Dual View on Clear-Sky Top-of-Atmosphere Albedos from Meteosat Second Generation Satellites
AArticle
Dual-View Clear-Sky Top-of-Atmosphere AlbedoFrom Meteosat Second Generation Satellites
Alexandre Payez * , Steven Dewitte and Nicolas Clerbaux
Royal Meteorological Institute of Belgium, Ringlaan 3 Avenue Circulaire, B-1180 Brussels, Belgium;[email protected] (A.P.); [email protected] (S.D.); [email protected] (N.C.) * Correspondence: [email protected]: date; Accepted: date; Published: date
Abstract:
Geostationary observations offer the unique opportunity to resolve the diurnal cycle ofthe Earth’s Radiation Budget at the top of the atmosphere (TOA), crucial for climate-change studies.However, a drawback of the continuous temporal coverage of the geostationary orbit is the fixedviewing geometry. As a consequence, errors in the angular distribution models (ADMs) used in theradiance-to-flux conversion process can result in systematic errors of the estimated radiative fluxes.In this work, focusing on clear-sky reflected TOA observations, we compare the overlapping viewsfrom Meteosat Second Generation satellites at 0° and 41.5°E longitude which enable a quantificationof viewing-angle-dependent differences. Using data derived from the Spinning Enhanced Visible andInfraRed Imager (SEVIRI), we identify some of the main sources of discrepancies, and show that theycan be significantly reduced at the level of one month. This is achieved, separately for each satellite,via a masking procedure followed by an empirical fit at the pixel-level that takes into account allthe clear-sky data from that satellite, calculated separately per timeslot of the day, over the monthof November 2016. The method is then applied to each month of 2017, and gives a quadratic meanof the albedo root-mean squared difference over the dual-view region which is comparable frommonth to month, with a 2017 average value of 0.01. Sources of discrepancies include the difficulty toestimate the flux over the sunglint ocean region close to the limbs, the absence of dedicated angulardistribution models for the aerosol-over-ocean case in the data processing, and the existence of anobserver-dependent diurnal-asymmetry artefact affecting the clear-sky-albedo dependence on thesolar zenith angle particularly over land areas.
Keywords: top-of-atmosphere albedo; geostationary satellites; reflected solar radiation; angulardistribution models; diurnal-asymmetry artefact; SEVIRI
1. Introduction
The Earth’s Radiation Budget (ERB) at the top of the atmosphere (TOA) is a crucial observable andone of the Essential Climate Variables [1] defined by the Global Climate Observing System (GCOS) forclimate-change studies. For the Earth system, it describes the energy balance between what comes infrom the Sun and what leaves the Earth, both as reflected solar (shortwave) radiation and as outgoingthermal (longwave) emission. The global warming currently ongoing with unprecedented speed sincethe mid-20th century is a direct consequence of an overall imbalance in the ERB, predominantly causedby human activities from the industrial revolution to the present [2].Characterising as best as possible the state of the ERB can only be done from space, and for thatwe crucially need observer-independent quantities to be retrieved, knowing that satellite instruments a r X i v : . [ phy s i c s . a o - ph ] F e b of 18 can only directly provide observer-dependent radiances L in a given direction at a given time. Goingfrom the measured observer-dependent radiances to such observer-independent quantities involvestwo important steps. The first is called unfiltering and compensates for the spectral-dependence of theengineered instrument [3]. The second is the inversion—also known as angular conversion—which,from that unfiltered radiance in a given direction then associates an estimated observer-independentirradiance appropriate for the observed scene [4], typically via a collection of empirical angulardistribution models (ADMs), such as the Clouds and the Earth’s radiant Energy System (CERES)Tropical Rainfall Measurement Mission (TRMM) ADMs [5]. Formally, the irradiance or ‘flux’ F ( θ (cid:12) ) leaving an imaginary surface element at the top of the atmosphere (in units of W m − ) is the integral,over all the outgoing solid angles in a hemisphere, of the individual radiances L ( θ (cid:12) , θ vz , φ rel ) (in unitsof W m − sr − ) leaving that surface element [6]: F ( θ (cid:12) ) = (cid:90) hemisphere ↑ L ( θ (cid:12) , θ vz , φ rel ) cos θ vz d Ω (1) = (cid:90) π d φ rel (cid:90) π L ( θ (cid:12) , θ vz , φ rel ) cos θ vz sin θ vz d θ vz , (2)where θ (cid:12) is the solar zenith angle, θ vz is the viewing zenith angle, and φ rel is the relative azimuth angle.As well-known, this relation simply reduces to F ( θ (cid:12) ) = π L ( θ (cid:12) ) when the flux is isotropic (Lambertian).ADMs are then typically introduced at this point [6], and provide anisotropic factors which comparean equivalent Lambertian flux π L ( θ (cid:12) , θ vz , φ rel ) to the actual flux F ( θ (cid:12) ) given in Eq. (1): R ( θ (cid:12) , θ vz , φ rel ) = π L ( θ (cid:12) , θ vz , φ rel ) F ( θ (cid:12) ) . (3)With a proper set of empirical ADMs, Eq. (3) can then be inverted to derive the flux from the radiance.Finally, the albedo (a pure number between 0 and 1) is defined as the ratio of the reflected and incomingsolar fluxes: a ( θ (cid:12) ) = F