Introduction
Clear-sky observations provide a valuable addition to satellite Earth Radiation Budget (ERB) datasets and have been provided for all dedicated ERB missions since the Earth Radiation Budget Experiment (ERBE; Barkstrom et al. 1989) in the mid-1980s. These data products aid climate model validation (e.g., Potter and Cess (2004)) by allowing separation of the representation of clear-sky processes from the more uncertain cloud parameterizations. Observational studies of the forcing that are associated with components of the climate system, such as clouds and aerosol, also rely on such products to provide the baseline under cloud- or aerosol-free conditions (e.g., Ramanathan et al. 1989; Loeb and Kato 2002).
The Geostationary Earth Radiation Budget (GERB) radiometer on the Meteosat-8 satellite is the first instrument to make broadband radiation budget measurements from a geostationary orbit (Harries et al. 2005). This unique viewpoint provides excellent temporal sampling, with measurements of both the longwave and shortwave components every 15 min. GERB fluxes will be available to the wider scientific community in three forms—the instantaneous 15-min products, monthly mean fluxes, and a monthly mean diurnal cycle product. The excellent sampling that is possible from GERB means that the all-sky products can be produced as straightforward averages, with no requirement for complex temporal and spatial interpolation algorithms.
However, in many regions the sampling of clear-sky scenes is limited if a GERB footprint (∼50 km × 50 km at nadir) is required to be totally clear. Because clouds often display strong coherent diurnal cycles (e.g., Minnis and Harrison 1984), clear-sky sampling in a given region may always be limited to a particular portion of the day. The available clear observations then will not capture the often-substantial variability of outgoing longwave radiation (OLR) and shortwave flux that is associated with the diurnal cycle of insolation and surface heating. Additional processing is therefore required to produce accurate clear-sky monthly mean and mean diurnal cycle products for GERB. Because the monthly mean diurnal cycle is one of the primary products for GERB, the processing scheme that is developed here must correctly represent the clear-sky diurnal cycle shape, and not simply produce the correct overall mean.
The limited sampling of clear-sky regions from GERB results from the relatively large footprint size. At a high enough spatial resolution, cloud fractional coverage is essentially binary; pixels are either entirely cloud covered or totally clear. As the size of the satellite footprint increases the distribution broadens, and the probability of finding either a totally clear or an overcast footprints falls. At the 50 km × 50 km scale of a GERB footprint, many regions are therefore partially cloud covered. By supplementing this relatively low spatial resolution dataset with higher-resolution flux estimates, information from the clear portions of these partially cloudy footprints can be extracted, extending the coverage of the instantaneous clear-sky flux dataset. This not only reduces the need for diurnal models to account for missing clear observations, but also provides better sampling of the day-to-day variability in a given region.
The correlation between moist atmospheric conditions and cloud cover means that the clear-sky flux that is estimated from satellites is a scale-dependent quantity. Essentially, the variety of weather conditions that is sampled increases with increasing spatial resolution. At a high enough spatial resolution, where all pixels are either clear or overcast, all possible clear-sky information is extracted. However, for a satellite with a larger footprint size, such as GERB, only data from large, clear regions that are associated with unusually dry conditions are included, resulting in a biased flux estimate (Allan and Ringer 2003). By including information from clear regions of partially cloudy GERB footprints, more of this information is retained in the final lower-resolution dataset, helping to reduce this bias. While this does not remove the difference in clear-sky sampling between satellite and model data (Cess and Potter 1987), this approach will help to minimize such differences.
For GERB, this approach is made possible by the synergy with the Spinning Enhanced Visible and Infrared Imager (SEVIRI; Schmetz et al. 2002). This multichannel imager is the primary instrument on Meteosat-8, and has a spatial resolution of 3 km × 3 km at nadir. By combining coregistered data from the two instruments on Meteosat-8, a higher spatial resolution flux dataset can be generated (see section 2 below), and is used to provide information on the clear-sky flux within partially cloudy GERB footprints.
