Mitigation of Striping Noise in ATMS Calibration Counts by Symmetric Filters
1. Introduction
The Suomi National Polar-Orbiting Partnership (SNPP) satellite was successfully launched into a sun-synchronous polar orbit on 28 October 2011 with an equator crossing time of 1330 local time. The Advanced Technology Microwave Sounder (ATMS) onboard SNPP is a new cross-track and line-scanning microwave radiometer. The ATMS combines the functionalities of the previous Advanced Microwave Sounding Unit A (AMSU-A) and Microwave Humidity Sounder (MHS) into a single instrument. The ATMS is the most advanced and state-of-the-art satellite-based microwave instrument that simultaneously provides temperature- and humidity-sounding information at the same 96 field-of-view (FOV) Earth view locations. Compared with its predecessors AMSU-A and MHS, the ATMS has several improvements including a wider swath width, additional sounding channels, and smaller noise equivalent delta temperatures (Weng et al. 2013b). Kim et al. (2014) evaluated the on-orbit performance of the ATMS and showed that the radiometric sensitivity was well maintained and that the radiometric accuracy met or even surpassed expectations. Many studies have focused on the calibration and validation of ATMS observations where radiances simulated by an atmospheric radiative transfer model with global numerical weather prediction (NWP) datasets (B) serve as references for observed radiances (O) (Weng et al. 2012, 2013b; Zou et al. 2014; Tian et al. 2018).
Bormann et al. (2013) discovered that striping-patterned noise was detectable in the differences between observations and simulations (O − B), suggesting a contamination of striping noise in ATMS observations. The diagnosis and mitigation of high-frequency striping noise are challenging tasks that must be undertaken to fully explore the potential of the ATMS to NWP and climate studies (Zou et al. 2013; Tian and Zou 2016, 2018; Zou and Tian 2018). Wu and Huang (2009) and Wu et al. (2009) proposed an ensemble empirical mode decomposition (EEMD) method for extracting from raw data different frequency components. For a given time series, the EEMD method uses information about the minima and maxima of the riding waves in the set of noise-added ensemble data time series itself and successively extracts the oscillatory components called intrinsic mode functions (IMFs) from the highest to the lowest frequencies. Unlike the preexisting harmonic base functions of the Fourier frequency transform, the IMFs of the EEMD method are locally adaptive basis functions extracted directly from the data, making them more physically representative. The EEMD method also works for data series representing nonlinear processes. Qin et al. (2013) pointed out that striping noise is contained in the first principle component (PC) generated from the principal component analysis (PCA) of ATMS observations and applied the EEMD method to extract the ATMS striping noise. This method cannot only remove the striping noise in temperature-sounding channels, but also humidity channels for which the striping phenomenon is not visible in O − B distributions. Specifically, the first three high-frequency IMFs are extracted from the first PC coefficient of antenna temperatures. The removed striping noise has a frequency range centered at ~10−2 s−1 and magnitudes of ~0.3 K for ATMS temperature channels and 1 K for ATMS humidity channels. Zou et al. (2017) and Zou and Tian (2019) further refined the PCA/EEMD method proposed by Qin et al. (2013) to make it also applicable to the window channels of the ATMS onboard both the SNPP satellite and the National Oceanic and Atmospheric Administration (NOAA)-20 satellite launched in 2017.
A detailed description of converting raw data counts to antenna temperatures through the ATMS calibration process is given in Weng et al. (2013b) and in the ATMS advanced technical baseline documentation (GSFC 2011). The two-point calibration involves converting Earth scene counts into antenna temperatures through a linear relationship defined by warm counts, cold counts, warm load temperature, and cold space temperatures. A quadratic term accounting for the nonlinear relationship between antenna temperatures and counts is also added. Conventionally, radiometric calibration error sources include target emissivity, measurement uncertainty, the Rayleigh approximation, and antenna sidelobe interception (Weng et al. 2013a). Figure 1 shows antenna temperature observations (Fig. 1a) and differences of antenna temperatures between observations O and model simulations B (Fig. 1b) for ATMS channel 8 over a swath at the ascending node of SNPP on 24 February 2012. An along-track striping noise feature, with its magnitude varying randomly in the along-track direction, can be seen in both the observations (Fig. 1a) and the O − B difference (Fig. 1b) fields. Warm counts, cold counts, and warm load temperatures are traditionally smoothed in an operational system using either a triangular or a boxcar filter to reduce the effect of radiometric instrument errors on antenna temperatures, while the scene counts are not smoothed. To more effectively suppress the instrument error due to noise, in this study, a new set of optimal filters for ATMS warm counts, cold counts, warm load temperature, and scene counts is thus proposed. Section 2 briefly describes ATMS instrument characteristics and the two-point calibration. Theoretical derivations of the weighting coefficients of the optimal filters are provided in section 3. Section 4 presents numerical results of the optimal filters and the characteristics of the striping noise removed by the optimal filters. A summary of this study is finally given in section 5.
