Relative Azimuthal-Angle Matching (RAM): A Screening Method for GEO-LEO Reﬂectance Comparison in Middle Latitude Forests

: This study introduced a data screening method for comparing the reﬂectances in middle latitude forest regions collected by a Geostationary Earth Observing (GEO) satellite and a Low Earth Orbit (LEO) satellite. This method attempts to reduce the differences between the relative azimuth angles of the GEO and LEO observations. The method, called relative azimuthal-angle matching (RAM), takes advantage of the high temporal resolution of the GEO satellites, which enables collection of a wide range of relative azimuth angles within a day. The performance of the RAM method was evaluated using data in the visible and near-infrared bands collected by the Himawari-8/Advanced Himawari Imager (AHI) and the Terra/Moderate Resolution Imaging Spectroradiometer (MODIS). The consistency of the reﬂectance pairs of MODIS and AHI selected by the RAM method was compared with the consistency of the reﬂectance pairs acquired simultaneously by the two sensors. The data were matched pixel-by-pixel after applying atmospheric corrections and cloud screening. The results show that RAM improved the reﬂectance ratio by approximately 10% for the red and NIR bands on average relative to the simultaneous observations. Signiﬁcant improvements in the two bands were observed (20%), especially among data collected in the fall and winter. Performance of RAM depends largely on season. Especially in summer, the reﬂectance pair chosen by RAM showed less consistency than solar zenith-angle matching (SZM). The results also indicated the relatively large inﬂuence of the spectral response functions on the green and red bands of the two sensors.


Introduction
Geostationary earth observing (GEO) satellites have played a major role in various fields of study for decades. The primary focus of their contribution historically has been in the atmospheric and oceanic sciences. In recent years, much attention has been paid to the applications of GEO satellite to land observation [1][2][3][4][5] because of the enhanced band configuration and calibration strategy [4,6,7]. These "new generation" GEO satellites, such as the Himawari-8 (2014-) [6], FY-4A [4], and GOES-16 (2016-) [7], have land monitoring capabilities with high radiometric and temporal resolutions, in addition to their primary atmosphere and ocean sciences monitoring capabilities. The enhanced capabilities will bring new observation opportunities, especially in land applications in which satellite data having such a high temporal resolution do not currently exist.
Limiting our discussion to land monitoring applications [8][9][10][11][12][13][14], the use of GEO satellite data will require us to address issues of data consistency between the established LEO satellite data and the GEO satellite data. A consistency analysis is expected to be conducted prior to any data analysis

