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<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0" article-type="research-article">
  <front>
    <journal-meta><journal-id journal-id-type="publisher">AMT</journal-id><journal-title-group>
    <journal-title>Atmospheric Measurement Techniques</journal-title>
    <abbrev-journal-title abbrev-type="publisher">AMT</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Atmos. Meas. Tech.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1867-8548</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/amt-15-3629-2022</article-id><title-group><article-title>An all-sky camera image classification method <?xmltex \hack{\break}?>using cloud cover features</article-title><alt-title>All-sky camera image classification method</alt-title>
      </title-group><?xmltex \runningtitle{All-sky camera image classification method}?><?xmltex \runningauthor{X. Li et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no">
          <name><surname>Li</surname><given-names>Xiaotong</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no">
          <name><surname>Wang</surname><given-names>Baozhu</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name><surname>Qiu</surname><given-names>Bo</given-names></name>
          <email>qiubo@hebut.edu.cn</email>
        </contrib>
        <contrib contrib-type="author" corresp="no">
          <name><surname>Wu</surname><given-names>Chao</given-names></name>
          
        </contrib>
        <aff id="aff1"><institution>School of Electronics and Information Engineering, Hebei University of
Technology, Tianjin, 300401, China</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Bo Qiu (qiubo@hebut.edu.cn)</corresp></author-notes><pub-date><day>16</day><month>June</month><year>2022</year></pub-date>
      
