Three Spot images taken during the FIRE experiment on stratocumulus are analyzed. From this high resolution data detailed observations of the true cloud radiance field may be made. The structure and inhomogeneity of these radiance fields hold important implications for the radiation budget, while the fine scale structure in radiance field provides information on cloud dynamics. Wieliki and Welsh, and Parker et al., have quantified the inhomogeneities of the cumulus clouds through a careful examination of the distribution of cloud (and hole) size as functions of an effective cloud diameter and radiance threshold. Cahalan (1988) has compared for different cloud types of (stratocumulus, fair weather cumulus, convective clouds in the ITCZ) the distributions of clouds (and holes) sizes, the relation between the size and the perimeter of these clouds (and holes), and examining the possibility of scale invariance. These results are extended from LANDSAT resolution (57 m and 30 m) to the Spot resolution (10 m) resolution in the case of boundary layer clouds. Particular emphasis is placed on the statistics of zones of high and low reflectivity as a function of a threshold reflectivity

Desbois, Michel

Seze, Genevieve

Smith, Leonard

English

NASA Technical Reports Server

Structures Observed on the Spot Radiance Fields 
During the FIRE Experiment 
srft 
Genevieve S e z e t  Leonard Smith and Michel D e s b o i g  
LMDDcole ~Polytechnique  91128 P a l a i s e a u  Cedex [France) * 
**DAMTP, Cambridge U n i v e r s i t y  (UK) 
Introduction 
Three Spot images taken during the FIRE experiment on stratocumulus (july 1987) have 
been analysed. From this fiigh resolution data detailed observations of the true cloud 
radiance field may be made. The structure and inhomogeneity of these radiance field's 
hold important implications for the radiation budget, while the Pine scale structure 
in radiance field provides information on cloud dynamics. Wieliki and Welsh (1986) and 
Parker et al. (1986) have quantified the inhomogeneities of the cumulus clouds through 
a careful examination of the distribution of cloud (and hole) size as functions of an 
effective cloud diameter and radiance threshold. Cahalan (1988) has compared for 
different cloud types (stratocumulus, fair wheather cumulus, convective clouds in the 
ITCZ) the distributions of clouds (and holes) sizes, the relation between the size and 
the perimeter of these clouds (and holes), and examining the possibility of scale 
invariance. We extended these results from Landsat resolution (57m and 30m) to the 
Spot resolut ion ( 10m) resolution in the case of boundary layer clos-.ds. Particular 
emphasis is placed on the statistics of zones of high and low reflectivity as a function 
of a threshold reflectivity. 
Data 
Each Spot instrument returns one panchromatic images (10m resolution) and three 
multispectral images (20m resolution). These images are obtained from the measure Of 
solare enery in a large spectral band (0.51-0.73) and three narfower bands at visible 
and infrared wavelengths. The saturation is reached in the panchromatique band for 30% 
of reflectivity and in the multispectral bands respectively for 500, 60% and 80% Of 
reflectivity. Data are discretized in digital count comprised between 0 and 255. In 
the panchromatic image the sea reflectivity corresponds to about 25 counts. 
Three different Spot scenes have been recorded during the FIRE experiment: One 60km 
by 80km scene on the 7th of july both in panchromatic mode and multispectral mode, one 
double scene of 120km by 120km on the 8th of july in panchromatic mode and on 60km by 
66km scene on the 19th both in panchromatic and multispectral mode. The 7th and 8th 
are very cloudy. However, inspite of the small variability in radiances, different 
structures appear. The scene for the 19th of july is on the opposite characterized 
by the presence of very small clouds. From these data sets, three regions of 1024 by 
1024 pixels (10km by 10km) have been extracted (Fig. 1). The first region is composed 
of a mixing of high re€lectivity and low reflectivity structures. The second region 
has increasing reflectivity from the center to the edges. Scene 3 is a almost clear 
sky with sparse small clouds of various size but .low reflectivity. 
Radiance field analysis 
For each of the three scenes, binary images have been constructed in order to study 
the size distribution of the high reflectivity and low reflectivity regions and their 
spatial dispersion. The images are constructed by using radiance threshold: for a 
certain threshold R ,  pixels having a radiance larger than R in the original image, are 
assigned the value 1 in the binary image while the other pixels are assigned the value 
0. The pixels with value 1 will be called high reflectivity pixels or "bright" pixels, 
whereas pixels with value 0 will be called low reflectivity pixels or "dark" pixels. 
The fraction 
and scene 2, 
percentage : 
of pixels in each state will vary with the chosen threshold: for scene 1 
