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Keywords:

  • trade wind cumuli;
  • cloud climatolog;
  • ASTER

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

[1] This study presents a comprehensive statistical overview of the macrophysical properties of trade wind cumulus clouds over the tropical western Atlantic using 152 scenes taken from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) between September and December 2004. The size distribution, shapes, and spatial distribution of cumulus clouds were examined with ASTER near-infrared data at 15 m resolution. The height distribution of these cumulus clouds was derived from ASTER thermal infrared data at 90 m resolution. The size distribution of cumuli exhibited a power law form and an exponent of 2.19 with a correlation coefficient of 0.99 using a direct power law fit method. The total cloud fraction of trade wind cumulus was 0.086, half of which was contributed from clouds smaller than 2 km in equivalent area diameter. An area-perimeter power law was observed with a dimension of 1.28 and a correlation coefficient of 0.87. The majority of cloudy pixels had cloud top altitudes around 1 km and increasing altitude with increasing cloud equivalent area diameter. Seventy-five percent of clouds have a nearest neighbor within a distance of 10 times their area-equivalent radius. Our results are compared to other studies of small cumulus taken over different parts of the world observed using different instruments. The statistics of cumuli observed in this study are poorly related to synoptic scale meteorological conditions from reanalysis data.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

[2] Trade wind cumuli's role in the climate and global energy cycle has prompted numerous model studies that attempt to characterize the dynamic and radiative interactions between trade wind cumuli and their environment (see Zhao and Austin [2005] for a review on modeling studies). Evaluating these cloud models requires quantitative information of cumuli macrophysical properties such as size distribution, morphology, cloud top height and spatial distribution [e.g., Siebesma and Cujipers, 1995; Zhao and Austin, 2005]. In addition, these macrophysical properties of cumulus clouds from observations can be used to synthesize cloud fields as input into three-dimensional (3-D) radiative transfer models [e.g., Evans and Wiscombe, 2004; Zuidema et al., 2003]. Although these macrophysical properties can be measured from ground-based or in situ instruments, only satellites can provide large enough spatial and temporal coverage to effectively sample these clouds. However, satellite studies of trade wind cumuli have been difficult because the ground instantaneous field of view of typical meteorological satellite instruments tend to be larger than the typical horizontal extent of individual clouds. A proper study of these clouds demands high-resolution satellite data.

[3] Past studies of cumulus macrophysical properties using high-resolution 2-D images taken from aircraft, space shuttle and satellite instruments are summarized in Table 1. Results from these studies are compared with results from our study. Table 1 does not include past studies that only focus on cumulus spatial distributions, since they are not extensively compared to our study (see section 8 for further explanation). The spatial resolution of the data used in the studies listed in Table 1 ranged from 28.5 to 57 m. However, the statistics on the macrophysical properties of cumulus were based on only a handful of scenes. Furthermore, all the scenes analyzed were subjectively selected subsets (subscenes) of larger scenes and manually cut to show only the cumuli-dominated area. It is probable that the statistics derived from limited, subjectively sampled clouds could be biased. In addition, several macrophysical properties of cumuli (e.g., spatial distribution) depend on scene size, making statistics derived from scenes of different sizes difficult to compare. Cumulus properties can also be spatially dependent owing to variation in the metrological conditions from one region of the world to another. Therefore it may not be appropriate to merge the statistics on cumuli properties from different regions. To generate robust statistics of cumuli for a particular region not only requires high-resolution data but also long-term observations. We accomplish this in this study using a 15 m resolution data set from the Advanced Spaceborne Thermal Emission Reflection Radiometer (ASTER). Using several months of ASTER data over the tropical southwestern Atlantic Ocean, we provide a comprehensive examination of the macrophysical properties of trade wind cumuli and derive robust statistics.

Table 1. Past Studies on Cumulus Macrophysical Properties Using 2-D High-Resolution Imagesa
ReferenceData DescriptionLocationNumber of ScenesSubscenes?Statistical Properties
Size DistributionbFractal DimensioncAverage Cloud Fraction
InstrumentDomain, km2Spatial resolution, mλ1λ2Dc, kmd1d2dc, km
  • a

    Studies focusing on only cumulus spatial distribution are not included.

  • b

    Power law defined by equation (1).

  • c

    Power law defined by equation (7) for area perimeters.

  • d

    NR means not reported.

  • e

    LANDSAT Multispectral Scanner (MSS).

  • f

    LANDSAT Thematic Mapper (TM).

  • g

    Moderate Resolution Imaging Spectrometer (MODIS) Airborne Simulator (MAS).

  • h

    Single-line least squares fit.

  • i

    Double-line least squares fit with a scale break.

  • j

    Direct power law fit.

