Calibration of Suomi national polar-orbiting partnership advanced technology microwave sounder

Authors


Abstract

[1] The Suomi National Polar-Orbiting Partnership (NPP) satellite was launched on 28 October 2011 and carries the Advanced Technology Microwave Sounder (ATMS) on board. ATMS is a cross-track scanning instrument observing in 22 channels at frequencies ranging from 23 to 183 GHz, permitting the measurements of the atmospheric temperature and moisture under most weather conditions. In this study, the ATMS radiometric calibration algorithm used in the operational system is first evaluated through independent analyses of prelaunch thermal vacuum data. It is found that the ATMS peak nonlinearity for all the channels is less than 0.5 K, which is well within the specification. For the characterization of the ATMS instrument sensitivity or noise equivalent differential temperatures (NEDT), both standard deviation and Allan variance of warm counts are computed and compared. It is shown that NEDT derived from the standard deviation is about three to five times larger than that from the Allan variance. The difference results from a nonstationary component in the standard deviation of warm counts. The Allan variance is better suited than the standard deviation for describing NEDT. In the ATMS sensor brightness temperature data record (SDR) processing algorithm, the antenna gain efficiencies of main beam, cross-polarization beam, and side lobes must be derived accurately from the antenna gain distribution function. However, uncertainties remain in computing the efficiencies at ATMS high frequencies. Thus, ATMS antenna brightness temperature data records (TDR) at channels 1 to 15 are converted to SDR with the actual beam efficiencies whereas those for channels 16 to 22 are only corrected for the near-field sidelobe contributions. The biases of ATMS SDR measurements to the simulations are consistent between GPS RO and NWP data and are generally less than 0.5 K for those temperature-sounding channels where both the forward model and input atmospheric profiles are reliable.

1 Introduction

[2] On 28 October 2011, the Suomi National Polar-Orbiting Partnership (SNPP) satellite was successfully launched into an orbit which has an inclination angle of 98.7° to the equator and is 824 km above the Earth. On board the SNPP satellite, the Advanced Technology Microwave Sounder (ATMS) is a cross-track scanning instrument and has 22 channels at frequencies ranging from 23 to 183 GHz for profiling the atmospheric temperature and moisture under clear and cloudy conditions. Table 1 summarizes the general information of the ATMS 22 channels. So far, ATMS data including calibration, geolocation, telemetry, and housekeeping have been processed at the ground Interface Data and Processing Segment (IDPS) since the SNPP launch. ATMS data was declared at the provisional maturity level on 3 January 2013. The ATMS antenna brightness temperature data record (TDR) and sensor data record (SDR) have been distributed to the user community from NOAA's Comprehensive Large Array-Data Stewardship Systems (CLASS) for various applications.

Table 1. Requirements and Characteristics of the ATMS 22 Channels, Including the Channel Weighting Function Peaks at a US Standard Atmospheric Condition
ChannelCenter Frequency (GHz)Maximum Bandpass Width (GHz)Quasi PolarizationAccuracy (K)NEΔT (K)Static Beamwidth (deg)Weighting Function Peak (hPa)
123.80.27QV1.000.705.2Window
231.40.18QV1.000.805.2Window
350.30.18QH0.750.902.2Window
451.760.40QH0.750.702.2950
552.80.40QH0.750.702.2850
653.596±0.1150.17QH0.750.702.2700
754.40.40QH0.750.702.2400
854.940.40QH0.750.702.2250
955.50.33QH0.750.702.2200
1057.290.33QH0.750.752.2100
1157.29±0.2170.078QH0.751.202.250
1257.29±0.322±0.0480.036QH0.751.202.225
1357.29±0.322±0.0220.016QH0.751.502.210
1457.29±0.322±0.0100.008QH0.752.402.25
1557.29±0.322±0.00450.003QH0.753.602.22
1688.22.0QV1.000.502.2Window
17165.53.0QH1.000.601.1Window
18183.31±7.02.0QH1.000.801.1800
19183.31±4.52.0QH1.000.801.1700
20183.31±3.01.0QH1.000.801.1500
21183.31±1.81.0QH1.000.801.1400
22183.31±1.00.5QH1.000.901.1300

[3] Preliminary investigations of ATMS data quality and its potential applications were discussed elsewhere. Weng et al. [2013] provided ATMS channel specifications and bias characteristics and illustrated a capability of ATMS to provide more detailed thermal structures of tropical cyclones than its heritage predecessors. The scan angle-dependent features in the ATMS antenna brightness temperatures were analyzed using its pitch-over maneuver data [Weng et al., 2013]. It was found that the contributions of spacecraft radiation through the near-field sidelobes or the emission from the flat reflector (E. Kim et al., S-NPP ATMS instrument pre-launch and on-orbit performance evaluation, submitted to Journal of Geophysical Research: Atmospheres, 2013) are significant and result in the scan angle-dependent ATMS antenna brightness temperatures. The scan angle biases at ATMS upper level sounding channels were further quantified by using the Global Positioning System (GPS) Radio Occultation (RO) data as inputs to the radiative transfer model [Zou et al., 2013]. Today, ATMS radiance data are successfully assimilated into the NOAA global and regional forecast models and the ECMWF global forecast system. The impacts of the ATMS data assimilation on global and regional forecasts can be found in the studies of Bormann et al. [2013] and Zou et al. [2013].