thresholds have been chosen so as to obtain a "dark" ("bright") pixel 
lo%, 3 0 % ,  SO%, 70%, 90%. For the clear scene on the 19th (scene 3 1 ,  more 
271 
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https://ntrs.nasa.gov/search.jsp?R=19910001190 2020-03-19T20:30:05+00:00Z
than 93% of the pixels are clear sky. In this case, four thresholds have been chosen 
as to have 93%, 95%, 97%, 98% of the pixels darker than the threshoJd. 
As the radiance threshold is increased the binary images of the first scene more and 
more resembles an open cell or cumulus cloud field. In binary images of scene 2, the 
interior hole becomes sucessively better defined, the similarity with an open cell is 
enhanced. For images of the third scene, the effect of increasing the threshold is 
first to mask noise over the sea, then to decrease the cloud surface area. For each 
threshold-related binary image, the number of "dark" and "bright" regions have been 
determined; then for each of these regions various parameters have been computed. We 
will concentrate only on two of them: the surface area or the number of pixels forming 
the region and the so called "perimeter*8 or the number of pixel edges which are at 
boundary between a "dark" and a "bright" pixel. From the surface area an equivalent 
diameter has been computed (see Wieliki and Welsh, 1986). To study their distributions 
the "dark" ("bright") surface areas have been gathered in classes of equal step of 
ln(2) in ln(D). Boundary between class increase by factor of 2 (lorn, 20m, 40m ... ) 
Figure 2 show these distributions for scene 2 and the 5 thresholds on a log/log plot. 
For scene 1 and 2, the observed dependence in the number of regions, and the distri- 
bution of the surface area of these regions versus thresholds indicates that as the 
percentage of "bright"( "dark") pixels increases, the number of areas increases first 
and then decreases; at first as the "bright" ("dark") pixel percentage increases the 
number of new regions which appear is larger than the number of regions which are 
gathered, then the reverse situation occurs. The magnitude of these increases and 
decreases and the percentage value for the break point are related to the spatial or- 
ganisation of the bright and dark areas. For a given percentage, the number of small 
"dark" regions (10m to 160111 in equivalent diameter) is larger than the number of small 
"bright" regions. Especially, the darkest pixels are wider spread in small regions than 
the brightest pixels. For scene 1 the number of "bright"("dark") regions for a certain 
percentage is higher than for scene 2; the spatial mixing of the "bright" and "dark" 
regions of various area surface is larger in scene 1. 
For a given percentage of "bright" ("dark") pixels, the number of region decrease 
versus surface area increase is obvious; this increase is relatively uniform on the 
log/log plot (Fig. 2) for surface area larger than 10m and smaller than 1280111. Excep- 
tions are 90% cases of "bright"/"dark" regions, the number of regions and specially 
of small regions consequently decreases. The relatilly uniform decrease observed, is 
in agreement with previous results found by Cahalan (1988) for Landsat cloudy scenes; 
these results show that distributions of surface areas of clouds (or holes) often 
decrease versus surface area increase as a power law; the exponent is related to the 
cloud field beiing studied. This exponent is defined as the area exponents by Lovejoy 
and Shwertzer (1988). For boundary layer clouds, Cahalan finds an exponent value of 
1.5 for low thresholds, and observes an increase of this exponent for increasing 
thresholds. In the present study, when the power Law aproximation seems reasonable ( 
a percentage of pixels smaller than 90% and generally surface areas between 20m and 
1240m), the exponent value found ranges between 1. and 1.3. 
The length of the boundary has also been computed, i t  appears that in the case of a 
small threshold the number of boundary pixel is larger than in the case of a high 
threshold, because of the larger spatial dispersion of the darkest pixels as compared 
to the brightest pixels. In order to have a measure of the complexity of the boundary 
of these "bright" ("dark") regions, we have plotted for each region its perimeter value 
versus the root mean square of its surface area on a log/log scale. The same linear 
relationship as found by Lovejoy (1982) on Goes images and by Cahalan (1988) on Lansat 
appears on these graphs; the fitted slope is close to 1.3. 
For scene 3 the number of "bright" or "cloud" regions is small, and the diameter of 
these clouds is generally between 1 0 m  and 360111. The large decrease of the number of 
regions (1135 to 562) occurs for thresholds between 29 and 31 which only correspond 
to about 0 . 4 %  reflectivity difference. This decrease is due to the disparition of 
272 
noisy sea pixels. A s  for scene 1 and 2 the decrease of the distribution slope with 