reflected ( θ (cid:12) ) F incoming ( θ (cid:12) ) , where F incoming ( θ (cid:12) ) = E (cid:12) cos θ (cid:12) ; (4) E (cid:12) being the solar constant [7] corrected for the Sun–Earth distance [8].For climate models, it is moreover important to precisely monitor the internal structures of theERB over the globe and throughout the day, seeing that these govern important aspects of the climateon our planet; in particular, its diurnal cycle, and especially the formation of clouds during the day,is a key component of the tropical climate [9]. Most dedicated ERB observations thus far have beenmade from Low-Earth-Orbit (LEO) satellites. Chiefly among these are Sun-synchronous polar orbiters,such as NASA’s Terra and Aqua satellites, which have been observing over the last two decades withthe CERES instrument [10] each location on Earth—though not more than twice per day outsideof the polar regions. The joint EUMETSAT/ESA geostationary (GEO) Meteosat Second Generation(MSG) satellites are actually in a unique position to complement these observations and observe thediurnal cycle, and this for two reasons. The first is that their geostationary orbits offer the advantageof an excellent temporal sampling of the observed locations throughout the day. The second is thatthey embark both the multispectral Spinning Enhanced Visible and InfraRed Imager (SEVIRI) with12 spectral channels at a nadir resolution of 3 km (1 km for the high-resolution visible channel) [11],and the broadband Geostationary Earth Radiation Budget (GERB) instrument with nadir resolutionof 50 km [12]. Every 15 minutes both these instruments provide observations of the full Earth diskseen from the satellite viewpoint. They do have the disadvantage of fixed viewing angles though.Compared to LEO satellites, this makes the measurements of the broadband TOA radiative fluxes more Note that wide-field-of-view instruments, which cannot provide spatial information, are not considered in this work. of 18 sensitive to angular-dependent errors. It is therefore particularly important to address any remainingobserver-dependent systematics in flux or albedo data, knowing that such unphysical artefacts wouldintroduce errors, e.g. in the Earth’s Radiation Budget determination.Interestingly, we now actually have the opportunity to cross-check retrieved GEO products.Indeed, since the end of the year 2016, there have been two MSG satellites at different longitudes andwith overlapping scenes. One of them is at 0° longitude (MSG-3, replaced by MSG-4 on 2018/02/20),and the other is at 41.5°E longitude, providing the ’Indian Ocean Data Coverage’ (MSG-1, whichshould be replaced by MSG-2 at 45.5°E longitude in 2022; see e.g.
Ref. [13]). Taking advantage of thisdual view, our aim with this work is then to compare, quantify the discrepancies and try to addressthem in order to make GEO-derived products as useful as possible. For simplicity the focus will onlybe on the clear-sky top-of-atmosphere broadband shortwave albedo, and we will often simply referto it as the ‘albedo’. In the following, we are only going to use and consider pure SEVIRI syntheticproducts: the so-called ‘GERB-like’ GL-SEV products [14]. Involving a narrowband-to-broadbandprocedure [15] and relying on the CERES TRMM ADMs [5] for the angular-conversion process, theseproducts consist of HDF5 files available every 15 minutes (96 per day), containing 3 × ×
2. Dual-view comparison method
The same treatment is applied independently to GL-SEV images from MSG-3 (SEV3) and MSG-1(SEV1), and is done one month at a time. For that month, and for each individual HHMM timeslotamong the 15-minute timeslots, our basic treatment is the following:• for each day at that timeslot, we first derive the instantaneous clear-sky TOA albedo image afterapplying the appropriate masks— e.g. keeping only those pixels for which the cloud-cover layeris zero (as discussed in the following, we are going to apply a number of extra conditions);• then, similarly to what is done for monthly hourly products , we use all these images to calculatethe monthly “representative albedo image” at that timeslot: in this work, we considered boththe mean and the median, and unless otherwise stated we will show results obtained using themedian albedo (robust statistics);• in a common 0.5° × x will store the albedo difference x = x SEV3 − x SEV1 , (5)which would be 0 for all pixel if the calibration of SEV1 and SEV3 was the same, if there were nonarrowband-to-broadband nor angular-dependent errors, and if the impact of having differentclear-sky atmospheric paths from a given scene to each of the two satellites can be reduced to astrictly angular issue—an assumption already implicit in the radiance-to-flux conversion.Once this treatment is done, we can proceed and apply statistics over the whole set of 96‘SEV3 − SEV1’ images: for each pixel x , using all of the ( t =
1, ..., n t x ) timeslots for which we have We use what are, at the time of writing, the very latest available products covering the dual-view period: GL-SEV HR V003.These can be obtained via the https://gerb.oma.be website. For monthly hourly products, see for instance the CERES SYN1deg [16] and the CM SAF MMDC [17] and [18] products. of 18 non-masked data at that location, we calculate the root-mean-squared difference or root-mean-squareddeviation ( i.e. the square root of the mean squared albedo difference):RMSD = (cid:118)(cid:117)(cid:117)(cid:116) n t x n tx ∑ t = x t ; (6)the bias ( i.e. the mean albedo difference): bias = n t x n tx ∑ t = x t ; (7)and finally the bias-corrected standard deviation σ , from the corresponding variance: σ = n t x n tx ∑ t = ( x t − bias ) = RMSD − bias . (8)