[4] This work describes in details the ATMS calibration process from raw data records to the antenna brightness temperatures and sensor data records. In section 2, the ATMS instrument characteristics are presented. In section 3, the ATMS radiometric calibration procedure is described with respect to the two-point calibration algorithm. Section 4 presents the methodology for ATMS noise sensitivity characterization. The algorithms of ATMS TDR to SDR conversion are highlighted in section 5. Independent on-orbit SDR accuracy assessments using either the NCEP GFS 6 h forecasts or the collocated GPS RO as inputs to the NWP Community Radiative Transfer Model (CRTM) are given in section 6. Section 7 summarizes the overall ATMS performances from our calibration and validation research.

2 Instrument Description

[5] ATMS scan angle ranges within ±52.725° from the nadir direction. It has 22 channels with the first 16 channels primarily for temperature soundings from the surface to about 1 hPa (~45 km) and the remaining six channels for humidity soundings in the troposphere from the surface to about 200 hPa (~15 km). The ATMS channels 3–16 have a beam width of 2.2°, which is smaller than that of the corresponding AMSU-A channels 3–16. However, the beam width of the ATMS channels 1–2 is 5.2°, which is much larger than that of the corresponding AMSU-A channels 1–2. The ATMS channels 17–22 have a beam width of 1.1°, which is the same as that of the AMSU-B and MHS channels.

[6] Figure 1 shows a schematic diagram of the assembling position of ATMS on the SNPP platform. The antenna reflectors rotate counterclockwise relative to the spacecraft direction of motion (i.e., the x direction) to complete three revolutions in 8 s. The scan mechanism is synchronized to the spacecraft clock with a “sync” pulse every 8 s (i.e., at every third revolution). As shown in Figure 2, each ATMS scan cycle is divided into three segments. In the first segment, the earth is viewed at 96 different scan angles, which are distributed symmetrically around the nadir direction. Such 96 ATMS field-of-view (FOV) samples are taken “on the fly” with each FOV sample representing the midpoint of a brief sampling interval of about 18 ms. With a scan rate of 61.6° per second, the angular sampling interval is 1.11°. Therefore, the angular range between the first and last (i.e., 96th) sample centroids is 105.45° (i.e., ±52.725° relative to nadir). As soon as completing one scan line, the antenna accelerates and moves to a position that points to an unobstructed view of space (i.e., between the Earth's limb and the spacecraft horizon). Then it resumes the same slow scan speed as it scans across the Earth scenes. In this period, four consecutive cold calibration measurements are taken. Next, the antenna accelerates again to the zenith direction where the blackbody target is located, and takes four consecutive warm calibration measurements with the same slow scan speed. Finally, it accelerates back to the starting position and then slows down to the normal scan speed for continuing the next scan cycle. More details of the ATMS scan mechanism can be found in [JPSS ATMS ATBD, 2011].

Figure 1.

Schematic diagram of ATMS instrument layout [JPSS ATMS ATBD, 2011].

Figure 2.

ATMS scan cycle during which 96 Earth views, four cold and four warm calibrations are made. The angle at each cold calibration position is defined with respect to the y axis of the anti-Sun direction.

[7] ATMS has two sets of receiving antenna and reflector. One serves for channels 1–15 with frequencies below 60 GHz and another serves for channels 16–22 with frequencies above 60 GHz. Each receiving antenna is paired with a plane reflector mounted on a scan axis at a 45° tilt angle so that the incoming radiation is reflected from a direction perpendicular to the scan axis into a direction along the scan axis (i.e., a 90° reflection) (see Figure 3). With the scan axis oriented in the along-track direction, this results in a cross-track scan pattern. The reflected radiation is focused by a stationary parabolic reflector onto a dichroic plate, and then either reflected to or passed through to a feedhorn. Each aperture/reflector serves two frequency bands for a total of four bands.

Figure 3.

Schematic diagram of ATMS antenna subsystem. The top portion shows the antenna subsystem for K/Ka and V bands whereas the lower portion is for W/G bands.

3 ATMS Radiometric Calibration

[8] ATMS antenna/receiver system measures the radiation from two calibration sources during every scan cycle. The first source is the well-known cosmic background radiation. This source (often called as “cold space”) is viewed immediately after the Earth has been scanned. The second source is an internal blackbody calibration target (often called as “warm load”), whose physical temperature is the same as the instrument internal ambient temperature. This warm source is viewed immediately after the space calibration view. Every scan cycle (8/3 s) contains the above three consecutive views: Earth scene, cold space, and warm calibration measurements. Such a thorough radiometer calibration procedure allows the most impacts from ATMS system gain variations to be automatically eliminated since the two calibration measurements used for computing the gain involve the same optical and electrical signal paths as that of the Earth scene measurements. Thus, ATMS has an advantage over those calibration systems using switched internal calibration sources, which yields the calibration measurements having slightly different signal paths than that of the Earth scene measurements.

[9] The two calibration measurements are used to accurately determine the so-called radiometer transfer function, which converts the measured digitized output (i.e., counts) to a radiometric brightness temperature [JPSS ATMS ATBD, 2011]. The ATMS radiometric calibration flow chart corresponding to the interface data processing system (IDPS) is provided in Figure 4. The current ATMS antenna brightness temperature is obtained through the following equation:

display math(1)

where Qch is the channel based (subscript, ch) quadratic correction term; μ is a free parameter defined in [Mo, 1999]; x is a function of the cold space temperature and calibration warm target temperatures (see Appendix A); math formula is the averaged gain function at the ith scan line, defined via

display math(2a)
display math(2b)
display math(2c)
Figure 4.