Here we present the processing scheme that is proposed for the generation of monthly mean and monthly mean diurnal clear-sky flux products for GERB. The use of the higher spatial resolution flux dataset to improve the sampling of clear-sky fluxes for GERB is investigated, and the impact on the accuracy of the corresponding temporally averaged clear-sky flux products is assessed. The resulting improvement in sampling makes diurnal interpolation of longwave clear-sky fluxes possible on a daily basis. In section 5, these data are used to develop a modified version of the ERBE half-sine model for interpolation of clear-sky fluxes over land, and the accuracy of this approach is investigated. The suggested processing scheme is outlined in section 7.
Data
As part of the GERB data processing, estimates of the broadband radiance are obtained at a 3 × 3 SEVIRI pixel scale (∼10 km × 10 km, hereinafter referred to as the intermediate scale) via a multichannel regression (Clerbaux and Dewitte 1999). These are converted to flux using the Clouds and the Earth’s Radiant Energy System (CERES; Wielicki et al. 1996) angular dependency models (ADMs; Loeb et al. 2003) in the shortwave, and using theoretical limb-darkening values combined with a regression on the SEVIRI channels in the longwave (Clerbaux et al. 2003). An explicit scene identification is therefore required during daylight hours to select the appropriate ADM. Because these data are essentially an estimate of what GERB will observe, they are referred to as “GERB-like” fluxes, and are archived at the Royal Meteorological Institute of Belgium (RMIB).
Resolution-enhanced GERB data products will be available at this intermediate scale. To produce these, correction factors are derived through comparison of the GERB-like estimates (spatially averaged and convolved with the GERB point-spread function) with the actual observations from GERB. The correction factors are then interpolated back to the intermediate scale, providing a more accurate measure of the flux at this resolution, tied to the larger-scale GERB observations (Gonzalez et al. 2000). For a more complete description of the GERB data processing and products, see Harries et al. (2005).
For this study, clear regions are identified through the combination of two cloud flags based on SEVIRI data. This approach is similar to that employed for the second generation of radiation budget products from the CERES radiometer, where a multispectral cloud detection (Minnis et al. 1999) is performed using data from the Moderate Resolution Imaging Spectroradiometer (MODIS; for CERES on Terra and Aqua) or the Visible Infrared Scanner [(VIRS) for CERES on the Tropical Rainfall Measuring Mission (TRMM)], and provides better discrimination of clear scenes than can be achieved through thresholds on the broadband data alone.
Ipe et al. (2004) describe the cloud-detection algorithm that is used for daytime scene identification in the GERB processing system. This is a visible channel–only detection, based on an optical depth thresholding approach. Here, this is used in conjunction with the cloud mask that is derived operationally from the thermal channels on SEVIRI at the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) Meteorological Products Extraction Facility (MPEF) (Lutz 1999). Both flags produce a binary clear–cloudy classification at the SEVIRI pixel scale. For an intermediate-scale region to be defined as “clear,” all SEVIRI pixels within it are required to be clear according to both flags during daytime, while only the MPEF flag is used at night.
Using this approach, some residual cloud contamination was found in clear regions around the edges of detected clouds. Clear intermediate-scale regions neighboring cloudy ones are therefore redefined to be cloudy and are excluded from the analysis.
Ultimately a combined cloud detection using both visible and thermal channels on SEVIRI will be developed specifically for this purpose, in order to ensure a long-term consistent clear-sky flux dataset. The performance is, however, expected to be similar to the combined cloud mask used here.
Here we wish to investigate whether the resolution-enhanced GERB data products that are described above allow for improved clear-sky flux products at the nominal GERB spatial resolution to be produced. Because the validation of GERB data is ongoing, the uncorrected GERB-like fluxes, based entirely on SEVIRI data, are used here to determine the temporal and spatial sampling errors that are associated with the two different sampling regimes for the example month of April 2004. The results that are shown are for 1200 UTC; similar behavior is, however, observed at other times.
Sampling improvements
By augmenting the observations from totally clear GERB footprints with information from clear subregions of partially cloudy footprints using the intermediate-scale data, we significantly improve the temporal sampling. The increase in the number of days with clear-sky observations during April 2004 at 1200 UTC that is achieved by using this approach is shown in Fig. 1. The limited sampling when ∼50 km × 50 km GERB footprints are required to be to totally clear is immediately apparent, as is the dramatic improvement in sampling when higher resolution data is used.
