3.1.1 SSM/I

A combined usage of different data sources is necessary for the SSM/I instruments, as they cover different time periods and have different coverage due to missing files, checksum errors, and corrupt data records. An analysis of SSM/I data from different sources (Ritchie et al., 1998), including NESDIS TDR and RSS data, showed no systematic differences between these data sets. Moreover, our own analysis showed that apart from the geolocation, which is different in the RSS files (Wentz, 1991), the same information is available in all data files.

To merge the scans from all different sources, unique MD5 hash values are computed from the calibration data. The MD5 algorithm is a cryptographic hash function that takes a block of data and returns a unique fixed size hash value that can be used as a fingerprint to identify a specific data block (Rivest, 1992). This MD5 hash value is used in the processing to find identical scan lines and to correctly merge all available data records to compile the FCDR files. During the first processing step antenna temperatures are reverted to Earth counts using the calibration coefficients provided in the data files. This must be done because the preprocessed TDR input data can contain erroneous calibration slopes and offsets caused by an averaging of the calibration data without quality control tests (Ritchie et al., 1998).

In the following processing step the spacecraft position and the geolocation are computed, and the water–land surface type is assigned to each field of view (FOV). A first raw data calibration is carried out to convert from Earth counts to antenna temperatures (TAs). From these intermediate level 1a data records, yearly monitoring files are compiled where the calibration and geolocation are sampled at fixed orbit angle positions. These files are analysed to identify periods where moonlight (cold view intrusion) or sunlight (hot view intrusion) affect the calibration in order to compile correction tables. They are then used to correct the cold and hot calibration counts. The final calibration coefficients are derived and the antenna temperatures are computed. An along-scan correction is applied to the TAs to account for a non-uniformity of the measured antenna temperatures along a scan line. The corrected antenna temperatures are then converted to brightness temperatures and the inter-sensor calibration offsets are computed.

Now the sea ice concentration is derived from this intermediate level 1b data record for each FOV, and daily gridded ice masks are compiled (see Sect. 3.4). These maps are then used to assign the sea ice and sea ice margin surface types. The Earth incidence angle normalization offsets are computed for water-type FOVs and the high-resolution channels are averaged to provide additional information matching the antenna pattern at the lower resolution.

3.1.2 SSMIS

The SSMIS BASE data record files from CSU have been compiled from the original TDR and were reorganized into single orbit granules with duplicate scans mostly removed. Spacecraft position and velocity have been added by CSU based on North American Aerospace Defense Command (NORAD) orbital data.

Following the procedures developed for SSM/I, remaining duplicate scan lines in the SSMIS CSU BASE and the original TDR files are first screened and filtered using MD5 hash values of the calibration data. The SSMIS NORAD orbital data sets are not freely available. Therefore the spacecraft position in the CSU BASE data files is used to fit daily orbital data sets, which can then be used in the FOV geolocation procedure. The following processing steps are similar to the SSM/I processing. As an additional step for SSMIS, an emissive reflector correction is applied for SSMIS_F16 and SSMIS_F17.

3.1.3 SMMR

The SMMR data record processing can not be performed starting from the actual observed Earth counts but has to start from the level 1B Pathfinder data record. Therefore the processing steps differ from SSMI(S) above.

A detailed description of the level 1B processing steps is given in Njoku et al. (1998) and summarized here for reference. The level 1B Pathfinder data record is a collection of T_B and instrument metadata, archived as single orbit granules in Hierarchical Data Format (HDF). Input to the level 1B processor is level 1A antenna temperature tapes (TAT). The level 1B data processing was performed in daily segments, and all algorithms used for running averages were initialized at the beginning of the day and also after data gaps longer than 1 min. After reading and decoding, the radiometric calibration was carried out for each scan line. This was followed by spillover corrections, an absolute calibration correction, as well as corrections for long-term and short-term drifts. The resulting corrected antenna temperatures were then interpolated along and across scan lines to co-locate all observations to the 37 GHz FOV locations. Finally the polarization mixing was corrected and a quality status flag was generated for each scan to indicate potential quality losses. This quality flag is also copied to the final FCDR data record for reference.

The CM SAF FCDR processing starts with a further filtering of this level 1B data record. Unique MD5 hash values are computed from the calibration data. All orbit granules for 1 d are filtered using the MD5 hash values. The data record is also screened for erroneous geolocation, and valid scans are merged into daily SMMR FCDR NetCDF files. The scan times are only available rounded to full seconds. The original time fraction is needed for a correct navigation of the spacecraft position and is therefore estimated with a linear regression fit using all scans from 1 d. The water–land surface type is assigned to each FOV using the same land–sea mask as for the SSMI(S) data records.

The radiometer noise-equivalent temperatures are estimated from recomputed calibration coefficients for each channel. An along-scan correction is applied to the T_B values at 37 GHz to account for a non-uniformity of the measured T_B values along the scan line. Finally the inter-calibration offsets are computed, and quality flags and global metadata are assigned.

3.2.1 Geolocation for SSM/I and SSMIS

The quality of the SSM/I geolocation has been examined by Poe and Conway (1990) and Colton and Poe (1999). The operational requirement of geolocating SSM/I data is defined by half the 3 dB beam diameter of the high-resolution 85 GHz channels, which translates to a location error requirement of about 7 km. The studies showed that the predicted spacecraft ephemeris in the data records caused an error of up to 15 km. Since July 1989 the operational processing has changed and the new ephemeris error is typically less than 2–3 km. To reduce the SSM/I FOV geolocation error below the requirement, a fixed set of spacecraft attitude corrections was determined (Colton and Poe, 1999). These attitude corrections were defined for each instrument. Colton and Poe (1999) finally conclude that the root-mean-square value of the geolocation error of the SSM/I FOV is less than 4 km.