ATMS radiometric calibration flow chart corresponding to the process in Suomi NPP ground processing system. Np is the number of measurements made at every scan line for warm and cold targets. TB denotes the brightness temperature in Kelvin.

[10] The other terms used in equations (1), (2a), (2b), and (2c) are that math formula is the warm load brightness temperature; math formula is the scene count; math formula is the warm load count at the ith scan line of the jth sample, math formula is the cold space count at the ith scan line of the jth sample; Wi is the weighting coefficient obtained from using either a triangular or boxcar function for averaging the warm and cold counts of (2Ns + 1) consecutive scan lines; and Gch(i) is the calibration gain at the ith scan line. Overbar on each variable represents an average over a number of scan lines.

[11] Calculations of the averaged warm load and cold space counts, math formula and math formula, depend on the weighting coefficients as well as the number of scan line involved in the averaging (i.e., 2Ns + 1). For example, with the application of a triangular function, the weighting coefficients of all ATMS channels for the kth scan line are averaged as follows:

display math(3)

[12] Other details of the radiometric calibration from radiance to brightness temperature can be found in Appendix A.

[13] The nonlinearity parameter, Qch in equation (1) is estimated using the prelaunch thermal vacuum (TVAC) data sets that are measured at different scene temperatures. For SNPP ATMS TVAC test, the scene temperature is typically measured between 93 and 330 K. However, for ATMS on-orbit calibration, the cold calibration temperature is approximately 3 K. Thus, the nonlinearity value must be estimated by extrapolating the TVAC data down to 3 K. In general, the nonlinear parameter Qch can be expressed as a quadratic function of scene temperature (Tb,ch) as

display math(4)

where bi,ch (i = 0, 1, 2; ch = 1, …, 22) are unknown coefficients. The values of them can be obtained by applying a least square fit to the TVAC data measured within the temperature range of 93 to 330 K. Then, by applying these coefficients back into equation (4), one can compute Qch for all scene temperatures within and beyond the range of 93 to 330 K. One example of bi,ch is given in Table 2. Figure 5 presents an example of the Qch(Tb,ch) of ATMS channel 1, obtained from applying the TVAC measured scene temperatures for cold plate (CP) at 5°C from redundancy configuration 1 (RC1). The peak nonlinearity is located near 170 K, which is about in the middle between 3 and 330 K. Table 3 provides the maximum nonlinearity, math formula, for a scene temperature range between 3 K and 276 K for all 22 ATMS channels and the 4 RCs. The values derived from our analysis, which is labeled as STAR (i.e., the Center for Satellite Applications and Research), are consistent with those derived from the Northrop Grumman Electronic Systems (NGES) analysis. Table 4 lists the nonlinearity values at other cold plate temperatures from four RCs (also, see the NGES Technique Report 14029B, 2007).

Table 2. An Example Set of Quadratic Coefficients From Fitting the Nonlinearity Data Measured for ATMS CP RC1 at +5°Ca
 NGESSTAR
Chan.b0b1b2 (× 10−4)b0b1b2 (× 10−4)
  1. aThe fitting coefficients are based on data within the scene temperature of 93 K to 330 K. For each RC, the mean quadratic coefficients are derived at three separate instrument temperature conditions (+20°C, +5°C, and10°C).
1−0.88100.0072−0.1370−0.88140.0072−0.1371
2−0.70100.0047−0.0691−0.70150.0047−0.0692
3−0.16100.0038−0.1080−0.16080.0038−0.1079
4−0.29700.0055−0.1480−0.29750.0055−0.1481
5−0.28700.0054−0.1460−0.28740.0054−0.1461
6−0.07800.0027−0.0772−0.07870.0027−0.0774
7−0.06660.0027−0.0785−0.06660.0027−0.0785
8−0.23600.0049−0.1370−0.23630.0049−0.1371
90.04790.0007−0.02240.04750.0007−0.0225
10−0.21500.0050−0.1430−0.21570.0050−0.1432
11−0.14400.0043−0.1250−0.14410.0043−0.1250
12−0.16800.0044−0.1280−0.16800.0044−0.1280
13−0.15200.0040−0.1120−0.15170.0040−0.1119
140.09530.0013−0.04850.09270.0014−0.0492
15−0.03210.0029−0.0924−0.03410.0030−0.0930
16−1.51000.0110−0.1790−1.50810.0110−0.1786
17−0.48700.0080−0.2080−0.48380.0080−0.2072
18−0.22700.0057−0.1600−0.22430.0057−0.1594
19−0.22900.0059−0.1660−0.22640.0058−0.1654
20−0.32400.0071−0.1960−0.32010.0071−0.1951
21−0.22800.0060−0.1660−0.22230.0059−0.1646
22−0.29400.0070−0.1950−0.28990.0070−0.1939
Figure 5.

Nonlinearity of ATMS channel 1, calculated for cold plate (CP) at 5°C for redundancy configuration 1 (RC1). The data from the thermal vacuum experiments are shown as circles on the curve. Black solid curve represents the regression curve. Dashed line represents the peak nonlinearity.