To extract information from clear subregions, the average over the clear intermediate-scale pixels is assumed to be representative of the entire footprint. In the longwave, the observed clear fluxes can be averaged directly, while in the shortwave, fluxes are converted to albedos, averaged, and converted back to flux using the mean incident shortwave radiation (ISW) averaged over the entire GERB footprint. This is essentially the same approach as that used in gridding ERBE and CERES observations into 2.5° × 2.5° or 1.0° × 1.0° regions (Young et al. 1998), but allows consistent all-sky and clear-sky products to be defined for GERB without degrading the resolution of the well-sampled all-sky flux estimates. The disadvantage of this approach is that it can introduce spatial sampling errors, in particular, where the GERB footprint covers a mixture of scenes (e.g., is over a coastal region). To minimize this effect, an estimate of the GERB-scale clear-sky flux is only made if at least one intermediate-scale region of each scene type is clear, and a weighted average (weighted by the fractional coverage of each scene type) is used.
Error analysis
Whether the improved data coverage seen in Fig. 1 when higher-resolution data are included results in an increase in the accuracy of the corresponding monthly time step mean fluxes will depend on the balance between the spatial sampling errors introduced and the reduction in the temporal sampling errors obtained.
Temporal sampling errors
Figure 1 shows that in many areas no clear-sky observations can be made at 1200 UTC during a month if a GERB footprint is required to be totally clear. In many other areas, observations are possible on very few days in the month. As well as the obvious limitation in the coverage of the data, significant temporal sampling errors will be introduced if the average of the available data is used to represent the monthly time step mean flux in these latter regions.
Day-to-day variations in clear-sky longwave flux may be associated with changes in humidity and temperature, while changes in the clear-sky shortwave flux are primarily associated with changes in the surface albedo. Over land, this may be the result of changes in vegetation cover or surface moisture; over ocean, phytoplankton concentrations and wind effects are important. Variability in the cloud-free flux may also be the result of day-to-day changes in aerosol concentration or distribution. Systematic changes in the shortwave flux related to the changing insolation are avoided through the conversion to albedo; however, the dependence of albedo on the solar zenith angle will result in a small residual variation over the course of a month.
To estimate the magnitude of the temporal sampling error if an n-day average is used to approximate the monthly time step mean, a subsampling study was carried out for each scene type in regions where large amounts of clear-sky data are available. For the selected time step, footprints where clear observations (totally clear GERB footprint) were possible on 15 or more days during a month were identified. The 15 clear days are not required to be consecutive. A 15-day time period was chosen to provide a reasonable sample for most surface types. As is clear from Fig. 1, for periods longer than this very few regions can be included. Even with the choice of a 15-day period, sampling of some scenes (ocean and dark vegetation) is limited at a single time step in a given month. The magnitude of the temporal sampling error that was found varies by a few watts per squared meter with the time of day and season; however, the reduction in error as the sampling is improved shows the same form in all cases.
For each footprint, the “true” clear-sky flux estimate (averaged over all 15 days) was found. The error in using an n-day mean (for n = 1–14) to represent this was then estimated. Combinations of n days out of 15 were picked at random, and the differences between the n-day mean and the true value found. A distribution of these differences was built up and the standard deviation was calculated. This provides an estimate of the temporal sampling error for that footprint. This process was repeated for all footprints with 15 or more clear days. The mean of the error estimates from all footprints of a given scene type is taken as an estimate of the typical temporal sampling error for that scene type. Figure 2 illustrates this process, and examples of the resulting error estimates are shown in Fig. 3. In the shortwave, fluxes are converted to albedo and the “equivalent” flux is calculated by multiplication by the monthly mean ISW prior to analysis, to avoid the effects of changing insulation during the month.
To estimate the error in the monthly time-step mean if only n days of data are available, these results must be extrapolated to a 30 (31)-day period. Over bright desert, it is possible to find a reasonable sample of footprints with 25 or more clear days. The analysis described above was repeated for this sample, and the shape of the curves was compared. Based on this comparison, it was decided that the temporal sampling errors should be extrapolated as follows: for 5 or fewer days, the error in using n days to estimate the time step mean is assumed to be the same as the error that is found for the 15-day period for that n. For n greater than 5, the error is assumed to decrease linearly between the error that is observed for that scene for n equal to 5 and zero error when all days are sampled. This is illustrated in Fig. 4, which also shows the good agreement between the error estimate that is extrapolated in this manner from the 15-day data and the observations for footprints with 25 or more clear days.
