a. VIRS

TRMM was launched on 27 November 1997 and circles the earth in a precessing 35° inclined orbit where it observes areas equatorward of ∼37° latitude at all local hours and viewing zenith angles (VZA) up to 45°. The 2-km-resolution VIRS calibrated radiances, based on prelaunch and onboard procedures (Barnes et al. 2000), were obtained the from level 1B01 version 5a (V5) data through March 2004 and from version 6 (V6) data thereafter. The V6 calibrations were also applied post facto to the radiances taken between 1998 and March 2004 to provide a complete up-to-date time series of V6 data. The VIRS calibration has been evaluated using comparisons with other self-calibrated satellite sensors (Minnis et al. 2002) including the broadband CERES scanners (Wielicki et al. 1998), the second Along Track Scanning Radiometer (Smith et al. 1997), and the Terra MODIS, and using lunar models, solar calibrations, and MODIS data (Lyu and Barnes 2003). Those comparisons provided calibration corrections for apparent trends in the data and demonstrated the stability of the instrument. The main difference in channel 1 between versions 5a and 6, as noted earlier, is that the gain was corrected to account for an apparent linear degradation in the response determined from the solar measurements of Lyu and Barnes (2003) taken from 1998 through 2001. Based on the responsivities reported by Lyu and Barnes (2003), the gains for V5 and V6 are 0.014 43 and (0.014 33 + DSR 0.483 × 10⁻⁶) W m⁻² sr⁻¹ μm⁻¹C⁻¹, where DSR is number of days since the reference date of 1 January 1998 and C is the observed brightness count.

The VIRS channel 1 (VIS) radiance is obtained from the following equation:

View Expanded

where a is the gain, and C_o is the space count. The VIRS solar constant E_υ is 531.7 W m⁻² sr⁻¹μm⁻¹. For comparisons with MODIS data, the VIRS radiances are normalized as in Minnis et al. (2002) to equivalent Geostationary Operational Environmental Satellite (GOES) radiances by multiplying them by the ratio of the GOES and VIRS solar constants (E_o/E_υ = 0.991). Here the nominal GOES solar constant E_o is 526.9 W m⁻²sr⁻¹ μm⁻¹. To minimize the effects of parallax, navigation errors, and advection, the VIRS radiances are averaged on a 0.5° equal-angle grid for matching with Terra and Aqua.

b. MODIS

Terra MODIS began producing its first usable imagery during February 2000. It scans to a VZA of ∼70° providing a swath that is 2330 km wide. Aqua MODIS started operational scanning in July 2002. Terra and Aqua have equatorial crossing times of 1030 and 1330 LT, respectively. Their orbital tracks cross at 70°N and 70°S. A subset of the collection 4, 1-km-resolution Terra MOD021KM and Aqua MYD021KM data are used here (see http://ladsweb.nascom.nasa.gov/) through December 2005. Collection 5 data are used thereafter. The prelaunch calibration characteristics of the MODIS channels are discussed by Barnes et al. (1998). The MODIS radiances are computed in the same manner as the VIRS radiances where there is a gain and offset for each channel. For comparisons with other imager data, the MODIS channel 1 (0.645 μm) radiances are averaged in 0.5° regions. When compared with each other and CERES data, the Terra and Aqua MODIS VIS channels are assumed to be equivalent even though the solar constants, 509.3 and 510.0 W m⁻² μm⁻¹ sr⁻¹, for their respective spectral filter functions differ by 0.12%. For comparison with the VIRS data, the Terra and Aqua radiances L_T and L_A, respectively, are normalized using the ratio of the GOES solar constant to 509.83 W m⁻² μm⁻¹ sr⁻¹. This approach to intersatellite calibration uses the GOES solar constant as a reference simply for convenience because it provides continuity with previous calibrations (Minnis et al. 2002).

c. CERES broadband SW radiances

The CERES instruments on Terra and Aqua consist of two programmable scanners. One scanner operates primarily in the cross-track mode and the other mostly in the rotating-azimuth plane scanning (RAPS) mode. This study uses the unfiltered radiances taken between March 2000 and December 2005 and between July 2002 and March 2005 by the main cross-track scanners, flight models FM-1 and FM-4 on Terra and Aqua, respectively. The scanners have a nominal subsatellite resolution of 20 km and view out to a nadir angle of 90°. Each radiance measurement is reported in the CERES Single Scanner Footprint (SSF) product (Geier et al. 2003), which includes many parameters including 1-km cloud products and selected raw MODIS radiances convolved into the CERES scanner field of view (Wielicki et al. 1998). Thus, the cross-track CERES radiances are optimally matched with the narrowband MODIS data in terms of space, time, and viewing angles. The instantaneous uncertainty in the unfiltered SW radiance is 0.6%. Each CERES radiance is classified as ocean, land, or desert based on the predominant surface type in the field of view.

