1. Introduction

To validate model predictions of future changes to the earth’s climate, it is important to maintain measurements of the earth radiation budget (ERB) from space. ERB parameters are the emitted thermal or longwave (LW; 5 μm < λ < 100 μm) and scattered solar or shortwave (SW; 0.2 μm < λ < 5 μm) radiative fluxes leaving Earth. Such measurements, when combined with knowledge of the solar constant, tell of the net heat engine energy input that drives all weather and climate on the earth. The measurement accuracy and calibration stability required to detect model-predicted effects of cloud–climate feedbacks on the ERB has recently been estimated by Ohring et al. (2005). The standards called for are an absolute accuracy of 1 W m⁻², a calibration stability of ±0.3% decade⁻¹ for SW flux, and ±0.5% decade⁻¹ for LW flux. The Clouds and the Earth’s Radiant Energy System (CERES; Wielicki et al. 1996) is currently the only satellite program monitoring global ERB parameters from space. For the CERES edition 2 (Ed2) data release, design specifications called for an absolute accuracy of ±1% and calibration stability of also around ±1% during an estimated 5-yr mission life (i.e., ±2% decade⁻¹; see Wielicki et al. 1996). The new requirements for ERB climate calibration stability are therefore significantly beyond those originally specified for the CERES program. The target accuracies and stabilities are made all the more challenging given the discovery of contaminant spectral darkening (Matthews et al. 2005b), which significantly degrades CERES telescope transmission in the UV region. This paper details methods of estimating the stability of existing edition 2 SW CERES measurements, as well as those that have been adjusted to account for UV optical degradation using the “Rev1” spectral darkening factors (see NASA 2008a,b). Also, a new experimental calibration methodology as described in detail by Matthews et al. (2006, 2007a,b) is presented. These are efforts to assign coloration to the spectral darkening effects on the CERES optics while achieving a higher stability for ERB measurements. The results when this calibration is used to invert CERES data in a test edition are shown in validation studies as well as in comparison to edition 2 results. Finally, estimates of the potential stability of the new calibration when combined with regular raster-scan lunar data are made. This does not currently represent calibration intended for use in an official CERES data release. It is merely a summary of the work to date on compensating for contaminant issues on the CERES optics.

2. CERES spectral darkening and Rev1 adjustment factors

CERES edition 2 data have been released in the forms of Earth Radiation Budget Experiment (ERBE)-like and single scanner footprint (SSF) datasets. ERBE-like data use the same inversion methods of the ERBE mission (Barkstrom 1984), relying on the scene identification by the maximum likelihood estimation technique (MLE; Wielicki and Green 1989). SSF data use imager measurements taken from the same satellite to perform scene identification. PFM uses Visible and Infrared Radiometer System (VIRS) imager data (Simpson et al. 1996), whereas FM1–FM4 utilize measurements from the Moderate Resolution Imaging Spectroradiometer (MODIS) instruments (Salomonson et al. 1989). With the production of several years of SSF edition 2 data from the Terra satellite, it became apparent that the measurements suggested a significant drop in the solar radiance scattered from the earth’s oceans. The magnitude of this was almost 2% within a period of less than 4 yr (see Fig. 3a). As described by Loeb (2004), this was not consistent with datasets from other solar wavelength Earth viewing instruments in orbit. Hence, attention was turned to possible causes of SW instrument degradation that would not show up using the edition 2 calibration methodology of Spence et al. (2004). A reasonable explanation seemed to be that the CERES optics were undergoing a significant drop in transmission of blue/UV photons because of optical contamination. However, little to no change in the visible to near-infrared (NIR) response would need to be occurring. This is exactly what occurred on the Long Duration Exposure Facility experiment (LDEF; Clark and Dibattista 1978), which retrieved an ERB radiometer after almost 6 yr in low Earth orbit (LEO) using the shuttle. Such an effect, described as “spectral darkening” (Matthews et al. 2005b), would not be detectable using the onboard SWICS calibration lamps because they are largely devoid of UV output (see Fig. 3b).

Proximity of two CERES units on both Terra and Aqua platforms (Fig. 1c) enabled the use of direct comparisons between nadir measurements made by the separate instruments. Comparing near-simultaneous nadir footprints sampled within 1.65 s of each other allows the monitoring of how one CERES instrument’s response changes relative to another on the same satellite. Until 2005, the CERES instruments spent the majority of the time operating in one of two orientations called cross-track (XTRACK) and rotating azimuth plane (RAPS) modes. The scan plane for XTRACK was held perpendicular to the satellite motion, which gave the ideal coverage for collecting ERB data. In RAPS mode, the telescope was continuously rotated in azimuth for purposes of measuring targets with multiple viewing/solar geometries. RAPS mode was necessary for the construction of sophisticated angular dependency models (ADMs; Green and Hinton 1996; Loeb et al. 2005), which are required to convert CERES measurements of radiance to flux (or irradiance).

The following equations describe the SW measurements made by the CERES instruments at time t of Earth radiance :

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For ERB studies, the unfiltered radiance result of Eq. (1) is required; however, the use of silver-coated mirrors and quartz filters in the CERES telescope result in a nonflat spectral response of the optics (Fig. 2). CERES therefore makes a measurement of “filtered radiance” as described by Eq. (2), where r_sw(λ, t) is the fractional spectral response and g_sw(t) is the fractional change in radiometric gain of the CERES SW channel (where gain tells the output in counts per unit of radiance converted to heat within the detector). Hence, the filtered radiance is generated from detector counts V as RF = V/G⁰, where G⁰ is the ground measured gain value in counts per W m⁻² sr⁻¹ [e.g., on ground g_sw = 1 in Eq. (2), and if the gain is found to increase in flight by 1% then g_sw = 1.01]. For the edition 2 data release, the monthly updates to SW gain g_sw were estimated by observing the change in detector counts when viewing the onboard SWICS lamps. Inversion of filtered radiance RF into unfiltered radiance R can be done using Eq. (4), with estimates of the gain change g_sw and the filtering factor f_i for Earth scene i [based on moderate resolution atmospheric transmission (MODTRAN) simulations of , as in Loeb et al. (2001)].

Figure 3c shows Terra direct comparison of ERBE-like SW channel nadir footprint filtered radiance RF^sw for the first five years of the mission [i.e., this is the percent difference in filtered radiance between FM2 and FM1 defined by Eq. (2)]. It clearly indicates how the instrument operating in RAPS mode always drops in SW response compared to its XTRACK mode counterpart. Until 2002, the instruments alternated every three months between RAPS and XTRACK modes (creating the oscillatory nature in Fig. 3c at the mission start). From then until mid-2005, FM2 was held continuously in RAPS mode, which resulted in a steady drop in its SW response compared to FM1. Figure 3c shows both the direct comparison of all-sky and clear-ocean footprints separately. The 2002–05 period tells how the relative drop in the RAPS instrument SW response to the “blue” scene of clear ocean is significantly greater than for all sky. Figure 3c also therefore suggests that the RAPS instrument drop in optical throughput for an Earth scene with high fractional blue/UV content is more severe than for the all-sky case (as observed by LDEF in Fig. 3b).

Interestingly, the SWICS calibrations indicated no significant changes in SW detector radiometric gains for FM1 and FM2 during this period (see Spence et al. 2004). With no apparent change in gain, the 2% drop in Earth scattered flux within 4 yr (Fig. 3a) could only be caused by a significant but undetectable reduction in optical transmission and hence filtering factor f_i [Eq. (3)].

