International Journal of Remote Sensingszantai/publi/ASz_IJRS... · 2009. 1. 21. · A. SZANTAI*, F. DE´SALMAND and M. DESBOIS Laboratoire de Me´te´orologie Dynamique, Ecole Polytechnique,

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A method for the construction of cloud trajectories fromseries of satellite imagesA. Szantai; F. Desalmand; M. Desbois

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int. j. remote sensing, 2002, vol. 23, no. 8, 1699–1732

A method for the construction of cloud trajectories from series of

satellite images

A. SZANTAI*, F. DESALMAND and M. DESBOIS

Laboratoire de Meteorologie Dynamique, Ecole Polytechnique,91128 Palaiseau, France

(Received 18 October 1999; in �nal form 26 March 2001 )

Abstract. Knowledge of the trajectories of atmospheric structures is useful inmeteorology, in particular for the study of the persistence of clouds at mesoscaleand for studies of the large-scale atmospheric circulation. For this purpose, amethod for the construction of cloud trajectories has been developed and ispresented in this article. This method extends traditional techniques used tocalculate cloud motion vectors from satellite images, representing the wind at asingle instant and the motion over a short time interval (typically Øh), to themeasurement of the motion of the same clouds over a long duration, up to 60 h.Trajectories of clouds have been constructed from series of Meteosat images inthe thermal IR, the WV (water vapour) and the VISible channels. Similarly, pureWV structures have been tracked in the WV channel. The duration of a trajectoryis mainly related to the lifetime of the tracked structure, but also dependent onits spatial scale. A lesser image quality or a larger time interval between imagesreduces this duration. The use of severe quality tests enables reliable tracking ofa limited number of clouds or WV structures, whereas more tolerant tests leadto larger groups of less precise trajectories nevertheless suitable for the study oflarge-scale motions.

1. Introduction

The structure and evolution of large synoptic systems, such as atmospheric lows

of temperate latitudes, and their main climatic characteristics (areas of formation

and motion, lifetime) have been studied for several decades. The physical processes

involved in these systems are also quite well understood. A practical application of

these properties is the weather forecast, which nowadays gives reliable results over

a period of �ve days. The mechanisms involved in the formation of various cloud

types must also be reproduced as closely as possible to reality in climate models,

because the interaction between clouds and radiation plays an essential role in the

retroactions and equilibria of the climate.

Forecast models are nevertheless unable to reconstruct correctly speci�c, fast

evolving, meteorological situations. For example, some winter storms observed over

*e-mail: [email protected]

Internationa l Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-590 1 online © 2002 Taylor & Francis Ltd

http://www.tandf.co.uk/journalsDOI: 10.1080/01431160110075541

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A. Szantai et al.1700

Western Europe result from the evolution of fronts associated to a primary extra-

tropical low. In such situations, it is possible that small-scale processes have an

in�uence on larger scale processes. From an observational point of view, the life

cycle of meteorological structures, i.e. their formation, their evolution and their

disappearance, is not well known; only ‘snapshots’ are available at speci�c instants.

In the case of cyclogenesis, the �rst ‘images’, necessary for a reliable forecast, are

missing. In practice, it is easier to obtain individual ‘images’ than to track these

meteorological objects during their whole lifetime. These ‘images’ are reconstructed

from synoptic measurements made from meteorological stations on land or on the

sea (from ships or buoys) , from aeroplanes, radiosondes and satellites (which in turn

send real images).

The observation of the temporal evolution of clouds at diVerent space and time

scales could improve our understanding of the physical processes involved in their

formation, their persistence and their dissipation. Our method for the calculation

of trajectories from satellite images was developed for this purpose. Its use could

help to characterize clouds more realistically and thus be of bene�t to general

(meteorological and climatic) circulation models.

The Lagrangian approach of motion, which is implicit in the determination of

trajectories, is currently used in several �elds of atmospheric sciences. Trajectories

of cyclones and hurricanes over the North Atlantic have been reconstructed since

1871 (Neumann et al. 1978). Trajectories of pollutants have also been determined.

These can be of natural origin: dust storms originating from the Sahara desert have

been observed over the Atlantic Ocean and the Caribbean (Carlson and Prospero

1972, Bertrand et al. 1975); or the result of chemical or radioactive pollution: the

fallout of the ‘radioactive cloud’ emitted by the Chernobyl nuclear power plant in

1986 had a strong ecological impact. Its trajectories (there have been several emis-

sions) have been reconstructed from analysed data and a circulation model, and

con�rmed by ground samplings of radioactive dust (containing 137Cs) (Strauss and

Gros 1986, Albergel et al. 1988). Balloons have also been used to investigate the

atmospheric circulation. Their trajectories were �rst constructed at lower levels of

the troposphere (Angell and Pack 1960). During large-scale experiments like EOLE

(Morel and Bandeen 1973, Desbois 1976) and TWERLE (TWERLE team 1977),

trajectories at high level were also determined in selected regions.

Geostationary satellites have the advantage to provide images at short time inter-

vals. The evolution of clouds can be observed on them with a far better temporal

resolution (Øh for Meteosat images) than the resolution provided by classical measure-

ments (generally 6 h or 12 h). The spatial resolution of these images is also well

adapted for a precise study of meteorological objects at synoptic scale such as

extratropical lows, or at mesoscale such as tropical convective systems. In the �rst

studies, squall lines in tropical regions were identi�ed and tracked visually on a

series of images (Aspliden et al. 1976, Desbois et al. 1988). Automatic methods were

also developed: convective cloud clusters are extracted with the use of a threshold

on the brightness temperature deduced from thermal infrared images. Basically, a

convective cluster can be tracked if the areas it covers on two consecutive images

overlap. With this type of method, the motion of convective clusters over North

America (Maddox 1980), in the region of Borneo (Williams and Houze 1989) and

over Africa (Arnaud et al. 1992, Laing and Fritsch 1993) has been reconstructed.

The motion of extratropical cyclones can also be reconstructed from a series of

images. A recently developed method reconstructs the motion of a singularity, in

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Construction of cloud trajectories f rom satellite images 1701

this case the centre of a spiral, and its neighbouring points can be represented with

a two-dimensional linear model. The parameters de�ning the position of the centre

of rotation and characterizing its motion are estimated by a statistical method

(Maurizot et al. 1997 ).

Another recent development from satellite images is the determination of large-

scale atmospheric motions: water vapour transport (which can also be determined

from three-dimensional analyses (Pierrehumbert and Roca 1998)) has been recon-

structed from groups of trajectories. Such groups show the circulation of upper

tropospheric water vapour from the intertropical convergence zone and South Paci�c

convergence zone to subtropical subsidence zones (Soden 1998).

This article is focused on the principle, possible applications and limits of a

method for the construction of cloud trajectories from a series of images taken by a

geostationary satellite. No scienti�c result will be presented, but possible applications

of this method will be proposed. Its aim is the tracking of small cloud structures, at

a scale about or smaller than 200 km. In §2, the method used for the determination

of cloud motion vectors from two images will be brie�y reviewed. In §3, this method

will be extended in a simple way to construct cloud trajectories and the quality of

the latter will be estimated. Section 4 will describe necessary improvements for the

construction of representative trajectories. In §5, a variation on this improved method

will enable the tracking of cold cloud elements, selected by a threshold on brightness

temperatures (BT). Several trajectory �elds of structures tracked in the thermal

infrared (IR) and water vapour absorption (WV) channels will be presented, the

possible but limited use of trajectories in the visible (VIS) will also be mentioned.

The complete trajectory of a cloud, from its birth to its dissipation, can be constructed

with an extension of the method presented in §6. The representativeness and

signi�cance of the trajectories in the diVerent channels will also be discussed.

2. Computation of cloud motion winds

The motion of the clouds can be measured on satellite images, and thus the

velocity of the clouds, depending on the time interval between consecutive images,

can be deduced. From an image-processing point of view, the automatic measure of

the motion of moving elements, in our case clouds and pure (non-cloud) water

vapour structures, on images can be classi�ed into three main categories.

1. Region based tracking methods. Methods in this category were among the

�rst to be developed (Endlich et al. 1971). Groups of (contiguous) pixels with speci�c

characteristics are identi�ed on a pair of images and matched, the motion of each

group can then be deduced. Such pixel groups include convective cloud clusters,

individual clouds and synoptic scale structures such as extratropical lows, already

mentioned in §1. The tracking of cloud edges (characterized by their curvature) (Cote

and Tatnall 1995) is also relevant to this category.

2. Pixel-based tracking methods started to be investigated later (Horn and

Schunck 1981). Basically the motion of each individual pixel is measured and a

dense �eld of vectors is obtained. For practical reasons, the computation may be

limited to a sampling grid or to a limited area. This category includes, in large part,

optical �ow methods (see for example Stiller and Konrad 1999 for a review). Although

such dense vector �elds are of potential interest for meteorologists, few developments

have been made in order to apply such methods beyond a few cases (Eriksson 1988,

Bannehr et al. 1996). Among the limiting reasons are:

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– the highly variable nature of clouds and atmospheric structures at the

timescale used (generally Øh between consecutive images) reduces the reliab-

ility of the measured vectors. An attempt to use a high temporal resolution

(down to 1 min between images) , with the help of a massively parallel

supercomputer, showed the potential of using dense vector �elds to improve

our comprehension of the dynamics and evolution of cyclones (Hasler

et al. 1998 );

– the diYculty in validating the calculated motion �elds with other meteorolo-

gical data: wind measurements and analyses generally do not have suYcient

spatial resolution to be compared with dense motion vector �elds.

