a procedure for the detection and removal of cloud...

880 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 36, NO. 3, MAY 1998

A Procedure for the Detection and Removal ofCloud Shadow from AVHRR Data over Land

James J. Simpson and James R. Stitt,Member, IEEE

Abstract—Although the accurate detection of cloud shadow inAVHRR scenes is important for many atmospheric and terrestrialapplications, relatively little work in this area has appeared inthe literature. This paper presents a new multispectral algorithmfor cloud shadow detection and removal in daytime AVHRRscenes over land. It uses a combination of geometric and opticalconstraints, derived from the pixel-by-pixel cross-track geometryof the scene and image analysis methods to detect cloud shadow.The procedure works well in tropical and midlatitude regionsunder varying atmospheric conditions (wet–dry) and with differ-ent types of terrain. Results also show that underdetected cloudshadow can produce errors of 30–40% in observed reflectancesfor affected pixels. Moreover, radiative transfer calculations showthat the effects of cloud shadow are comparable to or exceedthose of aerosol contamination for affected pixels. The procedureis computationally efficient and hence could be used to produceimproved weather forecast, land cover, and land analysis prod-ucts. The method is not intended for use under conditions of poorsolar illumination and/or poor viewing geometry.

I. INTRODUCTION

A. Importance of Cloud Shadow Detection

SHADOWING of the ground by clouds can generatemesoscale temperature gradients that significantly impact

weather. Shadowing effects, for example, were important forproper numerical simulation of the mesoscale atmosphericcirculations that led to a major convective storm system inEngland [1]. Likewise, in a numerical simulation of stormactivity in the Texas Panhandle on April 24–25, 1982, itwas shown that cloud shadow produces 1) a much morecomplicated surface temperature field, 2) a large change inplanetary boundary layer depth, and 3) substantial boundarylayer convergence zones compared to simulations withoutcloud shadow included [2]. Results from these case studiesare further supported by the work of Lipton [3] who showed1) the substantial impact of shadowing on boundary layerdevelopment and mesoscale circulation, 2) the value ofassimilated shadow retrievals using a case study, and 3)that cloud shadow assimilation is preferable to ignoringshadow, even if the errors in the retrieval-assimilation processhappen to compound one another. The effect of cloudshadow on the generation and modification of other typesof mesoscale circulation, such as the development of sea

Manuscript received March 26, 1997; revised July 31, 1997. This work wassupported in part by the Marine Life Research Group of the Scripps Institutionof Oceanography and a NASA Atmospheric Sciences project (Dr. J. Dodge).

The authors are with the Digital Image Analysis Laboratory, Universityof California, San Diego, La Jolla, CA 92093-0237 USA (e-mail: [email protected]).

Publisher Item Identifier S 0196-2892(98)02855-1.

breeze and thermally induced up-slope flows, has also beendemonstrated [4].

Cloud shadow affects the accuracy of vegetation estimatesas well. Such estimates are important because terrestrial vege-tation, the main component of continental biomass [5], affectsthe climate system over a broad range of time and space scalesby modifying the surface energy balance and by influencingthe exchanges of water and carbon dioxide between the landsurface and the atmosphere [6]. Early studies emphasizedthat dust, aerosols, Rayleigh scattering and small clouds tendto increase the visible reflectance, with respect to the near-infrared, and thus reduce the Normalized Difference Vege-tation Index (NDVI) estimates of vegetation. Until recently,however, relatively little attention had been paid to the effectsof cloud shadow on NDVI, although Pech [7] showed that,in general, vegetation and greenness indexes are compromisedby the effects of undetected shadow because shadow has agreater influence on the near infrared than the visible. Viovy[8] also recognized the noise characteristics that undetectedshadow imparts to NDVI.

This paper develops a new, statistically reproducible, andcomputationally efficient procedure for the detection of cloudshadow in daytime Advanced Very High-Resolution Radiome-ter (AVHRR) scenes over land. Results show that the effectsof undetected cloud shadow are comparable to or exceed thoseof aerosol contamination for affected pixels and they seriouslydegrade both the magnitude and frequency distribution ofNDVI estimates.

B. Difficulties with Computing Cloud Shadow

Cloud shadow results from the projection of the cloudstructure onto the local plane of the earth, with respect toa preferential direction of incoming solar radiation. Solarazimuth angle determines the direction of preferred cloudshadow, based on the relative position of the sun and the cloud.Cloud height, solar azimuth, and zenith angles determine cloudshadow length.

For a curved earth surface, the geometry [Fig. 1(a)] definesthe cloud height in terms of the arc length of cloud shadowon the earth’s surface , the radius of the earth , the earthangle , the solar zenith angle , the Euclidean length of theside of the triangle (opposite ), the angle of deviationfrom a flat plane , and , which is the complimentary angle toangle . The earth angle is given by . Thus, the heightof the cloud , in terms of measurable geometric quantities, is

(1)

0196–2892/98$10.00 1998 IEEE

SIMPSON AND STITT: DETECTION AND REMOVAL OF CLOUD SHADOW FROM AVHRR DATA 881

(a)

(b)

Fig. 1. Geometry of the cloud shadow problems, which relates cloud shadowlength Ls to cloud heightH. (a) Curvilinear geometry and (b) flat planeapproximation.

Because in (1). Therefore, a flat planeapproximation [Fig. 1(b)] is generally used for cloud shadowestimation. For a given azimuth angle, the cloud shadow length

, projected onto the flat plane by the sun-cloud system, isgiven in terms of the solar zenith angleand the cloud height

(2)

At local solar noon, is zero and cloud shadow isminimal. Near sunrise and sunset, is large and the lengthof the cloud shadow can become very long. Atis undefined.

For almost all satellite-based observing systems, (1) and (2)are underdetermined because bothand are unknowns.In principle, data from the Along Track Scanning Radiometer(ATSR) could circumvent this problem by combining infor-mation from its forward and nadir views in a stereographicanalysis to determine cloud height. Unfortunately, even here,the problem can be compromised because visible and 1.6-mdata from the ATSR generally have some orbit-dependentglint contamination in one of the views (see [9] for details).Thus, shadow determination generally involves making someexplicit or implicit assumption about cloud height. Gurney[10], for example, used ana priori estimate of cloud height.

Fig. 2. Overview of the cloud shadow detection process. The various setsf g identified in the figure are produced at different steps in the analysis andare defined in the text.

Some investigators have inferred cloud height from cloudtop temperature. Others have used methods of digital imageanalysis applied to the data itself to close the problem [11].Our approach to closure (see below) also uses elements ofdigital image analysis, but differs substantially from that of[11]. The relative merits of each of these methods is discussedin Section V-E.

