# MODIS-Based AVHRR Cloud and Snow Separation Algorithm

Jose Luis Villaescusa-Nadal, Eric Vermote, Belen Franch, Andres

Santamaria-Artigas, Jean-Claude Roger, Sergii Skakun

► To cite this version:

Jose Luis Villaescusa-Nadal, Eric Vermote, Belen Franch, Andres Santamaria-Artigas, Jean-Claude Roger, et al.. MODIS-Based AVHRR Cloud and Snow Separation Algorithm. IEEE Transactions on Geoscience and Remote Sensing, 2021, 60, pp.1-13. 10.1109/TGRS.2021.3059428. [hal-03469658]

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# MODIS-Based AVHRR Cloud and Snow Separation Algorithm

Jose Luis Villaescusa-Nadal<sup>1,2</sup>, Eric Vermote, Member, IEEE, Belen Franch<sup>1,2</sup>, Andrés E. Santamaría-Artigas<sup>1,2</sup>, Jean-Claude Roger<sup>1,2</sup>, and Sergii Skakun<sup>1,2</sup>

**Abstract**—The long-term data record (LTDR) has the goal of developing a quality and consistent Advanced Very High Resolution Radiometer (AVHRR) surface reflectance and albedo products dating back to 1982 at 0.05° spatial resolution. Distinguishing between cloud and snow is of critical importance when analyzing global albedo trends, for they influence the Earth's energy balance. However, this task is specially challenging when working with AVHRR given its limited spectral bands. Therefore, the current version of the LTDR does not distinguish between snow and clouds. To this end, we propose the Moderate Resolution Imaging Spectroradiometer (MODIS)-based AVHRR Class Separation Algorithm (MACSSA), whose goal is to identify clear land and snow pixels using AVHRR data. We make use of a combination of optical and thermal information from satellite and reanalysis data, along with monthly climatology information. These are used as inputs for two different support vector machine (SVM) models, which are then applied to AVHRR data to retrieve the MACSSA predicted tags. These are compared first against reference tags retrieved from the MYD10C1 product over pixels with less than 2-min overpass time difference between MODIS Aqua and NOAA16–19, distributed all around the world, and second against the Climate Change Initiative Cloud (Cloud_cci AVHRR) project. We found the product to be highly accurate in identifying clear land pixels, with a probability of detection of clear pixels (PODclear) of 97%. The discrimination of snow and clouds shows a PODsnow of 89%, which is encouraging given the spectral limitations of the AVHRR sensor.

**Index Terms**—Advanced Very High Resolution Radiometer (AVHRR), cloud, long-term data record (LTDR), Moderate Resolution Imaging Spectroradiometer (MODIS)-based AVHRR Class Separation Algorithm (MACSSA), MODIS, snow, support vector machine (SVM).

## I. INTRODUCTION

LONG-TERM consistent data records are becoming crucial in improving the detection, attribution, and prediction of global climate and environmental changes, as well as

Manuscript received August 31, 2020; revised November 7, 2020 and January 18, 2021; accepted February 11, 2021. This work was supported in part by the NASA Grant Land Atmosphere Processing and Science Support under Grant 80NSSC18M0063 and in part by the program Generacio Talent of Generalitat Valenciana (CIDEGENT/2018/009). (Corresponding author: Jose Luis Villaescusa-Nadal.)

Jose Luis Villaescusa-Nadal, Andrés E. Santamaría-Artigas, Jean-Claude Roger, and Sergii Skakun are with the Department of Geographical Sciences, University of Maryland, College Park, MD 20742 USA, and also with the NASA Goddard Space Flight Center, Greenbelt, MD 20771 USA (e-mail: jvillas@umd.edu; asantam@umd.edu; roger63@umd.edu; skakun@umd.edu).

Eric Vermote is with the NASA Goddard Space Flight Center, Greenbelt, MD 20771 USA (e-mail: Eric.F.Vermote@nasa.gov).

Belen Franch is with the Physics Department, Universitat de Valencia, 46100 Valencia, Spain, and also with the University of Maryland, College Park, MD 20742 USA (e-mail: befranch@umd.edu).

Color versions of one or more figures in this article are available at https://doi.org/10.1109/TGRS.2021.3059428.

Digital Object Identifier 10.1109/TGRS.2021.3059428

helping decision makers respond and adapt to climate change and other variability in advance [1]–[3]. In this context, the long-term data record (LTDR) product [4] from NASA provides daily global surface reflectance at 0.05° spatial resolution (Climate Modeling Grid or CMG) from Advanced Very High Resolution Radiometer (AVHRR) data, which has been aboard NOAA satellites all the way from NOAA7 to NOAA19 (1982–2020). The product, which currently spans over a period of 38 years, serves as a valuable resource for the remote sensing and climate research community interested in the dynamics and evolution of the Earth’s biosphere in the last 40 years. It aims to provide a global land climate data record (CDR), introducing the calculation of the surface albedo. To achieve a consistent surface reflectance product, accurate calibration [5], [6], atmospheric correction [7], [8], and directional effects correction [9]–[11] are performed, using the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor as a reference. The utility of this product has been demonstrated in the literature for a wide variety of applications such as snow cover estimation [12], agricultural modeling [5], leaf area index (LAI) and Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) retrieval [13], [14], global vegetation monitoring [15], [16], burned area mapping [17], and albedo estimation products [18].

Surface albedo is a property of the land and the overlying atmosphere. It is defined as the ratio between the upwelling and downwelling flux of shortwave solar radiation, over the upward semi-hemispherical space [19], and therefore quantifies the fraction of sunlight reflected by the Earth’s surface. Its knowledge is of critical importance for the monitoring of land surface processes and plays an important role in energy-budget considerations within climate and weather-prediction models. For this reason, it has been listed by the Global Climate Observing System (GCOS) as an Essential Climate Variable [2], [20]. Surface albedo retrieval methods generally differ between snow and snow-free pixels, so a reliable knowledge of the surface type is required. This means that a cloud mask with the ability to accurately discriminate between snow and clouds is required, because, despite them having similar albedo values, the implications they have on the Earth’s energy budget are profoundly different [21].

Misclassification of clouds can lead to significant errors in the retrieval of biophysical or atmospheric parameters [22], [23]. Cloud detection algorithms normally make use of the optical and thermal bands available in satellite sensors; clouds tend to be brighter and colder than the underlying surface. However, the capacity to detect clouds and, more importantly, to discriminate between clouds and snow,
<table><caption>TABLE I
MODIS AND AVHRR ANALOGOUS BANDS AND THEIR BANDWIDTH. BAND 3A IS ONLY AVAILABLE ON AVHRR/3, ABOARD FOR THE FIRST TIME IN NOAA15, BUT ONLY EITHER BAND 3A OR BAND 3B IS ACTIVATED AT A GIVEN TIME</caption><thead><tr><th colspan="2">MODIS Terra/Aqua</th><th colspan="2">AVHRR/2</th><th colspan="2">AVHRR/3</th></tr><tr><th>Band</th><th>λ (μm)</th><th>Band</th><th>λ (μm)</th><th>Band</th><th>λ (μm)</th></tr></thead><tbody><tr><td>B1</td><td>0.62-0.67</td><td>B1</td><td>0.58-0.68</td><td>B1</td><td>0.58-0.68</td></tr><tr><td>B2</td><td>0.84-0.88</td><td>B2</td><td>0.725-1.00</td><td>B2</td><td>0.725-1.00</td></tr><tr><td>B6</td><td>1.63-1.65</td><td>-</td><td>-</td><td>B3A</td><td>1.58-1.64</td></tr><tr><td>T20</td><td>3.66-3.84</td><td>T3B</td><td>3.55-3.93</td><td>T3B</td><td>3.55-3.93</td></tr><tr><td>T31</td><td>10.78-11.28</td><td>T4</td><td>10.30-11.30</td><td>T4</td><td>10.30-11.30</td></tr><tr><td>T32</td><td>11.77-12.27</td><td>T5</td><td>11.50-12.50</td><td>T5</td><td>11.50-12.50</td></tr></tbody></table>

depends heavily on the sensor's design and characteristics. Sensors with bands in the 0.66- and 1.6-μm window, for example, are able to calculate the normalized difference snow index (NDSI), which identifies snow pixels with a high degree of accuracy [24]. Sensors without thermal bands, such as Multispectral Instrument (MSI) aboard Sentinel-2, have to rely on angular techniques such as cloud parallax [25], [26]. Other methods include multitemporal cloud screening [27] or the use of feature identification such as color, texture, and shape [28]. In the case of the AVHRR sensor, the absence of critical bands limits the information available to tackle this issue. There are two AVHRR generations present in the LTDR product, formed by the sensors AVHRR/2 and AVHRR/3. Table I shows the bands available in each one. The AVHRR/2 has two optical channels (0.63 and 0.86 μm) and three thermal channels (3.7, 11, and 12 μm), while the AVHRR/3, launched on satellites from 1998 onward, has an extra band (1.6 μm); however, only one of the 3.7 or 1.6 μm is available at any given time.