Table 3. The Peak Nonlinearity Values for All 22 Channels for CP RC1, RC2, RC5, and RC6 at +5°C, Obtained From a Temperature Range of 3–276 K
Chan.RC1RC2RC5RC6
NGESSTARNGESSTARNGESSTARNGESSTAR
10.25530.25540.27580.27600.28130.28150.28690.2873
20.12870.12890.15050.15080.15040.15090.15430.1547
30.20120.20110.21430.21430.24780.24800.19380.1941
40.27580.27600.28320.28350.26270.26270.27020.2706
50.27200.27220.29250.29250.28880.28910.27390.2741
60.14380.14420.17230.17280.19940.19990.19560.1961
70.14630.14620.15520.15540.14220.14220.14680.1471
80.25530.25540.26270.26280.27580.27580.25900.2590
90.04170.04200.05850.05860.07940.07920.06880.0690
100.26640.26680.22540.22570.21990.22020.22360.2241
110.23290.23300.27760.27780.33910.33950.30180.3020
120.23850.23850.20680.20690.24040.24020.23850.2385
130.20870.20850.15630.15720.17890.17870.15040.1502
140.09040.09160.09220.09310.16450.16400.13230.1329
150.17220.17330.23100.23160.28320.28180.31300.3144
160.33350.33270.34840.34740.33350.33280.33540.3340
170.38750.38610.35590.35470.38750.38700.34280.3421
180.29810.29690.31120.30970.30370.30290.28320.2817
190.30930.30810.30740.30640.32610.32460.31300.3115
200.36520.36340.34470.34310.32980.32910.33720.3357
210.30930.30670.28130.27930.30370.30210.32050.3184
220.36330.36140.30180.30080.35400.35250.36330.3615
Table 4. The Peak Nonlinearity Values for All 22 Channels for CP RC1, RC2, RC5, and RC6 at (a) −10°C, (b) +5°C, and (c) +20°C, Given by the NGES Technique Report 14029B
Chan.NGES Technique Report 14029B
RC1RC2RC5RC6
(a) at −10°C
10.22700.23400.22300.2190
2−0.0200−0.0260−0.0190−0.0280
30.16100.16300.18200.1660
40.21500.22200.20900.2140
50.21500.21500.22100.2140
60.12400.14900.14700.1290
70.13500.12700.12200.1440
80.21600.22200.23000.2280
90.02000.05000.06600.0580
100.15600.16200.15800.1770
110.23800.19400.20300.1770
120.16300.12900.15700.1920
130.10300.03000.06300.0790
140.0510−0.00500.00800.0480
150.11800.23700.17700.2080
160.34000.33300.33300.3440
170.38700.34600.38200.3560
180.29400.33800.30600.2890
190.30400.34500.33300.2940
200.35000.34800.36200.3250
210.30900.34600.33500.3150
220.40400.40200.39100.3270
(b) at +5°C
10.25400.27400.28000.2870
20.12800.15000.15000.1540
30.20000.21300.24700.1930
40.27500.28200.26100.2700
50.27100.29100.28800.2730
60.14300.17200.19900.1950
70.14600.15500.14200.1460
80.25400.26200.27500.2580
90.04200.05800.07900.0690
100.26500.22500.22000.2220
110.23300.27600.33900.3000
120.23800.20600.23900.2380
130.20800.15600.17800.1500
140.09000.09200.16400.1320
150.17200.22900.28200.3120
160.33300.34700.33300.3350
170.38700.35500.38600.3420
180.29800.31000.30200.2830
190.30800.30500.32500.3120
200.36400.34400.32800.3360
210.30800.27900.30300.3190
220.36200.30000.35200.3620
(c) at +20°C
10.35400.35200.35700.3470
20.53200.53300.56100.5540
30.25900.29500.26900.2800
40.32900.31700.33400.3270
50.32300.33500.33900.3320
60.23700.22100.24100.2080
70.17200.20000.19200.1870
80.31800.33800.33000.2990
90.10800.11400.09400.0910
100.27700.28700.30900.3030
110.34000.32500.31300.3290
120.28400.27200.32100.2890
130.19900.28200.22000.1750
140.17000.11600.18000.2010
150.18400.54400.40500.2350
160.40600.40600.38900.3990
170.47200.44000.44000.4160
180.30800.35300.30100.3400
190.36700.32500.32500.3680
200.41700.33500.39000.3530
210.37200.37900.40200.3330
220.42500.42500.37600.4090

[14] In the ATMS TDR processing algorithm, the blackbody brightness temperature, math formula, is determined from its physical (or kinetic) temperature measured by the embedded platinum resistance thermometers (PRTs). The blackbody and cold space calibration counts, Cw and Cc, are averaged over several calibration cycles before being used in equation (2c) to obtain the calibrated gain.

[15] The ith channel cold space brightness temperature, math formula (ch = 1, …, 22), is estimated by adding two correction terms to the cold space temperature, Tc. The first correction term, math formula, takes into account the Earth radiation into the antenna side lobes and the second correction term, math formula, corrects the error introduced by the Rayleigh-Jeans (RJ) approximation. Specifically, math formula is written as

display math(5)

[16] Details on these two correction terms can be found in Weng et al. [2012] and Weng and Zou [2013].

[17] The averaged warm load temperature for the ith scan is determined from the multiple PRT temperatures Tw(k,j) (k = i − Ns, …, i + Ns; j = 1, …, Np). Depending on user's need, a temperature-dependent bias correction from either ATMS telemetry file (i.e., math formula) or user-defined values can be applied via equation (6).

display math(6)

where Tw(k,j) is the jth PRT temperature for the kth scan; math formula is the energy contributed from the channel-dependent receiving shelf temperature, and Wi,j is the weighting coefficient. If a PRT is deemed to be bad by user, it is then excluded from the calibration process and the corresponding weighting coefficient is set to zero in the parameter file. Values of math formula are provided in Table 7. Theoretically, the warm load temperature also needs to be adjusted for the error introduced by Rayleigh-Jeans' approximation, i.e.,

display math(7)

[18] Since the warm load temperature is normally operating above 280 K, the errors are typically negligible at lower ATMS frequencies [Weng and Zou, 2013].