II. CLOUD SHADOW SEGMENTATION

Several variables are needed to fully characterize the rela-tion between cloud and shadow: solar azimuth angle, solarzenith angle, cloud height, and cloud edge; each is usedto constrain and/or optimize the problem of cloud shadowdetection and removal. The height of the cloud and the solarzenith angle determine cloud shadow length. The solar azimuthangle determines the direction the cloud shadow is cast by thecloud structure. Here, cloud edge is only used to optimizethe search process by restricting cloud shadow detection tooptically relevant areas, as defined by the other variables. Nopattern matching is done.

The cloud shadow detection procedure has six steps (Fig. 2).The set of cloud contaminated pixels in the AVHRR scene


is first identified using the AVHRR Split-and-Merge Clustering(ASMC) algorithm [12]. This method can be used to detectclouds over land for tropical and temperate as well as dry andmoist environments. For reader convenience, an overview ofthe method is given in Appendix A; details are found in [12].

The set of cloud edge pixels is extracted from theset of cloud pixels . Elements of are determinedby examination of elements of in relation to the spatialstructure found in small subregions (3 3 pixels kernels)around each element of using the following criterion. Iffor a given kernel there exists a pixel and a pixel

, where , then , whereis the center pixel in a subregion.

Each pixel in is adjacent to other cloud edge pixels.The relation between a pixel and its edgeneighbors, computed within a 3 3 area, determines auniquely observed edge shape for that pixel at the local scalebecause it can only have edge pixels above and below (avertical shape), to its left and right (a horizontal shape), ordiagonally [Fig. 3(a)].

Eight cloud edge shapes are defined (two horizontal, twovertical, and four diagonal) by the criteria cited above. Aredundancy exists because a pixel can be on the near side or thefar side of a cloud, with respect to the sun. Of course, a cloudedge pixel that lies on the near side of a cloud, relative to thesun, produces cloud shadow that is not seen by the radiometerbecause it falls under the cloud. The solar azimuth angle isused to constrain the eight edge shapes to those that have thehighest probability of producing cloud shadow, that is, theedges on the far side of the cloud, with respect to the sun. Foreach solar azimuth angle, we define two cloud edge shapesthat are most likely to produce cloud shadow. Therefore, foreach pixel in , a logical comparison is made betweenobserved and theoretical edge shapes. If for the given pixel’ssolar azimuth angle the observed edge shape corresponds toeither of the two shapes associated with the pixel’s azimuthangle, that pixel is included in ep , the set of cloud edgepixels with preferred orientation (relative to the scene-specificgeometry) for cloud shadow generation.

For each pixel in ep , a pixel area is iterativelyprojected directly away from the sun by using the solarazimuth angle [Fig. 3(b)] and is evaluated for cloud shadow.The iterative procedure is initialized using a 55 area. For tileprojection, the cloud edge pixel ep becomes the upperright corner of the pixel projection if , thelower right corner if , the lower left corner if

, and the upper left corner if. (Note that and are equivalent). is increased by

increments of one to an upper bound of 50. Pixels within thedynamically determined tile sizes T SIZEare excluded as cloud shadow contaminated using an image-specific dynamic threshold applied as follows:

1) all pixels in the tile are scaled by the image mean;2) dynamic threshold is computed as , where

is the mean and is the standard deviation of theunscaled image-wide Channel 2 albedo, excluding waterand cloud pixels;

3) a pixel in the tile is assigned to if its scaledalbedo value is below the dynamic threshold.

Tile projection stops as soon as nonshadow pixels are en-countered [Fig. 3(c)]. The combination of tile projection toa maximum size with a pixel-specific directionof tile projection for each pixel in ep provides for acomputationally efficient and accurate identification of cloudshadow contaminated pixels [Fig. 3(d)].

Channel 2 data are used because they are minimally af-fected by atmospheric attenuation (ozone, molecular scatter-ing, aerosols), as compared to Channel 1 data [13]. Tanre etal. [13] also showed that, although Channel 2 reflectance isattenuated by water vapor, the apparent surface bidirectionalreflectance distribution function (BRDF) seen by the satellite ismuch more strongly affected by aerosols than by water vapor.Our choice of Channel 2 data is consistent with the abovemodeling studies and simplifies the atmospheric correctionrequirements, which are intrinsically difficult to meet, espe-cially in the absence of appropriate field observations. Waterpixels are excluded prior to cloud and cloud shadow detection(see Section III). Thus, low-reflectance water pixels cannotbe misclassified as cloud shadow. The Channel 2 data arescaled by the image mean because scaling tends to produce acloud shadow range that is invariant over randomly selectedimages. The dynamic threshold was chosen for severalreasons. In general, for a scene with water and cloudremoved, and therefore the dynamic threshold represents pixelsone standard deviation from the image-wide mean, a relativelylow percentage of the image distribution. also is a goodmeasure of spatial variability within multivariate data (e.g.,[14]). Moreover, the number of cloud shadow pixels detectedis insensitive to the chosen dynamic threshold (Appendix II).

The 5 5 initial tile size allows for cases in which someclear, bright land might exist between cloud and shadowbecause, at cloud-land boundaries, cloud structures tend to be-come diffuse and more optically transparent. Fragmentation ofclouds into pieces of subpixel scale size also occurs near cloud-land boundaries. These subpixel scale effects, combined withthe nonspatially uniform weights of the sensor’s integratingaperture, generally produce anomalous values of the measuredradiance at these boundaries. The upper bound ofis based on the known height distributions of high, middle,and low clouds in the atmosphere [15]. For an AVHRR pixelsize (1.1 km at nadir), gives a maximum physicallyallowable shadow length of 77.8 km, which is sufficient todetect cloud shadow under conditions of valid illuminationand viewing (see Section V).

After iterative tile projection, a local homogeneity test isapplied to pixels that surround . Statistics are computedon the Channel 2 Channel 1 albedo differences within 33 kernels centered on these surrounding pixels. This spectraldifference is used to compensate for possible errors (calibrationuncertainty, atmospheric effects) in the Channel 2 data. If atile contains more than two pixels classified as cloud shadow,the local minimum, maximum, mean, and standard deviationof the shadow pixels within the local tile are computed.From these values, a local dynamic threshold max meanis computed. Again, water and cloud pixels in the tile are


Fig. 3. Cloud shadow geometry. (a) The theoretical cloud edge shapes associated with specific ranges of solar azimuth angle. Two of the eight overlappingazimuth angle groups are shown as curved dashed lines. The key in (a) associates a specific theoretical edge shape with a given azimuth angle range. (b) Idealizedcloud edge and selection of most likely edges to produce cloud shadow, based on sun orientation, relative to a given pixel. (c) Detail of the iterative tile projectionfrom an element offCepg as a function of tile size parameterq. (d) Tile projections for other elements offCepg along a cloud edge. See Section II for details.

excluded. Any nonshadow pixel within the local tile whoseChannel 2 Channel 1 difference is below the local dynamicthreshold is reclassified as cloud shadow. This local scale test

evaluates pixels in close proximity to the initially defined cloudshadow-clear land edge and assigns as cloud shadow any pixelwhose difference value is slightly above the local maximum


TABLE IINFORMATION FOR THE IMAGES SHOWN IN THIS ARTICLE. THESE DATA ARE REPRESENTATIVE

OF A LARGER NUMBER OF IMAGES ANALYZED (BUT NOT SHOWN) FOR THIS STUDY

shadow difference. Such pixels are combined with toform .

