Impact of Changes in Minimum Reﬂectance on Cloud Discrimination

: Greenhouse Gases Observing SATellite-2 (GOSAT-2) will be launched in ﬁscal year 2018. GOSAT-2 will be equipped with two Earth-observing instruments: the Thermal and Near-infrared Sensor for carbon Observation Fourier Transform Spectrometer 2 (TANSO-FTS-2) and TANSO-Cloud and Aerosol Imager 2 (CAI-2). CAI-2 can be used to perform cloud discrimination in each band. The cloud discrimination algorithm uses minimum reﬂectance (R min ) for comparisons with observed top-of-atmosphere reﬂectance. The creation of cloud-free R min requires 10 CAI or CAI-2 data. Thus, R min is created from CAI L1B data for a 30-day period in GOSAT, with a revisit time of 3 days. It is necessary to change the way in which 10 observations are chosen for GOSAT-2, which has a revisit time of 6 days. Additionally, R min processing for GOSAT CAI data was updated to version 02.00 in December 2016. Along with this change, the resolution of R min changed from 1/30 ◦ to 500 m. We examined the impact of changes in R min on cloud discrimination results using GOSAT CAI data. In particular, we performed comparisons of: (1) R min calculated using different methods to choose the 10 observations and (2) R min calculated using different generation procedures and spatial resolutions. The results were as follows: (1) The impact of using different methods to choose the 10 observations on cloud discrimination results was small, except for a few cases, e.g., snow-covered regions and sun-glint regions; (2) Cloud discrimination results using R min in version 02.00 were better than results obtained using R min in the previous version, apart from some special situations. The main causes of this were as follows: (1) The change of used band from band 2 to band 1 for R min calculation; (2) The change of spatial resolution of R min from 1/30 ◦ to 500-m.


Introduction
Greenhouse gases Observing SATellite-2 (GOSAT-2) will be launched in fiscal year 2018.GOSAT-2 will be equipped with two Earth-observing instruments: the Thermal and Near-infrared Sensor for carbon Observation Fourier Transform Spectrometer 2 (TANSO-FTS-2) and the TANSO-Cloud and Aerosol Imager 2 (CAI-2).CAI-2 is a push-broom imaging sensor that has forward-and backward-looking bands (±20 • ) for observing the optical properties of aerosols and clouds and for monitoring the status of transboundary air pollution over oceans to avoid sun-glint.In contrast, the existing GOSAT TANSO-CAI obtains measurements at a fixed angle close to the nadir [1].An important function of CAI-2 is cloud discrimination using each band to identify and reject cloud-contaminated FTS-2 data; the presence of clouds in the instantaneous field-of-view (IFOV) of FTS-2 leads to errors in estimates of atmospheric greenhouse gas concentrations.For GOSAT CAI L2 cloud flag products, the Cloud and Aerosol Unbiased Decision Intellectual Algorithm (CLAUDIA1) [2,3] is used.For GOSAT-2 CAI-2 L2 cloud discrimination products, CLAUDIA3 [4] with support vector machines, a supervised pattern recognition method, is used [5].CLAUDIA3 can determine the hyperplane in high dimensional feature space indicates the importance of features for cloud discrimination, which optimally separates a typical cloud and clear-sky training data in feature space [4].
We have previously considered various aspects of CAI-2 L2 cloud discrimination products.We evaluated the accuracy of obtaining cloud-free FTS-2 data with a narrow IFOV, which is expected to decrease the probability of cloud contamination in the IFOV of FTS-2, but could potentially increase the underestimation of CO 2 concentrations by overlooking small clouds [6].We also performed a usability evaluation of the graphics processing unit (GPU) for cloud discrimination processing.The results suggested that CPU and GPU hybrid parallel processing for cloud discrimination will increase in the future, as the data transfer speed between the host and device memory becomes faster [7].The observed time difference between FTS-2 and CAI-2 may be longer than that between FTS and CAI because the CAI-2 has forward-and backward-looking bands, in contrast to observations at the nadir using CAI.Consequently, we examined the probability of cloud contamination within the IFOV of the FTS-2 from cloud moving into the area after cloud-free observation by CAI-2 and proposed a method for cloud discrimination by screening cloud-contaminated FTS-2 data against CAI-2 data [8].Cloud discrimination in sun-glint regions over the ocean is particularly challenging.It is effective to use forward and backward cloud discrimination in areas that do not include sun-glint regions.This strategy is based on the assumption that forward and backward cloud discrimination results have the same accuracy.Under this situation, we examined the difference between forward and backward cloud discrimination using CLAUDIA1 with the Multi-angle Imaging SpectroRadiometer (MISR) aboard Terra, which provides radiometrically and geometrically calibrated images for spectral bands at nine widely spaced angles [9].Furthermore, we examined the impact of different support vectors on cloud discrimination products by analyzing the impacts of the time period for obtaining training data and the generation procedure for support vectors on the cloud discrimination efficiency [5].Thus, comparisons between CLAUDIA1 and CLAUDIA3 are ongoing.
Both CLAUDIA1 and CLAUDIA3 use minimum reflectance data (R min ) for comparisons with observed top-of-atmosphere (TOA) reflectance because R min is assumed to reflect observations under cloud-free and aerosol-free conditions.Generally, the cloud reflectance is greater than R min , except over snow, ice, or some desert soils [10].Therefore some existing studies also used R min for estimation of TOA clear-sky reflectance [11] and cloud cover index which can be interpreted as the percentage of the cloud cover per pixel [10,12].For the same reason, R min has also been used to estimate aerosol optical depth [13].For cloud discrimination, both CLAUDIA1 and CLAUDIA3 use R min for the near infrared (NIR) band in land regions and R min for the visible red band in water regions.To use R min can remove the effect of surfaces, but it will cause misjudgment if clouds or cloud shadows remain in R min .If all used pixel is cloud to create R min , cloud pixels remain in R min ('cloud remains' hereafter).Cloud remains in R min cause to overlook clouds.Obtaining cloud-free R min requires 10 CAI or CAI-2 observations [14].Thus, R min is created from CAI L1B data over 30 days in GOSAT, with a revisit time of 3 days.However, it is necessary to change the method for choosing the 10 observations with a change in the revisit time to 6 days in GOSAT-2.R min processing for GOSAT CAI data was updated to version 02.00 in December of 2016, changing the resolution of R min from 1/30 • to 500 m.Accordingly, we examined the impact of changes in R min on CLAUDIA1 results using GOSAT CAI data; CLAUDIA3 uses hyperplanes and therefore the impact of R min is not direct.The examinations consisted of two parts: (i) comparisons of R min calculated using different methods to choose the 10 observations and (ii) comparisons of R min calculated using different generation procedures and different spatial resolutions.