Method
GEO-LEO reflectance comparisons in a middle latitude are illustrated in Figure 1. The right polar plot in Figure 1 shows the angular positions of the MODIS and AHI satellites in one of our ROIs, a forest in Kochi, Japan. In the polar plot, blue circles (filled or empty) represent combinations of the view zenith and view azimuth angles in the MODIS data, which cover all sixteen observations within a single revisit cycle (from 11 May 2016 to 26 May 2016) of the Terra satellite. The view zenith angle of the MODIS data varies from 0 • (nadir) to 60 • . The angular position of the AHI observations, depicted by the red filled circle, remains fixed at one location due to its geostationary orbit. The polar plot indicates the fact that the two sensors never observe this ROI from the same direction. The geometrical mismatch between the GEO and LEO satellites makes reflectance comparisons difficult, especially for targets with an unknown directional dependency (often modeled using the BRDF). For example, the left figure in Figure 1 shows a scatter plot of the MODIS band-4 reflectance observations acquired over three consecutive days versus the reflectances of the AHI band-2 simultaneous observations over the ROI. The figure shows systematic differences, suggesting that the angular mismatch caused significant biases, even though we selected simultaneous observations as a screening criterion in the GEO and LEO satellites reflectance comparisons over a middle latitude forest region. Again, in contrast to the MODIS observations, AHI observes the same target always from a fixed direction, resulting in fixed view zenith and view azimuth angles for the target. This fact is indicated by the red filled circle in the polar plot shown in Figure 1. The view zenith and azimuth angles of AHI for this specific target were 40 • and 168 • , respectively. Although there is no freedom of choice regarding the view angles of AHI, the advantage of AHI is its high temporal resolution (10 min for the full-disk observation mode). Because of this advantage, the illumination direction (pairs of solar zenith and solar azimuth angles) varies significantly from sunrise to sunset, as indicated by the empty black circles in the polar plot shown in Figure 1. This temporal high resolution brings a variety of choices in both the solar zenith and relative azimuth angles for the AHI observations. The wide range of angular variations suggests the possibility of a better screening criterion than the criterion of simultaneous observation in the context of GEO-LEO reflectance comparisons at middle latitudes. One candidate screening criterion is the selection of AHI observations based on the relative azimuth angle: We always have a choice of AHI observation with relative azimuth angles that are nearly identical to those of the MODIS observations. This criterion is referred to here as relative azimuthal-angle matching (RAM). The selection of simultaneous AHI and MODIS observations is standard practice. Simultaneous observations yield the same solar zenith angle (and different relative azimuth angle); therefore, we denote this criterion the solar zenith-angle matching (SZM) criterion in this study.
Differences between the RAM and SZM methods are summarized in Table 1 by focusing on the angular conditions satisfied and the differences in the atmospheric conditions. During the initial data screening process for AHI-MODIS comparisons, we can select MODIS observations with a view zenith angle closest to that of the AHI data (e.g., an angle of 40 • , depicted by filled blue circles in the polar plot shown in Figure 1). Once this choice is made based on the MODIS view-zenith angle, one has at least two screening criteria: (a) SZM (choice of AHI data with the solar zenith angle closest to that of the MODIS observation); and (b) RAM (choice of AHI data with the relative azimuth angle closest to that of the MODIS observation). Figure 2a shows the angular position of the sun and sensors for an AHI scene selected using the SZM method. The idea of using simultaneous/near-simultaneous observations has been used in other intercalibration studies. The directions of the sun relative to the two sensors are not, in general, identical (clockwise or counter-clockwise) for an ROI, and the relative azimuth angles between the sensor and the sun are not identical in the AHI and MODIS observations. Figure 2b shows an example of the RAM method. This method sacrifices consistency in observation time rather than sacrificing consistency in the relative azimuth angle. Again, it should be noted that the SZM method involves the choice of nearly simultaneous observations of AHI with MODIS. The SZM method guarantees identical atmospheric conditions for the GEO and LEO observations, whereas RAM does not (due to differences in the observation times). In the RAM method, the two sensors observe a target from different view azimuth angles, although the relative azimuth angle is nearly identical. In other words, RAM assumes that surface scattering is rotationally symmetric in the azimuthal direction. Thus, the performance of the RAM method depends on the level of rotational symmetry. Despite differences in the atmospheric conditions for the two observations and the assumption of rotational symmetry, our hypothesis is that for targets located at middle latitudes, SZM would not always be the better pair selection method compared to RAM in the context of GEO-LEO reflectance comparisons. This study investigated this point to improve our understanding of GEO-LEO inter-comparisons at middle latitudes. Table 1. Differences in the geometric and atmospheric conditions of the LEO and GEO observation pairs selected using the SZM and RAM methods. The mark "o" indicates that the GEO and LEO observation conditions are nearly identical. The numbers indicate the ranges of absolute differences in this study. The SZM method corresponds to simultaneous data acquisition; therefore, the atmospheric conditions will be identical.

Data Description
To meet our objectives, we set several conditions to be satisfied by selected test sites. The first condition is the location of the sites. Because the ray-matching method condition in the context of GEO-LEO comparisons is generally limited to 20 • north or south of the equator, targets of this study should be located outside of the latitude range. We set the condition to be even more stringent; the target must be located in a middle latitude region, preferably beyond 30 • north or south of the equator. By setting this restriction, the geometric requirements of the ray-matching method are not satisfied. The meridian of the Himawari-8, 140.7 • E, was used as the reference meridian of each test site. The second condition applied to the surface type. Forest targets, our primary interest, should be moderately uniform and homogeneous. Moreover, the terrain of the forest targets is preferably mountainous rather than a flat surface, which would make the conditions more difficult to satisfy using the RAM method. In addition to the forest targets, we must also select a test site corresponding to a non-vegetated surface as a reference location near the forest targets. By comparing the results of the mountainous forest with those obtained from non-vegetated flat targets, the influence of the vegetation quantity on the GEO-LEO comparison can be evaluated. These considerations and restrictions led us to select two pairs of forested and urban sites from the northern hemisphere, as described below.

Test Site
Four regions of interest (ROIs) located in Japan were used as our test sites ( Figure 3). The ROIs include two forest sites: one from Kochi Prefecture on Shikoku Island and one from Aichi Prefecture on Honshu Island. Both ROIs were 20 km by 20 km. The ROIs of the non-vegetation targets were chosen from urban areas near the forest sites. The urban site near the Kochi Forest was 3 km by 5 km, and that near the Aichi Forest was 10 km by 10 km, as summarized in Table 2. The locations of these ROIs are shown on the map of the MODIS leaf area index (LAI) in Figure 3. The data obtained from MOD15A2H [30] on 17 May 2017 were used to verify the LAI over the ROIs.
The LAIs and its spatiotemporal variations were analyzed over the two forest sites. The daily LAI data from MOD15A2H were used by focusing on a one-year period in 2017. We used the data that passed all the quality control examination based on the FparLai_QC flags. Especially in this analysis, the flag was also used to identify pixels with a LAI value retrieved using the radiative transfer (RT) model algorithm. The yearly average and standard deviation at each site was computed using the daily data only if more than 25% of all pixels passed the cloud and FparLai_QC flag screening criteria. After screening, we computed the spatially and temporally averaged LAI over the year 2017 over the two forest ROIs. The average LAIs over the Kochi and Aichi Forests were both 2.3, and the corresponding standard deviations were 0.38 and 0.46, respectively. These results revealed small variations in the LAIs over these ROIs. This trend was confirmed from the High-Resolution Land Use and Land Cover (HRLULC) map data (30 m grid) distributed by JAXA [31]. The land cover map indicated that the proportions of evergreen needle-leaved forest (ENF) and evergreen broad-leaved forest (EBF) in the Kochi Forest were 66.5% and 25.7%, respectively. In the Aichi Forest, the proportions were 83.9% and 4.4%, respectively. Therefore, the two ROIs were mostly composed of ENF and EBF, yielding spatially homogeneous and temporally stable LAIs over the ROIs.

