Editorial Type:
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Article Type:
Research Article

Real-Time Determination of Earth Radiation Budget Spectral Signatures for Nonlinear Unfiltering of Results from MERBE

Grant Matthews Zedika Solutions LLC, Fort Wayne, Indiana

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Print Publication:
01 Feb 2018
DOI:
https://doi.org/10.1175/JAMC-D-16-0406.1
Page(s):
273–294
Open access

Abstract

Among the best ways to gain more certainty in climate model prediction is to compare and constrain simulations with worldwide satellite measurements of the Earth radiation budget (ERB) short- and longwave radiant fluxes (SW and LW), which drive climate processes. Recent calls to ensure orbital ERB measurements track true climate, rather than instrument changes, led to the creation of the Moon and Earth Radiation Budget Experiment (MERBE). This independent project is recalibrating multiple existing ERB devices from different international space agencies so they adhere to common SI-traceable radiometric standards, by regularly sampling the unaltering constants of lunar reflectivity/emissivity, thus ensuring no artificial trends exist. This work details the use of MODTRAN to give an instantaneous SW and LW Earth spectrum for all scenes viewed by devices in the project, to then be used with instrument spectral responses for unfiltering radiances. In the majority of cases when data from a collocated imager are available, a dual-layer unfiltering is also performed separately on cloudy and cloud-free areas, yielding clear and overcast ERB spectral results. Additionally, use is made of improved in-flight methods to derive spectral responses from a previous American Meteorological Society study, and comparisons between Earth MERBE radiances from two identical devices operating on Terra/Aqua are shown along with results from the CERES project. These demonstrate an order of magnitude improvement in relative accuracy for edition 1 MERBE results over CERES and show that the latest CERES data are less accurate and stable than claimed.

Denotes content that is immediately available upon publication as open access.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Grant Matthews, grant.matthews@zedikasolv.com

Abstract

Among the best ways to gain more certainty in climate model prediction is to compare and constrain simulations with worldwide satellite measurements of the Earth radiation budget (ERB) short- and longwave radiant fluxes (SW and LW), which drive climate processes. Recent calls to ensure orbital ERB measurements track true climate, rather than instrument changes, led to the creation of the Moon and Earth Radiation Budget Experiment (MERBE). This independent project is recalibrating multiple existing ERB devices from different international space agencies so they adhere to common SI-traceable radiometric standards, by regularly sampling the unaltering constants of lunar reflectivity/emissivity, thus ensuring no artificial trends exist. This work details the use of MODTRAN to give an instantaneous SW and LW Earth spectrum for all scenes viewed by devices in the project, to then be used with instrument spectral responses for unfiltering radiances. In the majority of cases when data from a collocated imager are available, a dual-layer unfiltering is also performed separately on cloudy and cloud-free areas, yielding clear and overcast ERB spectral results. Additionally, use is made of improved in-flight methods to derive spectral responses from a previous American Meteorological Society study, and comparisons between Earth MERBE radiances from two identical devices operating on Terra/Aqua are shown along with results from the CERES project. These demonstrate an order of magnitude improvement in relative accuracy for edition 1 MERBE results over CERES and show that the latest CERES data are less accurate and stable than claimed.

Denotes content that is immediately available upon publication as open access.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Grant Matthews, grant.matthews@zedikasolv.com
Keywords: Algorithms; Climate records; Instrumentation/sensors; Remote sensing; Satellite observations; Cloud parameterizations

1. Introduction

Clouds are of particular interest for climate change studies because they both cool Earth by reflecting shortwave sunlight radiance (SW of wavelengths λ = 0.2–5 μm) and also warm it as they trap outgoing thermal longwave (LW λ > 5 μm ) energy emitted back to space. These leaving SW and LW fluxes are components in the Earth radiation budget (ERB), which can only be globally measured by satellites in orbit. For climate monitoring, such irradiances must be recorded in combination with continuous measurements of Earth’s incoming solar power I0, which has to also be observed from space [the Moon and Earth Radiation Budget Experiment (MERBE) I0 values from the Variability of Solar Irradiance and Gravity Oscillations (VIRGO) composite are available for download; Matthews 2016c]. To add to confidence in any global circulation model (GCM) computer predictions of future climate change specifically from cloud radiative forcing (CRF), their simulations of the past and present can be compared with actual measured ERB data (e.g., using the satellite missions in Table 1). The monitored scattered SW solar (sol) and LW emitted thermal (th) spectrally integrated flux energies are defined in Eqs. (1) and (2), for their corresponding source radiance L shown by Fig. 1 (where ψ and ϕ are longitude and latitude, θvz and ϕraz are viewing zenith and azimuth angles as in Fig. 2, and dΩ = sinθvzdθvzdϕraz):
e1
e2
Physically such measurements must be made using orbiting radiometer instruments that utilize various optical components and broadband detectors that convert light to heat. However, studies such as Ohring et al. (2005), Fox et al. (2011), and Wielicki et al. (2013) specifically analyzed data accuracy and calibration quality such as that from the most established ERB mission called the Clouds and the Earth’s Radiant Energy System (CERES; Wielicki et al. 1996), which since 1998 is on the low-Earth-orbit satellites TRMM, Terra, Aqua, and SNPP (see the appendix). They found it insufficient for the task of detecting ERB cloud feedback and SW CRF signal trends in the near future, since on mere decadal scales they are smaller than the untracked CERES calibration drifts found by Loeb et al. (2007b). Space shuttle retrievals of satellite optics have then also shown in-orbit contamination and solar exposure to degrade ERB type telescope transmission by up to 30% in the ultraviolet (UV; Clark and DiBattista 1978). None of the current ERB missions in Table 1 has built in successful ways of monitoring or compensating for such effects in its retrieved Earth data. For example, the CERES onboard SW calibration lamp outputs were found to drift without possibility of such changes being monitored by Priestley et al. (2000), and those same Terra/Aqua instrument’s solar diffusers also intended for calibration were found to be unusable by Priestley et al. (2011). Only diffusers with built-in independent monitoring detectors have been found useful, as in Chen et al. (2016), but to date no ERB device has this capability. The National Research Council (2007) decadal survey hence concluded that the single most critical issue for current climate change observations was their lack of accuracy and low confidence in observing the small climate change signals over long decade time scales. The only satellite mission that has managed to track calibration changes to the 1σ or better desired 0.3% accuracy levels of Ohring et al. (2005) is the SeaWiFS project (Hooker et al. 1992; Barnes et al. 2004), which made monthly maneuvers to perform lunar scans (i.e., since the moon’s reflectivity is a constant; Kieffer 1997). SeaWiFS Earth-leaving solar radiance measurements were hence shown to have at least 0.1% decade−1 calibration stability (Eplee et al. 2012).
Table 1.

Past, existing, and future satellite missions measuring ERB parameters.

Table 1.
Fig. 1.
Fig. 1.

The SW, Total, and WN telescope channel spectral responses rc(λ) as determined on the ground for the CERES devices with example reflected solar and emitted thermal radiance spectra (λ)and (λ).

Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0406.1

Fig. 2.
Fig. 2.