Most pixel-based tracking methods are particularly sensitive to problems limiting

all measurements of motion on any type of images such as:

– the aperture problem: measurements are more reliable in a direction perpen-

dicular to the edge of an object (a cloud in our case) than in a direction

parallel to it;

– the occlusion problem: on the second image of a pair, a moving object

(cloud) masks some pixels on its frontal edge and unmasks other pixels on

its rear edge. The motion of these masked/unmasked pixels cannot be

reconstructed directly;

– the semi-transparency problem: the motion of an object (cloud at a low

altitude) may be viewed through another semi-transparent object (thin cloud

(cirrus) above, at a higher altitude) , possibly moving in another direction.

The simultaneous measurement of both motions is impossible for a vast

majority of methods.

3. Block-based matching methods. The �rst methods of this category were

developed and applied at the same time as region-based tracking methods (Leese

et al. 1971). Basically, a block of pixels (generally a square of pixels centred on a

grid point) on the �rst image of a pair is matched with a similar block on the second

image. From the distance between the positions of this block (or its centre) on both

images, the motion of the clouds can be deduced and thus their velocity, which

corresponds generally to the velocity of the wind. In the following subsections, a

method used to compute cloud motion winds (CMWs) or, in an extended sense,

atmospheric motion winds measured by satellites will be detailed. This includes the

measurement of the motion of pure water vapour structures in the WV channel,

which is possible in cloudless areas. The characteristics of these winds and some

problems related to their determination will also be discussed. This description of

the CMW calculation method is necessary because it is the primary tool for the

construction of trajectories.

2.1. Measurement of the motion of clouds

Cloud motion winds are one of the most useful products derived from geostation-

ary satellites. They are produced operationally (see for example Schmetz et al. 1993,

Nieman et al. 1997) and are currently assimilated in forecast models. CMWs are

generated automatically nowadays from a pair of images and computed with a cross-

correlation method (Leese et al. 1971). For each computation of a CMW, the

correlation between a square of pixels extracted on the �rst image of a pair (the

target window) and a square of pixels of the same size extracted on the second image

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inside a larger window (the search window) is computed for all possible displacements

(which are determined by the size of both target and search windows). The displace-

ment in pixels of the tracked structure(s) is determined by the relative position of

the target and search window that corresponds to the maximal value of the correla-

tion. If the geographical position corresponding to the position of the vector on the

image disc is known, the velocity of the tracked structure(s) can be deduced from

the displacement in pixels and from the time interval between images. The determina-

tion of the maximal cross-correlation is a maximum likelihood estimator (Wu 1995).

Another method can be used to compute CMWs: the Euclidean distance (or sum

of squared diVerences) method. The same de�nitions of pixel sets (target and search

windows) are used, but in this case the displacement vector in pixels (DL , DC) at

location (L0, C

0) is determined from the minimal value of the sum of squared

diVerences of the pixel values (numerical counts) associated to each pixel:

SSD(L0, C

0, DL , DC)=A æ

LT/2Õ 1

l=LT/2

æCT/2Õ1

c=ÕCT/2

W (L0, C

0, l, c)

.{i2(L

0+l+DL , C

0+c+DC)i

1{L

0+l, C

0+c)}2B (1)

where i1

is the pixel value on �rst image (target window); i2

is the pixel value on

second image; LT , CT are the number of lines and columns of the target window;

and W is the weighting function, equal to 1 for most applications.

Instead of the maximum of the correlation. Both methods have been considered

as giving similar results (Sitbon et al. 1974), but recent studies have shown that

diVerent results can be expected in a minority of cases (Wu et al. 1996, Dew and

Holmlund 2000). The Euclidean distance method is computationally a little faster

and we have chosen it for the measurement of cloud motion and thus for the

construction of their trajectories.

A series of quality tests eliminates inconsistent CMWs, which do not correspond

to a realistic motion of clouds. Commonly used tests include:

Comparison to the maximal possible displacement : If the maximal possible displace-

ment (determined by the size of the target and search windows) is reached, the CMW

is rejected.

A temporal symmetry check (Bowen et al. 1979): For this test, three images (taken

at instants tDt, t and t+Dt ) are used. Each vector, computed from the central and

last images (at t and t+Dt ) is compared to the collocated vector, computed from

the �rst and central images, and is eliminated if both vectors show too great a

diVerence. The comparison can be realized on the vector diVerence, on the diVerence

or ratio between their speed, or on the diVerence between their direction, with the

use of selected thresholds.

A spatial consistency check (Green et al. 1975): Each CMW is compared with its

closest neighbours. If it shows large diVerences in velocity, speed and/or direction

with one or several of its neighbours (or with their average, according to the test

used), the vector is rejected.

A comparison with a forecast wind from a general circulation model : The height

of a CMW can be estimated from satellite images (see §2.2). If the CMW at this

estimated level shows large diVerences from the forecast wind at the same (or closest)

level, it is rejected.

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Another test can suppress very small or zero CMWs: the absence of displacement

can correspond to the tracking of terrain features (which do not move) or to the

tracking of orographic clouds; in this case, clouds appear to be blocked by mountains,

although local measurements can show strong winds. The value of the correlation

coeYcient can also be used as a selection criterion: if it is too small, the corresponding

CMW is refused.

The manual elimination of inconsistent CMWs, i.e. by a human operator, tends

to be abandoned nowadays or at least reduced, as automatic quality tests have

improved and as the number of CMWs can be very large, especially in operational

applications (Holmlund 1996, Nieman et al. 1997 ).

2.2. Height assignment

The measured CMW is representative of the motion of the air masses at a

particular level, generally at the level of (a part of ) the tracked cloud. Exceptions

are orographic clouds and stationary wave clouds, which appear motionless, and

some cirrus clouds which move slower than the surrounding air in regions of strong

winds ( jet streams) (Schmetz and Holmlund 1992). The height of the tracked clouds

can be estimated from satellite data by several methods. The most commonly used

methods are:

T he measurement of the thermal infrared brightness temperature: The brightness

temperature (BT) of the cold pixels inside the target window is measured in the

thermal infrared channel (between 10 and 13 mm). It generally corresponds to the

cloud tops and represents their physical temperature, assuming a blackbody emission

of the cloud. Exceptions are semi-transparent clouds (the measured radiance comes

from these clouds and from the surface or clouds located below) and small clouds

covering only a portion of a pixel (the measured radiance originates partly from

these clouds and partly from the surface). The BT will be reduced due to the

absorption of CO2

and WV molecules located above the observed cloud. Water

vapour aVects especially the BT of low-level clouds in the tropics and clouds located

close to the edges of the Earth disk. In the case of aged high convective clouds, their

top temperature can be lowered by radiative cooling and appear to be colder than

the surrounding air.

The real brightness temperature of a cloud can be expressed as:

TB cloud

=TB measured

+DTB

(2)

The atmospheric correction DTB

can take values from 2 K or less for high-level

clouds at temperate latitudes (Saunders 1988) to 12 K or more in some tropical

regions (such extreme values have been observed for sea surface temperature

measurements).

When the brightness temperature is identi�ed with the physical temperature of

the tracked cloud, its pressure level can be deduced from a temperature pro�le

(provided by a radiosonde if available, or from a model analysis or forecast) in the

vicinity. The height of the tracked cloud is then deduced from the hydrostatic

equation by the relation:

zcloud

=R

ag P

ln(Pcloud)

ln(Psurface)

Tv(P)d( ln(P)) (3)

where Ra=287 J KÕ 1 kgÕ1 : gas constant for dry air; g=9.81 m sÕ2 : magnitude of

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gravity; and Tv

is the virtual temperature of air at pressure P (can be deduced from

a temperature and relative humidity pro�le.

T he estimation of the height of low-level clouds from the IR brightness temperature:

CMWs are close to the wind measured at the base of low-level clouds (Hasler et al.

1979). Thus, the previously described method which estimates the cloud top temper-

ature is inappropriate because it leads to an underestimated pressure level (or an

overestimated height) of the cloud. In recent methods, the IR histogram of the pixels

of the target window is �tted by Hermite polynomials (Le Marshall et al. 1994 ) or

by Gaussian curves (Ottenbacher et al. 1997). From these functions, the temperature

of the cloud base can be estimated. With the help of a temperature pro�le (from

other types of measures) , a more realistic pressure level can then be deduced.