This study uses CERES Terra Edition 2B and Aqua Edition 1B SSF cross-track data. Significant drifts in the FM-1 and FM-4 SW gains were found after processing of these editions began (Spence et al. 2004). Matthews et al. (2005) developed a set of scaling factors to account for the gain changes due to sensor degradation (additional information is available online at http://eosweb.larc.nasa.gov/PRODOCS/ceres/SSF/Quality_ Summaries/CER_SSF_Terra_Edition2A.html and at http://eosweb.larc.nasa.gov/PRODOCS/ceres/SSF/Quality_Summaries/CER_SSF_Aqua_Edition2A.html). Those revisions (Rev1) are applied to all of the CERES radiances used here prior to comparison with the MODIS data. Initially, the resulting data were estimated to have a stability uncertainty of 0.12% yr⁻¹ (Matthews et al. 2005). More recent comparisons of 5.5 yr of tropical CERES SW radiance anomalies with their counterparts derived from extremely well-characterized VIS radiances from the Sea-viewing Wide Field-of-view Sensor (R. A. Barnes et al. 2004; Eplee et al. 2004) indicate that the CERES Terra SW stability is on the order of 0.2% ± 0.5% decade⁻¹ (Loeb et al. 2007). Comparisons of CERES Aqua and Terra anomalies between July 2002 and 2005 (Loeb et al. 2007) reveal that the Rev1-corrected Aqua SW radiances still retain a small trend of approximately −0.4% yr⁻¹ relative to those measured by Terra FM-1.

a. Cross-satellite and instrument correlations

Minnis et al. (2002) found that CERES and VIRS data taken over the ocean at solar zenith angles (SZAs) < 45° were optimal for examining relative trends between the respective broadband and narrowband channels. Therefore, only SSF data taken over water surfaces for SZA 45° and unaffected by sun glint are used here to determine a linear regression each day between MODIS and CERES on each satellite. Areas with significant sun glint were identified using the ocean bidirectional reflectance model of Minnis and Harrison (1984), which provides anisotropic correction factors χ as a function of viewing and illumination angles. For all values of SZA, pixels with χ > 1.4 and a relative azimuth angle (RAA) < 75° were assumed to be affected by sun glint and rejected. Pixels with SZA < 25° and χ > 1.5 for all values of RAA were also rejected.

For Terra,

View Expanded

where L_SWT is the CERES SW radiance. Likewise, for Aqua,

View Expanded

The relative trends in the calibrations are examined using two parameters: daily values of the slopes for variable offsets and for an offset forced to zero (average ratio of SW to VIS reflectances) for ocean only when SZA < 45° and daily mean ratios of the bidirectional reflectances for bright scenes (SW albedo exceeding 0.2) over all surfaces when SZA < 78°. The latter are denoted as bright scene bidirectional reflectances (BRR).

The imager data are matched in the same manner used by Minnis et al. (2002) to determine regression fits between the normalized 0.5° mean radiances. The correlations use those pairs of collocated radiances that are taken within 15 min of each other, are unaffected by sun glint, and have differences of less than 15° between their respective VZAs and RAAs. All of the correlations using VIRS data are based only on pixels taken over the ocean between 37°N and 37°S. The direct Terra–Aqua comparisons use data taken over oceans and the Antarctic and Greenland ice sheets as in Loeb (1997) and Tahnk and Coakley (2002) near 70° latitude. The data are matched every month for each pair of satellites.