Satellite Data
We used GOSAT CAI Level 1B products, which can be downloaded from GOSAT Data Archive Service (GDAS, https://data2.gosat.nies.go.jp/index_en.html).GOSAT returns to a similar footprint after 44 orbits (44 CAI paths) in 3 days.The satellite ground path of one orbit is divided into 60 equidistant CAI frames.The study area and data period were the same as those used in a previous study [5] (Figure 1; Table 1).The spatial resolution of these products (pixel size at the nadir) was 500 m and the image size was 2048 × 1355 pixels (approximately 1000 × 680 km) (Table 2).

Satellite Data
We used GOSAT CAI Level 1B products, which can be downloaded from GOSAT Data Archive Service (GDAS, https://data2.gosat.nies.go.jp/index_en.html).GOSAT returns to a similar footprint after 44 orbits (44 CAI paths) in 3 days.The satellite ground path of one orbit is divided into 60 equidistant CAI frames.The study area and data period were the same as those used in a previous study [5] (Figure 1; Table 1).The spatial resolution of these products (pixel size at the nadir) was 500 m and the image size was 2048 × 1355 pixels (approximately 1000 × 680 km) (Table 2).Table 1.GOSAT CAI Level 1B product used in this study.Land cover was derived from the MODerate resolution Imaging Spectroradiometer (MODIS) land cover type product (MCD12).Japan scenes include urban areas.

Methods to Choose the 10 Observations
In this section, we describe three different methods to choose the 10 observations.Although R min is created from the CAI L1B data for the past 30 days in GOSAT, with a revisit time of 3 days, R min for GOSAT-2 is calculated using data obtained over 60 days with a recurrent cycle of 6 days.We compared CLAUDIA1 results obtained using three different methods to choose the 10 observations, i.e., the past one month for GOSAT (−1 month), one month before and after for GOSAT-2 (±1 month), and past two months for GOSAT-2 (−2 months) (Figure 2).The generation procedure for these comparisons is referred to as Procedure 1.

Methods to Choose the 10 Observations
In this section, we describe three different methods to choose the 10 observations.Although Rmin is created from the CAI L1B data for the past 30 days in GOSAT, with a revisit time of 3 days, Rmin for GOSAT-2 is calculated using data obtained over 60 days with a recurrent cycle of 6 days.We compared CLAUDIA1 results obtained using three different methods to choose the 10 observations, i.e., the past one month for GOSAT (−1 month), one month before and after for GOSAT-2 (±1 month), and past two months for GOSAT-2 (−2 months) (Figure 2).The generation procedure for these comparisons is referred to as Procedure 1.

Rmin Generation Procedure for Cloud and Aerosol Imager
In this section, we describe the Rmin generation procedures.Rmin at a 1/30° resolution (hereafter Rmin1) is generated by the following procedure for CAI version 01.00 (Procedure 1) (Figure 3).
First, steps (i)-(iii) are performed for each CAI L1B product.
i. Separate land and water regions using land/sea flag in CAI L1B products The land/sea flag is generated from the Shuttle Radar Topography Mission's (SRTM) 15 arcseconds land/sea mask [15] and U.S. Geological Survey (USGS) Global Land 1-KM Advanced Very High Resolution Radiometer (AVHRR) Project data [16] for areas with latitudes higher than ±60°.ii.
Calculate the minimum TOA reflectance for band 2 for every mesh, treating land and water regions as distinct.
Next, steps (iv)-(v) are performed using 10 CAI L1B products for each mesh. iv.
Calculate the minimum and second-minimum TOA reflectance for each mesh using the results of step (ii) v.
Correct for cloud shadows by using the minimum and second-minimum TOA reflectance calculated in step (iv).Cloud shadow correction method, as follows: where R1st and R2nd indicate the minimum and second-minimum reflectance, respectively; R1st,bandn indicates the minimum reflectance of band n [17] Cloud shadow correction is also necessary because cloud shadows remain in Rmin causes to misjudge clear-sky pixels as cloud pixels.

