# Assessments of F16 Special Sensor Microwave Imager and Sounder Antenna Temperatures at Lower Atmospheric Sounding Channels

Authors: Banghua Yan; Fuzhong Weng
Journal: Advances in Meteorology
 (2009)

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## Abstract

The main reflector of the Special Sensor Microwave Imager/Sounder (SSMIS) aboard the Defense Meteorological Satellite Program (DMSP) F-16 satellite emits variable radiation, and the SSMIS warm calibration load is intruded by direct and indirect solar radiation. These contamination sources produce antenna brightness temperature anomalies of around 2 K at SSMIS sounding channels which are obviously inappropriate for assimilation into numerical weather prediction models and remote sensing retrievals of atmospheric and surface parameters. In this study, antenna brightness temperature anomalies at several lower atmospheric sounding (LAS) channels are assessed, and the algorithm is developed for corrections of these antenna temperature anomalies. When compared against radiative transfer model simulations and simultaneous observations from AMSU-A aboard NOAA-16, the SSMIS antenna temperatures at 52.8, 53.6, 54.4, 55.5, 57.3, and 59.4 GHz after the anomaly correction exhibit small residual errors (<0.5 K). After such SSMIS antenna temperatures are applied to the National Center for Environmental Prediction Numerical Weather Prediction (NWP) model, more satellite data is used and the analysis field of the geopotential height is significantly improved throughout troposphere and lower stratosphere. Therefore, the SSMIS antenna temperatures after the anomaly correction have demonstrated their potentials in NWP models.


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## Body

## 1. Introduction

On October 18, 2003, the F16 satellite was successfully launched and carried the
first Special Sensor Microwave Imager/Sounder (SSMIS). The SSMIS instrument has
twenty four channels to measure the Earth’s radiation at frequencies between 19
and 183 GHz [1]. It is the first operational microwave satellite
radiometer for profiling temperature and humidity using a conical scanning mode
so that the viewing area and slant path remain nearly constant
as it scans the earth. The SSMIS observations also allow simultaneous
retrievals of surface and atmospheric parameters with a uniform spatial
resolution across the scan swath. However, the accuracy of SSMIS-derived
surface and atmospheric products is critically dependent on the accuracy of the
brightness temperature measurements.National
Oceanic and Atmospheric Administration (NOAA) receives the F16 SSMIS data in
both antenna brightness temperature data record (TDR) and sensor brightness
temperature data record (SDR) formats through a data sharing agreement with the
Defense Meteorological Satellite Program (DMSP). NOAA then distributes the data to the international user
community through the National Environmental Satellites, Data, and Information
Service (NESDIS). Here, TDR data contains observation time, geo-location,
earth-viewing antenna temperatures, cold counts, warm   counts, and so forth,
whereas SDR data contains the observation time, geolocation, earth-viewing
brightness temperatures [2]. Soon after launch of the SSMIS, some anomalies
were discovered in the TDR data for sounding channels primarily due to (a)  thermal emission by the main reflector and (b) unaccounted
solar radiation impinging on the calibration target [3–11]. Similar anomalies are also observed
in SSMIS SDR data.In
this study, the anomalies in the SSMIS antenna temperatures at the LAS channels
are characterized using the original information provided in the SSMIS TDR. In
Section2, the major characteristics of radiance anomalies at the SSMIS LAS
channels are described. Section 3 focuses on the methodology of the algorithm.
The SSMIS radiances with anomaly corrections are evaluated in Section 4.


