fibre and the WV Dark Stripe

In cases where Fibres are associated with the Warm Front, they appear mostly in the leading part of the jet streak. In cases of the Cold Front, Fibres usually lie within the wind maximum or in the entrance region of the jet streak.

When compared to jet axes, Fibres can in most cases be found along the zero-line of shear vorticity or slightly shifted to the anticyclonic side of the jet. Some exceptions occur in Warm Front cases (see Meteorological Physical Background ).

06 November 2003/ 06.00 UTC - Meteosat IR image, yellow: isotachs, violet: zero line of shear vorticity 300 hPa

The diagrams above show the location of wind maximum and zero-line of shear vorticity behind Ana and Kata Cold Fronts. Fibres form in the entrance region or adjacent to the jet streak.

17 June 2003/12.00 UTC - Meteosat IR image; yellow: isotachs, violet: zero line of shear vorticity 300 hPa

In the Warm Front case, the jet axis follows the cloud band along the cyclonic side. Fibres mostly form in the leading part of the jet streak and mostly on the anticyclonic side, but there are some exceptions (see Meteorological Physical Background ).

Supporting Parameters

  • Relative humidity - necessary condition for the formation of clouds
    Distribution of humidity in the model fields is governed by the synoptic scale features with which Fibres are associated.
  • Warm conveyor belt - the Jet Fibre coincides with the limiting streamline.

06 November 2003/06.00 UTC - Meteosat IR image, blue: relative humidity 300hPa
17 June 2003/12.00 UTC - Meteosat IR image, blue: relative humidity 300hPa
05 November 2003/06.00 UTC - Meteosat IR image; magenta: relative streams 304K - system velocity 216° 12 m/s; yellow: isobars 304K

Typical Appearance In Vertical Cross Sections

Jet Fibres usually develop in the vicinity of, or directly above a Warm or Cold Front, therefore it is not very easy to recognise them in cross sections. Moreover, the distribution of meteorological parameters reflects what is going on in those synoptic scale systems. In other words, Jet Fibres are not clearly seen in cross-sections and they have no specific appearance. However, the distribution of key parameters associated with the fibres can give some indicators for their most likely location.

Several vertical cross-sections, perpendicular to fibres, have been examined. Typical parameters studied were:

  • Isotachs
    The jet streak is located near the maximum radiance in WV and IR of the fibre
    Fibres are located near to the jet axis, in most cases shifted slightly to the anticyclonic side
  • Relative humidity
    A fibre is sometimes located near a secondary humidity maximum, but the main humidity maximum represents the frontal cloudiness.
  • Isentropes
    The slope of the isentropes shows the frontal zone

Jet Fibres behind the Cold Front

The isentropes show a downward inclined gradient zone of the Cold Front. The humidity distribution is dominated by the frontal humidity. High values of relative humidity can be found ahead of the frontal zone, along the slope of the isentropes. In some cases a secondary humidity maximum indicates a Fibre. The wind maximum is found right next to the Jet Fibre, with the Fibre being on the anticyclonic side of the jet.

13 January 2004/12.00 UTC - Meteosat IR image; position of vertical cross section indicated
13 January 2004/12.00 UTC - Vertical cross section; black: isentropes (ThetaE), yellow: isotachs, orange thin: IR pixel values, orange thick: WV pixel values
13 January 2004/12.00 UTC - Vertical cross section; black: isentropes (ThetaE), blue: relative humidity, orange thin: IR pixel values, orange thick: WV pixel values

Jet Fibres above the Warm Front Shield

The slope of the isentropes and the humidity distribution are typical for a Warm Front. The humidity maximum occurs along the slope of the isentropes. A secondary humidity maximum, representing the fibre, can be found on the anticyclonic side of the jet maximum. The jet maximum occurs above the forward part of the frontal surface.

16 February 2004/12.00 UTC - Meteosat IR image; position of vertical cross section indicated
16 February 2004/12.00 UTC - ALADIN Vertical cross section; black: isotachs, blue: relative humidity, wind arrows superimposed
16 February 2004/12.00 UTC - ALADIN Vertical cross section; black: isentropes (ThetaE), blue: relative humidity
16 February 2004/12.00 UTC - Vertical cross section; black: isentropes (ThetaE), yellow: isotachs, orange thin: IR pixel values, orange thick: WV pixel values
16 February 2004/12.00 UTC - Vertical cross section; black: isentropes (ThetaE), blue: relative humidity, orange thin: IR pixel values, orange thick: WV pixel values

Distribution of wind, humidity and equipotential temperature in a cross section through a Warm Front.