(a) Angles of satellite viewing and solar geometry θsz, θvz, and ϕraz from Table 2. (b) MODTRAN standard atmosphere regions and line to which actual Earth colatitudes Φ are interpolated during NH summer solstice. (c) Diagram of Earth’s orbit showing distance from sun Z and angle Θ from position of NH summer solstice.

Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0406.1

In 2002, every Terra–Aqua CERES ERB instrument began performing raster scans of Earth’s moon. It was later shown by Matthews (2008) that convolution integral mathematics could be used on these data to provide absolute measurements of lunar albedo and thermal output. Such results used the Matthews (2009) calibration coefficients independent from the CERES project and calculated to make sure the two ERB devices each on Terra or Aqua measured almost identical radiances for all near-simultaneous nadir Earth scenes (occurring every 3.3 s on Terra and Aqua, each with two identical ERB devices on board). The Matthews (2008) better-than-0.3% agreement between different lunar instrument scans made from the same satellite (but, important and unlike Earth nadir comparisons, made at separate times) therefore demonstrates the possibilities of the moon for assuring absolute accuracy transfer between completely different satellite platforms. Given the success of SeaWiFS, a viable option was therefore to find ways to improve inversion of already archived level 0 raw detector output results from ERB instruments with regularly taken lunar–solar scans [such as those built for projects of Jacobowitz and Tighe (1984), Barkstrom et al. (1989), Wielicki et al. (1996), Harries et al. (2005), Fox et al. (2011), and Wielicki et al. (2013)]. This is one goal of a new project called MERBE beginning in 2014, which is an undertaking entirely independent from NASA by a calibration consultancy company called Zedika Solutions LLC. It is an attempt in response to the needs highlighted by the National Research Council (2007) decadal survey to obtain a true climate observing system as rapidly as possible (see Cooke et al. 2014). The Matthews (2018a,b) studies detail further how additional accuracy improvements can be achieved using new signal processing and lunar calibration techniques. Specific to the beginning of the MERBE project and shown by Matthews (2018a), all orbiting and Terra/Aqua ERB instruments are recalibrated to measure a consistent lunar solar albedo, in addition to a constant thermal emissivity (both with a goal of ±0.3% 1σ absolute accuracy, and assuming a fixed mean illuminated moon surface temperature). This MERBE paper concentrates on the stage of inversion known as “unfiltering,” which is required to account for nonuniform telescope spectral response shape as in Clerbaux et al. (2008a,b). Correction of all measurements by Terra and Aqua ERB devices built for CERES has hence been performed by MERBE as a first step, paying higher attention to the diagnostic metrics available to evaluate calibration quality. The most important metric for verifying accuracy of spectral characterization and unfiltering processes as mentioned above is the direct comparison agreement of simultaneous nadir measurements for all Earth scenes irrespective of spectral content, from two identical ERB devices on the same satellite viewing the same target [as used in Figs. 15 and 16 of Priestley et al. (2011) and Priestley (2017a)]. Current ERB unfiltering algorithms of Loeb et al. (2001) assume almost entirely linear relationships between the desired broadband ERB measurements Re(ti), and detector product (ti). These are defined by Eqs. (4) and (5), respectively, for radiant energy source e at time ti and ERB telescope channel c. Given uncertainty estimates by Wielicki et al. (2013) and Loeb et al. (2009) of existing unfiltering processes and the presence of highly nonlinear and changing calibration parameters (Matthews 2009; Parfitt et al. 2016), today’s inversion techniques such as that described in Loeb et al. (2001) are insufficient to provide climate-quality results within the MERBE 0.3% accuracy goal. This article details a new way of producing unfiltered radiances from ERB detectors, using improved nonlinear techniques and also taking advantage of the advances in radiative transfer theory over the last 20 years.

Physical nature of ERB measurements

The integrated fluxes leaving Earth and calculated as in Eqs. (1) and (2) are typically produced based on electromagnetic measurements of angularly varying scattered and emitted radiance L (by transference into heat energy in a broadband detector). Then conversion of the radiant result to irradiance today uses anisotropic correction factors derived empirically in the past by Taylor and Stowe (1984), Green and Hinton (1996), and Loeb et al. (2007a). These will naturally need redetermination using better calibrated radiances to maximize accuracy of future MERBE data releases [although, as discussed by Cooke et al. (2014), this has lesser importance for climate change detection].

The focus on cloud processes for GCM studies requires high-spatial-resolution ERB radiance measurements with an Earth footprint of 50 km or less in size, and matched with simultaneous narrowband data from an imager also situated on the same satellite (e.g., AVHRR, VIRS, MODIS, SEVIRI, or VIIRS; see the appendix). This enables assignment of cloud property retrievals to ERB footprints (Minnis et al. 2011), which is necessary for effective advancement of CRF research. Such a small footprint to isolate cloudy and cloud-free regions where possible, is obtained using instrument focusing mirrors and relatively small broadband photon sensitive thermal detectors (e.g., bolometers for CERES). The reflectivity and absorptivity of such ERB optical components will vary throughout the wavelength region of interest (λ > 0.2 μm), as represented by spectral response rc(λ) in Eq. (5). All such channels have a parameter that is independent of wavelength and known as gain gc. This is the net voltage signal generated in the instrument per unit of heat power converted from light in the thermal detector. Each ERB telescope device also has a spatial field-of-view (FOV) shape represented as P(θ, ϕ) and often assumed to be wavelength independent [see Smith (1994), with an angular volume defined as being one for MERBE by Matthews (2008, 2018a)]. Both SW and LW radiances are usually recorded by the missions in Table 1 at time ti-dependent global positions, and with the same viewing geometry:
e3
e4
e5
e6

For simplicity, this study from here shall consider all calculations in the reference frame of the instrument, making the lower dimension simplification of Eq. (3) possible. This is because, as stated, the FOV weighted–averaged ψ, Φ, and viewing geometry values are themselves functions of time ti for a scanning and orbiting spacecraft instrument. The Eq. (5) daylight measurement i at the satellite will therefore consist of both reflected solar and emitted thermal energy (λ) + (λ) as shown in Fig. 1, for samples made at time ti. The fractional spectral responses rc(λ) displayed in the same figure exemplify the relative efficiency with which Earth-leaving photons are converted to heat within an ERB detector. All Earth-viewing ERB instruments must utilize transmissive components to select SW energy, again with inevitably in-orbit changing spectral throughput as shown by Clark and DiBattista (1978), Matthews (2009), and Matthews et al. (2006). Spectral response rc(λ) is typically the product of coated mirror reflectance, spectral filter transmission and detector absorption. Such ERB instruments have at least two separate radiometric channels designated SW and “Total” (tot) as in Fig. 1, often each with their own unique mirrors, filters and detector. SW channels use a synthetic quartz filter to transmit radiance in the range 0.2 < λ < 5 μm. The Total channel has no optical filters, so to have a significant mirror reflection dominated response across the entire ERB spectral region of interest (λ > 0.2 μm). LW measurements in sunlight are derived from the difference between Total and SW channel signals, which MERBE performs at higher accuracy than, for example, CERES because of the Matthews (2009) absolute solar wavelength balancing of the two channels [using the nighttime-trained “window” (WN) telescope to give the low thermal output of DCC in daytime]. This third WN channel only on CERES uses a zinc sulfide/cadmium telluride optic to transmit radiance in the atmospheric window region between 8 < λ < 12 μm. In broadband heat-measuring ERB detectors with offset signals already removed, time hysteresis deconvolution corrections should be made by an appropriate operator (Matthews 2018b). This is represented for MERBE by {⋅} in Eq. (6) for bolometers from the CERES devices. With this the detector voltage Vc(ti) is converted into the most immediate instrument product called filtered radiance (ti), using division as in Matthews (2009; 2018b) by the channel specific gain gc.