The linear regression fits are formulated as follows. For the Terra and VIRS VIS channels,

View Expanded

where a_i and b_i are the regression-derived relative gains and offsets. The subscript letters refer to the particular pair of imagers. Similarly, for Aqua and VIRS,

View Expanded

Finally, the Aqua radiances are expressed in terms of the Terra values as

View Expanded

In addition to the standard regressions above, the least squares regression analyses were also performed while forcing the offset b_i to zero, and by switching the x–y axes and then computing the mean least squares fit by averaging the x–y and y–x results. The former are referred to as force fits, while the latter are mean fits. Additionally, the slopes of the regression lines were also determined using principal component (PC) analysis. The temporal trends in the gains (slopes) and offsets are then computed using the values for all months together.

b. Deep convective cold cloud reflectance

Hu et al. (2004) pioneered the use of deep convective cloud (DCC) albedos as a means for estimating the relative stability of imager reflectance channels. Their approach assumes that, on average, the distribution of DCC broadband albedos remains constant over time. They used this approach along with narrowband–broadband conversion functions based on three reflectance channels to examine the relative stability of the VIRS and Terra MODIS. Their results confirmed the conclusions of Minnis et al. (2002) about the VIRS VIS stability between 1998 and 2000 and, based on 4 months of data, indicate that the Terra MODIS VIS channel is stable to within 1% between 2000 and 2002.

Doelling et al. (2004) used a similar approach with the same assumptions, but eliminated the conversion of the multispectral data to broadband albedos and developed a DCC technique (DCCT) for estimating calibration trends directly for single-channel spectral data. The DCCT develops a probability distribution functions (PDFs) of normalized VIS radiances each month over ocean for all pixels i between 30°N and 30°S that meet all of the following criteria:

View Expanded

where T₁₁ is the 10.8-μm channel brightness temperature, σ is the standard deviation of the specified quantity for the subject pixel and its eight adjacent pixels, and ρ is the VIS reflectance. The value of L_i is first corrected for anisotropy to obtain a Lambertian-equivalent radiance L_Ni by multiplying by the appropriate theoretical DCC anisotropic correction factor from Hu et al. (2004). The resulting spectral radiance is then normalized to SZA = 0° using the CERES SZA-dependent albedo model for overcast ice clouds over ocean with optical depths greater than 50 (Loeb et al. 2003). To ensure that the broadband CERES albedo model is applicable to the VIS data, all VIRS DCC L_N’s for 1 month were averaged according to SZA and compared with the CERES albedo model applied to estimate the radiance at all SZAs given the radiance at 0°. The resulting radiance curves in Fig. 2 show that the predicted radiances are all within about 1% of the observed averages out to SZA = 75°. The normalized radiances taken during the month are then used to form a PDF and compute the mean and mode radiances.

a. Cross-satellite and instrument correlations

1) VIRS versus MODIS

The scatterplots and regression fits for matched VIRS and Terra MODIS data are shown in Fig. 3 for July 2000 and June 2005. During July 2000 (Fig. 3a), the average value of a_VT is 1.030 compared to 0.941 during June 2005 (Fig. 3b), a drop of 7.6%. The corresponding offsets change from −1.5 to −0.4 W m⁻² sr⁻¹ μm⁻¹. Thus, the relative change between the two calibrations is primarily due to gain changes in one or both of the imagers. The PC fits (not shown) yield values of a_VT that fall by 8.1% from 1.036 to 0.941, while the force fits produce a 7.4% decrease. The least squares regression was also applied to the data after switching the axes; the average gains computed from the original and reversed-axis data changed from 1.036 to 0.949, values similar to those from the PC analysis. In all cases, the slope changes are statistically significant at the 95% confidence level according to the Student’s t test.

The gains were computed for all of the matched data and are plotted in Fig. 4 for the standard regression fits using Terra and Aqua data. Of all of the various fits, the dataset with the least noise over time is that based on the standard least squares regression. The gains for each month are separated according to the VIRS version numbers and fit to a trend line of the form,

View Expanded

where the subscript i refers to a given satellite pair, time DSR is in the number of days since the reference date (usually since launch of reference satellite), and the gain at the reference date C₀ and the trend C₁ are found by least squares regression using the gains from the standard x–y fits unless otherwise indicated. The means from the VIRS V5a and V6 fits against Terra MODIS data (Fig. 4a) are dramatically different with the latter yielding average values around 0.945 compared to about 1.028 for the former. The trend lines indicate virtually no change (decrease of less than 0.1% yr⁻¹) in the V5a slope, while the V6-Terra gains decrease at 1.4% yr⁻¹. Time series of the slopes resulting from linear regression fits using matched VIRS and Aqua MODIS data are plotted in Fig. 4b along with the computed trend lines. Here, the mean slopes for VIRS V5 and V6 are 1.047 and 0.965, respectively. The Aqua slopes are almost 0.02 larger than their Terra counterparts. The trend line for V5-Aqua is slightly positive (0.1% yr⁻¹) but not statistically significant. Conversely, the V6 trend line is negative with a 0.8% yr⁻¹ drop in the slope. Table 1 lists the trend line fits for both VIRS versions along with their corresponding squared linear correlation coefficients R.