## 2. SSMIS Radiance Anomalies at the LAS Channels

### 2.1. Brief Description of F16 SSMIS Instrument

The specifications of 24 SSMIS channels are
given in Table1. For reference purposes, the channels are grouped into four
subtypes corresponding to the lower atmospheric sounding (LAS) channels (e.g.,
channels 1–7), the upper atmospheric sounding (UAS) channels (e.g., channels
19–24), the imaging (IMA) channels (i.e., channels 8–11, and 17-18), and the
environmental (ENV) channels (e.g., channels 12–16), [1]. The
SSMIS consists of several major subsystems: antenna/calibration, receiver,
signal processing, scan drive, and deployment subsystems. The antenna/calibration subsystem includes the
main reflector, an array of feedhorns, a warm calibration load, and a cold
calibration reflector. The feedhorn array includes six corrugated
feedhorns.Table 1
Channel
characteristics of SSMIS sensor [1]. (1) Sampling refers to
along scan direction based on 833 km spacecraft altitude. (2) NEDT for
instrument temperature 0°C and calibration target 260 K with integration times of
8.4 msec for Channels 12–16; 12.6 msec for Channels 1–7, 24; and 25.2 msec for
Channels 19–23 and 4.2 msec for Channels 8–11, 17-18. (3) Number of subbands is
indicated by (n) next to individual 3-db width. (4) RCP denotes
right-hand circular polarization.)
ChannelCenter freq. (GHz)3-db width (MHz)Freq. stab. (MHz)Pol.NEDT (K)Sampling interval (km)150.338010V0.3437.5252.838910V0.3237.5353.59638010V0.3337.5454.438310V0.3337.5555.539110V0.3437.5657.2933010RCP0.4137.5759.423910RCP0.4037.581501642(2)200H0.8912.59183.31 ± 6.61526(2)200H0.9712.510183.31 ± 31019(2)200H0.6712.511183.31 ± 1513(2)200H0.8112.51219.3535575H0.33251319.3535775V0.31251422.23540175V0.43251537161675H0.25251637154575V0.20251791.6551418(2)100V0.3312.51891.6551411(2)100H0.3212.51963.283248 ± 0.2852711.35(2)0.08RCP2.7752060.792668 ± 0.3578921.35(2)0.08RCP2.7752160.792668 ± 0.357892 ± 0.0021.3(4)0.08RCP1.9752260.792668 ± 0.357892 ± 0.00552.6(4)0.12RCP1.3752360.792668 ± 0.357892 ± 0.0167.35(4)0.34RCP0.8752460.792668 ± 0.357892 ± 0.05026.5(4)0.84RCP0.937.5All SSMIS channels
are sampled every scan and a sampling period of 4.22 ms (corresponding to0.8°  azimuth scan increment)  is used for each channel. There
are 180 active sample positions where raw radiometric data of earth scenes are acquired
from each channel [2, 10]. These samples except for channels 8–11
and 17-18 are subjected to onboard flight software averaging in the along-scan
direction to improve the noise-equivalent difference temperature (NEDT) before
down-linking to the ground processing for final TDR calibration. For example,
for channels 1–7 and 24, three along-scan beams are averaged, resulting in 60
samples per scan; for channels 12–16, two adjacent along-scan beams are
averaged, resulting in 90 samples per scan; for channels 19–23, six along-scan
beams are averaged, resulting in 30 samples per scan, as summarized in Table 1.
For each scan, the feedhorns also pass beneath the stationary warm-load and
cold-space reflector calibration targets, where four samples of radiometric
counts for each calibration target are taken for all channels and are averaged
by the onboard flight software. The temperature of the warm load is provided by
three high-precision platinum resistance thermometer (PRT) probes.Once per rotation of the main reflector, the
energy from the Earth’s surface and atmosphere incident upon the reflector focuses on the feedhorn
assembly positioned in the reflector focal
plane. The receiver
subsystem accepts the energy from the six feedhorns and provided amplification,
filtering, and additional frequency multiplexing to output 24 discrete
frequency bands to the signal processing subsystem and then to the Operational Linescan System (OLS) under control of
the sensor signal processor and the flight software. The data are then
transmitted to the SSMIS ground processing by the OLS. Figure1 displays a block diagram of this process, which is
revised from Grumman [2]. In the SSMIS ground processing,
the TDR and SDR are further generated from the Sensor Data Records Processor  [2, 10]. Unfortunately, both main reflector emission and solar heating of
the warm calibration target occur in F16 SSMIS such that certain anomalies in
the SSMIS antenna temperatures are observed as illustrated next.Figure 1
SSMIS simplified block diagram [2].