      <volume>15</volume>
      <issue>11</issue>
      <fpage>3629</fpage><lpage>3639</lpage>
      <history>
        <date date-type="received"><day>11</day><month>November</month><year>2021</year></date>
           <date date-type="rev-request"><day>6</day><month>December</month><year>2021</year></date>
           <date date-type="rev-recd"><day>13</day><month>May</month><year>2022</year></date>
           <date date-type="accepted"><day>17</day><month>May</month><year>2022</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2022 Xiaotong Li et al.</copyright-statement>
        <copyright-year>2022</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022.html">This article is available from https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022.html</self-uri><self-uri xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022.pdf">The full text article is available as a PDF file from https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e107">The all-sky camera (ASC) images can reflect the local
cloud cover information, and the cloud cover is one of the first factors
considered for astronomical observatory site selection. Therefore, the
realization of automatic classification of the ASC images plays an important
role in astronomical observatory site selection. In this paper, three cloud
cover features are proposed for the TMT (Thirty Meter Telescope)
classification criteria, namely cloud weight, cloud area ratio and cloud
dispersion. After the features are quantified, four classifiers are used to
recognize the classes of the images. Four classes of ASC images are
identified: “clear”, “inner”, “outer” and “covered”. The proposed
method is evaluated on a large dataset, which contains 5000 ASC images taken
by an all-sky camera located in Xinjiang (38.19<inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N,
74.53<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E). In the end, the method achieves an accuracy
of 96.58 % and F1_score of 96.24 % by a random forest
(RF) classifier, which greatly improves the efficiency of automatic
processing of the ASC images.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e137">Clouds are visible aerosols composed of water vapor in the atmosphere
liquefied by cold, and they are important for the hydrological cycle and
energy balance of the Earth (Sodergren et al., 2017). The analysis of clouds
can provide a lot of valuable information such as weather prediction
(Westerhuis et al., 2020), climate prediction, astronomical observatory
site selection (Cao et al., 2020) and so on. For astronomical
observatory site selection, cloud cover is a factor that must be considered.
When the light emitted by a star reaches the telescope, it will be scattered
and absorbed by clouds in the atmosphere. Therefore, the cloud cover
determines the quality of the observation data and the available time for
astronomy. Currently, cloud observations are mainly based on satellite
remote sensing (Zhong et al., 2017; Young et al., 2018) and
ground-based observations (Nouri et al., 2019). Satellite cloud images can
capture large areas of cloud cover and directly observe the impact of clouds
on the Earth's radiation, which is suitable for atmospheric research.
However, the resolution of the images is low, making it impossible to study
more cloud details. Ground-based cloud images have a smaller observation
range and focus on monitoring the cloud thickness and distribution in local
areas, which has the advantages of flexible observation sites and rich image
information. This paper mainly focuses on the classification of ground-based
cloud images.</p>
      <p id="d1e140">The all-sky imaging device is an automatic observation instrument that can
replace humans. The device has a digital camera that can capture images of
half of the celestial sphere and can obtain details of clouds through
retrieval algorithms. With the emergence of more and more all-sky imaging
devices such as whole-sky imagers (WSIs; Sneha et al., 2020), total-sky imagers
(TSIs; Ryu et al., 2019), all-sky imagers (ASIs; Nouri et al., 2018) and all-sky cameras (ASCs; Fa et al., 2019), a large number of all-sky images have now
been generated, which provides a basis for the development of automatic
cloud image classification algorithms.</p>
      <p id="d1e143">Many researchers pay attention to the feature extraction technology of
different cloud types. Calbo and Sabburg (2008) classified eight types of
sky images using statistical features (smoothness, standard deviation,
uniformity) and features obtained after Fourier transform of the images.
Heinle et al. (2010) proposed a classification algorithm based on spectral
features in RGB color space and texture features extracted by gray-level
co-occurrence matrices (GLCMs). This method has a high accuracy for the
classification of seven different classes of clouds. Sun et al. (2009)
proposed a method where the local binary pattern (LBP) operator and the
contrast of local cloud image texture are used to classify sky conditions.
Li et al. (2016) expressed each image as a feature vector, which was
generated by calculating the weighted frequency of the microstructures
observed in the image. Dev et al. (2015) investigated an improved text-based
classification method that combines color and texture features to improve
the effect. The average accuracy on the Singapore Whole-Sky Imaging
Categories (SWIMCAT) dataset is 95 %. Gan et al. (2017) worked on
different size regions of the image, and they used a method based on sparse
coding which is effective in terms of localization and computation. Wan et
al. (2020) demonstrated that cloud classification results were not good if
only texture or color features are used. As a result, a mixture of texture,
color and spectral features were obtained from color images and then fed
into a random forest (Svetnik et al., 2003).</p>
      <p id="d1e146">In recent years, convolutional neural networks (CNNs) have shown very superior
effects in the field of image classification and have been applied to
all-sky image classification. Shi et al. (2017) used the output of the
shallow convolutional layer of CNN as cloud features and fed it into a
support vector machine (SVM) (Cristianini and Shawe-Taylor, 2000). Ye et al. (2017) extracted multiscale feature maps from pretrained CNN and then
employed the Fisher vector to encode them, finally sending them to a
classifier. Zhao et al. (2019) used the 3D-CNN model to extract the texture
features of the images and then output the classification results with a
fully connected layer. Zhao et al. (2020) proposed the improved frame
difference method extractor to detect and extract features from large images
into small images; then these small images were sent to a multi-channel CNN
classifier. Liu et al. (2021) proposed a context graph attention network
(CGAT) for the cloud classification, in which the context graph attention layer
learned the context attention coefficients and acquired the aggregated
features of nodes.</p>
      <p id="d1e150">The algorithms proposed above, both traditional and deep learning methods,
are based on texture, color and spectral features of cloud for
classification, and they are all for cloud shape classification of local
images or all-sky images. But for the astronomical observatory site
selection, cloud cover is also an important factor that must be considered
besides cloud shape. At present, few researchers have studied the
classification algorithm based on cloud cover. The existing cloud cover
calculation method only calculates the ratio of the cloud coverage area to
the effective area of the ASC images and does not provide a detailed
description of the cloud cover (Esteves et al., 2021). Therefore, we propose
three cloud cover features in this paper that introduce cloud thickness and
distribution position into the cloud cover calculation, and we classify the ASC
images according to the TMT classification criteria. The rest of the paper
is organized as follows. Section 2 introduces the dataset and TMT
classification criteria. Section 3 describes three cloud cover features and
the proposed classification method. Section 4 shows experiment results and
analysis of the results. Finally, Sect. 5 concludes our contributions.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Dataset and image classes</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Dataset</title>
      <p id="d1e168">Images used in this paper were taken by an all-sky camera located in
Xinjiang, China (38.19<inline-formula><mml:math id="M3" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 74.53<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E), and provided by
the Key Laboratory of Optical Astronomy at the National Astronomical
Observatories of Chinese Academy of Sciences. The ASC has two parts, a Sigma
4.5 mm fisheye lens and a Canon 700D camera providing a <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mn mathvariant="normal">180</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:mn mathvariant="normal">180</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> field of view. The frequency of shooting in
daytime is 20 min, increasing to 5 min per shot at night, and the
exposure time will be adjusted between 15 and 30 s depending on the
phase of the moon. The ASC images are stored in color JPEG format with a
resolution of <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:mn mathvariant="normal">480</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">720</mml:mn></mml:mrow></mml:math></inline-formula> pixels. In order to facilitate subsequent
processing, the images are cropped to retain only the central valid area,
and the cropped image size is <inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:mn mathvariant="normal">370</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">370</mml:mn></mml:mrow></mml:math></inline-formula> pixels. Note that the
captured image is originally rectangular but the mapped all sky is circular,
where the center is the zenith and the boundary is the horizon. Figure 1a
shows an example of the original ASC image, and Fig. 1b displays the cropped
ASC image.</p>
      <p id="d1e233">We screened the ASC images taken from January 2019 to November 2020 to
remove those that were overexposed or encountered bad weather. The screened
images are all classified by professionals using a similar manual cloud
identification method (see the next section) as described in the Thirty
Meter Telescope (TMT) site testing campaign paper (Skidmore et al., 2008).
In the end, a dataset with 5000 ASC images was obtained. We did our best to
ensure a balanced number of images of each class in the dataset.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e238">Example of ASC image. <bold>(a)</bold> Original RGB color ASC
image. <bold>(b)</bold> Resized RGB color ASC image of <bold>(a)</bold>.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022-f01.png"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Image classes</title>
      <p id="d1e264">Traditionally, the ASC image classification takes cloud shape as the basic
element, while considering the shape development and internal microstructure
of the clouds. However, the cloud cover in the image is the first important
factor to be considered for astronomical observatory site selection.
Therefore, we classify the ASC images following the method of Skidmore et
al. (2008, TMT classification criteria). The ASC images are divided into
inner and outer circles with zenith angles of <inline-formula><mml:math id="M8" display="inline"><mml:mn mathvariant="normal">44.7</mml:mn></mml:math></inline-formula> and
65<inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, respectively, and then the cloud cover is determined as clear,
outer, inner and covered according to the thickness and
distribution of the cloud on the ASC images. The classification definition
is shown in Table 1, and typical images of each class are shown in Fig. 2.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e286">The ASC image classes and corresponding description.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="2">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Class</oasis:entry>
         <oasis:entry colname="col2">Description</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Clear</oasis:entry>
         <oasis:entry colname="col2">No thick cloud within the inner circle (Fig. 2a).</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Outer</oasis:entry>
         <oasis:entry colname="col2">No thick cloud within the inner circle, has cloud within the outer circle (Fig. 2b).</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Inner</oasis:entry>
         <oasis:entry colname="col2">No more than 50 % cloud within both the inner and outer circles (Fig. 2c).</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Covered</oasis:entry>
         <oasis:entry colname="col2">Coverage of cloud within inner and outer circles is over 50 % (Fig. 2d).</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e351">ASC image samples from dataset. <bold>(a)</bold> Clear,
<bold>(b)</bold> outer, <bold>(c)</bold> inner and <bold>(d)</bold> covered.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022-f02.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Classification based on cloud cover features</title>
      <p id="d1e381">In this section, we first describe the cloud cover features proposed, and
then we introduce the overall process of the ASC image classification method
based on the cloud cover features. The framework is illustrated in Fig. 3.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e386">System framework.</p></caption>
        <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022-f03.png"/>