While this extrapolation can only be tested for desert scenes where sufficient clear-sky data are available to directly estimate the sampling errors, the similarity in the shape of the error curves that are found for all surfaces (see Fig. 3) suggests that its use for other scenes is reasonable. For all surfaces, the error decreases almost linearly with n for n greater than 5, and increases more rapidly at low n.
This change in behavior for n greater than and less than 5 days can be understood in terms of the typical time scales of atmospheric variability. During the course of a month, around five different weather regimes might be expected to occur; hence, a minimum of five observations are required to sample all of these. The error in using an n-day mean to represent the true value would be expected to fall more steeply as the number of days is increased at low n, because more different regimes are included, and then to decay more slowly at larger n, where increasing the number of days observed simply provides more samples of each regime. Given that the 15 subsampled clear days can be distributed through the month, all of the synoptic weather patterns during the month are likely to be averaged into the 15-day mean. Hence, at low n the error in the 15-day mean is essentially the same as that in the monthly mean, while at larger n, the error becomes a function of the fraction of the total number of days sampled.
It should be noted that, while these arguments are directly applicable in the extratropics, their extension to tropical regions is less clear. As sampling of clear sky is extremely limited in the Tropics, the error estimates that are made are based primarily on sub- and extratropical regions. Variability of the clear-sky longwave flux is expected to be smaller in tropical regions than in the midlatitudes (Brindley and Harries 2003), so the temporal sampling errors that are found here may be an overestimate for tropical regions. Although the improvement in accuracy with increased sampling may therefore be smaller than that which is estimated here for these regions, it is still expected to be significant given the initial lack of clear-sky data (Fig. 1).
The temporal sampling error estimate for each scene type can be combined with the statistics for the number of clear days at each location to produce a map of the resulting error in the monthly time step mean clear-sky flux if footprints are required to be completely clear at the GERB scale. This is shown for the 1200 UTC time step in Fig. 5. Different spatial distributions of error will occur in different months because of seasonal changes in the occurrence of cloud, for example, resulting from the migration of the intertropical convergence zone. As would be expected, errors are largest in the longwave (where larger day-to-day variability is expected), and for regions where very few observations are possible during the month (cf. Fig. 1). Again, the large areas where no estimate of the mean flux is possible (shown in white) are apparent.
These errors may, in fact, underestimate the true error that is made in using n days of data to represent the monthly mean, because only days when clear conditions dominate over a large region are used to estimate the day-to-day variability in the clear-sky flux. Larger differences in flux (particularly in the longwave) than those that are found here may occur between predominately dry, clear days and those when cloudier weather, and, hence, only smaller clear regions, are present. The magnitude of this effect will depend on the dominant meteorology of the region. For example, the full range of variability is likely to be less well captured in convective regions than for dry desert areas.
Spatial sampling errors
The temporal sampling errors seen in Fig. 5 will be significantly reduced if estimates of the clear-sky flux that are based on clear subregions are used. However, spatial sampling errors will be introduced.
The magnitude of the spatial sampling errors can be estimated in a similar manner to the temporal errors. Each GERB footprint contains 25 intermediate-scale regions. For each footprint where all 25 intermediate-scale regions are flagged as being clear, the true average (over all 25 regions) was compared with that over p(1–24) regions that are selected at random. This was repeated for up to 1000 combinations of p regions out of 25,1 and the standard deviation of the differences calculated. A spatial sampling error estimate is made for all of the regions with a completely clear GERB footprint at a given time step during the month. In many areas, multiple clear days can be found. In this case, the mean standard deviation found for that footprint is taken as the spatial sampling error estimate. A separate error estimate is made for each footprint, reflecting the observed spatial variability at that location. For footprints where no completely clear observation can be made, the mean value for the appropriate scene type is used instead.
Because spatial errors will be largest for mixed-surface footprints, coast and mixed-land surfaces are considered as separate scene types in this analysis. For these mixed scenes, the error estimates that are made will be overestimates of the actual error that is incurred, because no requirement for all scene types within the footprint to be sampled was included in the subsampling study.