In the optical spectrum, bands in the red (0.6 μm) and NIR (0.8 μm) are very useful to discriminate clear land from cloud and snow, since they appear much brighter than the underlying background. The use of the red band is preferred, since the NIR band can give high values for dense vegetation [29]. The NDVI is also useful in this regard, especially with the idea of using climatology information from MODIS. It is strongly related to the vegetation biomass [30] and, therefore, presents a clear seasonality, which can be exploited. For snow and cloud discrimination, however, the use of the red and NIR bands alone is insufficient, for they have similar values in both bands. Nonetheless, when combined with other variables, they are useful toward separating the classes defining thresholds along a hyperspace. Identification of clear land can be hampered for high SZA (>86°), so studies have made use of the BRDF corrected red band to tackle this issue [29], [31], [32]. The band in the SWIR (1.6 μm) carries information about the microphysical state of the cloud and presents significant contrast between cloud and snow [31]. It is also useful for the detection of low water clouds over snow-covered surfaces. In the absence of this band, the reflectance components of the 3.7-μm band can be used as an alternative [33].

In the thermal bands, the temperature difference between 3.7 and 12 μm and between 10.8 and 12 μm is used for the detection of thin cirrus clouds or the estimation of water vapor (WV) concentration [34]. The difference between 10.8 μm and the skin temperature (TS) can be used to detect

cirrus and optically thick clouds [35]. This is because the 10.8 band is slightly affected by the absorption of atmospheric gases [31], so it can be assumed that there are clouds if the difference between surface and brightness temperature is large. Finally, in the 3.7-μm band, clouds have a higher brightness temperature than snow, and allow for a slight discrimination between the classes [36].

Recent attempts in the literature have relied on ancillary data from climate models to complete the limited information available in the AVHRR sensor with a reliable degree of success [29], [31], [35]. However, they present lower accuracy when using AVHRR data without the 1.6-μm band [31], [32], or are optimized for a certain location and are not recommended for global application [29]. Musial et al. [31], for example, compared their probabilistic cloud mask (PCM) cloud and snow detection algorithm using AVHRR with the MOD10A1 product [37] and obtained a probability of detection (POD) of snow of ~60% when using the 1.6-μm channel and of ~40% when using the 3.7 μm instead. Since the LTDR product uses afternoon satellites, which have very limited or no access to the 1.6-μm channel, the computation of a reliable mask without the use of said band is of great necessity, especially in the context of producing an accurate surface albedo product.

In the current version of the LTDR product, a global cloud/clear mask distinguishes the two classes by using monthly climatological information from MODIS band 1 data. This simple approach provides a higher accuracy than using the previously used Clouds from AVHRR (CLAVR) algorithm [5], [38], but lower than other cloud masks available for AVHRR data [29], [31], [32], when comparing the results with MODIS data. Moreover, it does not provide a method to discriminate between cloud and snow. The main goal of this study is, therefore, to improve the current cloud mask by building on the current approach, and to create a reliable cloud/snow mask that yields high accuracy for AVHRR data and does not require the use of the 1.6-μm band. We first created a model using MODIS Terra data, which are spectrally adjusted to look as if it was acquired by AVHRR. We call this data MODIS AVHRR-like data. Then, we used this information and derived thresholds to apply them to AVHRR data on pixels within 2 min of the MODIS overpass. This way we ensure that the cloud masking reported by MODIS can be applied to the AVHRR data as truth without significant amounts of error.

The following article is divided as follows. Section I describes the introduction and rationale of features used in the literature. Section II presents the materials and workflow and explains the methodology used. Section III shows the main results of this article, which are discussed in Section IV. Finally, we present our conclusions in Section V.

## II. MATERIALS AND METHODS

### A. Data Acquisition

Table II shows a summary of the data used in this study. We downloaded all surface reflectance AVHRR bands from the LTDR product from 1982 to 2020 along with angular and overpass time information. The data are at 0.05° (~5 km)
<table><caption>TABLE II
SATELLITE AND REANALYSIS DATA USED IN THIS STUDY</caption><thead><tr><td>Name</td><td>Sensor</td><td>Spatial Resolution (°)</td><td>Frequency</td><td>Coverage</td><td>Span</td></tr></thead><tbody><tr><td>LTDR</td><td>AVHRR</td><td>0.05</td><td>Daily</td><td>Global</td><td>1982-2020</td></tr><tr><td>MYD09</td><td>MODIS Aqua</td><td>0.05</td><td>Daily</td><td>Global</td><td>2002-2020</td></tr><tr><td>MOD09</td><td>MODIS Terra</td><td>0.05</td><td>Daily</td><td>Global</td><td>2000-2020</td></tr><tr><td>MYD10C1</td><td>MODIS Aqua</td><td>0.05</td><td>Daily</td><td>Global</td><td>2002-2020</td></tr><tr><td>MOD10C1</td><td>MODIS Terra</td><td>0.05</td><td>Daily</td><td>Global</td><td>2000-2020</td></tr><tr><td>Cloud cci AVHRR PM</td><td>AVHRR</td><td>0.05</td><td>Daily</td><td>Global</td><td>1982-2016</td></tr><tr><td>MERRA-2</td><td>Reanalysis</td><td>0.5°x 0.625°</td><td>Hourly</td><td>Global</td><td>1982-2020</td></tr></tbody></table>

spatial resolution, have a daily temporal frequency, and are available globally. We then obtained MODIS Terra/Aqua data from 2000/2002 to 2020. In this case, we downloaded only those bands that are analogous to AVHRR bands, as shown in Table I, along with angular, overpass time, and WV information from the products MOD/MYD09. Both MODIS and AVHRR data are available for download through https://ladsweb.modaps.eosdis.nasa.gov/. We downloaded the TS and the WV from Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA2) data, since the LTDR product has no WV information for data before NOAA16.

The MERRA2 reanalysis provides hourly data at 0.5° lat × 0.625° lon resolution globally. To match the spatial and temporal resolutions to the satellite information used, we interpolated to CMG resolution and MODIS/AVHRR overpass times. Finally, to create reference tags for snow and cloud, which we use to validate the model, we downloaded the daily cloud, clear, and snow percentage information at CMG spatial resolution from the MOD10C1 product (available at https://nsidc.org/data/MOD10C1/versions/6). Daily cloud masks at CMG spatial resolution from the Cloud_cci AVHRR PMv3 data set [39], [40] were also downloaded for comparison with another AVHRR cloud product.

## B. Data Location

We downloaded all of the data specifically in two subsets. The first subset is for the creation of thresholds that will aid in the cloud and snow identification using MODIS data. We downloaded multispectral information from BEL-MANIP2 [41] pixels and expanded the database to include some snow pixels in Antarctica, Greenland and in snow-prone mountains. The specific bands downloaded are shown in Section II-D. The total number of pixels is 494, and the total number of dates is 6889, adding up to a total of ~3.4 million points. Fig. 1 shows the overall spatial distribution of the data points.

The second subset is for the application of the derived thresholds on AVHRR data. We selected pixels with an overpass difference of <2 min between AVHRR (N16–N19) and MODIS Aqua for 169 equally distributed days from 2002 to 2015. This minimizes the possibility that cloud positions have changed due to the overpass time difference between the satellites. This subset contains ~13 million data points, distributed around the globe, as shown in Fig. 2.