      </fig>

<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Cloud cover features</title>
      <p id="d1e402">The current TMT classification criteria are essentially only based on the
area ratio and distribution of the cloud regions in the ASC images with
insufficient consideration of cloud thickness and density of distribution,
and no intuitive and reliable quantitative indicators, so the classification
results are easily affected by subjective human factors. In this paper,
three cloud features are proposed for the above problems, namely cloud
weight, cloud area ratio and cloud dispersion. Cloud weight
indicates the thickness of the cloud, cloud area ratio represents the ratio
of the cloud area to the effective area of the image and cloud dispersion
reflects the distribution of cloud regions around the center of the ASC
images.</p>
<sec id="Ch1.S3.SS1.SSS1">
  <label>3.1.1</label><title>Cloud weight</title>
      <p id="d1e412">The grayscale value <inline-formula><mml:math id="M10" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> of any pixel in the ASC image can be regarded as the
weighted superposition value of the grayscale value of multiple elements
such as cloud, sky background and impurities in an ideal state, as shown in
Eq. (1). The ideal state means that the grayscale value of the pixel is
contributed by only one element and no other elements are involved, and the
pixel can be regarded as the “pure pixel” of the element.
              <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M11" display="block"><mml:mrow><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:msub><mml:mi>G</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi>G</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:msub><mml:mi>G</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, …, <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> denote the grayscale value of the
pure pixel of different elements. <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, …,
<inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the weights of the contribution of the pure pixel of
each element to the actual grayscale value of the image pixel.</p>
      <p id="d1e540">For an ASC image, the grayscale value of the cloud region ideally is
superimposed by the grayscale value of the sky background and cloud.
Therefore, the grayscale value of cloud region can be defined by the
superimposed model as
              <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M18" display="block"><mml:mrow><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sky</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">α</mml:mi></mml:mrow></mml:mfenced><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M19" display="inline"><mml:mi>G</mml:mi></mml:math></inline-formula> is the true grayscale value of the cloud region; <inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sky</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the
grayscale value of the sky background in an ideal state. Since the shooting
time of the image is known, the grayscale value of the sky background can be
obtained by using images of different dates but the same moment; <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
is the grayscale value of cloud in the ideal state; <inline-formula><mml:math id="M22" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> is the weight
of the contribution of the sky background to the actual grayscale value of
the pixel in the ideal state. During the shooting process of ASC, the sky
background will be blocked by clouds. As the cloud becomes thicker and
thicker, the contribution of the sky background to the grayscale value of
cloud region will gradually decrease, and this phenomenon will be more
obvious in the initial stage when the cloud thickness increases. When the
cloud thickness increases to a certain degree, the grayscale value of cloud
region is almost completely contributed by the cloud, so the relational
expression between <inline-formula><mml:math id="M23" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is approximately a
monotonically decreasing concave function. After extensive experimental
verification, the relationship between the two is derived in this paper as
              <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M25" display="block"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sky</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sky</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            According to Eqs. (2)–(3), <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is calculated as follows:
              <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M27" display="block"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>G</mml:mi><mml:mo>+</mml:mo><mml:msqrt><mml:mrow><mml:msup><mml:mi>G</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sky</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi>G</mml:mi></mml:mrow></mml:mfenced><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sky</mml:mi></mml:msub></mml:mrow></mml:msqrt></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            In order to verify the validity of the cloud grayscale value obtained by the
superposition model, we process the grayscale image of the local cloud
region according to Eq. (4), and the result is shown in Fig. 4. Figure 4a
shows the original grayscale image, and Fig. 4b is the grayscale image in
the ideal state obtained. By comparison, it can be found that the grayscale
value of the processed image is significantly lower in the thin cloud part,
which eliminates the influence of the sky background on the cloud grayscale
value, thereby better reflecting the cloud contour. Therefore, the grayscale
image processed by the superposition model reflects the grayscale value and
the number of cloud pixels more realistically.</p>
      <p id="d1e727">Based on the previous derivation, we proposed “cloud weight” to indicate
the thickness of the clouds. Since there are large differences in color and
brightness between clouds and sky in ASC images, this section defines the
cloud weight by exploring the relationship between pixel grayscale value,
cloud reflectivity, light intensity and cloud thickness.</p>
      <p id="d1e730">In grayscale images, the magnitude of the grayscale value is related to the
reflectivity of the object and the intensity of the incident light. The
grayscale value can represent the brightness of the pixel, which is
determined by the reflectivity and the intensity of the incident light.
Therefore, the grayscale value of a cloud pixel <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is calculated
as
              <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M29" display="block"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>r</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>l</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> indicates the grayscale value of the pixel in the ideal
state, <inline-formula><mml:math id="M31" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> represents the reflectivity of the cloud to the light and <inline-formula><mml:math id="M32" display="inline"><mml:mi>l</mml:mi></mml:math></inline-formula> is
the intensity of the incident light. Generally speaking, the reflectivity of
the cloud to the light <inline-formula><mml:math id="M33" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> is proportional to the cloud thickness <inline-formula><mml:math id="M34" display="inline"><mml:mi>w</mml:mi></mml:math></inline-formula>. The
thicker the cloud, the higher the reflectivity. According to the theory of
radiative transfer, the expression between the two is approximately
              <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M35" display="block"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="italic">λ</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="italic">ω</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M36" display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula> is the correlation coefficient. The incident light
intensity <inline-formula><mml:math id="M37" display="inline"><mml:mi>l</mml:mi></mml:math></inline-formula> is determined by the incident light, and the incident light
sources are the same for the cloud and sky background. Compared with cloud,
the sky background is simpler and does not have an overly complex function
change in mapping the light source onto the grayscale image, so the
magnitude of the sky background grayscale value <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sky</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is proportional to
the intensity of the light source. Then <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sky</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is
              <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M40" display="block"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sky</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="italic">μ</mml:mi><mml:mi>l</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M41" display="inline"><mml:mi mathvariant="italic">μ</mml:mi></mml:math></inline-formula> is the positive correlation coefficient. According to Eqs. (5)–(7), <inline-formula><mml:math id="M42" display="inline"><mml:mi>w</mml:mi></mml:math></inline-formula> is calculated as follows.
              <disp-formula id="Ch1.E8" content-type="numbered"><label>8</label><mml:math id="M43" display="block"><mml:mrow><mml:mi>w</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mi mathvariant="normal">ln</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="italic">μ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="italic">λ</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sky</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced></mml:mrow></mml:math></disp-formula>
            Since <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">sky</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> have a fixed range of grayscale, and <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:mi mathvariant="italic">μ</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:math></inline-formula> is a constant which does not affect the classification result,
the value of <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:mi mathvariant="italic">μ</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="italic">λ</mml:mi></mml:mrow></mml:math></inline-formula> is taken as 0.1 in this paper after
extensive experimental verification. Then the value of <inline-formula><mml:math id="M48" display="inline"><mml:mi>w</mml:mi></mml:math></inline-formula> represents the
relative size of the cloud weight, which can approximately reflect the
thickness of the cloud. In order to facilitate subsequent calculations and
comparisons, we normalized <inline-formula><mml:math id="M49" display="inline"><mml:mi>w</mml:mi></mml:math></inline-formula> as follows.
              <disp-formula id="Ch1.E9" content-type="numbered"><label>9</label><mml:math id="M50" display="block"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>w</mml:mi><mml:mo>-</mml:mo><mml:mo>min⁡</mml:mo><mml:mo>(</mml:mo><mml:mi>w</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="normal">max</mml:mi><mml:mo>(</mml:mo><mml:mi>w</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi mathvariant="normal">min</mml:mi><mml:mo>(</mml:mo><mml:mi>w</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the normalized value of cloud weight, and <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:mi mathvariant="normal">min</mml:mi><mml:mo>(</mml:mo><mml:mi>w</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:mi mathvariant="normal">max</mml:mi><mml:mo>(</mml:mo><mml:mi>w</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
represent the minimum and maximum values of cloud weight in the cloud
region of the image, respectively.</p>
      <p id="d1e1091">This section defines the cloud weight based on the grayscale value to
reflect the thickness of the cloud. The physical meaning of cloud weight is
the difference between the brightness of the cloud and sky background, which
can approximate the thickness of the cloud region. The feature of cloud
weight makes the evaluation of cloud thickness completely based on grayscale
images, which promotes the automatic processing of ASC images.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e1096">Comparison of cloud image. <bold>(a)</bold> Original
grayscale image and <bold>(b)</bold> processed grayscale image.</p></caption>
            <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022-f04.png"/>