2) Terra versus Aqua MODIS

Figure 5 plots the matched Terra and Aqua MODIS radiances and linear regression fits for July 2002 and 2005. The squared linear correlation coefficients are 0.99 for both plots with a slight increase in the slope between 2002 and 2005. This increase is confirmed in Fig. 6, which shows the average least squares fits and the gains for the fits forced to zero offsets. The relative gains from the PC fits (not shown) are identical to the mean least squares fits. The difference in the a_AT increase between the forced and mean fits is insignificant. Based on the mean fit results, Aqua radiances are 1% greater than their Terra counterparts at the beginning of the Aqua period and rise to 2.4% 3.25 yr later. Overall, the Aqua radiances increase by 0.46% yr⁻¹ relative to Terra each year.

The trend line from Fig. 6 for a_AT is

View Expanded

where DSR is the Aqua launch date, 14 May 2002. This result (see Table 1 also) suggests that the Terra MODIS channel 1 response has been degrading at roughly 0.34% yr⁻¹ relative to its Aqua counterpart.

b. Deep convective cloud radiances

Figure 10 shows the monthly PDFs of VIRS version 5a DCC pixel radiances observed between the DSR of 1 January 1998 and April 2003. While the width of the distributions varies, the mode values are all very consistent between 470 and 490 W m⁻² sr⁻¹ μm⁻¹. All frequencies approach zero around 520 W m⁻² sr⁻¹ μm⁻¹. The average mean and mode for the V5a period of record are 460 and 482 W m⁻² sr⁻¹ μm⁻¹, respectively. For the V6 record, the corresponding values are 440 and 470 W m⁻² sr⁻¹ μm⁻¹. The means and modes for each month were normalized by dividing each value by the period averages. The resulting trends for the normalized means are plotted in Fig. 11 along with the linear fits for each version. Time series from the normalized modes are very similar to those in Fig. 11 as indicated in the values listed in Table 3. The trend for the V5a normalized mean data (open circles) is 1.001–6.156 × 10⁻⁷ day⁻¹, which translates to a statistically insignificant decrease of 0.02% yr⁻¹. The trend in the mode data translates to only −0.03% yr⁻¹. Version 6 (solid squares) produces a very significant trend, 0.948 + 2.907 × 10⁻⁵ day⁻¹, in the normalized DCC radiances that converts to an 8.9% rise over 9 yr. This result is similar to that found in Fig. 4a.

The Terra and Aqua MODIS DCC normalized mean and mode radiance trends were computed in a similar manner and are plotted in Fig. 12 and listed with their VIRS counterparts in Table 3. The trends for the mean and mode for Terra (Fig. 12a) are nearly identical with an average value of −7.77 × 10⁻⁶ day⁻¹, which translates to a decrease of 2.8% decade⁻¹. The Aqua mean trend (Fig. 12b) is similar in magnitude, but positive, while the mode trend is slightly negative. The Aqua mean trend, 1.36 × 10⁻⁵ day⁻¹, is significantly different from zero at the 90% confidence level. The average trend for the two components is 6.0 × 10⁻⁶ day⁻¹, or 0.2% yr⁻¹. Because of the discrepancy between the mode and mean trends, it is difficult to conclude that the Aqua trend is significant overall.

a. Apparent trend in Terra VIS channel

Comparisons between the Terra CERES SW and the MODIS VIS channels (Figs. 8a and 9a) and between the Aqua and Terra VIS channels (Fig. 6) together with the DCC analyses (Fig. 12) suggest that the response of the Terra VIS channel is degrading and the gain has not been increased sufficiently over the course of its lifetime through the onboard calibration process. The trends in the gain range from −0.23 to −0.34% yr⁻¹ for the CERES and Aqua comparisons, respectively. The magnitude of the former is similar to the DCC analysis, while the latter number is based on a shorter period and assumes stability in the Aqua response. Using daily averages of Terra CERES SW and MODIS VIS channel, near-nadir tropical radiances, Loeb et al. (2007) found that the relative stability of the CERES/MODIS data relative to 2000 was better than 1% yr⁻¹. Their Fig. 2 shows that between 2000 and 2001, the mean CERES radiance decreased relative to the MODIS radiance by 0.5% and remained between 0.5% and 0.8% through 2003. It then increased abruptly up to values between 0.05% and 0.2% greater than the year 2000 values.