Postprocessing is done to eliminate statistical outliers inthe cloud-free and cloud shadow-free data. Using a 33 search area pixels entirely surrounded by clouds, cloudshadow, or both are identified and classified as shadow. (Note:postprocessing is visible from Fig. 4(f)–(h).) The histogramof the candidate cloud-free and cloud shadow-free Channel2 Channel 1 difference is also computed, and pixels whosedifference is 3 below the mean image difference are assignedto to form the final cloud shadow class . Typ-ically, only 20–30 pixels from a 512 512 image are soreassigned.

III. D ATA AND PREPROCESSINGSTEPS

Data over the western United States and Mexico werecaptured directly by the Scripps Institution of Oceanography(SIO), University of California, San Diego. Images fromEurope, Africa, Australia, South America, and Asia werecaptured locally in High Resolution Picture Transmission(HRPT) mode by either NOAA or Australian field stationsand subsequently archived at SIO. Image name, general geo-graphical location, center latitude and longitude, date, localtime, size, satellite, climate, and terrain characteristics aregiven in Table I. Climate and terrain characteristics are fromthe World Scene Climate Regions analysis [16]. These imagesprovide examples of both highly variable atmospheric moistureconditions and highly variable land forms. Data were ingestedat full spatial resolution from archive tapes and calibrated togeophysical units ([17], and updates). Oceans and large inlandwater bodies (blue) and coastlines (red) were excluded fromthe analysis using GIS coastlines, polygon fill operations, andmorphological transformations [18]. A total of 50 images were

analyzed. Because of space limitations, only representativeresults for the climates and land forms studied are presented(Table I).

IV. RESULTS

A. Example of the Entire Cloud ShadowDetection and Removal Procedure

Fig. 4(a) is a 512 512 image of Channel 2 albedoover Somalia and the Horn of Africa taken on October 9,1984. Regions of high (low) albedo are mapped to white(black). Clear land has intermediate gray shades. Clouds andpronounced cloud shadow are evident in the scene. Data inthe lower central portion of this scene, delineated by the smallorange box, are now examined in detail. Panels (b) and (c) arethe Channel 2 albedo and Channel 4 brightness temperature(BT), respectively, for the data in the small orange box butmagnified six times to aid visualization. Low (high) BT’s inpanel (c) are mapped white (dark gray). Thus, bright, coldclouds appear white. The cloud shadow [Fig. 4(b)] is easilyseen as the black structure adjacent to the cloud. As expected,the shape of the cloud shadow closely follows that of thecloud. The BT’s [Fig. 4(c)] are coldest for the cloud (white),warmest for the clear land (dark shades), and relatively coolerthan the clear land and warmer than the cloud for the cloudshadow (light gray). Again, the shape of the cloud shadowstructure observed in the Channel 4 BT closely resembles thatof the cloud.

Panels (d)–(h) are identical to panel (b) (they share itsgrayscale stretch) but have results from the different steps inthe process shown as color overlays. The set of cloudpixels identified by the ASMC process is the yellow overlayin panel (d). The set of cloud edge pixels is delineated


Fig. 4. (a) Channel 2 albedo for a region of Somalia and the Horn of Africa. High (low) albedo is mapped to white (black) shades. The small orange boxshows a region of the scene to be examined in detail. Panels (b)–(h) show data from the region of the orange box magnified six times to aid visualization.Panel (b) shows a pronounced cloud (white) and corresponding cloud shadow (black). Note the similar shape of the cloud and cloud shadow. Panel (c) showsthe Channel 4 brightness temperature (BT). Clouds are cold (white), clear land is warm (dark gray shades), and the cloud shadow temperature (light grayshade) is cooler than the clear land temperature and warmer than the cloud temperature. Again, the shape of the thermal signature of the cloud shadow issimilar to that of the cloud. Panels (d)–(h) are identical to panel (b), except the set of cloud pixelsfCg is shown as the yellow overlay in panel (d), theset of cloud edge pixelsfCeg is shown in panel (e), the set of preferential cloud edge pixelsfCepg is the orange overlay in panel (f), while the initial setof cloud shadow pixelsfCSig is shown in green, the set of cloud shadow edge pixels appear as a green overlay in panel (g), the combined cloudfCgand final cloud shadowfCSg masks appear as the yellow and green overlays in panel (h), respectively.


TABLE IISTATISTICS FOR THEPERCENT DIFFERENCE INREFLECTANCE BETWEEN CLOUD

SHADOW CONTAMINATED AND CLOSEST PROXIMITY CLEAR LAND PIXELS

in panel (e). Panel (f) shows the set of preferred cloud edgepixels ep in orange and the initial set of cloudshadow pixels (green) determined by Step 4 of the algorithm.The set of cloud shadow edge pixels about which the localhomogeneity test (Step 5) is performed is shown as the greenedge in panel (g). Panel (h) shows the cloud mask (yellow) andfinal cloud shadow set in green. Shadow in the upperleft-hand corner of panels (f) and (h) is associated with a cloudnot shown in panels (b) and (c), but visible in panel (a).

The thermal signature of cloud shadow was carefully exam-ined for all images used in this study (not shown). Generally, itis not as pronounced as that in Fig. 4(c). Many factors (emis-sivity of land surface, thermal inertia of land surface, velocityof the clouds) complicate the use of thermal data (comparedto visible data) for cloud shadow detection. Therefore, we donot use a thermal signature in the cloud shadow analysis.

B. Other Examples

Figs. 5–7 each show results for two different scenes. Panels(a) and (b) show AVHRR Channel 1 and 2 data calibratedto albedo (%), respectively. The previously defined grayscaleconvention for albedo is used. Panel (c) is identical to panel(b), except that the ASMC cloud mask for the imageis overlaid in yellow and the detected cloud shadowis overlaid in green. Panels (d), (e), and (f) are analogous toPanels (a), (b), and (c), respectively, except for a differentscene. Local albedo statistics, which show the reduction insurface albedo due to cloud shadow, are given in Table II.