3. One month: sample results and improvements
Since our aim is to assess and compare the retrieved products from the two different MSGsatellites, here we use the fluxes exactly as they are given in the GL-SEV products. Note in particularthat, as part of the data processing of these products, a shortwave flux over the sunglint region isprovided [19], and that the case of ‘aerosol over ocean’ pixels is treated there as ‘clear-sky ocean’ withthe use of identical CERES TRMM ADMs.Figure 1 ( a ) shows the root-mean-squared-difference result that we obtain from our comparisonwhen we naively use the shortwave fluxes whenever they are defined in the GL-SEV products. Among the most salient features that we can see is that there are issues related to unidentified clouds,which actually occur mainly at large viewing and solar zenith angles. What is then probably the moststriking difference are the large extended regions (dark blue) in the bottom left and the bottom rightof the image, where the discrepancies can be larger than 0.10. These can actually be linked to thesunglint regions (when the viewing direction coincides with the specular sunlight reflection off theocean surface) getting close to either of the limbs of the overlapping area: the left one corresponds toMSG-1 and the right one, to MSG-3. Other areas over the ocean with discrepancies which can reach ∼ ∼ We can now try to improve the consistency between the albedo values retrieved from the twosatellites by first applying a number of masks and cuts.First of all, what is frequently done in the literature is to cut on the zenith angles as the quality isexpected to suffer from increasing errors at large values; see e.g.
Refs. [20,21]. The exact threshold mayslightly differ from paper to paper; here we use θ (cid:12) , θ vz < After doing that, we can see that thingsare already improved (see Figure 1 ( b )), but notice that the discrepancies which we identified for the The albedo is set to 1 where it exceeds this value. Such pixels are not masked, to help identify and address potential issues. For consistency with an aerosol-optical-depth mask applied in the following, as there is no retrieval at larger zenith angles. of 18 ( a ) l a t i t ud e ( ° ) longitude (°) − − − −
30 0 30 60 90 ≥ . . . . . a l b e d o r oo t - m e a n s q u a r e dd i ff e r e n ce ( b ) l a t i t ud e ( ° ) longitude (°) − − − −
30 0 30 60 90 ≥ . . . . . a l b e d o r oo t - m e a n s q u a r e dd i ff e r e n ce ( c ) l a t i t ud e ( ° ) longitude (°) − − − −
30 0 30 60 90 ≥ . . . . . a l b e d o r oo t - m e a n s q u a r e dd i ff e r e n ce ( d ) l a t i t ud e ( ° ) longitude (°) − − − −
30 0 30 60 90 ≥ . . . . . a l b e d o r oo t - m e a n s q u a r e dd i ff e r e n ce Figure 1.
Albedo root-mean squared difference (RMSD, Eq. (6)) over the dual-view region seen byboth MSG-3 and MSG-1 for the month of November 2016, after applying different masks. ( a , top left )Clear-sky, without further constraints: the shortwave flux information is used wherever it is defined,simply provided that the corresponding cloud cover at that time and place is zero. ( b , top right ) Sameas ( a ), but only if the solar and the viewing zenith angles are < c , bottom left ) Same as ( b ), but nowadding a sunglint mask, requiring the tilt angle to be >
25° over ocean pixels. ( d , bottom right ) Same as( c ), now adding an aerosol mask over ocean, requiring that the aerosol optical depth at 0.6 µ m is < >
40° over ocean pixels. sunglint and the aerosol areas in particular actually remain of the same order, respectively > ∼ c ).After applying these different masks, the discrepancies related to aerosols over the oceanare still clearly visible and still of the order of ∼ , we are going to mask these aerosol-loaded regions over ocean pixels. There is anaerosol-optical-depth retrieval over the ocean in the GERB/GL-SEV processing [22]; we can thereforeuse the aerosol-optical-depth observations at 0.6 µ m, and only keep those pixels for which this opticaldepth is smaller than 0.1. For consistency with the aerosol-retrieval algorithm and to avoid introducingartefacts in the images, the sunglint mask used in the previous step is then enlarged to only keep tiltangles greater than 40° over ocean pixels. This is our final result using masks; it is shown in Figure 1 ( d ). Note that the CERES team proposes a method to account for aerosols in the clear-sky ocean ADM; see Ref [5]. However, thiscorrection is not actually applied in the GL-SEV processing. The presence of aerosols results in a quite diffuse reflection; very different from the strong specular reflection in the clear-skyocean case. The use of clear-sky ocean ADMs that do not take aerosols into account is therefore particularly problematic. of 18
Its decomposition in terms of standard deviation and bias is given in Figure 2, from which one can seethat the standard deviation typically contributes much more to the RMSD than does the bias. l a t i t ud e ( ° ) longitude (°) − −
30 0 30 60 90 − − ≥ . . . . . s t a nd a r dd e v i a t i o n l a t i t ud e ( ° ) longitude (°) − − − −
30 0 30 60 90 ≤ − . ≥ . − . . b i a s Figure 2.