Satellite Data
Himawari-8 is located at 140.7 • E longitude and observes regions in East Asia and the Western Pacific. The standard data providing "Full Disk" coverage were downloaded from the National Institute of Information and Communications Technology (NICT) Science Cloud. The temporal resolution of the Full Disk observation is 10 min. We compared four visible and near-infrared bands (band 1-4) of the AHI with the corresponding MODIS bands in this study. The central wavelengths of the four AHI bands were 460 nm, 510 nm, 640 nm, and 860 nm. The spatial resolution was 1 km at the sub-satellite point, except in band 3. The resolution of band 3 was 0.5 km [6]. The data from band-3 were averaged over 2 by 2 pixel blocks to match the resolution of the other bands. The scaled digital counts (called the calibrated reflectances) were then transformed into the actual reflectance by considering the solar zenith angle and the square of the sun-earth distance using the calibration coefficients provided.
The Terra satellite is in LEO with a morning overpass time and 16-day revisit cycle. We used the MODIS Calibrated Radiances, the Daily L1B Swath 1 km (MOD021KM) Collection 6 [32] and MODIS Geolocation Fields Daily L1A Swath 1 km (MOD03) Collection 6 [33], downloaded from the Level-1 and Atmosphere Archive and Distribution System (LAADS) Distributed Active Archive Center (DAAC). Bands 3, 4, 1, and 2 of the MODIS data corresponded to bands 1-4 of the AHI data, respectively. The central wavelengths of the MODIS bands were 465.7 nm, 553.7 nm, 646.3 nm, and 856.5 nm, respectively [34]. The digital counts were also transformed into actual reflectances in the same manner as was used with the AHI data [35]. The MODIS cloud mask data (MOD35) Collection 6.1 [36] was also used for screening purposes.
In this work, the data acquisition times for both the AHI and MODIS data were represented by four digits, "HHMM", derived from the time stamp included in the file name, where "HH" and "MM" stand for the hour and minute of the day, respectively. The time stamp in the file name indicated the beginning of the scan for a full AHI disk and the 5-min MODIS granule. Note that the true observation time for each location was slightly different (1-5 min) from this abbreviated information.

Algorithm
The AHI and MODIS reflectances were compared using the algorithm illustrated in Figure 4. The figure provides an overview of the data processing flow in this study. The entire process was divided into two parts: (a) geometric condition retrieval; and (b) preprocessing and screening (see Figure 4). Part (a) involved identifying pairs of data acquisition times in the MODIS and AHI observations that satisfied the SZM or RAM criteria. The process began with the selection of the MODIS scenes based on a view zenith angle criterion (Section 4.1). After this selection, data from the same orbital path were collected so that only MODIS data having a view zenith angle identical to that of the AHI data were prepared for processing. The outputs from this process were the time of day for the SZM and RAM data that satisfied the geometric conditions of these screening methods. Part (b) of the flowchart mainly performed preprocessing and screening, such as data preparation and compositing for AHI (Section 4.2), atmospheric corrections (Section 4.3), and cloud screening (Section 4.4). After the second analysis step, two pairs of MODIS and AHI reflectances were obtained at each pixel (1 km resolution) and in each band; one pair corresponded to the SZM method and the other to the RAM method (Section 4.5). Finally, the reflectance ratios between the two sensors were computed (Section 4.6). These processes are explained in detail below.