R min Generation Procedure for Cloud and Aerosol Imager
In this section, we describe the R min generation procedures.R min at a 1/30 • resolution (hereafter R min 1) is generated by the following procedure for CAI version 01.00 (Procedure 1) (Figure 3).
First, steps (i)-(iii) are performed for each CAI L1B product.
i. Separate land and water regions using land/sea flag in CAI L1B products The land/sea flag is generated from the Shuttle Radar Topography Mission's (SRTM) 15 arcseconds land/sea mask [15] and U.S. Geological Survey (USGS) Global Land 1-KM Advanced Very High Resolution Radiometer (AVHRR) Project data [16] for areas with latitudes higher than ±60 • .ii. Divide region into 1/30 • meshes.iii.Calculate the minimum TOA reflectance for band 2 for every mesh, treating land and water regions as distinct.
Next, steps (iv)-(v) are performed using 10 CAI L1B products for each mesh.
iv. Calculate the minimum and second-minimum TOA reflectance for each mesh using the results of step (ii) v.
Correct for cloud shadows by using the minimum and second-minimum TOA reflectance calculated in step (iv).Cloud shadow correction method, as follows: where R 1st and R 2nd indicate the minimum and second-minimum reflectance, respectively; R 1st,bandn indicates the minimum reflectance of band n [17] Cloud shadow correction is also necessary because cloud shadows remain in R min causes to misjudge clear-sky pixels as cloud pixels.
The R min generation procedure for CAI version 02.00 (Procedure 2) differs from Procedure 1 as follows: it includes the addition of a simple cloud screening test; the use of band 1, rather than band 2, to calculate the minimum TOA reflectance; steps (ii)-(iii) are not performed in Procedure 2; and an iterative process for (iv)-(v) is performed.R min at a 500-m spatial resolution (hereafter, R min 2) was calculated.The Rmin generation procedure for CAI version 02.00 (Procedure 2) differs from Procedure 1 as follows: it includes the addition of a simple cloud screening test; the use of band 1, rather than band 2, to calculate the minimum TOA reflectance; steps (ii)-(iii) are not performed in Procedure 2; and an iterative process for (iv)-(v) is performed.Rmin at a 500-m spatial resolution (hereafter, Rmin2) was calculated.

Comparative Analysis
In this section, we describe evaluation indices used in this study.In this study, "degree of agreement (DA)" was defined as the ratio of the number of pixels for which the standard image and output from the cloud discrimination algorithm agreed to the total number of pixels in the input image."Overlook" was defined as the ratio of the number of pixels identified as clear-sky in the output and cloudy in the standard image to the number of pixels that were identified as cloudy in the standard image."Overestimate" was defined as the ratio of the number of pixels identified as cloudy in the output and clear-sky in the standard image to the number of pixels identified as clear-sky in the standard image.Each was defined by the following equations (the std subscript indicates standard results):

Comparison among Methods to Choose the 10 Observations
We compared Rmin calculated using different methods to choose the 10 observations.Figure 4 shows the averaged Rmin for each CAI scene generated using these different methods, i.e., −1 month, −2 months, and ±1 month.
In Australia, Borneo, and Algeria, there were no marked seasonal changes or differences between −1 month Rmin, −2 months Rmin, and ±1 month Rmin.In Japan and Thailand, every Rmin for band 3 in the summer for the Northern Hemisphere was greater than those for the other seasons due to seasonal vegetation changes.In Japan, Mongolia, Canada, and Alaska, every Rmin for both bands 2 and 3 in the winter for the Northern Hemisphere was greater than those in the other seasons due to snow or ice cover.
Figure 5 shows comparative cloud discrimination results using various methods to choose the 10 observations.

Comparative Analysis
In this section, we describe evaluation indices used in this study.In this study, "degree of agreement (DA)" was defined as the ratio of the number of pixels for which the standard image and output from the cloud discrimination algorithm agreed to the total number of pixels in the input image."Overlook" was defined as the ratio of the number of pixels identified as clear-sky in the output and cloudy in the standard image to the number of pixels that were identified as cloudy in the standard image."Overestimate" was defined as the ratio of the number of pixels identified as cloudy in the output and clear-sky in the standard image to the number of pixels identified as clear-sky in the standard image.Each was defined by the following equations (the std subscript indicates standard results):

Comparison among Methods to Choose the 10 Observations
We compared R min calculated using different methods to choose the 10 observations.Figure 4 shows the averaged R min for each CAI scene generated using these different methods, i.e., −1 month, −2 months, and ±1 month.
In Australia, Borneo, and Algeria, there were no marked seasonal changes or differences between −1 month R min , −2 months R min , and ±1 month R min .In Japan and Thailand, every R min for band 3 in the summer for the Northern Hemisphere was greater than those for the other seasons due to seasonal vegetation changes.In Japan, Mongolia, Canada, and Alaska, every R min for both bands 2 and 3 in the winter for the Northern Hemisphere was greater than those in the other seasons due to snow or ice cover.
Figure 5 shows comparative cloud discrimination results using various methods to choose the 10 observations.In Australia, Borneo, and Thailand (Path 9, Frame 28), DA between −1 month, ±1 month, and −2 months was always greater than 99%, suggesting that there was no difference between methods.In Japan, there was a slight difference (the lowest DA was 97.4%) in cloud discrimination results among methods.In Algeria, there was a difference (the lowest DA was 95.8%) in cloud discrimination results.In Thailand (Path 9, Frame 29), there was a difference in cloud discrimination results in October (the lowest DA was 96.4%).In Mongolia, Canada, and Alaska, there was a difference (the lowest DA was 54.3%) among R min methods with snow or ice.In Australia, Borneo, and Thailand (Path 9, Frame 28), DA between −1 month, ±1 month, and −2 months was always greater than 99%, suggesting that there was no difference between methods.In Japan, there was a slight difference (the lowest DA was 97.4%) in cloud discrimination results among methods.In Algeria, there was a difference (the lowest DA was 95.8%) in cloud discrimination results.In Thailand (Path 9, Frame 29), there was a difference in cloud discrimination results in October (the lowest DA was 96.4%).In Mongolia, Canada, and Alaska, there was a difference (the lowest DA was 54.3%) among Rmin methods with snow or ice.