## C. Data Preparation

Fig. 3 shows a summary of the methodology employed in this article. Once we have downloaded all of the data required,

<figure><img src="image_2.png" /><figcaption>Fig. 1. Distribution of the data points used for data training and threshold selection.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. Frequency of the pixels used in the study with a <2-min difference in time overpass between MODIS Aqua and NOAA, at CMG spatial resolution (0.05°), for 169 days distributed along the year from 2002 to 2015. No data are represented in gray.</figcaption></figure>

we proceed to prepare the data for analysis. The ultimate goal is to create thresholds that can classify clear, cloud, and snow using MODIS data, and apply this model to AVHRR data. Since different sensors have different bandwidths and different relative spectral response (RSR) functions, there are uncertainties associated with this process. In order to decrease these uncertainties, and to calculate thresholds that work for all sensors present in the record, we spectrally adjusted the MODIS data to AVHRR data (Note: We use the band notation following AVHRR sensor nomenclature, but we are using MODIS data here). This is what we call the MODIS simulated AVHRR data. The idea is to select a reference sensor (among all AVHRRs), which sets the common radiometric scale for all the target sensors. We used the parameters to obtain what they would have measured had they been designed with the same RSR function as the reference sensor. The choice of the reference sensor in this case is AVHRR/2 aboard NOAA14.
<figure><img src="image_4.png" /><figcaption>Fig. 3. General workflow of the methodology employed in this article. D<sub>L</sub> and D<sub>S</sub> are the displacement to clear land pixels and displacement to clear snow pixels, respectively, as defined in Section II-D.</figcaption></figure>

However, this choice simply modifies the spectral adjustment parameters used. The target sensor is, therefore, MODIS Aqua.

In the optical bands, we followed the model derived in Villaescusa-Nadal *et al.* [42]: we used a SBAF exponential model, dependent on the NDVI for the red band (1), and a multilinear model also dependent on the NDVI for the near infrared (NIR) band (2). For the thermal bands, we used a linear model to adjust band 3B (3), and a SBAF exponential model, dependent on the temperature difference T4 − T5 to adjust T4 and T5 (4)

$$
\rho_{B1,ref} = \rho_{B1,tar} \times (a \cdot e^{b \cdot \text{NDVI}} + c \cdot e^{d \cdot \text{NDVI}}) \quad (1)
$$

$$
\rho_{B2,ref} = a * \rho_{B1,tar} + b \times \rho_{B2,tar} + c \times \text{NDVI} + d \times \text{NDVI}^2 \quad (2)
$$

$$
\rho_{3B,ref} = a + b \times \rho_{B3B,tar} \quad (3)
$$

$$
T4(T5)_{\text{ref}} = T4(T5)_{\text{tar}} \times (a \cdot e^{b \cdot (T4-T5)} + c \cdot e^{d \cdot (T4-T5)}). \quad (4)
$$

Here, ρ is the surface reflectance, and T is the temperature. Subindices ref and tar correspond to reference and target sensors, respectively. Table III shows the spectral adjustment parameters used in this study. Coefficients for all of the sensors used in the LTDR product and this article can be found in Tables VIII–XII.

The next step in the data preparation involves calculating the
monthly MODIS average for all bands available. The goal of

<table><caption>TABLE III
SPECTRAL ADJUSTMENT COEFFICIENTS USED TO ADJUST MODIS
TERRA BANDS TO NOAA-14'S AVHRR/2 BANDS</caption>
  <thead>
    <tr>
      <th>Band</th>
      <th>Model Type</th>
      <th colspan="4">Parameter</th>
    </tr>
    <tr>
      <th></th>
      <th></th>
      <th>a</th>
      <th>b</th>
      <th>c</th>
      <th>d</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>1</td>
      <td>SBAF<br>exponential</td>
      <td>0.98</td>
      <td>5.78E-02</td>
      <td>5.00E-03</td>
      <td>5.4038</td>
    </tr>
    <tr>
      <td>2</td>
      <td>Multilinear</td>
      <td>5.49E-02</td>
      <td>0.94</td>
      <td>1.20E-02</td>
      <td>-1.35E-02</td>
    </tr>
    <tr>
      <td>20</td>
      <td>Linear</td>
      <td>1.01</td>
      <td>-1.03</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <td>31</td>
      <td>SBAF<br>exponential</td>
      <td>4.26E-04</td>
      <td>-4.12</td>
      <td>0.99</td>
      <td>5.62E-04</td>
    </tr>
    <tr>
      <td>32</td>
      <td>SBAF<br>exponential</td>
      <td>1.04E-03</td>
      <td>-2.56</td>
      <td>0.99</td>
      <td>-4.25E-04</td>
    </tr>
  </tbody>
</table>

this step is to use a pixel’s seasonality information to improve
cloud detection. Typically, the reflectance of a pixel will vary
throughout the year. If a clear land pixel is usually within a
certain range of values (defined by the standard deviation) in
the summer, if the reflectance lies within those values in the
same month, we can assume it will likely be clear too. If,
however, the reflectance value lies beyond that range, we can
assume it is likely that the pixel is cloud or snow contaminated.
The larger the difference between the reflectance and the
climatological average, the more likely it is that the pixel is
cloud or snow contaminated. To obtain these climatological
averages, we calculated the average of every month for clear
pixels, using MODIS Terra from 2000 to 2015, along with the
standard deviation.

To determine the true land cover of a pixel to be used as a
reference, we used the MOD10C1 product. This information
can be combined with the spectral information to increase the
probability of accurate detection. We also used this product to
create a historical snow mask. It is often the case that clouds
and snow can be misclassified. If, for example, we detected
snow in equatorial latitudes, we can be almost completely sure
that a cloud has been incorrectly tagged as snow. We can,
therefore, count the cases of snow on different pixels for
the whole time series (2000–2020) and assign to each one
a probability of detecting snow. Fig. 4 shows the snow
probability map used in this article. Pixels with zero counts
are assigned a probability of snow cover of 0%, while pixels
covered by snow all-year round are assigned a probability
of 100%. MYD10C1 does not detect clouds in Antarctica
and considers it to be covered by snow permanently, so the
probability across the continent is homogenous. This value
provides no indication about the cloud cover, but it allows us
to minimize errors when detecting snow and clear land.

The final step toward data preparation is the calculation
of the band T3B reflectance. The radiance obtained in this
wavelength is a combination of both reflected and emitted
components. Since the reflectance component is useful toward
discriminating clouds and snow and for cloud detection [29],
[31], [32], [35], it is of interest for this study to obtain
it. To do so, we used the algorithm derived by Roger and
Vermote [34], which estimates the reflectance by subtracting
the thermal contribution from the total signal and dividing the
remaining signal component by the atmospheric transmission
and solar irradiance. This method requires the use of the WV,
which in the case of MODIS data is available in the product.
<figure><img src="image_5.png" /><figcaption>Fig. 4. Probability of snow cover for every land pixel, obtained using MOD10C1 snow information. The probability per pixel is assigned considering the snow information from the products full-time series. Antarctica has 100% probability of snow, but the color bar reaches a maximum of 70% for visualization purposes.</figcaption></figure>

For AVHRR data, however, the only WV available is from 2000 to onward (which is derived from MODIS). For this reason, we used the MERRA-2 reanalysis WV, interpolated to AVHRR spatial and temporal resolution for dates before 2000. This method, along with similar methods employed in the literature for the retrieval of the reflectance, presents high uncertainties (>10%) for low sun geometry. To avoid this, we removed from the data set every pixel with an SZA > 75°. This also deals with issues discerning cloud at said angles of observation, but limits the amount of data available, especially over polar latitudes.