The quality of the SSMIS geolocation has been examined by Poe et al. (2008). This study showed geolocation errors in excess of 20–30 km. An automated analysis methodology was developed during the F16 cal/val (calibration and validation) period. As the main sources of the errors, angular misalignments and timing problems have been identified. A set of fixed attitude corrections are found during the cal/val period for each SSMIS to reduce the geolocation error to less than 4–5 km.

In order to provide a homogeneous and consistent geolocation in the CM SAF FCDR, the attitude corrections must be applied consistently throughout the entire time period. The geolocation data are therefore recalculated by CM SAF during the reprocessing using the latest available set of corrections. The spacecraft position is predicted with the Simplified General Perturbations model (SGP4) (Hoots and Roehrich, 1988). This model uses NORAD ephemeris data sets to predict position and velocity of Earth-orbiting objects. These orbital data are distributed in a two-line element (TLE) data format. The SSM/I element sets for the time period up to January 2000 are freely available and used until December 1999. SSMIS element sets are not freely available. In order to use the SGP4 model for the entire time period, ephemeris data from the raw data records have been used to find the orbit elements in a minimization fitting procedure for all SSM/I data files after 2000. For SSMIS, the spacecraft position, added in the BASE data files, is used to fit the orbit elements.

These fitted ephemeris data are determined for each day and then smoothed using a moving averaging window of ±7 d. A comparable method is used by Wentz (1991) to fit a simple orbit model. The accuracy is usually better than 1 km compared to original data and compared to time periods with available NORAD element sets. The spacecraft position is predicted for all scan start times and archived in the FCDR data files.

During the geolocation procedure the spacecraft position is then linearly interpolated to each pixel time in an Earth-centred inertial (ECI) coordinate frame by applying a rotation matrix. The rotation axis is found as the vector cross product between two consecutive spacecraft positions. The magnitude of the position vector is linearly interpolated. From this spacecraft position at pixel time, the location of the FOV on the Earth surface is found as the intersection of the antenna beam with the Earth surface following the geolocation procedure described in Hollinger et al. (1989) and Wentz (1991). While comparing the new and the original geolocation, it was found that both usually agree within ±2 km. The deviations can be attributed to simplifications in the operational processor. The original raw data records (RDRs) also show a gradual degradation within a few days followed by sudden jumps when the ephemeris data set was updated in the operational processing.

While the SSM/I had only surface channels, the geolocation procedure for SSMIS must account for three different groups of feedhorns with different reference heights of the geodetic latitude and longitude. The reference heights are selected similar to the operational algorithm:

• imaging channels (SSM/I like, 19–91 GHz) to Earth's surface,

• lower air sounding channels (50–59, 150–183 GHz) to 11 km height,

• upper air sounding channels (60–63 GHz) to 60 km height.

New spacecraft attitude corrections for pitch and roll for the SSM/I platforms are found using a method similar to the approach of Berg et al. (2013), where the roll angle is estimated from the slope of the mean T_B values along the scan line. Changes in spacecraft roll and pitch have a distinct effect on the vertically polarized T_B values: A change in pitch modifies the curvature along the scan, and a change in roll results in a gradient along the scan. The method from Berg et al. (2013) has been modified to fit both angle offsets, roll and pitch, from the T_B variation along the scan. Instead of using only vertically polarized channels for the minimization procedure as in the original technique (Berg et al., 2013), polarization differences are employed as the horizontally polarized channels are much less affected. This minimizes the influence of cold intrusions at the scan edge. All FOV positions, weighted with the position-dependent variability, can be used to find mean values for pitch and roll offsets. After applying the correction, the T_B variation along the scan appears very similar for all instruments. Corrections for yaw and elevation offsets for the SSM/I instruments are found empirically from a coastline analysis using the high-resolution horizontal 85 GHz channel. The implemented attitude corrections for the SSMIS platforms are taken from the operational configuration (Kummerow et al., 2013) without modifications.

Another geolocation problem that was identified by CM SAF in the raw data records of the SSM/I and SSMIS instruments is an inconsistent handling of leap seconds. During the time period from 1987 to 2015 13 leap seconds are officially inserted to account for variations in the Earth's rotation in order to keep the Coordinated Universal Time close to the mean solar time (Bulletin C, https://www.iers.org/IERS/EN/Publications/Bulletins/bulletins.html, last access: 20 January 2020, IERS, 2020). It can take up to 7 d before a leap second is introduced to the data record. The time difference itself is not problematic if the observation time and the ephemeris time in the TLE sets are updated synchronously. However, a geolocation error of about 7 km was found in the original geolocation data if this is not the case. This has been corrected in the CM SAF FCDR, and the observation times are changed in a way that all leap seconds are introduced at the correct position.

3.2.2 Geolocation for SMMR

The SMMR was observing the Earth surface with a reflector that scanned by oscillating about the vertical axis between azimuth angles of ±25^∘. Separate radiometers were used for vertical and horizontal polarization only at 37 GHz. The channels at other frequencies used a single radiometer time-shared between vertical and horizontal polarization. On the first half of each scan cycle (from right to left), these radiometers measured at vertical polarization, while on the second half of the scan cycle (from left to right) horizontal polarization was measured. The 37 GHz vertical and horizontal polarization were measured on both halves of the scan cycle. This original scan pattern and FOV geolocation are not provided in the level 1B data files. Instead all observations were interpolated to the corresponding 37 GHz positions with 47 scan positions for each half-scan. This FOV geolocation remains unchanged in the FCDR data processing.

The actual spacecraft position is used to fit the SGP4 orbit model and to estimate daily TLE sets. The TLE sets from the full data record are completed with TLE sets from http://www.spacetrack.org/ (last access: 19 August 2019), filtered and smoothed using a moving averaging window of ±7 d to compile daily element sets for the entire data record period similar to the SSMI(S) procedures. In the following processing step, the new TLE sets are now used to predict the spacecraft position of each scan line. If the predicted and the archived positions are offset by more than 6 km, the scan is marked in the scan quality flag with a geolocation error. Fractional revolution number and local azimuth angles (not available in the level 1B files) are computed using the predicted spacecraft position. Also, scan angles, reflected sun-footprint angles, and EIA are only available at 30 fixed positions per scan line in the level 1B data record. These variables are interpolated to each of the 94 FOV full scan positions.