Comparison among Different Generation Procedures
We compared Rmin calculated using different generation procedures.Figure 6 shows the averaged Rmin in each CAI scene for various land cover types.
Rmin1 of band 2 was lower than Rmin2 of band 2 because the minimum TOA reflectance in 1/30° meshes was calculated using band 2 in Procedure 1 and the minimum TOA reflectance in each pixel was calculated in Procedure 2.
Rmin1 of band 3 was greater than Rmin2 of band 3 in Japan, Borneo, and Thailand.In Japan, Mongolia, Canada, and Alaska, both bands 2 and 3 in the winter for the Northern Hemisphere were greater than those in other seasons due to snow or ice cover.
In Figure 7, for Overlook and Overestimate, cloud discrimination results using Rmin1 were used as standard images.Overlook was greater than Overestimate, except in Canada.This means that Rmin2 tends to identify clear-sky more frequently than Rmin1.This can be explained by the following reasons.

i.
Rmin1 of band 2 is lower than Rmin2 of band 2. ii.
Rmin of band 2 is used for cloud discrimination on land regions.Land pixels occupy most of the test scenes.
There were also water pixels and some complex effects, such as cloud remains in Rmin, the difference between bands used to generate Rmin, and a simple cloud screening test of Procedure 2 (Figure 8).

Comparison among Different Generation Procedures
We compared R min calculated using different generation procedures.Figure 6 shows the averaged R min in each CAI scene for various land cover types.
R min 1 of band 2 was lower than R min 2 of band 2 because the minimum TOA reflectance in 1/30 • meshes was calculated using band 2 in Procedure 1 and the minimum TOA reflectance in each pixel was calculated in Procedure 2.
R min 1 of band 3 was greater than R min 2 of band 3 in Japan, Borneo, and Thailand.In Japan, Mongolia, Canada, and Alaska, both bands 2 and 3 in the winter for the Northern Hemisphere were greater than those in other seasons due to snow or ice cover.
In Figure 7, for Overlook and Overestimate, cloud discrimination results using R min 1 were used as standard images.Overlook was greater than Overestimate, except in Canada.This means that R min 2 tends to identify clear-sky more frequently than R min 1.This can be explained by the following reasons.

i.
R min 1 of band 2 is lower than R min 2 of band 2. ii.R min of band 2 is used for cloud discrimination on land regions.Land pixels occupy most of the test scenes.
There were also water pixels and some complex effects, such as cloud remains in R min , the difference between bands used to generate R min , and a simple cloud screening test of Procedure 2 (Figure 8).
In Australia and Algeria, which have highly reflective surfaces, Overlook was always high (average Overlook was 36.4%),regardless of the season.DA in Alaska was lower than that in the other regions.In Japan, Mongolia and Canada, Overlook in the winter for the Northern Hemisphere was greater than that in the other seasons, so that DA in winter was lower than that in the other seasons.In Australia and Algeria, which have highly reflective surfaces, Overlook was always high (average Overlook was 36.4%),regardless of the season.DA in Alaska was lower than that in the other regions.In Japan, Mongolia and Canada, Overlook in the winter for the Northern Hemisphere was greater than that in the other seasons, so that DA in winter was lower than that in the other seasons.

Differences among Methods Used to Choose the 10 Observations
First, we discuss the differences in Rmin with respect to the method used to obtain the 10 observations (Figure 4).In Thailand, ±1 month Rmin was lower than −1 month Rmin and −2 months Rmin in October.This may explain why Rmin in November was lower than that in summer in the Northern Hemisphere.In other words, ±1 month Rmin preempts the Rmin decline due to seasonal vegetation changes.In the same way, ±1 months Rmin preempts the thawing of snow in Alaska in July.Conversely, −2 months Rmin was lower than −1 month Rmin and ±1 month Rmin in Mongolia in January and in Canada in November.This means that −2 months Rmin included data for areas before any snowfall.
Second, we discuss cloud discrimination using Rmin obtained by different methods for choosing the 10 observations (Figure 5).In Japan, there was a slight difference in cloud discrimination results that could be explained by overlooked optically thin clouds in each result.This was explained by the use of Rmin for cloud remains over the ocean (Figure 9).
In Algeria, there was a difference in cloud discrimination results due to the overestimation of clouds (Figure 5) arising from the use of Rmin values when cloud shadow is present (Figure 10).