Decomposition of Figure 1 ( d ) in terms of standard deviation ( left ) and bias ( right ). Now, if we furthermore compare the statistics over the entire image obtained when naively usingthe fluxes as provided in the GL-SEV products (Figure 1 ( a )) to the ones that we obtained after themasking procedures we just described (Figure 1 ( d )), we obtain the results given in Table 1. Table 1.
Summary statistics, where (cid:104)·(cid:105) stands for the average over all the contributing pixels. (cid:113) (cid:104)
RMSD (cid:105) (cid:113) (cid:104) σ (cid:105) (cid:104)| bias |(cid:105) naively 0.055 0.052 0.012with all the masks 0.014 0.013 0.004 These summary statistics provide a single value after looping over all the ( x =
1, . . . , N x )non-masked pixels in the corresponding image. More precisely, denoting the RMSD, σ , and biasof a given pixel via a · x subscript, the quantities given in that table are the square root of the averagemean squared difference: (cid:113) (cid:104) RMSD (cid:105) = (cid:118)(cid:117)(cid:117)(cid:116) N x N x ∑ x = RMSD x ; (9)the square root of the average variance: (cid:113) (cid:104) σ (cid:105) = (cid:118)(cid:117)(cid:117)(cid:116) N x N x ∑ x = σ x ; (10)and finally, the mean absolute bias (or mean absolute difference): (cid:104)| bias |(cid:105) = N x N x ∑ x = | bias x | . (11)In particular, we see in Table 1 that the quadratic mean of the RMSD over all pixels, Eq. (9), issignificantly reduced, going from 0.055 to 0.014.The consistency is much improved after this masking procedure, but we stress once again thatwe actually had to mask the aerosol over ocean case in order to obtain these results, and that havingaccess to correct fluxes also in such cases is clearly a high priority; see e.g. Ref [23]. of 18
We now move on to discuss a well-known issue with geostationary data: due to the fixedviewing geometry from GEO, there can be a systematic diurnal-asymmetry artefact in GEO shortwavefluxes [24]; see also Ref. [25].In the majority of cases however, no asymmetry in the clear-sky top-of-atmosphere albedo isactually expected between the (local time) morning and afternoon. That is, at least if the surfaceproperties do not change over time [26]. Indeed, the albedo over land essentially evolves as a functionof the solar zenith angle, which is symmetrical with respect to the local noon [27,28]: a ( θ (cid:12) ) = a + d + d cos θ (cid:12) , (12)with parameters a = a ( θ (cid:12) = ) and d , a dimensionless parameter tied to how exactly the albedochanges with cos θ (cid:12) . Equation (12) is extensively found in the literature, both for TOA and surfacealbedo studies as a function of the solar zenith angle; see Ref. [29] for a very detailed study which alsoreviews the literature. This functional form was first introduced in Ref. [27] for the case of infinitecanopies. It was then used in Ref. [28] for all types of land surfaces. As shown in Figure 3, one cancheck against the CERES ADMs that the same functional form can be used over ocean pixels (rms ofresiduals: 0.005); this is using the average wind speed model. a (1 + d ) / (1 + 2 d cos θ ⊙ )CERES TRMM clear-sky oceancos θ ⊙ a l b e d o . . . . . . . . . . . . . . . . . . Figure 3.
CERES TRMM ADMs: albedo in the clear-sky ocean case, fit with the functional form Eq. (12).
Knowing that the albedo, just like the flux, is expected to be only a function of the solar zenithangle at any single time and knowing the general functional form of this dependence, we can thentake benefit of the GEO temporal sampling and consider all the observations at different times inorder to obtain a more robust and consistent result at the level of one month. Following this methodwill provide a corrected monthly mean (level-3) GL-SEV product; it does not directly correct theinstantaneous level (level-2). Note that this assumes that the surface properties and the atmospherictransmission affecting the clear-sky top-of-atmosphere radiation do not significantly change over thatperiod of one month.In Figure 4 ( left ), we show an example of the diurnal-asymmetry artefact in a case of a rarelycloudy sample pixel taken in the Sahara (18.62° latitude, 25.52° longitude), for which we can thereforeget a very detailed view of the clear-sky-TOA-albedo temporal evolution throughout the day. This isseen from MSG-3 and we can clearly see that there are in fact two branches for similar values of thecosine of the solar zenith angle, the higher branch in this case corresponding to the morning, and theafternoon branch being the lower one. In this figure, each pair of colour and small symbols correspondsto the instantaneous clear-sky-TOA albedo for different days at the same timeslot. For each of these,we also overlay a summary representative (mean or median) value for that timeslot as a larger symbol of 18 . . . . . . . . . . θ ⊙ a l b e d o SEV3 . . . . . . . . . . θ ⊙ a l b e d o SEV1
Figure 4.
