Dissecting effects of orbital drift of polar-orbiting satellites onaccuracy and trends of cloud fractional cover climate data records

Abstract. Radiometers such as the AVHRR mounted aboard a series of the NOAA and MetOp polar-orbiting satellites provide 4-decade-long global climate data records (CDRs) of cloud fractional cover. Generation of such long datasets requires combining data from consecutive satellite platforms. A varying number of satellites operating simultaneously in the morning and afternoon orbits, together with the satellite orbital drift cause the uneven sampling of the cloudiness diurnal cycle along a course of CDR. This in turn leads to significant biases, spurious trends and inhomogeneities in the data records of climate variables featuring the distinct diurnal cycle (such as clouds). To quantify the uncertainty and magnitude of spurious trends in the AVHRR-based cloudiness CDRs, we sampled the 30-minute reference CM SAF Cloud Fractional Cover dataset derived from Meteosat First and Second Generation (COMET) at times of the NOAA and MetOp satellites overpasses. The sampled cloud fractional cover (CFC) time series were aggregated to monthly means and compared with the reference COMET dataset covering the Meteosat disc (up to 60 degrees N/S/W/E). For individual NOAA/MetOp satellites the errors in mean monthly CFC reach ± 10 % (bias) and ± 7 % per decade (spurious trends). For the combined data record consisting of several NOAA/MetOp satellites, the CFC bias is 3 % and the spurious trends are 1 % per decade. This study proves that before 2002 the AVHRR-derived CFC CDRs do not comply with the GCOS temporal stability requirement of 1 % CFC per decade just due to the satellite orbital drift effect. After this date the requirement is fulfilled due to the numerous NOAA/MetOp satellites operating simultaneously. Yet, the time series starting in 2003 is shorter than 30 years that voids climatological analyses. We expect that the error estimates provided in this study will allow for a correct interpretation of the AVHRR-based CFC CDRs and ultimately will contribute to the development of a novel satellite orbital drift correction methodology widely accepted by the AVHRR-based CDRs providers.


MetOp-A and MetOp-B, and the afternoon satellites: . The morning satellites cross the equator on the lit side in the morning as opposed to the afternoon satellites that do so in the afternoon. To derive the Level-2b products, the aggregation methodology proposed by Heidinger et al. (2014) is employed, that for each satellite selects only two instantaneous AVHRR observations per day (separately for ascending and descending satellite nodes) with the lowest 95 sensor viewing angles. In the ascending node, satellite orbits around the Earth northwards and in the descending node it orbits southwards on the lit side (Ignatov et al., 2004). The Level-2b composites are aggregated from the Level-2a instantaneous retrievals that correspond to a single satellite acquisition. Due to the orbit convergence, the number of acquisitions per satellite per day may vary from 2 at the equator to 14 near the poles.
In spite of some adjustments to the raw AVHRR GAC Level-1b imagery applied during a derivation of the CLARA-A2 Level-2b (e.g. a removal of duplicated and overlapping orbits) , it can be assumed that the selected AVHRR acquisitions times are representative for other CDRs such as Cloud_cci or PATMOS-x. Thus, the results of this study are valid for other AVHRR-based cloud climatologies. Ultimately, the Level-2b CLARA-A2 dataset was used to generate the Level-3 monthly mean cloud fraction composites with and without a distinction between the satellite nodes.
In addition to the AVHRR acquisition times, we used CFC trends observed in the CLARA-A2 CDR for a sake of comparison 105 with the spurious trends estimated in our study.

COMET CDR derived from Meteosat geostationary satellites
The CM SAF Cloud Fractional Cover dataset from Meteosat First and Second Generation (COMET, Stöckli et al., 2017bStöckli et al., , 2019 was derived from the MVIRI and SEVIRI imagers aboard a series of Meteosat geostationary satellites. The COMET cloud fraction climatology covers a period 1991-2015 and features the high temporal (30-minute) and low spatial (0.05×0.05 110 deg) resolutions. It is derived by means of the novel naïve Bayesian classifier (Stöckli et al., 2017a) that features a high accuracy with the overall mean bias below 1% between the COMET CFC and referential SYNOP measurements . The CFC trends revealed by COMET are consistent with the trends observed in the top-of-atmosphere reflected radiation and surface solar radiation satellite products (Pfeifroth et al., 2018).
Within the study, the cloud fraction diurnal cycles were extracted from the COMET Monthly Mean Diurnal Cycle (MMDC) 115 product. The COMET MMDC has been already validated against the SYNOP cloud observations, and it was proven to be suitable for the analysis of climatic trends and variability in the cloudiness diurnal cycle (Bojanowski and Musiał, 2018). Such accurate dataset was used for the generation of the AVHRR-like synthetic dataset (i.e. out of the COMET dataset), which was further used to quantify the magnitude of the spurious temporal trends.