With this drop in optical response being so significant to affect climate records, it was decided to develop adjustments or “revisions” to edition 2 SW data that would compensate for spectral darkening effects. These adjustments were derived based on two fundamental assumptions. First, it was presumed that the SWICS lamp output is perfectly stable in flight and in a spectral region unaffected by LDEF-like degradation (Fig. 3b). Second, it was assumed that the optical degradation only occurs when an instrument operates in the RAPS mode. This allows the XTRACK instrument to be used as a calibration standard from which the drop in filtering factor f_i of the other instrument can be estimated [for full derivation of the Rev1 factors, see Matthews et al. (2005b)]. Because, as shown in Fig. 3c, there was a significant difference in the changes in response to the scenes of all sky and clear ocean, it was decided to derive two different revisions for each instrument that cover both of these scenes separately (i.e., the all-sky adjustment is multiplied with unfiltered Ed2 SW for all scenes except clear ocean). Such adjustments for the Terra instruments are shown in Fig. 3d. They suggest a drop in FM1 response of just over 1%, whereas the FM2 instrument, with its longer time in RAPS mode, degraded by 1.5%–2% over the same period. As expected, Fig. 3d illustrates how the estimated darkening occurs in 3-month periods and ceases completely for FM1 beyond 2001 (when that instrument was placed permanently in XTRACK, thus preventing any suspected darkening). Comparison of the Rev1 values for all sky and clear ocean again shows how the darkening of response occurs to a greater extent for clear ocean (as the ocean scene has a higher proportion of spectral energy situated toward the blue/UV end of the spectrum). Such monthly revisions were designed for direct application to already released edition 2 CERES unfiltered SW data products and are available from the CERES data quality summaries (see NASA 2008a,b; Fig. 3e). Once adjusted by using these figures, the CERES SW data are then called edition 2 Rev1.

3. Estimates of CERES Ed2 and Ed2 Rev1 SW data stability

The work of Loeb et al. (2007) performed multi-instrument comparisons of CERES top-of-atmosphere SW radiance with other Earth observing instruments on both the same and different satellites. These showed that there was good agreement between Rev1-adjusted tropical ocean Terra SW data and anticorrelated measurements of the photosynthetically active radiance (PAR) product made by the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) ocean color instrument (Hooker et al. 1992). This was significant because the SeaWiFS instrument uses monthly views of the Moon to update the gains of its photodiode detectors, giving its radiance measurements very good stability. The FM1 Ed2 Rev1 SW flux measurements were also found to agree with the collocated MODIS solar radiances to within ±1% decade⁻¹. Rev1-adjusted CERES tropical SW measurements were also compared between the Aqua and Terra CERES instruments (FM4 and FM1). Here, however, the Aqua measurements were found to drop in comparison to those made on Terra with 95% confidence in the difference between relative trends. This indicated that the use of the Rev1 assumptions had not provided stable calibration of either Terra or Aqua SW (or perhaps both). One possibility is the suspected ground contamination of the Aqua CERES optics discussed in Matthews et al. (2007b). This may have resulted in a slightly different contaminant affecting the Aqua telescopes, one that continues to degrade in throughput whether operating in RAPS or XTRACK mode. Another possibility is highlighted by the apparent negligible change in Terra SW gains indicated by the SWICS calibrations (Spence et al. 2004). In all cases with the CERES total channels, the radiometric gain of the CERES bolometers was seen to increase in the vacuum of space by 0.5%–1%, based on regular views of the onboard blackbodies. Physically, this is as expected because the bolometers operate in a Wheatstone bridge configuration, relying on the temperature difference induced in the irradiated active flake when compared with a shielded compensating flake. Outgassing from the bolometer in a vacuum will therefore serve to reduce the thermal mass of the detector and give a greater temperature change per unit of radiance absorbed. As described in Matthews et al. (2005a), this will increase the effective first-time constant gain of the bolometer and thus increase g_sw in Eq. (2). It was therefore unexpected that the Terra SW channels should exhibit no gain increase throughout the mission, implying perhaps that the onboard lamps had actually dimmed in the first 4 yr.

The Terra/Aqua trend discrepancy alone highlighted that an independent SW stability metric was needed in order to be sure of which physical spectral darkening effects were afflicting each CERES instrument. The metric chosen was that of deep convective cloud (DCC) albedo. DCC is defined as tropical ocean-region clouds with optical thickness τ > 120, temperature < 205 K, and a MODIS 0.6-μm radiance uniformity within the CERES footprint of less than 3% (where the footprints were found using the cloud properties stored in the SSF product). As very optically thick, cold, and uniform clouds, these are assumed to represent ice particle reflectors on the edge of space [because, as in Kratz et al. (2002), they are presumed to have very little water vapor or ozone above them]. Described in Matthews et al. (2006), the radiance measurements from these clouds are adjusted by using the state-of-the-art anisotropic factors (Loeb et al. 2005) into outgoing irradiance. This is then adjusted to overhead Sun using TRMM direction models (N. Loeb 2005, personal communication) and combined with the incoming solar flux from that day to give a DCC albedo figure. It is noted that this metric will therefore have a slight dependence on the stability of cloud retrievals from the MODIS and VIRS instruments (Minnis et al. 1998).

Figure 4a shows the edition 2 DCC albedo as measured by all CERES instruments (including PFM) and covers the period of January 1998–December 2006. The plots are deseasonalized to remove any slight annual cycles. Note that FM1 is missing January and February 2006 and FM2 is missing July and August 2005; this is because of the instruments being stowed as part of the spectral darkening investigations of Matthews et al. (2005b). The plot clearly shows statistically significant drops in DCC albedo as measured by Terra until around 2002. See Table 1 for estimates of edition 2 mission life SW calibration trends μ. The slope standard error σ_μ or half the 95% confidence interval is calculated using the following for n months of data measured at times t_k (in decades):

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where ε is the autocorrelation coefficient of the noise in unfiltered DCC albedo Θ_k measured in months k, as described by Weatherhead et al. (1998); that is, Θ_k = εΘ_k−1 + η, for DCC albedo ε = 0.3, with ±0.128 95% confidence interval. Accounting for autocorrelation is necessary in environmental data such as DCC albedo because each monthly measurement is not entirely independent from that of the preceding month (e.g., an aerosol release in July could affect DCC albedo in both July and August). Hence, ν is the offset in the linear regression of Θ_k against t_k. From 2002, where FM1 is held in XTRACK, the DCC albedo actually increases for this instrument, whereas FM2 remains somewhat stable. This stability of FM2 is perhaps because, as described in Spence et al. (2004), the edition 2 FM2 SW spectral response was lowered in this period [thereby decreasing f_i in Eq. (4) and increasing SW result ]. Also shown in Fig. 4a is the consistent drop of Aqua (FM3 and FM4) edition 2 DCC albedo all the time the instruments are operating until March 2005 (with mission life trends beyond −3% decade⁻¹ as shown in Table 1). From April 2005 onward, where the FM4 SW channel had failed forcing FM3 to remain in XTRACK, the FM3 DCC albedo appears to stabilize.