Plank [1969]camera on aircraft16 × 32NRdFlorida Coast12yesNRNRNRNRNRNR0.25
Wielicki and Welch [1986]MMSe170 × 18557United States, tropical western Atlantic, western Arkansas, Gulf of Mexico4yesNRNRNRNRNRNR0.15–0.19
Cahalan and Joseph [1989]MMS170 × 18557Pacific, South America, Florida coast16yesNRNRNR1.271.550.50.45
 TMf65 × 6528.5Pacific, South America, Florida coast19yes0.892.760.51.341.470.50.55
Sengupta et al. [1990]MMS170 × 18557tropical Atlantic, Gulf of Mexico, United States, France10yes1.392.351.01.20–1.271.50–1.730.5NR
Benner and Curry [1998]MASg37 × 3750tropical western and central Pacific, Maldives, Somali coast, Coral Sea, Caribbean Sea17yes1.983.060.91.231.3740.50.0925
 space shuttle110 × 14530tropical western and central Pacific, Maldives, Somali coast, Coral Sea, Caribbean Sea5yes0.942.910.61.101.340.50.090
Gotoh and Fujii [1998]TM65 × 6528.5Japan1yesNRNRNR1.3641.6770.7NR
This studyASTER60 × 6015tropical western Atlantic152no2.85h2.85none1.281.28NR0.086
       1.88i3.180.6    
       2.19j2.19none    

[4] The paper is organized as follows. ASTER data are described in section 2. Section 3 presents the procedure for cloud masking and labeling. Sections 48 cover the statistics on trade wind cumuli properties including cloud size, cloud fraction, cloud area–perimeter relationship, cloud height, and spatial distribution. Section 9 summarizes and discusses our results.

2. ASTER Data

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

[5] ASTER is onboard the EOS Terra spacecraft, which crosses the equator around 10:30 local time in a 705 km Sun-synchronous orbit. Details of the ASTER instrument and its performance can be found in the work of Abrams [2000]. In brief, ASTER has two cameras. One camera, which points at nadir, has three visible and near-infrared (VIR) spectral bands (0.5 to 1.0 μm) with 15 m spatial resolution, six shortwave infrared (SWIR) spectral bands (1.0 to 2.5 μm) with 30 m spatial resolution, and five thermal infrared (TIR) spectral bands (8 to 12 μm) with 90 m spatial resolution. The other camera, which points backward in the along-track direction, has only one spectral band (0.78 to 0.86 μm) with 15 m spatial resolution. VIR and SWIR data are 8 bits, and TIR data are 12 bits. ASTER produces about 650 scenes per day, with each scene having a spatial coverage of 60 × 60 km2.

[6] Although ASTER data are primarily collected over land, the instrument was tasked to acquire data over the tropical western Atlantic Ocean (20°–12°N latitude, 66°–55°W longitude) between September and December 2004 to overlap with the Rain In Cumulus over the Ocean (RICO) experiment (details of the RICO project can be found at http://www.joss.ucar.edu/rico/). The time period and location of the RICO experiment was chosen to best represent the maritime trade wind cumuli of the Western and West-Central Atlantic. The ASTER data used in this study were Version 4 Level 1B calibrated radiance. In total, there are 403 scenes from 29 separate days. Any scene visually identified as contaminated by cirrus, dominated by stratus clouds, or filled with poor quality data (e.g., striping) were wholly discarded from our analysis, reducing the number to 152 scenes (60 × 60 km2 each) from 24 separate days. The remaining scenes are dominated by cumuliform clouds, where we simply refer to them as trade wind cumuli. The number of the scenes used were 77, 30, 23, and 22 for the months of September, October, November, and December, respectively. Figure 1 shows a histogram of the cloud fraction in each scene for the 152 ASTER scenes calculated from the cloud mask described in section 3.

image

Figure 1. A histogram of cloud fraction per Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) scene for the 152 ASTER scenes examined in this study.

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3. Cloud Masking and Labeling

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

[7] The initial step was to generate cloud masks, which classify satellite instantaneous fields of view (pixels) as either clear or cloudy, for each ASTER scene. The quality of the cloud masks directly impacts the accuracy of the statistics. ASTER does not have cloud products available to the public and we had to derive the cloud masks on our own. Although there are numerous cloud detection algorithms (see, e.g., Goodman and Henderson-Sellers [1988] for a review), a single threshold approach was appropriate for this study, given that the variation of clear radiance within an ASTER scene was small and the radiative and spatial contrast between bright clouds and the dark ocean was large. A single threshold was manually selected for each scene using Channel 3N (0.78 ∼ 0.8 μm) at 15 m resolution, given that the Sun-view geometry, aerosol concentration, sea surface roughness, etc., varied from one scene to the next. Channel 3N was chosen because of its high spatial resolution, low atmospheric scattering and absorption, and low surface reflectance. A pixel was flagged cloudy if its digital number, which can be converted to radiance, was larger than the threshold. Otherwise, it was flagged clear.

[8] An accepted way to evaluate the performance of a cloud mask is to visually compare it with its corresponding radiance image using interactive visualization software [e.g., Ackerman et al., 1998; Berendes et al., 2004; Zhao and Di Girolamo, 2004]. Hence we manually tuned the threshold for each scene until the resulting cloud mask passed visual inspections (see Wielicki and Welch [1986] and Wielicki and Parker [1992] for further discussions on manually setting thresholds). Table 2 lists the thresholds for each ASTER scene used in this study. Figure 2 shows an example of an ASTER subscene (20 × 20 km2) along with its cloud mask collected on 9 December 2004.

image

Figure 2. (a) Subscene (20 × 24 km2) of an ASTER Channel 3N image taken on 2 December 2004 and (b) the subscene's cloud mask. For the cloud mask, white represents clouds, and black represents clear.