Bi- or multispectral methods based on transmitted radiation: These methods are

able to correct the eVects of semi-transparency and partial coverage of pixels by

cloud elements on the brightness temperature. The measured radiance at wavelength

l can be expressed as:

R(l)=(1ne(l))Rcs

(l)+ne(l)Rcl

(l) (4)

where n is the cloud coverage of the pixel (0 n 1); e(l) is the emissivity of the

cloud (0 e(l) 1); Rcs

(l) is the clear sky radiance; and Rcl

(l) is the radiance of the

cloud. If the radiance is measured at two or more wavelengths and for two pixels in

closely located areas of diVerent cloud coverage, the emissivity is almost constant

(independent of wavelength) . From these measurements and from a collocated tem-

perature and humidity pro�le (used to determine the transmission of the atmosphere

at diVerent pressure levels), the ‘real’ radiance of the cloud, Rcl

, can be calculated

and thus its blackbody temperature and pressure level can be determined. This

method was �rst and successfully applied with three CO2

absorption channels at

13.3, 14 and 14.2 mm, thus its name ‘CO2

slicing method’ (Smith and Platt 1978,

Menzel et al. 1983, Wylie and Menzel 1989). Results of similar quality have been

obtained from the thermal IR and one CO2

channel (at 13.2 mm) (Nieman et al.

1993). Unfortunately, this method cannot be used nowadays owing to the absence

of CO2

absorption channels on all operating geostationary satellites. (One of these

channels, around 14 mm, will be available on future Meteosat Second Generation

satellites.)

A similar method based on measurements in WV absorption channel (around

6.3 mm) and the thermal IR channel has been proposed to estimate the height of

cirrus clouds (Cayla and Tomassini 1978, Szejwach 1982). Compared to other

measurements, this method tends to overestimate the pressure, except in dry areas

where the pressure is underestimated (Menzel et al. 1993, Nieman et al. 1993). This

method is used operationally by EUMETSAT and NOAA agencies (Schmetz et al.

1993, Nieman et al. 1997 ).

The stereographic method consists in observing simultaneously the same point

on a cloud from two satellites. If the distance between the satellites is known, the

height of the cloud can be calculated (Ondrejka and Conover 1966, Hasler 1981,

Hasler et al. 1991). This method necessitates two satellites with an overlapping

area of observation and works best if they are well synchronized. It is not used

operationally today.

As this article is focused on the tracking of cloud and atmospheric (pure WV)

structures on satellite images, no precise height assignment will be attempted. The

(uncorrected) BT of the tracked structures will be the only parameter directly related

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to height computed along the trajectory. And although this parameter may be

insuYcient for a precise height estimation, it may nevertheless be useful to show the

evolution of clouds and structures with time.

2.3. Problems related to the computation of cloud motion winds

Several parameters have an in�uence on the number and quality of consistent

CMWs: the size of the target and search windows; the time interval between

consecutive images; the position of the vector on the Earth disk on the images; and

the presence of rotational motion.

2.3.1. Size of the windows

The sizes of the target and search windows (LT lines, CT columns and LS lines,

CS columns respectively) have an in�uence on the existence of signi�cant CMWs.

With a very small target window, small cloud elements, which are more likely to

travel with the same (small-scale) velocity as the surrounding air, are tracked. But

this measurement is sensitive to the noise on the numerical counts and the risk of

tracking the wrong element is increased. Using a large target window reduces this

noise. But in this case, the measured CMW will be representative of the wind only

if all elements inside the window move at the same velocities. If several elements

move with diVerent velocities, the CMW will represent the motion of one of them,

or a kind of ‘averaged’ motion. The use of a large target window also increases the

computation time.

Target windows of various sizes have been used in several studies. For an

experiment over the North Atlantic (FRONTS 87), Lunnon and Lowe (1992) used

square target windows of 8×8, 16×16 and 32×32 pixels and rectangular ones

(8×16 and 16×32 pixels). They found that 16×16 windows enabled a better tracking

of low-level clouds in this area. Another study (Lunnon et al. 1992) about cirrus

clouds (during the International Cirrus Experiment in September/October 1989) was

realized with images in the WV channel and validated with aircraft measurements.

The best results were obtained with a 16×32 pixels target window. Wade et al.

(1992) calculated vectors with square target windows with sides between 4 and 32

pixels in a region between latitudes 40° and 61° N. They found an optimal size of

24 pixels. For cloud-free areas on Meteosat images in the WV channel, Buche et al.

(1990) found that WV structures are better tracked with a 48×48 pixels target

window. For the computation of trajectories, we will use mainly a 32×32 pixels

target window; this is also the size used operationally by EUMETSAT.

The size of the search window is determined by the maximal desired displacement.

In practice, winds measured in the troposphere rarely exceed 200 km hÕ 1 . The

maximal possible displacement is de�ned by the relations:

DLmax

=(L SLT )/2 (in lines) (5)

DCmax

=(CSCT )/2 (in columns) (6)

As an example, for window widths of CT=32 and CS=80 pixels, the maximal

displacement is 24 pixels. With the pixel size of Meteosat of 4.5 km (close to the

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centre of the Earth disk)* , this corresponds to a motion of 108 km and thus to a

velocity of 216 km hÕ1 if the two images used are Øh apart.

2.3.2. T ime interval between images

The time interval between the two images used for the computation of CMWs

is Øh on currently operating geostationary satellites. A consequence is that short-

lived clouds, with a lifetime of less than Øh, cannot be tracked. In special operating

conditions, this time interval can be reduced to 5 min on Meteosat (e.g. for the

Mesoscale Alpine Project experiment) or even down to 30 s over a limited area on

the last GOES satellites (Purdom 1996). On the other hand, CMWs have been

determined from ISCCP B2 images (Meteosat images with a sampling of every sixth

line and every sixth column of pixels) with a 3-h time interval for climatological

studies (Desbois et al. 1988 ).

2.3.3. Position of the vector on the Earth disk

The side of a pixel on the Earth’s surface increases from the centre to the edge

of the Earth disk. This aVects the area covered by the target and search windows,

and also the quality of the CMW. For example, for two Meteosat images Øh apart,

an error of one pixel in one direction leads to an error of 9 km hÕ 1 close to the

subsatellite point (0° N, 0° E—one pixel has a side of 4.5 km), an error of approxi-

mately 14 km hÕ 1 over Western Europe (50° N—one pixel equals approximately

8 km in the north/south direction) up to more than 100 km hÕ 1 close to the edge of

the Earth disk. To minimize these eVects, the starting points for the computation of

trajectories will not exceed 60° N in latitude.

2.3.4. Rotational motion

Rotational motion has been determined from satellite images for oceanic currents

(Kamachi 1989), but is not part of the CMW computation for two main reasons:

1. if the time interval between consecutive images is small (this is generally the

case for Øh), rotation can be neglected in comparison with translatory motion

in most regions;

2. the determination of the rotation angle increases greatly the computation time.

For each possible rotation angle, all the pixel values of the search window

have to be interpolated to the same grid as the target window before computing

the (translational) displacement vector.

2.3.5. DiVerences between measured winds and cloud motion winds

To summarize, the diVerences between winds measured with ‘classical instru-

ments’, for example rawinsondes, and CMWs, deduced from the motion of clouds

or atmospheric features observed on satellite images, can have diVerent origins

(Hubert 1979):

physical causes: the tracked cloud moves at a diVerent (generally slower) velocity

than the surrounding air masses; this is the case for motionless orographic clouds

or lee wave clouds (formed only in the presence of wind) and for cirrus clouds slower

than the associated strong high-level winds (in jet streams) , already mentioned;

*In fact this corresponds to the distance between the centre of two neighbouring pixels.The real size of a pixel is 5 km, but a small part of the surface it covers is overlapping withits neighbours.

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limitations of the tracking algorithm: the principle of most block matching algo-

rithms is to recognize a similar structure on two images according to a statistical

criterion: the minimization of the Euclidean distance or the maximization of the

correlation. Thus changes of this structure with time may not be recognized. An

inconsistent motion can be measured when clouds appear, evolve fast or disappear,

when two or several clouds of similar aspect are in the vicinity (the algorithm may

track the wrong cloud), when several cloud elements inside the target window move

diVerently (the algorithm will measure some kind of ‘averaged’ motion, or the motion

of one of these cloud elements), or when (a part of ) a large featureless cloud is tracked.

The temporal and spatial scales of the tracked clouds can also in�uence the

values of the measured CMW. A CMW measured with a large target window may

re�ect the motion of a large cloud structure, respectively of a group of smaller clouds,

whereas a small target window will produce a vector representing the motion of a

part of this structure, respectively of one (or several) cloud(s) of this group. This can

be the case for an expanding cloud.

2.4. Conclusion about cloud motion winds

This section describes the methods used to compute CMWs and some related

problems, such as the height estimation of these winds. A more complete description

can be found in a thesis work (Szantai 1996).