Differences among Methods Used to Choose the 10 Observations
First, we discuss the differences in R min with respect to the method used to obtain the 10 observations (Figure 4).In Thailand, ±1 month R min was lower than −1 month R min and −2 months R min in October.This may explain why R min in November was lower than that in summer in the Northern Hemisphere.In other words, ±1 month R min preempts the R min decline due to seasonal vegetation changes.In the same way, ±1 months R min preempts the thawing of snow in Alaska in July.Conversely, −2 months R min was lower than −1 month R min and ±1 month R min in Mongolia in January and in Canada in November.This means that −2 months R min included data for areas before any snowfall.
Second, we discuss cloud discrimination using R min obtained by different methods for choosing the 10 observations (Figure 5).In Japan, there was a slight difference in cloud discrimination results that could be explained by overlooked optically thin clouds in each result.This was explained by the use of R min for cloud remains over the ocean (Figure 9).
In Algeria, there was a difference in cloud discrimination results due to the overestimation of clouds (Figure 5) arising from the use of R min values when cloud shadow is present (Figure 10).
In Thailand (Path 9, Frame 29), there was a difference in cloud discrimination results in October (Figure 5).The −2 months R min was generated from CAI data from the beginning of August to the beginning of October, −1 month R min was generated from CAI L1B data from the beginning of September to the beginning of October, and ±1 month R min was generated from CAI L1B data from the beginning of September to late October.There were sun-glint regions over the ocean until the beginning of October in this area (Figure 11).Cloud discrimination results overlook optically thin clouds when R min was generated from only the sun-glint period.
In Mongolia, Canada, and Alaska, there was a difference in R min depending on snow or ice (Figure 5).In particular, there was a difference between R min generated from CAI data during only the snow-covered period and R min generated from CAI data including the period after snow melting.The former had a tendency to overlook clouds, and the latter had a tendency to misjudge snow and ice as clouds.In Thailand (Path 9, Frame 29), there was a difference in cloud discrimination results in October (Figure 5).The −2 months Rmin was generated from CAI data from the beginning of August to the beginning of October, −1 month Rmin was generated from CAI L1B data from the beginning of September to the beginning of October, and ±1 month Rmin was generated from CAI L1B data from the beginning of September to late October.There were sun-glint regions over the ocean until the beginning of October in this area (Figure 11).Cloud discrimination results overlook optically thin clouds when Rmin was generated from only the sun-glint period.In Mongolia, Canada, and Alaska, there was a difference in Rmin depending on snow or ice (Figure 5).In particular, there was a difference between Rmin generated from CAI data during only the snow-covered period and Rmin generated from CAI data including the period after snow melting.The former had a tendency to overlook clouds, and the latter had a tendency to misjudge snow and ice as clouds.

Discussion of the Differences of Rmin among Generation Procedures
In this section, we evaluated differences in Rmin depending on the generation procedure (Figure 6).Rmin1 of band 3 was greater than Rmin2 of band 3 in Japan, Borneo, and Thailand.Vegetation has a low reflectance in the visible red band and high reflectance in the NIR band.Thus, estimates of Rmin using band 2 have a tendency to select vegetation pixels.Accordingly, Rmin1 of band 3 was greater than Rmin2 of band 3 in regions with high vegetation cover.In Japan and Thailand, Rmin for band 3 from spring to autumn in the Northern hemisphere was greater than that in the other seasons due to seasonal vegetation changes.
Neither Rmin1 nor Rmin2 could remove clouds in regions with a high cloud cover ratio or cloud shadows on regions with high surface reflectance.In general, tropical rainforests have a high cloud cover ratio due to evaporation along with photosynthesis of vegetation.As shown in Figure 12a,b, many clouds remain in both Rmin1 and Rmin2, although Rmin1 was smoothed somewhat owing to its lower spatial resolution than that of Rmin2.For desert regions, there were whitish pixels for which Rmin of band 1 was greater than that around pixels in a RGB composite image of Rmin1 (Figure 12d).The Rmin generation procedure using band 2 could not remove optically thin clouds in highly reflective regions.Furthermore, both Rmin1 and Rmin2 could not remove cloud shadows in highly reflective regions (Figure 12d,e).

Discussion of the Differences of R min among Generation Procedures
In this section, we evaluated differences in R min depending on the generation procedure (Figure 6).R min 1 of band 3 was greater than R min 2 of band 3 in Japan, Borneo, and Thailand.Vegetation has a low reflectance in the visible red band and high reflectance in the NIR band.Thus, estimates of R min using band 2 have a tendency to select vegetation pixels.Accordingly, R min 1 of band 3 was greater than R min 2 of band 3 in regions with high vegetation cover.In Japan and Thailand, R min for band 3 from spring to autumn in the Northern hemisphere was greater than that in the other seasons due to seasonal vegetation changes.
Neither R min 1 nor R min 2 could remove clouds in regions with a high cloud cover ratio or cloud shadows on regions with high surface reflectance.In general, tropical rainforests have a high cloud cover ratio due to evaporation along with photosynthesis of vegetation.As shown in Figure 12a,b, many clouds remain in both R min 1 and R min 2, although R min 1 was smoothed somewhat owing to its lower spatial resolution than that of R min 2. For desert regions, there were whitish pixels for which R min of band 1 was greater than that around pixels in a RGB composite image of R min 1 (Figure 12d).The R min generation procedure using band 2 could not remove optically thin clouds in highly reflective regions.Furthermore, both R min 1 and R min 2 could not remove cloud shadows in highly reflective regions (Figure 12d,e).

Discussion of the Differences of Cloud Discrimination Results among Generation Procedures
In this section, we evaluated cloud discrimination using Rmin obtained by different generation procedures (Figure 7).

Highly Reflective Surface
In Australia and Algeria, which have highly reflective surfaces, Overlook was always high, regardless of the season.Rmin2 results had a tendency to overlook optically thin clouds in comparison

Discussion of the Differences of Cloud Discrimination Results among Generation Procedures
In this section, we evaluated cloud discrimination using R min obtained by different generation procedures (Figure 7).

Highly Reflective Surface
In Australia and Algeria, which have highly reflective surfaces, Overlook was always high, regardless of the season.R min 2 results had a tendency to overlook optically thin clouds in comparison with R min 1 results (Figure 13).On the other hand, the local highly reflective surface where R min 1 incorrectly identified clouds was slightly improved in the R min 2 results (Figure 14).Procedure 1 chooses lower TOA reflectance pixels in 1/30 • meshes when there is a local highly reflective surface.For this reason, R min 2 results have a tendency to overlook optically thin clouds and R min 1 results have a tendency to overestimate local high reflectance surfaces as clouds in regions with highly reflective surfaces.However, there are few cases in which cloud shadows cause the misidentification of highly reflective surfaces as cloudy.

