2.1.

MODIS

MODIS has 16 TEB, covering the midwave infrared (MWIR: bands 20 to 25) and long-wave infrared (LWIR: bands 27 to 36) spectral regions. All TEB are located on two cold focal plane assemblies (CFPAs): a short-wave and midwave infrared (SMIR) FPA and an LWIR FPA. The CFPAs are nominally controlled on-orbit at 83 K using a passive radiative cooler. Bands 20 to 25 and 27 to 30 consist of 10 photovoltaic (PV) detectors per band, while bands 31 to 36 consist of 10 photoconductive detectors per band. The on-board BB serves as the primary calibration source and the space view provides a reference for the instrument background and offsets. The BB temperature is measured using a set of 12 thermistors. For nominal operations, the BB temperature is set at 290 K for Terra MODIS and 285 K for Aqua MODIS. MODIS TEB calibration uses a quadratic calibration algorithm on a scan-by-scan basis for each TEB detector. ^1,23 During the BB WUCD cycles, the BB temperature varies from instrument ambient ($\sim 270\mathrm{K}$) to 315 K. The BB WUCD is used to characterize the on-orbit change in the instrument’s nonlinear response coefficients. The linear coefficient of the response function for each TEB is calibrated scan-by-scan with the nonlinear coefficient and offset from an offline lookup table (LUT) derived from the quarterly WUCD events.

Terra and Aqua MODIS C6.1 L1B has significant improvements compared to previous collections.¹ One of the major improvements is the reduction of the electronic crosstalk effect. As the mission has progressed, the effects of electronic crosstalk among the Terra MODIS PV-LWIR bands 27 to 30 have become increasingly large and its impact on L1B products has grown.²⁴ To characterize and correct the signal contamination from electronic crosstalk, Moon observations have been used to derive the appropriate correction coefficients, which are applied to the detector’s digital response data for Terra MODIS bands 27 to 30. The correction has been implemented in C6.1 over the entire mission and is being continuously monitored and updated in the forward production.

2.2.

AHI

The Himawari-8 spacecraft was launched on October 7, 2014 at an altitude of $\sim \mathrm{35,800}\mathrm{km}$, longitude of $\sim 140.7°$ east, covering the East Asia and Western Pacific regions. The primary instrument aboard Himawari-8, AHI, is a 16-channel multispectral imager that captures visible and infrared images of the Asia-Pacific region.²⁵ AHI has a very similar design and spectral channels as Advanced Baseline Imager (ABI) on-board US GOES-16. Both the instruments were designed and built by Harris Corporation (formerly ITT Exelis Geospatial Systems) and represent a significant improvement over the imager on-board previous GOES satellites.²⁶ AHI uses two scan mirrors (north-south and east-west scan mirrors) and produces a full disk observation every 10 min with a resolution down to 500 m.²⁷ The AHI instrument features higher spatial, spectral, and radiometric resolution than previous imagers on-board geostationary satellites, besides shortened scanning. It has 3 visible, 3 near-infrared, and 10 infrared bands. The spatial resolution is 2 km at nadir for TEB. The TEBs show a significant nonlinear response and hence a quadratic response function is used for the calibration.²⁸ The linear coefficient of the response function for each channel is calibrated every 10 min using an on-board BB with the nonlinear coefficients derived from prelaunch testing. Compared to previous imagers on-board geostationary satellites, AHI and ABI provide more spectral channels, higher spatial resolution, and enhanced radiometric calibration accuracy.

2.3.

Spectral Matching Bands

The MODIS and AHI matching bands are listed in Table 1 and their RSR functions are shown in Fig. 1. The method used in this work is the double difference and AHI is used as a bridge to facilitate a comparison between Terra and Aqua MODIS. Hence, the effect of differences in spectral response function between MODIS and AHI is insignificant to the first order. However, for a specific site, the spectral mismatch can have an effect that varies seasonally or with observation time. The analysis in this work uses the averaged results over the entire year to minimize this effect. For most of the matching bands, AHI bands have broader spectral response functions than MODIS. Four matching MODIS bands, 20 to 23, are compared with AHI band 7 centered at $3.9\mu \mathrm{m}$.