Image 1 [Fig. 5(a)] is the same scene over Somalia shownin Fig. 4(a). The albedos [Figs. 5(a) and (b)] show that thisis a relatively complex scene to classify. Both large- andsmall-scale cloud structures appear in the scene. Moreover,the scene has both highly reflective arid land surfaces (So-malia) and moist tropical interior regions. Its climate is hotand arid, and the terrain includes a coastal mountain range[16]. The ASMC cloud detection procedure was successfulin identifying these complex cloud structures [yellow overlayin Fig. 5(c)]. Very bright areas in the scene not detected ascloud correspond to the high-reflectance Karkar desert and theDarie hills of Ethiopia [16]. These high-reflectance areas haveobserved satellite temperatures between 30–38C, supportingthe ASMC’s classification as cloud-free land. Regions ofcloud shadow, in close proximity to cloud, are also clearly

visible in Figs. 5(a) and (b). The location of detected cloudshadow [green overlay in Fig. 5(c)] is consistent withthe location of clouds in the scene and with the location of thesun, as determined by the orbit-dependent solar azimuth andzenith angles. Note that, in the upper right-hand and lower left-hand parts of the scene, there are a few isolated cloud shadowpixels. At the scale shown in this figure, the few cloud pixelspresent in these regions are not visible but can be seen on ahigh-resolution image display. It is mathematically impossiblefor the cloud shadow algorithm to detect cloud shadow unlesscloud is present.

Image 2 [Fig. 5(d)] is a scene over part of the Amazon basin.It has a tropical climate, and the terrain is characterized by lowmountains and sloping hills (Table I). Both large and smallclouds and especially sharp cloud shadows also are visible[Fig. 5(d) and (e)]. Fig. 5(f) shows the ASMC cloud mask(yellow) and the cloud shadow mask (green).

Image 3 [Fig. 6(a)] shows a region of Australia. The terrainconsists of flat plains, and the climate is hot and arid (Table I).The albedo images [Fig. 6(a) and (b)] show a complex patternof broken clouds and large adjacent regions contaminated bycloud shadow. The cloud and cloud shadow isolated by thecloud and cloud shadow masks are shown in Fig. 6(c).

Image 4 [Fig. 6(d)] shows a region of the western UnitedStates with the San Francisco Bay in the lower left-handcorner. This region contains nearly all climate zones, andthe terrain varies between rough high mountains (the SierraNevada), inland deserts, and large cultivated valleys (Table I).Because of the highly reflective desert regions, cloud screen-ing is particularly difficult. Nonetheless, the ASMC cloudmask isolated the various cloud types found in the scene[Fig. 6(f)]. Regions of pronounced cloud shadow are also ev-ident [Fig. 6(d) and (e)], and the new procedure was effectivein detecting them [Fig. 6(f)].

Image 5 [Fig. 7(a)] shows a region of Oregon. The North-ern Cascade range runs down the center of this scene andpronounced clouds are trapped against the western flanks ofthe mountains. The position of the sun (late afternoon image),combined with the locations of the dominant cloud structures,produced the strong pattern of cloud shadow found alongthe eastern flanks of the mountains. The new procedure waseffective in detecting the cloud shadow (Fig. 7c).

Image 6 [Fig. 7(d)] shows a region of Ireland and the BritishIsles. Pronounced cloud shadow is clearly visible in the Irishpart of the scene. The new procedure was effective in detectingthe cloud shadow [Fig. 7(f)].

V. DISCUSSION AND CONCLUSIONS

A. Effect of Cloud Shadow

The effect of cloud shadow on satellite-observed landsurface albedo was quantitatively evaluated by computingthe difference between the observed reflectance of a cloudshadow contaminated pixel and the closest cloud-free andcloud shadow-free pixel using 5 5 tiles centered aboutthe cloud shadow contaminated and the clear pixels beingevaluated. Local scale differences are used for this analysis


Fig. 5. AVHRR image (Image 1) showing parts of Somalia and the Horn of Africa. (a) Channel 1 albedo (%), (b) Channel 2 albedo (%), and (c) ASMCcloud maskfCg in yellow and cloud shadow maskfCSg in green. Water shown in blue and red designates a coastline or shoreline. Water and coastlinepixels are not used in the analysis. Panels (d), (e), and (f) are analogous to panels (a), (b), and (c), except for Image 2 of a region of the Amazon Basin.


Fig. 6. Analogous to Fig. 5, except for Image 3 [panels (a), (b), and (c)] is over part of Australia and Image 4 [panels (d), (e), and (f)] is over partof a region of the United States.


Fig. 7. Analogous to Fig. 5, except for Image 5 [panels (a), (b), and (c)] is over part of Oregon and Image 6 [panels (d), (e), and (f)] is over partsof Ireland and Great Britain.


because 1) cloud shadow is a local scale, as opposed to imagescale, process (Figs. 4–7), 2) natural variability in clear landsurface reflectance (and emissivity) is generally very large fora typical terrestrial scene, and 3) statistics, computed on the5 5 tiles, have more statistical degrees of freedom thanisolated pixel differences. The computation was performed forall pixels in a given scene that were identified as cloud shadowcontaminated. Table II gives the mean percent difference,standard deviation, maximum percent difference, and numberof points evaluated. For the six scenes shown in this study, themean differences between shadowed land and nearest clearalbedo ranged from 27.1% (Image 2, Amazon) to 42% (Image6, Great Britain). Thus, cloud shadow significantly reducesthe albedo of a pixel observed by the satellite, relative touncontaminated pixels in close proximity to it. This effect isconsistent with the basic viewing and illumination physics ofthe problem; namely, pixels contaminated by cloud shadowhave significantly lower reflectance than the actual reflectance.Generally, the mean magnitude of this effect on the local scalevaries between 30–40%, and the standard deviation variesbetween 10–20%. The mean magnitude of the effect and itsstandard deviation, however, are also a function of cloudtype and structure. Thus, images with many small brokenclouds have a proportionately larger number of cloud edges,compared to more homogeneous clouds, and hence, for agiven illumination and viewing geometry, broken clouds tendto produce more cloud shadow in the scene [e.g., Fig. 6(a)].

B. Closure Between and

Cloud height and cloud shadow length are linked (1),(2). Satellite image data generally provide no direct measure of

. Therefore, either an explicit or implicit assumption aboutcloud height is required if cloud shadow is to be determinedfrom most satellite data.