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Table 2. List of the Thresholds for Each ASTER Scene Used in This Studya
ASTER File NameThreshold
  • a

    The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) file name for each scene is the name given in the ASTER archive at the NASA Land Processes Distributed Active Archive Center (LPDAAC). Thresholds are set for ASTER Channel 3N (0.78 ∼ 0.8 μm) digital numbers.

AST_L1B_00309152004140557_09282004120748.hdf27
AST_L1B_00309152004140606_09282004120827.hdf26
AST_L1B_00309152004140614_09282004120842.hdf26
AST_L1B_00309152004140623_09282004121146.hdf27
AST_L1B_00309152004140632_09282004121306.hdf29
AST_L1B_00309152004140641_09282004121401.hdf30
AST_L1B_00309182004143752_09302004114635.hdf41
AST_L1B_00309202004142242_10022004122438.hdf36
AST_L1B_00309202004142250_10022004122511.hdf36
AST_L1B_00309202004142259_10022004122534.hdf37
AST_L1B_00309202004142308_10022004122556.hdf37
AST_L1B_00309202004142317_10022004122651.hdf37
AST_L1B_00309202004142326_10022004122657.hdf39
AST_L1B_00309202004142335_10022004122708.hdf40
AST_L1B_00309202004142344_10022004122804.hdf40
AST_L1B_00309202004142352_10022004122811.hdf41
AST_L1B_00309202004142401_10022004123250.hdf42
AST_L1B_00309202004142410_10022004123314.hdf43
AST_L1B_00309202004142419_10022004123320.hdf48
AST_L1B_00309202004142428_10022004123335.hdf48
AST_L1B_00309202004142437_10022004123403.hdf53
AST_L1B_00309202004142445_10022004123539.hdf56
AST_L1B_00309202004142454_10022004123446.hdf58
AST_L1B_00309202004142530_10022004123547.hdf99
AST_L1B_00309222004141139_10042004140939.hdf23
AST_L1B_00309222004141148_10042004141131.hdf24
AST_L1B_00309222004141157_10042004141240.hdf26
AST_L1B_00309222004141223_10042004141453.hdf26
AST_L1B_00309222004141232_10042004141522.hdf27
AST_L1B_00309222004141241_10042004141702.hdf27
AST_L1B_00309222004141250_10042004141627.hdf27
AST_L1B_00309222004141259_10042004141726.hdf29
AST_L1B_00309222004141307_10042004141803.hdf33
AST_L1B_00309222004141316_10042004141831.hdf33
AST_L1B_00309232004145335_10052004133522.hdf35
AST_L1B_00309232004145343_10052004134107.hdf36
AST_L1B_00309232004145352_10052004134335.hdf38
AST_L1B_00309232004145401_10052004134142.hdf39
AST_L1B_00309232004145410_10052004134258.hdf42
AST_L1B_00309232004145419_10052004134236.hdf42
AST_L1B_00309232004145428_10052004134307.hdf43
AST_L1B_00309252004144147_10072004115751.hdf40
AST_L1B_00309252004144156_10072004110938.hdf39
AST_L1B_00309252004144205_10072004110939.hdf40
AST_L1B_00309252004144214_10072004110851.hdf49
AST_L1B_00309252004144223_10072004110918.hdf43
AST_L1B_00309252004144232_10072004111002.hdf50
AST_L1B_00309252004144241_10072004110905.hdf53
AST_L1B_00309252004144249_10072004111119.hdf54
AST_L1B_00309252004144307_10072004112530.hdf58
AST_L1B_00309252004144316_10072004112532.hdf51
AST_L1B_00309272004142858_10092004100929.hdf20
AST_L1B_00309272004142925_10092004101248.hdf22
AST_L1B_00309272004142934_10092004101419.hdf22
AST_L1B_00309272004142943_10092004101336.hdf22
AST_L1B_00309272004142951_10092004101419.hdf18
AST_L1B_00309272004143000_10092004101439.hdf20
AST_L1B_00309272004143009_10092004101522.hdf22
AST_L1B_00309272004143018_10092004102011.hdf23
AST_L1B_00309272004143027_10092004102215.hdf23
AST_L1B_00309272004143045_10092004102206.hdf28
AST_L1B_00309272004143053_10092004102222.hdf28
AST_L1B_00309272004143102_10092004102157.hdf28
AST_L1B_00309272004143111_10092004102329.hdf28
AST_L1B_00309292004141645_10102004115140.hdf20
AST_L1B_00309292004141653_10102004115323.hdf26
AST_L1B_00309292004141720_10102004115646.hdf18
AST_L1B_00309292004141729_10102004115737.hdf18
AST_L1B_00309292004141738_10102004115852.hdf22
AST_L1B_00309292004141747_10102004115940.hdf22
AST_L1B_00309292004141831_10102004120158.hdf36
AST_L1B_00309292004141840_10102004120235.hdf30
AST_L1B_00309292004141848_10102004120332.hdf30
AST_L1B_00309292004141857_10102004120753.hdf28
AST_L1B_00309292004141906_10102004120803.hdf31
AST_L1B_00309292004141915_10102004120836.hdf32
AST_L1B_00309292004141924_10102004120858.hdf32