Other methods have been developed recently to improve the selection of CMWs,

but they use the same basic tests including the height assignment (see §2.2) for an

estimation of the quality. In the method used at EUMETSAT, after a preliminary

elimination of too small and too large vectors, a single quality indicator (QI) is

calculated for each CMW; it takes into account the diVerences between one vector

and its closest neighbours (for spatial consistency) , its collocated predecessor (for

temporal consistency) and the forecast wind at the estimated height (Holmlund 1998):

QI=æN

i= 1

wiW

i

æN

i=1

wi

(7)

where wi

is a test-dependent weight, Wi

a normalization (tanh-based) function and

N the number of tests. In the method used operationally by NOAA/NESDIS, a

recursive �lter is used. CMWs are selected with similar quality tests and a BT-based

height assignment. During an iterative process, they are compared to short-range

analysed (�rst guess) winds and temperatures at diVerent pressure levels, and a

quality �ag (recursive �lter �ag (RFF)) is de�ned. If the �ag is above a chosen

threshold, the corresponding CMW is rejected (Hayden and Purser 1995, Menzel

et al. 1996 ).

In the following sections we used the basic tests described in §2.1 (without

comparison with forecast data and without a precise height assignment ) because itreinforces and isolates the in�uence of each individual test and because this article

focuses on the tracking aspects. However, all the methods previously described

constitute a toolbox useful for a precise description of the evolution of clouds.

3. Basic method for the computation of trajectories

3.1. Data

The trajectory computation method has been tested �rst on a series of half-hourly Meteosat IR images of 18 October 1989, between 0:00 and 23:00 UTC. These

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images cover Europe, the central and western Mediterranean Sea and a part of the

north-eastern Atlantic Ocean (�gure 1). The 16:00 image has a small defect, a shift

of a few lines and columns of pixels above 40° approximately. The trajectory compu-

tation starts on a regular grid, one starting point every 5° in latitude (between 40°and 60° N) and longitude. No preliminary selection of the elements to track is

undertaken prior to the trajectory computation. Four synoptic meteorological

elements can be observed on these images:

1. clouds related to an extratropical low, located south of Greenland and Iceland,

moving westwards;

2. a large band of clouds oriented in a south-west/north-east direction oV the

west European coast, which bends in a west/east direction over Scandinavia

and then in a north-west/south-east direction over Eastern Europe; a part of

this band composed mainly of high-level clouds is associated with a jet stream,

according to synoptic charts;

3. a large cloudless area over Central and Eastern Europe associated with an

anticyclone;

4. and an area over the Iberian peninsula, France and the western Mediterranean

Sea, covered with various (mainly convective) clouds which move eastwards.

3.2. T rajectory computation

The calculation of trajectories is an extension of the computation of CMWs to

a series of images (Szantai and Desbois 1994). The Euclidean distance (or sum of

squared diVerences) method is used to calculate cloud motion vectors (CMV). The

term ‘cloud motion vector’ emphasizes the displacement aspect in the motion of the

cloud, whereas the term ‘cloud motion wind’ emphasizes the velocity aspect. As

described in the previous section, for each position, the CMV is obtained for the

minimal value of the sum of squared diVerences computed between a target window

(or template, of 32×32 pixels) taken on the �rst image and a portion of a larger

window (search window, of 80×80 pixels) taken on the second image. The position

pointed by the end of each vector de�nes the starting position for the computation

of the next vector of the trajectory, obtained from the second and third images of

the series. This process is iterated up to the end of the series of images. No quality

test is performed on the vectors along the trajectories. For each trajectory, there is

always one vector less than the number of images, except in the case where the

moving clouds get too close to the sides of the image or to the Earth disk; in this

case the trajectory computation is prematurely interrupted.

Besides the position of the centre of the target window, several parameters are

determined along the trajectories: the speed and direction, the brightness temperature

of cold pixels, i.e. the average BT of the pixels (inside the target window) which have

a pixel value below the [average of all the pixels of the target window minus the

standard deviation of all these pixels]. For selected trajectories, consecutive target

windows containing the tracked clouds can also be extracted and displayed for

visual check.

3.3. T rajectories in the inf rared channel (18 October 1989)

Figure 2 shows the 54 trajectories with colours corresponding to the BT of cold

clouds previously de�ned. Most trajectories show a regular motion. The anticlockwise

rotation of the extratropical low over the Atlantic Ocean and the north-east/east/

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Figure 1. Initial situation of the study area, 18 October 1989, 0:00 UTC, IR channel. (Highbrightness temperatures are dark, low ones are light.)

Figure 2. Trajectories in the IR channel, 18 October 1989, between 0:00 and 23:00 UTC.The target and search window, and the maximal displacement vector (24 pixels)are drawn in the lower right corner. BT colours: black, BT <40°C; dark blue,40 BT <30°C; light blue, 30 BT <20°C; green, 20 BT <10°C; red,10 BT<0°C; pink, BT>0°C.

south-eastward motion of the band of clouds associated to the jet stream can be

clearly identi�ed. But several trajectories (nos 19, 23, 31, 43, 44, 51, 53 and 54)

contain vectors with a large variation in direction (more than 90°). Some trajectories

(nos 23, 31, 46, 53 and 54) include vectors with unrealistic speeds of more than

70 m sÕ 1 , which are rarely observed (i.e. in the core of jet streams or close to the

centre of tropical cyclones). Vectors with a large variation of speed and/or direction

are probably not associated to a physical motion of the tracked cloud elements.

Some trajectories (beginning of 31, trajectory 41) contain ‘no displacement’

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vectors. These vectors correspond to cloudless areas: the corresponding brightness

temperatures are high (above 0° C).

3.4. Qualitative study of inconsistent vectors

To estimate the quality of CMVs along all the trajectories, each vector undergoes

a series of tests and is thereafter classi�ed:

1. vectors reaching a side of the image or the limit of the Earth disk (this stops

the trajectory computation) ;

2. vectors with the maximal displacement in at least one direction (in this case

24 pixels);

3. ‘no displacement’ vectors;

(At this stage, an unclassi�ed vector undergoes comparisons with the previous vector.

These tests cannot be applied to the �rst vector of a trajectory, which has no

predecessor.)

4. small vectors: in a pair of consecutive vectors, if one of them corresponds to

a small speed, below a chosen threshold (arbitrarily set to 3 m sÕ1 ), it does

not undergo the following tests;

5. vectors with a large change in speed: if the ratio between the smallest and the

largest vector of a pair is below a chosen threshold Rs

(set to 0.5):

0<V

minV

max

<Rs

(8)

6. vectors with a large change in direction: when the two vectors are at an angle

larger than a chosen threshold DDIRmax

set to 45°:

|direction(vi(t ), v

i(t+Dt ) |>DDIR

max(on trajectory i) (9)

7. vectors that satisfy both previous conditions (5 and 6) can be grouped together;

8. All the remaining vectors, which can be classi�ed as ‘vectors without problems’.

Table 1 shows the results for the 18 October 1989 trajectories in the IR channel.

It appears that three quarters of the vectors are classi�ed as ‘without problems’

(80% of the vectors, if the less severe thresholds of 0.33 for the speed ratio and 60°for the direction change are used). Computations of trajectories at other dates, in

other climatic regions or with other channels (in particular WV) have shown that

this class remains the largest one. Noisy images can lower the percentage of this class.

3.5. Causes of inconsistent vectors

In the following paragraphs, a vector will be quali�ed as inconsistent if it shows

a large change in direction or speed with its predecessor (classes 5, 6 and 7), or if it

has the maximal displacement (class 2).

Before trying to correct trajectories, it is necessary to check that large �uctuations

in speed or direction are accidental and do not correspond to real variations aVecting

the velocity of the tracked clouds. For this purpose, inconsistent vectors are arti�cially

corrected. A duplicate of the previous vector, assumed to be correct, replaces an

inconsistent vector. The end of this vector becomes the origin of a new trajectory.

This type of arti�cial correction has been applied to three trajectories with inconsist-

ent vectors (nos 23, 31 and 51 in �gure 3). The direction of the corrected trajectories

appears to be the same as the direction of the original trajectory, before the

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Table 1. Percentages of correct and inconsistent vectors on IR trajectories of 18 October1989, for R

s=0.5 and DDIR

max=45° (in parentheses, for R

s=0.33 and DDIR

max=60°).

Vector classes 1 2 3 4

Maximal NoTotal number of Vectors close to displacement displacement Smallvectors side of image vectors vectors vectors

2353 0.3% 0.1% 6.2% 5.3%

Vector classes 5 6 7 8

Vectors withVectors with Vectors with large variation Vectorslarge speed large change of speed and withoutvariation of direction direction problems

5.4% 5.4% 3.3% 73.9%(1.9%) (4.8%) (1.1%) (80.2%)

Figure 3. Three IR trajectories containing inconsistent vectors and their extension.

inconsistent vector. But at the end of the �rst extension of trajectory 23, two

consecutive correction attempts cannot extend this trajectory any more: this is the

physical end of the trajectory. Movie loops on a computer monitor show that the

cloud is dissipating at that time. The extension of trajectory 51 has the same direction

as the �rst seven vectors of the original, but the vectors of the extension have a

smaller speed. A possible explanation is that new clouds tracked along the extension

are located at a lower level, where the wind is weaker.

We have identi�ed on movie loops several causes that explain abrupt changes of

speed and direction along trajectories:

T he tracking of a similar structure (�gure 4). On trajectory 31, the large inconsist-

ent vector is due to the tracking of the wrong cloud, whose aspect has become closer

to the aspect of the original cloud, which has evolved in the meantime.