This DCC metric then gives a new way to estimate stability of edition 2 products. Figure 4a clearly shows an overall drop in all Terra/Aqua SW data that correlates with time spent in RAPS mode. Figure 4b then shows the same edition 2 data after the Rev1 adjustments have been made; note that there are no Rev1 adjustments for PFM. Assuming that the DCC albedo is indeed a stable metric, this enables analysis of the quality of the Rev1 adjustment for restoring climate stability to CERES data. As described in section 2, the Rev1 adjustment was derived using the assumption that the onboard SWICS lamps were perfectly stable and that instrument optics degrade only while operating in RAPS mode. The adjustment appears to have successfully reduced the difference between the FM1 and FM2 measurements of DCC. However, both FM1 and FM2 (Terra) now exhibit statistically significant positive trends in Fig. 4b, implying that the Rev1 adjustment had overcompensated for the optical degradation (see Table 1). As mentioned, a possible physical cause of these ∼+1% decade⁻¹ trends is that the Terra SWICS lamps dimmed during the mission. This resulted in no SW gain changes being made in the edition 2 release. Therefore, the asymptotic rise of the FM1 and FM2 curves (Fig. 4b) may somewhat represent the true gain change of the Terra SW bolometers as they outgas (note the resemblance with the observed total channel gain increases using blackbodies displayed in Fig. 8). Conversely, the Aqua instruments FM3 and FM4 continue to show significant, although reduced, negative trends after the Rev1 adjustment (the FM4 trend is now just outside statistical significance because of lack of data). This is consistent with Loeb et al. (2007), who found a significant +3.8 W m⁻² decade⁻¹ (+1.5% decade⁻¹) trend when FM1 SW data were compared to FM4 globally. Again from the Rev1 assumptions, the only physical cause of a continued drop in Aqua DCC albedo is that the contaminant continued to polymerize and darken, even when the instrument was operating in XTRACK mode. This suggests that the Aqua contaminant may differ somewhat from that afflicting the Terra instruments [possibly a result of the suspected ground contamination of the Aqua instruments discussed in Matthews et al. (2007b)]. However, the excellent agreement in Loeb et al. (2007) between the Rev1-adjusted FM1 SW tropical ocean data and the anticorrelated SeaWiFS PAR must be considered. It is likely that the tropical ocean scene spectrum typically has a higher proportion of its energy in the UV region than DCC. This could mean that although Rev1 appears to overcompensate by about 0.5% for the overcast DCC scene, it may in fact be a suitable compensation for the change in optical response to tropical ocean SW radiance.

Also strikingly apparent in Fig. 4b is an apparent 1% drop in SW measurements with each new satellite mission between TRMM (PFM) and Terra (FM1 and FM2), then Terra and Aqua (FM3 and FM4). Assuming that no significant biases were introduced because of the differences between TRMM, Terra, and Aqua ADMs, a possible physical cause of this is a degradation of the mirrors contained in the Transfer Active Cavity Radiometer (TACR). This was used to determine SW calibration source output during the ground calibration of the CERES instruments. Because the TACR gain is determined in the LW by using a blackbody, a 1% degradation in the SW reflectivity of its mirror will translate directly to a 1% overestimation of the CERES SW gain [i.e., g_sw in Eq. (4)]. At present, this cannot be verified because the TACR is still in use in calibration of future CERES units; it does, however, warrant further investigation.

In summary, the use of DCC albedo to investigate stability of existing CERES calibration suggests that all edition 2 SW data exhibit significant negative calibration drifts, most likely because of the RAPS degradation. The Rev1 adjustments severely lessen these trends in Aqua data although they are not removed beyond statistical significance. For Terra, the Rev1 adjustments seem to have overcompensated, inducing slight positive trends in SW measurements of DCC. Although not the direct subject of this paper, the absolute SW accuracy differences between the three satellite platforms are also highlighted, with Terra 1% below TRMM and Aqua a further 1% below Terra.

4. CERES spectral darkening calibration

Section 3 showed that the Rev1 adjustments appear to have restored CERES SW measurements to the specified ±2% decade⁻¹ stability (i.e., ±1% per 5-yr lifetime stability). This, however, is not sufficient to meet the requirements of Ohring et al. (2005), meaning that a more rigorous calibration methodology is required. The following section summarizes the work of Matthews et al. (2006, 2007a,b), who attempt to spectrally resolve the contaminant effects on CERES calibration.

It was decided to utilize imager data contained within the SSF product to give detailed information on the scenes viewed by the CERES instruments. This would allow a MODTRAN spectral signature to be assigned to each footprint. That information was tied to the raw detector output or filtered radiance RF [Eq. (2)]. Hence, both the effects of bolometer gain change and optical degradation were left present and undisturbed in the CERES data. The next step was to develop a comprehensive model of how contaminant could mobilize to the optics and then polymerize. The assumption is made that the contaminant arrives on the optics only if the instrument is in RAPS mode, when the telescope is exposed to the ram direction of travel (Figs. 5a,b). Then, LEO atomic oxygen enters the telescope and is free to interact with optical coatings or some contaminant reservoir. Molecules can then be mobilized to other optical surfaces and then fixed to them by Earth scattered UV.

As shown in Fig. 3b, experience from previous missions such as LDEF (Clark and Dibattista 1978) suggests that LEO optical contaminant absorption increases with a shorter wavelength. The darkening model developed here must therefore represent mathematically how this absorption varies throughout the electromagnetic spectrum. The LDEF experiment showed that, once space-bound contaminants are fixed to optics, UV continues to polymerize any remaining solo molecules into more and more lengthy absorbing molecular chains. Typically, radiation tends to interact most strongly with targets of size similar to the wavelength of its photons. Given the contaminant transmission observed on LDEF, in this model it is assumed the population density P of the molecules drops off exponentially with its size. This means both the contaminant population density and hence its absorption a also falls off exponentially with increasing length/wavelength λ [Eqs. (7) and (8)]:

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The transmission Tr(λ) of a “unit thickness” of polymerized contaminant is found in Eq. (9) as the fractional absorption subtracted from 1 [unit thickness is a dimensionless parameter related to optical thickness τ, because τ is found from the natural logarithm of Eq. (9)]. This mathematical form agrees very well with the change in transmission seen on LDEF (Fig. 3b). Knowledge of the precise reason for the exponential shape would require detailed study of the physical chemistry relevant to the contaminant involved. Because this is not currently possible, the general approximation of Eq. (9) is used here for contaminant transmission. The actual cause of this spectral shape warrants investigation by a future study.

Given the Eq. (9) representation of polymerized contaminant transmission, the model must now simulate how the thickness of fully polymerized contaminant molecules, called type B, increases. This will be based on the amount of time exposed to the ram direction and the continuous polymerization by Earth scattered UV (Fig. 5b). Hence, the model therefore assumes that contaminant is mobilized to arrive at the optics only when they are exposed to the ram direction (Fig. 5a). Upon arrival, a fraction β of the molecules is already polymerized into absorbing chains (type B molecules). Then, every day, a fraction ρ of the remaining unpolymerized and unabsorbing type A molecules polymerize with UV exposure to become type B absorbers. Hence, if N(t) is the thickness amount of contaminant mobilized to the optic in a particular month, then the rate of change in thickness of polymerized/absorbing molecule layer B(t) is given by the following:

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Figure 5c gives an example of how Eq. (10) will respond to a forcing impulse of contaminant thickness one at the mission start (i.e., a onetime contamination event). In this case, β = 0.4, so of the contaminant mobilized to the optics 40% of the molecules are already polymerized (type B absorbers). Then, in this simplified example, the remaining 60% of type A molecules continue to polymerize at a rate of 50% month⁻¹ (i.e., ρ = 0.5). Hence, now an estimate of N(t), or how much contaminant arrives on the optics during a day of ram exposure, must therefore be provided. It is assumed that the contaminant is mobilized from a finite reservoir at a rate that is proportional to the amount remaining (with ψ being the linear scaling factor). If the total amount of contaminant contained in the reservoir at the start of mission is Q, then the arrival rate after time t_r spent exposed to the ram direction is given by

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Knowing the time each instrument telescope has spent exposed to the ram direction in each month of the mission, it is therefore possible to estimate how much contaminant arrived in that particular month. It is noted that the period 2000–06 represents a reduction in solar output and hence reduced LEO atomic oxygen flux. It may be that this is the true cause of the drop in N(t) during this period rather than a depletion of the contaminant reservoir. However, it is likely that the exponential fall off in contaminant arrival from Eq. (11) is also an appropriate fit for the drop that would be caused by a reducing atomic oxygen flux.