The SMMR data record contains erroneous data, which have to be flagged in a first processing step during the geolocation. The spacecraft attitude information (roll, pitch, yaw angles) is scanned for zero-filled values and outliers. These angles were used without quality control in the level 1B processing to compute the EIAs. Errors in the EIA are mostly caused by anomalies in the attitude angles. Therefore the zero-filled values and outliers in the attitudes angles and the EIA are replaced with interpolated values. However, no extrapolation is applied and incorrect values at the beginning or end of the data files are set to undefined. The original quality flag status is unset accordingly in this case as the original flagging is no longer necessary due to the interpolation.

3.3.1 SSM/I

An SSM/I FOV at 85 GHz covers about 20 % of the area sampled at 37 GHz. The sampling distance for the 85 GHz channel is 12.5 km and for the 37 GHz channel 25 km. The high-frequency channels are thus sampled twice as often in the along- and across-track directions compared to all other SSM/I channels. In order to get a comparable coverage with the 85 GHz channels, nine neighbouring pixels of the high-resolution scan lines are averaged to match the size of the corresponding 37 GHz pixel. The high-resolution 85 GHz T_B values are averaged with a Gaussian weighted distance w from the centre FOV resembling the 37 GHz main antenna pattern:

where $h_s=s\cdot \mathrm{2}$ and $h_c=c\cdot \mathrm{2}$ are the high-resolution along-track and across-track indices respectively and s and c are the corresponding low-resolution indices. The Gaussian weights for the surrounding 8 pixels depend on the relative position of the centre pixel along the scan line c due to the distortion of the conical scanning system at the scan edges. An array of precalculated averaging weights is used in the data processing, providing a fixed set of nine specific weighting coefficients for each of the 64 FOVs in the lower SSM/I resolution.

3.3.2 SSMIS

Due to the higher frequency, a single FOV at 91 GHz covers only about 17 % of the area sampled at 37 GHz. The lower-resolution channels are averaged on board the spacecraft, combining two neighbouring observations. Hence, the 91 GHz channels are sampled twice as often in the along-scan direction compared to the 37 GHz channels, and the actual centre positions are no longer co-registered with the non-averaged high-resolution FOV positions. In order to get a comparable coverage with the 91 GHz channels, six neighbouring beam positions (two along scan, three along track) are averaged to match the resolution of the corresponding 37 GHz footprint. The averaging is performed similar to Eq. (1), by weighting the individual brightness temperatures with their distance w from the centre FOV.

3.5.1 SSM/I

The SSM/I calibration equation is defined as follows (Hollinger et al., 1987):

where T_A is the antenna temperature, C^e denotes the measured counts when the radiometer is switched to the antenna (Earth view), S is the calibration slope, and O is the offset. The warm calibration target of the SSM/I is an internal black-body radiator with three embedded thermistors, constantly measuring its temperature. The cold reference target is a mirror pointing to the cold space, with an assumed constant radiometric background temperature at 2.7 K. The radiometer views the internal warm and cold calibration targets once during a scan rotation. For all seven instrument channels five radiometric readings are taken for both calibration targets during an A scan, and five additional measurements are taken for the two 85 GHz channels during a B scan. The three embedded thermistor readings are available once per scan pair. The calibration slopes S in kelvin per count and offsets O in kelvin for each instrument channel are calculated following Hollinger et al. (1987) as follows:

where $〈\stackrel{\mathrm{‾}}{C^{\text{h}}}〉$ denotes smoothed mean warm counts, $〈\stackrel{\mathrm{‾}}{C^{\text{c}}}〉$ denotes smoothed mean cold counts, $〈\stackrel{\mathrm{‾}}{T^{\text{h}}}〉$ denotes smoothed mean warm target temperature, and T^c is the cold target temperature. The smoothed scan line mean values for the cold counts C^c, the warm counts C^h, and the warm target temperature T^h are derived by first averaging all available measurements for each scan pair that passes the quality control:

where $C_s^{\text{c}}$, $C_s^{\text{h}}$, and $T_s^{\text{h}}$ are the individual samples of the warm target, the cold target, and the warm load target thermistors respectively. In order to further reduce the noise in the calibration input values, an additional Gaussian smoothing of these scan line mean values, denoted with the 〈  〉 operator is applied:

where w_i denotes the Gaussian across-scan weighting coefficients. The moving averaging kernel spans the g preceding and g following mean scan line values. The kernel half-size g is set to 5 for all SSM/I sensors. This smoothing process introduces an artificial error correlation in the smoothed calibration coefficients. However, as the variance of the calculated T_B values is dominated by the variance in the independently measured Earth's counts C^e, the impact of the error correlation in the smoothed calibration coefficients on the final brightness temperatures can be neglected.

The temperature of the warm target T^hl needs to be corrected using the temperature of the forward radiator plate T^pl to account for radiative coupling between the warm load and the top plate of the rotating drum assembly which faces the warm load when not being viewed:

The value for ε is empirically determined from thermal-vacuum calibration (Hollinger et al., 1987). The original value of ε=0.99 has been changed to sensor-specific values determined during the inter-sensor calibration procedure (see Sect. 5) for this FCDR. Calculated slopes and offsets are archived in the FCDR data files for traceability. The antenna temperatures are then calculated from the Earth counts C^e for each FOV using Eq. (2). Keeping the calibration coefficients in the data record allows us to revert the original Earth counts from the temperatures.

3.5.2 SSMIS

The calibration of SSMIS follows the SSM/I calibration with Eqs. (2) and (3). The cold and warm calibration view counts and the warm target temperature are already averaged by the SSMIS on-board software and are down-linked as scan line mean values. The across-scan averaging kernel half-width g in Eq. (5) is set to eight scan lines for channels 1–7, four scan lines for channels 8–18, and 32 scan lines for channels 19–24. This setup also corresponds to the latest operational ground processing software configuration (Kummerow et al., 2013).