AST_L1B_00310012004140550_10122004103315.hdf29
AST_L1B_00310012004140559_10122004103332.hdf30
AST_L1B_00310012004140617_10122004103331.hdf28
AST_L1B_00310022004144755_10132004123153.hdf24
AST_L1B_00310022004144804_10132004123305.hdf26
AST_L1B_00310022004144812_10132004123325.hdf26
AST_L1B_00310022004144821_10132004123520.hdf26
AST_L1B_00310082004141223_10222004113452.hdf30
AST_L1B_00310082004141232_10222004113357.hdf24
AST_L1B_00310182004144742_10312004094830.hdf18
AST_L1B_00310182004144751_10312004094733.hdf22
AST_L1B_00310182004144800_10312004094915.hdf22
AST_L1B_00310182004144809_10312004094918.hdf18
AST_L1B_00310182004144818_10312004094845.hdf23
AST_L1B_00310182004144928_10312004095131.hdf30
AST_L1B_00310202004143612_11012004110326.hdf31
AST_L1B_00310202004143629_11012004121958.hdf30
AST_L1B_00310202004143647_11012004121704.hdf35
AST_L1B_00310242004141235_11052004104453.hdf23
AST_L1B_00310242004141244_11052004104422.hdf24
AST_L1B_00310242004141253_11052004104549.hdf27
AST_L1B_00310252004145412_11062004101058.hdf20
AST_L1B_00310252004145430_11062004101307.hdf16
AST_L1B_00310272004144335_11072004092756.hdf20
AST_L1B_00310292004142953_11092004112753.hdf26
AST_L1B_00310292004143002_11092004112826.hdf23
AST_L1B_00310292004143020_11092004112845.hdf19
AST_L1B_00310292004143029_11092004112856.hdf24
AST_L1B_00310292004143038_11092004113032.hdf25
AST_L1B_00310292004143055_11092004113244.hdf27
AST_L1B_00311092004141221_11212004101131.hdf10
AST_L1B_00311092004141229_11212004101606.hdf9
AST_L1B_00311092004141238_11212004101723.hdf11
AST_L1B_00311092004141247_11212004101749.hdf11
AST_L1B_00311142004143057_11252004104426.hdf20
AST_L1B_00311142004143106_11252004104422.hdf24
AST_L1B_00311212004143456_12152004102110.hdf11
AST_L1B_00311212004143504_12152004101456.hdf8
AST_L1B_00311212004143513_12152004102210.hdf11
AST_L1B_00311212004143531_12152004102328.hdf14
AST_L1B_00311212004143540_12152004102521.hdf17
AST_L1B_00311232004142249_12032004184139.hdf12
AST_L1B_00311232004142258_12032004184228.hdf8
AST_L1B_00311232004142307_12032004184113.hdf8
AST_L1B_00311282004144111_12112004125113.hdf13
AST_L1B_00311282004144120_12112004125143.hdf17
AST_L1B_00311282004144147_12112004125400.hdf8
AST_L1B_00311282004144155_12112004125411.hdf13
AST_L1B_00311282004144204_12112004125617.hdf13
AST_L1B_00311282004144257_12112004130507.hdf17
AST_L1B_00311282004144306_12112004130410.hdf18
AST_L1B_00311282004144315_12112004130546.hdf13
AST_L1B_00311282004144333_12112004130849.hdf13
AST_L1B_00312022004141642_12152004110719.hdf5
AST_L1B_00312022004141651_12152004110804.hdf5
AST_L1B_00312022004141700_12152004110757.hdf6
AST_L1B_00312022004141709_12152004111047.hdf5
AST_L1B_00312022004141718_12152004110839.hdf6
AST_L1B_00312092004142226_12242004184845.hdf11
AST_L1B_00312092004142235_12242004184743.hdf11
AST_L1B_00312092004142244_12242004184730.hdf10
AST_L1B_00312092004142253_12242004184817.hdf9
AST_L1B_00312092004142302_12242004184826.hdf10
AST_L1B_00312092004142311_12242004185036.hdf9
AST_L1B_00312092004142319_12242004185103.hdf9
AST_L1B_00312092004142328_12242004184919.hdf9
AST_L1B_00312092004142337_12242004185229.hdf9
AST_L1B_00312092004142346_12242004185003.hdf9
AST_L1B_00312092004142355_12242004185015.hdf9
AST_L1B_00312092004142404_12242004185045.hdf10
AST_L1B_00312092004142412_12242004185143.hdf7
AST_L1B_00312092004142421_12242004185205.hdf12
AST_L1B_00312092004142430_12242004185612.hdf12
AST_L1B_00312092004142439_12242004185524.hdf19
AST_L1B_00312092004142457_12242004185805.hdf16

[9] Once pixels were classified as either clear or cloudy, they were grouped into individual clouds (details of the procedure can be found in the work of Zhao [2006]). Two cloudy pixels that share one edge but not one vertex, belong to the same cloud (in the computer vision literature, this is called “4-connected” [e.g., Shapiro and Stockman, 2001]). The total number of the clouds found within the 152 scenes is 1,097,165, which is at least 2 orders of magnitude larger than any other previous study.