MODIS Scene Selection Based on the AHI View Zenith Angle
Our algorithm began by focusing on a single revisit cycle of Terra. During the duration of one revisit cycle, MODIS observes an ROI from 16 different orbital paths, resulting in 16 different combinations of view zenith and view azimuth angles for a given ROI. Among these observations (MOD02), the view zenith angle varied from 0 • to nearly 60 • , as shown in Figure 1. This wide range of variation in the view zenith angle enabled us to select the angle closest to the AHI view zenith angle. Two choices are available: the west-looking observation and the east-looking observation. Among these two choices, the choice of the west-looking observations may be advantageous relative to the other for targets in the northern hemisphere. This constraint arises from the condition applied using the RAM method. In the RAM method, it is necessary to select an AHI observation having a relative azimuth angle that is nearly identical to that of the MODIS observation. West-looking observations result in smaller relative azimuth angles than the east-looking observations. It enables the RAM method to use data observed at relatively earlier time of the afternoon, which increases observation chances especially in winter before sunset. Note that the selection of the MODIS view zenith angle is common to both the SZM and RAM methods. Thus, our first step was to identify the MOD02 scene (out of 16 observations) having the view zenith angle closest to that of the AHI observation from among the west-looking observations.
The Himawari-8 is a geostationary satellite; therefore, view zenith and view azimuth angles of AHI are fixed for each target. These fixed angles can vary depending on the ROI location. Each ROI requires retrieval of the view zenith and view azimuth angles of the AHI observation prior to selecting the MODIS data. In summary, MODIS data selection was carried out in the following order: (1) AHI view zenith angle for the ROI; and (2) selection of the MODIS data from among the 16-day observations with a view zenith angle closest to the AHI view zenith angle. This process was repeated every 16 days from 7 July 2015 to 31 August 2018 (three years). After applying these processes, we identified and selected one MOD02 for each 16-day window.
The next step was to filter out the MODIS data, pixel by pixel, based on the quality assurance (QA) flags of the MOD35 data. The "unobstructed FOV QA Flag" could be used to identify "confident clear" pixels. The pixels deemed "confident clear" were counted for all selected MODIS data over the three years (7 July 2015 to 31 August 2018). By focusing on a single month, three years of scenes were analyzed. We further selected the best monthly scenes from the three-year collections. The best scene was determined based on the number of pixels remaining after screening based on the QA flags. Finally, we selected one MODIS scene for each month, regardless of the year. Table 3 summarizes the best MODIS scene and the number of pixels remaining after the screening process had sorted pixels by day of the year (DOY), regardless of the year difference. As outputs of this stage, we retrieved two different times of the day: the MODIS data acquisition time, which was used to select AHI data in the SZM method, and the time of the AHI observation that yielded the same relative azimuth angle as the MODIS observation. The latter time could be retrieved by simulating the dynamics of the solar position over the observation day for each ROI. We summarized the outputs (times for the SZM and RAM methods) along with the DOY selected in this study ( Table 4). Note that the DOY shown in the table corresponds to the selected MODIS data summarized in Table 3

AHI Data Selection and Weekly Composites for the SZM and RAM Methods
The first step of Part (b) involved selecting AHI candidate data for comparison. We combined AHI data over one week periods for each MODIS observation to span three days before and after the MODIS observation. Although AHI observed the ROIs every 10 min, not all data were used. The data were screened based on the time information retrieved at the end of the previous analysis section, Part (a). We only used AHI data having an observation time close to either the SZM or RAM on each day. At this stage, we selected seven AHI scenes in the SZM and RAM methods, for a total of 14 scenes at each ROI.
These data were then composited to produce two datasets by targeting a specific time of observation. One set was for the SZM method and the other was used for the RAM method. For this selection, the time information obtained from the previous process (Part (a)) were used as the inputs. The AHI data selected for the SZM and RAM methods are illustrated in Figure 5. These data were then subjected to a compositing process. For each pixel, a single observation result from among the seven candidates was selected by comparing the apparent temperatures retrieved from the AHI band 14. This temperature comparison provided an initial cloud screening process. The screening algorithm is known as the Maximum apparent Temperature (MaT) [37] and can detect and screen observations influenced by clouds and cloud shadows. This approach provided two composite scenes: one using the SZM method, and the other using the RAM method. The rest of the process (described in the following sections) was performed only on the MODIS and AHI data listed in Tables 3 and 4 Figure 5. Overview of the AHI data composite. AHI data collected over seven consecutive days were used to create a single image for each of the SZM and RAM methods (for a total of two images). The SZM and RAM images differed with respect to the data acquisition time. The central date of the AHI observation period is the same as that designated for the MODIS data.

Atmospheric Corrections
Atmospheric corrections were performed to address molecular scattering and ozone absorption effects [29]. We decided to process the atmospheric corrections conservatively according to the methods of Chang et al. [27] to avoid introducing artificial differences with over-corrections of the atmospheric influences. This study applied one algorithm to both the MODIS and AHI images in exactly the same way [29] to avoid introducing differences into the sensor data. Our correction scheme is relatively conservative compared to full atmospheric corrections that account for gaseous absorption and aerosol scattering. Note that these influences remained present in the compared data, denoted top-of-canopy (TOC) reflectances in this study. Differences arising from atmospheric corrections were effectively avoided by applying a common algorithm to the top-of-atmosphere (TOA) reflectances obtained from the MODIS and AHI sensors. The atmospheric corrections applied to the two sensors differed only with respect to the sensor-specific Spectral Response Functions (SRFs) used to compute look-up tables (LUTs) of the scattering and absorption cross-sections (wavelength-dependent optical depths). A series of particle transport simulations [38] was performed assuming spatially one-dimensional conditions (plane parallel) and two angular parameters, the S 40 approximation [39]. We obtained the path radiance, bi-hemispherical reflectance, and transmittance as a function of the viewing and illumination angles, and the optical depth. These simulation results were then stored in LUTs as a function of those parameters [40]. The optical depth of the Rayleigh scattering was determined by the elevation of each pixel, which was interpolated from the digital elevation model of the Earth topography 5-min grid (ETOPO5) [41]. The ozone absorption correction was implemented using the absorption cross-sections stored in the 6S code [42] based on the values observed by the Aura/Ozone Monitoring Instrument (OMI) sensor [43]. In summary, Rayleigh scattering effects were corrected using the LUTs developed based on the pixel elevations interpolated from the ETOPO5. The ozone absorption effects were corrected based on the observation data reported by Aura/OMI.