The configuration of the on-board averaging software has changed over time for SSMIS_F16 and SSMIS_F17. The original setup was to average the radiometric readings of the cold and warm target of the current scan and the seven preceding scan lines and is thus asymmetric. Because this configuration resulted in a striping pattern, the on-board across-scan averaging was eventually switched off after revolution number 29808 for SSMIS_F16 and revolution number 1062 for SSMIS_F17. In order to get a symmetric average of the calibration counts for the time period when only the asymmetric mean values are available, the averaging window for channels 8–18 must be expanded to a minimum of 14 scans. This results from averaging the two eight-scan mean values at scan n and at scan n+7. This larger averaging kernel size reduces the noise in the affected SSMIS_F16 and SSMIS_F17 channels during the aforementioned time period.

3.5.3 SMMR

The calibration method applied in the Pathfinder level 1B data record for SMMR was taken from the SMMR CELL data record (Fu et al., 1988):

where T_A is the antenna temperature, and C^e, C^h, and C^c are the measured counts when the radiometer is switched to the antenna (Earth view), the warm load calibration, and cold load calibration respectively. The calibration coefficients S and I are defined as functions of the instrument's component temperatures:

The Δ_fh term is a correction for temperature gradients from the multi-frequency feedhorn along the feedhorn waveguide to the receiver and is given by

with T_sw, T_fh, and T_fw as the Dicke switch, feedhorn, and feedhorn waveguide temperatures respectively.

The Δ_ch term is a correction for temperature gradients from the cold-sky calibration horn along the calibration horn waveguide to the receiver and is given by

with T_ch and T_cw as the calibration horn and calibration horn waveguide temperatures. The calibration coefficients $a_{\mathrm{1},\mathrm{2},\mathrm{3}}$, α_1,2, and β_1,2 are given in Njoku et al. (1998).

The warm calibration target of the SMMR is the internal ambient temperature at ≈ 300 K. The cold reference target is the cold space, viewed with three calibration horns (depending on frequency). The cold sky is assumed to be at a constant temperature of 2.7 K, i.e. cosmic background temperature. The radiometer views the internal warm and cold calibration targets once during a full scan cycle. The instrument temperatures are sampled every eight scans using platinum resistance thermistors and are embedded in the data record.

In order to reduce the noise, calibration warm and cold counts are smoothed in the level 1B data processing using a running one-sided average:

with s as the scan line number, w as the weight of the new data value, and 〈C^h,c〉 as the across-scan smoothed cold or warm count. A weight of w=0.1 was chosen as a compromise between noise reduction and overdamping.

Also, the instrument temperatures are averaged using the same method. As these temperatures are only available every eight scans, a weight of w=0.6 was used.

The calibration coefficients S and I are not available in the Pathfinder level 1B data records. In order to complete the data record and to estimate the instrument noise level, these coefficients are recalculated using Eqs. (8)–(10) and then archived in the SMMR FCDR data files for reference.

3.6.1 SSM/I along-scan correction

One of the first detected SSM/I calibration problems was a non-uniformity of the measured antenna temperatures along a scan line (Wentz, 1991; Colton and Poe, 1999). A rapid fall-off at the end of the Earth scan of nearly 1.5 to 2 K was found in all SSM/I channels. This systematic problem is caused by an intrusion of cosmic background energy by the glare Suppression System-B (Colton and Poe, 1999) into the antenna feedhorn reducing the observed scene temperature and thus causing a scan-position- and scene-temperature-dependent offset.

This intrusion effect can be treated as an antenna beam position energy loss. It can be corrected by multiplying the antenna temperature T_A with a scan-position-dependent correction factor. This factor is derived in a two-step procedure. First, antenna temperatures for each sensor and channel with surface type classified as sea between 50^∘ S and 50^∘ N, thereby excluding areas with seasonally varying sea ice, are normalized to a constant Earth incidence angle (EIA). Then these temperatures are averaged into FOV-position bins for at least 1 year. The correction factor at each FOV position is computed as the ratio of the position averaged value to the average along the unaffected FOVs positions at the scan line centre (FOV positions 50–90). The derived along-scan correction factors are very similar for all SSM/I sensors. As an example, the along-scan correction for SSM/I_F13 is shown in Fig. 2. The see-saw pattern in the 85 GHz channels results from two sets of integrators being used, one for the odd and one for the even numbered positions with small differences remaining in the level 0 data.

Figure 2Along-scan correction for SSM/I_F13. The image shows the along-scan correction applied to a scene temperature of 200 K. Colours are as follows: blue – v19; cyan – h19; green – v22; red – v37; orange – h37; plum – v85; violet – h85.

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3.6.2 SSM/I cold-space reflector intrusions

The SSM/I calibration procedure assumes that the cold reference target is at the background cosmic temperature of 2.7 K. However, due to the open instrument design, it is possible, depending on the orbit parameters, that the moon is visible in the cold view. This leads to a short-term increase in the measured cold target radiation counts. The amplitude and length of this increase depend on the beam width of the channel as the fraction of the moon in the FOV compared to the cosmic background is larger for smaller beam widths. These events usually happen twice per month, depending on the orbit configuration. An example is shown in Fig. 3. This image is a two-dimensional representation of cold count anomalies as a function of the northward Equator crossing time on the x axis and the fractional orbit position on the y axis. One image column is exactly one orbit with the start of the orbit at the time given on the abscissa, and one image row is always at the same orbit angle position. The image depicts two intrusion events, the first one over the North Pole on 14 November and the second one on 19 November shortly before crossing the South Pole.

Figure 3Cold count anomaly (a) from the SSM/I_F13 channel at 37 GHz, v-pol for November 2005. The y axis represents the fractional orbit angle with an ascending Equator crossing at 0 and descending Equator crossing at 0.5. The x axis represents the time of the orbit start at the ascending Equator crossing. A cross section of the absolute cold counts through the maximum of the first intrusion event is shown in (b). Positions with identified cold count anomalies are between the vertical lines. The locally fitted reconstruction spline is plotted in cyan.