Filtered radiance as represented by Eq. (5) will therefore vary because of both light intensity and also spectral content because of the nonuniform rc(λ) functions. The tilde in the result of Eq. (5) indicates the measurement’s raw nature, prior to any spectral inversion that is being developed in this study. Lack of a tilde then means the result is no longer dependent on a mixture of both SW solar and LW thermal radiance. In practice and for use of any broadband Earth observing instrument where rc(λ) varies with wavelength, the inversion described earlier as unfiltering must be performed on the raw detector result (ti). This paper hence describes an improvement of such processes taking advantage of current modeling/computational capabilities and therefore has relevance to the reprocessing of data from all missions listed in Table 1 as part of the MERBE project.

2. MERBE unfiltering

Complete but presently unused in-flight determination of improved spectral responses for ERB instruments that meet the higher climate accuracy standards of Ohring et al. (2005) has been described previously in detail by Matthews et al. (2006, 2007a,b) and Matthews (2009). To summarize, orbiting TRMM, Terra, and Aqua ERB telescopes had high atomic oxygen exposure and subsequent contamination degradation because of pointing in the satellite ram direction (see Matthews et al. 2006; Matthews 2007), which requires a dynamic compensation to be made within the unfiltering process outlined by Clerbaux et al. (2008a). A physical contaminant calibration methodology was therefore developed by Matthews (2009) to derive the time changing spectral responses and was shown to give superior relative accuracy for all measured Earth scenes between two collocated ERB devices (e.g., on the same satellite platform of Terra or Aqua, which as mentioned both have two CERES devices on board). This study now combines such predeveloped spectral characterization with the Matthews (2018b) improved MERBE detector signal inversion, Matthews (2018a) stability from lunar scans, and the new nonlinear unfiltering techniques being described here. In addition, it will be shown that MERBE unfiltering also provides an instantaneous solar and thermal MODTRAN (Berk et al. 2006) spectrum for all measurements, whose integrated values are constrained to match the lunar-calibrated and hence SI-traceable ERB data (Matthews 2018a) that give traceability and a level of confidence in the measurement results.

The purpose of the unfiltering process is to use the Eq. (5) raw measured filtered radiances , , and to make the most accurate estimates possible of the SW and LW ERB radiance parameters Rsol and Rth [Eq. (4)]. MERBE instrument unfiltering shall follow the also earlier documented scene specific methodologies of Matthews (2009), which are detailed in Eqs. (7)–(18). The quantity from Eq. (7) is a parameter that can be derived based on an infrared (IR)-only sensitive channel such as a WN telescope, and referred to as thermal “quartz filter leakage.” It quantifies the small component of Earth emitted radiance (λ) with wavelengths below 5 μm, that will pass through the SW channel’s quartz filter to arrive at its detector (see Fig. 1). Like previous work by Loeb et al. (2001) this can accurately be represented for CERES devices using the Eq. (8) quadratic coefficients a1, a2, and a3, determined empirically for CERES devices by monthly comparison between SW and the thermal only sensitive WN channel output at night. Equation (10) then produces the purely reflected solar energy sensitive filtered result Fsw during daylight [Eq. (9)]. The quantity from Eq. (11) is then the Matthews (2009) “filtering factor,” or the ratio of in-band solar filtered and unfiltered radiance for scene i:
e7
e8
e9
e10
e11
e12
Being fundamental for this study, nonlinear unfiltering of the scattered SW result shall be performed by as in Eq. (12). Examination of Eq. (11) and the value’s sensitivity to the shape of (λ) gives indications of the accuracy of the unfiltering process. For example, consider how of Eq. (11) for a perfect cavity detector with a constant flat spectral response of rsw(λ) = 0.9, will have no dependence on the scene spectral energy distribution (λ). This illustrates how ERB data accuracy has lower requirements on knowledge of scene spectral shape when the instrument has a highly uniform spectral response.
Next the LW unfiltering must be performed using the Total channel filtering factor from Eq. (14), which is the ratio of solar heat power generated in its detector to that converted in the SW channel. The similarities between the solar wavelength spectral responses of Total and SW telescopes shown in Fig. 1 ensures that this parameter varies in a more linear fashion with different scenes than the Eq. (11) value. It does, however, require very precise absolute balancing of rsw(λ) and rtot(λ) for SW wavelengths as in Matthews (2009), to prevent the inaccurately low daytime LW results from the CERES project [see the implausible negative day minus night difference in Fig. 11b of Priestley et al. (2011)]. The solely thermal radiance sensitive filtered result Flw is then obtained and unfiltered by Eqs. (15)–(18):
e13
e14
e15
e16
e17
e18
All inversion described above therefore requires high-quality estimations of both solar and thermal radiance spectral shape for each scene. This required knowledge is called a “spectral signature” M and is defined by Eq. (19) for MERBE to be proportional to Le(λ), but independent of integrated broadband energy Re:
e19
Given an SI-traceable Re value, the integral of Eq. (19) will of course be equally accurate. For MERBE the radiative transfer code called MODTRAN is used for estimating these spectral signatures, but it would be inefficient to run such code on a scene by scene basis to give such M e(λ) results. A faster way is needed to use MODTRAN results to estimate spectral signatures in real time, based on a database of full radiative transfer runs.

a. MODTRAN 5.3 ERB spectral signatures

While remaining practical, MERBE uses modern computing capabilities to make spectral representations for unfiltering more comprehensive than the techniques used by Loeb et al. (2001). Spectra shall hence be quickly generated for each satellite footprint based on the conditions of geographical location, measured solar input I0, date and viewing-sun geometries (see Table 2 for the discrete geometric simulation angles chosen, as also illustrated by Fig. 2a). Earth radiance spectra can be calculated using Berk et al. (2006) MODTRAN 5.3 standard atmospheres named “tropical,” “midlatitude,” and “Arctic” (for both summer and winter). This allows for five distinct conditions during Northern Hemisphere (NH) summer, which are defined at the latitude regions shown in Fig. 2b. Assuming this represents Earth at summer solstice (21 June), the distribution with latitude is then rotated by 180° about the equator to give simulations of NH winter solstice. Since Earth’s atmosphere varies seasonally between these two states, a general MODTRAN simulated parameter A at these five colatitude Φ positions is hence found using Eq. (20), where Θ is the post NH summer solstice angle of Earth’s rotation around the sun as in Fig. 2c (and is the NH summer MODTRAN value also at that time):
e20
To give a typical example of the Eq. (20) variable , it could represent, say, MODTRAN estimates of relative radiant amplitude at 320 nm for a particular Earth scene type during the NH solstice [specifically the Fourier series coefficients Ai,k,n shown later in Eq. (23) that make up a fit to the MODTRAN values of Fig. 4a]. For general colatitude locations Φ between these five regional points, the model coefficients calculated by Eq. (20) are then linearly interpolated to the dashed line in Fig. 2b.
Table 2.