Precise Cloud Screening
The pixels contaminated by clouds remained present in the composited AHI scenes. These artifacts were identified finally by visual inspection during the study. Prior to the visual inspection, cloud influences were removed from our comparison by conducting precise cloud screening based on the brightness temperature and reflectance data according to the methods reported by Ishida and Nakajima, and Shang et al. [44,45]. The AHI observation results were considered to be cloudy if at least either one of the conditions described in Equation (1) or (2) holds, where T b7 and T b14 are the brightness temperature of the AHI bands 7 and 14, respectively. v represents the NDVI computed from the TOC reflectances of the AHI. T t and v t are the thresholds of the brightness temperature and NDVI, respectively. Note that we chose different values of T t and v t for the forest and urban areas. The cloud screening process using the brightness temperature was not applied to the urban areas. The land cover-dependent thresholds are summarized in Table 5. The pixels assumed to be cloudy were labeled for elimination from the AHI data. Furthermore, an additional cloud detection process was conducted over the remaining pixels (with no label). For this purpose, we computed the average and standard deviations of the red reflectances over the ROI. If at least one of the red reflectances in the AHI or MODIS data exceeded the average value over the ROI by twice the standard deviation, the observation was considered to be influenced by clouds. Table 5. Thresholds (T t and v t ) for the forest and urban ROIs.

T t v t
Forest −6.5 0.470 Urban -−0.037 In summary, we performed cloud screening multiple times in different ways. For the MODIS data, we used the MOD35 QA flag (confident clear). For the AHI data, the MaT algorithm was employed as the initial screening process. Finally, algorithms based on the temperature and NDVI [44,45] and the red band thresholding were used to further filter out the cloud influence. Recall that red reflectance thresholding was used for both the MODIS and AHI data. Only the pairs of pixels remaining after the screening processes were compared in this study.

AHI-MODIS Data Match-Up
All pixels in the MODIS data within the ROIs were paired with the collocated pixels of the AHI data based on the nearest neighbor algorithm over the geographic coordinates. Pixel pairs containing cloudy pixels either or both the AHI and MODIS observations, as determined in the previous analysis step, were not used in the subsequent processes. Table 6 lists the number of pixels remaining after the AHI-MODIS data match-up over each ROI and using each pair selection method (SZM or RAM).

Evaluation Method
As an indicator of the reflectance comparison, we employed the reflectance ratio between the corresponding bands of the two sensors. This ratio has been used in many studies, especially in time-trend analysis [48]. Because our comparisons were performed as a function of the DOY, we followed this standard approach for the comparison. The reflectance ratio (r i,j ) was defined by where the subscript i indicates the MODIS/AHI scene pixel number, and j is used to identify the date of data acquisition (scene identifier in this study). The subscripts M and A indicate the MODIS and AHI origin of the data, respectively. The arithmetic mean of r i,j is represented by r j and is computed using all available pixels remaining after applying the cloud screenings process to the jth scene. The area-averaged reflectances, r j , are considered to be "consistent" when r j is close to unity. Finally, the consistency between the sensors in the paired jth scene is evaluated based on the difference from unity, E j , defined by E j = |1 − r j |. (4) Inconsistencies between the sensors arise from a variety of factors. Among these factors, differences in the geometric conditions, such as the solar zenith and relative azimuth angles, are central to determining the consistency in this study. We analyzed the results based on differences in the geometric conditions. We denoted the differences in the solar zenith angles between the MODIS and AHI as d θ j . Similarly, differences in the relative azimuth angle are denoted by d φ j . These variables are defined as where θ and φ represent differences in the solar zenith and relative azimuth angles, respectively. The area-averaged values of θ and φ are also defined by θ and φ, respectively. The reflectance ratio r i,j is used for not only actual data but also simulation data. Numerical simulations were performed to quantitatively examine the influences of the SRF differences between the MODIS and AHI data. A radiative transfer model, PROSAIL [49], was employed. The spectral reflectances of the AHI and MODIS were simulated by spectrally convolving the reflectances of the vegetation canopy with the SRFs for each band as a function of two parameters, namely, LAI and "psoil", which is a blending coefficient of two distinctive soil spectra: dry and wet soil.