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As these events only affect the cold reference target, the impact on the calibrated antenna temperatures is scene dependent and larger for lower scene temperatures. The best way to correct this effect is to apply a band-pass filter to remove the additional signal induced from the moonlight. Under normal conditions the variation in the cold counts is periodic and changes very little from orbit to orbit. This allows us to easily detect the anomalies as shown in Fig. 3.

A procedure has been developed which automatically detects the moonlight intrusion events using a Laplace filter as an edge detection algorithm. The Laplace operator computes the second derivatives of an image, measuring the rate at which the first derivatives change. This determines if a change in adjacent pixel values is from an edge or continuous progression. In order to use standard image filtering techniques to detect the intrusion events, yearly monitoring files are compiled for each sensor and channel. The calibration data are sampled at fixed orbit angle positions. The discrete cold count Laplace operator Δ^c is then defined as

with i and j as the along-orbit and across-orbit image indices respectively, k as the kernel size, and ${\widehat{C}}^{\text{c}}$ as the sampled cold counts. This image is then smoothed and periods with moonlight intrusion are detected where the derived Laplacian is significantly larger then 1 standard deviation of the background field. These periods are regarded as missing data and reconstructed along the orbit using a spline interpolation procedure from the neighbouring smoothed valid values (see Fig. 3, cyan line). The difference between the original and the reconstructed values is smoothed and removed from the original values. This procedure works similarly to a local band-pass filter but can also deal with undefined data. Corrected scan lines are also flagged during the final data processing using a processing control flag.

3.6.3 SSM/I warm load intrusions

Another problem in the SSM/I calibration data that has been identified is sunlight intrusion into the warm reference black-body target. This occurs during certain orbit constellations when the satellite platform is leaving and entering the Earth shadow.

Figure 4Edge detection results (Laplace operator) for calculated first-guess slopes from the SSM/I_F13 channel at 19 GHz, h-pol for November 2005 (a) and a cross section of the first-guess slope (b) with two sunlight intrusion events. The satellite leaves the Earth's shadow at approximately position 0.28 and enters the Earth's shadow at position 0.85. Positions with identified warm target anomalies are between the vertical lines. The locally fitted reconstruction splines are plotted in cyan.

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The issue is caused by an illumination of the black-body tines due to either direct or reflected sunlight. The sunlight causes a fast instant response in the calibration measurements of the SSM/I as the radiation heats the tines of the black body while the black-body core remains unaffected or is just slowly heating up. As the warm load temperature sensors are embedded into the core of the black body, they do not measure the temperature of the calibration target at the tines but the core temperature. With the delayed response of the temperature sensors to the increased radiation, the net effect is a sharp artificial discontinuity (decrease) in the calibration gain. Figure 4 shows an example for the detection of intrusion events. The intrusions occur around the orbit positions 0.23 and 0.81. When the satellite leaves the Earth's shadow, the whole instrument warms up, and the warm load temperature also increases. When the intrusion ceases, the black-body core and surface temperature are balanced again (around position 0.32). However, if the satellite enters the Earth's shadow, the intrusion effect is more pronounced. As long as the sunlight falls on the warm load, a negative anomaly can be observed in the calibration slopes, because the core temperature of the black body remains nearly constant. When the sunlight intrusion vanishes (around position 0.9) a sharp increase is visible in the slope when measured warm load target temperature and the observed radiation are balanced again.

This sunlight intrusion effect depends on the channel frequency and is strongest at the lower frequencies. The procedure to correct for this intrusion is similar to the correction for the moonlight intrusions, but in the sunlight case the warm target counts are affected. All significant sunlight intrusion events are detected using the edge detection algorithm applied to the slope anomalies. The discrete Laplace operator Δ^s is applied to the sampled calibration slopes $\widehat{S}$:

The intrusion periods are filtered and reconstructed from a spline interpolation using the neighbouring smoothed valid slope values (see Fig. 4, cyan line). The difference between the original and the reconstructed slope values is smoothed to obtain the intrusion-induced anomaly and then used to correct the computed slopes. Finally the corrected slopes and the warm load calibration temperature are used to convert the slope anomaly into warm load count offset maps. These corrections are applied during the final data processing to correct the intrusion events. Affected scans are also flagged using a processing control flag.

An example for the edge detection algorithm (applied Laplace operator) is shown in Fig. 4. The positions of the sunlight intrusion events are identified as positive and negative anomaly lines. The geographic positions of the intrusions depict a seasonal cycle caused by the varying relative angle of the satellite to the sun. The pattern also changes from year to year due to the orbit drift and changing Equator crossing times. Therefore the correction maps are compiled for each year separately.

3.6.4 SSMIS along-scan correction

Similar to the non-uniformity of the measured antenna temperatures along a scan line for SSM/I, the SSMIS sensors also show a rapid decrease near the end and beginning of the Earth-viewing scene T_B values (Kunkee et al., 2008b). A rapid fall-off at the end of the Earth scan is found for channels 15 and 16 (37 GHz), due to intrusions into the feedhorn by the warm load cover and for the beginning of the scan line for channels 12–14 (19 and 22 GHz), due to intrusions by the cold-sky reflector. The strongest effect can be observed for the SSMIS_F17 channels 15–16, when the last five beam positions are biased by more than 8 K.

This effect is corrected following the approach for SSM/I by multiplying the antenna temperature with a scan-position-dependent correction factor. The along-scan correction for the SSMIS_F16 instrument is exemplarily shown in Fig. 5.

Figure 5Along-scan correction for SSMIS_F16. The image shows the along-scan correction applied to a scene temperature of 200 K. Colours are as follows: blue – v19; cyan – h19; green – v22; red – v37; orange – h37; plum – v91; violet – h91.