Diurnal-asymmetry artefact for the same location in the Sahara, seen from MSG-3 ( left ) andMSG-1 ( right ); see main text. For each timeslot ( i.e. each colour + symbol pair), the large symbolinside a diamond shape shows the median albedo versus the mean cos θ (cid:12) for that timeslot, while thecorresponding smaller symbols denote the instantaneous data used to compute those. inside a diamond shape—unless otherwise stated all such results shown here were obtained using themedian albedo versus the mean cosine of the solar zenith angle at the corresponding timeslot.In Figure 4 ( right ), we show the same case, but now seen from MSG-1. Notice how the twobranches are then actually swapped: the higher branch corresponding to the afternoon in this case,and the morning branch being the lower one. This complete contradiction at the qualitative levelhighlights the fact that this asymmetry cannot be of physical origin. The problem is rather related toimperfections in the ADMs used to convert radiances into flux, which, due to the fixed view of GEOobservations, are then turned into systematic errors. This well-known situation is not specific to thisgiven pixel, but truly an ubiquitous observation.Since the existence of these branches is not physical , one thing that we can do is to fit the albedoas a function of the solar zenith angle according to the functional form of Eq. (12), and then use that tocalculate the representative mean or median albedo, before projecting. These fits are done by non-linearleast-squares optimisations taking into account all the available information over the n t x timeslots: min a , d (cid:32) n tx ∑ t = (cid:20) a t − a + d + d µ t (cid:21) (cid:33) independently for each GEO pixel; (13)where for each timeslot t , µ t = cos θ (cid:12) , t and a t are respectively the instantaneous values for the cosineof the solar zenith angle and for the albedo derived from the GL-SEV products. We do stress that theobjective here is not to provide a predictive model of what the albedo might be, based on the scene;rather, this is merely an empirical fit, using only all the data for a given pixel over a complete month.In the case of our example, the results are shown in Figure 5. Figure 6 shows another sample pixel,this time in the Horn of Africa and with remaining unidentified clouds from the MSG-3 viewpoint,especially in the morning (latitude 7.45°, longitude 48.70°). Note that rather similar results are obtained While the branches themselves cannot be physical, one can notice the presence of overimposed instantaneous patterns.In contrast to the branches, those are actually consistent between the two satellites at corresponding times and likely ofphysical origin. They are in fact already present in SEVIRI narrowband radiances. See Appendix A. Further note that any actual observer-independent physical effect with a significant impact on the albedo should remainclearly visible even with swapped branches from MSG-3 to MSG-1. If there were dew [26] in the early morning for instance,the shape of the two morning branches would then be similarly skewed upwards and the apparent symmetry seen herewhen swapping the morning and afternoon branches would be lost. This is done using the NLopt library [30]. Having tested several of the available algorithms, we find that the derivative-free
NEWUOA [31] and gradient-based
SLSQP [32] algorithms are especially reliable, fast, and accurate for the problem at hand. of 18 when using the mean instead of the median albedo, but the fit is then necessarily more sensitive tothe presence of unidentified clouds, systematically leading to a larger a and therefore larger albedovalues for as a function of cos ( θ (cid:12) ) in those cases. Another interesting thing to notice is that, as thissecond example pixel is close to being at the same longitude as the MSG-1 satellite, seen from there,the branches are then not so spread but close to being indistinguishable from one another. . . . . . . . . . . θ ⊙ a l b e d o a f t e r n oo nb r a n c h m o r n i n g b r a n c h SEV3 . . . . . . . . . . θ ⊙ a l b e d o m o r n i n g b r a n c h a f t e r n oo nb r a n c h SEV1
Figure 5.
Same as Figure 4, but with the corresponding fit given in Eq. (12) now overlaid in both cases. . . . . . . . . . . θ ⊙ a l b e d o a f t e r n oo n b r a n c h m o r n i n g b r a n c h SEV3 . . . . . . . . . . θ ⊙ a l b e d o m o r n i n g b r a n c h a f t e r n oo n b r a n c h SEV1
Figure 6.
Same as Figure 5, but for another sample location (Horn of Africa).