Overall error in monthly time step mean
To estimate the overall error in the monthly time step mean flux when estimates from clear subregions are included, the spatial and temporal sampling errors that are calculated above must be combined with the observed sampling pattern for a particular month.
Comparison of Figs. 5 and 6 where both have data indicates a significant reduction in the overall error when data from the clear intermediate-scale regions are included. Typically, the errors are reduced by a factor of 2; for example, the average error for ocean scenes where both approaches provide an estimate is reduced from 6.0 (3.6) to 2.6 (1.6) W m−2 for the longwave (shortwave).
As discussed in section 1, the inclusion of information from more humid, cloudier conditions through the use of the higher-resolution flux data is also expected to reduce the bias to warm, dry conditions in the longwave clear-sky flux. Averaged over the GERB field of view, a reduction of ∼1 W m−2 in the time step mean clear-sky longwave flux is found when higher-resolution data are included, but with significant regional variations.
Although the use of higher-resolution flux data provides a dramatic improvement in data coverage, sampling is still poor in some areas. This will lead to a poor estimate of the monthly mean flux, particularly in the longwave, and suggests the need for additional methods to fill the remaining missing clear-sky data.
Diurnal interpolation methods
In the ERBE and CERES missions, diurnal models are used to temporally interpolate the available observations. This is necessary because of the limited sampling of a given location that is possible from a low Earth orbit. For ERBE-like processing of ERBE and CERES data, empirical models are used for the interpolation of both all- and clear-sky data. For the second-generation CERES datasets geostationary data are used to provide an estimate of the shape of the diurnal variation in flux, improving the all-sky interpolation (Young et al. 1998).
For GERB, the good temporal sampling means that no interpolation is required for the all-sky data, and if the approach outlined above is followed, only limited filling is required even for clear skies. This larger volume of available data also provides greater flexibility in the choice of interpolation methods.
For clear-sky shortwave data, both CERES and ERBE use directional models of the variation of albedo with solar zenith angle to fill missing data on a daily basis. To be consistent with the use of CERES TRMM ADMs in the radiance-to-flux conversion for GERB, these directional models will be used for the interpolation of GERB shortwave data in a similar manner. Validation of this approach for GERB is ongoing and is not discussed further here; however, no significant difference from previous missions is anticipated.
Over the ocean, where the amplitude of the longwave diurnal cycle is small (Yang and Slingo 2001), ERBE and CERES use straightforward linear interpolation of the available clear-sky observations. As more data are available from GERB, we propose to fill data in on a daily basis with the average of the clear-sky observations. The example in Fig. 7 indicates that this is reasonable, and the accuracy is assessed further in section 6.
For longwave clear-sky fluxes over land, ERBE and CERES use a half-sine model peaking at local noon. In the ERBE and CERES ERBE-like datasets, sampling of clear scenes is so limited that in many regions insufficient data are available to allow for fitting of the half-sine model on individual days. Data are therefore averaged into hour boxes over the course of the month, and the interpolation is performed for the monthly mean diurnal cycle. For the second-generation CERES product, flux estimates from geostationary data, corrected to match with CERES at overpass times, are used to augment the CERES observations and the half-sine model is fitted to the combined dataset on a daily basis (Young et al. 1998).
The ERBE half-sine model is constrained to peak at local noon, making no allowance for the effects of thermal inertia. Although this has been shown to provide an accurate estimate of the diurnally averaged longwave flux (Brooks and Minnis 1984), this prescribed shape may distort the shape of the diurnal cycle and hence lead to errors in a monthly time-step mean clear-sky product.
To ensure that no spurious results are returned, the values of the fit parameters are constrained to remain within a reasonable range. To perform the fit, at least one observation in each of the preceding and subsequent nights, and at least one daytime observation more than 2 h away from sunrise or sunset, are also required.
Examples of the resulting diurnal interpolation are shown in Fig. 7. Clearly the original ERBE model provides a significantly worse fit to the data, peaking too early in the day, and missing the decay in flux at night. However, although the instantaneous errors in using the unmodified ERBE half-sine fit are large, errors at different times cancel, and the error in the diurnal mean flux (averaged over all time steps) is relatively small. In the case of the desert footprint shown in Fig. 7, the difference in the diurnally averaged flux for the two models is less than 1 W m−2, despite instantaneous differences of nearly 30 W m−2. The use of this model to obtain an overall monthly mean flux is therefore reasonable; however, it is not appropriate to produce monthly mean diurnal products, such as that planned for GERB.