Table 1

The center wavelength for the matching bands of MODIS and AHI.

Fig. 1

The spectral response function of the selected bands of MODIS (Terra in blue and Aqua in red) and AHI (light blue).

The imperfect matching between AHI bands and MODIS bands can impact the comparison results between MODIS and AHI. As presented in Refs. 12 and 13, the double difference method, by using intermediate transfer instrument as a reference, can be used to compare MODIS and AVHRR, as well as LEO-GEO-LEO comparison.^12,13 To minimize the spectral mismatch impact, a selected type of stable and uniform scene should be used. In this work, uniform clear sky ocean and desert sites are selected for applying the double difference method, as presented in Sec. 3.1. The uniformity and cloud screening, presented in Sec. 3.2, are also necessary to ensure a stable reference for this double difference technique. The slight spectral difference between Terra MODIS and Aqua MODIS has insignificant impact on the comparison between Terra and Aqua MODIS. This effect is discussed in Sec. 5.1.

3.1.

Site Selection and Resampling

In this paper, an area of ocean located under AHI nadir and a site around the Strzelecki Desert to the south of AHI nadir have been selected.^29,30 The full disk of AHI does not cover the widely used North African desert sites, including Libya 4. The Strzelecki Desert in South Australia has been used previously as a bright calibration target.^29,30 When AHI views the site near its nadir, the zero angle of the AHI east-west scan mirror and small view angle may enhance its reference accuracy. The BT varies with time of a day and solar angle. The observation time difference also introduces uncertainty due to the presence of clouds and varying atmospheric conditions. Hence, the comparisons should be performed using simultaneous overpasses with minimal time difference. MODIS images a given site in daytime and in nighttime once every 1 to 2 days. AHI images the Earth’s full disk every 10 min. The higher temporal sampling of AHI makes it possible to shorten the overpass time difference between MODIS and AHI for the selected sites. For clear sky measurements, the effects of up to 5 min time difference can be averaged out and the impact on the comparison will be greatly reduced.

This work employs a pixel-to-pixel comparison between MODIS and AHI. However, the AHI pixel size at nadir is 2 km for the TEB and MODIS pixel size at nadir is 1 km for the TEB. The geolocation error and pixel mismatch should also be considered. The MODIS measurements with different view angles are used for comparison and a correction of the view angle dependence is necessary. Table 2 lists the geolocation of the site and MODIS overpass time (day and night).

Table 2

The latitude and longitude ranges (in degrees) of the calibration sites, AHI pixel number, MODIS overpass time, and overpass granule number used for comparison in year 2017.

The L1B data from MODIS C6.1 and AHI are processed for comparison. There are two methods for the comparison for the selected site. (1) Average all pixels within the enclosed region of interest and then perform a BT comparison and (2) resample the pixels within the enclosed region of interest from one of the instruments and then perform a pixel-to-pixel comparison. The first method is simpler, but may introduce additional uncertainties. It also causes issue for the area with small number of cloudy pixels. In this paper, a pixel-to-pixel comparison after resampling is used. The MODIS data are resampled and interpolated to the AHI grid over the selected area, as shown in Fig. 2. Even though scene uniformity was a major consideration in the site selection process, the presence of clouds can cause nonuniformity over the site. The pixel-to-pixel comparison after resampling enhances the comparison accuracy and also allows the comparison to be performed over a broad range of BTs.

Fig. 2

(a) The AHI image of selected ocean site (granule time stamp 20171228_1550). (b) Aqua MODIS image covering the same site (granule time stamp 2017362.1550). The yellow lines are the latitude and longitude boundaries for the site. (c) Resampled Aqua MODIS image of the site with AHI grid.

3.2.