## D. Model and Features Selection

Once all the data are processed and harmonized, we can proceed to the creation of the models using the MODIS “AVHRR-like” data. These models aim to separate clear land, cloud, and snow classes, through the derivation of thresholds on selected features. The initial selection of these features is based on physical reasoning, similar to that presented in Section I-B. Using this argumentation, we can narrow down all the inputs available in our study to those relevant to the discrimination of a certain class. After we have our initial selection, the final selection is done based on empirical results obtained after running several models with different band combinations: Bands that provide significant improvements are added, while those that provide no improvement or just a slight, nonsignificant improvement are not added or not included at all. The final features used are those that maximize the POD and minimize the false alarm rate (FAR). Ideally, the number of inputs is small and the accuracy is high, in order to maintain a reliable and robust model that can later be applied to the actual AVHRR data.

Two models are presented in this study. The first one is used to discriminate between clear land and cloud/snow pixels, while the second one is only applied to cloud/snow classified pixels and is used to separate both classes. The features used for each model are shown in Tables IV and V. In the clear model, we make use of the MODIS climatology for the red band and for the NDVI, and of the normalized variables T5 and T4-Ts (the normalized counterpart of the variables is expressed

<table><caption>TABLE IV
VARIABLES USED AS INPUTS IN THE CREATION OF THE CLEAR LAND SVM MODEL, ALONG WITH THEIR AVERAGE AND STANDARD DEVIATION</caption><thead><tr><th>Clear Land Model</th><th>x<sub>1</sub></th><th>x<sub>2</sub></th><th>x<sub>3</sub></th><th>x<sub>4</sub></th></tr></thead><tbody><tr><td>Name</td><td>B1 clim.</td><td>NDVI clim.</td><td>T5</td><td>T4-Ts</td></tr><tr><td>Mean</td><td>0.22</td><td>0.17</td><td>276.20</td><td>-17.85</td></tr><tr><td>Std</td><td>0.26</td><td>0.22</td><td>24.80</td><td>20.13</td></tr></tbody></table>

<table><caption>TABLE V
SAME AS TABLE IV BUT FOR THE SNOW MODEL</caption><thead><tr><th>Snow Model</th><th>x<sub>1</sub></th><th>x<sub>2</sub></th><th>x<sub>3</sub></th><th>x<sub>4</sub></th><th>x<sub>5</sub></th><th>x<sub>6</sub></th><th>x<sub>7</sub></th></tr></thead><tbody><tr><td>Name</td><td>B1</td><td>B2</td><td>B3B</td><td>T4</td><td>T3-T5</td><td>T4-Ts</td><td>WV</td></tr><tr><td>Mean</td><td>0.55</td><td>0.60</td><td>0.09</td><td>262.27</td><td>27.43</td><td>-29.49</td><td>1.07</td></tr><tr><td>Std</td><td>0.28</td><td>0.24</td><td>0.07</td><td>19.86</td><td>12.39</td><td>20.87</td><td>1.06</td></tr></tbody></table>

in italic from now on). For the snow model, the climatological variables computed from MODIS did not prove to be valuable for the class separation, possibly due to the lower seasonality present on snow pixels, compared with vegetation pixels. For this reason, we used the information from the optical bands B1 and B2, along with the reflectance component of the B3B, and then used T4, T3-T5, T4-Ts, and WV. In the case of the optical bands, this precise combination of bands matches the results obtained in [43], which used B1, B2 and the reflectance B3B to simulate the B3A band (1.6 µm). In the case of the thermal bands, T4, T3-T5, and T4-Ts are commonly used in cloud/snow discrimination, while the combination of T4-T5 is typically used to detect cirrus clouds instead of the WV. In our case, we found that the use of the WV concentration provided a slightly better accuracy in the model, which is not surprising considering the dependence of T4-T5 on the WV concentration [31].

With these features, we created an n-dimensional hyperspace (where n is the number of variables in the model). In this hyperspace, we have two different clusters, grouped using what we consider in this study the true information of the pixel from MOD10C1 data. In the first model, the two clusters are clear land and cloud/snow, whereas in the second model, they are cloud and snow. The idea is to find an n-dimensional plane that can separate these two clusters, so that the average displacement of pixels within that class to the hyperplane is maximized. To do this, we make use of support vector machines (SVMs), a supervised machine-learning model that has been used widely in the literature for classification in remote sensing applications [24], [44], [45].

We used this method as the main model for this study above other machine learning algorithms such as Neural Networks or Regression Trees for three reasons: First, we wanted to use a more transparent method that allows us to understand the exact process happening in the training algorithm. Second, we wanted to use a model that allows users to apply it to their data in an intuitive way. In this case, the output of the model is the equation of a hyperplane, which users can apply to their own data. Finally, this approach allows us to compute the displacement of each pixel to the hyperplane. If the displacement is positive, the pixel belongs to one class, while if it is negative, it belongs to a different class. The
higher or lower the displacement value, the more likely the pixel is to belong to one class or another. In cloud detection, the decision of tagging something as cloudy or clear, for example, even when tagging it manually, is not a universal principle. This also might depend on the application, where perhaps a very restrictive cloud mask needs to be applied. Therefore, a continuous approach, as opposed to a branched approach, allows us to make arguments about the percentage cloud cover on a certain pixel or the thickness of the clouds present. Pixels with a displacement to the hyperplane close to zero are more likely to be mixed pixels or thin clouds.

For the first model, we use a linear hyperplane, since we found the data to be linearly separable. The process to obtain the displacement to the hyperplane obtained using the linear SVM model is as follows: first, the variables are normalized by subtracting the mean and dividing by the standard deviation of the distributions. This is done to create dimensionless variables that can be included comparably to the model. Then, they are input to the SVM model, which yields the hyperplane's coefficients that provide optimal separation of the two classes. The following equation shows the equation of a plane in three dimensions with variables ($x_1, x_2, x_3$):

$$ \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \beta_0 = 0. \quad (5) $$

If we define a random point with coordinates ($x_0, y_0, z_0$), we can then calculate the displacement of a pixel to this plane as

$$ D = \frac{\beta_1x_0 + \beta_2y_0 + \beta_3z_0 + \beta_0}{\sqrt{(\beta_1^2 + \beta_2^2 + \beta_3^2)}}. \quad (6) $$

Each pixel will, therefore, have two displacement values associated with it, namely, $D_L$ for the displacement to the clear land cluster and $D_S$ for the displacement to the snow cluster. If $D_L < 0$, the pixel is considered to be clear land. If $D_L > 0$, and $D_S < 0$, the pixel is considered to be clear snow. Finally, if both $D_L > 0$ and $D_S > 0$, then the pixel is tagged as cloudy.

The data of the second model, however, cannot be separated linearly, so we employ a polynomial kernel through the “Kernel Trick” commonly used in SVM models for more efficient computation [46], [47]. In this case, the calculation of the displacement of a pixel to the plane is not as straightforward and requires the knowledge of the support vectors and the trained Lagrange multipliers [47]. Details on the parameters used to build each model can be found in Appendix B.

We applied these models first to MODIS Aqua data, to ensure that they perform as accurately for Aqua data as they do for Terra data. This also serves as a reference of what the maximum correction we can achieve with this model on AVHRR data is, compared with the correction we actually get. Second, we applied them to the AVHRR data from the LTDR product we aim to correct and we compared the results of our classifications with the reference tags from MYD10C1. Finally, to compare our results to other cloud products obtained using AVHRR, we compare the MODIS-based AVHRR Class Separation Algorithm (MACSSA) to the Cloud_cci AVHRR PM data. These data contain only cloud information, so for this comparison, we transform the resulting tags to two classes:

<caption>TABLE VI</caption>

SAMPLE CONFUSION MATRIX TO ILLUSTRATE THE ERRORS INVOLVED WITH THE MODELS. HITS AND MISSES ARE TYPICALLY PRESENTED AS A PERCENTAGE