Fortunately, radiosonde and otherin situ data provide goodestimates of cloud height variability. Radiosonde data and aCO absorption technique [15], for example, can be used todefine three domains of cloud height: low cloud (550–1000mb), middle cloud (350–550 mb), and high cloud (100–350mb). Under the assumption of an isothermal atmosphere, atmo-spheric pressure and height are related as ,where is sea level pressure, is height (m) at pressure

(mb), and is a function of the ideal gas constant,the gravitational acceleration, and the atmospheric tempera-ture [19]. Under this assumption, the above pressure rangesfor different cloud types map to 0–5.5-km, 5.5–8.3-km, and8.3–18.4-km cloud height ranges for low, middle, and highclouds, respectively. Based on these values, we assume amaximum cloud height of 20 km to cover a worse-casecondition for producing cloud shadow. With this estimate ofmaximum cloud height, (1) and (2) can be used to estimatethe corresponding maximum horizontal cloud shadow lengthscales produced by the different types of cloud. For thiscalculation, the solar zenith angle must also be restricted toconditions of good illumination, that is, avoid periods nearsunrise and sunset when the Channel 1 and Channel 2 albedoobserved by AVHRR are inaccurate. Therefore, the valid

range of solar zenith angle is restricted to be (see[20, Appendix]). Under these conditions, the allowable lengthscales of cloud shadow for low, middle, and high clouds are0.5 to 13 km, 0.7 to 22 km, and 2 to 55 km, respectively. Thechoice of for Step 4 of the algorithm, when combinedwith the 1.1-km pixel scale of AVHRR data, produces a searchtile sufficiently large to detect cloud shadow produced by highcloud.

C. Effects of Cloud Vertical Extent on Cloud Shadow Detection

Cloud vertical extent is largely dependent on cloud type.High-level cirrus and cirrostratus have relatively little verticalextent [21]. They usually occur as sheetlike filaments orclusters. Fair-weather cumulus and cumulus, however, areknown for their vertical development and are characterized bytheir dome shape and sharp edge protuberances [21]. Typically,their base height is 0.5 km, and their vertical extent can be aslarge as 6 km. Cumulonimbus are heavy masses of dense cloudthat often rise in the form of towers and can achieve heightsnearing 13 km [21].

For clouds characterized by moderate-to-high vertical ex-tent, higher parts of the cloud can project shadow overadjacent, lower cloud and often beyond the cloud edge. Thiseffect can increase the cloud shadow length and can cause theshape of the cloud shadow to differ from that of the cloud.Under these conditions, two concerns arise when detectingcloud shadow.

1) Can the procedure effectively detect shadow cast byclouds with large vertical extent such as cumulus orcumulonimbus?

2) Is the procedure sensitive to alteration of the cloudshadow shape by the presence of clouds with largevertical development?

Table III shows that for a cloud with a 8-km vertical extentand a base height of 2 km (a typical cumulonimbus cloud[21]), the proposed method of cloud shadow detection suc-cessfully considers all physically possible cloud shadow pixels(using T SIZE iteratively), even at theboundary of poor illumination levels (solar elevation ).Moreover, the cloud shadow algorithm described herein onlyuses cloud edge to optimize the search process by restrictingcloud shadow detection to optically relevant areas (Fig. 3).Therefore, the iterative search tile method of shadow detectiondeveloped herein satisfies both special concerns cited above.Methods that rely on matching cloud edge and cloud shadowedge shapes to detect cloud shadow and/or cloud height (e.g.,[11]), however, can be adversely affected by the vertical extentof some cloud types.

D. Relative Effects of Cloud Shadow and AerosolContamination on Surface Albedo

The effects of aerosol contamination on the top-of-atmosphere (TOA) reflectance observed by a satellite wereinvestigated using aerosol models taken from MODTRAN[22] and a radiative transfer model developed by Stamnes[23]. Aerosol profiles and optical properties of variousaerosol types at 47 separate wavelengths are available


TABLE IIISENSITIVITY TO CLOUD HEIGHT EXTENT. MODELED EFFECT OFCLOUD VERTICAL EXTENT (km) ABOVE A BASE CLOUD HEIGHT OF 2 km FOR FOUR DIFFERENT

SOLAR ZENITH ANGLES (Z). CLOUD DIMENSIONS BASED ON VALUES IN THE LITERATURE [21]. THE ITERATIVE SEARCH TILE METHOD OF SHADOW DETECTION

WILL EVALUATE PIXELS AS FAR AS 77 km FROM THE EDGE, WELL WITHIN THE RANGE OF SHADOW LENGTH PROJECTED FROMCLOUDS WITH LARGE VERTICAL

EXTENT. CLOUD SHADOW LENGTHS ARE IN KILOMETERS. A NEGATIVE VALUE INDICATES THE SHADOW IS PROJECTED ON THECLOUD, NOT ON THE GROUND

from MODTRAN. These data can be used to calculatethe optical properties of a specified aerosol type in eachatmospheric layer and in each spectral band for the radiativetransfer computations by interpolation. The MODTRANmidlatitude rural spring/summer aerosol type was chosenfor the troposphere because it best characterized most ofthe image data analyzed (not all shown). The MODTRANbackground stratospheric aerosol model was also incorporatedinto the simulation. The MODTRAN-derived aerosol opticalproperties were combined with the optical properties of theatmosphere and other parameters (e.g., surface albedo andsolar zenith angle) to calculate the radiative fluxes at TOA.Thirty-three levels were used in the radiative transfer modelto resolve vertical inhomogeneity in the atmosphere. Thecomputed upward and downward fluxes at TOA were usedto calculate the albedo at TOA. The spectral band used inthis computation (0.57–0.69m) corresponds closely to thatof AVHRR Channel 1 (0.58–0.68m). The optical depthfor the aerosol is the value at the center of the spectral band.Modeled albedo at TOA versus aerosol optical depth for threedifferent surface albedos (0.6, 0.3, 0.1) are shown in Fig. 8.A value of corresponds to a clear sky condition, andthe largest shown in the figure corresponds to a visibilityof 2 km. The percent changes in satellite-observed albedodue to cloud shadow (Table II) are comparable to the percentchanges in modeled TOA albedo due to high aerosol loading(Fig. 8).

E. Comparisons with Other Methods

Early estimates of cloud height came from satellite-derivedcloud-top temperature. Such estimates often have errors500mb, half the height of the atmosphere [15]. If such estimatesof cloud height were used to evaluate cloud shadow, the

Fig. 8. Results from a radiative transfer calculation showing modeled albedoat top of atmosphere (TOA) in percent, as a function of aerosol optical depthfor three different surface albedos. Aerosol type is rural spring/summer fromMODTRAN. See Section V-D for details.

cloud shadow length scale would have similar errors [(1)and (2)].