### 2.2. F16 SSMIS Radiance Error Assessment

A powerful approach of monitoring the onorbit satellite instrument performance in satellite
cal/val research fields is to compare satellite-observed radiances with radiative
transfer model- (RTM-) simulated radiances. At microwave frequencies, the global brightness temperature
for oxygen sounding channels between 54 to 59 GHz can be accurately simulated
due to our knowledge of the oxygen absorption spectrum. It is also due to the
fact that radiation for these channels originates mainly from the atmosphere,
not the surface. As a result, at oxygen channels of 54.4, 55.5, 57.3, and 59.4 GHz, the simulation accuracy is mainly dependent on the temperature accuracy in
regions where the weighting function peaks.  For example, an error of 1 K in physical
temperature where the weighting function peaks can result in an error of 0.1 K
in simulated brightness temperature [1]. In this study, the Community RTM developed by the Joint Center
for Satellite Data Assimilation (JCSDA)   [12]  is employed to
simulate the brightness temperatures at SSMIS channels using the absorption
model developed by Rosenkranz [13]. Inputs of the absorption model consist of
temperature and water vapor profiles obtained from the global data assimilation
system (GDAS)  analysis by the National Center for Environmental Prediction
(NCEP). The performance of the GDAS analysis products is continuously monitored by the NCEP Environmental Modeling Center
(http://www.emc.ncep.noaa.gov/modelperf/). The root mean square error of GDAS temperature
profiles against radiosonde
measurements below 10 mb is smaller than 2 K, which results in an uncertainty
of about 0.2 K in simulations from 54 to 59 GHz. Initially, the errors in
simulated brightness temperatures are significantly less affected by the errors
in GDAS water vapor profile because they are not sensitive to water vapor
absorption. Also, the effects of cloud and rain are not taken into account in
these simulations due to the lack of information. This is reasonable for the
54.4, 55.5, 57.3, and 59.4 GHz channels because their weighting functions
typically peak above the absorption layer that consists of clouds and
precipitation. Thus, any bias beyond an uncertainty of around 0.2 (resulting
from the temperature profile) can be attributed to calibration errors. Note that the brightness temperatures for F16 SSMIS instruments used
in this study are converted from their antenna temperatures using the coefficients provided by the instrument manufacturer to NRL.Shown in Figure2 is the longitudinal mean
difference between observed and simulated antenna temperatures for F-16 SSMIS
54.4 GHz on March 20,
2005. For
a direct comparison between simulation and observation, the simulated
brightness temperatures have been converted hereinafter to the antenna
temperatures. TARM
is the arm temperature
of the main reflector (more explanations are given in Section 2.3).  Results
in Figure 2 show that antenna brightness temperature biases have strong
geographical dependence along with obvious reductions over several latitudinal zones
labeled as “I~V.” Similar features are observed at 55.5, 57.3, and 59.4 GHz
channels (referring to Figures 8 and 10). After this analysis was extended to
other days throughout the seasons, we found similar conclusions except for
their variable magnitudes with regions (refer to Figure 10(b)). At other LAS
channels, brightness temperatures over cloud-free oceans can be accurately
simulated because of our knowledge of ocean emissivity [14]. Antenna
temperature differences between the SSMIS observations and simulations at 50.3,
52.8, and 53.6 GHz are thus investigated over cloud-free oceans. Results show
that the differences at these three channels have similar features to the above
four sounding channels except for slightly distinctive magnitudes (figures are
omitted here).Figure 2
The observed arm temperature and the longitudinally antenna temperature differences at 54.4 GHz between the SSMIS TDR measurements and radiative transfer simulations, on March 20, 2005, where the results from90°S to 90°N correspond to the ascending node observations and those from 90°N to 90°S correspond to the descending node observations.These geographically and seasonally
dependent biases in SSMIS radiances at the LAS channels are considered as
anomalies because we normally anticipate the bias for these sounding channels
to be relatively small and independent of location and season. Root causes of
the anomalies had been investigated which resulted from thermal emission by the
SSMIS main reflector and solar intrusion on warm calibration target [3, 7, 9, 10], as briefly
described in Sections 2.3 and 2.4 correspondingly.


### 2.3. Thermal Emission from SSMIS Main Reflector

The SSMIS
antenna consists of an offset parabolic main reflector and array of
feedhorns that work in concert to produce the antenna power patterns by a
combination of the radiation patterns of the feedhorn and the main reflector. As the antenna views earth, brightness temperature of the earth scene incident upon the
antenna is received and spatially filtered by the antenna to form antenna
temperature (TA) at the
input of the feedhorn. For a perfect reflector, this antenna temperature is only
an integral of the scene brightness temperature distribution incident on the
main reflector and the co- and cross-polarized far-field antenna power patterns
[15]. For an emissive reflector, the radiance arrived
at the feedhorn becomes (1−εR)TA, where εR denotes the emissivity of the main reflector.Ideally,
the reflector should be lossless, that is, its reflectivity is unity and its
emissivity is zero. However, according to the SSMIS instrument calibration team,
the F16 SSMIS main reflector is not a perfect reflector due to impurities in
the reflector coating such that its emissivity could vary from 0.01 to 0.04 for
frequencies between 19 and 183 GHz, respectively [3, 10].
Furthermore, the main reflector is heated periodically by incident solar
radiation and emits a variable radiation with space and time. As a result, the
“extra” radiation comes at the expense of reduced radiation from the scene
reflected into the feedhorns due to the reduced efficiency of the reflecting
surface (i.e., εRTR) where TR denotes the effective reflector temperature which is
based on the feed illumination convolved with the temperature field of the
reflector. In the rest of the paper, the effective reflector temperature is simply
named to be reflector temperature. Therefore, the antenna temperature focused
on the feedhorn including the main reflector emission contribution is given by (1)TA′=(1−εR)TA+εRTR, where the channel frequency
and polarization of each variable are omitted for simplicity. However (1)  is
rewritten to be (2)TA′=TA+εR(TR−TA),  which implies that the
antenna emission εR(TR−TA) must be accounted
for in order to obtain the antenna temperature of the earth scene.The magnitude of this antenna emission is
linearly proportional to the reflector emissivity and the difference between
the reflector temperature and the antenna temperature. At the current stage, a
set of SSMIS emissivty for frequencies between 19 and 183 GHz was simulated
using the NRL multilayer
antenna model [3, 10]. The reflector temperature is
not provided in F-16. Instead, there is a thermometer mounted on the antenna
arm to measure the arm temperature named as TARM,
as shown in Figure 2. The correlation of the antenna temperature anomaly to TARM is observed except for several latitudinal zones where the
solar intrusion results in certain discontinuity. However, the TARM does not respond as fast
as the antenna temperature anomaly. This is caused by a slower response of the
arm to solar heating than the reflector face since the thermometer measuring TARM is 0.3 meter away from
the center of the main reflector. The difference between the arm and reflector
temperatures is on the order of several tenths of Kelvin according to our
retrieved reflector temperature provided in Section 3.2, which leads to at most 1 K underestimate of the antenna emission according to (2).  Therefore, to derive reflector temperatures is
a key issue for antenna emission correction.