T he dissipation and formation of clouds. In some cases, when the cloud dissipates,

the trajectory ‘catches’ a cloud of similar aspect in the vicinity (extensions of trajectory

23). For a part of the trajectories, the formation of clouds cannot be detected because

the clouds already exist when the tracking starts. The formation of a cloud is

observed when non-zero vectors appear on a previously motionless trajectory

(beginning of trajectory 31).

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Figure 4. Principle of the tracking of the wrong cloud.

T he tracking of a cloudless region. Trajectory 51 starts with the tracking of a

small cold cloud surrounded by a large warm area (the Mediterranean Sea, associated

with high BTs). The dissipation of this cloud is followed by an abrupt change of the

trajectory: the seventh vector is three times faster than its predecessor and in an

almost opposite direction. This is caused by the presence of the islands of Corsica

and Sardinia, which are colder than the surrounding sea at this time (3:00 UTC)

and season. The tracking algorithm �nds a minimal Euclidean distance oV the coast

of these islands, in a cloudless region. Along the rest of the trajectory, the target

window without any cloud threads its way through the surrounding clouds: this is

a non-physical trajectory of a cloudless area.

Orographic eVect. The presence of mountains can modify the �ow of the sur-

rounding air and induce the formation and persistence of clouds above or near their

summit. This eVect in�uences the end of trajectory 33: the Fagarasul mountains in

the Romanian Carpathians ‘slow down’ and de�ect the end of this trajectory to the

west (�gure 5).

In�uence of spatial and temporal scales. Trajectories have been computed with

modi�ed sizes of the target and search windows (�gure 6) and with a larger time

interval between images (1 h). Table 2 shows that the use of a smaller target window

or a larger time interval increases the percentage of inconsistent vectors. The large-

scale motions (cyclonic rotation, motion along the band of high-level clouds, eastward

motion of convective clouds over Spain and the western Mediterranean Sea) are

nevertheless visible on portions of a large number of trajectories.

All these causes generating inconsistent vectors have already been observed on

CMWs and were mentioned in the previous section. However, trajectories reveal

them better than CMWs because an inconsistent vector is generally preceded by a

series of correct vectors.

4. Improved method: construction of corrected trajectories

The previously computed trajectories are not representative of the motion of one

cloud (or group of clouds) over the whole period of the study. In addition, the end

of the trajectories is not determined by the disappearance of the tracked cloud(s)

but by the end of the series of images. To obtain trajectories representing the real

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Figure 5. EVect of the Fagarasul mountains (around 45°37ê N, 24°49ê E) on trajectory 33( low altitudes are dark, high ones are white).

Figure 6. Trajectories in the IR channel, computed with a target window of 16×16 pixels,with target window, search window and maximal displacement vector (at lower right)(cf. �gure 2).

motion of clouds, the method has been improved. The determination of each CMV

is now divided in four steps:

1. the computation of the Euclidean distance surface and its minimal values;

2. a series of quality tests;

3. the correction of the vector if it is inconsistent;

4. stopping tests, to end the trajectory if necessary.

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Table 2. Computation of trajectories at diVerent spatial and temporal scales. Percentage ofthe main classes of vectors.

Target Search Time interval Maximalwindow window between displacement(lines, ( lines, consecutive ( lines and

columns) columns) images (h) columns)

Original scale 32–32 80–80 1/2 24 pixelsReduced window 16–32 64–80 1/2 24 pixels

sizes 16–16 64–64 1/2 24 pixelsLarger time interval 32–32 80–80 1 24 pixels

VectorsTotal without Small Inconsistent

number problem vectors vectorsof vectors (8) (%) (4) (%) (2, 5, 6, 7) (%)

Original scale 2353 73.9 5.3 14.2Reduced window 2315 68.1 5.8 20.6

sizes 2347 54.8 7.4 32.3Larger time interval 1188 59.2 8.3 27.9

In a �nal step, each corrected trajectory as a whole undergoes some complementary

tests. Very short trajectories are removed as well as some questionable ones.

4.1. Preliminary step: computation of the Euclidean distance surface

For the computation of each CMV, the Euclidean distances corresponding to all

the possible displacements can be stored in a matrix, whose size (2 DLmax

+1 lines,

2 DPmax

+1 columns) depends on the maximal possible displacement in pixels. This

matrix can be represented in three dimensions as a surface (Euclidean distance

surface). Very few authors used other information than the position of the minimal

value for the determination of a motion vector. Anandan (1989) also computed the

curvature of the Euclidean distance surface along the two principal axes at the local

minimum positions as complementary quality indicators. In this study, we extract

all the local minima of the Euclidean distance matrix. In the �rst place, the CMV is

determined by the lowest value of these minima, as described in the previous section.

4.2. Quality tests

One of the basic assumptions in the construction and correction of trajectories

is that two measurements of a meteorological parameter (in this case the motion of

the cloud related to the wind) show only a small diVerence in most cases if they are

made simultaneously in a small neighbourhood, or at the same location but within

a short time interval. More precisely, these measurements have a correlation close

to one, which decreases with distance and time (Durst 1955, Gandin 1965). For this

reason, each CMV undergoes the series of quality tests before being corrected if

necessary. With the classi�cation de�ned in the previous section, we will attempt to

correct inconsistent vectors of classes 2 (extreme speed), 5 (important speed variation) ,

6 (important change in direction) and 7. The chosen threshold values on speed (Rs)

and direction (DDIRmax

) have been optimized after several trials to render realistic

motions. An Rs

value of 0.5 may seem large (the speed can be halved or doubled),

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but it can save some trajectories when non-translationa l motion is also present (for

example, the expansion of a convective cloud). A DDIRmax

value of 45° allows the

tracking of a cloud in a region of rotational motion (for example close to the centre

of rotation of extratropical lows). Similar ‘smoothness constraints’ have been used

by Hodges to construct the trajectories of speci�c features (in particular maximal

values of relative vorticity) in meteorological analyses (Hodges 1994).

4.3. Correction of inconsistent vectors

To correct an inconsistent CMV, we extract all the local minima of the Euclidean

distance matrix and use the vector determined during the previous step. The

Euclidean distance matrix can be used if at least two local minima (including the

one used for the initial, non-corrected vector computation) exist and if they are not

too numerous. (The maximum number of local minima has been set to 32 and is

rarely reached. A larger number indicates that at least one image of a pair has been

degraded by random noise or has a marked texture—for example a �eld of clouds

with a regular pattern.) The corrected CMV is given by the position of the local

minimum that is closest to the end of the vector obtained during the previous

iteration (�gure 7). If this corrected vector is of better quality (i.e. it matches quality

tests on velocity and direction), the computation of the trajectory can be continued,

otherwise it is stopped. The �rst two vectors of a trajectory undergo a modi�ed

version of these tests: if the �rst vector is small (below 5 m sÕ 1 ), the test on speed

variation is not applied. This enables the saving of some trajectories, which start at

or closely after the formation instant of the tracked cloud(s).

Figure 7. Correction of an inconsistent cloud motion vector ( jth vector, at instant t ontrajectory i). The corresponding target and search windows (right) and the Euclideandistance surface ( left) are represented with the original and corrected vectors. Lowvalues of the Euclidean distance are white, high values are dark grey.

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4.4. T ermination of trajectories

The computation of trajectories will automatically be interrupted in the following

cases:

1. the current vector is too close to a side of the image or to the limit of the

Earth disk;

2. the vector is inconsistent and cannot be corrected;

3. no displacement vector. This is generally associated with the dissipation of

the tracked clouds, and the (motionless) surface below is thereafter observed.

The whole set of trajectories is then re-examined. On some corrected trajectories, we

noticed that several consecutive vectors (in some cases a majority of vectors) had

been corrected, owing to an incorrect start of the trajectory (the �rst vector cannot

be completely checked) or to the dissipation of the tracked clouds simultaneously

followed by the tracking of clouds of similar aspect. To avoid this, when three

consecutive corrected vectors are found, we interrupt the trajectory on the �rst of

them. Finally, very short trajectories of three vectors or less are of little interest and

can easily be corrupted due to an inconsistent �rst vector; these trajectories are

therefore removed.

The complete procedure has been applied to the 47 IR images and a new set of

trajectories has been computed. A �rst attempt showed that all the trajectories but

one still remaining at 15:00 UTC are stopped at 16:00. This is caused by a shift of

several pixels on the 16:00 UTC image, con�rmed by a visual examination of this

image and the surrounding ones. (The study of other cases has shown that the

simultaneous termination of several trajectories should draw one’s attention in the

�rst place onto a problem concerning the quality of at least one image. A meteorolo-

gical phenomenon of short duration (e.g. the outburst of a convective cloud system)

does not aVect trajectories on such a large scale.) After the removal of the 16:00

faulty image, trajectories have been computed again (�gure 8); this time, several

trajectories persisted along the whole series of images. When compared to the

Figure 8. Corrected trajectories in the IR channel, 18 October 1989, between 0:00 and23:00 UTC (cf. �gure 2).