The method of Gurney [10] is based on two assumptions:1) assumeda priori static thresholds to identify cloud in thescene and 2) ana priori knowledge of cloud height, which isassumed constant throughout the scene. The ASMC algorithmuses image-specific, adaptive, joint, three-dimensional thresh-olds to label clouds in the scene (after the image-specific dy-namic segmentation step) and thus completely avoids the useof static thresholds (see [12]). Moreover, noa priori knowl-edge of cloud height is assumed in the cloud shadow com-


putation; rather, the new procedure uses an iterative methodto determine regions of homogeneous cloud shadow char-acteristics based on the AVHRR data within search tiles

T SIZE pixels. Image analysis methodsare then used to determine the observed cloud shadow withinthe geophysically realistic search zone.

Berendeset al. [11] use a semiautomated procedure todetect cloud, cloud shadow, and cloud height in LandsatMultispectral Scanner (MSS) data. Cloud detection, the firststep in their procedure, is done subjectively by inspection.Next, the LOG operator is used to detect cloud edges inthe scene, and the histogram of the minimum/maximumof an area around each cloud edge is computed. Staticthresholds are applied to histogram peaks to classify cloudsand cloud shadow. Then cloud edge and cloud shadowedge pairs, which exhibit very similar shapes, are chosenby visual inspection. A generalized Hough Transform,which matches parametric curves based on scalar and/orrotational transformations, is used to perform a patternmatching between cloud edge and cloud shadow edge pairsto determine their horizontal separation distance. Finally,cloud height is computed under the flat plane approximationusing the separation distance and the known solar zenithangle.

This method has several limitations. First, the histogramclassification of edges is dependent on the success of theLOG operator to accurately locate the cloud and shadowedges in the image. This calculation is very sensitive tothe value of used with the LOG operator (see [24, refer-ences]). The Hough transform pattern-matching method, asused by [11], requires that cloud edge/shadow edge pairsbe manually chosen; thus, making the procedure infeasiblefor large data sets or image wide analysis. Moreover, [11]assumes that the shadow seen by the Landsat imager isentirely produced by cloud pixels at the cloud edge, (i.e.,that the cloud has no vertical extent), but note that thevertical extent of clouds, even near the edges, is capableof distorting cloud shadows. Similarly, specific solar ge-ometry, coupled with optically thin cloud at the edge, of-ten causes cloud shadows to be larger or smaller than thecloud that produced it. Both of these effects can compromisepattern matching between cloud and cloud shadow edgesused by [11].

Our approach is fully automated, including the criticalfirst step of cloud detection. Thus, it is less subjective andmore amenable to large data set processing than the methodof [11]. Our cloud edge detection relies solely on localcloud morphological structure and has no adjustable parameteranalogous to the LOG operator’s. Moreover, cloud edgepixels are not used in a pattern matching sense to detect cloudshadow, as is done by [11]. Rather, the set of preferred cloudedge pixels ep is used to optimize the search process byrestricting cloud shadow detection to optically relevant areas(Fig. 3). The histogram of the maximum/minimum used by[11] is image specific and rarely (based on our computationalexperience) exhibits a particular peak that corresponds to cloudedge. In fact, cloud edge is often the most compromised areain a scene due to subpixel effects. We avoid this potential

problem because we do not use histograms to detect eithercloud or cloud edge.

A brute force method for eliminating cloud shadow can beimplemented by excluding all pixels within a 15–20-km staticzone surrounding all clouds in the scene. We performed suchan analysis (not shown) on Image 1 (characterized by smallclouds) and Image 2 (characterized by large clouds). In eachcase the ASMC cloud mask was used to locate clouds in thescene. The percent cloud cover for Images 1 and 2 is 20%and 28%, respectively. The brute force method detects 42%and 39% cloud shadow contaminated pixels, respectively. Thenew procedure (Fig. 2) identifies 13% and 6.8% cloud shadowpixels. These representative results show that such a bruteforce approach to cloud shadow detection will necessarilyexclude large regions of valid data because it also excludespixels along cloud edges parallel to the incoming radiation.Such edges cannot produce cloud shadow. The implication forcomposite images is even more troublesome.

F. Effect of Cloud Shadow on NDVI

Because plants have a distinct spectral signature (low re-flectance in the visible part of the solar spectrum, high re-flectance in the near infrared part of the spectrum [25]), Tucker[26] suggested that the presence of living vegetation could bedetected from satellite data (e.g., AVHRR) if data from the redand near-infrared spectral regions were used. Since that time,the NDVI, defined as

NDVI (3)

has been used to study continental land cover, global vege-tation phenology, and net primary production of grasslands[27]–[29]. In (3), and are the measured reflectancesin the visible and near-infrared spectral regions, respectively.The NDVI ratio is bounded over the closed interval .NOAA Global Area Coverage (GAC) values of NDVI overdifferent land surfaces typically vary between0.1 and 0.6[30]. NOAA Local Area Coverage (LAC) values have abroader range [31]. Clouds, water, and snow are more re-flective in the visible than in the near-infrared and thus havenegative NDVI values [32]. Rocks and bare soil have similarresponses in the two spectral regions and thus can producesmall positive and/or negative NDVI values near zero [33].

Fig. 9(a) and (b) show histograms of NDVI for Image 2(Amazon Basin) and Image 3 (Australia), respectively. Thesecases were chosen because they represent the tropical anddesert vegetation cases, respectively. In each panel, threedifferent histograms are shown: scene containing land, cloudand cloud shadow (solid line), scene with cloud detected andremoved (dash dot line), and scene with cloud and cloudshadow detected and removed (dash line). In these graphs,colors are laid down in the order black, red, and green.Therefore, in regions of overlapping curves, only the colorlaid down last is visible. These histograms show that cloudshadow can produce both negative and low-positive valuesof NDVI, especially in highly vegetated areas where cloudshadow attenuates otherwise high NDVI values [Fig. 9(a)]and in desert regions [Fig. 9(b)] where exposed rock and


bare soil/sand with different reflectances are abundant. Be-cause of this natural variability in NDVI, simple thresholdingschemes cannot accurately classify pixels contaminated bycloud shadow in an arbitrary scene. From the point of viewof clear land analysis and particularly vegetation studies,cloud shadow contaminated pixels are properly considered asource of noise because they introduce inappropriate varianceinto the NDVI statistics. Unfortunately, such pixels havegenerally not been removed from NDVI-based land coverproducts. Moreover, biome boundaries are often identified onthe basis of spatial gradients in NDVI. This can lead to falsebiome classification through inaccurate estimates of spatialgradient, derived from cloud shadow contaminated NDVI.These problems can be significantly exacerbated in NOAAGVI products due to their GAC-reduced spatial resolution andthe tests used to remove clouds in the GAC data. (Note that therelatively low-NDVI mode value 0.3 for the Amazon scene[Fig. 9(a)] partially results from uncorrected aerosol and watervapor effects [13]. Correction for these effects is not centralto the present discussion.)