<table><caption>TABLE VII</caption><thead><tr><th>Sample matrix</th><th>AVHRR clear</th><th>AVHRR cloud/snow</th><th>Hits</th><th>Misses</th></tr></thead><tbody><tr><td>MODIS clear</td><td>N<sub>A</sub></td><td>N<sub>B</sub></td><td>N<sub>A</sub>/(N<sub>A</sub>+N<sub>B</sub>)</td><td>N<sub>B</sub>/(N<sub>A</sub>+N<sub>B</sub>)</td></tr><tr><td>MODIS cloud/snow</td><td>N<sub>C</sub></td><td>N<sub>D</sub></td><td>N<sub>D</sub>/(N<sub>C</sub>+N<sub>D</sub>)</td><td>N<sub>C</sub>/(N<sub>C</sub>+N<sub>D</sub>)</td></tr><tr><td>Hits</td><td>N<sub>A</sub>/(N<sub>A</sub>+N<sub>C</sub>)</td><td>N<sub>D</sub>/(N<sub>B</sub>+N<sub>D</sub>)</td><td colspan="2">OA = (N<sub>A</sub>+N<sub>D</sub>)/N</td></tr><tr><td>Misses</td><td>N<sub>C</sub>/(N<sub>A</sub>+N<sub>C</sub>)</td><td>N<sub>B</sub>/(N<sub>B</sub>+N<sub>D</sub>)</td><td colspan="2"></td></tr></tbody></table>

PARAMETERS OF THE HYPERPLANE OBTAINED FOR THE CLEAR LAND MODEL, AS EXPLAINED IN (5)

<table><thead><tr><th></th><th>Parameter</th><th>β<sub>0</sub></th><th>β<sub>1</sub></th><th>β<sub>2</sub></th><th>β<sub>3</sub></th><th>β<sub>4</sub></th></tr></thead><tbody><tr><th rowspan="2">Clear Land model</th><th>Variable</th><td>-</td><td>B1 clim.</td><td>NDVI clim.</td><td>T5</td><td>T4-T5</td></tr><tr><th>Value</th><td>1.04</td><td>3.29</td><td>0.76</td><td>-2.78</td><td>-2.17</td></tr></tbody></table>

cloud and no cloud. To obtain the latter, we simply merge the snow and clear classes into one. We then also compare the Cloud_cci AVHRR PM mask to the MODIS Aqua mask to analyze which of the two AVHRR models provides a better agreement with MODIS data.

In order to compare and analyze these results, a confusion matrix is often used. A confusion matrix shows the absolute values of the pixels correctly tagged in the diagonal and the absolute values of incorrectly tagged pixels in the off diagonal. Table VI shows a sample confusion matrix of $N = N_A + N_B + N_C + N_D$ total pixels, with MODIS tags on the rows (truth) and AVHRR tags on the columns (predictions). The rest of the rows and columns are used to indicate the percentage of hits and misses; the green shaded cells are typically known as the POD of a certain class, while the yellow shaded cells are known as the FAR of a class. The overall accuracy (OA), which can be calculated as shown in the bottom-right of the table, indicates the effective hit rate of the model; the percentage of total pixels correctly tagged from the total amount.

### III. RESULTS

Table VII shows the hyperplane parameters obtained from the clear land model. Using these $\beta$ values and the variable names from Table IV, one can express the equation of the plane following equation 5. Fig. 6 shows a histogram of the displacement $D_L$ when the clear land model is applied to MODIS (top panel) and when it is applied to AVHRR data (middle). The green and red bars represent those tagged as clear and cloud/snow by MYD10C1, respectively, while the black dotted line centered at $D_L = 0$ represents the threshold that separates the two classes. Therefore, any overlap between the two distributions represents the misclassifications and, therefore, shows the quality of performance of the model. In the bottom panel, we plot the confusion matrices of the resultant tags from the MACSSA algorithm compared with the reference tags from MYD10C1. These results show that when applying the model derived from MODIS Terra data to MODIS Aqua data, the accuracy of the classification is very
<figure><img src="image_6.png" /><figcaption>Fig. 5. Confusion matrix of the current LTDR AVHRR approach using only Band 1 climatology.</figcaption></figure>

high, as confirmed by the 99.3% OA, the 99.5% probability of distribution of clear pixels, and the 1% false alarm rate. When applied on AVHRR, the accuracy is lower, yielding a 96.7% OA, a 97.1% POD<sub>clear</sub>, and a 4.4% FAR<sub>clear</sub>. Fig. 5 shows the confusion matrix of the mask currently used in the LTDR product, with a lower OA (95.04%), a lower POD<sub>clear</sub> (93.2%), and a higher FAR<sub>clear</sub> of 4.7%. This shows that the proposed model yields a significant improvement especially in the POD<sub>clear</sub> from the current model used in this product. Transforming the results from the SPARC algorithm [29] into similar classes, we observe that they report an OA of around 94%, when comparing with a multispectral maximum likelihood classifier (MLC), but a POD<sub>clear</sub> of around 80%. These results are similar to the comparison of the PCM algorithm [31] with a CASLIPSO/CALIOP LIDAR mask [48], which yield around 80% OA and 85% POD<sub>clear</sub>, but a high FAR<sub>clear</sub> of almost 40% using NOAA 18.

Fig. 7 shows an analogous figure to Fig. 6 but for D<sub>S</sub> (snow and cloud discrimination). The blue bars represent snow, while the red bars represent clouds. Here, the difference between the model applied to MODIS Aqua data and to AVHRR data is similar; POD<sub>snow</sub> is 97% for the former, and 92% for the latter. FAR<sub>snow</sub> is, however, quite similar, with only around 1% difference (11.8% versus 10.6%). The current model used for this product has no snow detection, so we cannot compare our results with it. In the case of the PCM algorithm, they retrieve, without the use of band 3A, a POD<sub>snow</sub> of around 45%, with a FAR<sub>snow</sub> of around 10%. The SPARC algorithm shows a much better performance with a POD<sub>snow</sub> of around 98%, but a FAR<sub>snow</sub> of 13%, when comparing their model to a maximum likelihood classification using AVHRR, and using band 3A.

When including cloud edges, which are reported in the MODIS cloud mask, into the algorithm, the results yield around 2% less in OA and POD<sub>clear</sub>, and around 2% higher FAR<sub>clear</sub>. They mostly translate into more pixels having a D<sub>L</sub> close to zero that increase the misclassification. In the case of the snow detection, however, the effect of the cloud

<figure><img src="image_7.png" /><figcaption>Fig. 6. (Top) We show a histogram of the displacement to the clear land cluster of MODIS pixels. Green and red bars are those tagged as clear and cloud/snow by MYD10C1, respectively. The black dotted line represents the line that separates clear and cloud/snow according to our model. (Middle) We show the same, but using AVHRR data. (Bottom) We show their confusion matrices. Clear pixels represent land pixels that are neither cloudy nor snowy.</figcaption></figure>

edges lowers POD<sub>snow</sub> to around 80%. For this reason, we did not consider the cloud edges in this model. Potentially, they should be masked as such, and disregarded for the final data depending on the user's potential use and application.

Fig. 8 shows the final confusion matrices for the three classes using MODIS Aqua (left) and AVHRR (right) data. These results show that this model can accurately discriminate between the three classes using AVHRR data with a 96% OA, and probabilities of detection of 97%, 96%, and 89% for clear land, cloud, and snow pixels. The detection of clear and cloud pixels is of high quality, while the snow detection, as anticipated, presents confusion when discerning cloud and snow (FAR<sub>snow</sub> = 9%). The application of the model in MODIS Aqua data shows exceptional results overall (OA = 98.9%), with the mentioned errors in cloud and snow
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Analogous to Fig. 6 but for the snow cluster. In this case, the blue bars represent snow, while the red bars represent clouds.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 8. Total confusion matrices of the models applied on (Left) MODIS Aqua and (Right) AVHRR. Clear pixels mean clear land pixels. The OA is shown in the title.</figcaption></figure>

discrimination. This is not surprising considering that the model was derived using MODIS Terra data, and MODIS Aqua data are almost identical.

Fig. 9 shows the confusion matrices of the combinations between MACSSA, MODIS Aqua, and Cloud_cci AVHRR for the Cloud and No Cloud classes. The results show that

<figure><img src="image_11.png" /><figcaption>Fig. 9. Confusion matrices of the MACSSA model compared with the (Top left) MODIS Aqua, for cloud versus no cloud, (Top right) MACSSA versus the Cloud_cci AVHRR, and (Bottom left) Cloud_cci AVHRR versus MODIS Aqua.</figcaption></figure>

the agreement between MACSSA and MODIS Aqua (OA = 94.6%) is slightly better than the agreement between Cloud_cci AVHRR and MODIS Aqua (OA = 93.6%), with around 2% lower FAR$_{Nocloud}$ and a slightly higher OA. While the performances of both models compared with MODIS Aqua are similar, the actual difference between both AVHRR products is noteworthy. The overall agreement between them is of ~93%, with significant differences in the No Cloud class detection.