Those results are somewhat at odds with the findings in Figs. 8a and 9a. The latter suggests that if anything, the CERES SW slightly increased relative to MODIS during 2001–03 relative to 2000. A close examination of Fig. 8a reveals a semiannual cycle with peaks around the equinoxes (days 80 and 267) and minima around the solstices (days 171 and 354). The cycles are ill-defined during the first 2 yr because the FM-1 scanner was intermittently placed in the RAPS mode resulting in some significant data gaps. Although no cross-track data are available for day 80 during 2001 (day 445), the maximum slopes during 2000 are nearly identical to those seen during the period from 2001 through 2003, but the peak slopes during 2004–05 are 1.5% greater than those during the previous 4 yr. That relative difference is somewhat consistent with the results of Loeb et al. (2007) and is similar to the variations in Fig. 9a. The discrepancy between the present results and those from Loeb et al. (2007) for the 2001–03 period relative to the 2000 baseline reference is likely due to a combination of effects. The Loeb et al. (2007) spatial and angular sampling is different and the large gaps during 2000 probably biased the mean radiances and slopes for that year compared to the other years, especially 2002 and 2003. Based on the maximum slopes during each year, it appears that differences between the first and the following 3 yr are negligible, but are significant during the final 2 yr.

Further examination of the time series in Fig. 8a reveals a sudden shift of 1% or more in the slope around day 1415 (15 November 2003). Review of the channel 1 calibration gains revealed that the lookup tables (LUTs) for the reflective channels were updated every 2 weeks or so. The Terra MODIS channel 1 gain increased by 0.06% and 0.23% on 3 and 21 October, respectively. The next change, a decrease of 1.17% from 0.027 041 to 0.026 729, was implemented on 19 November, day 1419, which corresponds to the jump in Fig. 8a. Despite the relatively frequent LUT changes, there appear to be no other discontinuities in the CERES–MODIS time series (Fig. 8a) of the magnitude seen on 1419. Using data taken separately before and after day 1419, the trends for the earlier and later periods are −8.950 × 10⁻⁷ and −3.405 × 10⁻⁶ μm day⁻¹, respectively, while the corresponding offsets are 0.7121 and 0.7242, a 1.6% difference. The trends translate to −0.05 and −0.17% yr⁻¹, respectively, and are not statistically significant. Using those trends and offsets, the respective slopes on day 1419 are 0.7108 and 0.7194, a 1.21% difference, a value very close to the 1.17% decrease in the gain that occurred on day 1419. This result along with the comparison with CERES suggests that the LUT change on day 1419 was too large and that subsequent changes did not rectify the difference.

The reason for this relatively large change in the calibration is not clear. Consultation of the Terra MODIS LUT history (http://www.mcst.ssai.biz/L1B/L1B_docs/V4_LATEST_L1B_DOCUMENTS/L1B_Terra_LUT_History.txt) reveals that a different set of LUTs was generated for the period from 2 July through 31 October 2003 for a nonproduction dataset (V4.3.0.2M_ Terra) to account for an undercorrection that apparently resulted from using a degradation trend algorithm based on data prior to 2 July instead of using the actual solar diffuser measurements. The latter were not used because the solar diffuser door was left open on 2 July. Since the CERES–MODIS slopes (Fig. 8a) taken after day 1418 are clearly greater than their pre-1419 counterparts, it is unlikely that changing the data between 2 July and 31 October during 2003 would remove the discontinuity; they would only change its time of occurrence. At the time of this writing, it is not clear that the discontinuity was removed in the special dataset. It appears that the discontinuity has been replaced by linear interpolation in the Terra MODIS collection 5 dataset, but that the plateau in the calibration after day 1418 remains.