In Figure 7, we show the root-mean square difference in clear-sky albedo retrieved from SEV3 andSEV1, where we both use all the masks that were introduced in Section 3.2 and the imposed angularconsistency discussed here before projecting onto the latitude–longitude grid. We request at leastthree timeslots with defined albedo in order to make the fit and otherwise mask the correspondingpixel. The corresponding summary statistics over all defined pixels are given in Table 2. In particular,we can see that the quadratic mean of the RMSD over the whole image is now as low as 0.008 in theoverlapping region, and that no large discrepancy remains. Within the RMSD, the standard deviationshown in Figure 8 ( left ) is much decreased as a result of the fit (compare to Figure 2 ( left )). Notice thatthe bias shown in Figure 8 ( right ), remains small, even though the average absolute bias is slightlylarger overall after applying the fit: over the northern part of the African continent and the Arabianpeninsula in particular we can see a slightly strengthened trend with a positive bias (light red colour) tothe west of 20.75°E (halfway between 0° and 41.5°E) and a negative bias to the east (light blue colour). One could also further include a minimum requested range in cos ( θ (cid:12) ) , especially for high latitudes in winter.0 of 18 l a t i t ud e ( ° ) longitude (°) − − − −
30 0 30 60 90 ≥ . . . . . a l b e d o r oo t - m e a n s q u a r e dd i ff e r e n ce Figure 7.
Same as Figure 1 ( d ), but now with imposed angular consistency. l a t i t ud e ( ° ) longitude (°) − −
30 0 30 60 90 − − ≥ . . . . . s t a nd a r dd e v i a t i o n l a t i t ud e ( ° ) longitude (°) − − − −
30 0 30 60 90 ≤ − . ≥ . − . . b i a s Figure 8.
Decomposition of Figure 7 in terms of standard deviation ( left ) and bias ( right ). Table 2.
Summary statistics; compare to Table 1. (cid:113) (cid:104)
RMSD (cid:105) (cid:113) (cid:104) σ (cid:105) (cid:104)| bias |(cid:105) with all the masks + empirical fits 0.008 0.004 0.005 Note that, alternatively, one could instead already proceed with a simple binning in cos θ (cid:12) . Anapproach of this type was actually adopted in a preliminary study with just two bins [33], and theresults obtained for the same month ( (cid:112) (cid:104) RMSD (cid:105) = 0.012, (cid:112) (cid:104) σ (cid:105) = (cid:104)| bias |(cid:105) = Using false colour rendering, Figure 9 shows the merged overhead albedo a in the different casespresented in Figure 1. The colours were chosen so that typical values over the ocean ( a ∼ a ∼ a ∼ ∼ a ∼ c ) close to India and the Gulf of Guinea in particular. For each pixel, we used the fittedparameters obtained when imposing the functional form discussed in the previous section. For anoverhead Sun, a can be simply calculated from a = a ( θ (cid:12) = ) = a + d + d . (14) Whenever the albedo is defined for both SEV3 and SEV1 for a given latitude–longitude pixel, an averageis taken. The original sharp discontinuities between satellite views are significantly decreased as themasks described in Sec. 3.2 (zenith-angles ( b ), sunglint ( c ), and aerosols ( d )) are being applied. ( a ) l a t i t ud e ( ° ) longitude (°) − − − −
30 0 30 60 90 ≤ . ≥ . . . . . . . . c l e a r - s ky T O A o v e r h e a d a l b e d o ( b ) l a t i t ud e ( ° ) longitude (°) − − − −
30 0 30 60 90 ≤ . ≥ . . . . . . . . c l e a r - s ky T O A o v e r h e a d a l b e d o ( c ) l a t i t ud e ( ° ) longitude (°) − − − −
30 0 30 60 90 ≤ . ≥ . . . . . . . . c l e a r - s ky T O A o v e r h e a d a l b e d o ( d ) l a t i t ud e ( ° ) longitude (°) − − − −
30 0 30 60 90 ≤ . ≥ . . . . . . . . c l e a r - s ky T O A o v e r h e a d a l b e d o Figure 9.
Overhead albedo, shown in the different masked cases of Figure 1 after imposing the angularconsistency given in Eq. (12) throughout the month: ( a , top left ) no mask; ( b , top right ) zenith-anglemasks; ( c , bottom left ) additional sunglint mask; ( d , bottom right ) additional aerosol mask (final result). Before applying the method described above to a full year of data, let us take a closer look at thespatial distribution of the observer-dependent diurnal-asymmetry artefact. It is indeed interesting tobe able to visualise it, not only one pixel at a time, but for all pixels at once, from the viewpoint ofeach satellite. We are going to fit the morning and afternoon branches separately and compare them. This will highlight where, according to each satellite, morning albedos appear larger than afternoonalbedos and vice versa . Though the shapes of the individual branches are not strictly given by Eq. (12),this fitting procedure will provide instructive results. Figure 10 shows at pixel-level the result of suchfits for both SEV3 and SEV1, for the rarely cloudy Sahara location discussed in Sec. 3.3. To keep asmany pixels as possible while making sure that each branch is well-sampled and not overly sensitiveto the curvature change close to the tip around the local noon, we find that a good trade-off is to onlykeep pixels with non-masked data spanning at least 12 different timeslots for each branch. A few aerosol-loaded pixels remain west of Africa in the dual-view region, even in Figure 9 ( d ). Correctly masked whenseen from MSG-3, they were not identified from MSG-1 (being close to the viewing-zenith limit), and thus reintroduced. For each pixel, we define the branches themselves with respect to the local noon, determined as the UTC timeslot with thelargest mean cos ( θ (cid:12) ) value (akin to Ref. [24]); the local midnight is calculated as local noon plus 12 hours, modulo 24 hours. Due to the tip, we can expect higher branches to be slightly steeper, and lower branches, flatter. While this can artificiallyincrease the difference between branches for each pixel, it will not affect the qualitative result ( i.e. which is higher or lower).2 of 18 . . . . . . . . . . θ ⊙ a l b e d o a f t e r n oo nb r a n c h m o r n i n g b r a n c h SEV3 . . . . . . . . . . θ ⊙ a l b e d o m o r n i n g b r a n c h a f t e r n oo nb r a n c h SEV1
Figure 10.