4. Cloud Size Distribution

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

[10] The cloud size distribution represents the fraction of total clouds within a finite range of sizes. The cloud size distribution is used to calculate mass flux, energy transport, and other quantities in cloud models, and it is one of the key parameters used to evaluate cloud models against observations (see Neggers et al. [2003] for a review), and has therefore been reported in numerous studies (Table 1). Early studies showed cloud size was exponentially distributed [e.g., Plank, 1969; Wielicki and Welch, 1986]. It has now been well accepted (see Benner and Curry [1998] for an excellent review) that the cloud size distribution can be best represented in a power law form:

  • equation image

where D is the cloud area–equivalent diameter, and a and λ are constants. Many studies on cumulus clouds reported that the cloud size distribution have a double power law form: n(D) ∝ image (D < Dc); n(D) ∝ image (D > Dc), where Dc is called a scale break. The values of λ1, λ2 and Dc varies from one study to another (Table 1). Despite the large discrepancy in the value of Dc in Table 1, the natural question that may be asked is why a scale break exists? The most popular answer is that the scale break may be caused by differences in cloud dynamics between small clouds and large clouds (see Sengupta et al. [1990] for a detailed discussion). Nevertheless, under or subjectively sampling clouds may artificially create a scale break in the cloud size distribution as well, and this cannot be decoupled from the cloud dynamical argument. From the point of view of finding the function that best represents the data, a double-power law fit will always be equal to or better than a single-power law fit, a triple-power law fit will always be equal to or better than a double-power law fit, and so on. Thus our analysis below focuses on how to best represent the data objectively.

[11] The widely used approach to calculate λ is to take the natural logarithm of both sides of equation (1),

  • equation image

which is a linear equation. Thus λ can be equal to the slope of the line using a simple least squares fit to the data on a ln n(D) versus ln D plot. The solid step line in Figure 3 shows the histogram of all the clouds smaller than 7 km in diameter binned to a 100 m diameter increment in logarithmic coordinates. The bins with D > 7 km start to have zero or one cloud indicating that clouds larger than 7 km in diameter might be poorly sampled and therefore were not included in the analysis of cloud size distribution. It is not difficult to conceive how the bin width can alter the appearance of a histogram. Although there are numerous algorithms for choosing an optimal bin width, none of them is superior to the others. Details on how to construct histogram algorithms are beyond the scope of this paper (see Wand [1997] for a review). Given the finite number of clouds and the cloud size range that have been examined, a 100 m bin width was a proper choice based on the discussions in the work of Wand [1997]. To our knowledge, cloud size distributions using 100 m bin width is the smallest bin width ever used, and is the bin width used by Benner and Curry [1998].

image

Figure 3. Normalized distribution of cloud equivalent diameter with a 100 m bin width, using clouds smaller than 7 km in diameter from 152 ASTER scenes. The solid histogram is from observations. The dashed histogram is from direct power law fit, and the straight line represents a single power law fit.

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[12] A single least squares fit to the center of each bin in Figure 3 gives λ = 2.85. Double power law fits give λ1 = 1.88, λ2 = 3.18, and Dc = 0.6 km, which has the least residual. If a histogram is plotted for each scene, two or more apparent scale breaks appeared for some scenes. For most of the scenes, however, it was difficult to visually identify any apparent scale break. When λ from a single least squares fit is calculated for each day, the daily averaged λ varied between 2.58 and 3.55. Averaging the daily average λ over the 24 days of data gave 3.01.

[13] Following a similar discussion in the work of Fraile and Garcia-Ortega [2005], one can easily prove that this traditional method of least squares line fitting to equation (2), called the “line-fit” method, generates more weights to larger clouds, which can be clearly seen in Figure 3 (see Zhao [2006] for a detailed derivation of this point). However, large clouds tend to be poorly sampled, hence the fitting generates larger errors for small clouds than large clouds. In addition, the fitting result is sensitive to a binning strategy including the choice of bin width, the locations of the first and last bins, and the location within the bin (e.g., the bin center) one chooses to fit to (e.g., the least squares fit to the upper bound of each bin in Figure 3 gives λ = 3.07). Without the detail information of a fitting process, it is not appropriate to directly compare the results amongst different studies.