          </fig>

</sec>
<sec id="Ch1.S3.SS1.SSS2">
  <label>3.1.2</label><title>Cloud area ratio</title>
      <p id="d1e1119">At present, the common cloud area ratio calculation methods include ISCCP
(Evan et al., 2007), CLAVR-1 (Wang et al., 2013) and CLAVR-X (Kim
et al., 2016). ISCCP divides pixels into non-cloud and cloud pixels and
assigns weights of 0 and 1, respectively, to calculate the ratio of the
weighted sum of the two to the total number of pixels as the final result.
CLAVR-1 divides the pixels into non-cloud, mixed cloud and cloud and then
assigns weights of 0, 0.5 and 1, respectively, to calculate the ratio of
cloud area. CLAVR-X classifies the image pixels into non-cloud, thin cloud,
medium cloud and thick cloud according to the cloud thickness, and the
weights are adjusted according to the cloud thickness. All the above
calculation models divide the pixels into limited categories and assign
weights respectively. Although cloud thickness and cloud coverage area are
considered two cloud cover features, the division of cloud thickness is
slightly rough. In the previous section, we completed the preliminary
exploration of cloud weight and obtained a more accurate and scientific
numerical representation of cloud thickness, so that the weight of cloud
pixels can be optimized more accurately.</p>
      <p id="d1e1122">This work refines the weight for each pixel of the ASC images and redefines
the calculation model of cloud area ratio. We use the cloud weight derived
in the previous section to represent the weight of cloud pixels and define
the ratio of the weighted sum of all pixels to the effective area of the
image as the cloud area ratio (CAR), whose equation is
              <disp-formula id="Ch1.E10" content-type="numbered"><label>10</label><mml:math id="M54" display="block"><mml:mrow><mml:mi mathvariant="normal">CAR</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo movablelimits="false">∑</mml:mo><mml:munderover><mml:mi/><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub></mml:mrow></mml:munderover><mml:msubsup><mml:mi>w</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msubsup></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">all</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the total number of cloud pixels in the image,
<inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msubsup><mml:mi>w</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula> denotes the cloud weight of the <inline-formula><mml:math id="M57" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>th cloud pixel and <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">all</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
represents the total number of pixels in the effective area of the ASC
image.</p>
</sec>
<sec id="Ch1.S3.SS1.SSS3">
  <label>3.1.3</label><title>Cloud dispersion</title>
      <p id="d1e1220">Cloud dispersion (CD) is proposed mainly to indicate the influence degree of
the distance between cloud and the center of the ASC image on astronomical
observation results. The closer to the center, the greater the influence.
Cloud dispersion is a quantitative representation of this effect. Generally
speaking, cloud dispersion has three determinants: cloud area, cloud
thickness and the distance between cloud and the center of the image.
Therefore, we divide the image into <inline-formula><mml:math id="M59" display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula> regions, namely <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The area of <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is denoted as <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the
average cloud thickness is denoted as <inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the absolute distance
between the center of the region and the center of the ASC image is <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.
In order to facilitate the calculation, we convert the absolute distance to
the relative distance <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mi>R</mml:mi></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M66" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> represents the
radius of the effective area of the image. Then cloud dispersion of an ASC
image can be represented using Eq. (11):
              <disp-formula id="Ch1.E11" content-type="numbered"><label>11</label><mml:math id="M67" display="block"><mml:mrow><mml:mi mathvariant="normal">CD</mml:mi><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:msubsup><mml:msub><mml:mi>s</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mi>f</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup></mml:mrow></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is an influence degree function with <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> as the independent variable. The smaller the <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, the greater
the influence on the observation results and the greater the value of
<inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. From the above, it can be seen that <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
is a function that decreases monotonously with <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and the
influence on the observation results is greatest when the cloud is located
at the image center. Since the classification of the ASC images in this
paper is based on the TMT classification criteria, it is necessary to
consider the influence of the inner and outer circles when setting the
parameters. After many experiments and comparison studies with the results
of manual observation, we set the value of influence degree at the center of
the ASC image to 1, the inner circle to 0.7 and the outer circle to 0. After
linear fitting by the MATLAB curve fitting toolbox, <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is shown
in the Fig. 5. The expression is Eq. (12), where the sine term is to correct
the fitted quadratic function to satisfy the decreasing condition.
              <disp-formula id="Ch1.E12" content-type="numbered"><label>12</label><mml:math id="M75" display="block"><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi>f</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup></mml:mrow></mml:mfenced></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">24.33</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">sin</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>-</mml:mo><mml:mi mathvariant="italic">π</mml:mi></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1.228</mml:mn><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">121.8</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e1574">Curve fitting between <inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> is the relative distance between the center of cloud
and the center of ASC image, and <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the influence degree
function with <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> as the independent variable.</p></caption>
            <?xmltex \igopts{width=184.942913pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022-f05.png"/>