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3.1 Deriving reference and artificial AVHRR-like CFC time series from the COMET MMDC dataset To estimate errors and spurious trends in the AVHRR-based CFC CDR induced by the satellite orbital drift and variable number of AVHRR observations a day, the artificial time series was derived from the geostationary COMET CFC dataset sampled at the AVHRR observation times (i.e. COMET CFC "as seen" by the AVHRR sensors). Further, the artificial AVHRR-like CFC was compared with the COMET CFC to estimate errors and spurious trends in the AVHRR-based dataset. The conceptual 125 scheme of the applied methodology is presented in Fig. 2.
To generate AVHRR-like CFC time series, first the COMET CFC MMDC was aggregated to a 0.75×0.75 degree grid by means of the first-order conservative remapping (Jones, 1999;CDO 2018). Then for every grid and month we computed a mean multi-annual CFC diurnal cycle to which we fitted the cubic smoothing spline model (Chambers and Hastie, 1992  Secondly, the objective of the study is to analyse spurious trends in the AVHRR CFC CDRs caused by the orbital drift and sampling issues and not to analyse climatic trends in the CFC diurnal cycles revealed by the COMET dataset. For this please 140 refer to Bojanowski and Musiał (2018).

Assessing errors and spurious trends of the artificial AVHRR-like CFC dataset
To assess the reliability of the artificial AVHRR-like monthly mean CFC dataset, the mean bias error (MBE) as well as the biascorrected root mean square error (bcRMSE) were computed (see Appendix A for details) between this dataset and the referential mean monthly COMET CFC. The errors were estimated for each 0.75×0.75 deg grid, separately for each NOAA/MetOp 145 satellite, with and without the distinction between satellite nodes (ascending, descending). It has to be noted that the estimated error for a single satellite has two components. The first error component is related to how accurately one (for a single node) 6 https://doi.org/10.5194/amt-2020-91 Preprint. Discussion started: 23 March 2020 c Author(s) 2020. CC BY 4.0 License. or two (for both nodes) discrete AVHRR-based CFC estimates per day represent a daily CFC mean value. Without the orbital drift and climatic change of the CFC diurnal cycle, this error should be stable over the course of a satellite operating time. The second error component is related to the change of the AVHRR acquisition time induced by the orbital drift and its magnitude 150 varies with the increasing satellite drift. The magnitude of the error depends on the phase and amplitude of the CFC diurnal cycle. If the amplitude is large, the small shift in time of satellite observation will cause an error. Yet, if the amplitude is very small, for instance in a region of constant overcast, even a large change in the observation time does not introduce any error.
To assess the magnitude of spurious temporal trends in the Level-3 AVHRR CFC monthly means, the trend in MBE was calculated between the reference and artificial AVHRR-like datasets. For this analysis, we used monotonic trends derived using 155 the Theil-Sen estimates (Theil, 1950), and their significance was estimated with the Mann-Kendall test (Kendall, 1938;Mann, 1945). For multiple comparisons of the statistical significance of each grid, we applied the adjustment of the p-value using the method of Benjamini and Hochberg (1995). As for the performance assessment, the trends were calculated for individual satellites and nodes, as well as for the three aforementioned synthetic CDRs (AVHRR.AM, AVHRR.PM, AVHRR.AM+PM).
We have excluded from the analysis the MetOp platforms as they do not feature the orbital drift ( Fig. 1). Finally, we juxtaposed 160 the theoretical spurious trends in the AVHRR-like Level-3 datasets with the temporal trends derived from the CLARA-A2 CDR.