Using the parameters that are returned from the fit to the modified half-sine model, it is possible to estimate the time of maximum OLR throughout the GERB field of view. On each day where sufficient clear observations are available for a fit to be made, the time of maximum OLR is calculated. No estimate of the time of maximum OLR is made if the amplitude of the diurnal cycle is less than 5 W m−2. Figure 8 shows the mean and standard deviation (over the course of the month) of the time of maximum OLR for each footprint. Maximum OLR typically occurs between three and six time steps (from 45 min to 1.5 h) after local noon. In convective regions the peak OLR occurs even later in the day, 2–3 h after local noon. However, estimates are more uncertain in this region because of the small amplitudes of diurnal variation (in many cases less than 5 W m−2, in which case no estimate of the time of maximum OLR is made), and because of the relatively poor sampling of clear conditions in this region.
Accuracy of the proposed LW interpolation
To test the accuracy of the proposed model, the error in filling the longwave clear-sky flux using the modified half-sine model is approximated as the residual between the fit and the observations at the time step of interest. Over ocean, the residual is simply the difference between an observation and the mean of the observations at other times on that day. Residuals are calculated for all days with observations at a given time step, and the mean and standard deviation are calculated. If the fit is unbiased, then the mean residual should be zero, while the standard deviation provides an estimate of the filling error. It should be noted that this is only an estimate of the error, because the diurnal model is only used to fill data where no sampling of the clear sky is possible, while residuals can only be calculated when an observation can be made.
To investigate if the residuals for the modified half-sine model are representative of the error in cases of sparse sampling, 10 footprints of each land surface type that were clear at all time steps were selected. For each of the selected footprints, 200 different minimally subsampled datasets (such that each has close to the minimum number of data points required to fit the diurnal model) were created and the modified half-sine fit was performed for each. The difference between the value predicted by the fit to the subsampled data and the actual observation can then be found in each case. Distributions of these differences show small biases (generally ∼1 W m−2 or less, with a maximum of ∼3 W m−2 for the “dark desert” around 1800 UTC) and standard deviations similar in magnitude to the residuals calculated previously. This agreement indicates that, even when minimal clear-sky data are available, the modified half-sine fit is generally well constrained and the residual to the fit provides a reliable error estimate.
We note that there may be additional variations in the shape of the clear-sky diurnal cycle on cloudy days that cannot be determined from clear-sky satellite observations and therefore are not included in the error that is estimated here. For example, extrapolation from clear morning conditions to estimate the clear-sky flux on a cloudy afternoon may result in an overestimate if the presence of the cloud subdues the afternoon temperature relative to that seen on clear days.
Using the modified half-sine fit over land [Eq. (4)] and the constant extrapolation over ocean, the mean residual is zero (to within ±2 W m−2, though slightly larger biases are seen in some land regions close to sunset) and the standard deviation is generally less than 5 W m−2 throughout the GERB field of view. As would be expected from Fig. 7, significant bias errors (nonzero mean residuals) are found over land if the original ERBE model is used.
Figure 9 shows the resulting error in the filled monthly time step mean longwave flux for April 2004 at 1200 UTC both with and without the use of information from clear subregions. Comparison between Figs. 5 and 6 shows a distinct reduction in the error when the diurnal model is used to fill unsampled clear scenes in both cases. It is also apparent that a more accurate flux estimate with more complete coverage is obtained when information from clear subregions of partially cloudy GERB footprints is used.
Table 1 summarizes the impact on the data coverage and the spatially averaged sampling error of each step in the proposed processing for the 1200 UTC time step. The values that are given here are specific to this month and time. Differences in clear-sky sampling through the day or seasonally lead to variations in data coverage and, hence, in the distributions and average values of the sampling errors. However, the reduction in error and improvement in data coverage when higher-resolution flux data and diurnal modeling are used is repeatable from month to month. For example, in June 2004, more clear-sky data are observed at the GERB footprint resolution at 1200 UTC (15% as compared with 10% for April), and the average errors are correspondingly lower (e.g., 2.6 as compared with 3.7 W m−2 for the longwave flux). However, as for the April data that are shown here, the use of higher-resolution flux data provides an approximately twofold reduction in this error, and diurnal interpolation leads to a further factor-of-3 reduction in error.