Following the analysis of the overall performance of the model compared with our reference, we proceed to analyze the behavior of the algorithm both spatially and temporally.

In the first place, we applied this model on global images obtained from the LTDR product to grasp the spatial behavior of the algorithm. Fig. 10 shows tags obtained using the model described in this article for a N16 image acquired on February 15, 2004 (top) and the magnitude $Ts-T4$ for the same date (bottom). We chose to show $Ts-T4$ along with the tags, so that we can visually verify the correct behavior of the algorithm when tagging clouds (higher difference means higher chance of cloud detection). Land pixels with no data or faulty information are shown in gray. Clouds are not shown in the water, because the MACSSA algorithm is intended over land pixels only. These results show that, first, the snow is detected in places where snow is expected, such as northern latitudes and Antarctica, or in mountain ridges such as the Rocky Mountains, the Himalayas, or the Alps. Second, the detection of clear land pixels is, as predicted, of good quality, and the patterns of clouds in both images are identifiably similar. Even though it cannot be easily noticed from a global image, the product presents some issues when detecting coastlines, where they are misclassified as cloud, instead of clear land.

In the second place, we applied the model to two pixels for the whole LTDR data set, to analyze the temporal behavior
<figure><img src="image_12.png" /><figcaption>Fig. 10. Tags obtained using the model described in this article for a (Top) N16 image acquired on February 15, 2004 and the (Bottom) magnitude $T_s-T_4$ for the same date. Land pixels with no data are shown in gray. Clouds are not shown in the water, because the algorithm used in this article is intended over land pixels only.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 11. Displacement to the land cluster $D_L$ of a pixel of open shrublands in Argentina (−38.65, −67.05) and the displacement to the snow cluster ($D_S$) of a snow pixel in Greenland (70.95, −46.05) for the whole time series of the LTDR product (1982–2019).</figcaption></figure>

of the model, and its consistency over the different sensors. Fig. 11 shows the displacement to the land cluster $D_L$ of a pixel of open shrublands in Argentina (38.65S, 67.05W) and the displacement to the snow cluster ($D_S$) of a snow pixel in Greenland (70.95N, 46.05W) for the whole time series (1982–2019). The results show that first, both $D_L$ and $D_S$ exhibit seasonality in their value. This is expected, given the nature of the algorithm, which is formed by bands whose values vary throughout the year. In the case of the snow pixel, during winter $D_S$ is lowest, suggesting a higher confidence in the determination of snow over cloud. Second, the results

show a consistent behavior over the different NOAA satellites used, which are displayed using different colors.

## IV. DISCUSSION

The MACSSA approach used in this article was developed using pixels distributed around the world, covering a wide range of land covers, observation, and atmospheric conditions as an input. The tags retrieved were then compared against reference tags covering, as Fig. 2 shows, almost every pixel around the world and obtaining reliable results. This serves as an indication of the overall robust performance of the model over different observation and atmospheric conditions, which can, therefore, be applied to the LTDR product to detect clear land and snow pixels to a good degree of accuracy.

Regarding the use of climatological information, we found it to be particularly useful for detecting clear land pixels, since the vegetation phenology is well captured on the monthly averages calculated. For the case of snow detection, however, climatological information provided no extra information compared with using the optical and thermal bands directly. The use of a priori information (probability of snow cover) aided in reducing the number of misclassifications, especially on pixels with a lot of cloud cover such as equatorial latitudes. Similarly, ancillary information derived from Merra-2 was useful for both clear land and snow detection. Nonetheless, limitations with these kinds of approaches arise when trying to use the model for prediction outside of the climatological time range used. The average values do not consider land cover changes and trends, very likely present in such a long time series, which would translate in increased inaccuracies in the pre-MODIS era (1982–2000).

While this effect could be very pronounced when dealing with snow detection, due to a receding snow trend in northern latitudes, in clear land pixels, the effects are mitigated. Clear land pixels combine climatological information with instantaneous multispectral data, limiting the amount of influence the trend component can have on the performance of the model.

When applying the models derived using MODIS data to AVHRR data, the performance of the product on the latter was ~2% less accurate in both models, despite our efforts to minimize these errors. This difference in performance can be attributed to calibration issues between the sensors. The individual bands were analyzed and presented very small and acceptable differences between them for coincident pixels. However, there was significant error in the computation of $T_3-T_5$, which persisted even after the spectral adjustment. This might be due to the known issues in the calibration of thermal AVHRR bands [49], [50]. Finally, since both satellites have different observation angles, it is entirely possible that for some coincident pixels, the MODIS satellite was observing a clear or snow pixel, while the NOAA satellite was observing a cloud, or vice versa, since clouds have a 3-D structure. These small differences can add up to a significant variation in performance between the two sensors.

Even so, it is important to note that in the development of this model, we considered the tags provided by MYD10C1 to be the truth, and developed the model around it. The amount to which this product can be considered the truth depends on its
validation with real measurements. The MOD10C1 product, which is used to derive the model parameters, has a 93% agreement with different ground measurements and satellite observations. This is sufficiently high for our applications, especially considering that the MOD10C1 product provides percentage clear, snow, and cloud cover [37]. This product provides significant errors only when a thin layer of snow is present. In the case of MYD10C1, band 6 (1.6 µm) of MODIS Aqua has nonfunctioning detectors, so they use band 7 (2.1 µm) instead. The results for cloud detection are almost identical to MODIS Terra; however, Hall et al. [37] reported subtle differences in the snow detection over dense forests. For the sake of our application, however, we consider these differences negligible, considering the limitations the AVHRR sensor has on discerning cloud and snow, and the potential errors provided by changes in spatial resolution when comparing instead with ground data or higher resolution products.

The comparison of the MACSSA approach to another AVHRR-derived cloud mask, shows that, while using data corrected using different algorithms, and significantly different cloud retrieval approaches, both products compare similar to the selected reference MODIS Aqua data. The direct comparison between both AVHRR products, however, shows that they are not so similar between them. Since the POD of the No Cloud class is below 90%, it is likely these differences occur mostly in the snow detection and cloud/snow discrimination. The better performance with MODIS of the MACSSA approach is expected, considering the nature of the model; however, this comes at a price. In this study, we can only detect three classes: clear land, cloud, and snow. Arguably, it can be said that we only detect two classes and that the cloud class combines everything that does not fit on the first two, which includes mostly clouds. Other algorithms using AVHRR data, however, are able to distinguish between cirrus, cirrus over snow, sea ice, thin cloud, and thick cloud [29], are more physically based, and, therefore, allow an easier physical interpretation of the model [35], or have the ability to detect clouds and snow at night [31].

While the temporal analysis indicates that the performance of the algorithm is consistent throughout the decades that the LTDR product spans, it also suggests quite visibly how the performance of a seasonal threshold could benefit the model and improve the results. This is especially true in $D_L$, where its calculation already involves some kind of seasonal threshold by means of the monthly climatological data.

Other limitations of this product include its performance over cloud edges and coastlines, which present problems in the current version of the algorithm. The recommended approach for cloud edges depends on the application. For a restrictive cloud mask, tagging cloud edges as clouds is desirable, to ensure high quality of the land pixels, at the cost of fewer observations. This cost is a small price to pay given more than 38 years of observations available in this product. For a more permissive cloud edge masking approach, the use of the displacement to the hyperplane serves as an indication of the amount of cloud contamination in a pixel. The use of the MOD09 product for the computation of the climatological clear land mask is very useful for cloud detection, but could present inaccuracies in dates before the

appearance of MODIS (2000). The higher the slope of the trend of a certain pixel, the less likely it is that the average from 2000 to 2015 represents the value of a pixel from 1982, and the higher the uncertainty involved in the process. This would effectively result in a change on the $\beta_0$ parameter of the hyperplanes derived, which can be modified and adjusted to the actual sensor of use.