With knowledge of contaminant arrival rate N(t), which acts as a forcing function to Eq. (10), it is possible to use a Z domain–derived recursive filter (see, e.g., Matthews et al. 2005a) and simulate the thickness of polymerized contaminant B(t) on the SW optics for each month of the mission. Such simulations for the CERES instruments are shown in Fig. 7. These illustrate how, after the FM1 instrument was locked in cross-track mode from the end of 2001 onward, arrival of contaminant ceased. Hence, the thickness B(t) then approaches an asymptote as the remaining type A molecules continue to polymerize into the type B absorbers. However, on the FM2 instrument, the thickness of molecule B absorbers continues to grow because of prolonged exposure to ram direction (Fig. 7b, right). Eventually, a fall off occurs toward the end of the period as a result of the contaminant reservoir becoming depleted, reducing the monthly arrival rate N(t) (Fig. 7b, left; as mentioned this may also be due to a drop in the atomic oxygen flux).

Because optical thickness of a contaminant unit layer is found as the natural logarithm of Eq. (9), the SW channel spectral response in month k of the mission can now be derived by using

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where is the SW channel spectral response measured in the ground calibration.

A way of determining the most appropriate model parameters M, α, ρ, β, ψ, and Q for each instrument must now be found by using a gradient descent algorithm, as described by Matthews et al. (2006). This starts by finding the exponential gain change that accompanies the model spectral response variation from Eq. (13) and its implied change to the filtering factor [Eq. (3), where n = 2 for FM2 and FM4 and n = 1 for FM1 and FM3]. This is done to remove any statistically significant trends in the DCC albedo [i.e., the filtered DCC albedo and SW gain are related as ]. Then the iteration simply adjusts the model parameters up and down systematically. This is done to find the best possible gains and filtering factor f_iⁿ(k) combinations that minimize the quantity ϒ in Eq. (14) for N months of nadir directly compared data [i.e., MODTRAN simulations of all-sky and clear-water monthly average spectra are used with the model spectral responses to generate and from Eq. (3)]. The gradient descent iteration is graphically represented by Fig. 6.

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The optimal results in determining contaminant amounts for Terra and Aqua instruments are shown in Fig. 7 (the resulting mission life changes to the SW spectral responses are then shown in Fig. 10, left). These indicate how the model finds the Aqua contaminant (Figs. 7c,d) to have a far longer polymerization time constant ρ⁻¹ than that for Terra (Figs. 7a,b). The suggestion is that the Aqua contaminant continued to polymerize for several years after arrival on the optics, meaning that there is significant degradation even when operating in XTRACK mode. This would be the cause of the continued negative trend in Aqua DCC albedo even after the Rev1 adjustments (see Table 1 and Fig. 4b, remembering that Rev1 assumed no XTRACK degradation).

With the estimates obtained of changes to SW gains and spectral responses, the next step is to use biweekly blackbody calibration data to estimate the changes to the total and WN channel gains. Then the direct compare balancing perturbation described in Matthews et al. (2007b) is applied. This makes very minor adjustments to the gains so that two instruments on the same satellite measure identical nighttime LW and WN radiance. The adjustment also ensures that all instruments measure the same DCC albedo as the PFM instrument (believed to be the most accurate in the SW as it was first calibrated when the TACR mirrors were fresh). The derived gain changes for all five CERES instruments are shown in Fig. 8. These illustrate how typically the gain of the total or SW channel increases by 0.5%–1% over the course of a mission (because of bolometer outgassing, etc.). The blackbody calibrations for the FM2 instrument suggest a seasonal cycle in the total channel gain that correlates with the changes in orbital beta angle and hence the solar heating of the instrument. For this reason, the direct compare balancing of Matthews et al. (2007b) utilized the FM1 total channel calibrations to define this seasonal cycle (through the use of nighttime LW direct compare). Hence, it remains in the test edition total channel gain shown in Fig. 8c, because it is believed to be a real variation in the gain .

Interestingly, the WN channel gain is often seen to decrease based on blackbody calibrations. It is highly likely that this is not actually because of a decrease in the bolometer gain. Instead there may be a drop in the throughput of the WN filter as a result of the same contamination that afflicts the SW channel when in RAPS mode (note that the WN filter is in the same place in the telescope as the SW filter, as shown in Fig. 5b).

The final step in the calibration is to spectrally balance the solar wavelength portion of the total channel spectral response with the newly derived SW response. This uses a modified three-channel comparison as done for edition 2 (Spence et al. 2004). Shown in Fig. 2, the total channel is equally responsive to both SW and LW radiance. Hence, in order to isolate the solar response, a way of estimating how much of the filtered total channel signal is caused by thermal radiance is required. As discussed by Kratz et al. (2002), the spectral shapes of thermal emissions of DCC are quite well approximated by using Planck functions. This, combined with the small amount of water vapor above DCC, makes it possible to establish a relationship between the WN and total channel signals for nighttime DCC footprints. These polynomial training coefficients can then be used in daytime DCC data to accurately estimate how much of the total channel signal is due to thermal radiance. Then, as described by Matthews et al. (2007a), the thermal component of the total signal is removed, leaving purely that from solar radiance scattered by DCC. With the SW radiance known accurately from the now-calibrated SW channel, it is hence possible to estimate the change in total solar response (TSR) compared to its ground measured value , for every month of the mission:

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This is also done for the clear-water and clear-land scenes, although for these the presence of significant water vapor means that the WN channel cannot be relied upon to give an accurate measure of that thermal signal in the total channel. Hence, the estimates of clear-water and clear-land scattered TSR_Clr.W(k) and TSR_Clr.L(k), respectively, are only used to detect relative drifts rather than the absolute response [i.e., in the first month, TSR_Clr.W(0) and TSR_Clr.L(0) are forced to equal the accurately derived TSR_dcc(0) value, assuming the ground measurements of the total channel UV response shape are accurate, as in Matthews et al. (2007a)].

Figures 9a–d illustrate both Terra and Aqua test edition estimates of the changes in TSR for the scenes of DCC, clear water, and clear land. In all cases, the results suggest that the total channels are less responsive to SW radiance at the mission start than the ground measurements imply, by greater than 1% [i.e., TSR_i(0) < 0.99]. In fact, the size of the required start-of-mission drop in response increases with each new instrument. The more recent FM3 and FM4 instruments appear to have a 3% less responsive total channel for solar wavelengths than ground calibration suggested. Again, this may be because of a continued degradation of the SW response of mirrors used in the TACR for the ground calibration. Interestingly, all five instruments show a significant mission life dispersion in their changes in response to DCC, clear water, and clear land. Figure 9b shows that, in the case of FM2, a >1% increase in DCC response is accompanied by a 2.5% decrease in transmission of clear-water scattered sunlight (which has a higher UV percent content). A physical explanation for this could be that the total channel mirrors are subject to different types of contaminant that affect separate spectral regions. The first may be similar to that afflicting the SW channel, absorbing strongly in the UV and polymerizing with continued exposure to Earth scattered sunlight. A second contaminant is assumed to be more like a black absorber, acting like soot on an optic and reducing its net throughput. It is then possible that exposure to atomic oxygen in the RAPS mode serves to clean this second contaminant from the mirror, increasing the net telescope throughput (like atomic oxygen cleaning as found on LDEF). Finally, it has to be assumed that there is a third contaminant or mirror degradation mechanism that affects only the NIR response (1.5 μm < λ < 2.5 μm). This is because, as shown in Figs. 9a–d, the total channel response to the “red” scene of clear land is very close to or even below that of the “white” DCC scene. This implies a reduced blue and red scene response compared to that for the white DCC target. The only explanation is for degradation to be occurring in both the UV and NIR spectral regions and to a greater extent than for the visible region.