Summary of proposed processing
Figure 10 shows the proposed processing steps in the generation of clear-sky monthly mean and monthly time step mean flux products for GERB.
A SEVIRI-based cloud mask is used to identify totally clear GERB footprints where the clear-sky flux is immediately available. Higher-resolution 3 × 3 SEVIRI pixel intermediate-scale flux and cloud mask data are then used to estimate the clear-sky flux in partially cloudy GERB footprints using information from clear subregions. These data are combined to produce a reasonably well-sampled instantaneous clear-sky flux product. A diurnal model is then fitted to these data, allowing values of the clear-sky flux to be estimated for overcast GERB footprints on days with at least 6 (out of a possible 96) clear observations during the day.
The filled dataset is then averaged for each time step over all of the days to produce a monthly mean diurnal cycle, and over all of the times to determine the overall monthly mean flux. These two products will ultimately form part of the GERB data archive.
In the shortwave part of the spectrum, changing solar insulation during the month means that a further correction is required to account for the days where no clear observations are possible. This can either be achieved by correcting for the difference in incident flux or by filling data on the remaining days by some other method. Work is ongoing to determine the optimum interpolation scheme for shortwave fluxes for GERB, the outcome of which will be presented separately
Conclusions
The use of information from clear subregions to estimate the clear-sky flux in partially cloudy GERB footprints provides a dramatic improvement in the sampling of clear-sky observations over the course of a month. Analysis shows that the resulting reduction in temporal sampling errors more than compensates for the spatial sampling errors that are introduced.
However, even using this approach, clear-sky sampling remains limited in some regions, indicating the need for additional filling of unsampled clear scenes, particularly in the longwave. A modified, more flexible version of the ERBE half-sine model is found to provide a good fit to the available data, resulting in accurate estimates of the monthly time step mean, and, hence, the overall monthly mean longwave flux, from the filled clear-sky data.
The ERBE half-sine model is found to be a relatively poor fit to the clear-sky observations. The model is constrained to peak at local noon, while the typical time of maximum OLR is found to be 45 min to 1.5 h after local noon. Use of the ERBE model will therefore distort the shape of the clear-sky longwave diurnal cycle, making it unsuitable for producing a monthly mean diurnal cycle product.
Even when only a few clear-sky observations are available during a day, the proposed model provides a well-constrained fit to the diurnal cycle shape. This well-constrained behavior suggests that this model may also be suitable for use in the processing of second-generation merged CERES and geostationary data products, providing a more accurate representation of the diurnal cycle of clear-sky OLR than that of the ERBE half-sine model.
All fluxes used in this study are GERB-like estimates based solely on narrowband imager data from SEVIRI. The absolute accuracy of the flux estimates is therefore limited; however, comparisons with preliminary prerelease GERB data indicate that the temporal and spatial variability of the clear-sky fluxes is well represented in this data, confirming its value for the preparation of algorithms for the GERB project. The final products will use resolution-enhanced GERB data, corrected to match the broadband observations at the larger scale, providing good absolute accuracy in the final products.
Acknowledgments
Many thanks are given to the GERB project teams at Imperial College and the Royal Meteorological Institute of Belgium for help and suggestions, and specifically to Nicolas Clerbaux for providing the GERB-like data used. Thanks also are given to the anonymous reviewers for the helpful suggestions for improvement.
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Map of number of days in Apr 2004 for which a clear-sky flux estimate can be made at 1200 UTC, (left) if only totally clear footprints are included and (right) if information from clear subregions is used.
Citation: Journal of Applied Meteorology 44, 9; 10.1175/JAM2291.1
Method to estimate temporal sampling errors: n (4 in this example) days are picked at random, and the difference between the mean flux for these n days and the true mean is found. This is repeated for different combinations of n days to build up a distribution of differences. The standard deviation of this distribution provides an estimate of the temporal sampling error introduced by using n days to represent the true mean for that footprint. Because estimates can only be made for a limited number of footprints, a “typical” sampling error is found for each scene type as the mean of all available estimates.