Uniformity and Cloud Screening

As stated earlier, the spatial resolution for AHI TEB is 2 km while it is only 1 km for MODIS TEB. The data resampling and sensor spatial uncertainty reduce the comparison accuracy when using observations over a nonuniform scene. The observation time difference also has effects if there are clouds present or the atmospheric conditions change between the two overpasses. MODIS C6.1 level 2 products (MOD35 for Terra and MYD35 for Aqua) are used for identifying cloudy and clear sky measurements.³¹ The cloud mask has four values indicating cloudy, partially cloudy, partially clear, and clear. The pixels selected for comparison are totally clear sky. The scene uniformity is assessed using the cloud mask of surrounding pixels. A pixel selected for comparison should have the same cloud mask status (clear) over the $3\times 3$ resampled AHI pixels. Additional uniformity filtering is also applied by using the variation over nine ($3\times 3$) AHI pixels to reduce the effect of scattering from neighboring pixels. In addition, this additional uniformity filtering also reduces the geomatching effect on the comparison.

Figure 3 shows the pixel number after the uniformity and clear sky filtering. The blue symbols are the pixel number for a day and the red lines denote a 30-day moving average to show the seasonal trend. The desert site is located at the south of the Himawari-8 suborbital point. However, the ocean site has large cloud impact and the number of days and the number pixels with uniformly clear sky is much lower than the number obtained from the desert site. Measurement uncertainty decreases by square root of number of samples. Therefore, the desert site can enhance the comparison accuracy. The nighttime desert observations show a strong seasonal variation for both Aqua and Terra MODIS. Since clear sky filtering has been applied, the pixel number also varies with season.

Fig. 3

The AHI pixel count for the selected sites after the uniformity and clear sky filtering. The blue symbols are the pixel number for a day of the year (2017) and the red lines are the 30-day moving average to show the seasonal trend. The left hand charts are for Aqua and right charts are for Terra. (a) and (b) Nighttime desert, (c) and (d) daytime desert, (e) and (f) nighttime ocean, and (g) and (h) daytime ocean.

3.3.

Correction and Comparison

When analyzing the MODIS–AHI comparison, a view angle dependence in the MODIS measurements was observed. The selected sites have a fixed view for AHI and its measurements used as reference do not affect MODIS view angle dependence. For the desert site, AHI measurements have a fixed view angle. The MODIS–AHI difference from both sites exhibit a MODIS view angle dependence. The view angle dependence is analyzed by using an empirical model for both sites. Figure 4 shows a flowchart for the MODIS intercomparison using AHI as bridge.

Fig. 4

Flowchart for the MODIS comparison using AHI as bridge and the processing for clear sky and uniformity filtering, view angle correction, and statistical analysis.

For each pair of matching bands, the AHI BT measurements and MODIS BT measurements as well as the cloud mask are processed for the selected area. Based on the AHI grid, MODIS BT and cloud mask are resampled. After clear sky and uniformity filtering, the pixel-to-pixel MODIS–AHI differences are calculated. The view angle dependence is corrected using the empirical model. The Terra–AHI and Aqua–AHI difference as well as their precision are assessed using statistical analysis. The Terra–Aqua difference is derived by using the double difference and its precision is estimated from a statistical analysis.

4.1.

MODIS–AHI Difference

In this work, the averaged comparisons from the year 2017 are analyzed. The 1-year averaging process will mitigate the impact due to seasonal fluctuations and also reduce the uncertainties associated with this comparison. The collocated L1B data with closest observation time for AHI and MODIS are collected and processed using the method described in Sec. 3. The differences between AHI and Aqua MODIS and between AHI and Terra MODIS are computed for all the spectrally matched bands. Figure 5 shows examples of the MODIS–AHI comparison for select bands using nighttime clear sky over the ocean site. Figure 6 shows examples of the MODIS–AHI comparison for selected bands over the desert site using nighttime clear sky observations. Bands 30 and 31 are selected to show on both Figs. 5 and 6. Band 31 is relatively stable for both Terra and Aqua MODIS and can be used as a reference. Band 30 shows the largest Terra–Aqua difference for both sites. The significant spectral difference between the matched band pairs, as well as their calibration uncertainty, makes the MODIS–AHI difference scene and BT dependent. The dependence has been demonstrated using MODTRAN modeling for typical ocean and desert scenes along with the MODIS and AHI RSR shown in Fig. 1.