Despite the limitations mentioned, the results show a clear improvement from the current LTDR product version. First, there is an improved performance of the clear land pixels detection, making use of more AVHRR bands. Second, there is an inclusion of the cloud/snow discrimination algorithm, which was previously not considered. Finally, every pixel is assigned a value of the displacement to the hyperplane that separates the classes, which can potentially be associated with the thickness of the cloud cover, or serve as an indication of the percentage of mixed features within a pixel.

Future versions of MACSSA algorithm will focus on the derivation of cloud shadow, for which a combination of a geometric and climatological approach shows promise. To exploit the nature of this algorithm fully, a formal association of the displacement to the percentage of cloud cover or the thickness of a cloud can be done using the same MYD10C1 product as truth, since it provides cloud percentage information. To solve specific problems such as the misclassification of clouds over coastlines, targeted solutions can be achieved using a *posteriori* information, so that the rest of the pixels around the globe are not affected by model modifications. The model could also be applied a third time to create a separation of clusters within the cloud cluster that could detect cirrus or thin clouds over thicker clouds. Finally, another improvement could be used to add a seasonal and trend component to the thresholds derived. The former could be applied by obtaining a different model for every month, with different hyperplane parameters, while the latter could be applied by calculating the trend component of every pixel and applying a linear correction to the seasonal thresholds derived.

V. CONCLUSION

In this article, we propose the MACSSA, whose goal is to identify clear land and snow pixels using AVHRR data. The MACSSA algorithm was designed to be applied over the LTDR product, at 0.05° spatial resolution, which covers different NOAA satellites from 1982 to 2020. The algorithm uses data from the MOD09 product, which are spectrally adjusted to look like analogous to AVHRR bands. To complete the limited information that AVHRR bands provide, we download the TS from MERRA-2 reanalysis data. After data homogenization, the data were used as input for first, an SVM model that discriminates clear land pixels from clouds and snow, and second, using only those previously tagged as clouds and snow, an SVM model to discriminate between them. We used clear, cloud, and snow percentage information from the MOD10C1 product to determine the reference land cover. These models were then applied to AVHRR data over pixels with less than 2-min overpass time difference between MODIS Aqua and NOAA16-19. We analyzed the results over pixels all around the world and over individual images, and found the product to be very accurate in identifying clear land
<table><caption>TABLE VIII
SPECTRAL ADJUSTMENT PARAMETERS FOR THE DIFFERENT SENSORS USED IN THIS STUDY FOR BAND 1</caption><thead><tr><th rowspan="2">Sensor</th><th colspan="4">B1</th></tr><tr><th>a</th><th>b</th><th>c</th><th>d</th></tr></thead><tbody><tr><td>N07</td><td>1.00E+00</td><td>1.25E-01</td><td>1.45E-04</td><td>8.53E+00</td></tr><tr><td>N09</td><td>1.11E-04</td><td>8.36E+00</td><td>1.00E+00</td><td>7.20E-02</td></tr><tr><td>N11</td><td>1.00E+00</td><td>7.62E-02</td><td>2.27E-04</td><td>7.64E+00</td></tr><tr><td>N16</td><td>9.95E-01</td><td>1.47E-01</td><td>9.02E-04</td><td>6.99E+00</td></tr><tr><td>N18</td><td>9.93E-01</td><td>1.15E-01</td><td>2.10E-03</td><td>6.07E+00</td></tr><tr><td>N19</td><td>2.70E-03</td><td>5.84E+00</td><td>9.93E-01</td><td>1.10E-01</td></tr><tr><td>Aqua</td><td>4.90E-03</td><td>5.42E+00</td><td>9.81E-01</td><td>5.85E-02</td></tr><tr><td>Terra</td><td>9.81E-01</td><td>5.78E-02</td><td>5.00E-03</td><td>5.40E+00</td></tr></tbody></table>

<table><caption>TABLE IX
ANALOGOUS TO TABLE A BUT FOR BAND 2</caption><thead><tr><th rowspan="2">Sensor</th><th colspan="4">B2</th></tr><tr><th>a</th><th>b</th><th>c</th><th>d</th></tr></thead><tbody><tr><td>N07</td><td>-1.75E-02</td><td>1.02E+00</td><td>5.68E-03</td><td>-5.80E-03</td></tr><tr><td>N09</td><td>-8.06E-03</td><td>1.01E+00</td><td>8.80E-03</td><td>-9.89E-03</td></tr><tr><td>N11</td><td>-6.97E-03</td><td>1.01E+00</td><td>9.49E-03</td><td>-1.09E-02</td></tr><tr><td>N16</td><td>1.68E-02</td><td>9.83E-01</td><td>6.17E-03</td><td>-7.33E-03</td></tr><tr><td>N18</td><td>1.69E-02</td><td>9.82E-01</td><td>1.46E-04</td><td>-1.22E-04</td></tr><tr><td>N19</td><td>1.50E-02</td><td>9.86E-01</td><td>1.64E-02</td><td>-1.94E-02</td></tr><tr><td>Aqua</td><td>5.48E-02</td><td>9.39E-01</td><td>1.13E-02</td><td>-1.28E-02</td></tr><tr><td>Terra</td><td>5.49E-02</td><td>9.39E-01</td><td>1.20E-02</td><td>-1.35E-02</td></tr></tbody></table>

<table><caption>TABLE X
ANALOGOUS TO TABLE A BUT FOR BAND 3B (THERMAL)</caption><thead><tr><th rowspan="2">Sensor</th><th colspan="2">T3B</th></tr><tr><th>a</th><th>b</th></tr></thead><tbody><tr><td>N07</td><td>9.88E-01</td><td>-1.98E-01</td></tr><tr><td>N09</td><td>9.86E-01</td><td>-2.96E-01</td></tr><tr><td>N11</td><td>9.89E-01</td><td>-3.21E-01</td></tr><tr><td>N16</td><td>9.83E-01</td><td>-5.68E-01</td></tr><tr><td>N18</td><td>9.99E-01</td><td>-2.61E-01</td></tr><tr><td>N19</td><td>9.95E-01</td><td>-3.37E-01</td></tr><tr><td>Aqua</td><td>1.01E+00</td><td>-1.05E+00</td></tr><tr><td>Terra</td><td>1.01E+00</td><td>-1.03E+00</td></tr></tbody></table>

pixels, with a POD<sub>clear</sub> of 97%. The discrimination of snow and clouds is of less quality, with a POD<sub>snow</sub> of 89%; however, considering the limited tools available in the AVHRR sensor to do this, the results are encouraging and reliable for application on daily images from the LTDR product.

The first version of the MACSSA approach used in this article comes with limitations on the amount of classes detected, misclassifications of coastlines, and especially on the detection of cloud edges. Nonetheless, future versions will aim to tackle these issues in order to provide a model that can discriminate a larger number of classes, especially within cloud types. It will also aim to provide a reliable direct association between displacement to the hyperplanes dividing the classes and cloud fraction percentage of a certain pixel, and the incorporation of a cloud shadow detection. However, these limitations are acceptable in the broader scope of this article, which aims to obtain cloud and snow information for the development of a global surface albedo data set using the LTDR product, where a very restrictive cloud mask is required and the information on different cloud types is not of great significance. This is also the case for other applications needing land pixels of the upmost quality, where the masking of clouds is essential to increase the accuracy of the results.