Citation: Journal of Applied Meteorology 44, 9; 10.1175/JAM2291.1
Temporal sampling error estimates in the time step mean (left) longwave and (right) shortwave fluxes from (top) bright desert, (middle) bright vegetation, and (bottom) ocean scenes. Based on 1853, 340, and 67 scenes (for the respective surface type) in Apr 2004 at 1200 UTC. Behavior at other times and for other months is similar. Errors for all surfaces show similar variation with n, deviating from an approximately linear increase for n less than 5.
Citation: Journal of Applied Meteorology 44, 9; 10.1175/JAM2291.1
Temporal error estimates in the time step mean (left) longwave and (right) shortwave flux for bright desert scenes. The crosses show the original errors estimated for a 15-day period and the line shows the error predicted for a 25-day period based on these data using the procedure described in the text. The error estimates from directly subsampling data for footprints with 25 or more clear days are also shown as diamonds.
Citation: Journal of Applied Meteorology 44, 9; 10.1175/JAM2291.1
Map of errors in the 1200 UTC monthly time step mean (left) longwave and (right) shortwave fluxes resulting from limited temporal sampling. Regions where no clear observations are possible at 1200 UTC are left white.
Citation: Journal of Applied Meteorology 44, 9; 10.1175/JAM2291.1
Estimated error in the monthly time step mean flux for Apr 2004 at 1200 UTC resulting from temporal and spatial sampling errors for the (left) longwave and (right) shortwave fluxes. A clear-sky estimate is made if there are any clear subregions within a GERB footprint. Estimates from all available clear subregions are averaged. White regions indicate where no estimate of the mean flux can be made.
Citation: Journal of Applied Meteorology 44, 9; 10.1175/JAM2291.1
Examples of diurnal interpolation in the longwave: available clear-sky measurements (crosses), modified half-sine fit (solid line), and unmodified ERBE half-sine fit (dashed line). Fits are shown for (top left) desert, (top right) bright vegetation, (bottom left) dark vegetation, and (bottom right) ocean. The x axis is labeled as GERB time steps (15 min) from 0000 UTC.
Citation: Journal of Applied Meteorology 44, 9; 10.1175/JAM2291.1
(left) Mean and (right) standard deviation of the time of maximum OLR based on fits to daily clear-sky data in Apr 2004. The time is given as number of GERB time steps (15-min intervals) after local noon. No estimate of the time of maximum OLR is made if the amplitude of diurnal variation is less than 5 W m−2.
Citation: Journal of Applied Meteorology 44, 9; 10.1175/JAM2291.1
Rms error in filled monthly time step mean longwave fluxes for Apr 2004 at 1200 UTC (left) where information from clear subregions is included, and (right) where only totally clear GERB footprints are used. The error estimate includes spatial and temporal sampling errors and errors in fitting daily data. As before, regions where no estimate can be made are left white.
Citation: Journal of Applied Meteorology 44, 9; 10.1175/JAM2291.1
Flowchart of the proposed processing of GERB and SEVIRI data to produce monthly mean and monthly time step mean clear-sky flux products. Diamonds indicate input data, and ovals indicate products.
Citation: Journal of Applied Meteorology 44, 9; 10.1175/JAM2291.1
Summary of the improvement in data coverage and associated reduction in sampling error for the 1200 UTC time step. The error estimate is the average of the errors for all footprints where an estimate can be made in each case. The reduction in error as more data are included is therefore partially compensated for by the inclusion of errors for the less-well-sampled regions where no estimate was previously available. Figures in parentheses show the error that is averaged only over the region with data originally (i.e., 57% of the disk). The data coverage is also described in the following two ways: (a) the percentage of footprints within the GERB disk where an estimate of the time step mean flux can be made (i.e., percentage of footprints with at least one clear-sky estimate) and (b) the percentage of the total number of possible clear-sky observations for which some estimate is made. For this measure to be 100%, a clear-sky estimate would be required on all days at all footprints. This statistic clearly shows the benefit of using high-resolution data.
In some cases the maximum possible number of combination of p pixels in 25 is much larger than 1000; however, to run all of the possible combinations is exceedingly computationally expensive. To check that the 1000 combinations were adequate to sample the full variability, a test case was run with 10 000 samples. The resulting error estimate agreed very well with that when only 1000 samples were used; therefore, 1000 samples were deemed to be sufficient.