Results
The results of the AHI and MODIS reflectance comparisons are presented in Section 5.1. We conducted numerical simulations using a radiative transfer model of the vegetation canopy. This simulation evaluated the effects of the differences in the SRFs across the sensors: The SRF differences are especially significant in the green bands. We investigated the influence of the SRFs thoroughly to validate our results in Section 5.2. Figure 6a,b show the reflectance ratios obtained using the SZM and RAM methods applied to the forests in Kochi, respectively. The ratios were plotted as a function of the DOY so that their seasonal variations could be observed in the figures. The circles represent the area-averaged ratios (r j ) for four bands. The error bars indicate the standard deviation of the ratio (r i,j ). The error bars in Figure 6a,b for a DOY of 154 are larger than the error bars obtained on other DOYs. These results suggest the presence of a factor rendering the data unreliable. The influence of cloud cover was suspected, and visual inspection confirmed that cloud influence was indeed present in the MODIS screened data. Thus, special caution was needed to interpret the data for this specific DOY.

Comparison Results Based on the Actual Data
The SZM results shown in Figure 6a reveal that the average ratio r j varied from 0.5 to 1.8. The ratio tended to exceed unity over the period between DOYs 133 and 218 and tended to be lower than unity in other periods. This trend was investigated by plotting the differences between the sensor geometric conditions. In these figures, the empty square indicates differences in the solar zenith angles (d θ j ), and the empty triangle indicates differences in the relative azimuth angles (d φ j ). Recall that differences in the solar zenith angles (empty circles) were nearly zero for the SZM method. Differences in the relative azimuth angles varied significantly. The differences became especially large during the winter season. Thus, ratios far from unity for d φ j became large. This correlation raised questions about the screening strategy for the geometric conditions in the GEO-LEO comparison. These results suggest that the differences between the relative azimuth angles of the sensors was most likely a major factor in producing reflectance inconsistencies. This can be inferred from the RAM results, as shown in Figure 6b. A comparison of Figure 6a,b reveals that the value of r j was closer to unity for the RAM method. This improvement was obtained by adjusting the relative azimuth angle in the RAM method. The reflectance inconsistencies displayed another notable trend in the green band variations. The ratios of the green bands were larger than the ratios of the other three bands, especially for DOYs 133-245. This was attributed to differences in the MODIS and AHI SRFs, which were numerically validated using an RT model (Section 5.2). By contrast, the smallest value of r j was the red band. The value mostly fell below 1.0, suggesting that the red band was also influenced by the SRF differences. This point is addressed in the following subsection.
The SZM and RAM results obtained in the Aichi Forest ROI (Figure 6c,d), showing trends in r j similar to those from Kochi. This means that, compared to the SZM method, the RAM method tends to select more consistent pair of reflectances between the two sensors.
We also compared the results of the SZM and RAM methods for the urban areas in Kochi and Aichi, as shown in Figure 7a,b, respectively. The value of r j obtained from the SZM method varied from 0.6 to 1.2, whereas the value obtained from the RAM method was closer to unity (0.8-1.3), except over certain dates (DOYs 119-245). Similar improvements were seen in the results obtained from the Aichi Urban ROI (Figure 7c,d). Interestingly, the band dependencies of the r j were much smaller, except in the blue band, than were observed over the forest targets. This result was attributed to the relatively flatter spectra of the urban surfaces compared to those of the forests. This trend was prominent in the green bands. The ratio of the green band did not exceed that of other bands during the summer season because less vegetation cover was present in the urban ROIs.  Figure 8 shows the cumulative errors defined by the sum of E j over the four bands for the SZM and RAM methods. The cumulative errors of the SZM and RAM methods are plotted side by side in the figure. Differences in the geometrical conditions (differences in the angles between the two sensors) are plotted on the secondary axis (right axis) as a function of the DOY. In these figures, a smaller absolute value indicates better agreement between the sensor reflectances or geometric conditions. The left bar with the solid lines shows the results obtained using the SZM method, and the right bar with the dashed lines shows the results obtained using the RAM method. The cumulative errors in the RAM method were smaller than those obtained in the SZM method, with a few exceptions (Figure 8a,b). This trend can also be seen in the urban ROI results (Figure 8c,d). These results indicate better consistency in the RAM results than in the SZM results. We compared the cumulative errors for the red and NIR bands in Figure 9. This comparison is mainly used for vegetation monitoring, and the red and NIR bands are used most frequently. These results confirmed that the selection of the reflectance pairs by the RAM method provided better consistency than selection by the SZM method.
As a summary of this subsection, we tabulated the results of our comparisons to confirm the trends described above. The SZM and RAM performance differences in E j , defined by |1 − r j RAM | − |1 − r j SZM |, are summarized in Tables 7 and 8. The differences are tabulated based on band, month, and ROI. Note that the negative value in the tables indicates cases in which RAM provides better results (more consistent results) than SZM. In the table, the negative values are highlighted by color. A negative value occurred over 81% of the Kochi Forest, 69% of the Aichi Forest, 67% of the Kochi Urban Area, and 88% of the Aichi Urban Area. The results in October and November show especially large negative values, indicating greater improvement of the RAM method compared to the SZM method. Although positive cases occurred in a fair fraction of cases, the magnitudes of the positive values were smaller than the magnitudes of the negative values, except in the green band. These results suggest that the RAM method selected more consistent pairs of reflectances in most cases. The green band provided relatively large positive values, especially in the spring and summer seasons over the forest ROIs. This observation was attributed to SRF differences between the MODIS and AHI, as discussed in our previous study [29]. Special caution is needed when using green bands interchangeably. This point is further addressed in the following subsection. Table 7. Summary of |1 − r j RAM | − |1 − r j SZM | for the two forest ROIs. Negative values indicate a better performance of the RAM method than the SZM method.  Table 8. Summary of |1 − r j RAM | − |1 − r j SZM | for the two urban ROIs. Negative values indicate that the RAM method performed better than the SZM method.  Figure 10 shows the SRFs of the two sensors and simulated reflectances of each band on the vegetation. The input parameters of the model assumed in this study are summarized in Table 9. In the figure, note that the SRFs of the green bands differ to a greater extent than the SRFs of the other three bands. The SRF of the AHI green band is located below the green spectral peak of the canopy spectrum. By contrast, the SRF of the MODIS green band is located on the green peak. This SRF difference could be the cause of the effects observed in the previous subsection.