[14] To avoid the limitation of the line-fit method, we used the mean of all the cloud sizes, equation image, to estimate λ:

  • equation image

where n is the total number of clouds. From equation (1), the probability density function of D can be written as: f(D) = (λ − 1)Dλ. The expected value of D, E(D) is simply

  • equation image

where D0 and Du are the smallest and largest cloud sizes among all the clouds, respectively. If the number of samples is sufficiently large, then equation imageE(D), and λ can be solved by combining equations (3) and (4). Using this method, we obtained λ = 2.19. We name this method the “direct power law” fit method. Unlike the “line-fit” method, this method is statistically unbiased with an equal weight assigned to each data point (see Zhao [2006] for a detailed derivation of this point). In order to test the goodness-of-fit of the direct power law fit, we calculated the number of clouds in each 100 m bin from equation (1) with λ = 2.19 and then plot the results as the dashed step line in Figure 3. The correlation coefficient of this fitting is 0.996. Again, λ, obtained from the direct power law fit can be directly applied to the modeling studies with no binning procedures required.

5. Cloud Fraction Distribution

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

[15] In this study, cloud fraction is defined as the ratio of the number of cloud pixels to the total number of pixels. Figure 4 gives the cloud fraction and cumulative cloud fraction as a function of cloud size using bin intervals of 100 m. The total cloud fraction of all 152 scenes is 0.086. Half of the total cloud fraction is contributed from clouds less than 2 km in diameter. Note the cloud fraction distribution is no longer smooth for cloud diameters larger than 3 km. This is simply because few clouds larger than 3 km were sampled. The majority of the bins between 10 km to 30 km only contain one cloud. Since cloud area is proportional to cloud diameter, the cloud fraction increases within this bin range.

image

Figure 4. Cloud fraction and cumulative cloud fraction as a function of cloud equivalent diameter with a 100 m increment.

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[16] Figure 4 also shows a peak in cloud fraction at cloud diameters between 400 and 500 m. However, the peak should not exist if clouds have a size distribution as prescribed by equation (1). Using equation (1), the total fraction of clouds having a size D can be expressed as

  • equation image

Therefore

  • equation image

If λ = 2.19, F should decrease monotonically with D, and no peak should exist. However, deriving equations (5) and (6) from equation (1) was done under the assumption that within each bin, cloud sizes are also continuously distributed and follow the same distribution as prescribed in equation (1). However, the assumption is invalid since clouds are measured by finite resolution data and the observed clouds may not follow this rule in each finite bin. This explanation holds true for the double power law fit. If λ1 < 1.88 and λ2 > 3.18, then equation image < 0 when D < Dc and equation image > 0 when D > Dc. Therefore, theoretically, the peak in Figure 4 should be located at Dc, which was measured 0.6 km using the double power law fit method. This is very close to the observed peak of 0.4–0.5 km. The differences may be due to the true underlying distribution not being a double power law or issues dealing with sampling.

6. Cloud Area–Perimeter Relationship

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

[17] Lovejoy [1982] was the first to report a scaling relationship between cloud perimeter and cloud area:

  • equation image

where A is the cloud area, P is the cloud perimeter, and d is called the fractal dimension. The value of d characterizes the degree of complexity in cloud shape. If clouds have regular shapes (e.g., a circle), d will be unity. The more contorted cloud shapes are, the larger d will be. As a scaling exponent, d is highly related to turbulent flow behavior, and has been used as one of the Reynolds number similarity arguments in cloud models [e.g., Siebesma and Jonker, 2000]. Additionally, scaling relationships can be used to construct cloud fields for 3-D radiative transfer models [e.g., Marshak et al., 1995].

[18] Figure 5 gives the log-log scatterplot of cloud perimeter versus cloud area. The perimeter of each cloud was defined as the total lengths of all the edges adjacent to noncloudy pixels and cloud area was the product of the number of cloudy pixels and the size of each pixel. Although there are different ways to define a cloud perimeter, they all produce identical results (see Cahalan and Joseph [1989] for further discussion). Using a least squares fit, the slope of the fit line is d = 1.28 and the correlation coefficient is 0.87. Note, d is smaller than most other studies listed in Table 1, indicating that the cumulus clouds we sampled have smoother shapes. Figure 5 shows no apparent scale break.

image

Figure 5. Log-log scatterplot of cloud perimeter versus cloud area. Only clouds larger than 12 pixels are plotted.

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[19] Figure 5 only shows clouds larger than 12 pixels (∼ 2700 m2), since the shapes of clouds smaller 12 pixels become sensitive to pixel shape (see Cahalan and Joseph [1989] for further discussion). Since the pixel shape is regular, d becomes smaller when more small clouds are included in the analysis. When the clouds smaller than 12 pixels were included (68% of the total cloud population), d dropped to 1.24 and the correlation coefficient was 0.91. The drop in the valued of d was small, because sufficient amounts of large clouds were sampled in this study.