          </fig>

      <p id="d1e1660">In actual calculations, this paper takes each pixel as the calculation unit,
which can make the measurement of cloud dispersion accurate to the pixel
level. Then the region <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represents the individual image pixel whose
area <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is 1, and the cloud thickness <inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> can be expressed by the
cloud weight in Sect. 3.1.1. According to Eqs. (11)–(12), the cloud
dispersion calculation model based on pixels can be obtained as
              <disp-formula id="Ch1.E13" content-type="numbered"><label>13</label><mml:math id="M84" display="block"><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="normal">CD</mml:mi></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">cloud</mml:mi></mml:msub></mml:mrow></mml:msubsup><mml:msubsup><mml:mi>w</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msubsup><mml:mfenced close="" open="["><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">24.33</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">sin</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>-</mml:mo><mml:mi mathvariant="italic">π</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mfenced open="" close="]"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1.228</mml:mn><mml:msup><mml:mfenced open="(" close=")"><mml:mrow><mml:msubsup><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mn mathvariant="normal">121.8</mml:mn></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
</sec>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Classification of ASC images</title>
<sec id="Ch1.S3.SS2.SSS1">
  <label>3.2.1</label><title>Pre-processing</title>
      <p id="d1e1804">Since the extraction of cloud cover features is based on the grayscale
images of the cloud region, it is necessary to extract the cloud region in
the ASC images first. Sunlight has a high grayscale value and is very easily
mistaken for cloud when performing cloud detection in the ASC images.
Therefore, it is very important to remove the influence of sunlight. We use
the difference method to filter the sunlight in this paper. For a given ASC
image, the shooting time and the latitude and longitude of the shooting
location are known, so we can use the image with different dates but the
same moment as the clear-sky background image with the same sun elevation
angle as the original image. The grayscale images of two images are first
obtained, and the difference operation is performed to acquire the image
after removing the sun. Then the cloud detection results are obtained using
the binarization method. Finally, the cloud region is extracted by applying
the image multiplication method.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e1809">Cloud extraction result. <bold>(a)</bold> Original ASC image,
<bold>(b)</bold> real clear background image with the same solar elevation angle
as <bold>(a)</bold>, <bold>(c)</bold> grayscale image of <bold>(a)</bold>, <bold>(d)</bold> grayscale image of <bold>(b)</bold>, <bold>(e)</bold> difference of <bold>(c)</bold> and <bold>(d)</bold>, <bold>(f)</bold> cloud detection result, and <bold>(g)</bold> cloud
extraction result.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022-f06.png"/>