Snow or Ice
In Japan, Mongolia, and Canada, DA in winter of the Northern Hemisphere was lower than that in the other seasons (Figure 7).Since the CAI is not equipped with thermal infrared bands, cloud discrimination based on the temperature at the top of clouds is not feasible.Accordingly, it is difficult to discriminate between clouds and ice or snow [5].The lower DA in Alaska than that in the other regions (Figure 7) can be attributed to the same source of error.However, regions with ice and snow, where R min 1 results were misidentified as clouds, were slightly improved in R min 2 (Figure 15).This can be explained by the tendency for R min 1 to be lower than R min 2, and cases in which R min 1 chooses pixels lacking snow around snow pixels in 1/30 • meshes (Figure 16).In Japan, Mongolia, and Canada, DA in winter of the Northern Hemisphere was lower than that in the other seasons (Figure 7).Since the CAI is not equipped with thermal infrared bands, cloud discrimination based on the temperature at the top of clouds is not feasible.Accordingly, it is difficult to discriminate between clouds and ice or snow [5].The lower DA in Alaska than that in the other regions (Figure 7) can be attributed to the same source of error.However, regions with ice and snow, where Rmin1 results were misidentified as clouds, were slightly improved in Rmin2 (Figure 15).This can be explained by the tendency for Rmin1 to be lower than Rmin2, and cases in which Rmin1 chooses pixels lacking snow around snow pixels in 1/30° meshes (Figure 16).

Cloud Remain
In some cases, R min 2 was lower than R min 1 according to cloud remains in R min due to the high cloud cover ratio, which caused Overestimate (Figure 17).Overestimates in Canada and Alaska were greater than those in the other regions (Figure 7).Canada and Alaska, there was abundant snow or ice; accordingly, there were not almost areas that were judged as clear-sky areas in the R min 1 results.Therefore, when few clear-sky pixels in the R min 1 results changed to cloudy pixels in the R min 2 results, Overestimate was greater, according to the definition.In some cases, Rmin2 was lower than Rmin1 according to cloud remains in Rmin due to the high cloud cover ratio, which caused Overestimate (Figure 17).Overestimates in Canada and Alaska were greater than those in the other regions (Figure 7).Canada and Alaska, there was abundant snow or ice; accordingly, there were not almost areas that were judged as clear-sky areas in the Rmin1 results.Therefore, when few clear-sky pixels in the Rmin1 results changed to cloudy pixels in the Rmin2 results, Overestimate was greater, according to the definition.In Borneo and Thailand, in some cases, Rmin2 results overlooked optically thin clouds, even though Rmin1 results could identify the clouds over land regions, according to cloud remains in Rmin, due to a high cloud cover ratio (Figure 18).These cases on low reflectance surface were opposite from cases with highly reflective surfaces shown in Figure 17.In Borneo and Thailand, in some cases, R min 2 results overlooked optically thin clouds, even though R min 1 results could identify the clouds over land regions, according to cloud remains in R min , due to a high cloud cover ratio (Figure 18).These cases on low reflectance surface were opposite from cases with highly reflective surfaces shown in Figure 17.

The Boundaries between Land and Water
There were unexpected Rmin1 results in which clear-sky pixels were misidentified as clouds over water regions near the boundaries between land and water; however, Rmin2 results could identify these areas as clear sky (Figure 19).Procedure 1 chooses surrounding water pixels because its spatial resolution is 1/30° when there are mixed pixels of land and water.

The Boundaries between Land and Water
There were unexpected R min 1 results in which clear-sky pixels were misidentified as clouds over water regions near the boundaries between land and water; however, R min 2 results could identify these areas as clear sky (Figure 19).Procedure 1 chooses surrounding water pixels because its spatial resolution is 1/30 • when there are mixed pixels of land and water.

Sun-Glint
There were not almost differences between Rmin1 results and Rmin2 results in water sun-glint regions (Figure 20).

Conclusions
In this study, we had two major goals: i.
To compare Rmin calculated using different methods to choose 10 observations.ii.
To compare Rmin using different generation procedures and spatial resolutions.
The method used to choose the 10 observations had a minor impact on cloud discrimination results, with some exceptions, such as snow-covered regions and sun-glint regions.In Japan, the difference was caused by using Rmin when clouds over the ocean were not removed.However, this difference is not explained by differences in the selection of the 10 observations, but by random variation.In the same manner, the difference caused by using Rmin in which cloud shadows were not removed in Algeria does not depend on the way in which the 10 observations were chosen.Rmin for GOSAT-2 (−2 months and ±1 month) had a higher potential for the 10 observations to include the non-sun-glint period in sun-glint regions than Rmin for GOSAT (−1 month), because the data period used to generate Rmin for GOSAT-2 was longer than that for GOSAT.This has the effect of reducing the overlook of clouds.CLAUDIA raises thresholds in water sun-glint regions under the assumption that Rmin does not include water sun-glint pixels.Furthermore, Rmin for GOSAT-2 (−2 months and ±1 month) has a higher potential to use 10 observations that include the period after snow melting in

Sun-Glint
There were not almost differences between R min 1 results and R min 2 results in water sun-glint regions (Figure 20).

Sun-Glint
There were not almost differences between Rmin1 results and Rmin2 results in water sun-glint regions (Figure 20).