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uncorrected trajectory �eld (�gure 2), the new trajectories appear to be less numerous,

more regular and of shorter duration. Trajectories starting in initially cloudless areas

have disappeared. Trajectories 12 and 34 are (almost) identical to their originals.

The tracking has been improved for trajectories which had an inconsistent vector

shortly after their beginning (no. 46).

5. Computation of trajectories for diVerent channels

5.1. Water vapour trajectories

The WV absorption channel (5.7–7.1 mm), available on most geostationary met-

eorological satellites, detects WV structures at medium and high levels (between 600

and 300 hPa) and high-level clouds. Trajectories of these structures and clouds can

also be constructed. Figure 9 shows the extended trajectories, starting on 18 October

1989 at 0:00 UTC, computed on a series of images covering 60 h (the images with

major defaults, like the 16:00 UTC images which also had a large line shift, have

been removed. In such cases, consecutive images used for CMV computation are

separated by 1 h or more). Trajectories are mainly located in areas where high-level

clouds are present (in the area of the low over the Atlantic Ocean, along the band

of high-level clouds associated with the jet stream and in the convective area over

the western Mediterranean Sea). The limited number of trajectories in pure WV

regions (trajectories 52 and 54) can be explained by the lesser quality of the images

(which were degraded by instrumental noise) and the lack of contrast on WV

structures in these areas (anticyclonic region over central Europe and Italy) . Similar

observations have been made in the WV channel on CMWs, which are more likely

to be found in areas with high clouds (Laurent 1993). The duration of the trajectories

is also reduced by the image quality: the longest trajectory (37) lasts 23 h, although

some clouds are still present after the trajectory termination, according to the

corresponding IR trajectory, which is very close, and to observations of movie loops.

A detailed comparison of trajectories in both IR and WV channels (�gures 8 and 9)

indicates that a majority of common trajectories show the same motion. In some

Figure 9. Trajectories in the WV channel, 18 October 1989, between 0:00 and 23:00 UTC,superimposed onto the 0:00 UTC WV image. The longest living trajectory is 37.

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cases, the trajectories are even identical. The use of the correction method and

interruption tests explains that the WV trajectory chart shows a more regular and

more realistic motion than the trajectory charts constructed with a simpler method

in the tropics by Soden (Soden 1998). In the latter method, each vector has only

undergone a self-symmetry test (see also §6.2), and non-self-symmetri c vectors have

been replaced by their predecessor. Only trajectories with less than 10% corrected

vectors were retained.

5.2. Speci�c tracking of high-level clouds

In the method described in the previous sections, all the pixels of the target

window are used for the computation of the displacement vector. It can be adapted

to a more selective tracking of cold, high-level clouds by selecting only the pixels

above a chosen BT threshold for the Euclidean distance computation and the

deduced cloud CMV (Schmetz and Nuret 1987). (This is realized in practice by

setting the weighting function W of equation (1) to 1 for the pixels of the target

window with a pixel count corresponding to a BT below the threshold value, and

by setting W to 0 for the pixel values above this threshold.) This selection reduces

the in�uence of low-level clouds and the Earth surface, which in some cases slow

down CMVs, and in some cases enables the tracking of high-level clouds in situations

where the trajectory computation using all the pixels was not successful. Besides the

selection of ‘cold pixels’, the only diVerence is the introduction of a complementary

termination test on trajectories: when the number of cold pixels becomes too small,

below a chosen threshold (set in this study to 6.25% of all the possible pixels of the

target window); this corresponds generally to the dissipation of the cloud.

In �gure 10, WV trajectories of high-level clouds, with a BT below 40° C are

represented. They are less numerous than trajectories computed without temperature

Figure 10. Trajectories of high-level clouds in the WV channel, after a selection of the pixelswith a BT below 40°C; starting on 18 October 1989 at 0:00 UTC, with the end ofthe longest living trajectory (46) on 19 October 1989 at 21:30 UTC.

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selection (18 and 22 trajectories respectively) . Whereas some trajectories are identical

with and without cold pixel selection (possibly due to a large proportion of high-

level clouds inside the target window—for example trajectory 37), in other cases the

tracked elements along trajectories with a cold pixel selection can move in a slightly

diVerent direction (trajectory 47) and with a diVerent, generally higher speed (traject-

ory 36). DiVerences between trajectories with the same origin can be related to

motions at diVerent levels. Trajectories with a cold pixel selection appear to be more

representative of the motion of active areas (for example convective areas).

5.3. T rajectories in the visible channel

Trajectories have also been constructed from Meteosat images in the visible

channel (VIS) (0.4–1.1 mm), which is better adapted for the tracking of low-level

clouds and has a better spatial resolution (the side of a VIS pixel is 2.5 km). The

main limitation is that these images are in practice available only during daytime

(between 8:30 and 17:30 UTC for the studied area). The use of a solar correction

(dividing the pixel value associated to the albedo by a factor of cos h0, where h

0is

the solar zenithal angle) enables better tracking, especially at the beginning of

trajectories.

6. Construction of complete trajectories

6.1. Meaning of trajectories

The trajectory �elds described in the previous sections have a variable duration,

limited mainly by the quality tests and the number of images: for the IR trajectory

�eld shown in �gure 8, among the 35 trajectories, seven of them (20%) have a

duration of 23.5 h. Nevertheless, the motion of identi�ed cloud structures along

trajectories has to be checked. Movie loops con�rm that such structures remain and

evolve inside the target window during the tracking (�gure 11 for trajectory 50). For

a precise determination of the evolution of the clouds, speci�c parameters, in particu-

lar the BT of the cold pixels* or the BT of the coldest pixel inside the target window,

can give indications about the life cycle of diVerent clouds. For example, the life

cycle of several cloud structures along trajectory 50 has been identi�ed on the BT

curves (�gure 12). In particular, the growth of a high-level cloud can be recognized

in the upper left part of the target windows between 7:00 and 10:00 UTC; its

progressive dissipation can be observed between 13:00 and 15:00 UTC. Such observa-

tions show that trajectories do not represent the motion of a single isolated cloud

in most cases, but rather the motion of several small clouds or portions of large

clouds (or pure WV structures, in the WV channel ), embedded in the atmospheric

�ow at a speci�c (not precisely known) level. Inside the target window, some clouds

may dissipate or merge, while other cloud elements appear. But the main condition

is that the content of the target window does not change too strongly in the interval

between two consecutive images (Øh in most cases).

*Various methods can be used to determine the brightness temperature of the cold pixels.In this article, for each target window, this brightness temperature is derived from the averagenumerical count of all the pixels that have a value below a threshold. This threshold isdetermined by the average of the numerical count of all the pixels of the target window minusthe standard deviation of these numerical counts. Therefore the value of this threshold varieswith each correlation window.

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Figure 11. Consecutive target windows (inside squares) and their immediate surroundingsalong trajectory 50, IR channel. (The 16:00 UTC image has not been used for theconstruction of this trajectory.)

Figure 12. Brightness temperature of the coldest pixel (Tmin

) and average BT of the coldpixels (T

cold) along trajectory 50, and identi�ed cloud structures. 1, cloud in lower left

corner (dissipating); 2, at left centre; 3, high-level cloud at top, left and centre; 4, smallbright cloud just above centre; 5, several small cloud structures; 6, growing cloudalong lower edge, at left.

6.2. Computation of the opposite vector

Basically, the uncertainty on the measurement of each vector is 0.5 pixel in each

direction. But complementary tests are necessary to check the quality of the previ-

ously constructed trajectories; these tests may give an indication of tracking errors.

For this purpose, a ‘self-symmetry’ test, based on the computation of the opposite

vector, has been added. For each vector computed between two images (between

image number n and n+1), we compute the ‘opposite’ vector (between image n+1

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and n). The end of the direct vector gives the position of the centre of the target

window for the computation of the opposite vector. The search windows of both

vectors have the same centre, the origin of the direct vector. We have an excellent

tracking if the opposite vector has exactly the same magnitude and the opposite

direction of the direct vector.

Figure 13 shows the diVerence between both vectors in the IR channel. Isolated

non-self-symmetric vectors (with a pixel diVerence of more than two pixels in either

direction—lines or columns—between the direct and opposite vectors) can be

observed along several trajectories (nos 10, 11, 13, 14, 20, 22, 30, 37 and 50). More

than 20% of non-self-symmetric vectors are scattered along some trajectories (nos

3, 5, 8 and 15) or concentrated along the �nal part of other trajectories (nos 26

and 46). An important diVerence between the direct and opposite vectors can be

explained by the presence of several features of similar aspect in the search window

or may be due to changes in shape or size of the tracked features. Therefore

interrupting the trajectory computation as soon as a non-self-symmetric vector is

found is a good way to improve the quality of trajectory �elds, but at the cost of

having shorter trajectories. A vector diVerence of two pixels between direct and

opposite vector should be tolerated for this rather severe quality test, thus allowing

small deformations of the tracked features.