7. Cloud Top Height Distribution

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

[20] Cloud top height is another important property of the cloud macrophysical structure. ASTER 12 μm data (channel 14) was used to retrieve the cloud top height for each 90 m cloudy pixel. Channel 14 was chosen because it had the least amount of water vapor absorption among the TIR channels. The height retrieval procedure was as follows. First, a 90 m pixel in a Channel 14 scene was flagged cloudy only if all the 15 m subpixels within the corresponding Channel 3N scene were cloudy on the basis of the 15 m cloud mask (section 3). Therefore cloud height is only retrieved for a fully cloud-covered 90 m pixel under the assumption that all 15 m cloudy pixels are fully cloud covered. Secondly, the radiance for each cloudy pixel was then converted into brightness temperature (BT) following the same procedure documented in the ASTER Level 2 product manual [Alley and Jentoft-Nilsen, 2001], where it is documented that the error in the BT retrieval is less than 0.2 degree in Kelvin. Finally, the BT was converted into a cloud top height by equating it with the temperature profile from a 12Z sounding launched from the nearby island of Guadeloupe, collected on the day of the ASTER overpass. Only two soundings, 0Z and 12Z were launched per day from Guadeloupe. The 12Z soundings are used because they are closer to the ASTER overpass time (about 14Z) than 0Z.

[21] The above retrieval algorithm is based on the assumption that cloud emissivity is equal to one. However, this assumption may not be true under certain circumstances. Occasionally, 15 m cloudy pixels may not be fully cloud covered, and some pixels such as cloud edge pixels may contain thin clouds having an emissivity much less than one, hence biasing the resulting height low. Although we visually filtered out all the scenes with cirrus contamination, it is possible that some cloudy pixels were still contaminated by subvisual cirrus above, which could not be visually detected. The cloud heights for these pixels may be biased high. For Channel 14, some amount of water vapor absorption above cloud top may still occur, biasing the heights high as well. This bias can be quantified by comparing the output of a radiative transfer model with the observations. Using a typical sounding collected at Guadeloupe as input into the radiative transfer model, MODTRAN 4.0, (detailed descriptions of the MODTRAN 4.0 are available at: http://www.vs.afrl.af.mil/ProductLines/IR-Clutter/modtran4.aspx), the MODTRAN 4.0 cumulus cloud model was adjusted in altitude until the simulated radiances matched the observations. By turning water vapor absorption off, we found that neglecting water vapor absorption can bias the cloud heights up to 200 m. Errors in the soundings and the two hours time difference between soundings and ASTER measurements incurs further errors in the heights. If we assume a random error of 2°C, this would translate to a random error in height of ∼200 m.

[22] Figure 6 shows cloud top height frequency distribution for different range of cloud diameter. The distribution for each range of cloud diameters was normalized by the total number of cloudy pixels. The cloud diameter used in Figure 6 was derived from the 90 m cloud masks following the same procedure used to calculate cloud size from the 15 m cloud masks. Therefore the cloud diameters are smaller for 90 m data than the 15 m data, since only the 90 m cloudy pixels that were fully cloud covered were considered. The shape of the distribution is primarily determined by clouds larger than 4 km in diameter, which only accounts for less than 0.1% of the total number of clouds but 58% of the total number of pixels. Figure 6 shows a clear positive correlation between cloud diameter and cloud top height of a pixel. On average, cloudy pixels from large clouds are higher than those from small clouds. Only clouds larger than ∼3 km were able to reach above the boundary layer that, on average, was at an altitude of ∼2.5 km. The shape of the histogram varies only slightly for clouds between 1 km and 4 km. Note that most of the contribution to clouds lower than the lifting condensation level, which ranged from ∼600–800 m for all scenes, comes from clouds smaller than 1 km in diameter, and is likely due to partially cloudy pixels or cloud emissivities less than 1.

image

Figure 6. Normalized distribution of cloud top heights with a 100 m bin width.

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8. Spatial Distribution

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

[23] The earliest study on the spatial distribution of clouds was conducted by Plank [1969]. Since then, numerous papers on this topic have been published and several techniques has been developed to classify the organization of clouds of a cloud field into clustering, randomness, and regularity (see Nair et al. [1998] for a review). Cloud spatial distribution is a function of domain size, resolution, the number of cloud, and cloud morphology. To accurately determine the spatial distribution requires knowledge of what this field would look like if its clouds were truly randomly distributed. To accomplish this, clouds from observation must be redistributed randomly while preserving their original size and shape. However, this process requires extensive computer resources and simplifying assumptions (i.e., circular clouds) that limits its application. To avoid this limitation, we concentrated on reporting the statistics of the nearest neighbor distance (NND) in the observed cloud fields, since it is a property of the spatial distribution that is easily calculated and can be compared to other observations (real or modeled) having the same pixel and domain size. The distance of two clouds is the Euclidian distance between their mass centers [see Benner and Curry, 1998]. Figure 7 shows a histogram of the NND distribution with a peak around 50 m. However, the finite size of a cloud limits the minimum possible value of its NND. Therefore we plotted the histogram of the ratio of NND to cloud area–equivalent radius, half of the cloud area–equivalent diameter, in Figure 8. Approximately, 75% clouds have a nearest neighbor within a distance of 10 times less than their radius. The results may not be directly compared with past studies, since they used different instruments and domain sizes, which the statistics on the spatial distribution relies on.

image

Figure 7. Normalized distribution of the nearest neighbor distance (NND).