G. Performance

The cloud shadow analyses were performed on a Hewlett-Packard J210 workstation with 256-MB RAM and 8-GB disc.Although the J210 has two processing units, only one wasused. Image size is 512 512 pixels. Images are made fullyRAM resident to avoid I/O inefficiencies [34]. Cloud shadowdetection (Steps 2–6 in Fig. 2) takes 4–6 s per image. Thus,the cloud shadow procedure could be used to produce largeland product data sets. A full swath (typically 40002048pixels) would be processed in about 120–180 s.

H. Noise Issues

Dropouts in satellite images are usually associated with lossof synchronization between the satellite and ground receivingstation. Dropouts contain no information and can corrupt cloudand cloud shadow detection. Such lines should simply bedeleted from the image.

Random speckled noise may appear in satellite data. Suchnoise must be removed from the data prior to use of eitherthe ASMC algorithm or the cloud shadow detection procedurebecause the anomalous (high or low) values associated withthese pixels can compromise the various statistical measuresused. A selective median filter works well for removing thistype of noise [12].

AVHRR Channel 3 data often are contaminated with highlyvariable sensor noise. The ASMC procedure is unaffected bymoderate levels of Channel 3 noise. Occasionally, however,the peak-to-peak amplitude of the Channel 3 noise is toolarge and poor segmentation results. Use of Wiener filteringtechniques [35] will produce a restored Channel 3 signal.

I. Limitations

Algorithmic Limitations: Because the cloud shadow detec-tion procedure uses ASMC cloud detection as its first step,the limitations of the ASMC algorithm apply. A detaileddiscussion of these is given by [12]. Effectively, they place

(a)

(b)

Fig. 9. NDVI histograms for (a) Image 2 (Amazon Basin) and (b) Image 3(Australia desert). NDVI histograms: scene containing land, clouds, and cloudshadow (solid line), scene with cloud detected and removed (dash dot line),and scene with cloud and cloud shadow detected and removed (dash line).In these graphs, lines are laid down in the order solid, dash dot, and dash.Therefore, in regions of overlapping curves, only the line type laid down lastwill be visible.

very few limitations on the use of the algorithm. In fact, theASMC algorithm is currently being used by the United StatesNational Weather Service in conjunction with a new snowdetection algorithm [36] to estimate areal extent of snow coverin AVHRR scenes. Actual cloud shadow detection (Fig. 2,Steps 2–6) is sensitive to the accuracy of modeling the relevantillumination and viewing angles. A good orbit model andfrequently updated and accurate orbital elements are required.

No restriction on image size is imposed by either the ASMCor cloud shadow procedures. In fact, both have been used onimages as large as 1024 2048. Natural variation in landsurface characteristics and latitudinal dependences in cross-track geometry, however, imply that statistical dimensionalitycan be minimized by restricting scene size. Reduced sta-tistical dimensionality always produces better classificationskill. Therefore, we recommend decomposing large scenes(continental scale) into subsections, analyzing each subsection,and reassembling the final product. Given current limitationson most workstations, this also optimizes performance.


Data Limitations: Conditions of poor illumination can de-grade the quality of albedo observations (e.g., [20, Appendix]).Therefore, neither the ASMC algorithm nor the cloud shadowdetection procedure should be used under conditions of lowsun elevation (i.e., ). Typically, suchconditions occur within 1–2 h of sunrise and sunset. Areasof the image that are poorly viewed by the satellite producesimilar but less severe errors as poor pixel illumination. Withinthis context values of large satellite scan angle areassociated with a larger atmospheric path length for reflectedradiance and may produce errors in both Channel 1 (aerosol-related) and Channel 2 (water vapor-related) reflectances. Suchlarge deviations from nadir viewing should be avoided. Poorviewing geometry, especially when coupled with low solaraltitudes, can degrade the accuracy of both cloud shadowand cloud-base height estimates. Scene-specific orbits shouldalways be used to check viewing and illumination.

J. Application to MODIS Data

NASA is scheduled to launch the MOderate ResolutionImaging Spectroradiometer (MODIS) on its first EOS satellitelater this decade. The ASMC procedure can be adapted toMODIS data [12]. Thus, accurate orbit models and updatedorbital elements are all that is required for cloud shadowdetection in MODIS data using the new procedure.

APPENDIX IOVERVIEW OF THE ASMC CLOUD DETECTION ALGORITHM

The AVHRR ASMC algorithm [12] uses a partitional clus-tering algorithm augmented by a splitting and merging stepat each iteration to detect clouds in AVHRR data over land.The procedure produces clusters that simultaneously minimizewithin cluster variance and maximize between cluster variance.The clusters are assigned a geophysical label (e.g., cloud andclear) by using an adaptive labeling procedure.

A. Segmentation Step

The input data consist of -dimensional column vectors.Each column vector corresponds to a given pixel locationwithin the input image, and each component of the columnvector corresponds to a single spectral or derived value at thatlocation. For the ASMC algorithm, ; each vector isdefined as

(A.1)

where is the Channel 2 albedo, is the surface temperaturederived from Channel 4, and is the temperature differencebetween Channels 3 and 4, subject to the constraint thatnegative differences are mapped to zero.

The clustering operation proceeds as follows.

1) Distribute the initial cluster centers equidistantthroughout the range of the input data

(A.2)

where the maximum and minimum vectors of the entiredata set and , respectively, are defined asthe component-wise maximum and minimum of thespectral or derived inputs.

2) Assign each input vector to the nearest cluster centerby computing the Euclidean distance from the vector toeach cluster center

(A.3)

(where is the total number of clusters), and assign thevector to the cluster that corresponds to the minimum

. In (A.3) and elsewhere, superscript denotes thetranspose operation.

3) Compute the between-cluster scatter matrix

(A.4)

where is the number of vectors in cluster andis the mean vector of the input data set

(A.5)

4) Check for convergence based on the trace of the be-tween cluster scatter matrix Tr . Tr is a measureof between-cluster variance. Convergence occurs whenthere is negligible change in this measure from oneiteration to the next, i.e., if

Tr TrTr

tol (A.6)

we stop the clustering process and move on to thelabeling stage. In the convergence check above,represents the between-cluster scatter matrix from theprevious iteration and tol is a predefined numericaltolerance.

5) For each cluster , compute the distance between thecomponent-wise cluster maximum and minimum vectors

(A.7)

where the cluster minimum and maximum vectors aredefined by a procedure analogous to that used for theimage minimum and maximum vectors in (A.2); theyare the component-wise cluster minimum and maximumvectors. If is greater than the splitting threshold ,split the cluster by reassigning each vector to one oftwo new clusters, based on whether it is closer to themaximum or minimum.