Conclusions
In this study, we had two major goals: i.
To compare Rmin calculated using different methods to choose 10 observations.ii.
To compare Rmin using different generation procedures and spatial resolutions.
The method used to choose the 10 observations had a minor impact on cloud discrimination results, with some exceptions, such as snow-covered regions and sun-glint regions.In Japan, the difference was caused by using Rmin when clouds over the ocean were not removed.However, this difference is not explained by differences in the selection of the 10 observations, but by random variation.In the same manner, the difference caused by using Rmin in which cloud shadows were not removed in Algeria does not depend on the way in which the 10 observations were chosen.Rmin for GOSAT-2 (−2 months and ±1 month) had a higher potential for the 10 observations to include the non-sun-glint period in sun-glint regions than Rmin for GOSAT (−1 month), because the data period used to generate Rmin for GOSAT-2 was longer than that for GOSAT.This has the effect of reducing the overlook of clouds.CLAUDIA raises thresholds in water sun-glint regions under the assumption that Rmin does not include water sun-glint pixels.Furthermore, Rmin for GOSAT-2 (−2 months and ±1 month) has a higher potential to use 10 observations that include the period after snow melting in

Conclusions
In this study, we had two major goals: i.
To compare R min calculated using different methods to choose 10 observations.ii.To compare R min using different generation procedures and spatial resolutions.
The method used to choose the 10 observations had a minor impact on cloud discrimination results, with some exceptions, such as snow-covered regions and sun-glint regions.In Japan, the difference was caused by using R min when clouds over the ocean were not removed.However, this difference is not explained by differences in the selection of the 10 observations, but by random variation.In the same manner, the difference caused by using R min in which cloud shadows were not removed in Algeria does not depend on the way in which the 10 observations were chosen.R min for GOSAT-2 (−2 months and ±1 month) had a higher potential for the 10 observations to include the non-sun-glint period in sun-glint regions than R min for GOSAT (−1 month), because the data period used to generate R min for GOSAT-2 was longer than that for GOSAT.This has the effect of reducing the overlook of clouds.CLAUDIA raises thresholds in water sun-glint regions under the assumption that R min does not include water sun-glint pixels.Furthermore, R min for GOSAT-2 (−2 months and ±1 month) has a higher potential to use 10 observations that include the period after snow melting in snow-covered regions than R min for GOSAT (−1 month).GOSAT-2 had fewer cases in which clouds were overlooked, but more cases in which snow or ice was misjudged as clouds compared with GOSAT in snow-covered regions.With respect to R min of −2 months or ±1 month for GOSAT-2, R min of ±1 months was better than that of −2 months in general because the average for ±1 month agreed with observations.From the viewpoint of steady processing for GOSAT-2 CAI-2 data, cloud discrimination processing using R min of ±1 month cannot be performed unless a period of 1 month from the observation date elapses.
This study also demonstrated the impact of using R min generated by different procedures.Cloud discrimination results using R min 2 generated by Procedure 2 had the following tendencies in comparison with results using R min 1 generated by Procedure 1. i.
R min 2 results had a greater tendency to identify clear sky in comparison with R min 1 results.ii.R min 2 results had a tendency to overlook optically thin clouds over local highly reflective surfaces.iii.R min 2 results had a tendency to accurately identify local highly reflective surfaces as clouds.iv.Ice and snow regions where R min 1 results misidentified clouds were slightly improved in R min 2 results.v.
For regions with a high cloud cover ratio, R min 2 results occasionally overlooked optically thin clouds according to cloud remains in R min .vi. Water regions near the boundary between land and water where R min 1 results misidentified clouds were improved in R min 2 results.vii.Furthermore, there were almost no differences between R min 1 results and R min 2 results in water sun-glint regions.
For these reasons, R min 2 results were better than R min 1 results, except for particular situations, e.g., those described in ii and v above.

Figure 1 .
Figure 1.Study areas.Black rectangles indicate the locations of Cloud and Aerosol Imager (CAI) frames.

Figure 1 .
Figure 1.Study areas.Black rectangles indicate the locations of Cloud and Aerosol Imager (CAI) frames.

Figure 2 .
Figure 2. Summary of methods to choose the 10 observations for GOSAT and GOSAT-2.

Figure 2 .
Figure 2. Summary of methods to choose the 10 observations for GOSAT and GOSAT-2.
-sky std Both clear-sky + Cloudy despite clear-sky std .

Figure 4 .
Figure 4.The averaged Rmin for each CAI scene generated using different methods to choose the 10 observations, i.e., −1 month, −2 months, and ±1 month.The blue line is −1 month Rmin of band 2 and

Figure 4 .
Figure 4.The averaged R min for each CAI scene generated using different methods to choose the 10 observations, i.e., −1 month, −2 months, and ±1 month.The blue line is −1 month R min of band 2 and the red line is that of band3.The blue dot line is −2 month R min of band 2 and the red dot line is that of band 3. The green dot line is ±1 month R min of band 2 and the orange dot line is that of band 3.
Remote Sens. 2018, 10, x FOR PEER REVIEW 7 of 21 the red line is that of band3.The blue dot line is −2 month Rmin of band 2 and the red dot line is that of band 3. The green dot line is ±1 month Rmin of band 2 and the orange dot line is that of band 3.

Figure 5 .
Figure 5. Degree of Agreement between −1 month, ±1 month, and −2 months for various land cover types.The red line represents Degree of Agreement between −1 month and ±1 month; the blue line represents that between −1 month and −2 months; the green dot line represents that between ±1 month and −2 months.

Figure 5 .
Figure 5. Degree of Agreement between −1 month, ±1 month, and −2 months for various land cover types.The red line represents Degree of Agreement between −1 month and ±1 month; the blue line represents that between −1 month and −2 months; the green dot line represents that between ±1 month and −2 months.

Figure 6 .
Figure 6.The averaged Rmin in each CAI scene for various land cover types for Rmin1 of band 2, Rmin1 of band 3, Rmin2 of band 2, and Rmin2 of band 3. The gaps in the final panel (Alaska) are where low solar elevation angles prevented sufficient data collection.The blue line is Rmin1 of band 2 and the red line is that of band 3. The blue dot line is Rmin2 of band 2 and the red line is that of band 3.