The spectral balancing technique of Matthews et al. (2007a) is hence adapted to find the required UV and NIR change in total channel response so to match the blue, red, and white calibration metrics. This is done by finding the monthly change to the total channel spectral response using

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The function sh(λ, k) is used to make a smooth lowering of the total channel response in the NIR region (1.5 μm < λ < 2.5 μm) based on the iterative value Γ(k) for each month (see Figs. 9e,f). Here, M and α are the same contaminant model parameters found in the SW study of Matthews et al. (2006). Thus, this makes the assumption that the total channel is also affected by the same UV absorbing contaminant as the SW channel. For each month, the optimum contaminant thickness θ(k), NIR fractional response drop Γ(k), and net throughput change ϕ(k) are then found by a simple iteration to precisely match the TSR_dcc(k), TSR_Clr.W(k), and TSR_Clr.L(k) values. The total channel adjustments necessary to match all three balancing metrics after one year in orbit (compared to ground calibration) are shown in Figs. 9e,f. These illustrate how the UV and NIR total channel response underwent significant degradation in the first year alone. The exact cause of the NIR degradation is not known at this time. It is assumed to possibly be the result of strong contaminant absorption lines, perhaps in the 1.5 μm < λ < 1.75 μm region where a significant proportion of clear-land scattered solar energy resides (note that the total channel mirrors are not sheltered behind filtering optics and hence have had exposure to both air and atomic oxygen). The simple NIR lowering function of Eq. (16) is used for this study however to match the red clear-land metric. It is significant that all four CERES EOS instruments do exhibit similar drops in NIR total channel response. If a further study can determine the precise shape of the NIR absorption, such a function could be used in place of sh(λ, k).

Figure 10 then compares the resulting test edition–estimated UV/visible changes to all CERES total channels (Fig. 10, right) with those found for the SW (Fig. 10, left). These indicate how in all cases the total channel optics darken considerably in the UV, indeed to a greater extent than was found to occur in the SW channels. At the same time, all total channel telescopes also show a net increase in throughput for most visible radiance of wavelength greater than 0.5 μm. This again is a curious observation, the precise cause of which is also not yet known. The assumption was of the presence of multiple types of contaminant. Some are polymerizing and/or with strong NIR absorption lines. Another is perhaps a sootlike black substance that is cleaned from the optics throughout the mission by atomic oxygen. These assumptions may be valid; however, further investigation is warranted.

5. Validation of test results and comparison with edition 2

To test the success of the spectral darkening calibration parameters, an offline run of a test edition was made at the National Aeronautics and Space Administration (NASA) Langley Research Center by using the gains and spectral responses presented in this study. The most fundamental check on the SW calibration stability comes from observing the resulting DCC albedo after CERES data have gone through the full SSF inversion process. The test edition DCC albedo is displayed in Fig. 4c and shows that all CERES instruments have been successfully placed on the PFM (TRMM) SW radiometric scale. Also, as shown in Table 1, none of the instruments now measures trends in the DCC stability metric to statistical significance.

A second and more involved check on the calibration is to observe the direct comparison between near-simultaneous nadir unfiltered footprints [Eq. (4)]. This is to see if any trends or biases existing in the edition 2 release have been reduced (i.e., because two “perfectly calibrated” instruments will measure identical unfiltered nadir radiances). Figures 11 and 12 show percent comparisons of edition 2, edition 2 Rev1, and test edition unfiltered SW radiance between two CERES units on the same satellite.

Figures 11a and 12a show significant mission life trends in edition 2 direct comparisons, especially for the clear-water scene. Also note in Fig. 11a the significant and increasing Terra scene dispersion between the blue clear-water and red desert scenes. In the Rev1-adjusted data (Figs. 11b, 12b), these trends are significantly reduced but the dispersion largely remains. Even though a separate Rev1 adjustment was derived for clear ocean, this was based on the ERBE-like scene identification, unlike the test data, which used the SSF imager radiances to identify clear water. The ERBE-like scene of clear ocean is found by MLE and hence is likely to contain more cloud contamination than the SSF scene clear water. Therefore, it has less UV percent content, possibly making the Rev1 adjustment insufficient for application to the SSF clear-water scene. In the test edition for Terra shown in Fig. 11c, all the trends and red/blue scene dispersion are decreased significantly [as the result of minimizing the quantity ϒ in Eq. (14)]. A slight trend is still present in clear water. This is most likely because of the slight difference in the model inversion using Eq. (4) and that of production as described by Loeb et al. (2001); also, clear water is a very “dark” scene, so a ∼+0.2% drift is very small in terms of watts per meters squared.

Note the 1% start-of-mission scene dispersion for Ed2 Aqua SW direct compare between red desert and blue clear water (see Figs. 12a,b). As mentioned earlier, it is suspected that the Aqua CERES optics were contaminated on ground before launch. Therefore, it may be possible that this scene dispersion at the mission start is because the SW spectral response shape of one or both of the Aqua instruments did not precisely match that measured in ground calibration. Hence, it is assumed that one of the instruments (in this case, FM4) had a nonzero thickness of contaminant at the mission start. This thickness is iteratively determined before the final balancing of SW gains is performed (for full details, see Matthews et al. 2007b). Figure 12c then shows the results of Aqua SW direct compare using the test edition run. This indicates that the 1% initial scene dispersion is removed and the slight trends in Ed2 and Ed2 Rev1 are significantly reduced.

Figure 13 shows Ed2 and test edition direct compare for both night and day unfiltered LW measurements on Terra. As indicated earlier, dispersion in direct compare suggests inaccuracies in the precise knowledge of telescope spectral-response shape (because the CERES bolometers are very linear detectors). Interestingly, Fig. 13a shows a 0.5% dispersion between the warmest and coldest nighttime scenes (i.e., clear water and overcast). This suggests slight inaccuracies in one or both of the Terra total channel spectral responses in the 5–10-μm range (see Fig. 2). Because the new calibration methodology makes no attempt to alter the spectral response in this wavelength region, this dispersion remains in the nighttime direct compare for the test edition (Fig. 13b). However, the nighttime balancing of Matthews et al. (2007b) has removed the near −0.5% trend in the edition 2 plot as well as the seasonal cycle present in the overcast direct compare (see Fig. 13a). Because stability of nighttime LW currently relies entirely on blackbody calibration, it is thought that this drift was caused by anomalous variation in the FM2 blackbody output. This is because the FM2 total blackbody calibrations showed a variation that correlates to the initial 15-min orbit shift of Terra from 2000 to 2002. This may mean that the FM2 blackbody temperature control may be affected by the change in solar heating as the orientation of the instrument and the Sun varied during the orbit shift [hence, why in the Terra balancing of Matthews et al. (2007b) FM1 is used as the calibration standard].

It is true to say that the CERES measurement of daytime LW radiance is the most complex to perform. This is because it requires subtracting the SW channel signal from that of the total to measure only the intensity of thermal photons. Such complexities are highlighted by the 1.25% dispersion between hot and cold scenes shown in the edition 2 daytime LW direct compare of Fig. 13c. Throughout the mission, this plot also shows a −1% drift in the difference between FM2 and FM1, indicating significant calibration drifts in one or both of the instrument’s daytime LW measurements. With the initial scene dispersion greater than that seen at night (Fig. 13a), the only explanation is inaccurate knowledge of the solar wavelength spectral response shape of one or both of the total channels. Hence, as with the SW channel and described by Matthews et al. (2007b), it is assumed that one of the total telescopes (FM1) was contaminated before activation. The optimum start of mission contamination is then iteratively calculated based on direct compare data (as in Matthews et al. 2007b). The Ed2 three-channel balancing of the SW and total spectral responses (Spence et al. 2004) used gray changes to the solar wavelength region of the total channel (that is to say the entire spectral response below 3 μm was moved up or down by the same amount). Section 4 showed how the spectral darkening analysis suggests that the total channel optics undergo severe UV degradation even in comparison to the SW channel. It is therefore likely that the drifts seen in Fig. 13c occur because the Ed2 gray changes are not sufficient to account for the varying changes in response to solar radiance scattered from clear water and deserts. Figure 13d shows that the spectral balancing of Matthews et al. (2007a) and cross-instrument unification of Matthews et al. (2007b) have served to almost completely remove the daytime LW additional scene dispersion. Also the trends between the two units are significantly reduced.