Simulation Results by an RT Model
The simulated reflectance ratios are shown as contour plots in Figure 11. The ratios were close to 1.0 in the blue and NIR bands (Figure 11a,d). The ratio in the red band reached 0.9, larger than the value, 1.0, obtained in the blue and NIR bands. By contrast, the ratio of the green band (Figure 11b) was far higher than 1.0: The maximum value even reached 2.0 in the simulation. Note that the green band ratio increased as the LAI increased. This suggested that the green band ratio for the forest ROI tended to be higher than for the urban ROI. This also suggested that the ratio tended to be highest during the summer. This trend corresponded very well to the results obtained from the data comparisons. As mentioned in the previous subsection, relatively large values of the green band ratios (1.1-1.8) were observed over the forest ROIs ( Figure 6) during the spring through the fall. This effect was observed especially during the summer. Thus, the simulation confirmed our interpretation of the results. In addition to the green band trend, a similar trend was observed in the red band ratio. The low value of the red band ratio (0.9-1.0) in the simulation (Figure 11c) corresponded well with the trends shown in the previous subsection (e.g., Figure 6a,b). In those figures, the red band ratio tended to be lower than that of the other bands. These results indicated that the red band consistency was influenced by the SRF differences, to a certain extent. Figure 10. SRFs for the AHI and MODIS, and spectral reflectances of the vegetation canopy simulated using PROSAIL. The values of LAI and psoil were assumed to be 2.5 and 0.0, respectively. Circles indicate the spectrally convoluted reflectances using SRFs. In the green bands, reflectance differences between AHI and MODIS were greater than in the other bands. Table 9. Input parameters for the PROSAIL algorithm used in the numerical simulations. The LIDF is the leaf inclination distribution function. The parameter psoil was used to describe the moisture-induced reflectance changes in the soil surface (from wet to dry).    Figure 11. Contour plots of the simulated MODIS to AHI reflectance ratios for (a) blue, (b) green, (c) red, and (d) NIR bands as a function of LAI and soil moisture surface effects. Ratios were close to 1.0 in the blue and NIR bands, whereas ratios were much higher than 1.0 in the green band and were smaller than 1.0 in the red band.