Same case as Figure 5, with each branch fitted to enable the visualisation shown in Figure 11.
SEV3 ≤ − . ≥ . − . . a : m o r n i n g–a f t e r n oo nd i ff e r e n ce SEV1 ≤ − . ≥ . − . . a : m o r n i n g–a f t e r n oo nd i ff e r e n ce Figure 11.
Visualisation of the diurnal asymmetry artefact. This compares for each pixel the a fitparameters (albedo corresponding to θ (cid:12) = ( a − a ) .The asymmetry, seen from MSG-3 ( left ) or MSG-1 ( right ), is obviously strongly observer dependent. Figure 11 then compares for each pixel the a parameter obtained when fitting the morningbranch (AM) to the one obtained for the afternoon branch (PM). The gaps in ocean pixels are largelydue to the sunglint and aerosol masks on the ocean, which prevent meeting our fit-quality requirements.As we focus on the common region seen from both satellites and centred on Africa, we see that thetwo satellites strongly disagree on which branch would be larger than the other virtually everywhere.From the point of view of MSG-3 ( left panel), compared to the satellite position (centre of the image),the albedo tends to be systematically larger during the morning than in the afternoon for pixels onthe right of the image ( i.e greener on the right), while the situation tends to be reversed to the leftof the image, where the afternoon albedo is then larger than the morning albedo ( i.e redder on theleft). In other words, the retrieved albedos for pixels to the east of the satellite tend to be brighter inthe morning, and those to the west, brighter in the afternoon, as seen also in Figure 12. Seen fromMSG-1 ( right panel), there seems to be a similar left/right trend with respect to the satellite position atthe centre of the image. This again highlights that this diurnal asymmetry is a viewing-angle issue.Note that the rare exceptions where both satellites agree appear to be mostly linked to overimposed cloud-identification issues, such as in Gabon or near the Horn of Africa in the morning (see alsoFigure 12). Without correcting this artefact, SEV3 would tell that most of Africa has a larger albedo in themorning, while SEV1 would tell that it is larger in the afternoon instead. SEV3 ≥ . . . . . a o b t a i n e d f o r t h a t b r a n c h SEV3 ≥ . . . . . a o b t a i n e d f o r t h a t b r a n c h SEV1 ≥ . . . . . a o b t a i n e d f o r t h a t b r a n c h SEV1 ≥ . . . . . a o b t a i n e d f o r t h a t b r a n c h Figure 12.
Morning and afternoon a -fit-parameter mapping, for both MSG-3 and MSG-1.
4. One year
Finally, we now simply apply the treatment discussed in Secs. 3.2 and 3.3 to each of the months ofthe year 2017. Again, this is done independently for MSG-3 and MSG-1. As before, we compare theresults and compute the summary statistics; these are given in Table 3. As expected, the results arecomparable to those given in Tables 1 and 2 and the consistency is systematically much improved. Forcompleteness, note that in the 2017 data which was available for us to compute those, there were sixentire days with missing GL-SEV data from MSG-1: from January 17th to January 22th (MSG-1 SEVIRIdecontamination), and on November 12th. The large afternoon effect in South America is similarly due to a cloud-detection issue. Note that trying to address it withmasks and cuts ultimately creates an imbalance between the branches (artificially giving more weight to one of them). Thisissue should preferably be dealt with within the GL-SEV data processing itself. As a corollary, this of course also means that, together with Ref. [29], we do not find that the morning albedo is systematicallylarger than the afternoon one when such a diurnal asymmetry is present— i.e. what one might have expected if an actualphenomenon such as dew was at play [26].4 of 18
Table 3.
Summary statistics; compare to Tables 1 and 2. masks only month (cid:113) (cid:104)
RMSD (cid:105) (cid:113) (cid:104) σ (cid:105) (cid:104)| bias |(cid:105) masks + empirical fits month (cid:113) (cid:104) RMSD (cid:105) (cid:113) (cid:104) σ (cid:105) (cid:104)| bias |(cid:105) Further averaging these monthly results for the quadratic mean of the RMSD, the quadratic meanof the standard deviation, and the mean absolute bias over all the months of 2017 in the masks-onlycase respectively gives 0.017, 0.015, and 0.005. When empirical fits are also used, one then respectivelyobtains 0.010, 0.006, and 0.005.