          </fig>

      <p id="d1e1856">Figure 6 shows an example to illustrate the various steps of extracting
cloud region. Figure 6a is the acquired original ASC image, and Fig. 6b is
the clear-sky background image with the same sun elevation angle. Figure 6c
and d are the grayscale images of Fig. 6a and b, respectively,
which have very similar brightness distributions. Figure 6e is the result of
Fig. 6c minus Fig. 6d, and it can be seen that the influence of the sun has
been completely eliminated. The cloud region shown in Fig. 6f can then be
obtained by binarization, and the final extracted cloud region (Fig. 6g) can
be obtained by multiplying Fig. 6f with Fig. 6c. Generally speaking, the
cloud detection accuracy of traditional methods around the sun and
near-horizon regions is relatively low, but the method used in this paper
achieves better results. For thin cloud regions, this method can also
accurately identify them. In addition, it is possible to exclude bright
noises due to light refraction because they are in the same position and
have similar brightness in Fig. 6c and d.</p>
</sec>
<sec id="Ch1.S3.SS2.SSS2">
  <label>3.2.2</label><title>Extraction of cloud cover features</title>
      <p id="d1e1867">In this paper, we proposed three cloud cover features: cloud weight, cloud
area ratio and cloud dispersion, which basically contain the information of
cloud coverage area, thickness and distribution location. We represent the
computational models of three features separately, which should
theoretically match the TMT classification criteria. In order to improve the
accuracy of ASC image classification, we extracted five features of each
image separately, including cloud area ratio (CAR), cloud dispersion
(CD), inner circle cloud weight (<inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, outer circle cloud weight
(<inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and global cloud weight (<inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Among them, <inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> represents the average cloud weight within the inner circle, <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
denotes the average cloud weight between the inner and the outer circle, and
<inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> indicates the average cloud weight within the outer circle. In addition,
the effective range of both CAR and CD is within the outer circle. The
steps of the feature extraction algorithm are shown in Algorithm 1.</p>
      <p id="d1e1943"><?xmltex \hack{\begin{figure*}[t]}?><?xmltex \igopts{width=455.244094pt}?><inline-graphic xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022-g01.png"/><?xmltex \hack{\end{figure*}}?></p>
      <p id="d1e1951">Table 2 shows examples of the value of cloud cover features for each type of
ASC image, and the values are normalized for the convenience of comparison.
As can be seen from the table, the size of the cloud weight is determined by
the thickness of the cloud in the specified area, so there is no obvious
difference between the cloud weight of each type image. However, it has a
great influence on CAR and CD, and the size of cloud weight in the inner
and outer circles affects the classification of ASC images based on TMT
classification criteria, so the <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">o</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are used as
features for classification in this paper. The CAR and CD are derived on
the basis of cloud weight, and the two have an overall positive correlation.
In addition, there are obvious differences between the values of different
categories. Figure 7 shows the distribution of CAR and CD for the four
ASC images. As Fig. 7 illustrates, the distribution of feature values of
each type of ASC image is concentrated in a certain range. The CAR and CD
of clear and covered have a more obvious division in values, while
the overlap phenomenon exists in inner and outer. The distribution
ranges of CAR and CD are relatively similar for each class of ASC image,
but the overlapping part of CD for inner and outer is reduced
compared with CAR, which indicates that considering the information of
cloud location distribution can distinguish the image classes more
effectively. Therefore, the CAR and CD can be used as features to
classify the ASC images.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e1991">Examples of cloud cover features for each type of ASC image.</p></caption>
  <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022-t02.png"/>
</table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e2001">Distribution of feature value for each type of ASC image.
<bold>(a)</bold> Distribution of CAR and <bold>(b)</bold> distribution of CD.</p></caption>
            <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022-f07.png"/>

          </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e2018">Some misclassified ASC images. <bold>(a)</bold> Outer to
inner, <bold>(b)</bold> outer to clear, <bold>(c)</bold> inner to
covered and <bold>(d)</bold> inner to outer.</p></caption>
            <?xmltex \igopts{width=355.659449pt}?><graphic xlink:href="https://amt.copernicus.org/articles/15/3629/2022/amt-15-3629-2022-f08.png"/>

          </fig>

</sec>
<sec id="Ch1.S3.SS2.SSS3">
  <label>3.2.3</label><title>Selection of classifier and training sample</title>
      <p id="d1e2047">The above features are integrated into a feature set to feed into the
classifier for training. To test the effectiveness of our proposed cloud
cover features for classification, we selected four classifiers: decision
tree (DT), support vector machine (SVM), K nearest neighbor (KNN) and random
forest (RF). There are a total of 5000 different types of ASC images in the
dataset, and we selected 4000 images for training the classifier and 1000 images for testing the effectiveness.</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Results and discussion</title>
      <p id="d1e2060">In this section we evaluate the effectiveness of cloud cover features for
the classification of ASC images. Then we analyze and discuss the
classification results.</p>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Experiment results</title>
      <p id="d1e2070">The dataset is trained and tested using the method in the previous section.
To evaluate the classification performance more comprehensively, we use
accuracy, precision and recall as evaluation metrics. The accuracy can be
calculated based on positive and negative classes as
            <disp-formula id="Ch1.E14" content-type="numbered"><label>14</label><mml:math id="M94" display="block"><mml:mrow><mml:mi mathvariant="normal">accuracy</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">TP</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">TN</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">TP</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">TN</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">FP</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">FN</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where TP (true positive) is the number of correctly classified instances for
a specific class, TN (true negative) is the number of correctly classified
instances for the remaining types, FP (false positive) is the number of
misclassified instances for the remaining types and FN (false negative) is
the number of misclassified instances for a specific class. And the
precision and recall can be expressed as

                <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M95" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E15"><mml:mtd><mml:mtext>15</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="normal">precision</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi mathvariant="normal">TP</mml:mi><mml:mrow><mml:mi mathvariant="normal">TP</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">FP</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E16"><mml:mtd><mml:mtext>16</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="normal">recall</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi mathvariant="normal">TP</mml:mi><mml:mrow><mml:mi mathvariant="normal">TP</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">FN</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            In addition, we use F1_score in the evaluation, which can be
expressed as
            <disp-formula id="Ch1.E17" content-type="numbered"><label>17</label><mml:math id="M96" display="block"><mml:mrow><mml:mi mathvariant="normal">F</mml:mi><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="normal">_</mml:mi><mml:mi mathvariant="normal">score</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>×</mml:mo><mml:mi mathvariant="normal">precision</mml:mi><mml:mo>×</mml:mo><mml:mi mathvariant="normal">recall</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">precision</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">recall</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The final test results of the four classifiers are shown in Table 3. It can
be seen that the average accuracy of each classifier is more than 95 %,
indicating that the cloud weight, cloud area ratio and cloud dispersion
proposed are effective cloud cover features that can classify ASC images
based on the TMT classification criteria, which greatly promotes the
automatic processing of the images. The precision and recall of clear
and covered are greater than 95 %, while outer and inner are
both less than 95 %, indicating that outer and inner are easy to
be misclassified. Among the four classifiers, the best performer is RF,
which has an average accuracy of 96.58 % and F1_score of
96.24 %.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><?xmltex \currentcnt{3}?><label>Table 3</label><caption><p id="d1e2204">Comparison of results of four classifiers.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="11">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="center"/>
     <oasis:colspec colnum="3" colname="col3" align="center"/>
     <oasis:colspec colnum="4" colname="col4" align="center"/>
     <oasis:colspec colnum="5" colname="col5" align="center" colsep="1"/>
     <oasis:colspec colnum="6" colname="col6" align="center"/>
     <oasis:colspec colnum="7" colname="col7" align="center"/>
     <oasis:colspec colnum="8" colname="col8" align="center"/>
     <oasis:colspec colnum="9" colname="col9" align="center"/>
     <oasis:colspec colnum="10" colname="col10" align="center"/>
     <oasis:colspec colnum="11" colname="col11" align="center"/>
     <oasis:thead>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="1">Classifier</oasis:entry>