Discrete geometry angles of solar zenith θsz, viewing zenith θvz, and relative azimuth ϕraz used in MODTRAN simulations (see Fig. 2a).

Table 2.

MODTRAN also allows for separate SW spectrally reflective representations of over 20 different scene types, including those from the International Geosphere–Biosphere Programme (National Center for Atmospheric Research 2017; see Table 3). Although the broadband ERB rc(λ) functions limit unfiltering inaccuracies from varying fine line spectral energies, appropriate aerosol models should also be used in all MODTRAN simulations. As also shown in Table 3, a couple of suitable aerosol models are selected for each IGBP scene type, along with an aerosol free case. The spectral signature used for unfiltering is then generated as the mean of the three MODTRAN spectra for these different aerosol conditions.

Table 3.

Scene types used in MERBE MODTRAN simulations and three chosen aerosol types over which spectra are averaged [first 18 are from IGBP defined by the National Center for Atmospheric Research (2017)].

Table 3.

Table 1 additionally showed that the satellite missions of interest to MERBE span a period that begins in the late 1970s. For completeness and to approximate changes in greenhouse gas (GHG) and CFC airborne constituents over this period, different atmospheric concentrations are hence chosen to use in MODTRAN for the years 1976, 1990, and 2017 [i.e., the used Table 4 values are approximated/projected from the GHG forcing index of Butler and Montzka (2017)]. Spectral generation of periods other than these years then again uses linear interpolation between the three distinct spectra generated for these chosen dates.

Table 4.

GHG and CFC atmospheric concentrations used in MERBE MODTRAN 5.3 simulations to represent years 1976, 1990, and 2017 (CO2 is in parts per million, all other GHGs are in parts per billion, and CFCs are in parts per trillion).

Table 4.

The final but most important atmospheric conditions needing simulation for MERBE are the various cloud types. This is done based on the cloud classifications discussed by the ISCCP and Hahn et al. (2001), which suggest the four optical depth versus pressure regions separated by the dashed lines in Fig. 3. The 25 different MODTRAN cloud types shown in this figure and listed in Table 5 were selected specifically to cover the entire distribution of clouds in these four regions. So, with multiple different cloud types each with three possible aerosol conditions, every scene and geometry is then represented by 75 separate MODTRAN simulations (see squares in Fig. 4a). After the average of the three possible aerosol type spectra is taken, 25 Fourier series coefficients Ai,k,n are then calculated for each wavelength k to use in Eq. (23) (i.e., acting as a low-pass filter fit like that shown in Fig. 4a to actual MODTRAN values). Examination of Eqs. (4) and (19) confirms that the aforementioned spectral signature represented by M e(λ) is independent of radiant power with an integral of one. However, since all MODTRAN solar simulations for MERBE are performed assuming a constant solar input I0 of 1361 W m−2, it is also necessary to use the Eq. (21) factor z in Eq. (22)’s normalization of SW filtered radiance to become (using Earth orbit radius Z in au; 1 au = 149 597 870 700 m). This accurately adjusts actual data to the energy levels used in MODTRAN simulations, which are those measured at mean solar output and an Earth–sun distance Z of exactly 1 astronomical unit [see Fig. 2c, where I0 values are taken from the VIRGO composite of Frohlich (2017), constructed from multiple satellite missions since the 1970s]. The resulting Eq. (23) MERBE solar result has a spectral resolution Δλsw of up to 10 nm, with and being the start and end solar wavelengths chosen as 200 and 5190 nm, respectively [see Eq. (24)]:
e21
e22
eq1
e23
Such spectra are produced for each ERB footprint with a computationally fast matrix multiplication, using Fourier sine amplitudes Ai,k,n and the adjusted solar input SW filtered radiance result from Eq. (22). Additionally, with an integral of one and units of μm−1, can then be directly used in the Eq. (24) digital calculation of the SW filtering factor [i.e., equivalent to Eq. (11) but with no denominator required]. Figure 5 shows example solar spectral signatures generated by Eq. (23) for the different IGBP scenes of ocean, grassland, and desert. They illustrate the change in spectral shape as the broadband ERB radiant power Rsol varies from the minimum to maximum quantity estimated by MODTRAN. Figure 5a displays the most important change in spectral shape for an ERB device such as CERES that uses silver mirrors, which occurs between clear blue and heavily overcast deep convective cloud ocean scenes.
Fig. 3.
Fig. 3.

Regions of ISCCP cloud classifications defined by Hahn et al. (2001) and distribution of MODTRAN simulations ran for every scene type.

Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0406.1

Table 5.

Cloud field scene types used in MERBE MODTRAN 5.3 simulations and based on ISCCP definitions of Hahn et al. (2001).

Table 5.
Fig. 4.
Fig. 4.

(a) MODTRAN SW spectral signature amplitudes for ocean scenes at 320 nm and Eq. (23) Fourier series low-pass fit. (b) MODTRAN LW spectral signature amplitudes for ocean scenes at 909 cm−1 and Eq. (26) Fourier series low-pass fit.

Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0406.1

Fig. 5.
Fig. 5.

Example MERBE solar spectral signatures M sol(λ) for full range of scene-integrated power and scenes of (a) ocean, (b) grassland, and (c) desert.

Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0406.1

The same solar spectral signature is also used in Eq. (25) for generation of the ratio between Total and SW channel solar wavelength net responses [identical to Eq. (14)]. In contrast to previous techniques such as Loeb et al. (2001), this then enables the SW-independent daytime LW filtered result to be derived from Eqs. (15) and (16) by an equally nonlinear process:
e24
e25
For the LW and this time in wavenumbers, using similarly derived Fourier coefficients Bi,k,n the thermal spectral signature is produced by Eq. (26) based on the filtered result Flw (where has a spectral resolution Δλlw of up to 1 cm−1, between = 5 and = 4004 cm−1). As with the SW unfiltering this enables quick access to the MODTRAN database for an estimate of thermal spectra without the need to run the full radiative transfer code, and calculate the filtering factor :
e26
eq2
e27
Figure 4b shows an example low-pass Fourier series fit to the corresponding IR MODTRAN simulation values, this time at 909 cm−1. LW spectral signatures for the same ocean, grassland, and desert scenes displayed for the SW in Fig. 5 are then illustrated by Fig. 6. In addition to allowing more accurate unfiltering of radiance, both these solar and thermal spectral signatures are also made available to data users by MERBE freeware that operates the tensors A and B.
Fig. 6.
Fig. 6.

As in Fig. 5, but for thermal spectral signatures M th(λ).

Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0406.1

b. Dual-layer unfiltering

Most effective CRF research requires isolation of overcast and cloudless sky regions across the globe, to distinguish warming effects both with and without clouds present. Since instruments like CERES have an Earth footprint as big as 50 km in size, many of their measurements are part cloudy, part clear, which can complicate their direct use in CRF studies. The existing Energy Balanced and Filled (EBAF; Loeb et al. 2009) CERES product hence used linear regression with higher-spatial-resolution onboard imager data from MODIS, attempting to estimate both the clear and cloudy global fluxes (albeit as regional monthly means). The CERES Single Satellite Footprint (SSF; Minnis et al. 2011) data product is being entirely recreated for MERBE, now with SI-traceable fluxes in place of those from the CERES project (contact author for free data access). These files already contain both these visible and IR imager channel radiances H and Q, but partitioned into clear and cloudy regions after convolution with ground measurements of the ERB device FOV [P(θ, ϕ) from Eq. (3); see Minnis et al. 2011]. To maximize accuracy and optimize its use in CRF studies, daily MERBE data shall hence also make use of such scene identification and radiances from the accompanying imager to separate instantaneous clear and cloudy ERB fluxes. Such a new MERBE process is described as dual-layer unfiltering and begins by scaling such imager results H and Q to ERB data. rvis(λ) in Eq. (28) is the visible imager H channel spectral response from Xiong (2002), where for MODIS on the Terra and Aqua platforms this is centered at a wavelength of 0.6455 μm (while the IR channel result Q is made around the 11.02 μm point). Using MODTRAN spectra for (λ), it is possible to estimate the scene i-dependent imager to ERB SW filtering factor ∇i of Eq. (30). Such a factor is again represented using a nonlinear Fourier summation with amplitudes Ci,n as in Eq. (32). To account for possible calibration drifts and imager detector nonlinearities (Qu et al. 2006), H and Q are regressed against and data on a monthly basis, allowing mission life updating of ρ or υ values in Eqs. (29) and (33) (based on 100% clear or overcast scenes only):
e28
e29
e30
e31
eq3
e32
e33
e34
If desired it will be simple to also use these comparisons to identify and later eliminate artificial calibration trends in all imagers that share a satellite platform with a device in the MERBE program. This could then facilitate new imager cloud retrievals for a MERBE edition 2 release based on measurements now meeting the requirements of Ohring et al. (2005), Fox et al. (2011), and Wielicki et al. (2013), decades sooner than currently thought possible.
It is, however, likely not sufficiently accurate for climate studies using instantaneous partly cloudy data to rely on mere regression and extrapolation of ERB parameters from narrowband imager results alone (as in Loeb et al. 2009). The recalibrated SSF product additionally provides a parameter α, which tells the estimation of the ERB FOV fraction that is deemed clear of clouds. The term β in Eq. (35) is then the corresponding overcast fraction for a particular FOV, while Hclr, Qclr, Hovc, and Qovc are the instantaneous SSF imager clear (clr) and overcast (ovc) radiances, respectively (weighted by the ERB device FOV; Minnis et al. 2011). To further minimize imager detector or modeling extrapolation errors, the clear and overcast solar ratio γi is then found using Eq. (36). With this the dual-layer filtered SW radiances can hence be calculated by Eqs. (37) and (38), making uncertainties largely systematic in the ratio and hence as small as possible in the final results:
e35
e36
e37
e38
e39
These separate clear and overcast SW filtered radiances then allow generation of two corresponding solar spectra using the Fourier series tensor of Eq. (23) (see the bottom-left panel of Fig. 7). Unfiltered clear and cloudy radiances and are then produced from division by the appropriate filtering factors as in Eq. (12). The final all-sky solar spectral signature is then found by Eq. (39) and used to calculate the MERBE unfiltered all-sky result for a partially cloudy scene, in addition to the filtered LW measurement Flw from Eqs. (15) and (16).
Fig. 7.
Fig. 7.

Separate instantaneous Fourier tensor (top) flux and (bottom) radiance spectral signatures for clear, cloudy, and all-sky scenes used in MERBE nonlinear unfiltering and also made available to the climate community. The animation of Matthews (2015) shows the tensor operating in real time.

Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0406.1

Similarly, the Eq. (40) thermal ratio χi is then used to calculate clear and cloudy filtered LW radiances from Eqs. (41) and (42) (note the clear/overcast formats of γi and χi are the reciprocal of each other so the denominator is usually the greater):
e40
e41
e42
e43
Near identical as for the solar region, during mixed footprints this allows use of the Eq. (26) Fourier series tensor to generate both clear and cloudy LW spectral signatures that unfilter the separate filtered radiances (bottom-right panel of Fig. 7), creating and along with the all-sky thermal spectral signature from Eq. (43). It was considered how MERBE results where the imager radiances are unavailable may become biased because this will then rely on single-layer unfiltering. However, in tests the monthly mean change in unfiltered radiances was found to be always less than 0.01%, when the dual-layer process was turned off.

As with the potential to compare solar (and LW/WN) MERBE data with the accompanying imager radiances, such new SI-traceable thermal results could likewise be compared with IR spectrometer outputs on the satellites of Aqua and SNPP [e.g., from AIRS and Cross-Track Infrared Sounder (CrIS); see the appendix]. Spectrally resolved measurement comparisons with broadband results have been done in the past by Huang et al. (2012). Because of MERBE LW data stability based on the moon and shown by Matthews (2018a), that type of analysis may be used to identify any currently undetected calibration drifts in these same satellite thermal spectrometers. This could significantly bring forward the arrival of desired thermal spectral fingerprint benchmarks (Bantges et al. 2016), again decades sooner than that possible with new sounder instruments currently in development (see Wielicki et al. 2013).

Also included in the Fourier series tensor is a hemispherical integration product of the MODTRAN results, allowing users to obtain irradiance spectra for each MERBE scene as in Eq. (44) [both SW and LW plots of are additionally shown in the top row of Fig. 7 and the animation of Matthews (2015)]:
e44

3. Results

a. Relative accuracy through in-flight spectral characterization

Decadal-length records exist from each of the two CERES Flight Models (CFM) that are on board the Terra and Aqua satellite platforms (with CFM1 and CFM2 on Terra and CFM3 and CFM4 on Aqua). A MERBE fundamental criteria dictates that different but correctly calibrated ERB instruments viewing the same Earth target from the same satellite must measure minimal difference for all scenes, irrespective of their spectral content. Direct comparisons of Terra or Aqua midscan Earth nadir footprints taken by the pair of collocated devices within 3.3 s of each other are a fundamental way of assessing the quality of ERB spectral calibration and unfiltering. They are especially important for these Terra/Aqua data, where previous to 2005 the two CERES devices on each satellite would take turns to operate in the climate gathering cross-track mode for three months at a time, while the other was in rotating azimuth plane mode (to collect data for development of the anisotropic factors mentioned in section 1). Agreement between two devices is no indication of either accuracy or stability, but it can be used to assess the minimum possible error or trend that can be assigned to a particular dataset. As a climate data record from Terra or Aqua is constructed from cross-track data alone, the first few years of continuous Terra or Aqua ERB records will contain quarterly biases if the two instruments used disagree significantly.