Fig. 5

The MODIS–AHI difference versus MODIS BT using the ocean site (nighttime clear sky) under AHI nadir. The red symbols are the Terra–AHI difference and blue symbols are Aqua–AHI difference.

Fig. 6

The MODIS–AHI difference using the Strzelecki Desert site (nighttime clear sky). The red symbols are the Terra–AHI difference and blue symbols are Aqua–AHI difference.

Since an entire year data are used, the scene temperature varies for all the bands. The ocean measurements have a narrow BT range while desert site has a larger BT range. As shown in Sec. 3.3, the desert site provides more clear sky samples. The MODIS–AHI difference covers a different range for each site. As mentioned in Sec. 3.3, the large MODIS–AHI difference includes a view angle effect that needs to be corrected. It also shows that the correction is band dependent.

4.2.

View Angle Dependency Correction

The MODIS–AHI difference exhibits a MODIS view angle dependence for both ocean and desert sites. Even for a non-nadir desert site, the view angle dependence of AHI measurements is not an issue as it has the same bias for both Terra–AHI and Aqua–AHI differences. The bias is then removed in the double difference for the Terra–Aqua comparison. The view angle correction is empirically modeled and corrected to achieve an improved MODIS–AHI difference. Before applying the empirical model, the symmetry of the measurements on either side of nadir was verified. The symmetrical pattern is an indicator of the accuracy of the RVS for these bands. The daytime measurements do not exhibit the symmetrical feature (see discussion in Sec. 5.3) and are not included in the final results of comparisons.

After examining different models, an empirical model is selected to represent the view angle symmetry as

The examples shown in Fig. 7 are the comparisons using the ocean site and in Fig. 8 using the desert site; the pink lines are the fitting for the Terra–AHI difference and green lines are the fitting for the Aqua–AHI difference. The coefficients $c_{\mathrm{0,1},2}$ derived from the regressions in Figs. 7 and 8 are used to correct the view angle effect. The corrected MODIS–AHI difference as function MODIS frame number is shown in Fig. 9 for the ocean site and Fig. 10 for desert site. These view angle corrected MODIS–AHI differences are used to determine the Terra–Aqua difference.

Fig. 7

The MODIS–AHI difference as a function MODIS frame number over the ocean site. The red symbols are the Terra–AHI difference and blue symbols are Aqua–AHI difference. The pink line is the fit using empirical model for Terra–AHI difference and green line is the fit for Aqua–AHI difference.

Fig. 8

The MODIS–AHI difference as a function MODIS frame number over the desert site. The red symbols are the Terra–AHI difference and blue symbols are Aqua–AHI difference. The pink line is the fit using empirical model for Terra–AHI difference and green line is the fit for Aqua–AHI difference.

Fig. 9

The corrected MODIS–AHI difference as a function MODIS frame using the ocean site. The red symbols are the Terra–AHI difference and blue symbols are Aqua–AHI difference.

Fig. 10

The corrected MODIS–AHI difference as a function MODIS frame number for the desert site. The red symbols are the Terra–AHI difference and blue symbols are Aqua–AHI difference.

The distribution of the MODIS–AHI difference over the desert site shows a larger range in comparison with the ocean site. There are two factors that may contribute to the increased distribution. The first is that the desert site has more clear-sky samples (pixels) covering a broader temperature range used for the comparison and the second is that the nonuniformity combined with geo-mismatching may also introduce larger noise. After correction, a residual view angle dependence is observed for some bands, for example, bands 27 and 33, especially for the desert site. For the desert site, the selected area is larger and some variations are present. The pixel matching in both location and size can introduce noise, especially for large view angles. However, it contributes random noise and the impact on the comparison is largely reduced by using a large amount of samples.