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3.6.5 SSMIS cold-space reflector intrusions

Due to the heritage design from the SSM/I, the moonlight intrusions into the cold-space reflector are also inherited by SSMIS. The correction procedure principally follows the one from the SSM/I. However, the SSMIS consists of six individual feedhorns with slightly different alignments. This leads to a small shift in the location of the intrusion, which has to be accounted for, and the correction is carried out for each feedhorn separately.

3.6.6 SSMIS warm load intrusions

As with the cold-space reflector intrusions, the sunlight intrusion into the warm calibration black-body target is also inherited by the SSMIS. In fact, the warm load intrusion were detected first in SSMIS_F16 (Kunkee et al., 2008a) because they are stronger and cover a significantly larger part of the orbit. Kunkee et al. (2008a) identified two intrusion regions where the sun directly shines on the warm load tines and two regions where the radiation is reflected from the top of the SSMIS canister onto the warm load target. In order to mitigate the direct intrusions, a fence was installed aboard F17 and F18.

Figure 6Edge detection results (Laplace operator) for calculated first-guess slopes from the SSMIS_F16 channel at 91 GHz, h-pol for 2010 (a) and a cross section of first-guess slope (b) for one orbit in June 2010 (right). Four regions with warm load intrusion are identified around orbit positions 0.04, 0.15, 0.48, and 0.65.

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Following the approach developed for SSM/I, the sunlight intrusion events for the SSMIS are detected by applying the Laplace operator Eq. (13) to the calibration slope. An example showing four sunlight intrusion events at orbit positions 0.04, 0.15, 0.48, and 0.65 is presented in Fig. 6 for SSMIS_F16. Apart from the regularly repeated short-term moonlight intrusion events, which occur around orbit positions 0.3 and 0.7, strong regular stripes can be identified in Fig. 6a. The negative anomaly regions in the Laplacian, flanked with positive anomalies, are the regions with sunlight intrusions affecting the calibration gain. These patterns are not static at a geographic position but vary during the year as a function of the solar elevation and azimuth angles relative to the spacecraft platform. Also, spacecraft structure elements, like solar panels, can shade the warm load during some periods of the year. This can be observed in February (March) around orbit position 0.5, where the anomaly abruptly stops (starts). The additional fence on DMSP F17 and F18 is working well (not shown here). Only during a 3-month period, when the sun is above the installed fence, is an intrusion visible for SSMIS_F17, and just a small intrusion region for SSMIS_F18 can be identified throughout the year. The basic correction method again follows that of SSM/I. However, as a consequence of the aforementioned factors, it is not possible to compile one static intrusion map for each channel; instead yearly correction maps are compiled for each channel. In order to minimize the noise, the SSM/I procedure has been adapted to convert the observed count anomalies into an anomaly in the warm target temperature first. These temperature anomalies are then averaged across all channels sharing one feedhorn and eventually converted back to channel-specific count anomalies.

3.6.7 SSMIS emission from main reflector

The SSMIS main reflector appears to be emissive (Bell, 2008; Kunkee et al., 2008a), which results in an additional radiation emitting from the reflector at the reflector's temperature and thus modifying the measured scene temperature. The magnitude of this effect depends on the temperature difference between the reflector and the Earth scene. The reflector temperature varies along the orbit due to solar heating when not being covered in the Earth shadow. The strongest signal can be observed when the spacecraft leaves the Earth shadow and the reflector temperature increases by about 80 K within a few minutes.

If the temperature of the main reflector T_refl and its emissivity ε_refl are known, the emission effect can be corrected with

Values for ε_refl were found by comparing observed minus background residuals from data assimilation experiments by Bell (2008). Emissivity values derived for the Universal Preprocessor (UPP) version 2 are applied in this FCDR unchanged for all non SSM/I-like channels. Emissivity values for the SSM/I-like channels are fitted again during the inter-calibration minimization procedure because the given values turned out to be not at the required precision. The values are determined by using SSMIS_F18 as the reference target, because no significant emissivity was found for its reflector.

From SSMIS_F17 onward, a temperature sensor is placed at the back of the reflector to measure T_refl directly, but for SSMIS_F16 the closest available sensor is placed on the rim of the main reflector, close to the support arm. The temperature of the reflector can be constructed from the arm temperature T_arm using a lagged correction following Bell (2008). The reconstructed reflector temperature is computed for F16 and saved in the FCDR data files. The reflector temperature for all sensors is linearly interpolated to the observation time as the housekeeping data records are not available for each scan line and the antenna temperatures are corrected with Eq. (14).

3.6.8 SMMR Pathfinder level 1B corrections

In the level 1B processing, corrections for absolute calibration, long-term drifts, short-term drifts, and polarization mixing are applied. The level 1B corrections applied to the antenna temperatures are explained in detail in Njoku et al. (1998) and summarized in the following two subsections.

(a) SMMR calibration offset adjustments

A two-point linear absolute calibration adjustment to the SMMR data record was estimated by Njoku et al. (1998) using ocean areas acting as the cold calibration target and the internal ambient instrument warm load as the warm calibration target. The coefficients were derived over calm, cloud-free oceanic areas, characterized by low emissivity values. Modelled T_B values were compared to the observed SMMR T_B values to derive a linear calibration adjustment to the antenna temperatures:

where $T_{\text{A}}^{\prime }$ is the normalized SMMR antenna temperature (after spillover correction), $T_{{\text{A}}_c}^{\prime }$ is the corrected antenna temperature value, and a, b are the linear calibration adjustment coefficients. The calibration constraints can be written as

where $T_{\text{B}}^{\text{o}}$ is the mean observed SMMR brightness temperature for the cold calibration target and $T_{\text{B}}^{\text{m}}$ is the corresponding modelled brightness temperature. Solving these equations for the coefficients a and b yields

The calibration correction coefficients a and b depend on the warm load equivalent brightness I^′ and are updated online for each new set of calibration data. The values for $T_{\text{B}}^{\text{m}}$ and $T_{\text{B}}^{\text{o}}$ are given in Njoku et al. (1998).