(a) Brightness temperatures at channel 8 in the ascending node on 24 Feb 2012. (b) The differences of brightness temperatures at channel 8 between the observed and those simulated by the Community Radiative Transfer Model on 24 Feb 2012.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
2. ATMS instrument and observation features
a. ATMS channel characteristics
The ATMS is a cross-track, line-scanning sensor. It takes 2.67 s to complete one scan cycle, which contains 96 FOVs for all 22 ATMS microwave temperature- and humidity-sounding channels. With a sampling interval of 1.11°, the scan angle of the outmost FOV is 52.7°. ATMS channels 1–3 and 5–16 have similar central frequencies as channels 1–15 of the traditional microwave temperature-sounding instrument AMSU-A. ATMS channels 17–22 contain channels with similar central frequencies as the five channels from the traditional humidity-sounding instrument MHS. Compared with its predecessors AMSU-A and MHS, the ATMS has an extra temperature channel 4 with its weighting function located in the lower troposphere and two new humidity channels 19 and 21. The swath width of the ATMS is 2500 km, which is wider than both AMSU-A and MHS swath widths, leaving almost no data gaps between two neighboring swaths over the entire globe. The beam widths of channels 1–2, 3–16, and 17–22 are 5.2°, 2.2°, and 1.1°, respectively.
b. Derivation of antenna temperatures from raw counts
3. Methodology
a. The EEMD method
b. Optimal symmetrical filters on warm counts and cold counts
c. Optimal symmetrical filters for scene counts
4. Numerical results
a. Spectrum analyses of IMFs of calibration counts
Data series of warm counts, cold counts, warm load temperatures, and the first PC coefficient of scene counts for all ATMS channels within 55°S–55°N on 24 February 2012 were decomposed into a series of IMFs. Figure 2 shows the Fourier spectra of the first six IMFs as a function of frequency for warm counts and cold counts at channel 8. As the IMF number increases, its peak amplitude is located at increasingly lower frequencies. Noise at high frequencies is captured in the first few IMFs, and large-scale variations are captured in the remaining IMFs. The main criterion to decide which IMFs are noise, or how many IMFs to remove, is whether the peak amplitude of a certain IMF continues to decline. At the beginning of the fourth IMF for both warm counts and cold counts, the peak amplitude is no longer smaller than that of the previous IMFs. So the first three IMFs are primarily noise signals. The magnitudes of the first three IMFs at low frequencies are small, suggesting that removing the first three IMFs will not change the warm count or cold count features at low frequencies. Results obtained for the other 21 ATMS channels are similar (not shown). Therefore in this study, the first three IMFs are removed for both warm counts and cold counts at all ATMS channels.
Fourier spectra with 81-point running means for the first six IMFs of (a) warm counts and (b) cold counts at channel 8 on 24 Feb 2012.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
Figure 3 shows the Fourier spectra of the first six IMFs for warm load temperatures. Note that the fifth and sixth IMFs peak at the same frequency but that the amplitude of the sixth IMF is smaller than that of the fifth IMF. This suggests that no significant signal can be found at lower frequencies starting from the sixth IMF. Unlike warm counts or cold counts that change only in the along-track direction, ideal warm load temperatures should have constant values, implying zero Fourier spectra for the true signal. Thus, a total of five IMFs are removed from warm load temperatures. Figure 4 shows the Fourier spectra of the first six IMFs of the first PC coefficient for scene counts at channel 8. The fourth IMF has much larger magnitudes than the third IMF at both the peak and low frequencies. Therefore, removing the first three IMFs is enough to eliminate the noise while keeping the large-scale information. A similar analysis was carried out for all 22 channels. Table 1 lists the total number of IMFs removed from scene counts for each ATMS channel. For ATMS window channels 1–2 and 16, only two IMFs need to be removed because two IMFs are sufficient to capture the data noise. For the remaining channels, three IMFs are removed.