         <oasis:entry rowsep="1" namest="col2" nameend="col5" colsep="1">Recall </oasis:entry>

         <oasis:entry rowsep="1" namest="col6" nameend="col9">Precision </oasis:entry>

         <oasis:entry rowsep="1" colname="col10" morerows="1">Accuracy</oasis:entry>

         <oasis:entry rowsep="1" colname="col11" morerows="1">F1_score</oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">Clear</oasis:entry>

         <oasis:entry colname="col3">Outer</oasis:entry>

         <oasis:entry colname="col4">Inner</oasis:entry>

         <oasis:entry colname="col5">Covered</oasis:entry>

         <oasis:entry colname="col6">Clear</oasis:entry>

         <oasis:entry colname="col7">Outer</oasis:entry>

         <oasis:entry colname="col8">Inner</oasis:entry>

         <oasis:entry colname="col9">Covered</oasis:entry>

       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>

         <oasis:entry colname="col1">SVM</oasis:entry>

         <oasis:entry colname="col2">96.16</oasis:entry>

         <oasis:entry colname="col3">93.16</oasis:entry>

         <oasis:entry colname="col4">95.07</oasis:entry>

         <oasis:entry colname="col5">99.04</oasis:entry>

         <oasis:entry colname="col6">97.27</oasis:entry>

         <oasis:entry colname="col7">93.17</oasis:entry>

         <oasis:entry colname="col8">95.04</oasis:entry>

         <oasis:entry colname="col9">98.78</oasis:entry>

         <oasis:entry colname="col10">95.87</oasis:entry>

         <oasis:entry colname="col11">96.27</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">KNN</oasis:entry>

         <oasis:entry colname="col2">98.52</oasis:entry>

         <oasis:entry colname="col3">93.05</oasis:entry>

         <oasis:entry colname="col4">94.24</oasis:entry>

         <oasis:entry colname="col5">97.89</oasis:entry>

         <oasis:entry colname="col6">96.34</oasis:entry>

         <oasis:entry colname="col7">94.21</oasis:entry>

         <oasis:entry colname="col8">93.18</oasis:entry>

         <oasis:entry colname="col9">98.67</oasis:entry>

         <oasis:entry colname="col10">95.36</oasis:entry>

         <oasis:entry colname="col11">95.92</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">DT</oasis:entry>

         <oasis:entry colname="col2">97.54</oasis:entry>

         <oasis:entry colname="col3">92.67</oasis:entry>

         <oasis:entry colname="col4">94.68</oasis:entry>

         <oasis:entry colname="col5">98.26</oasis:entry>

         <oasis:entry colname="col6">96.95</oasis:entry>

         <oasis:entry colname="col7">93.15</oasis:entry>

         <oasis:entry colname="col8">94.06</oasis:entry>

         <oasis:entry colname="col9">98.57</oasis:entry>

         <oasis:entry colname="col10">96.04</oasis:entry>

         <oasis:entry colname="col11">96.28</oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">RF</oasis:entry>