4.3.

Terra and Aqua Difference

As shown in Figs. 9 and 10, the comparison between AHI with Terra MODIS and AHI with Aqua MODIS shows distributions close to Gaussian for most bands. To assess the impact of this behavior on the comparison, the distribution is first quantified. Figures 11 and 12 show that the distribution over nighttime ocean and desert for select bands. The distribution is normalized to the peak count. The distribution of MODIS–AHI differences is very close to a Gaussian shape. The exception is band 27 over the desert site; the distribution is symmetrical but the shape does not follow a smooth Gaussian function. This may be related to the crosstalk issue and is discussed in Sec. 5.2.

Fig. 11

The distribution of MODIS–AHI differences measured for selected bands over nighttime ocean. The red is for Terra–AHI difference and blue is for Aqua–AHI difference.

Fig. 12

The distribution of MODIS–AHI differences measured for selected bands over nighttime desert. The red is for Terra–AHI difference and blue is for Aqua–AHI difference. The distribution is normalized to the peak count.

A Gaussian profile is used to estimate the impact of these random effects. The Gaussian function is used as $A\exp [-\frac{{(x-x_0)}^2}{2{\sigma }^2}]$. When applying it to the distribution of MODIS–AHI differences, $x$ is the scene BT, $x_0$ is the BT difference corresponding to the Gaussian peak, $\sigma$ is the Gaussian width representing the uncertainty of the comparison, and $A$ is the peak value before normalization. Two methods are used to derive the Terra–Aqua difference. The first method is to average the Terra–AHI differences and Aqua–AHI differences, respectively. Then the Terra–Aqua difference is derived using the double difference. The second method is to fit the Terra–AHI and Aqua–AHI differences to the Gaussian distribution and then take the difference between the two peaks.

Table 3 lists the Terra–Aqua difference for the different scenes from the two methods. The results from the two methods are consistent. The Terra–Aqua difference is up to 0.6 K except for bands 21 and 30. A linear calibration equation is used for band 21, widely used for fire detection. The uncertainty of its BT over oceans and deserts is larger than other bands. Band 30 has the largest difference and that difference is site dependent. Over the ocean, the difference is around 1.75 K, while over the desert, the difference is around 0.68 K. The large difference and scene dependence may be related to crosstalk.

Table 3

Terra–Aqua BT difference (K) for different scenes using the two methods.

4.4.

Precision Comparison

The width of the distribution of MODIS–AHI difference includes uncertainties in the MODIS measurements, AHI measurements, and the comparison, as expressed as

Since the same method is applied for both Terra–AHI and Aqua–AHI differences. The AHI measurement uncertainty and comparison method uncertainty, the second and third terms in Eq. (2), are almost the same for Terra–AHI and Aqua–AHI differences. Therefore, we can write

The values of ${\sigma }_{\text{Terra}-\mathrm{AHI}}^2$ and ${\sigma }_{\text{Aqua}-\mathrm{AHI}}^2$ are derived from the Gaussian fits to the MODIS–AHI differences. For the precision comparison, if the MODIS with a smaller uncertainty is selected as a reference, the extra noise of the other MODIS is then estimated

By applying Eq. (3), the extra noise can be derived using

The extra noise, calculated using this equation for each band and scene, is listed in Table 4. For the majority of the comparisons, Aqua is the more stable. The bold indicates cases where Terra is considered more stable. The noise in the table is for a single measurement. More detailed discussion will be given in Sec. 5.4.

Table 4

MODIS–AHI comparison precision analysis. Terra extra noise using Aqua as reference. Exceptions are boldfaced indicating cases where Aqua has extra noise. In the calculation, more digits are used while the value in table is round to mK.

5.1.