surface area increase (for surface area between 20m and 320m) is relatively uniform. 
The slopes observed range between - . 8  and -.?. 
On the other hand, a box counting technic On a regular grid has been used to study 
the spatial distribution of these "bright" ("dark") regions. B o x  counting technics 
have been developped as a way to estimate the dimension of fractal sets (Lovejoy and 
Shertzer, 1988). It has also been used to study the efEect of sensor resolution (Shenk 
and Salomonson 1972). To apply this technic, different resolution grids are defined, 
for resolution elements varying from a quarter of the image (lowest resolution), to 
one pixel (highest resolution) and dividing at each step the resolution element by 4;  
then for each resolution the percentage of "bright" ("dark") coverage is determined 
by counting the number of resolution elements containning at least one "bright" 
("dark") pixel. For each scene and each threshold, the percentages of "bright" and 
"dark" coverages in function of the resolution (Eps) have been plotted. For each curve 
several parameters have been extracted. The first parameter is the exponent dO which 
for a fractal set equal its dimension. dO is obtained by fitting a a power law ( 
M(Eps)=Eps**dO ) through the scatter. The other parameters MO, Beta and A are obtained 
by fitting a function F ( F=MO+A*Eps**Beta ) .  F is an empirical scaling law to 
determine the "true area" of assumed "fat fractal" set (Farmer and Umberger, 1985; 
Smith, 1986). 
These different parameters vary in function of the increase of the "bright" ("dark") 
pixel percentage and of the scene studied. They are related to the surface area dis- 
tribution of the "bright" and "dark" regidns and to their relative spatial disposition. 
For high percentages, dO is close t o  2 ,  the fractal dimension of an area beiing 2 .  
However as the percentage of "bright" ("dark") pixels decreases dO decreases due to 
the region increasing scatter. Correlatively, A and Beta increase. For a given 
percentage of "dark" and "bright" pixels, the value of dO for "dark" regions is smaller 
than for "bright" regions, especially for the lowest percentages (1.5 and 1.7); On the 
opposite A and Beta are larger in the case of "dark" regions. Th'ese differences between 
the "dark" and "bright" cases are related to the larger number of regions found for 
the darkest image than for the brightest image. Differences are observed between scene 
1 and scene 2 in these parameter values and are related to the spatial organisation 
Of the "bright" and "dark" region in these regions; especially, the differences between 
the parameters associated to the "dark" areas and to the "bright" areas are larger for 
scene 1 than scene 2. 
Conclusion 
Some results found are in agreement with previous studies on satellite high resolution 
data; the number of "bright" and "dark" region decrease versus surface area increase 
can be in some cases aproximated by a power law; the perimeter and the surface area 
are found to be a power law related with an exponent close to 1.3. However, our study 
focussed, at least for two of the scenes, on the change in the scales of variability 
versus the percentage of pixels declared "thick" ("thin"). This shows the possibility 
for differentiating spatial structures in an apparently homogeneous cloud field. The 
parameters obtained from the fat fractal scaling can give usefull indications on these 
Structures, and allow to aproximate the error in cloud cover estimation from coarse 
resolution data: further studies must be pursued to ckeck the conditions for which fat 
fractal scaling can be applied to the cloud radiance field. The third scene shows the 
existence of very small and low refectivity clouds and the importance of noise in the 
data for the choice of a cloud/no cloud detection threshold. This study has to be 
continued on more scenes: the comparison between the 10m and 20m resolution images has 
to be developped and simultaneously the effect of a spatial sampling or averaging of 
the data must be tested. Comparison of these 60km by 60km Spot scenes with the 
corresponding lkm resolution Goes radiance field has to be done. 
273 
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258 1301-1314. 
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areas of the "thick" regions in scene 2 "thick" pixel percentage (M(Eps)) with 
for 5 thresholds; the , , , , , cocres- the estimated percentage M ( 0 )  versus 
pond to thresholds 108,30%,50%,70\,90%. resolution Eps for 4 thresholds: the , 
, , , , correspond to thresholds 
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274 
a) 2048 by 2048 pixel square 
Centered on reglon I ;  the black 
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radiance 100 ( 2 5 5 ) .  
c) 2048 by 2048 plxel square: reglon 3 
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27 


Structures observed on the spot radiance fields during the FIRE experiment

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