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image

Figure 8. Normalized distribution of the ratio of NND to cloud area–equivalent radius.

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9. Summary and Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

[24] ASTER measurements over the tropical western Atlantic were used to extensively examine the macrophysical properties of more than one million cumulus clouds from 152 scenes collected over 24 days during September through December 2004. The following summarizes our results:

[25] 1. Cloud size distribution can be expressed in a power law form. The exponent index is 3.07 with the traditional least squares fit method, and 2.19 with the direct power–law fit method. The double power law fits give indexes of 1.88 and 3.18 with a scale break at 0.6 km.

[26] 2. The total cloud fraction of trade wind cumulus cloud fraction is 0.086, half of which is contributed from clouds less than 2 km in diameter.

[27] 3. An area-perimeter power law was observed with a dimension 1.28. This is smaller than typically shown in the past studies, indicating that cumulus clouds we sampled have more regular shapes than those in other studies. No apparent scale break was found.

[28] 4. Cumulus cloud top heights were retrieved only for fully cloudy pixels at 90 m resolutions with an IR technique. The distribution of cloud top heights peaked ∼1 km in altitude. A clear positive correlation between cloud diameter and cloud top height was also observed.

[29] 5. Approximately, 75% of clouds have a nearest neighbor distance within 10 times their area-equivalent radius.

[30] Our results were compared to those of previous studies in Table 1. Differences between the different studies listed in Table 1 may be due to time, location, instrument spatial resolution, domain size, and sampling issues. Although our statistical analysis of the macrophysical properties of trade wind cumuli is the most comprehensive to date, whether it is representative of other oceanic trade wind regions or even other time periods remains to be proven.

[31] Uncertainties in the cloud masks used to generate the cumuli statistics in this study are difficult to assess. In a few studies, the sensitivity of the cloud statistics with threshold used in cloud detection are examined [e.g., Wielicki and Welch, 1986]. Of the cloud macrophysical properties examined here, cloud fraction has been shown to be the most sensitive to changes in threshold [e.g., Wielicki and Welch, 1986]. Given that the thresholds (Table 2) used to generate the cloud masks have been judged to be optimized (see section 3), we can assume that the uncertainty in cloud fraction for cumulus clouds comes from pixels near cloud edge [cf. Di Girolamo and Davies, 1997]. Of the total cloud fraction of 0.086 derived from the 152 ASTER scenes, cloud edge pixels only contributed 0.011 to the cloud fraction. Cloud size distribution has been shown to be insensitive to threshold, because large clouds will replace small clouds in the size distribution with decreasing threshold, while small clouds will replace large clouds in the size distribution with increasing threshold [Wielicki and Welch, 1986]. Similarly, since the value of a threshold in a reasonable range primarily affects cloud edge pixels not cloud center pixels, statistics on cloud spatial distribution is also insensitive to thresholds. In this study, cloud top height is retrieved for each 90 m pixel. Varying the value of a threshold only affects the number of 90 m pixels that can be used to retrieve cloud top height, but not the values of the cloud top height.

[32] Finally, it is critical to place the cloud statistics derived in this study within the meteorological conditions driving the clouds. Although not shown here, we did stratify the observed cloud properties by selected meteorological variables, including the average 500–700 mbar relative humidity, 850 mbar wind speed and vertical wind velocity, and wind shear between lifting condensation level and boundary layer top. The meteorological data kindly provided by F. Yang (2004) were derived using the column version of environmental prediction global forecast system developed at the National Centers for Environmental Predication. However, we did not find any relationship between the meteorological conditions and any of the cloud macrophysical properties (see Zhao [2006] for plots of meteorological conditions against the cloud macrophysical properties). Our hypothesis is that the forecasted meteorological data simply cannot capture the mesoscale meteorological conditions that drive the clouds. Unfortunately, this is the best meteorological data set available to us. Forthcoming meteorological conditions from in situ observations collected during RICO may help, but the lack of space-time coincidence with ASTER will limit their utility in extending our analysis, except for providing a summary of the meteorological conditions under which trade wind cumuli form.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

[33] This research is partially supported by a grant from the National Research Foundation and from the National Aeronautics and Space Administration's New Investigator Program. We thank Bob Rauber and Pier Siebesma for useful discussions and Eric Snodgrass for the assistance of acquiring ASTER data. We are grateful to Fanglin Yang and Steven Krueger for the meteorological data set. We also thank three reviewers for suggested improvement.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. ASTER Data
  5. 3. Cloud Masking and Labeling
  6. 4. Cloud Size Distribution
  7. 5. Cloud Fraction Distribution
  8. 6. Cloud Area–Perimeter Relationship
  9. 7. Cloud Top Height Distribution
  10. 8. Spatial Distribution
  11. 9. Summary and Discussion
  12. Acknowledgments
  13. References
  14. Supporting Information
FilenameFormatSizeDescription
jgrd13107-sup-0001-t01.txtplain text document2KTab-delimited Table 1.
jgrd13107-sup-0002-t02.txtplain text document8KTab-delimited Table 2.

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