(b) SMMR correction for short- and long-term drifts

Ageing of the radiometer components can lead to a slow but steady degradation in the radiometer performance. Njoku et al. (1998) studied the long-term evolution of the mean T_B values in all SMMR channels. The largest drift was found for the channel at 21 GHz, v-pol with an increase of 36 K until March 1985 when it was turned off. The observed drifts are corrected in the level 1B data record using a polynomial fit of the globally averaged antenna temperatures, after removing mean seasonal cycle variations. The polarization mixing was not corrected for in order to keep the signals from each radiometer independent at this stage. Otherwise the strong drift in the horizontal polarization at 21 GHz would have been mixed into the vertical polarized channel.

Also, orbit-dependent solar illumination of the instrument can affect the radiometric calibration. Although temperature gradients are accounted for in the SMMR calibration using Eqs. (7) and (8), not all effects might be compensated accurately. Especially when the spacecraft leaves or enters the Earth's shadow, strong temperature gradients can be observed, possibly leading to unmodelled thermal emissions in the waveguides and switches of the instrument (Francis, 1987).

To correct for this type of errors, orbit-dependent corrections were derived following a method described by Francis (1987). Mean brightness temperature differences between ascending and descending orbits were analysed to derive T_B drift corrections as a function of the spacecraft ecliptic angle. The corrections are derived for each year and then linearly interpolated to the observation time.

The corrections for long-term drifts T_lt and short-term drifts T_st were incorporated into the calibration by replacing the calibration correction coefficients a and b in Eq. (17) with drift-corrected coefficients a_n and b_n. However, as the original coefficients a_n and b_n are not available in the data records and the short-term and long-term correction maps are not available in Njoku et al. (1998), it is not possible to undo the applied corrections and to revert the original antenna temperatures. Therefore, any other additional correction must be carried out on top of the already applied level 1B corrections.

3.6.9 SMMR along-scan correction

A general along-scan non-uniformity of the SMMR antenna temperatures is to be expected, due to the design of the radiometer, causing a scan-angle-dependent cross-polarization coupling. Although most of this effect is removed by the applied scan-position-dependent polarization mixing correction (see Sect. A3), significant variations in the final T_B values can remain. To analyse these, the match-up data set with observed and modelled brightness temperatures from the inter-calibration procedure (see Sect. 5.3) has been used here.

Figure 7Scan-angle-dependent correction for the SMMR instruments. This image shows the along-scan correction at a common scene temperature of 200 K. Nadir is at position 24. Channel colours are as follows: blue – v18; cyan – h18; green – v21; red – v37; orange – h37.

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Differences between observed and modelled T_B values for each channel with surface type classified as sea between 50^∘ S and 50^∘ N are averaged into FOV position bins for the complete SMMR time period at 10 d intervals. Then a factor at each FOV position is computed as the ratio of the position-averaged value to the unaffected FOVs at the scan line centre (azimuth = 0). The time mean results are shown in Fig. 7 for a nominal scene temperature at 200 K. Most pronounced features are the large offsets of about 1 K for the channel at 21 GHz, v-pol on the left scan side and for the channel at 37 GHz, h-pol on the right scan side. The other channels show small offsets on the left side (0–0.3 K) and small but a little larger offsets at the right side (0.2–0.5 K). The large differences at 21 GHz, v-pol are not constant over time (not shown here) and are most likely caused by the polarization mixing from the problematic channel at 21 GHz, h-pol. This channel depicts a strong trend and degradation with time, which can not be removed completely by the long-term drift corrections and polarization mixing decoupling procedure. Also, the observed differences in the 18 GHz channels are not constant over time, but they do show a seasonal variation with smaller offsets in Northern Hemisphere winter and larger offsets in Northern Hemisphere summer months. Only the deviations in the 37 GHz channels are constant over time.

Following these results, only the along-scan biases in the 37 GHz channels are corrected in the CM SAF SMMR FCDR. As the differences in the vertical polarization are much smaller than in the horizontal polarization, the cross-polarization is assumed to be zero and the bias correction reduces to a scan-position-dependent factor similar to the SSMI(S) correction procedure.

6.2.1 Warm load reference uncertainty

The calibration uncertainty of the warm load was determined pre-launch for SSM/I_F08 by comparison with a variable-precision calibration reference target over a range of 100 to 375 K during thermal vacuum calibration. These tests show no systematic calibration error (Hollinger et al., 1989). Kunkee et al. (2008c) refer to an absolute uncertainty of 0.1 K for SSMIS. However, no information on pre-launch measurements of the temperature sensors is available for SMMR. A common value of 0.1 K is employed for all instruments.

6.2.2 Cosmic background reference uncertainty

An analysis of the calibration reflector antenna patterns, when the SSM/I is in the calibration position, reveals that the reception of Earth and spacecraft radiation is extremely small (less than a few tenths of a degree). Thus it is believed that the SSM/I calibration reflector provides a clear view of the cosmic background to the feedhorn and hence provides a highly accurate black-body calibration reference (Hollinger et al., 1989). However, this is not the case during phases when parts of the moon are in the field of view of the reflector (see Sect. 3.6.2). These short-lived intrusion events can cause an underestimation of the true scene temperature of up to 0.5 K, depending on the channel frequency and scene temperature. As the SSMIS employs the same cold calibration method, the same problem arises and the same maximum bias is assumed.

The SMMR suffers from periodic sunlight intrusion events into the cold-sky calibration horns. This usually occurs once during each orbit over the southern polar region. These regions are not used in the calibration. Instead the cold counts are linearly interpolated between the last valid values (Njoku et al., 1998). Apart from these events, it is believed that the SMMR calibration horns provide a clear view of the cosmic background.

To account for these short-term SSMI(S) intrusions and the uncertainties in the SMMR calibration interpolation, a mean uncertainty of 0.1 K is assumed for all instruments, keeping in mind that only small parts of the orbit are affected.