Impact of discrete diurnal cycle sampling on the CFC time series
The impact of under-sampling of the cloudiness diurnal cycle on the CFC CDRs is related to representativeness of one (for 165 a single node) or two (for both nodes) observations in respect to the mean daily CFC. The largest positive bias up to 10% is revealed for the nigh-time (2 AM) observations of the afternoon satellites' descending node, whereas the negative bias for afternoon satellites' ascending node (2 PM) and morning satellites' descending node (7 AM) (Fig. 3). The magnitude of bias is similar for all afternoon satellites, because their initial (before-drifting) time of acquisition was similar. Among the morning satellites, the bias for NOAA-12 and NOAA-15 differs as their initial observation time was 2-3 hours earlier than for the rest 170 of the morning satellites. For the ascending and descending nodes combined, the bias is lower than for the single nodes, which shows that two observations (approx. 12h apart) can substantially better represent the daily CFC than a single observation. Yet, this is partly due to cancelling out the larger negative and positive biases of the individual nodes.
The spatial distribution of the error is similar for all afternoon and morning satellites, and related to CFC diurnal cycle regimes (Fig. 4). The ascending node of afternoon satellites related to daytime conditions generally reveals a negative bias over the ocean, and a positive one over land (Fig. 5). For the descending node, the spatial pattern is reversed. In both cases, the largest bias (up to ±10%) can be observed over the Southeast and North-east Atlantic. However, in the tropics the bias has the same sign as over the ocean, which is related to a similar phase of the CFC diurnal cycle. For the combined nodes, the bias is largely reduced (up to ±2%) and follows the land-ocean pattern of the afternoon satellites.
node asc desc asc_desc Figure 3. Distribution of the mean CFC bias error caused by the discrete sampling of the CFC diurnal cycle presented for each NOAA satellite and each node (asc-ascending, desc-descending, asc_desc-ascending and descending combined). The lower and upper hinges correspond to the 25th and 75th percentiles, while whiskers extend from the hinge to the largest and lowest values within 1.5 times the inter-quartile range.
The 2-3 hour difference in the image acquisition time between NOAA-12 & 15 and the other morning satellites leads to 180 a noticeably different spatial distribution of the error (Fig. 6). The NOAA-12 and NOAA-15 follow the spatial pattern of the afternoon satellites, but with the lower bias values. The NOAA-17 and MetOp platforms show different biases over land (e.g. between Europe and Africa). Moreover, for these satellites a generally greater negative bias for the descending node leads to larger biases for combined ascending and descending nodes.
The bias-corrected root mean square error computed between the AVHRR-like CFC and referential COMET CFC can reach 185 up to 9% due to the under-sampling of the CFC diurnal cycle. The differences between the morning and afternoon satellites are not as evident as for the bias (Fig. 7). For the combined nodes, the average bcRMSE does not exceed 2.5% with the maximum below 4%.
The time of satellite observation does not significantly influence the bcRMSE variability between the sensors. The error for both morning and afternoon satellites and single satellite node reveals similar spatial distribution with the highest bcRMSE over 190 the Atlantic and over Africa (Fig. 8, 9), where the CFC diurnal cycle has the largest diurnal amplitude (Fig. 4). Nevertheless, these spatial patterns are almost not apparent for the combined satellite nodes (two available observations per day) and the overall bcRMSE is lower. This proves that the CFC CDRs without the distinction between ascending and descending satellite nodes provide significantly more accurate mean monthly estimates.

Impact of satellite orbital drift on spurious CFC temporal trends for individual platforms 195
The satellite orbital drift induces spurious temporal trends reaching up to ±7% CFC per decade in the AVHRR-like CDRs  magnitude of these trends is observed for the NOAA-7 and NOAA-9 satellites due to their quickest orbital drift. Reversely, CFC time series derived from satellites with the limited orbital drift (e.g. NOAA-19) feature low values of spurious CFC trends.

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The MetOp platforms were excluded from the analysis as they do not feature the satellite drift. Figure 11 shows the spatial distribution of the statistically significant spurious temporal trends for the afternoon satellites.
It has to be noted that statistical significance of these trends is also affected by the length of the time series of each satellite.
For the ascending node the spurious trends are positive over ocean and negative over land. However, for the Southeast Atlantic the trend is negative, which is related to a different CFC diurnal regime in this area (Fig. 4). The spurious trends for NOAA-205 14 and NOAA-16 do not reveal this pattern over the ocean. These two satellites drifted more than other afternoon satellites, and their shift in a local time of observation passed a local extreme in the diurnal CFC cycle, which in turn has flattened the temporal trend. The spurious trends for the ascending node dominate the trends observed for the combined nodes, which reveal statistically significant trends with a clear spatial pattern: positive values over ocean (< 6%), and negative over land (> -3%).
For the morning satellites (Fig. 12)   observed for the combined nodes. The NOAA-15 satellite due to its long operational period (almost 20 years) reached the maximal drift, after which it started to return to the initial equatorial local crossing time (Fig. 1). This in turn lowers the overall value of the spurious trend to ±1%.

and MetOps satellite imagery
Cloud cover climate data records derived from a combination of NOAA and MetOp satellites feature: spurious trends of ±1% CFC per decade, up to ±3% MBE and up to 4% bcRMSE, just due to the under-sampling of the CFC diurnal cycle and the orbital drift. These errors are further combined with the cloud retrieval errors. For the CDRs derived from the morning NOAA satellites, the bias reveals a distinct spatial pattern with positive values over ocean and negative over land (Fig. 13). The opposite 220 spatial pattern is apparent for the afternoon satellites. The CDR derived from the combined morning and afternoon satellites reveals lower MBE and bcRMSE values than the CDR derived from the morning/afternoon satellites separately.
The datasets show similar bcRMSE spatial patterns for the morning and afternoon satellites, however with larger errors in the latter (Fig. 14). The bcRMSE does not exceed 2% in most areas apart from East and South Africa. As for the MBE, the dataset from combined morning and afternoon satellites reveals the highest performance.