Figure 13 explores what happens to the calibrations if the Terra MODIS radiances are increased by 1.17% after day 1418, a correction that accounts for the change found in the MODIS calibration record discussed above. The mean radiances from Fig. 12a before and after day 1418 are indicated in solid squares and open triangles, respectively, in Fig. 13a. The open squares in Fig. 13a are the result of increasing the normalized radiances after day 1418 by 1.17%. Using all of the data corresponding to the squares in Fig. 13a yields a DCC slope for Terra of 2.151 × 10⁻⁶ day⁻¹, a value (0.079% yr⁻¹) that is insignificantly different from zero. Thus, assuming a 1.17% offset in the LUTs on day 1419 eliminates the apparent trend in the Terra channel 1 gain. These results strengthen the findings of Loeb et al. (2007). By accounting for more of the sampling gaps here and applying the 1.17% adjustment after day 1418 to the linear fit slopes in Fig. 8a, the trend in the slopes is −0.06% yr⁻¹. The range in the annual mean slopes is only 0.46% with an average interannual difference of less than 0.1% yr⁻¹. This result between the Terra MODIS VIS and CERES SW channels is substantially better than the 1% yr⁻¹ interannual stability found by Loeb et al. (2007).

Applying that same correction, dividing the relative gains by 1.0117, to the relative gains in Fig. 6 after day 567 (corresponds to 1418 in Fig. 13) yields the points and regression fit shown in Fig. 13b. Two trends are shown. The standard linear regression slope (denoted as x–y) is only −0.08% yr⁻¹, and the trend based on forcing each fit to go through the origin is −0.02% yr⁻¹. Both trends are statistically insignificant and confirm that with the correction for the Terra discontinuity, the Terra VIS channel is stable to better than less than 0.1% yr⁻¹. Even with the correction, the radiances measured by Aqua are, on average, 1.0% greater than those from Terra. Thus, to ensure consistency between the two sensors, one of the two calibrations must be normalized to the other.

b. Aqua trends

The results so far indicate that the Aqua MODIS VIS channel gain has changed by a negligible amount (Fig. 12b mode plot and Fig. 13b) up to 0.27% yr⁻¹ (Fig. 12b mean plot). Comparison with the CERES SW in Fig. 8b suggests that the Aqua VIS gain increased by 0.31% yr⁻¹ or the CERES SW decreased by the same amount. The results in Fig. 9b for the last 2 yr of the data record (the first 2 yr contain too many missing data points for a reliable trend) produce a drop of −0.41% yr⁻¹. As noted earlier, Loeb et al. (2007) found that the Aqua CERES SW fluxes decreased by −0.40% yr⁻¹ relative to their Terra counterparts. A similar result, −0.37% yr⁻¹ (G. Matthews 2006, personal communication), was found using a DCC analysis of the CERES SW data (Matthews et al. 2006). Given the consistency between the various results, it is concluded that the trends in Figs. 8b and 9b are almost entirely due to the degradation in the CERES SW instrument and that the mean trend in Fig. 12b does not represent the true degradation in the Aqua VIS channel response. The trends in Fig. 13b and the mode variation in Fig. 12b suggest that the Aqua VIS channel response, like that for Terra, degrades at less than 0.1% yr⁻¹. Further uncertainties in the Aqua trend are examined in the next section.

c. Trend in VIRS VIS channel

From the comparisons in Fig. 4 and the results in Fig. 11, it is clear that the VIRS V6 calibration has a significant trend. Lyu and Barnes (2003) developed the responsivity (gain) correction for V6 based on observations of the sun through the VIRS solar diffuser. Because the radiance observed through the diffuser decreased almost linearly at a rate of 1.15% yr⁻¹ during the first 4 yr of operation and no change was seen in the corresponding channel 2 (1.6 μm) radiances, it was assumed that the sensor response was degrading, not the diffuser reflectivity. The trend in the V6 normalized gain in Fig. 11 is 1.04% yr⁻¹, a value that is 10% smaller in magnitude than the operational correction applied to the gain in V6. If the sensor response were degrading as predicted, then the V5 DCC data should have produced a decrease in the normalized gain and the V6 DCC trend should have been negligible. For the same period (DSR = 0–1460) used by Lyu and Barnes (2003), the relative change in the average of the mean and mode V5a DCC radiances is −0.17% yr⁻¹, a value suggesting much less degradation in the channel 1 sensor than expected. Preliminary DCC analyses of the V5a and V6 VIRS channel 2 mode gains yield trends of 0.14 and 0.08% yr⁻¹, respectively, confirming that there is no degradation in the channel 2 sensor. Lyu and Barnes (2003) had no other information to assess their conclusion that the channel 1 sensor, rather than the solar diffuser, was degrading. The additional data examined here suggest that there was no degradation in the solar diffuser.