As in Fig. 2, but for warm load temperatures. Five IMFs are removed.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
As in Fig. 2, but for the first PC coefficient of scene counts at channel 8. Three IMFs are removed.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
Channel frequencies, peak weighting functions (WFs), filter spans (FSs) of optimal striping filters for ATMS warm counts and cold counts, and scene counts.
b. Properties of the optimal symmetrical filters
As described in sections 3 and 4, the EEMD-smoothed warm counts, cold counts, warm load temperatures, and scene counts are then taken as training samples to establish the optimal filters expressed in (5) and (17). To decide on the filter span N, weighting coefficients and cost functions of (2N + 1) point symmetrical optimal filters with different spans ranging from 2 to 30 were calculated. Cost functions describe how close the counts smoothed by EEMD are to those by the optimal filter and have different magnitudes at different channels. Figure 5 shows variations in the normalized cost functions of the optimal filters as a function of filter span for warm counts, cold counts, and scene counts at all ATMS channels. The cost functions drop rapidly as the filter span N increases, suggesting that the optimal filters tend to capture the EEMD features more closely if more scanlines are involved. The goal is to remove striping noise with the least number of scanlines in the optimal filter. The black circles in Fig. 5 indicate the selected filter spans of the optimal filters (see also Table 1). Surface channels have narrower filters mainly because there are only two IMFs removed, making changes to the counts data smaller. Temperature-sounding channels have wider filters than humidity-sounding channels for warm counts and cold counts, but narrower filters for scene counts.
Normalized cost function as a function of filter span N for (top) warm counts, (middle) cold counts, and (bottom) scene counts. The number of scanlines involved in the optimal filter is indicated by circles.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
Figure 6 shows weighting coefficients of the optimal filters for warm counts, cold counts, and scene counts at all channels. All weighting coefficients have symmetrical parabolic shapes. This suggests that data points with identical distances to the filtering point weigh exactly the same within any filter. Also, those closer to the filtering point (n = 0) are weighted more than data points farther away. The filtering points themselves appear to have the greatest importance, while data points farther away have less impact on the smoothed counts, which is reasonable. Weighting coefficients with the same distance to the filtered points have similar magnitudes for warm counts and cold counts at different channels. Scene counts at channels 1–2 and 16 have larger weighting coefficients than those for the other channels because the sum of the weighting coefficients of any filter is unity, and fewer scanlines are involved in these three window channels.
Weighting coefficients of optimal filters for (top) warm counts, (middle) cold counts, and (bottom) scene counts.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
Figure 7 shows the spectral response functions calculated with the optimal weighting coefficients shown in Fig. 6 according to (11). For warm counts, cold counts, and scene counts at all channels, the response functions are ~1 until they drop sharply to around zero at ~10−2 s−1. The magnitudes of low-frequency signals are thus not altered, and the high-frequency noise is significantly reduced. The counts data at low frequencies are not changed much by the optimal filters. Also, the majority of noise removed centered around 10−2 s−1. This implies that the optimal filters remove striping information while retaining large-scale signals. The contours over the dark blue shaded areas all have the value of 0.01 because of the oscillations in response function values. For scene counts, the response functions at window channels 1–2 and 16 decrease from 1 to 0 at higher frequencies, suggesting that more signals are retained. It agrees with the fact that only two IMFs are removed, compared to three IMFs at other channels. Although corrections might be different among ATMS channels, warm load temperatures do not change as the channel number changes. Figure 8 shows the cost functions, weighting coefficients, and response functions for warm load temperatures.
Response functions for (top) warm counts, (middle) cold counts, and (bottom) scene counts calculated with the weighting coefficients in Fig. 5. Contours over dark blue shaded areas all have the value of 0.01 because of oscillations of the response functions.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
(a) Normalized cost function as a function of filter span N for the warm load temperature. The number of scanlines involved in the optimal filter is shown by the circle. (b) Weighting coefficients and (c) response function for warm load temperatures.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
c. Comparison between the optimal filters and the boxcar filters
Figures 9 and 10 show the warm counts and cold counts before and after application of optimal filters at channels 8 and 22, respectively. After the optimal filters are applied, warm counts and cold counts become much smoother without any visible noise at both channels while the larger-scale variations are kept, proving the effectiveness of the optimal filters. Conventionally, 17-point boxcar filters are used to smooth warm counts and cold counts. Figure 11 shows the variations in warm counts and cold counts after applying both the optimal filter and the boxcar filter. Compared with the optimal filter, the boxcar filter fails to smooth out all visible noise and significantly reduces the magnitudes of the minimum and maximum values.