Table 3 presents the proportion of self-symmetric vectors represented in �gure 13

and for two other situations (one in the IR channel, the other one in the WV channel)

during one day with a large number of trajectories covering the whole Meteosat

disk north of 35° S. The results for the 18 October 1989 IR trajectories validate

the use of a vector correction and trajectory interruption tests; the proportion of

non-self-symmetric vectors has been reduced thereafter.

The interruption of trajectories on a non-satisfactory self-symmetry test leads to

a further reduction in the number of vectors by less than a half of the corrected set

Figure 13. DiVerence in pixels between direct and opposite vectors, coded in colour: black,direct and return vector identical; blue, diVerence of one line or/and one column ofpixels; green, diVerence of two lines or/and two columns of pixels; red, diVerence ofmore than two lines or two columns of pixels.

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Table

3.

Nu

mb

ero

ftr

aje

cto

ries

an

dvec

tors

,and

diV

eren

cein

pix

els

bet

wee

ndir

ect

an

do

pp

osi

tevec

tors

(ab

solu

tevalu

eo

fth

ela

rges

td

iVer

ence

bet

wee

nlin

esor

colu

mn

so

fth

esu

mof

the

two

vec

tors

)fo

rth

ree

situ

ati

ons

(18

Oct

ob

er1989,

IRch

an

nel

;18

Feb

ruary

1996,

IRand

WV

chan

nel

s).

DiV

eren

cein

pix

els

Num

ber

of

Tim

eN

um

ber

of

Num

ber

(bet

wee

ndir

ect

and

vec

tors

Date

(UT

C)

Chann

eltr

aje

ctori

esof

vec

tors

op

po

site

vec

tors

)(%

of

tota

l)Sel

ecti

on

test

sC

om

men

t

18

Oct

ober

1989

0:0

0–23:3

0IR

54

2345

0pix

el1573

(67.1

)N

ose

lect

ion

U

nco

rrec

ted

1–2

pix

els

522

(22.3

)N

oco

rrec

tion

traje

ctori

es(�

gure

3)

>2

pix

els

250

(10.6

)

18

Oct

ober

1989

0:0

0–23:3

0IR

35

864

0pix

el632

(73.1

)Sp

eed

and

dir

ecti

on

Tra

ject

ori

esaft

erm

ild

1–2

pix

els

177

(20.5

)te

sts+

traje

ctori

esof

test

s(�

gure

11

)>

2pix

els

55

(6.3

)>

3vec

tors

18

Oct

ober

1989

0:0

0–23:3

0IR

26

502

0pix

el411

(81.9

)Sp

eed

and

dir

ecti

on

Tra

ject

ori

esaft

er1–2

pix

els

91

(18.1

)te

sts+

traje

ctori

esof

sever

ete

sts

>2

pix

els

0(0

)>

3vec

tors

+se

lf-

sym

met

ryte

st

18–19

Feb

ruary

17:3

0–17:3

0IR

857

21

060

0pix

el16

883

(80.2

)Sp

eed

and

dir

ecti

on

Wh

ole

dis

k

1996

1–2

pix

els

3214

(15.2

)te

sts+

traje

ctori

esof

traje

ctori

esaft

er>

2pix

els

963

(4.6

)>

3vec

tors

mild

test

s

18–19

Feb

ruary

17:3

0–17:3

0IR

722

16

169

0pix

el13

749

(85.0

)Sp

eed

and

dir

ecti

on

Tra

ject

ori

esaft

er1996

1–2

pix

els

2420

(15.0

)te

sts+

traje

ctori

esof

sever

ete

sts

>2

pix

els

0(0

)>

3vec

tors

+se

lf-

sym

met

ryte

st

18–19

Feb

ruary

17:3

0–17:3

0W

V774

13

982

0pix

el10

189

(72.9

)Sp

eed

and

dir

ecti

on

Wh

ole

dis

k

1996

1–2

pix

els

2911

(20.8

)te

sts+

traje

ctori

esof

traje

ctori

esaft

er>

2pix

els

882

(6.3

)>

3vec

tors

mild

test

s

18–19

Feb

ruary

17:3

0–17:3

0W

V611

10

046

0pix

el8016

(79.8

)Sp

eed

and

dir

ecti

on

Tra

ject

ori

esaft

er1996

1–2

pix

els

2030

(20.2

)te

sts+

traje

ctori

esof

sever

ete

sts

>2

pix

els

0(0

)>

3vec

tors

+se

lf-

sym

met

ryte

st

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of trajectories (23% less vectors for the 18 February 1996 IR case, 42% less vectors

for the 18 October 1989 IR case) and to a reduction of the number of trajectories

by less than a quarter (16% less trajectories for the 18 February 1996 IR case, 25%

less trajectories for the 18 October 1989 IR case), with the bene�t of having more

consistent results. This supplementary process is needed for the computation of

reliable trajectories representing the motion of clouds during their whole lifetime.

6.3. Construction of all complete trajectories at a given time

In the previous sections, all trajectories started at the same instant, which corre-

sponds to various moments of the life cycle of the tracked elements. This led us to

adapt the method previously described to enable the construction of the complete

trajectory of a cloud or cloud ensemble, from its birth or apparition to its dissipation.

For this purpose, complete trajectories are computed in four steps.

1. The direct trajectories, starting from selected positions (for example on a

regular grid) at a chosen time (t0), are computed (forward computation, from present

to future). All the previous quality tests and corrections, including the interruption

of trajectories on non-self-symmetric vectors, are applied except the suppression of

short trajectories ( less than four vectors) . The �nal instant of a trajectory is t0+Dt

1,

where Dt1

is the duration of this trajectory.

2. The backward trajectories, starting at the same time from the same positions,

are computed backwards in time (from the present back to the past), with the same

conditions as the direct trajectories. The instant of termination of the corresponding

backward trajectory is t0Dt

2, with a duration Dt

2.

3. Complementary quality tests are applied on the �rst vector of the direct

and the corresponding backward trajectory: both vectors must have close speeds

and directions close to opposite. The same threshold values on speed (Rs=0.5) and

direction (DDIRmax

=45°) are used to compare the �rst vector of a direct trajectory

and the opposite of the �rst vector of the corresponding backward trajectory. If the

vectors pass the tests successfully, the direct and backward trajectories are joined to

form the complete, reconstructed trajectory (named b+d hereafter) . This trajectory

is retained for the next step. When at least one of these complementary tests is not

satis�ed, this can be caused: (a) by the dissipation of a cloud or cloud system ( long

backward trajectory with no, or a very short, non-signi�cant, direct trajectory—in

this case, only the backward trajectory is kept for the next step); (b) by its formation

(long direct trajectory without backward trajectory) ; or (c) by the presence of two

clouds or cloud systems with a diVerent but consistent motion (long direct and

backward trajectory) .

4. The goal of the last step is to con�rm that the trajectories previously con-

structed are of good quality. For each of them, the end position and the instant of

termination of the backward trajectory (t0Dt

2) determine the starting position and

instant of a new, recalculated trajectory, computed forward over the whole series of

images used for the direct and backward trajectory computation. In practice, two

favourable cases for comparisons can be distinguished:

– the recalculated trajectory has a longer or the same duration (i.e. more

vectors or the same number of vectors) as the b+d trajectory;

– the recalculated trajectory has a shorter duration than the b+d trajectory,

but still exists at the instant used as time reference (t0).

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In both cases, if the recalculated trajectory is identical or stays very close to a portion

or the totality of the original b+d trajectory, then we can assume that the cloud

has been tracked correctly. This can be checked by comparing the distance in pixels

(de) between the end position of the recalculated and the b+d trajectories to the

average length of both trajectories (lc), computed over their common duration. For

this purpose, the quality ratio R has been de�ned:

R=100de

lc

(in %) (10)

A ratio of 10% has been set as a threshold for the identi�cation of ‘good’ trajectories

whereas a 5% ratio selects ‘high quality’ trajectories.

6.4. Results and interpretation

Three sets of complete trajectories have been constructed as examples: one centred

on 18 October 1989, 00:00 UTC, in the IR channel, and two cases centred on

18 February 1996, 17:30 UTC, covering the whole Meteosat disk above 35° S, in

the IR and WV channels respectively (these cases are extensions of the previous

examples).

Figure 14 represents the recalculated IR trajectories over a period between

17 February, 17:30 UTC and 19 February 1996, 17:30 UTC. The original direct and

backward trajectories were started at 17:30 UTC on 18 February. All recalculated

trajectories suitable for a comparison with the b+d originals are represented; they

correspond to clouds located preferentially in a limited number of areas:

– clouds at all levels around the extratropical low around 30° N, 30° W;

– high-level clouds associated to jet streams: over the North Atlantic Ocean/

Northern Europe (between 50° and 60° N), the South Atlantic Ocean

(30–35° S) and north-west Africa (African jet);

– high-level clouds at the top of convective cloud clusters in the intertropical

convergence zone (across the equator, and over East Africa around 5° S,

25° E);

– marine stratocumulus clouds in the south-eastern Atlantic;

– and at a lesser extent, low-level clouds around an anticyclone at 45° N,

20–40° W;

Figure 14 also reveals that the trajectories of good quality (red: R 5%; green:

5<R 10%), i.e. where the recalculated trajectory is close to the original b+d

trajectory, represent about 50% of the original set, although they are surrounded by

trajectories of lesser quality, which show a similar motion (blue). Some clouds appear

to be easier to track, probably because they have a unique, clearly identi�able and

stable shape, and because no other structures—clouds or land features—disturb the

tracking. This may also indicate that some cloud elements of a large cloud ensemble

have a longer lifetime than others located in their vicinity. Similar results are observed

for the two other examples (table 4). Trajectories in the WV channel mainly track

high-level clouds rather than pure WV structures, as had already been observed in

the cases described in §5.1 and 5.2.