Figure 6 .
Figure 6.The averaged R min in each CAI scene for various land cover types for R min 1 of band 2, R min 1 of band 3, R min 2 of band 2, and R min 2 of band 3. The gaps in the final panel (Alaska) are where low solar elevation angles prevented sufficient data collection.The blue line is R min 1 of band 2 and the red line is that of band 3. The blue dot line is R min 2 of band 2 and the red line is that of band 3.

Figure 7 .
Figure 7. Degree of Agreement, Overlook, and Overestimate for various land cover types.Rmin1 results were used as standard images.The blue line represents Degree of Agreement, the red line represents Overlook, and the green line represents Overestimate.

Figure 7 .
Figure 7. Degree of Agreement, Overlook, and Overestimate for various land cover types.R min 1 results were used as standard images.The blue line represents Degree of Agreement, the red line represents Overlook, and the green line represents Overestimate.

Figure 8 .
Figure 8. Difference between R min 1 and R min 2. (a) RGB image obtained on 31 March 2014 in Japan (R: Band 2, G: Band 3, B: Band 1); (b) Difference between R min 1 and R min 2 using band 2 for land regions; (c) Difference between R min 1 and R min 2 using band 3 for water regions.

Figure 9 . 21 Figure 9 .
Figure 9. Cloud remains in R min over water regions on April 3, 2014 in Japan.(a) Difference between ±1 month and −2 months R min results; (b) ±1 month R min image (R: ±1 month R min of band 2, G: ±1 month R min of band 3, B: ±1 month R min of band 1); (c) −2 months R min image (R: −2 months R min of band 2, G: −2 months R min of band 3, B: −2 months R min of band 1).

Figure 12 .
Figure 12.Cloud and cloud shadow remains in R min .(a) RGB composite image of R min 1 in Borneo (R: Band 2, G: Band 3, B: Band 1); (b) RGB composite image of R min 2.There are many cloud remains; (c) RGB image on 2 July 2012 in Algeria (R: Band 2, G: Band 3, B: Band 1); (d) RGB composite image of R min 1.Whitish pixels indicate optically thin cloud remains; (e) RGB composite image of R min 2. Black pixels indicate cloud shadow remains.

Figure 13 .
Figure 13.Optically thin clouds over local highly reflective surfaces.(a) RGB image on 1 April 2013 in Algeria (R: Band 2, G: Band 3, B: Band 1); (b) Difference between R min 1 and R min 2 results.Vertical black lines indicate pixels with invalid values for band 4; (c) R min 1 for band 2; (d) R min 2 for band 2.

Figure 14 .
Figure 14.Local highly reflective surface.(a) RGB image obtained on 3 October 2012 in Australia (R: Band 2, G: Band 3, B: Band 1); (b) Difference between R min 1 and R min 2 results; (c) Difference between R min 1 and R min 2 for band 2.

Figure 15 .
Figure 15.Cloud discrimination in snow and ice regions.(a) RGB image obtained on 1 June 2013 in Alaska (R: Band 2, G: Band 3, B: Band 1); (b) Difference between Rmin1 and Rmin2 results.Black areas indicate pixels that have invalid values for band 4; (c) Difference between Rmin1 and Rmin2 of band 2.

Figure 15 .
Figure 15.Cloud discrimination in snow and ice regions.(a) RGB image obtained on 1 June 2013 in Alaska (R: Band 2, G: Band 3, B: Band 1); (b) Difference between R min 1 and R min 2 results.Black areas indicate pixels that have invalid values for band 4; (c) Difference between R min 1 and R min 2 of band 2.

Figure 15 .
Cloud discrimination in snow and ice regions.(a) RGB image obtained on 1 June 2013 in Alaska (R: Band 2, G: Band 3, B: Band 1); (b) Difference between Rmin1 and Rmin2 results.Black areas indicate pixels that have invalid values for band 4; (c) Difference between Rmin1 and Rmin2 of band 2.

Figure
Figure Instance in which R min 2 could discriminate between clouds and snow.(a) RGB image obtained on 1 May 2013 in Mongolia (R: Band 2, G: Band 3, B: Band 1); (b) Difference between R min 1 and R min 2 results; (c) Difference between R min 1 and R min 2 of band 2.

Figure 17 .
Figure 17.Cloud remains in R min over water regions.(a) RGB image obtained on 3 July 2012 in Japan (R: Band 2, G: Band 3, B: Band 1); (b) Difference between R min 1 and R min 2 results; (c) R min 1 of band 3. Cloud remains in R min 1; (d) R min 2 of band 3; (e) Difference between R min 1 and R min 2 of band 3. Black areas mainly caused by cloud remains in R min 1.

Figure 18 .
Figure 18.Cloud remains in R min over land regions.(a) RGB image obtained on 3 October 2012 in Borneo (R: Band 2, G: Band 3, B: Band 1); (b) Difference between R min 1 and R min 2 results; (c) R min 1 of band 2. Cloud remains in R min 1; (d) R min 2 of band 2. Cloud remains in R min 2; (e) Difference between R min 1 and R min 2 of band 2.

Figure 19 .
Figure 19.The boundary between land and water.(a) RGB image obtained on 2 January 2013 in Japan (R: Band 2, G: Band 3, B: Band 1); (b) Difference between R min 1 and R min 2 results.

Table 1 .
GOSAT CAI Level 1B product used in this study.Land cover was derived from the MODerate resolution Imaging Spectroradiometer (MODIS) land cover type product (MCD12).Japan scenes include urban areas.