Spectral Mismatching

There are two kinds of spectral mismatching. One is between MODIS and AHI. Its effect on Terra–Aqua comparison is generally canceled using double difference method, which has been discussed in Sec. 2.3. The second is the spectral mismatch between the two MODIS instruments. Terra and Aqua MODIS were designed to have the same spectral bands. However, a slight difference between the RSR of these instruments exists and was characterized extensively during prelaunch testing. The radiometric calibration of the MODIS TEB use a detector-specific RSR characterized from prelaunch measurements. However, the BT measurement for certain scenes observed by the two instruments in different seasons will be impacted due to the RSR mismatch. The BT difference due to their RSR mismatch is estimated using the modeled radiance spectrum for each band for typical ocean and desert scenes using MODTRAN.³²

Figure 13 shows the BT spectrum from MODTRAN modeling for a typical ocean site and the RSR for band 27 of two MODIS instruments with AHI band 9 and MODIS band 30 with AHI band 12. The RSR are from prelaunch tests and implemented in L1B BT calculations. Bands 27 and 30 have largest impact from the spectral mismatching. The spectral resolution in MODIS prelaunch tests is large and is different between Terra and Aqua. The large spectral resolution and their difference between Terra and Aqua, combined with large fluctuation and features of BT spectrum, can introduce uncertainty in the analysis of the spectral mismatching effect, especially for bands 27 and 30. In addition, the comparison in this analysis uses an entire year of measurements and these estimates from a typical scene are only for Ref. 33. Table 5 lists their difference from the modeling. For most bands, the impact is up to 0.3 K, except bands 27 and 30.

Fig. 13

The BT spectrum from MODTRAN modeling for a typical ocean site and the RSR for MODIS band 27 with AHI band 9 and MODIS band 30 with AHI band 12.

Table 5

The impact of the RSR difference on the Terra and Aqua comparison over typical ocean and desert scenes using MODTRAN modeling results.

5.2.

Terra PV LWIR Crosstalk Impact

Terra has a known electronic crosstalk issue for LWIR bands 27 to 30. The crosstalk correction has been applied to the Collection 6.1 L1B data which is used in this work.²⁴ The crosstalk coefficients are derived from scheduled lunar observation and are updated if the coefficients change beyond a certain limit. As shown in Table 4, Terra bands 27 to 30 have large bias and extra noise comparison with Aqua. It is known that the crosstalk has a large impact on Terra bands 27 and 30 calibration and L1B product. Due to the time delay, the uncertainty of the crosstalk coefficients, and fluctuations in the sending bands, some residual crosstalk effect can impact the L1B data.

Table 3 shows a larger Terra–Aqua difference for bands 27 and 30 than those of other bands, except band 23. The Terra–Aqua differences for these two bands also have larger scene dependences. These issues can be attributed to residual impacts of crosstalk postcorrection. In addition, the crosstalk effect will also have seasonal variations and, as a result, the width of the Gaussian distributions becomes larger. As shown in Table 4 for bands 27 to 30, Terra has extra noise in relation to Aqua, which is larger than other bands, except band 21 over desert. However, the distributions of Terra–AHI difference are symmetric and most of them are still nearly Gaussian, except band 27 which has a symmetric non-Gaussian shape over desert. The impact of the crosstalk effects is random and will increase the comparison uncertainty. By collecting large number of samples, these effects are reduced. The systematic effects are included in the Terra–Aqua difference for these bands, which are mostly scene dependent.

5.3.

Scene Effects

For the assessment of TEB performance, the nighttime measurements have an advantage, especially for MWIR bands. The empirical model cannot be applied to the daytime MODIS–AHI difference as function of frame number. For comparison, Fig. 14 shows an example for band 22. The MODIS–AHI difference during nighttime is symmetric around the nadir frame and the empirical model for view angle dependence works reasonably well. The daytime measurement is not symmetric across frames and therefore cannot be corrected using the empirical modeling. In addition, the two MODIS instruments have different overpass times and the ground BT range is also different. For some bands, saturation affects the Terra–AHI and Aqua–AHI comparison differently.