<table><caption>TABLE XI
ANALOGOUS TO TABLE A BUT FOR BAND 4 (THERMAL)</caption><thead><tr><th rowspan="2">Sensor</th><th colspan="4">T4</th></tr><tr><th>a</th><th>b</th><th>c</th><th>d</th></tr></thead><tbody><tr><td>N07</td><td>3.61E-05</td><td>-4.03E+00</td><td>1.00E+00</td><td>4.81E-05</td></tr><tr><td>N09</td><td>1.43E-05</td><td>-2.88E+00</td><td>1.00E+00</td><td>-2.53E-05</td></tr><tr><td>N11</td><td>3.70E-05</td><td>-3.82E+00</td><td>1.00E+00</td><td>2.21E-05</td></tr><tr><td>N16</td><td>1.33E-05</td><td>-3.74E+00</td><td>1.00E+00</td><td>3.12E-04</td></tr><tr><td>N18</td><td>2.41E-05</td><td>-2.96E+00</td><td>1.00E+00</td><td>3.82E-05</td></tr><tr><td>N19</td><td>3.08E-05</td><td>-3.47E+00</td><td>1.00E+00</td><td>2.83E-05</td></tr><tr><td>Aqua</td><td>4.29E-04</td><td>-3.97E+00</td><td>9.99E-01</td><td>5.48E-04</td></tr><tr><td>Terra</td><td>4.26E-04</td><td>-4.12E+00</td><td>9.99E-01</td><td>5.62E-04</td></tr></tbody></table>

<table><caption>TABLE XII
ANALOGOUS TO TABLE A BUT FOR BAND 5 (THERMAL)</caption><thead><tr><th rowspan="2">Sensor</th><th colspan="4">T5</th></tr><tr><th>a</th><th>b</th><th>c</th><th>d</th></tr></thead><tbody><tr><td>N07</td><td>2.71E-04</td><td>-4.04E+00</td><td>1.00E+00</td><td>-3.29E-04</td></tr><tr><td>N09</td><td>4.69E-04</td><td>-3.65E+00</td><td>9.99E-01</td><td>-5.87E-04</td></tr><tr><td>N11</td><td>4.35E-04</td><td>-3.46E+00</td><td>9.99E-01</td><td>-4.65E-04</td></tr><tr><td>N16</td><td>1.00E+00</td><td>6.06E-05</td><td>-1.94E-04</td><td>-2.09E+00</td></tr><tr><td>N18</td><td>1.00E+00</td><td>1.32E-04</td><td>-1.39E-04</td><td>-2.69E+00</td></tr><tr><td>N19</td><td>1.00E+00</td><td>3.35E-04</td><td>-4.29E-04</td><td>-2.97E+00</td></tr><tr><td>Aqua</td><td>1.06E-03</td><td>-2.52E+00</td><td>9.99E-01</td><td>-4.07E-04</td></tr><tr><td>Terra</td><td>1.04E-03</td><td>-2.56E+00</td><td>9.99E-01</td><td>-4.25E-04</td></tr></tbody></table>

<table><caption>TABLE XIII
PARAMETERS USED FOR THE SVM CLASSIFICATION CLEAR LAND MODEL</caption><thead><tr><th colspan="2">Clear Land model</th></tr></thead><tbody><tr><td>BoxConstraint</td><td>456.24</td></tr><tr><td>KernelScale</td><td>259.2</td></tr><tr><td>Standardize</td><td>True</td></tr><tr><td>KernelFunction</td><td>Linear</td></tr></tbody></table>

<table><caption>TABLE XIV
SAME AS TABLE B1 BUT FOR THE SNOW/CLOUD MODEL</caption><thead><tr><th colspan="2">Snow/Cloud model</th></tr></thead><tbody><tr><td>BoxConstraint</td><td>0.034</td></tr><tr><td>KernelScale</td><td>0.267</td></tr><tr><td>Standardize</td><td>True</td></tr><tr><td>KernelFunction</td><td>Polynomial</td></tr><tr><td>PolynomialOrder</td><td>2</td></tr></tbody></table>

## APPENDIX A

Tables VIII–XII show the spectral adjustment parameters for the different sensors used in this study, using NOAA14 as a reference. The equations used for each band can be found in (1)–(4). The band wavelengths can be found in Table I.

## APPENDIX B

The classification SVM models for this article were made using the programming software MATLAB’s machine learning toolbox. The specific parameters used as inputs for the SVM function fitcsvm.m [51] are shown in Tables XIII and XIV.

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<figure><img src="image_14.png" /></figure>

**Belen Franch** received the Ph.D. degree in physics from the University of Valencia, Valencia, Spain, in 2013.

She is a Distinguished Researcher with the University of Valencia and an Associate Adjunct Professor with the Department of Geographical Sciences, University of Maryland, College Park, MD, USA. She is the co-lead of the yield monitoring working group of the NASA Harvest program and is a member of the ExCom of the GEOGLAM initiative. Her research interests include agriculture monitoring, atmospheric correction in the solar spectral range, the study and application of BRDF inversion methods, and land surface albedo estimation and analysis.

<figure><img src="image_15.png" /></figure>

**Andrés E. Santamaría-Artigas** received the B.S. degree in sciences of the renewable natural resources and the engineering degree in renewable natural resources from the University of Chile, Santiago, Chile, in 2012 and 2015, respectively. He is pursuing the doctorate degree with the Department of Geographical Sciences, University of Maryland, College Park, MD, USA.

He is a Research Scientist with Terrestrial Information Systems Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD. His research interests include calibration and validation of remote sensors, aerosol retrieval, radiative transfer, and data assimilation

<figure><img src="image_16.png" /></figure>

**Jean-Claude Roger** received the Ph.D. degree in atmospheric physics from the University of Lille 1, Lille, France, in 1991, for a thesis on "Spatial Studies in Polarized Light-Preparation of the POLDER instrument."

He became a Full Professor of atmospheric physics at the University Blaise Pascal, Clermont-Ferrand, France, in 2007. He works as a Research Professor at the Department of Geographical Sciences, University of Maryland, College Park, MD, USA. He also works at the NASA Goddard Space Flight Center, code 619, Greenbelt, MD. He does research on land and atmosphere applications (remote sensing, radiative transfer, polarization, field experiments, etc.). He is particularly involved in atmospheric correction, aerosols characterization for climatic impact, land product with application to agriculture, satellite Cal/Val exercises, and radiative transfer code development like 6S.

Dr. Roger is a Co-Pi of the CEOS-WGCV ACIX and CEOS-WGCV ACIX II-CMIX.

<figure><img src="image_17.png" /></figure>

**Jose Luis Villaescusa-Nadal** received the bachelor's degree in physics and the M.Sc. degree in remote sensing from the University of Valencia, Valencia, Spain, in 2015 and 2016, respectively, and the Ph.D. degree in geographical sciences from the University of Maryland, College Park, MD, USA, in 2020.

He works as a Post-Doctoral Associate with the University of Maryland, and NASA Goddard Space Flight Centre (GSFC), Greenbelt, MD. His research interests include cross calibration methods, BRDF correction, and land surface albedo retrieval, specifically for global studies application using coarse spatial resolution sensors.

<figure><img src="image_18.png" /></figure>

**Eric Vermote** (Member, IEEE) received the Ph.D. degree in atmospheric optics from the University of Lille, Lille, France, in 1990.

Until 2012, he was a Research Professor with the Department of Geographical Sciences, University of Maryland, College Park, MD, USA. He is a Research Physical Scientist with Terrestrial Information Systems Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD. He is a member of the Moderate Resolution Imaging Spectroradiometer Science Team, the NASA National Polar orbiting

Operational Environmental Satellite System Preparatory Project Science Team for the Visible Infrared Imaging Radiometer Suite instrument, and the Landsat Data Continuity Mission Science Team and is responsible for the atmospheric correction over land surfaces in the visible to middle infrared. His research interests are in radiative transfer modeling, vicarious calibration, atmospheric correction, aerosol retrieval, and the generation of climate data record for terrestrial studies.

<figure><img src="image_19.png" /></figure>

**Sergii Skakun** received the M.S. degree (Hons.) in applied mathematics from the Physics and Technology Institute, NTUU "Kyiv Polytechnic Institute," Kyiv, Ukraine, in 2004, and the Ph.D. degree in computer science from the National Academy of Sciences of Ukraine, Kyiv, in 2005.

He is an Assistant Professor at the Department of Geographical Sciences and College of Information Studies (iSchool), University of Maryland, College Park, MD, USA, and a Research Scientist at Terrestrial Information Systems Laboratory, NASA Goddard Space Flight Center (GSFC), Greenbelt, MD. His research interests are in advancing methods, models and emerging technologies in the area of data science for heterogeneous remote sensing data fusion, processing and analysis, and their applications to the areas of societal benefit.

Dr. Skakun is an Associate Editor of the *Remote Sensing of Environment*.