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Significant spurious trends up to 1%/dec are observed for the AVHRR-like CDR derived from all morning satellites (Fig. 15 node asc desc asc_desc Figure 7. Distribution of the CFC bias-corrected root mean square error caused by the discrete sampling of CFC diurnal cycle presented for each NOAA satellite and each node (asc-ascending, desc-descending, asc_desc-ascending and descending combined). The lower and upper hinges correspond to the 25th and 75th percentiles, while whiskers extend from the hinge to the largest and lowest values within 1.5 times the inter-quartile range.  Figure 9. Bias-corrected root mean square error of CFC caused by discrete sampling of CFC diurnal cycle, presented for each morning (AM) NOAA satellite and each node (asc-ascending, desc-descending, asc.desc-ascending and descending combined).

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This study presents the quantitative assessment of errors and spurious temporal trends in AVHRR-based CDRs induced by under-sampling of the CFC diurnal cycle and NOAA satellite orbital drift. For the individual satellites and specific locations, these CFC errors may reach up to ±10% (MBE), 9% (bcRMSE), and ±7%/dec (spurious trends). The datasets derived from a single satellite are not commonly used in the climate analyses, and usually they feature larger errors than the CDRs derived by combining several platforms. In this respect, the absolute CFC errors for the multi-AVHRR CDR can reach up to ±3% (MBE), 245 4% (bcRMSE) and ±1%/dec (spurious trends). The distinction between satellite platforms discussed in this study allows for assessment of the CFC errors for a limited period within the AVHRR CDR. This in turn provides a valuable information while selecting NOAA/MetOp satellites and time ranges to be included in a CDR. Furthermore, the distinction between the satellite nodes (ascending/descending) allows for performance assessment separately for the night-time and daytime conditions.
The CFC errors discussed here originate solely from the under-sampling of cloud cover diurnal cycle combined with the 250 satellite orbital drift effect, and as such are not related to the accuracy of the cloud discrimination (masking) on the AVHRR imagery. To assess the accuracy of a cloud mask, the instantaneous satellite observations originating from the Level-2 product are closely collocated with a reference observation to avoid bias caused by the time shift (Bojanowski et al., 2014). Nevertheless, while aggregating the instantaneous measurements to daily or monthly means, the problem of the under-sampling of ( P M ) Spurious trend in CFC (%/dec) node asc desc asc_desc Figure 10. Distribution of spurious trends in CFC caused by discrete sampling of CFC diurnal cycle presented for each NOAA satellite and each node (asc-ascending, desc-descending, asc_desc-ascending and descending combined). Trends for MetOp platforms are not presented due to lack of orbital drift. The lower and upper hinges correspond to the 25th and 75th percentiles, while whiskers extend from the hinge to the largest and lowest values within 1.5 times the inter-quartile range.   1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 (b) Figure 17. Time series of MBE and bcRMSE caused by orbital drift and discrete sampling of the CFC diurnal cycle presented for AVHRRlike CDR derived from combined morning and afternoon satellites.

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trends in CDR, we do not recommend a numerical subtraction of spurious from observed trends as a method for the AVHRRbased cloud CDR correction. We refer to the evidence of COMET's good performance and stability, but in our analysis we neglected potential climatological changes in the CFC diurnal cycles, as well as we used averaged monthly mean diurnal cycles. Notwithstanding, we expect that the results presented will allow for a realistic interpretation of the cloud CDRs derived 285 from the AVHRR sensors.

Conclusions
The Cloud Fractional Cover Climate Data Records (CFC CDRs) generated from the measurements of the AVHRR sensor mounted aboard a series of the NOAA and MetOp polar-orbiting satellites, are subject to errors originating from the undersampling of cloudiness diurnal cycle as well from the satellite orbital drift. These errors may lead to spurious temporal trends 290 revealed during climatological analyses. This study provide a unique quantitative assessment of the errors and spurious trends in the AVHRR-based CFC CDRs. For individual NOAA satellites the errors reach up to 10% of MBE and 7% per decade of spurious trends. For the entire data record encompassing all NOAA/MetOp satellites the values are 3% and 1%, respectively.
The spurious temporal trend of the AVHRR-like CFC CDR averaged over the Meteosat disc (-0.34 % per decade) complies with the GCOS temporal stability requirement of a maximum 1% per decade. Yet, there are regions where the spurious trends 295 exceed 1% per decade and consequently renders the AVHRR-based CFC CDRs not applicable to climatic analyses. The GCOS