Figure 14 shows the same direct comparison data for the LW measurements from the Aqua platform. Figures 14a,b show excellent agreement between the two instruments for nighttime direct compare in both the Ed2 and test edition run. This suggests that the knowledge of LW spectral-response shape and blackbody stability on Aqua may both be superior to that achieved on Terra.

Figure 14c shows a far more significant scene dispersion of 0.5% for the daytime LW Ed2 release, which grows and varies significantly throughout the mission. As with Terra, the spectral darkening studies found significant UV degradation of the Aqua total channel telescopes. Once this is accounted for in the test edition run (Fig. 14d), the increasing drift in this dispersion is significantly reduced. However, there remains a 0.5% dispersion and seasonal cycle between the red desert scene and the white overcast scene. As stated earlier, the Aqua optics are suspected to have received contamination on the ground. It is therefore possible that one or both of the total channels had developed absorption in the 1.5–2.5-μm region before launch. Unfortunately, the spectral darkening studies give no way to verify or characterize this; hence, the desert dispersion remains in the test edition.

Finally, Fig. 15 shows Ed2 and test edition direct comparisons of nighttime WN unfiltered radiance. Comparing Ed2 Figs. 15a,c with test edition Figs. 15b,d indicates the success of the all-sky nighttime gain balancing technique of Matthews et al. (2007b). This was designed to bring WN measurements by different instruments on the same satellite to a common radiometric scale. Also, it is of significance for the general theory behind this study to compare Figs. 15a,c with Figs. 11a and 12a, respectively. Note the similarity in shape between SW and WN direct compare on both Terra and Aqua platforms (e.g., with Terra being oscillatory in nature before a steady decline after FM2 was locked into RAPS mode). From Fig. 8, it was noted that the WN channel signal when viewing onboard blackbodies actually decreased in most cases. Because the effective responsivity of bolometers tends to increase because of outgassing in the vacuum of space, it was suggested that this might be caused by the RAPS contaminant-reducing telescope throughput in the WN spectral region (because the WN filter is in the same optical train position as the SW channel filter, as shown in Fig. 5b). Hence, the similar drop in Ed2 RAPS instrument WN response relative to its XTRACK counterpart further strengthens the contaminant mobilization theory on which the SW spectral darkening model was based. Note that the slight drops in WN gain indicated by blackbody data were deemed below the threshold of the noise within the calibrations (hence, why the minor RAPS degradation could not be completely removed in the Ed2 data release). Importantly, this also implies that the RAPS mode contaminant does have LW absorption properties. Unfortunately, there is no way to distinguish between gain and LW optical response changes based solely on blackbody calibrations. Hence, this work is forced to assume the LW transmission of the contaminant is spectrally flat. So, these gain adjustments hence account for both changes in bolometer responsivity and optical throughput at the same time. Providing the assumption of contaminant LW transmission uniformity is a fair approximation; however, the total channel calibration presented here should yield good daytime LW stability, beyond that of the Ed2 release.

Figures 16, 17, and 18 then show the percent differences of the test edition run with the already released edition 2 (and the user-adjusted SW Ed2 Rev1). In all cases, the nighttime LW and WN results in the test edition remain largely unchanged from edition 2 (because of a reexamination of the same blackbody data used for the Ed2 release). The large start of mission change to FM4 WN was to lower Aqua WN data to match the level suggested by the FM3 blackbody (see Fig. 18f). This was based on the suggestion by Matthews (2008) that analyzed CERES lunar data to show that the Aqua WN measurements were significantly above those of Terra. The Terra instruments are more trusted because, unlike those on Aqua, they are not suspected of ground contamination. Use of DCC albedo to place all SW measurements on the PFM radiometric scale results in significant increases in Terra and Aqua SW flux. However, throughout the mission, the Terra test edition SW tends to drop when compared to Ed2 Rev1 for all scenes except clear water (Figs. 17a,e). As mentioned, this is because the SW model and DCC albedo suggested that the SWICS lamps had dimmed on the Terra mission, resulting in the gain inversion value being incorrectly held constant. Conversely, the Aqua test edition SW shows significant positive trends when compared to edition 2 Rev1 (Figs. 18a,e). This is because, as the spectral darkening model found, the Aqua contaminant tended to have a far longer polymerization time constant than that of Terra. Hence, the Rev1 adjustment failed to adequately compensate for continued degradation of the Aqua instruments, even when operating in XTRACK. Interestingly, the PFM SW test edition tends to drop in comparison with Ed2 in the first 8 months. Then, in the month of March 2000, when PFM was temporarily reactivated, the scenes of overcast and desert remain below Ed2 levels. All-sky water and clear water, however, show an increase in the test edition. This is because PFM test edition calibration actually relies on the SWICS lamp to determine gain changes. The suggestion from the lamp is that the SW channel gain increased by over 1% (Fig. 8a). However, the PFM DCC albedo signal in Fig. 4a remains constant within statistical limits (note that no SW gain changes were made in the PFM Ed2 release becuase it was thought at the time that the lamp had become brighter). If the PFM SW gain g_sw had increased by 1%, as suggested by the SWICS, the conclusion can then be drawn that the SW optics must have at the same time degraded by a similar amount. This resulted in no significant change to the product g_swf_dcc. Hence, for the test edition, the monthly contaminant thickness B(k) used in Eq. (12) was simply found by iteration. This was done by assuming that PFM was subjected to the same contaminant type as Terra and to keep DCC albedo constant as the gain is increased.

Figures 17c,g and 18c,g show that the Terra daytime LW has tended to increase in the test edition compared to Ed2. This is because of the spectral balancing of Matthews et al. (2007a) that required a lowering of the total channel solar response from the mission start (see Fig. 9). A lower total channel solar response will cause a lower SW signal being subtracted from that of the total in the inversion of Loeb et al. (2001). This therefore results in a higher daytime LW result. Terra test edition day LW starts off 0.5%–1% higher than that of Ed2 and depending on the scene tends to increase in time by as much as 1% throughout the mission. For Aqua, the greatest initial increase is in cold scenes such as overcast, and then this increase actually tends to diminish throughout the mission.

6. Test edition calibration stability estimates

Ohring et al. (2005) detailed the calibration stability necessary to detect model-predicted changes to the ERB resulting from cloud feedbacks. These are currently one of the largest uncertainties in predictions of future climate change. Anthropogenic loading of the atmosphere with greenhouse gases is expected to perturb the climate at a rate of about 0.6 W m⁻² decade⁻¹. Models estimate that cloud–climate feedback could then further modify this forcing by ±25%, or ±0.15 W m⁻² decade⁻¹. Cloud radiative forcing (CRF), the difference between clear and cloudy flux, is measured at around 50 W m⁻² for SW and 30 W m⁻² for LW. The model-estimated cloud feedback perturbation of ±0.15 W m⁻² decade⁻¹ therefore represents ±0.3% of the SW and ±0.5% of the LW CRF signal. Hence, to detect CRF trends with 95% confidence, CERES calibration stabilities of ±0.15% and ±0.25% decade⁻¹ are required for SW and LW flux measurements, respectively (i.e., half of the 0.3% and 0.5% figures).