To determine how this V6 trend impacts the intercalibrations with Terra, the V6 points in Fig. 4a were multiplied by the DCC trend values, computed from the mean and mode fits in Table 3, to yield V6′ values. These are replotted in Fig. 14a along with the original V5a points (solid squares). The resulting linear fit yields a slightly negative trend (Table 4). However, it was found earlier that the Terra gain decreased by 1.17% on day 1419. Thus, the slopes determined after that date were multiplied by 1.0117 to account for the Terra change. These points (open circles) are easily seen above their original values in Fig. 14a. A final correction is needed to account for the change in responsivity between V5a and V6. The initial V5a channel 1 responsivity, 69.30 counts (mW cm⁻² sr⁻¹ μm⁻¹)⁻¹, reported by Lyu and Barnes (2003), is nominally 0.7% less than their V6 value of 69.782 counts (mW cm⁻² sr⁻¹ μm⁻¹)⁻¹. To achieve consistency with the V6′ gains, the V5a gains, a_TV5a, were divided by 0.993 to obtain the V5a′ gains, a_TV5a′, which are plotted as open triangles in Fig. 14a. Note that three of the gains, determined between days 1440 and 1560, were adjusted with both correction factors. The resulting linear fit to the combined V5a′ and V6′ gains is shown as the solid line in Fig. 14a. The trend line coefficients are listed in Table 4. After applying both correction factors, the apparent trend in the Terra MODIS gains relative to VIRS is −0.02% yr⁻¹, a statistically insignificant value.

Similarly, the V6′ values were computed for the VIRS-Aqua slopes and plotted as solid squares in Fig. 14b along with the V5 results from Fig. 4b. The resulting linear fit (dashed line) yields a slightly negative trend (Table 4) that becomes more negative (solid line) when the 0.7% responsivity correction is applied to the V5a data resulting in the V5a′ values (open circles). Without the correction, the slopes decrease at a rate of 0.06% yr⁻¹, an insignificant trend. With the correction, the Aqua-VIRS slopes drop at 0.30% yr⁻¹ (Table 4); however, this trend is not significant at the 90% confidence level. It suggests that Aqua response is degrading or that the VIRS sensor is becoming more sensitive over time. Given the other trend evidence for Aqua discussed in the previous section and the insignificance of this trend, it is concluded again that the Aqua visible channel has not suffered any significant degradation.

d. Summary

Only a few corrections are needed to achieve constancy better than 0.1%–0.2% yr⁻¹ in the VIRS and Terra and Aqua MODIS visible channel calibrations. When using VIRS V5a data, the radiances should be corrected to the V6 responsivity by dividing by 0.993. The VIRS V6 data should be adjusted using a correction based on the DCC normalized radiance trends in Table 3, either the mode trend or an average of the mean and mode trends. The Terra radiances should be increased by dividing by 1.0117 after 18 November 2003 to account for the shift in the Terra gain. No correction to the Aqua data appears to be necessary.

The only remaining differences between the sensors are their absolute calibrations. At the middle of their respective VIRS-matched time intervals, the Terra and Aqua radiances are 1.0352 and 1.0464, respectively, greater than their normalized VIRS counterparts. Likewise, the Aqua radiances are 1% greater than those from Terra. To explore theoretically how the different sensors should be related, the spectral response functions in Santa Barbara DISORT Atmospheric Radiative Transfer program (Richiazzi et al. 1998) and computations were performed over an ocean surface at several solar zenith angles using various aerosol types and concentrations and several cloud cover conditions. According to the theoretical calculations, the Aqua radiances should be, on average, 0.05% less than those from Terra. Thus, the differences between the Terra and Aqua found here are due to calibration. It was also found that the MODIS radiances, after normalization should be, on average, 1.048 greater than their VIRS counterparts. That value is very close to the mean slope found from the final VIRS-Aqua trend in Table 4 and differs by only 1% from the VIRS-Terra slope.

While the consistency between the Aqua and VIRS data suggest that both have excellent absolute calibrations and that either instrument could be a reliable reference, the consistency could be fortuitous and both gains could be off by the same amount. Determining which instrument has the best absolute calibration is beyond the scope of this paper.