6) Repeat Step 5 until nothing is split during that step.


7) For every pair of clusters, compute the distancebetween the cluster mean vectors

(A.8)

If is less than the merging threshold , combineall vectors in clusters and into a single cluster.

8) Repeat Step 7 until nothing is merged during that step.9) Based on the current cluster centers, repeat the

process beginning at Step 2.

The process outlined above uses four predetermined pa-rameters: the number of initial clusters , the splittingthreshold , the merging threshold , and the conver-gence tolerancetol . All four are relatively easy to determinebecause, as [37] has shown, the clustering procedure is largelyinsensitive to the values chosen.

B. Labeling Step

The labeling criteria for ASMC are based on an adaptivelydetermined decision plane that splits the three-dimensional(3-D) input space (albedo, temperature, temperaturedifference) into clear and cloudy regions. Define as theminimum albedo component of the-cluster mean vectors.Similarly, is the minimum temperature difference,and is the maximum temperature component. The scene-specific adaptive labeling threshold valuesth, th, and thare determined from an adaptive threshold of the appropriatecomponent of the input data of the entire image using thefollowing procedure:

1) for a given input component, select the image mean asan initial threshold;

2) use this value to divide the image into two groups havingnew means and ;

3) define a new threshold as the average ofand ; and4) iterate until the adaptively computed threshold remains

constant.

The complementary roles of the dynamic split and mergethresholds used to segment the image and the adaptive labelingthresholds used to label the segments (cloudy versus cloud-free) are discussed by [12].

Given a cluster mean vector with components ,the cluster is labeled as cloud if it falls outside the polyhedrondefined by the adaptive labeling thresholds and the extremaof the cluster means. A cluster will be labeled as cloud if theinner product of the cluster mean vector and the adaptivelydetermined decision plane is positive (i.e., if the normal vectorfrom the decision plane to the cluster center points outwardfrom the polyhedron). Detailed algebraic rules of labeling,based on the image-specific parameters defined above, aregiven by [12]. These rules do not compute a single staticthreshold for the entire scene.

C. Validation

Since publication of the ASMC procedure,in situ observa-tions have become available to quantitatively evaluate its clouddetection accuracy. The ASMC procedure, in conjunctionwith the Multi-Spectral Multi-Stage Snow Detection (MSSD)

Fig. 10. Incremental percent of pixels identified as cloud shadow plotted asa function of percent variation in the parametern of the dynamic threshold1 � n( �

m), wherem is image mean and� is standard deviation of cloud-

and water-free pixels in a scene. For all analyses shown in the paper, a valueof n = 1 was used.

algorithm [36], for example, has been used to separate snowfrom cloud and from clear land over a variety of terrestrialenvironments. Classification accuracy, based on a statisticalcomparison with 412 SNOTEL observations, is 97% [36]. TheASMC process has also been used to cloud screen Along TrackScanning Radiometer (ATSR) data over globally distributedocean images [9]. Sea surface temperatures (SST) at locationscorresponding to buoy data supplied by the British Meteo-rological Office were computed. The linear regression modelfor the ATSR-SST and buoy SST pairs has a slope of 0.995,intercept of 0.065, and correlation coefficient of 0.995. Themean difference between the 41 pairs is C Crms error. Again, the cloud detection accuracy of the ASMCprocedure is supported by the available ground truth data.

APPENDIX II

A. Scaled Albedo Values and Resolution

The albedo of either Channel 1 or Channel 2 is linearlyrelated to the counts of the channel by

(B.1)

Typically, the slope has values ranging from 0.105 to 0.108,has values ranging from3.5 to 3.8, and has the units of

albedo/counts [38]. A scaled albedo (SA) image (scale factoris the image mean) can be represented by

SANC

(B.2)

where in this application is the counts corresponding tothe mean land albedo used to scale the image. Dividing (B.2)by the slope , the equation for the scaled albedo becomes

SA NC (B.3)


Thus, for an SA image, the minimum resolution is given by

NC (B.4)

which is a constant for a specific image/sensor.

B. Sensitivity to Dynamic Thresholds

Step 4 of the cloud shadow detection procedure uses image-specific dynamic thresholds to classify pixels in the sceneas cloud shadow contaminated. The algebraic form of thethreshold is

(B.5)

where and are the mean and standard deviation of theChannel 2 albedo, respectively. The sensitivity of the cloudshadow classification to the chosen dynamic thresholdingmethod is evaluated by varying the weighting parameterin (B.5).

For the image used to compute the sensitivity graph(Fig. 10), , and , whichyields a resolution of 0.04 scaled units (B.4). This valueconfirms what is seen in the sensitivity graph; changes inby less than 4% show no change in the number of pixelsdetected as cloud shadow. The step function nature of thesensitivity curve [ 3% change in pixels detected as cloudshadow for 4% increments in in (B.5)] corresponds tothe quantization limit of the AVHRR Channel 1 and Channel2 sensors. All of our results use in (B.5). Therefore,the cloud shadow dynamic threshold used in Step 4 is withinthe albedo resolving limit of the AVHRR sensor. A similarargument holds for the dynamic threshold used in Step 5 ofthe cloud shadow procedure.

ACKNOWLEDGMENT

Helpful suggestions from Dr. M. Lynch of Curtin Univer-sity, Western Australia, improved the presentation. Dr. Z. Jinperformed the radiative transfer calculations. V. Batcheldertyped the manuscript.

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James J. Simpsonreceived the Bachelor’s degreein physics from the College of the Holy Cross,Worcester, MA, in 1968, the M.S. degree innuclear physics from the University of NotreDame, Notre Dame, IN, in 1970, and the Ph.D.degree in physical oceanography/air sea interactionprocesses from Oregon State University, Corvallis,in 1976.

He has been with the Scripps Institution ofOceanography, University of California, San Diego,since 1976. Since 1988, he has been Head and

Principal Investigator of the Scripps Satellite Oceanography Center and theDigital Image Analysis Laboratory. His present research interests includegeophysical imaging systems, image segmentations and classification, imagealgebras, physical/statistical-based algorithms for geophysical retrievals fromsatellite data, and the development of data management and distributionsystems for large geophysical data sets.

James R. Stitt (M’96) received the B.S. degree inphysics/biophysics from the University of Califor-nia, San Diego, in 1997.

He has been with the Digital Image Analysis Lab-oratory, San Diego’s Scripps Institution of Oceanog-raphy, University of California, since 1994. Previ-ous research has included methods of image seg-mentation, noise removal in satellite data using FIRfilter techniques, and physically motivated methodsof information retrieval from satellite data. Hispresent research interests are digital image process-

ing, data fusion, and mathematical modeling of physical processes.

a procedure for the detection and removal of cloud...

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