5. Conclusions
In this paper, we have had a closer look at the clear-sky top-of-atmosphere broadband shortwavealbedo retrieved from MSG geostationary satellites positioned at 0° and 41.5°E longitude, andcompared the results obtained over the very substantial overlapping region observed by both.This was first done for the month of November 2016. We could identify discrepancies which existat present in the GL-SEV products. Among the main sources of discrepancies, some in particular wereidentified to be due to the fluxes retrieved in the sunglint regions over ocean pixels close to the limbs,where the RMSD can locally well exceed values as large as 0.10; another important source of issuesbeing related to aerosol-loaded regions, where the RMSD can be as large as ∼ Author Contributions: conceptualisation, S.D. and A.P.; methodology, A.P.; software, A.P.; formal analysis,A.P.; validation, S.D. and N.C.; investigation, A.P., S.D. and N.C.; writing–original draft preparation, A.P.;writing–review and editing, N.C. and S.D; visualisation, A.P.
Funding:
This research was funded by the Solar-Terrestrial Centre of Excellence (STCE). The STCE is acollaboration between the Royal Meteorological Institute of Belgium (RMIB), the Royal Observatory of Belgium(ROB), and the Belgian Institute for Space Aeronomy (BISA).
Acknowledgments:
It is our pleasure to thank Christine Aebi for a careful reading of and various comments onthe manuscript.
Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of thestudy; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision topublish the results.
Abbreviations
The following abbreviations are used in this manuscript:ADM Angular Distribution ModelCERES Clouds and the Earth’s Radiant Energy SystemCM SAF Satellite Application Facility on Climate MonitoringERB Earth’s Radiation BudgetESA European Space AgencyEUMETSAT European Organisation for the Exploitation of Meteorological SatellitesGCOS Global Climate Observing SystemGEO Geostationary OrbitGERB Geostationary Earth Radiation BudgetGL-SEV SEVIRI ‘GERB-like’ synthetic productHDF Hierarchical Data FormatLEO Low Earth OrbitMMDC Monthly Mean Diurnal CycleMSG Meteosat Second GenerationNASA National Aeronautics and Space AdministrationRMSD (Albedo) Root-Mean Squared DifferenceSEVIRI Spinning Enhanced Visible and InfraRed ImagerSYN1deg Synoptic 1°TOA Top of AtmosphereTRMM Tropical Rainfall Measuring MissionUTC Coordinated Universal Time
Appendix A
Here, we show that the patterns visible in Figure 4 in the instantaneous albedo data at eachtimeslot are already present in the broadband GL-SEV radiances. To remove any influence from theADMs, Figure A1 shows this time the pseudo-albedo as a function of the day of the month for the10:00 UTC timeslot. Since this is independent of the ADMs, there is no angular correction applied atall for the surface type with respect to an ideal Lambertian surface; it is therefore expected that theexact pseudo-albedo values from MSG-3 or MSG-1 cannot be directly meaningfully compared. Whatmatters however is that a similar pattern/shape is clearly seen from each satellite over that timeslot.Such a pattern is actually even visible in the SEVIRI narrowband radiance data and the twoindependent satellites again appear to agree; these fluctuations are therefore very likely physical.Figure A2 shows the VIS0.8 and VIS0.6 channels, and VIS0.8 in particular is quite clearly reminiscentof the pattern in broadband GL-SEV synthetic data.Let us stress that the presence of such patterns is a general observation, not limited to this specificexample case (though the pattern shape itself of course changes for different pixels and periods oftime). They can sometimes surprisingly remain essentially unchanged at different times of the day, asis the case for the current Sahara example (seemingly same pattern repeated over different timeslots).
SEV1: broadband shortwave at 10:00SEV3: broadband shortwave at 10:00day of November 2016 π L / F i n c o m i n g SEV3 or SEV1 . . . Figure A1.
Consistent patterns in instantaneous data seen from MSG-3 (squares) and MSG-1 (dots).This shows the pseudo-albedo π L / F incoming , calculated directly from the broadband GL-SEV radiancesat 10:00 UTC, for every day of the month of 2016/11 in the Sahara sample case shown in Figure 4. Notethat in this case the pattern is inverted along the x -axis when shown as a function of the day of themonth instead of cos θ (cid:12) ( i.e. cos θ (cid:12) values are larger at the beginning of the month, smaller at the end). SEVIRI (MSG-1): VIS0.6 at 10:00SEVIRI (MSG-3): VIS0.6 at 10:00SEVIRI (MSG-1): VIS0.8 at 10:00SEVIRI (MSG-3): VIS0.8 at 10:00day of November 2016 π L / F i n c o m i n g SEVIRI (MSG-3 or MSG-1) . . . . . . . . . Figure A2.
Same as Figure A1, but this time using directly SEVIRI narrowband radiance data for thecorresponding pixels at 10:00 UTC, in the same 3 × References
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