Variations in (a) warm counts and (b) cold counts along 700 scanlines (i.e., a swath between ±55°N) before (gray lines) and after (red lines) removing three IMFs at channel 8.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
As in Fig. 9, but for channel 22.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
Variations in (a) warm counts and (b) cold counts with the optimal filter (red lines) and 17-point smoothing (blue lines) for channel 8.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
Response functions for channel 8 after application of the boxcar filter and the optimal filter, both with the same filter widths of 8, were also calculated. Figure 12 shows that the response function for the optimal filter falls from 1 to around 0 when the frequency increases. The magnitudes of low-frequency signals remain constant while those of high frequencies are significantly reduced. The response function for the boxcar filter starts to decrease sharply at frequencies lower than 10−2 s−1, implying that the boxcar filter suppresses low-frequency signals that should be retained. Another problem is that in the high-frequency range, where the major part of the noise still exists, the oscillatory behavior of the response function of the boxcar filter hinders this filter from completely removing the actual data noise.
Variations in the response function as a function of frequency for the 17-point filter (blue line) and the optimal filter (red line) applied to warm counts of channel 8. The red circles show the response function for channel 12 after application of the optimal filter. The response functions for the cold counts are the same as those shown here (figure omitted).
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
d. The effects of optimal filters on antenna temperatures
Smoothed warm counts, cold counts, and warm load temperatures are commonly used to calculate antenna temperatures. Scene counts are not smoothed. Figure 13 shows antenna temperatures for ATMS channel 8 at nadir calculated with and without applying the optimal filter to scene counts. Warm counts, cold counts, and warm load temperatures are all smoothed here using the optimal filter. Even if noise in the warm counts, cold counts, and warm load temperatures are effectively smoothed out, antenna temperatures are still contaminated with striping noise if the scene counts are not smoothed (Fig. 13b). This confirms the necessity of smoothing the scene counts.
(a) Variations in antenna temperature for channel 8 at nadir with (red) and without (blue) applying the optimal filter on the scene counts. Warm counts, cold counts, and warm load temperatures are all smoothed. (b) Antenna temperatures at channel 8 without smoothing scene counts.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
Figure 14 shows the global distributions of the striping noise extracted from antenna temperatures for ATMS channel 8. The destriping algorithm is also applicable to observations on other times. Figure 15 gives the regional distributions of the O − B differences in ATMS channel-8 antenna temperatures before (Fig. 1b) and after destriping on 24 February 2012 (Fig. 15a) and 1 March 1 2012 (Figs. 15c,d). The striping noise is ~0.3 K for channel 8, which agrees well with the results described by Qin et al. (2013). Striping patterns are faintly visible in the O − B field before destriping (Fig. 15b). These striping patterns are much less visible after destriping (Fig. 15c).
Striping noise (K) removed by the optimal symmetric filter for ATMS channel 8 at the ascending node on 24 Feb 2012.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
(a) ATMS channel-8 antenna temperature differences between observations and model simulations (i.e., O − B) on 24 Feb 2012 after the destriping using the optimal symmetric filter. ATMS channel-8 antenna temperatures between observations and model simulations (i.e., O − B) on 1 Mar 2012 (b) before and (c) after the destriping using the optimal symmetric filter.
Citation: Journal of Atmospheric and Oceanic Technology 36, 7; 10.1175/JTECH-D-18-0191.1
5. Summary and conclusions
An along-track striping phenomenon has been detected in global O − B distributions of ATMS temperature-sounding channels. The EEMD method is typically employed to characterize the noise in warm counts, cold counts, warm load temperatures, and scene counts. However, this method is not convenient for operational applications. The development of a set of optimal filters that can reduce noise in calibration counts as efficiently as the EEMD does is thus desirable. The conventionally used boxcar filters in satellite calibration tend to alter low-frequency weather signals when suppressing high-frequency noise. In this study, four sets of optimal symmetrical filters were designed and developed for the calibration counts of all 22 ATMS channels. The optimal filters efficiently removed striping noise within antenna temperatures while keeping the large-scale features intact. The necessity of smoothing the scene counts is further confirmed. If calibration counts are smoothed but scene counts are not, the striping noise will still exist and remain visible in global O − B distributions. Further investigation into the root cause of the striping noise is needed and impacts of striping noise on ATMS data applications in NWP and climate studies will be reported on in follow-on papers.
Acknowledgments
This research was supported by NOAA Grant NA14NES4320003. The authors thank Dr. Yuan Ma who conducted some work during her Ph.D. studies. The software developed to do the calculations in this study is available by contacting the first author at xtian15@terpmail.umd.edu.
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