The new calibration methodology presented here relies on DCC albedo for the SW and blackbodies for the nighttime LW measurement stability. Figure 13a showed that when FM1 and FM2 were calibrated for Ed2 separately, based on the two different onboard blackbodies, the nighttime LW measurements tended to drift between the two instruments. For this reason and based on the size of the drift in Fig. 13a, it is concluded that the CERES blackbodies provide a total channel gain stability of around ±0.5% decade⁻¹. The stability of DCC albedo and hence the test edition SW gain is perhaps a little harder to quantify. DCC were defined earlier as ocean clouds with temperatures less than 205 K, optical thickness greater than 120, and imager SW radiance uniformity within the CERES footprint of less than 3%. They are hence very tall, uniform, and optically thick clouds whose tops have been considered effectively constant reflectors on the edge of space. In the absence of a large aerosol eruption by a volcano that may serve to alter DCC ice particle diameter, this assumption should be valid. However, the stability of imager calibration must be considered because it is relied upon for cloud retrievals used to locate DCC footprints. The MODIS imagers on Terra and Aqua have excellent calibration provided by onboard blackbodies for the thermal channels and a monitored solar diffuser sphere for the SW channels. Figure 19a shows the result of a sensitivity study to determine the effect of ±1% drifts in SSF cloud retrievals on the derived CERES DCC albedo value. This was done by linearly varying the threshold limit of the DCC criteria. Hence, separate runs were performed where the cloud temperature limit T_ice varied throughout the mission from 205 to 207.05 K and the optical thickness cutoff τ_ice went from 120 to 118.8. These runs were compared with the albedo derived when the thresholds were held constant at the starting values (as was used to find the SW gain change g_sw). Finally, it is necessary to determine the potential effects of a drift in ice particle diameter size or calibration of the diameter retrieval. Hence, a run was performed where the DCC albedo in each month was normalized to match that of ice particles 65 μm in diameter. As described in Matthews et al. (2006), each month a linear regression of filtered DCC albedo χ_ice versus ice particle diameter Ω_ice was performed to establish the relationship χ_ice = M_iceΩ_ice + C. Then, each DCC footprint that month was adjusted by using the factor (M_ice65 + C)/(M_iceΩ_ice + C), thus normalizing it to a fixed ice diameter of 65 μm. For the sensitivity study, this run was then compared with one where the normalization constant varied from 65 to 65.65 μm throughout the mission. From Fig. 19a, the values of ∂χ_ice/∂Ω_ice, ∂χ_ice/∂T_ice, and ∂χ_ice/∂τ_ice (in percent per percent) are found to be 0.05, 0.15, and 0.055, respectively. Because there have been no significant volcanic eruptions in the lifetime of Terra or Aqua, it is assumed that the maximum possible drift in ice particle diameter ΔΩ_ice is ±1% decade⁻¹ (in the event of a future volcanic eruption this figure may need to be increased). Cloud-top temperature retrieval T_ice relies on the MODIS onboard blackbodies, which are assumed to have a stability comparable to those on CERES of ±0.5% decade⁻¹. Finally, the stability of the optical depth τ_ice retrieval, which relies on the MODIS solar diffuser, is estimated to have the lowest stability of ±2% decade⁻¹ (drift estimates verified by P. Minnis and S. Sun-Mack 2008, personal communication). The assumption is allowed that the drifts occur independent of each other because calibrations using MODIS blackbodies versus solar diffusers are most likely to have no correlation. It is also noted that these are estimated to be fairly conservative predictions of possible drifts in the SSF retrievals. Hence, with these assumptions allowed, the maximum drift per decade in the SW gain using DCC albedo is found by using

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This yields a maximum calibration drift of the SW channel of ±0.142% decade⁻¹ when DCC albedo is relied upon as a stability metric. It is noted that for scenes with increasing fractions of UV energy, such as clear water, then the percent stability value will also increase. This is because the spectral darkening model of section 4 is relied upon more to give the response change to a scene differing in spectrum from DCC. However, scenes such as clear water with high UV content tend to be far darker than DCC. So, if a stability for other scenes is required, then a fair estimate can be found from 0.142% of the average SW flux (i.e., ∼250 W m⁻² × 0.00142 = ±0.355 W m⁻²). This is then the smallest SW climate signal detectable by using the test edition calibration alone. The confidence with which a user can hence detect SW trends in n months of Terra/Aqua data can be calculated by using

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As in section 3, the autocorrelation coefficient ε for DCC is 0.3. Ideally, the calibration methodology presented here will force the slope μ → 0 and ν → Θ. With t_k being the time of month k in decades, the confidence in the SW calibration stability asymptotically approaches the value of σ_dcc(0.142). It is assumed that the result Σ[Θ_k − (μt_k + ν)]²/n, based on the existing data in Fig. 4c, can be used to give the variance of the parent population for DCC. Hence, it is possible to predict how the confidence in SW calibration stability will change throughout the mission. Figures 19b,c show the maximum SW stability obtainable for Terra and Aqua (diamonds with solid line). These indicate that for Terra the Ohring et al. (2005) SW target (gray dashed line) is reached after around 9 yr of measurements. For Aqua, the standard deviation of DCC data is slightly higher; hence, it takes over 10 yr to reach the SW target. However, given the 8 yr of data already taken from Terra, both of these targets may well be attainable. It is of course assumed in this study that a change in climate does not radically affect deep convective processes. Because such an occurrence could alter DCC albedo as defined here, this will need confirmation by future work.

As stated, the stability of nighttime LW measurements relies on the onboard blackbodies, which are thought to provide gain stability of ±0.5% decade⁻¹. As with DCC, it is therefore possible to estimate the maximum stability obtainable from n months of blackbody calibrated data by using

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where is the total detector signal when viewing the blackbody in month k and F(t_k) is the total channel exponential gain fit to the mission life blackbody counts (the shape of which is displayed in Fig. 8 as squares). Note that the autocorrelation adjustment is not necessary here because the internal calibration noise is considered independent in each new month. Again, the parent population variance of blackbody data can be found from and the stability of nighttime LW measurements estimated are shown for the first five years in Figs. 19b,c (triangles with solid line).

Stability of daytime LW measurements relies not only on the onboard blackbodies but also the spectral balancing of Matthews et al. (2007a) to ensure correct subtraction of the SW signal from that of the total channel. This spectral balancing also relies heavily on the three channel comparison using DCC but should be very reliable because it is a relative comparison between total and SW channels when viewing the same target. However, a conservative estimate of the additional instability caused by the spectral balancing must be made. Hence, the daytime LW confidence can be found by assuming the DCC drift error σ_dcc contributes an independent error source to that from the blackbodies:

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where and are the average daytime SW and LW radiance from Earth, used to adjust the effect of the σ_dcc percentage drift for the different magnitude of the LW signal. The resulting maximum daytime LW stability confidence σ_bbd(n) is also displayed in Figs. 19b,c (circles with solid line) for the first five years of Terra and Aqua. Hence, it can be seen that the blackbodies unfortunately cannot be relied upon to provide the stability to LW measurements required by Ohring et al. (2005) to 95% confidence (LW target shown as gray arrows).