4 ATMS Sensitivity

[19] The noise equivalent delta temperature (NEDT) for a specified channel describes the precision of measured radiances or brightness temperatures at the observing frequency. It is determined by computing the standard deviation of the brightness temperature of the warm calibration target, math formula as

display math(8)

where math formula is related to the warm count, math formula from the previously introduced linear calibration algorithm:

display math(9)

[20] Substituting equation (9) into equation (8) results in the following expression for computing NEDT at each ATMS channel from the recorded multiple readings of ATMS radiometric count and the gain function:

display math(10)

[21] The first summation in equation (10) represents an averaged deviation (by a factor of 4) of the four warm calibration measurements at the ith scan line and the second summation represents an average over a total of N scan lines. The mean warm counts and mean calibration gain are computed using equations (2a) and (2c), respectively.

[22] The standard deviation quantifies the spread of the statistical distribution of the measuring values around the mean. However, it is not always an appropriate parameter for describing a spread of the statistical distribution of the measuring values around the mean that is nonstationary. The ATMS warm calibration counts are subject to considerable long-term variations due largely to temperature-dependent instrument gain variations; these variations are removed by on-orbit calibration, and therefore do not contribute to actual radiometric sensitivity (i.e., NEDT). Therefore, to better describe the precision of ATMS radiances or brightness temperatures at the observed frequency, we use the so-called Allan deviation [Allan, 1987; Allan et al., 1997] , which is defined as follows:

display math(11)

where N is the total number of data and m is the number of samples.

[23] Figure 6 presents the variations of the along-track averaged warm counts of ATMS channel 1 from an ATMS orbit data on 24 February 2012 (Figure 6a), as well as the variations of the mean, the standard deviation, and the Allan deviation of the warm counts versus a large range of sample size (Figure 6b). As seen in Figure 6b, the mean is not stationary and it decreases as the sample size increases. The standard deviation is also not stationary but it increases as the sample size increases. However, it is clear that the Allan deviation is much more stable over the whole range of sample size, which makes the Allan deviation more objective, thus a more proper measure to the ATMS channel precision.

Figure 6.

(a) Variations of the along-track 17-scanline averaged warm count of ATMS channel 1 on the first ATMS swath on 24 February 2012. (b) Variation of the mean (blue, y axis on the right) and the standard deviation (red, y axis on the left) and the overlapping Allan deviation (green, y axis on the left) of the 17-scanline averaged warm counts with sample size.

[24] Figure 7 compares the NEDT values from equation (10) and the Allan deviation from equation (11). Both equations average data of 17 scan lines. It is noticed that the NEDT values (blue) for all ATMS channels are about 3–5 times larger than the Allan deviations (red). This is because the standard deviation used to quantify the sensitivity around the mean is not stationary. One related issue is that although the noises in ATMS measured brightness temperatures are well within the specification, the impact of the flicker noise shown in the measurements cannot be neglected. Mitigation of the flicker noise requires a significant effort and is beyond the scope of this paper. Since the launch of SNPP, ATMS NEDT is under monitoring, and is very stable and within specification (http://www.star.nesdis.noaa.gov/icvs/NPP/ipm_telemetry_npp_atms.php). The ATMS NEDT values are generally higher than the corresponding AMSU-A values mainly because the ATMS integration time is much shorter than that of AMSU-A [Weng et al., 2013]. Specifically, the ATMS integration time for all ATMS channels is about 18 ms while that for AMSU-A channels 1–2 and 3–15 are 165 ms and 158 ms, respectively. Thus, when averaged for equivalent sampling intervals, the sensitivity performance of ATMS is better than that for AMSU-A [Zou et al., 2013].

Figure 7.

Variations of NEDT and Allan deviation with channel number. The sample size (N) is 150 and the averaging factor (m) for the warm counts is 17. NEDT values (standard deviation, blue); Allan deviation (red).

5 ATMS TDR to SDR Algorithm

[25] For a cross-track scanning microwave radiometer, pure vertical (V) or horizontal (H) polarization measurements only occur at the nadir direction. At the other scan angles, the measurements represent a mixed contribution from both V and H polarizations. Thus, it is necessary to define the quasi-vertical and quasi-horizontal antenna brightness temperatures (TDR), math formula and math formula, via [Bormann et al., 2013] the following:

display math(12a)
display math(12b)

where math formula and math formula are the copolarized antenna main beam efficiencies; math formula and math formula are the cross-polarized antenna main beam efficiencies; math formula and math formula are the copolarized and cross-polarized antenna sidelobe beam efficiencies, respectively; and math formula and math formula are the cold space copolarized and cross-polarized sidelobe beam efficiencies. It is worth pointing out that each ATMS frequency channel only measures one single polarization, i.e., either horizontal or vertical (listed in Table 1). Therefore, in equations (12a) and (12b) there are, correspondingly, only one copolarization and one cross-polarization antenna beam efficiencies in pair for each of the antenna main beam, antenna sidelobe, and cold space sidelobe. Values of all the beam efficiencies are summarized in Tables 5, 6, and 7.