Discussion
The results obtained from the data comparisons (Section 5.1) indicate that the ratio in the green band was higher than the ratios in the other bands, especially during the spring and summer seasons. Interestingly, this trend was not observed during other periods. This effect must be strongly related to both the photosynthetic activities of the vegetation canopy, i.e., the coniferous forests [50], and to differences in the SRFs of the green band. This trend suggests that the reflectance consistency depends on the land cover. A similar dependence could be seen in the red band. The reflectance ratio of the red band tended to be lower than that of the other bands. These trends agreed well with the numerical simulation results, suggesting that a reduction in these influences could require prior knowledge of the vegetation quantity. This perspective raises another question to be addressed in the future.
The RAM method did not always provide more consistent comparisons than the SZM method. This could be seen during the summer. In this season, the solar zenith angle was small (close to its nadir). When the solar zenith angle becomes small, the influence of the relative azimuth angle tends to be small. Thus, adjustments to the relative azimuth angle using the RAM method are less significant. By contrast, the RAM method selected AHI data acquired at different times than the MODIS data, which introduced differences in the solar zenith angles of the MODIS and AHI data. During the summer, differences (in the solar zenith angle) reached 10 • from May to August, resulting in an even worse performance by the RAM method than by the SZM method.
Moreover, the performance loss of the RAM method was caused by the relatively early sunset around the winter solstice. The RAM method selected AHI data observed at later hours of the day during the winter. The observation time of RAM for the latest case reached 06:50 UTC (15:50 local time), as shown in Table 4. The time to sunset (Table 10) was only 1 h from the data acquisition time (07:45 UTC). Because the illumination conditions were shifted toward twilight, the atmosphere exerted a greater influence on the data. For these reasons, the RAM method was limited around the winter solstice.
Around the winter solstice, the illumination conditions selected by the SZM and RAM methods were largely different. This result was confirmed by plotting the reflectance ratios as a function of time over the entire day time. Figure 12a The RAM method tended to perform better than the SZM method during winter, except around the winter solstice. This was attributed to the relatively significant influence of the relative azimuth angle compared to the solar zenith angle. During winter, the solar zenith angle was so large that the influence caused by the difference in the relative azimuth angle became significant. Thus, the choice of the relative azimuth angle became more important than the choice of the solar zenith angle. This could explain the significant improvement in the SZM performance compared to the RAM performance during winter.
In addition to the influences of the geometric conditions and biophysical parameters, several other factors may have influenced the reflectance ratios: terrain and shadow effects, atmospheric conditions, BRDF, and rotational asymmetry. These factors may degrade the performance of the RAM method compared to the SZM method. Although thorough investigations are needed to identify the influences of each factor, such investigations may have trouble evaluating these influences independently. These influences are mutually related in a complex manner and differ from region to region. For instance, terrain effects are induced by differences in the solar zenith angle, view zenith, azimuth angle, and relative azimuth angle. Therefore, investigations into the evaluation methodology itself could be useful for GEO-LEO inter-comparisons of middle latitude regions.
Considering the measurement of the relative azimuth angle in the RAM method, two choices of rotational direction are available, namely, clockwise and counter-clockwise from the position of the AHI. In this study, we chose the clockwise measure for the relative azimuth angle to make the rotational direction identical to the one used for the MODIS observation. Selection of the counter-clockwise direction would have selected AHI data collected before sunrise during the winter. Thus, the choice of the clockwise angle was a requisite. Another advantage of this choice is that the number of available datasets is greater than for the counter-clockwise alternative, within the ROIs used in this study. The maximum value of the azimuth angle relative to the illumination angle at sunset is larger than the maximum value relative to the illumination angle at sunrise. For instance, over the ROI of Kochi city, 51 datasets are available on the summer solstice if we choose the clockwise angle. By contrast, only 33 datasets are available for the alternative choice (counter-clockwise). Similar trends were observed over all of the ROIs on the summer and winter solstices, as summarized in Table 10. Finally, the better choice of rotational direction for the relative azimuth angle depended on the geolocation and overpass time of a LEO satellite. Further investigations are needed to address this issue. Table 10. Sunrise and Sunset times in the ROIs during the summer and winter solstices [51]. Dates are represented by six digits: "YYMMDD".

Sunrise Time Sunset Time
Aichi (

Conclusions
This study proposed a data screening method, the Relative Azimuthal-angle Matching (RAM) method. The RAM method is a straightforward but unique technique for comparing GEO-LEO reflectances over forest targets located in middle latitude regions. The performance of the RAM method was validated by comparing the RAM results with those derived using the Solar Zenith-angle Matching (SZM) method. Data collected over three years were compared after processing using the RAM and SZM algorithms. The experimental results show that, in general, RAM was better than SZM throughout the year, except for the summer and a short period around the winter solstice. Especially in the autumn and winter, RAM outperformed SZM. These results were attributed to improvements in the relative azimuth angle by the RAM. The initial screening step used for GEO-LEO comparisons benefitted when the RAM method selected reflectance pairs with a smaller bias than the SZM method. This conclusion contradicts the intuition that simultaneous observations (SZM) would select better observation pairs. This study raises questions about the choice of screening criteria for middle latitude targets in the context of GEO-LEO comparison frameworks. Since our target ROIs were two similar mountainous forests with urban ROIs residing in each forest ROI, it was unrealistic to reach a definitive conclusion from the limited number of samples. Further studies will be needed to draw general conclusions on the advantage of RAM over SZM. Further studies are needed to clarify the limitations of the RAM method as a function of the data acquisition time, geolocation of the targets, and sensor pairs. Moreover, extending the discussion to higher level of data products such as spectral vegetation indices and biophysical parameters will also be needed to further examine the differences between RAM and SZM in the context of GEO-LEO inter-comparison.
Differences between the SRFs of the MODIS and AHI datasets were investigated using numerical simulations. The green band ratio was large compared to the results obtained in the other bands. We concluded that this result arose from differences in the SRFs of the two sensors. Furthermore, the red ratio was influenced to some extent by SRF differences. These influences depended on the value of the LAI, suggesting at the reflectance comparison depended on land cover and seasonal variations. This dependence should be corrected by accounting for the LAI level. This issue should be addressed thoroughly in the future.