If one compares Aladin and ECMWF cross-sections, it is clear that the ECMWF model does not resolve humidity in the upper troposphere well enough. The Aladin cross sections show a much better humidity distribution along the frontal zone and in the region where Jet Fibres occur.

Weather Events

Jet Fibres are high altitude cirrus clouds, therefore no weather phenomena on the ground are expected. However, they appear along the jet axis in the region of maximum wind, therefore jet related phenomena such as turbulence can be expected in that region.

Turbulence generally appears in the zone of high horizontal and vertical wind shear, around the jet streak, but most frequently on the left-hand side below the level of the jet core, or on the right side above the level of the jet core. Furthermore, a sharply curving jet stream on the pole ward side of a Warm Front Shield, is associated with greater turbulence than a straight jet stream behind the Cold Front. Jet fibres are often considered a good indication for clear-air turbulence (CAT) which may affect flights at high levels and is a major cause of discomfort and disruption to passengers in flights.

Associated with the Subtropical Jet Stream (STJ), but separate from it, areas of tropical CAT are observed. These may be identified by their high-cloud signature, cirrus ribbons.

Parameter Description
Precipitation
  • No precipitation or thunder caused by Jet Fibres.
  • Observed weather events are connected to the nearby synoptic scale system
Temperature
  • No change
Wind (incl. gusts)
  • No change at the surface
  • Strong wind and shear in upper levels
Other relevant information
  • High-level cloudiness in the form of fibres
  • For aviation, Jet Fibres are often considered a good indication of (clear air) turbulence.

09 October 2009/06.00 UTC - Meteosat IR image
09 October 2009/06.00 UTC - clouds and precipitation observations from synop reports
09 October 2009/06.00 UTC - cloud type observations from synop reports

Meteosat 8 IR image above shows an example of jet cloud fibres to the rear of a Cold Front, extended from Czech Republic over south Poland and Belarus. In the left image precipitation (green : rain and showers) and cloudiness (yellow: fog, light blue and gray: cloudiness in octas) can be noticed associated with a cold front. There is no significant weather events over south Poland and Belarus associated with jet cloud fibres. There are just different cloud types (right image) according to observations. Turbulence in the upper levels can be witness only through pilots reports.

References

General Meteorology and Basics

  • REITER E. R., 1963: Jet-stream meteorology, The University of Chicago Press, Chicago
  • VINNICHENKO N. K., N. Z. PINUS, S. M. SHMETER, and G. N. SHUR,1980: Turbulence in Free Atmosphere, Consultants Bureau, New York
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  • ENDLICH R. M. and MCLEAN G. S., 1957: The structure of the jet stream core. Journal of the Atmospheric Sciences: Vol. 14, No. 6, pp. 543-552.
  • ANDERSON A. D., 1957: Free-air turbulence. Journal of the Atmospheric Sciences: Vol. 14, No. 6, pp. 477-494.
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  • CONOVER J. H., 1960: Cirrus patterns and related air motions near the jet stream as derived by photography. Journal of the Atmospheric Sciences: Vol. 17, No. 5, pp. 532-546.
  • SASSEN K., D. O'C. STARR, G. G. MACE, M. R. POELLOT, S.H. MELFI, W. L. EBERHARD, J. D. SPINHIRNE, E.W. ELORANTA, D. E. HAGEN and J. HALLETT, 1995: The 5-6 December 1991 FIRE IFO II Jet Stream Cirrus Case Study: Possible Influences of Volcanic Aerosols. Journal of the Atmospheric Sciences: Vol. 52, No. 1, pp. 97-123.
  • GALVIN J.F.P., 2007: The weather and climate of the tropics, Part 2 - The subtropical jet streams. Weather: Vol. 62, No. 11, pp. 295-299.

General Satellite Meteorology

  • BADER M. J., FORBES G. S., GRANT J. R., LILLEY R. B. E. and WATERS A. J. 1995: Images in weather forecasting - a practical guide for interpreting satellite and radar imagery; Cambridge University Press
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Specific Satellite Meteorology

  • SASSEN K. and J. R. CAMPBELL, 2001: A Midlatitude Cirrus Cloud Climatology from the Facility for Atmospheric Remote Sensing. Part I: Macrophysical and Synoptic Properties. Journal of the Atmospheric Sciences: Vol. 58, No. 5, pp. 481-496.
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