Table 5. ATMS Antenna Main Beam Efficiencies Analyzed From Copolarization and Cross-Polarization Antenna Gain Distribution Functions
Channelmath formula (%)math formula (%)
B1B48B96B01B48B96
195.595.395.90.840.730.81
297.096.496.80.640.650.64
396.295.696.31.011.050.90
496.295.796.60.950.940.70
596.295.896.10.870.910.98
696.395.996.20.880.941.04
796.596.196.60.870.860.82
896.696.196.20.900.901.13
996.796.296.60.900.880.86
1097.397.197.20.920.910.93
1197.397.197.20.920.910.93
1297.397.197.20.920.910.93
1397.397.197.20.920.910.93
1497.397.197.20.920.910.93
1597.397.197.20.920.910.93
1690.991.391.74.714.654.54
1786.283.986.63.713.405.18
1886.585.285.23.313.465.12
1986.087.489.34.032.251.85
2086.087.489.34.032.251.85
2186.087.489.34.032.251.85
2286.087.489.34.032.251.85
Table 6. ATMS Antenna Sidelobe Earth Beam Efficiencies Analyzed From Copolarization and Cross-Polarization Antenna Gain Distribution Functions
Channelmath formula (%)math formula (%)
B1B48B96B01B48B96
12.303.102.010.560.540.35
21.552.251.530.350.370.22
31.712.461.740.450.510.44
41.932.491.830.430.450.33
51.862.401.800.470.500.39
61.752.321.720.440.510.44
71.662.211.660.440.430.32
81.622.111.540.370.460.45
91.632.131.610.330.410.34
101.181.471.120.270.280.26
111.181.471.120.270.280.26
121.181.471.120.270.280.26
131.181.471.120.270.280.26
141.181.471.120.270.280.26
151.181.471.120.270.280.26
161.342.121.451.331.360.87
173.835.683.491.731.831.66
185.105.304.801.411.591.51
195.105.304.801.411.591.51
205.175.375.011.441.370.95
215.175.375.011.441.370.95
225.175.375.011.441.370.95
Table 7. ATMS Antenna Sidelobe Cold Space Efficiencies Analyzed From Copolarization and Cross-Polarization Antenna Gain Distribution Functions During SNPP ATMS Thermal Vacuum Testsa
Channelmath formula + math formula (%)math formulamath formulamath formulaβ0β1
B1B48B96
  1. aCold space temperature is 2.73 K and the correction to the cold space temperature from uses of RJ approximation and the contributions to RJ cold space temperature from the sidelobe of the earth are shown. (pp = vv,hh; pq = vh,hv; Tc,RJ = 2.73 + ΔTc,RJ ).
10.780.290.950.0340.3980.0459990.05530.8123
20.490.360.760.1660.5280.0759990.03890.7167
30.600.380.580.1760.2200.0749990.04600.3781
40.520.420.570.1830.2060.086999−0.00100.4499
50.560.440.720.1890.2200.0830000.05270.3877
60.600.350.630.1940.2060.0859990.01440.4520
70.520.410.610.1980.2200.0889990.07300.4503
80.530.400.660.2020.2490.0879990.11330.4517
90.460.340.550.2160.2330.0759990.10490.4558
100.350.220.480.2160.2330.0850000.14190.5474
110.350.220.480.2160.2060.0840000.12710.5199
120.350.220.480.2160.2060.0879990.16750.4969
130.350.220.480.2160.2060.0609990.11900.5213
140.350.220.480.2160.2060.0104000.11870.5283
150.350.220.480.2160.2060.0420000.15830.6107
161.700.531.400.5060.6100.0159000.00651.1983
174.535.233.081.6380.1020.015500−0.06970.7106
183.694.423.361.9590.1260.015300−0.12000.9832
193.694.423.361.9590.1260.014699−0.06230.8911
203.413.592.891.9590.1260.015100−0.05250.8986
213.413.592.891.9590.1260.014399−0.01470.8773
223.413.592.891.9590.1260.016000−0.06891.0274

[26] The quasi-vertical and quasi-horizontal sensor brightness temperatures, math formula and math formula, are related to the pure vertically and horizontally polarized brightness temperatures, math formula and math formula, through the following relationships:

display math(13a)
display math(13b)

where θ is the scan angle. From equations (13a) and (13b), it is easy to see that both math formula and math formula vary with scan angle and are the same at the nadir and 45o scan angle.

[27] Polarization difference is only significant over an ocean surface. Figure 8 shows an example of the brightness temperatures estimated from both pure polarization and quasi-polarization at the selected ATMS channels. As shown in Figure 8, for all channels the brightness temperature differences between quasi-vertical and quasi-horizontal polarizations are correspondingly smaller than their counterparts from the pure polarizations.

Figure 8.

The brightness temperature with pure (dashed curve) and quasi- (solid curve) horizontal polarization (circle) and vertical (star) polarization states using the U.S/ standard atmospheric profile with sea surface wind speed being 5 m/s and sea surface temperature being 290 K.

[28] The last terms in equations (12a) and (12b), math formula and math formula, are considered as the radiation contributions from the antenna near-field sidelobe or other effects such as the emitted radiation from ATMS flat reflector (see E. Kim et al., submitted manuscript, 2013), and can be estimated from the ATMS pitch-maneuver data [Weng et al., 2013]. Using the ATMS pitch-maneuver data, the following relationships are derived:

display math(14a)
display math(14b)

where math formula and math formula (k = 0, 1) are the coefficients obtained by fitting the ATMS data during its pitch-maneuver period on 20 February 2012 [Weng et al., 2013], provided in Table 7. The antenna beam efficiencies for all ATMS channels are also listed in Table 7 as reference. For channels 16–22, the beam efficiencies have large uncertainties because of the high measurement noise level in the data sets. The values listed in Tables 5, 6, and 7 are derived without cutting the noise level in the ATMS antenna gain distribution data sets.