Fig. 14

The MODIS–AHI difference as function frame number for band 22 over daytime ocean, nighttime ocean, daytime desert, and nighttime desert. The red is for Terra–AHI difference and blue is for Aqua–AHI difference.

The asymmetric pattern of the MODIS measurements in the daytime is more significant for MWIR bands than LWIR bands. As shown in Fig. 14 for band 22, a clear view angle-dependent pattern is observed in the daytime measurements in comparison with the nighttime measurements. One is the sun glint effect at certain view angle range over the ocean scene. The second is the asymmetric measurement over the two sides around the nadir. As presented in Ref. 34, the surface solar reflectance during daytime impacts the measurement in the MWIR bands.³⁴ The BT calculated from the radiance measurement includes the reflected solar radiance that is solar angle dependent. For the selected site, the view angle and the overpass time are closely related in the case of each MODIS instrument. The solar angle for one side of nadir is different than the other side. The retrieved radiance is different for the two sides. It causes an asymmetric pattern of the radiance measurements, as shown in Fig. 14 daytime measurement for both ocean and desert sites.

As shown in Figs. 7 and 8, the clear sky ocean scene under AHI nadir provides a narrower BT range than the desert scene. The BT dependence of the Terra–Aqua difference is reduced. However, this ocean site has much less clear sky pixels. This double comparison will be applied to cloudy pixels to analyze Terra–Aqua difference at low BT in our future work. On the other hand, the desert site has more clear sky pixels which enhanced the comparison accuracy. The desert site is located at the south of AHI nadir and has a fixed view angle. The desert site provides a larger range of ground BT and significantly more clear sky pixels for comparison.

5.4.

Seasonal Variation

The seasonal variation is observed for MODIS–AHI difference and the comparison presented above is for the yearly averaged results. Figure 15 shows the daily averaged MODIS–AHI difference as function of day of the year, from clear sky nighttime desert site. Band 28 does not exhibit significant seasonal variation, whereas bands 29 and 31 show significant variation in the comparison. During the middle of the year, the MODIS–AHI difference shows more stable results. A significant seasonal variation is observed in the MODIS–AHI difference, as bands 23, 32, and 33. Both Terra–AHI difference and Aqua–AHI difference show the similar seasonal variation pattern for each band. Therefore, the seasonal variation impact on Terra–Aqua difference is small.

Fig. 15

The daily averaged MODIS–AHI difference as day of the year over nighttime desert. The red is for Terra–AHI difference and blue is for Aqua–AHI difference.

5.5.

Comparison Uncertainty

The precision assessment in Sec. 4.4 is for one pixel-to-pixel comparison between instruments. The term precision is used to differentiate it from uncertainty. If the uncertainty is completely due to random effects, the uncertainty can be assessed using the width of the Gaussian distribution. In addition, the uncertainty of the mean of the measurements is the uncertainty of a single measurement divided by square root of the number of samples. Applying this to the MODIS–AHI comparison, the uncertainty of the average of $N$ comparison samples is

In this work, the entire year of data after resampling gives the around 12,000 samples for clear sky ocean and 55,000 samples for clear sky desert. As shown in Table 4, band 27 has the largest uncertainty of the Terra–AHI comparisons: 0.72 K for ocean and 1.06 K for desert. Averaging of large number of sample provides an improvement of 110 times for ocean and 230 times for desert. As a result, the uncertainty from the random effects is now on the order of mK. However, as discussed above, the uncertainty of MODIS–AHI difference should include the impact due to spectral mismatch, scene dependence, and crosstalk effects for some bands. In addition, both MODIS and AHI instrument calibrations use a quadratic function. ^1,23 The impact of uncertainties of the calibration coefficients is BT dependent.³³ A BT-dependent comparison will be performed in our future analysis. For example, the desert scene has a relatively large BT range and the comparison can be assessed for various BT. In addition, totally cloudy scenes provide feasibility for the comparison over a low BT range.