7. Conclusions and prospects

The method presented in this article allows the automatic tracking of clouds

from series of satellite images in the VIS, IR and WV channels, and pure WV

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Figure 14. Recalculated IR trajectories between 17 February, 17:30 UTC and 19 February1996, 17:30 UTC, superimposed onto the IR image of 18 February, 17:30 UTC. Red,quality ratio R 5%; green, 5<R 10%; blue, R>10%.

structures from images in the WV channel. It is an extension of existing techniques

used to compute cloud motion winds and is adapted for the tracking of mesoscale

structures, with dimensions about 75 to 200 km.

Atmospheric structures, i.e. clouds in the IR, WV and VIS channels and pure

WV structures in the WV channel, have been successfully tracked over various

durations ranging from 1 h to several days. This study shows that diVerent factors

have an in�uence on the quality and representativeness of the tracking and should

be taken into account for studies about the motion and evolution of clouds.

1. The lifetime of the tracked structure is the ultimate limiting factor.

2. The aspect of the structure in comparison to its environment: clouds which

show a high contrast with their surroundings (surface or lower clouds) and without

any other cloud of similar aspect in the neighbourhood will be more easily tracked.

3. The quality of numerical images: a high level of noise will make the tracking

more diYcult. Navigation errors between consecutive images (shifts in lines or

columns) can interrupt the tracking, as has been observed in one of the cases

presented, and thus arti�cially reduce the measured lifetime of the structure(s).

4. A short time interval between images favours the tracking (a Øh interval has

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Table 4. Comparison of b+d and recalculated trajectories and vectors for three situations.Values for recalculated trajectories are indicated for three quality ratios (R<2 ,R 10% and R 5%). Percentages refer to recalculated trajectories and vectors.

Number of trajectories

Recalculated RecalculatedRecalculated trajectories trajectoriestrajectories R 10% R 5%

18 October 1989, IR 26 14 13(100%) (53.8%) (50.0%)

18 February 1996, IR 1042 579 473(100%) (55.6%) (45.4%)

18 February 1996, WV 1173 575 482(100%) (49.0%) (41.0%)

Number of vectors

Recalculated Recalculatedb+d Recalculated trajectories trajectories

trajectories trajectories R 10% R 5%

18 October 1989, IR 1116 612 445 416(182.4%) (100%) (72.7%) (68.0%)

18 February 1996, IR 35 956 27 870 22 464 18 706(129.0%) (100%) (80.6%) (67.1%)

18 February 1996, WV 24 808 18 299 13 874 11 540(135.6%) (100%) (75.5%) (63.1%)

been used in this study) . During a long time interval, it is more likely that a cloud

will change its size or aspect, and in the case of extreme evolutions make the tracking

impossible.

5. A practical limitation is the large amount of data (satellite images) needed to

obtain long sequences and thus long trajectories, although this problem tends to be

reduced nowadays with the increasing storage capacities of recent computers (for

example, a half-hourly sequence over 48 h of full resolution Meteosat IR or WV

images represents a volume of approximately 600 Mb).

6. The presence of clouds at diVerent levels probably limits the tracking, but this

eVect has not been investigated yet. Basically, when clouds at two diVerent levels

have converging trajectories and one layer masks at least partly the second one, the

trajectory following the most outstanding cloud features is continued. Theoretically,

the motion of two cloud layers moving with a diVerent motion should lead to the

presence of several minima in the Euclidean distance surface, and potentially enable

the determination of two CMVs (although the measurement of each Euclidean

distance minimum—i.e. each vector associated to one cloud layer—might be slightly

modi�ed by the presence of clouds from the other layer). Another way to extend the

trajectory with less visible features may consist of calculating CMVs using images

of another channel, where these features are prominent. For example, low-level clouds

and semi-transparent thin cirrus (at a high level ) can be tracked in the IR channel.

In cases of overlap of clouds from both types, thin cirrus may be tracked more easily

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in the WV channel, whereas low-level clouds (undetectable in the latter channel)

may be tracked correctly in the VIS channel.

For the construction of trajectories, new or little used quality or interruption

tests have been successfully introduced. Besides the tests between the speed and

direction of consecutive vectors, which are commonly used for the operational

computation of cloud motion winds, a self-symmetry test concerning each vector

taken alone has been introduced. The correction of inconsistent vectors, although

concerning only a limited proportion of vectors, is close in its principle to the use

of a Kalman �lter: an inconsistent vector is compared to a predicted vector, derived

from its predecessor and corrected if possible. The comparison of trajectories com-

puted in both directions (backwards and forwards) has also been introduced and

appears to be an eYcient quality test.

This study has also revealed two types of tracking. In the �rst case, robust

reversible trajectories have been constructed with the use of severe quality tests

including the interruption of trajectories on non-symmetric vectors and the rejection

of non-reversible trajectories. These ‘high quality trajectories’ allow a reliable tracking

of a limited number of atmospheric structures. In the second case, more trajectories

are retained, often with a longer duration but with a lesser quality; they include the

set of high-quality trajectories but also trajectories that contain non-reversible vectors

and non-reversible trajectories. All these trajectories are not suitable for a precise

tracking of atmospheric structures, but groups of trajectories give a qualitative but

realistic picture of large-scale atmospheric motions. Such trajectories can potentially

be used for statistical studies. The lack of robustness of this method without severe

quality tests can be explained by ambiguities in the tracking due to the presence of

structures with similar aspect in the vicinity (which may introduce an incorrect

tracking), to an important deformation of the structure between two consecutive

images or to structures located at diVerent levels and moving with a diVerent motion.

A second explanation is the turbulent and chaotic nature of atmospheric motions; a

small diVerence between the motion of two neighbouring atmospheric structures can

increase rapidly with time. The uncertainty of 0.5 pixel on the measurement of the

motion may also contribute to these diVerences.

In the standard method, no selection of pixels has been undertaken during the

construction of the trajectories. A variation of the method, which consists in selecting

cold pixels, leads in some cases to a speci�c tracking of high-level clouds. The

corresponding trajectories complete those calculated with the standard method. The

diVerences observed in the few cases where trajectories were computed with both

methods can be explained by the presence of structures at diVerent levels. A derived

method is suggested: it consists of using a mask provided by a cloud classi�cation

and corresponding to a particular type of clouds (thus excluding clouds of other

types) before computing the vectors of a trajectory. Another adaptation of the

standard method for case studies or for the tracking of speci�c types of clouds

consists in making a preliminary selection or construction of the starting points

instead of using a regular grid, as has been shown in the examples given. The

(uncorrected) brightness temperature appears to be an imprecise indicator about

the height of the tracked clouds or their motion vector: the same, relatively high

BT may correspond to a low-level warm cloud or to a high-level cold thin cloud.

Nevertheless, it appears that the changes in BT are small between consecutive vectors,

excluding rapid changes in the height or nature of the clouds. The visual aspect of

the evolving clouds (in line, patchy, etc.) along a trajectory (e.g. �gure 12) also

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indicates that these clouds are more likely located at a single level and that there is

no ‘jump’ between clouds at diVerent heights. These observations could be con�rmed

with the use of a precise height estimation method. Besides, such a method would

provide a description of the tracked structures as complete as possible.

The trajectory construction method is based on cloud motion wind calculation

techniques that have been validated for a long time. The comparison of trajectories

derived from satellite images with three-dimensional meteorological analyses should

provide a complementary validation, although the temporal resolution of analyses

(6 or 12 h) is not the same, and help for a height attribution of the tracked atmospheric

structures. Comparisons with the trajectories of balloons can also be undertaken

for case studies. A comparison of balloon trajectories launched for the INDOEX

experiment during the winter of 1998–99 with trajectories derived from Meteosat

5 images is under way at the Laboratoire de Meteorologie Dynamique.

The trajectory construction method described in this article can be applied for

meteorological and climatic studies. Possible applications include the study of the

evolution of large scale atmospheric structures, especially convergence (subsidence)

zones and divergence zones (in particular the intertropical convergence zone), and

at mesoscale the divergent motion of clouds generated on top of tropical convective

cloud clusters, or the motion of small cloud elements inside cyclones.

Acknowledgment

The Meteosat images were provided by the European Space Agency and by

EUMETSAT.

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International Journal of Remote Sensingszantai/publi/ASz_IJRS... · 2009. 1. 21. · A. SZANTAI*, F. DE´SALMAND and M. DESBOIS Laboratoire de Me´te´orologie Dynamique, Ecole Polytechnique,