Such biases are certain to exist in a SW climate record constructed using any Terra and Aqua CERES data as illustrated in the left panels of the top and top-middle rows of Fig. 8, which shows this direct comparison of near-simultaneous Earth nadir footprints from that project (noting once more that MERBE is an entirely separate experiment from the CERES project and hence MERBE data are not CERES data). In Fig. 8 (left panels) it is seen that throughout the mission the two separate CERES results are far from the target goal of zero difference, causing greater than 1% artificial shifts in climate records as the data source is swapped between the two instruments. These relative errors are larger than the 1-standard-deviation absolute accuracy of 0.9% claimed by Fox et al. (2011) and Wielicki et al. (2013) for the CERES mission. Significant relative trends are also present for CERES (Fig. 8, left panels of the top and top-middle rows), with differing magnitudes depending on the scene types, but most can be greater than the 0.2% decade−1 absolute stability also today being quoted by the CERES team (1 standard deviation; see Thomas et al. 2016; Loeb et al. 2016, 2017). Such scene dispersion and trends are largely due to incorrect characterization of the SW channel spectral responses, for example when UV-rich clear ocean scenes are viewed in comparison with clear land, with its higher fractional near IR content [see Fig. 5 and Matthews (2009)]. There is also a substantial anomalous month to month variation in the CERES direct comparison differences, far larger than the sampling noise of around 0.1%, which will introduce more artificial climate signals. Like all previous CERES edition releases shown by Matthews (2009), Priestley et al. (2011), and Priestley (2017a), the Aqua SW direct comparison still displays a significant start of mission difference for the clear ocean scene (Fig. 8, left panel of top-middle row). This persists and even grows larger up to March 2005 when the CFM4 instrument lost its SW channel, preventing the daytime direct comparison metric from continuing. It is suspected that this disagreement was due to the on-ground contamination event that occurred to both Aqua CERES devices prior to launch (Matthews et al. 2007a; Matthews 2009).

Fig. 8.
Fig. 8.

ERB daytime relative percent errors from both (left) CERES (edition 4) and (right) MERBE releases.

Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0406.1

Taking advantage of the discussed contaminant model and balancing methodologies from Matthews (2009) and Matthews et al. (2006, 2007a,b), equivalent results from the MERBE program are also shown (Fig. 8, right panels of the top and top-middle rows). Much as before with Matthews (2009), relative calibration errors are reduced by an order of magnitude for both Terra and Aqua SW MERBE data, when compared with the corresponding CERES results (Fig. 8, left panels of the top and top-middle rows). As explained in Matthews (2018a), the gains associated with these MERBE data are validated using the moon to have zero trends at 0.15% decade−1 or better confidence [2 standard deviations; see raw lunar data in Matthews (2016c)]. The start-of-mission contaminant thickness estimator of Matthews (2009) also removes the CERES scene-dependent biases existing at the beginning of the Aqua data (cf. the left and right panels of the top-middle row of Fig. 8). Most of same satellite MERBE SW Earth data (Fig. 8, right panels of the top and top-middle rows) agree to less than 0.2%.

Daytime LW measurements are among the most challenging to make with a broadband ERB instrument. Being a product involving the separate SW and Total radiometric channels, correct day LW results need precise and absolute spectral balancing of the two telescopes at solar wavelengths [i.e., using from Eq. (14) as in Matthews (2009)]. The left panels in the bottom-middle and bottom rows of Fig. 8 show Earth nadir footprint relative accuracies of same platform CERES LW measurements made from Terra or Aqua during daylight. These indicate that such data are subject to relative errors and trends similar in magnitude to SW CERES results shown directly above, again introducing 1% or more quarterly biases in a cross-track-only constructed day LW climate record. Of more importance is that these mere relative CERES inaccuracies are more than 2 times the specified 0.5% absolute LW accuracy originally defined by Wielicki et al. (1996) for the mission, as well as the relative trends often being far larger than the LW stability of 0.15% decade−1 value today still guaranteed to climate scientists [both 1 standard deviation; see Huang et al. (2012) and Loeb et al. (2017)]. Also of stark contrast is the comparison of these CERES daytime LW relative results with those made at night, where no subtraction of SW signal from that of the Total channel is needed (cf. the left panels of the bottom-middle and bottom rows of Figs. 8 and 9). The determination of Matthews (2009) that atomic oxygen from ram exposure was severely contaminating Terra–Aqua ERB SW channel optics also suggested there would be an equally important affliction to the exposed mirrors of a coaligned Total channel. Hence MERBE again uses absolute balancing methodologies from Matthews (2009) and Matthews et al. (2007b) where the same contamination model aligns SW and Total channels to ensure knowledge of (or errors in) the solar induced signals are systematic, completely removing them from the daytime LW result. Total channel gains are initially estimated using the onboard blackbodies, before slight linear adjustments using lunar thermal results are made to ensure no decadal trends exist (with 0.06%, 0.04 K decade−1 or better confidence—2 standard deviations; Matthews 2018a). The corresponding day LW direct comparisons for MERBE are shown in the right panels of the bottom-middle and bottom rows of Fig. 8. As with the SW, these again demonstrate an order of magnitude increase in relative accuracy and likely the first global cloud-resolving LW ERB dataset with possible accuracies within the specified CERES goal of 0.5% from Wielicki et al. (1996). Comparison of this with the corresponding night data in the right panels of the bottom-middle and bottom rows of Fig. 9 is also, like Matthews (2009), in far better agreement for MERBE, with both the day and night LW results now largely agreeing to better than 0.2%.

Fig. 9.
Fig. 9.

As in Fig. 8, but for nighttime.

Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0406.1

The results presented in the bottom-middle and bottom rows of Fig. 9 are from same satellite direct comparison of the most straightforward ERB measurements that are made of LW during nighttime. Discussed in section 2, the flat, near-cavity like spectral absorption of an ERB device in the thermal region means that unfiltering here is less dependent on knowledge of scene spectral content or instrument response (see Fig. 1). Hence both CERES and MERBE data for these nighttime scenes display relative accuracies almost entirely better than 0.1%. As for the daytime results, however, the MERBE data (Fig. 9, right panels of the bottom-middle and bottom rows) are of a quality beyond that of CERES.

b. Bias and trend estimates of CERES data absolute accuracy using lunar calibrated MERBE results

This last brief section makes a simple comparison between the latest CERES Earth data and new edition 1 MERBE results assuming accurate unfiltering and that they are made SI traceable and stable based on lunar scans by Matthews (2018a; data available in Matthews 2016c). These differences, which are based on ERB calibration that for the first time meets all available Earth and lunar consistency checks, then make a preliminary estimate of any absolute accuracy biases and trends in the newest CERES climate data currently available for GCM validation. Figure 10 shows such comparisons for all daytime SW and LW ERB measurements from the recent CERES edition 4 climate data release.

Fig. 10.
Fig. 10.

Daytime absolute percent errors from the CERES edition 4 release based on MERBE: (top and top middle) SW and (bottom middle and bottom) LW.

Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0406.1

For SW CERES results (Fig. 10, top and top-middle rows) the size of the errors is significant, varying from around 0% to −5% and in almost all cases negative. This emphasizes the dominating cause of the often discussed and implausible 5–7 W m−2 top-of-atmosphere positive global ERB input imbalance measured by CERES [likely due to use of an uncharacterized reference detector in ground calibration; see Folkman et al. (1994), McCarthy et al. (2013), Priestley et al. (2014), and Loeb (2017)]. Exactly like that found previously in Matthews (2009), the CFM3 and CFM4 Aqua SW CERES data (Fig. 10, top-middle row) tend to have a greater negative bias error than the Terra results (Fig. 10, top row). This is probably also mainly due to the known ground contamination event mentioned by Matthews (2009), which prompted the need for an 8% SW gain gsw decrease simply to make CERES Aqua results roughly match other data (Priestley 2017b). Another contributing factor to this larger CFM3 and CFM4 SW underestimate may be the Matthews (2009) past speculated degradation of this same uncharacterized on-ground reference detector, which was used in the later calibrations of the newer Aqua CERES devices. Of greater importance to climate science, however, is the significant artificial negative trends in all Terra CERES SW results (Fig. 10, top row), suggesting a large and false drop in global Earth albedo (especially the often-dubbed primary Terra “climate device” CFM1; Fig.10, left panel of top row). If correct, the most probable reason for this is that UV contaminant polymerization effects like that found on LDEF continued on the Terra ERB devices even after staying in the cross-track mode beyond 2001. Both CFM3 and CFM4 appear to exhibit rapid degradation–induced negative SW trends up to 2005 for CERES data (Fig. 10, top-middle row), when like for the Terra devices all exposure to ram direction contamination was stopped (and CFM4 failed). It is hence possible that artificial CERES SW calibration drifts exist and can be around 1% decade−1 in magnitude, further confirming the finding of section 3a that such data are far less stable than the 0.2% decade−1 standard that the climate community is still being told by Thomas et al. (2016) and Loeb et al. (2016, 2017). The various studies of Matthews (2009) and Matthews et al. (2006, 2007a,b) now used here for MERBE have discussed how the methodologies currently employed by CERES have no way of detecting and correcting for these effects in the climate data they produce.

Daytime LW CERES result errors (Fig. 10, bottom-middle and bottom rows) demonstrate smaller absolute biases than the SW but also display significant artificial and conversely almost entirely positive decadal trends. In the case of CERES Terra data from CFM1 and CFM2 (Fig. 10, bottom middle), this is largely due to the earlier discussed inaccurate balancing between the solar portions of SW and Total spectral responses (Matthews 2009).

Again if validated, the overall forms of the plots in Fig. 10 should be considered carefully by climate data users. This is because they may characterize artificial signals present in the latest CERES Earth climate data release, simply because of incorrect calibration parameters being used in data inversion. All the error data shown in these sections are available for download at Matthews (2016a,b), which also shows estimates of nighttime CERES LW and WN errors and artificial trends to be smaller than for the daytime, but in all cases statistically significant. Instantaneous CERES SSF errors can be also viewed at Matthews (2017).

4. Summary and conclusions

This paper details a new nonlinear method of unfiltering broadband detector signals to account for nonuniform telescope spectral responses and their in-orbit changes in the Moon and Earth Radiation Budget Experiment. MODTRAN 5.3 simulations are used to estimate the spectral shape (or signature) of the reflected solar and emitted thermal radiance leaving the top of the atmosphere, providing separate clear and cloudy results when a collocated imager is working. More comprehensive than existing unfiltering algorithms such as Loeb et al. (2001), the described inversion is now additionally tailored to account for IGBP scene type, geographical position, atmospheric composition and aerosol content, along with seasonal and solar output variations. Using Fourier series coefficients stored in a digital tensor, this then generates an instantaneous scene specific spectral signature for each MERBE footprint. Calculation of an unfiltering ratio from the instrument spectral response is then performed, where such device characteristics are derived using the pre-documented and improved in-flight spectral calibration methodologies of Matthews (2009) and Matthews et al. (2006, 2007a,b). Additionally, these spectral signatures can be generated by MERBE data users through a free release of the Fourier series spectral tensors.

Analysis of MERBE data relative accuracy using cross comparison of collocated ERB instruments on the same Terra or Aqua satellites shows an order-of-magnitude increase in relative measurement precision over CERES products. As was the case for past releases examined by Matthews et al. (2005), Matthews (2009), and Priestley et al. (2011), the latest CERES edition 4 results still exhibit large dispersive scene-dependent relative errors, which when corrected with Matthews (2009) MERBE spectral characterization accounts for this near factor of 10 improvement. The size of these relative errors in edition 4 CERES day LW results is more than 2 times the 0.5% absolute accuracy specified by Wielicki et al. (1996) for the CERES program, and additionally in the SW are greater than the 0.9% figure still quoted by Fox et al. (2011) and Wielicki et al. (2013) for those channels.

With MERBE results assumed to have been made SI traceable and stable to 0.15% decade−1 or better from lunar radiance (2 standard deviations; Matthews 2018a), the new edition 1 MERBE values were also compared with the latest CERES climate data release from the same instruments. This then suggests significant absolute bias errors and artificial calibration trends may be in such CERES results. It also indicates that every decadal length CERES SW record exhibits a negative bias of up to 5%, in addition to an incorrect change in Earth’s albedo that might be as large as −1% decade−1. This combined with the large relative calibration drifts in Fig. 8 (left panels) implies that CERES SW ERB measurements are not as accurate or stable as claimed by Wielicki et al. (2013), Fox et al. (2011), Thomas et al. (2016), and Loeb et al. (2016, 2017), and hence might be assumed by climate science. CERES LW data records of longer than 10 yr alternatively often suggest artificial drifts of more than +0.5% decade−1, possibly because of either unchecked onboard blackbody calibration changes or incorrect solar balancing as described by Matthews (2009) and Matthews et al. (2007b) of broadband spectral responses [CERES LW data stability is stated in Loeb et al. (2017) and Huang et al. (2012) to be 0.15% decade−1; 1 standard deviation]. Any artificial CERES calibration signals or trends shown this paper will naturally have equal impact on the recent edition 4 EBAF climate data release of CERES Science Team (2017).

To finish, a clarification should be made that will stand even in the event of these techniques used for the first edition 1 MERBE data release being later fully validated as successful. The lack of onboard technology to characterize instruments that are unreachable in orbit has required certain physically based assumptions to be made for MERBE, which effectively only “tick all the physically reasonable metric boxes” observable from Earth. The need for greater innovation to continue in spaceborne radiometry therefore remains stronger than ever.

Acknowledgments

Bolometer signals, instrument telemetry, and CERES edition 4 SSF results are from the NASA Langley Research Center Atmospheric Science Data Center. For free access to MERBE SSF data, contact the author at grant.matthews@zedikasolv.com.