         <oasis:entry colname="col2">98.38</oasis:entry>

         <oasis:entry colname="col3">93.84</oasis:entry>

         <oasis:entry colname="col4">95.27</oasis:entry>

         <oasis:entry colname="col5">98.84</oasis:entry>

         <oasis:entry colname="col6">99.04</oasis:entry>

         <oasis:entry colname="col7">94.26</oasis:entry>

         <oasis:entry colname="col8">95.13</oasis:entry>

         <oasis:entry colname="col9">98.43</oasis:entry>

         <oasis:entry colname="col10"><bold>96.58</bold></oasis:entry>

         <oasis:entry colname="col11"><bold>96.24</bold></oasis:entry>

       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Comparison experiments</title>
      <p id="d1e2446">In order to verify the effectiveness of the method, we compare with other
methods, including traditional methods and CNN-based methods. Among them,
Ojala et al. (2002) generate cloud features based on the difference of
grayscale value between the center pixel and the domain pixel of the local
region of the cloud image. Lazebnik et al. (2006) divide the image into
many sub-regions, then calculate the histogram of local features of each
one, and finally stitch to get the spatial feature information of the
image. Heinle et al. (2010) extract the color and texture features of the
image and use KNN for classification after combination. In addition, we also
selected CNN-based methods, such as CloudNet (Zhang et al., 2018), DeepCloud
(Ye et al., 2017), TGCN (Liu et al., 2020), Resnet50 and EfficientNet, which
are relatively new methods.</p>
      <p id="d1e2449">The classification accuracy of the method in this paper and other methods is
presented in Table 4. It can be seen from the table that the CNN-based
method performs better than the traditional method, because CNN can
continuously extract various features of the image through convolutional
operations to distinguish different kinds of images. And the classification
performance of this paper method is superior to all other methods, which
indicates that extracting specific cloud cover features for the
classification criteria of cloud images can enhance the discrimination of
different classes of cloud images.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T4"><?xmltex \currentcnt{4}?><label>Table 4</label><caption><p id="d1e2455">Comparison of results of different methods.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="2">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="center"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Method</oasis:entry>
         <oasis:entry colname="col2">Accuracy</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Ojala's method</oasis:entry>
         <oasis:entry colname="col2">76.63</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Lazebnik's method</oasis:entry>
         <oasis:entry colname="col2">80.23</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Heinle's method</oasis:entry>
         <oasis:entry colname="col2">87.68</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CloudNet</oasis:entry>
         <oasis:entry colname="col2">90.70</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DeepCloud</oasis:entry>
         <oasis:entry colname="col2">91.62</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TGCN</oasis:entry>
         <oasis:entry colname="col2">93.03</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Resnet50</oasis:entry>
         <oasis:entry colname="col2">92.88</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">EfficientNet</oasis:entry>
         <oasis:entry colname="col2">94.57</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Ours</oasis:entry>
         <oasis:entry colname="col2"><bold>96.58</bold></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Performance discussion</title>
      <p id="d1e2573">To further analyze the misclassification, we obtained the confusion matrix
of random forest classifier as shown in Table 5. It can be seen from the
table that the classification accuracy of covered and clear is
higher, while for outer and inner it is lower. The non-zero values of the
non-diagonal elements in the table represent the probability of
misclassification between classes. By looking at the misclassified images,
it can be learned that some outer images are misclassified as clear
or inner. Because some outer images have clouds in the inner circle,
but the thickness is extremely small, they will be misclassified as
inner. Or there are only scattered thin clouds in the outer circle, so
they are misclassified as clear. Inner images are also misclassified
as outer or covered. Some inner images have clouds in the inner
circle, but an incorrect classification is caused by the thickness, or some
inner images have a thin cloud thickness although the distribution of
clouds is wide, so it is easy to make a misjudgment. Figure 8 displays some
misclassified ASC images. The reason for misclassification is that the
thickness of some cloud regions is incorrectly identified. Although the
cloud cover features we proposed have taken into account the thickness of the
cloud, there is still room for further improvement.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T5"><?xmltex \currentcnt{5}?><label>Table 5</label><caption><p id="d1e2579">Confusion matrix of classification result using random
forest.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Ground</oasis:entry>
         <oasis:entry rowsep="1" namest="col2" nameend="col5" align="center">Classified </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Truth</oasis:entry>
         <oasis:entry colname="col2">Clear</oasis:entry>
         <oasis:entry colname="col3">Outer</oasis:entry>
         <oasis:entry colname="col4">Inner</oasis:entry>
         <oasis:entry colname="col5">Covered</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Clear</oasis:entry>
         <oasis:entry colname="col2">98.38</oasis:entry>
         <oasis:entry colname="col3">1.21</oasis:entry>
         <oasis:entry colname="col4">0.41</oasis:entry>
         <oasis:entry colname="col5">0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Outer</oasis:entry>
         <oasis:entry colname="col2">3.70</oasis:entry>
         <oasis:entry colname="col3">93.84</oasis:entry>
         <oasis:entry colname="col4">2.46</oasis:entry>
         <oasis:entry colname="col5">0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Inner</oasis:entry>
         <oasis:entry colname="col2">0</oasis:entry>
         <oasis:entry colname="col3">2.95</oasis:entry>
         <oasis:entry colname="col4">95.27</oasis:entry>
         <oasis:entry colname="col5">1.78</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Covered</oasis:entry>
         <oasis:entry colname="col2">0</oasis:entry>
         <oasis:entry colname="col3">0</oasis:entry>
         <oasis:entry colname="col4">1.16</oasis:entry>
         <oasis:entry colname="col5">98.84</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d1e2713">This paper proposes three cloud cover features according to the TMT
classification criteria, namely cloud weight, cloud area ratio and cloud
dispersion, and completes the classification of ASC images based on these
features. In this method, the cloud weight indicates the thickness of the
clouds, the cloud area ratio represents the distribution range of the cloud
and the cloud dispersion reflects the cloud influence degree on astronomical
observation results. We quantify these features and then use a classifier to
identify classes of ASC images. A large dataset is composed of ASC images
taken by the all-sky camera located in Xinjiang, China (38.19<inline-formula><mml:math id="M97" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N,
74.53<inline-formula><mml:math id="M98" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E), and evaluated to verify the effectiveness of the
method. The experiment results show that the highest classification accuracy
is 96.58 % and F1_score is 96.24 % by using the cloud
cover feature. Based on this method, astronomical observatory site selection
experts can greatly reduce the time to classify the ASC images, which will
also greatly improve the efficiency of image processing. With comprehensive
statistical data, they can choose the best site.</p>
      <p id="d1e2734">However, this method still has some shortcomings that need to be improved.
The classification accuracy of inner and outer images needs to be
increased, and better classification algorithms can be studied for these two
types. The sunlight in ASC images affects the brightness of clouds, and how
to better eliminate the influence of the sunlight is also a problem that
needs further research. In addition, this paper does not study the
classification of images in bad weather such as rain and fog, and we will
study new classification algorithms with such images in the future.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e2741">The data are provided by the National Astronomical Observatories, Chinese
Academy of Sciences (NAO-CAS), and we need to apply to the NAO-CAS before we
publish the dataset. The data will be made available from author Xiaotong Li
(865517454@qq.com) and corresponding author Bo Qiu (qiubo@hebut.edu.cn) upon
request.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e2747">XL and BQ conceived and designed the study. XL performed the experiments
and drafted the manuscript. BQ and CW proposed constructive suggestions on
the revision of the manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e2753">The contact author has declared that neither they nor their co-authors have any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e2759">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e2765">This research has been supported by the National Natural Science Foundation of China (grant no. U1931134).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e2771">This paper was edited by Dmitry Efremenko and reviewed by two anonymous referees.</p>
  </notes><ref-list>
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