[29] Assuming math formula and math formula, equations (12a) and (12b) can be rewritten as

display math(15a)
display math(15b)

[30] For a fixed scan angle and a given surface condition, math formula and math formula are related to each other via the following empirical models:

display math
display math

where Ah(θ) and Av(θ) are functions depending on the scan angle. At scan angles of 0° and 45°, and for the channels that are not impacted by the surface polarization, Ah(θ) = 1 and Av(θ) = 1. Thus, equations (15a) and (15b) can be further written as

display math(16a)
display math(16b)

[31] Tables 5, 6, and 7 list all the coefficients needed for the above conversion between antenna temperatures (TDR) and brightness temperatures (SDR). Note that ATMS channels 1–3 and 16 have 1 to 4% polarization spillover radiation. Thus, a correction must be made to account for the contribution of polarization spillover effect between TDR and SDR conversions. Moreover, for ATMS W and G bands (channels 16–22), the beam efficiencies listed in the tables remain highly uncertain. The ATMS vendor, NGES, has provided the W and G band beam efficiencies; however, the results have not been verified by others. Further investigation on this issue is required. Thus, for ATMS W and G bands, the current TDR data are only corrected for the near-field sidelobe contributions for the SDR data by setting the antenna main beam efficiency to 1.

[32] For ATMS channels 1, 2, and 16, TDRs are converted to SDRs using the following equation:

display math(17a)

[33] For the other ATMS channels,

display math(17b)

6 SDR Assessment

[34] The above ATMS TDR to SDR conversion algorithm is tested by comparing the ATMS SDR products (O) with the corresponding NWP CRTM simulation results (B) using either the NCEP GFS 6 h forecasts or GPS RO data as inputs. The first O-B comparison is shown in Figure 9. In this comparison, the NCEP GFS forecast fields include 64 layers from surface to about 0.1 hPa. The CRTM simulations during the period of 20–26 December 2011 are averaged from all the data over the ocean surfaces. For ATMS channels 2 and 8, only those data sets with cloud liquid water path (LWP) being less than 0.03 kg/m2, (total precipitable water) TPW being less than 10 kg/m2, and surface wind speed being less than 7 m/s are analyzed. For ATMS channels 16 and 20, cloud LWP is less than 0.03 kg/m2 and surface wind speed is less than 7 m/s. Overall, as seen in Figure 9, the ATMS observations compared quite favorably with model simulations, especially for the temperature-sounding channel (channel 8). Possible reasons for the wider spread shown in the other three channels may be (1) cloud impacts (i.e., some clouds may still exist even after applying the above quality control) and (2) model uncertainties, especially for the water vapor sounding channels (i.e., channel 20).

Figure 9.

Scatterplots of ATMS SDR observations (OSDR) and model simulation (BSDR) for ATMS channels 2, 8, 16, and 20 over ocean under dry, clear-sky, and calm conditions using data during the period of 20–26 December 2011.

[35] ATMS observations are also compared with the simulations with GPS RO profiles as input to CRTM. Since the geolocation of the perigee point (also called tangent point) of a single RO profile varies with altitude, the collocation between ATMS observations and GPS RO are performed at each perigee point. On the other hand, a satellite measurement at a specific frequency represents a weighted average of radiation emitted from different layers of the atmosphere. The measured radiation is most sensitive to the atmospheric temperature at the altitude where the weighting function (WF) reaches a maximum [Zou et al., 2013]. For each channel, the altitude of the peak WF is lowest at the nadir and increases with the scan angle. Considering the geolocation change of the perigee point of a GPS RO profile with altitude, the geolocation of a GPS RO is used to match the altitude at which the ATMS WF at a channel reaches the maximum. The spatial difference between ATMS and GPS RO is less than 50 km. The altitude of the maximum WF is determined by inputting the U.S. standard atmosphere profile into CRTM (see Table 1).

[36] Besides a horizontal spatial separation of less than 30 km at the altitude of peak weighting function, the collocation criteria are set by a time difference of no more than half hour. If there are more than one ATMS pixel measurements satisfying these collocation criteria, the one that is closest to the related Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) sounding is chosen and others are discarded. Because surface state variables and parameters are not provided by COSMIC ROs, only upper level temperature-sounding channels are simulated using COSMIC GPS RO data.

[37] ATMS observations are only compared with simulations under clear conditions. Over oceans, a cloud detection algorithm similar to Weng et al. [2003] is applied to separate the data in clear-sky conditions over ocean from total ATMS measurements [Weng et al., 2012]. Figure 10a presents the spatial distribution of the ATMS observations that are collocated with COSMIC GPS RO data in clear-sky conditions over ocean and between 60°S–-60°N from 10 December 2011 to 31 March 2013. Less data are found in the tropics than in middle latitudes due to less GPS RO data. For GPS RO simulations, we only simulated ATMS SDR at channel 6 to 13 since the GPS RO profiles are most reliable with the midtroposphere to lower stratosphere. For channels 6–13, the mean biases between ATMS observations and GFS simulations, and those between ATMS observations and GPS RO simulations are positive and of similar magnitudes (Figure 10b). This consistency indicates that the ATMS SDR products perform well. Moreover, the standard deviations of the differences between ATMS observations and CRTM simulations with GFS 6 h forecasts are higher than the ATMS NEDT values (Figure 7) but smaller than those of the differences between ATMS observations and GPS RO simulations. It is worth mentioning that the standard deviations of the differences between ATMS observations and CRTM simulations with GFS 6 h forecasts are much higher than the ATMS NEDT values for humidity channels and surface-sensitive channels. Accurate simulations of brightness temperatures for those surface-sensitive channels remain challenging due to the limited accuracy of the forward modeling components such as surface emissivity.