The study by Matthews (2008) detailed a new technique of accurately measuring scattered solar and emitted thermal radiance from the Moon by using the raster scan mode of the CERES instruments. Based on existing lunar measurements, it also predicted the potential stability that viewing the Moon could provide to CERES Earth viewing data. The conclusion was drawn that because of the severe underfilling of the CERES field of view by the lunar disc, it would take over 12 yr of Moon measurements to provide SW 2σ stability confidence of ±0.3% decade⁻¹ or better. However, the high temperature of the Moon’s illuminated surface [estimated by Matthews (2008) to be, on average, an approximate 92°C] means the signal-to-noise ratio in CERES lunar LW is considerably higher than for the SW. This means that, within five years, the Moon can be used as a check on blackbody stability to better than ±0.25% decade⁻¹. Hence, with more than five years of LW lunar measurements, any trend μ^m in the data can be used to adjust test edition total channel gains in a similar way to which the Rev1 adjustment was made to Ed2 SW data (Matthews et al. 2005b; i.e., to then be called something such as test edition LW Rev1):

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Equation (22) then allows an estimate of nighttime LW test edition Rev1 stability confidence. Here, represents LW Moon measurements twice per lunar cycle and m is the number of days of raster scan data collected. It must be considered for Terra and Aqua that regular CERES raster scans of the Moon did not begin until the year 2006. Hence, the potential LW calibration drift in the time Δt_nm (in decades), for which no lunar raster scans were made and the blackbodies were relied on for calibration, must be included [see Eq. (22)]. Once again, no adjustment for autocorrelation is necessary because lunar data show no significant correlation from the measurements of one day to the next (ε = 0.002 ± 0.25, 95% confidence). The stability of daytime LW measurements [Eq. (23)] also includes the addition of the spectral balancing error estimated to be σ_dcc(/) [Eq. (23)]. Assuming that the CERES instruments can last the maximum possible lifetime of their satellite platform (with 15 yr of fuel), the potential stability confidence of lunar data–adjusted LW test edition Rev1 data has been added to Figs. 19b,c (triangles and circles with dotted lines). At the point in time where lunar data begins to increase the stability of that obtained with blackbodies alone, the maximum stability curve (solid line) then follows the results from Eqs. (22) or (23). With Δt_nm = 0.6 decades for Terra, it takes nearly 11 yr for nighttime LW calibration stability to reach the Ohring et al. (2005) LW target. The daytime LW only achieves optimal stability after 15 yr. For Aqua, because Δt_nm is less at 0.4 decades, the night and day LW targets are met after 8 yr and nearly 13 yr, respectively. Hence, it is in theory possible for test edition CERES calibration, when combined with lunar raster-scan adjustments, to meet the required climate stability. This could allow detection of the predicted effects of cloud–climate feedbacks. However, it will require the Terra/Aqua platforms, MODIS, and the scanning CERES instruments to last virtually the entire maximum possible lifetime of 15 yr.

There is one CERES instrument–designated FM5 still set to launch soon on the National Polar-orbiting Operational Environmental Satellite System (NPOESS) Proprietary Project (NPP) platform. If this instrument begins raster scans of the Moon immediately, a prediction of the possible FM5 calibration stability can be made, as in Fig. 19d. Because here the term Δt_nm = 0, the lunar data become useful far earlier in the mission, achieving the required night and day LW stability in less than 5 and 10 yr, respectively.

Equation (24) gives the maximum possible calibration stability obtainable if lunar data are used to correct the SW test edition:

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where n is the total number of months and m is the number of days with raster scans of the Moon. This is also displayed in Figs. 19b,c (diamonds with dotted lines) but is shown to never exceed the stability from DCC albedo within the Terra/Aqua 15-yr life spans. However, as shown in Fig. 19d, if the FM5 instrument were to operate for 13 yr or more, then SW lunar raster data will begin to improve the stability of SW calibration beyond the stability of test edition using DCC albedo alone.

7. Conclusions

This paper summarized attempts to characterize the spectral changes occurring to all existing CERES instruments while in flight. The effects of spectral darkening of optics through contamination were shown to induce negative calibration drifts in all CERES Ed2 Terra and Aqua measurements of Earth scattered SW. However, the user-applied Rev1 adjustments were seen to restore Ed2 SW calibration stability to that specified in the CERES program (±2% decade⁻¹). This was determined based on the stability metric of DCC albedo. Such results suggest that the Terra onboard lamps had dimmed somewhat and that the Aqua contaminant continued to polymerize and degrade the optics even when in the non-ram-exposed XTRACK mode. Unfortunately, this stability is not currently thought as sufficient to observe the model-predicted effects of cloud feedback forcing on the ERB. Therefore, a new CERES calibration methodology that attempts to include spectral coloration changes to the inversion/unfiltering process was presented. This again used the stability metric of DCC albedo combined with a comprehensive contaminant mobilization/polymerization model. The technique has provided physical explanations for most of the calibration changes occurring to the CERES instruments. Spectral darkening appears to be caused by optical exposure to the ram direction of travel, which results in contaminant arrival on the telescope and further polymerization by Earth scattered UV. However, some observations still remain somewhat unexplained, such as the apparent large rise in tota channel responsivity to DCC scattered solar accompanied by a significant drops in UV and NIR radiance response. Some possible reasons involving different types of contaminant on total channel mirrors were presented. However, further investigation may be needed to fully diagnose the causes of changes to total channel telescope transmission.

A sensitivity study was also performed to quantify the stability provided by use of this new calibration methodology. Table 2 shows estimates of the smallest climate signal that can be detected using this test edition calibration on CERES data up to and including December 2006 (with the smallest signal that could ever be detected given 15 yr of data also shown in parenthesis). These suggest that given sufficient length of the data record, the desired stability in SW calibration of ±0.3% decade⁻¹ (2σ) is possible by using the methods presented here. It must again be noted that this SW calibration does assume a changing climate will not significantly alter deep convective processes. There is currently no evidence to suggest that a warmer/colder Earth would lead to an altered population density of clouds with optical thickness τ > 120. However, this will need verification by future Earth observing missions such as the Climate Absolute Radiance and Refractivity Observatory (CLARREO; available online at http://clarreo.larc.nasa.gov/index.html). Hence, for the moment, the SW stability figures presented represent the “best case” calibration possible using the methodology described.

The conclusion was also drawn that the onboard blackbodies cannot provide the LW stability necessary to detect cloud feedback perturbations to thermal climate forcing (hence, why the current LW stability in Table 2 is double that of the required ±0.5% decade⁻¹ figure). However, it is suggested that if the spectral darkening calibration methods are combined with regular raster scans of the Moon, then the requested thermal calibration stability becomes a possibility. This, of course, is dependent on the satellite platform, the CERES instrument, and the MODIS imagers continuing to operate for periods beyond their predicted lifetime. At present, it is not known how realistic this requirement is. However, in the event of instrument failure and potential data gap, a further study based on the noise in both DCC and lunar data could be performed. This would then determine the detrimental effects of a break in climate data so that optimal use is made of all available CERES measurements. As indicated by Fig. 19d, providing FM5 begins regular raster scans of the Moon immediately after activation; then, within nine years, all of the Ohring et al. (2005) stability targets are met. Because, at the time of writing, FM1 and FM2 are merely 6 months from completing nine years of continuous operation, this may be a very achievable goal. It is also noted that the climate variable being measured (e.g., CRF) will contain its own autocorrelated noise, which will add further independent uncertainty to the figures in Table 2.

As for the absolute SW accuracy of test edition measurements, it is by no means straightforward to assess the impacts of potential ground contamination or TACR mirror solar response degradation. DCC albedo has been used here to place all CERES instruments on the PFM SW radiometric scale. This assumes that it is the most accurate, because that instrument was calibrated when the TACR mirrors were new. However, at this point, it is not suggested that the accuracy of test edition SW is beyond that originally specified for the CERES project (Wielicki et al. 1996). To quantify the absolute accuracy of LW, the 0.5% scene dispersion in night LW direct compare (Fig. 13b) will also need considering. This is accompanied by the discovery by Matthews (2008) that thermal measurements of the Moon by FM1 and FM3 can differ by >0.5%. Hence, future work separate from this study is needed to fully quantify CERES absolute accuracy and assess if it can meet those specified by Ohring et al. (2005). Further improvements in the accuracy of ERB measurements will rely on better ways of determining ground-to-flight shifts in broadband calibration [e.g., the solar calibration design proposed in Fig. 8 of Matthews (2008), which would also allow monitoring of any climate change–induced shifts to deep convection].

Finally, it is important to again note that the calibration methodology described in section 4 is not currently used in any official edition of CERES data. This is simply a summary of the spectral darkening calibration studies and an estimation of the stability they can provide. However, if deemed appropriate, then the methods presented here may aid in the production of a forthcoming release of CERES ERB data.