APPENDIX

List of Acronyms

AVHRR

Advanced Very High Resolution Radiometer

CERES

Clouds and the Earth’s Radiant Energy System

CFC

Chlorofluorocarbon

CFM

CERES Flight Model

CRF

Cloud radiative forcing

DCC

Deep convective clouds

EBAF

Energy Balanced and Filled

ERB

Earth radiation budget

FOV

Field of view

GCM

Global circulation model

GHG

Greenhouse gas

IGBP

International Geosphere–Biosphere Programme

IR

Infrared

ISCCP

International Satellite Cloud Climatology Project

LDEF

Long Duration Exposure Facility

LW

Longwave

MERBE

Moon and Earth Radiation Budget Experiment

MODIS

Moderate Resolution Imaging Spectroradiometer

MODTRAN

Moderate resolution atmospheric transmission

NH

Northern Hemisphere

SNPP

Suomi National Polar-Orbiting Partnership

RAPS

Rotating azimuth plane scan

SeaWiFS

Sea-Viewing Wide Field-of-View Sensor

SEVIRI

Spinning Enhanced Visible and Infrared Imager

SI

Système Internationale

SSF

Single Satellite Footprint

SW

Shortwave

TRMM

Tropical Rainfall Measuring Mission

UV

Ultraviolet

VIIRS

Visible Infrared Imager Radiometer Suite

VIRS

Visible and Infrared Scanner

WN

Window (radiometric channel)

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  • Loeb, N. G., N. Manalo-Smith, W. Su, M. Shankar, and S. Thomas, 2016: CERES top-of-atmosphere Earth radiation budget climate data record: Accounting for in-orbit changes in instrument calibration. Remote Sens., 8, 182, https://doi.org/10.3390/rs8030182.

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  • Matthews, G., 2007: Animation of CERES contaminant exposure and polymerization mechanism. Zedika Solutions LLC, https://sites.google.com/site/zedikamerbe/CEREScontamination.wmv?attredirects=0&d=1.

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  • Matthews, G., 2009: In-flight spectral characterization and calibration stability estimates for the Clouds and the Earth’s Radiant Energy System (CERES). J. Atmos. Oceanic Technol., 26, 1685–1716, https://doi.org/10.1175/2009JTECHA1243.1.

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  • Matthews, G., 2015: Real-time MERBE Fourier series tensor spectral signatures from Aqua. CALCON Conf., Logan, UT, Space Dynamics Laboratory, https://sites.google.com/site/zedikamerbe/MERBEonAqua.mp4?attredirects=0&d=1.

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  • Matthews, G., 2018b: Signal processing enhancements to improve instantaneous accuracy of a scanning bolometer: Application to MERBE. IEEE Trans. Geosci. Remote Sens., in press.

    • Crossref
    • Export Citation

  • Matthews, G., K. Priestley, P. Spence, D. Cooper, and D. Walikainen, 2005: Compensation for spectral darkening of short wave optics occurring on the Cloud’s and the Earth’s Radiant Energy System. Earth Observing Systems X, J. J. Butler, Ed., Society of Photo-Optical Instrumentation Engineers (SPIE Proceedings, Vol. 5882), 588212, https://doi.org/10.1117/12.618972.

    • Crossref
    • Export Citation

  • Matthews, G., K. Priestley, N. G. Loeb, K. Loukachine, S. Thomas, D. Walikainen, and B. A. Wielicki, 2006: Coloration determination of spectral darkening occurring on a broadband Earth observing radiometer: Application to Clouds and the Earth’s Radiant Energy System (CERES). Earth Observing Systems XI, J. J. Butler, Ed., Society of Photo-Optical Instrumentation Engineers (SPIE Proceedings, Vol. 6296), 62960M, https://doi.org/10.1117/12.680884.

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    • Export Citation

  • Matthews, G., K. Priestley, and S. Thomas, 2007a: Transfer of radiometric standards between multiple low Earth orbit climate observing broadband radiometers: Application to CERES. Earth Observing Systems XII, J. J. Butler and J. Xiong, Eds., Society of Photo-Optical Instrumentation Engineers (SPIE Proceedings, Vol. 6677), 667701, https://doi.org/10.1117/12.734478.

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  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    The SW, Total, and WN telescope channel spectral responses rc(λ) as determined on the ground for the CERES devices with example reflected solar and emitted thermal radiance spectra (λ)and (λ).

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    (a) Angles of satellite viewing and solar geometry θsz, θvz, and ϕraz from Table 2. (b) MODTRAN standard atmosphere regions and line to which actual Earth colatitudes Φ are interpolated during NH summer solstice. (c) Diagram of Earth’s orbit showing distance from sun Z and angle Θ from position of NH summer solstice.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Regions of ISCCP cloud classifications defined by Hahn et al. (2001) and distribution of MODTRAN simulations ran for every scene type.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    (a) MODTRAN SW spectral signature amplitudes for ocean scenes at 320 nm and Eq. (23) Fourier series low-pass fit. (b) MODTRAN LW spectral signature amplitudes for ocean scenes at 909 cm−1 and Eq. (26) Fourier series low-pass fit.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Example MERBE solar spectral signatures M sol(λ) for full range of scene-integrated power and scenes of (a) ocean, (b) grassland, and (c) desert.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    As in Fig. 5, but for thermal spectral signatures M th(λ).

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    Separate instantaneous Fourier tensor (top) flux and (bottom) radiance spectral signatures for clear, cloudy, and all-sky scenes used in MERBE nonlinear unfiltering and also made available to the climate community. The animation of Matthews (2015) shows the tensor operating in real time.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    ERB daytime relative percent errors from both (left) CERES (edition 4) and (right) MERBE releases.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    As in Fig. 8, but for nighttime.

  • <sc>Fig</sc>. 10.
    View in gallery
    Fig. 10.

    Daytime absolute percent errors from the CERES edition 4 release based on MERBE: (top and top middle) SW and (bottom middle and bottom) LW.

Fig. 1.

The SW, Total, and WN telescope channel spectral responses rc(λ) as determined on the ground for the CERES devices with example reflected solar and emitted thermal radiance spectra (λ)and (λ).
Fig. 2.

(a) Angles of satellite viewing and solar geometry θsz, θvz, and ϕraz from Table 2. (b) MODTRAN standard atmosphere regions and line to which actual Earth colatitudes Φ are interpolated during NH summer solstice. (c) Diagram of Earth’s orbit showing distance from sun Z and angle Θ from position of NH summer solstice.
Fig. 3.

Regions of ISCCP cloud classifications defined by Hahn et al. (2001) and distribution of MODTRAN simulations ran for every scene type.
Fig. 4.

(a) MODTRAN SW spectral signature amplitudes for ocean scenes at 320 nm and Eq. (23) Fourier series low-pass fit. (b) MODTRAN LW spectral signature amplitudes for ocean scenes at 909 cm−1 and Eq. (26) Fourier series low-pass fit.
Fig. 5.

Example MERBE solar spectral signatures M sol(λ) for full range of scene-integrated power and scenes of (a) ocean, (b) grassland, and (c) desert.
Fig. 6.

As in Fig. 5, but for thermal spectral signatures M th(λ).
Fig. 7.

Separate instantaneous Fourier tensor (top) flux and (bottom) radiance spectral signatures for clear, cloudy, and all-sky scenes used in MERBE nonlinear unfiltering and also made available to the climate community. The animation of Matthews (2015) shows the tensor operating in real time.
Fig. 8.

ERB daytime relative percent errors from both (left) CERES (edition 4) and (right) MERBE releases.
Fig. 9.

As in Fig. 8, but for nighttime.
Fig. 10.

Daytime absolute percent errors from the CERES edition 4 release based on MERBE: (top and top middle) SW and (bottom middle and bottom) LW.
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