Figure 10.

(a) Spatial distribution of ATMS measurements at 45° scan angle under clear-sky condition over ocean between 60°S and 60°N that are collocated with COSMIC RO profiles from 10 December 2011 to 31 March 2013. (b) Bias and (c) standard deviation of the differences between ATMS SDR observations and CRTM simulations with GFS 6 h forecasts (solid bar) and GPS RO profiles (dashed bar).

7 Summary and Conclusions

[38] Presented here is a thorough end-to-end ATMS calibration and validation study. In this paper, the ATMS Earth scene counts are calibrated to antenna brightness temperatures (TDR) through a two-point calibration algorithm with a quadratic nonlinear correction. The nonlinearity term is derived from the prelaunch TVAC data with a maximum value less than 0.5 K. After applying the nonlinear correction, the absolute accuracy of TDR for all ATMS channels is generally about 0.2 to 0.5 K, which meets the specification. Unlike AMSU-A/MHS calibration operating in radiance, ATMS calibration to TDR is directly carried out in brightness temperature based on the RJ approximation. Thus, the cold space temperatures are corrected to the apparent brightness temperatures prior to its use in the two-point calibration. In future, we plan to modify the current ground processing system into a full radiance space.

[39] The current algorithm for quantifying the precision of the ATMS radiometric measurements, NEDT, is described. The NEDT values for all the channels are well within the instrument specification. However, through the sensitivity study of NEDT and the Allan deviation, we found that the Allan deviation may be a better metric for precision.

[40] Also, a new ATMS TDR to SDR algorithm is developed in this paper. This conversion is very important since SDR products can be directly used in the NWP models for satellite data assimilation. One thing needs to be pointed out: the convertibility is not always unique if ATMS antenna subsystem has a significant polarization spillover effect and/or a sidelobe contribution from the nearby scene cells. While ATMS antenna gain distribution functions were measured during the prelaunch period, there remain some uncertainties in characterization of sidelobe and cross-polarization at high frequencies. At the conditions where ATMS brightness temperatures at quasi-vertical and quasi-horizontal polarization states are the same, the conversion from TDR to SDR becomes unique assuming all the sidelobe contributions are estimated. At 45° scan angle, ATMS SDR can be uniquely derived from its TDR and therefore directly compared with simulations. It is shown that the biases of ATMS SDRs with respect to GPS RO and GFS simulation are similar in magnitude. The largest biases are found for surface-sensitive channels at both low and high frequencies. Further investigation is planned to assess errors in the forward modeling associated with surface emissivity and surface parameters from GFS.

Appendix A: Conversion of Radiometric Calibration from Radiance to Brightness Temperature

[41] A radiometric calibration in radiance was derived as follows [Mo, 1999]:

display math(A1)
display math(A2)
display math(A3)
display math(A4)

[42] Here all variables in the equation should be channel specific. For simplicity, the channel subscript is omitted in all the following deviations. In the history of NOAA operational calibration, equation (A1) is expressed in a quadratic form

display math(A5)

[43] So the calibration coefficients, a0, a1, and a2 can be expressed as follows:

display math(A6)
display math(A7)
display math(A8)

[44] In the above radiometric calibration equations, the Earth scene counts are typically converted to the radiance. In general, the radiance describes the amount of electromagnetic energy radiated from an earth scene in a specified direction, a solid angle and a frequency interval. Thus, it can be computed by its kinetic temperature (T) and wave number (υ)as follows:

display math(A9)

where k is the Boltzmann constant; h is the Planck constant; c is the speed of light (in m), C1 = 2hc2 = 1.1909 × 10− 8 W m−2 sr−1 cm−1 cm3, and math formula cm K. Equation (A8) is known as the Planck radiation law.

[45] Assuming math formula, the exponential function in Planck function can be expressed in Taylor series:

display math(A10)

[46] Substituting the first-order approximation of the above Taylor expansion into equation (A8) results in the following linear relationship between the blackbody temperature (T) and radiance (Rν)

display math(A11)

[47] Equation (A10) is called the Rayleigh-Jeans (RJ) approximation to Planck's function. At the ATMS frequency range of 23.8 GHz ≤ f ≤ 190.3 GHz), C2υ is generally less than 10 K, thus, the temperature in equation (A9) must be above 100 K. Substituting (A10) into equation (A1) results in

display math(A12)
display math(A13)

[48] The accuracy of the radiance calculated from RJ approximation varies with frequency and temperature. The radiometric calibration is processed through uses of equation (A12). As a result, the two-point calibration is derived in brightness temperature form as

display math(A14)

where the linear and nonlinear terms are expressed as

display math(A15)
display math(A16)
display math(A17)

respectively, where

display math

[49] The maximum nonlinearity value can be derived by performing the derivative with respect to x which is f(x) = 1 − 2x. Using Taylor's expansion for f(x) = x(1 − x) at x0 = 0.5 which is equal to math formula, then

display math(A18)

If the first two terms in (A15) are kept for the nonlinearity term, where

display math(A19)

Acknowledgments

[50] The views expressed in this publication are those of the authors and do not necessarily represent those of NOAA. Xiang Wang is supported by the Chinese Ministry of Science and Technology project 2010CB951600.

Ancillary