6.2.3 Radiometer/calibration non-linearity

Non-linearities in the calibration measurements and in the radiometer receiver may be expected. This can impact the radiometric calibration when a two-point linear calibration equation is applied. At observation temperatures equal to the calibration reference targets, the calibration uncertainty is the accuracy of the reference, which does not show a systematic uncertainty (see above). At intermediate temperatures, radiometer non-linearity and calibration reference temperature uncertainty contribute to the total uncertainty with the uncertainty weighted according to the difference between the observed scene and the calibration references. To test the radiometer absolute calibration, preflight thermal vacuum tests have been conducted for SSM/I (Colton and Poe, 1999). Calibration cycles were run for three different sensor temperatures: cold (0 ^∘C), ambient (28 ^∘C), and hot (38 ^∘C). For the on-orbit expected operating range the calibration errors are typically −1.4 to 0.5 K (Colton and Poe, 1999) and hence within the instrument specifications. The corresponding graphs in Colton and Poe (1999) point to a scene-temperature-dependent bias with a larger underestimation for colder scene temperatures. However, the measurements are believed to contain artefacts due to the actual test setup. The on-orbit calibration is expected to perform better than the pre-launch calibration tests indicate (Colton and Poe, 1999).

To test the SSMIS radiometer absolute calibration, thermal vacuum tests have been conducted for all SSMIS instruments, with all meeting the accuracy requirement of 1 K (Kunkee et al., 2008b). However, a scene-temperature-dependent offset is depicted in Fig. 6a in Kunkee et al. (2008b). Without more details being available, the same values as for SSM/I are used.

Thermal vacuum tests have also been conducted for the SMMR instrument at the Jet Propulsion Laboratory (JPL) for temperature levels ranging from 77 to 320 K (Gloersen, 1987). Within the observed radiometer switch temperature range of ±2 K, the differences between linear and quadratic calibration equations are found to be within 0.1 K for all channels.

6.2.4 Radiative coupling ε uncertainty

The radiative coupling coefficient ε was originally determined for SSM/I_F08 and has been used unchanged in the computation of the antenna temperatures (Eq. 6) since then. The correction due to this factor depends on the temperature difference between the warm load and the forward radiator plate. This correction is typically of the order of 0.1 K for an expected temperature difference of 10 K. However, some instruments show a very strong seasonal variation in the temperature difference reaching 40 K. A relative uncertainty of 1 % in ε can then lead to a bias of 0.4 K in the scene brightness temperature.

6.2.5 Uncertainty in the APC coefficients

During the ground instrument calibration, a radiometric characterization of the antenna properties is also performed. The performance was established from analyses of the antenna gain function as measured on an antenna range from which, amongst others, feedhorn spillover and cross-polarization loss were determined. The estimated absolute accuracy of the feedhorn spillover is 0.3 %–0.5 % and the relative cross-polarization accuracy is of the order of 5 %–10 % (Colton and Poe, 1999). The uncertainty in the spillover translates to a scene-dependent uncertainty of the order of about 1–1.5 K at a 300 K scene temperature. The uncertainty in the cross-polarization accuracy results in an uncertainty, depending on the scene polarization difference, of the order of 0.15–0.3 K for a scene with a 50 K difference between vertical and horizontal polarization. These values are also employed for SMMR and SSMIS.

6.2.6 SSMIS reflector emissivity

The emissive reflector problem is specific for the SSMIS. It leads to an additional systematic uncertainty which depends on the emissivity of the reflector (see Sect. 3.6.7). The emissivity itself is a function of the channel frequency and the temperature difference between the reflector and the observed target. Thus it is not only scene dependent but also a function of the orbit position when the reflector is heated by the solar radiation and cools in the Earth shadow. The strongest errors are to be expected when the spacecraft leaves the Earth's shadow with the reflector temperature increasing by about 80 K and at low scene temperatures. With the reflector temperature reaching about 300 K and the lowest scene temperatures around 150 K, a maximum difference of about 150 K can be expected. The error due to the emissivity of the reflector can then reach about 13 K for some of the sounding channels with an estimated emissivity of ε_refl=0.09. The largest error for the SSM/I-like environmental and imager channels appears at 91 GHz for SSMIS_F17. With an emissivity of 0.04 at this frequency, this can result in an error of about 6 K. This emissivity-induced error is corrected in the CM SAF FCDR. The expected uncertainty in the determination of the emissivity can be estimated as ±10 %, which then translates to a maximum remaining error of ±0.6 K.

6.2.7 Along-scan cross-polarization mixing

This systematic uncertainty source is specific for the SMMR as a result of the instrument design. The antenna system consists of a scanning parabolic reflector and a fixed multispectral feedhorn. This leads to a scan-angle-dependent polarization mixing, which is corrected for when the antenna temperature is converted to the T_B. This method was developed after launch by Gloersen (1987). Njoku et al. (1998) adopted this method and report the uncertainty of the fitted correction coefficients in the level 1B data record to be between 0.046 and 0.157 K with the remaining along-scan biases ranging between 0.2 and 0.5 K.

Total systematic uncertainty

The individual systematic uncertainty contributions are summarized in Table 1. If only a maximum range can be estimated, the corresponding standard uncertainty u_i is derived from the uncertainty range y_i assuming a uniform distribution of the uncertainty within the expected range of variation $\mathrm{\Delta }{a}_i=\left|\frac{y_{+}-y_{-}}{\mathrm{2}}\right|$:

The combined total expected standard systematic uncertainty

is then of the order of 0.7–1.1 K for SSMI(S) and 0.4–1 K for SMMR, with a significant dependence on the scene temperature due to the non-linearity and spillover terms and a minor dependence on the scene polarization. Overall, the total expected systematic uncertainty of the absolute calibration depends on the frequency, the scene temperature, and the polarization difference. As the random uncertainty scales with the number of observations, the systematic uncertainty has to be accounted for when comparing two climatological means of T_B values from different platforms.