### 2.4. Calibration Target Anomalies by Solar Intrusions

The SSMIS measurements are calibrated by
passing the feedhorns through two fixed reference targets: a warm load and a
cold space reflector. LetCS, CC, and CW denote the radiometric counts
of earth scene, cold space, and warm load,
respectively. Also, TC is
the deep space cosmic background temperature, and TW is the PRT-measured brightness temperature of the
warm load (PRT temperature). Generally, the scene counts are converted to the antenna temperature TA using the
warm load and cold space counts along with their corresponding brightness
temperatures, (3)TA=F(CS,CW,CC,TW,TC), where F is the calibration function.Obviously, the accuracy ofTA is affected by the selection of a calibration function F, which can be a linear or nonlinear
function. The nonlinearity can result from an imperfect square
law detector and/or intermediate frequency amplifier compression in the
receiver subsystem. Generally speaking, the calibration accuracy for a
microwave radiometer through a linear algorithm is not adequate [16–18]. However, the SSMIS nonlinear contribution at the LAS channels is not
investigated in this study. Instead, F  in (3) is assumed to be linearly related
to the antenna temperature and calibration parameters. Thus, we have (4)TA=TC+S(CS−CC),  where (5)S=TW−TCCW−CC.Obviously, accuracy of antenna temperature
relies on accuracy of calibration target information such as warm count, PRT temperature,
and cold count. Unfortunately, soon after launch of the SSMIS, solar radiation
impinges upon the surfaces of the warm load tines and results in rapid heating
of warm load tines over several geometric scenarios [19]. Detailed analyses are referred to Swadley
et al. [19]  and omitted here. A
direct result of this heating of warm load tines is a sudden short-term positive jump in warm counts which is named as
warm count anomaly or ΔCW (ΔCW > 0). Figure 3(a)
displays the time series of warm counts at channel 4 (54.4 GHz) for one orbit
of observations in Figure 2. The warm count anomalies are clearly seen in the
zones labeled as “I~V,” and
each zone is accompanied with short-term jumps in warm counts whose maximum
distributes between 20 and 60 counts.Time series ofCW, TW, gain, during one orbit of observations, on March 20, 2005 for (a)~(d) and on the first day of twelve months 2005 for (e), where a constant (orbital mean of corresponding counts) has been subtracted from the warm count to emphasize characteristics of warm count anomaly. (a) CW  at 54.4 GHz. (b) TW. (c) gain at 54.4 GHz. (d) CW  at 50.3, 52.8, 53.6, 54.4, 55.5, 57.3, 59.4 GHz. (e) Time series of CW at 54.4 GHz during one orbit in twelve months in 2005, where the numbers from 1 to 12 denote the month of data.
(a)(b)(c)(d)(e)However, this
solar intrusion does not cause obvious temperature anomaly and gradient in three warm load PRT temperatures.
Figure3(b) displays the time series of
three warm load PRT temperatures for the same orbit. More examples are given in Figures 4(a)–4(l), where the times series of three PRT
temperatures are shown during two orbits of observations for one day each month
in 2005. The maximum fluctuation in three PRT temperatures due to solar
intrusion is only around 0.2 K and the
affected region is also smaller than warm counts. According to the estimate of
the channel gain (Figure 3(c)), there is a variation of about 37 counts per 1 K. Thus,
the magnitude and phase of fluctuations in TW do not match with these of the fluctuations in CW. This
phenomenon is attributed primarily to the thermal inertia of the warm load and
the fact that the PRTs are imbedded deep enough inside the substrate of
the warm load and not at the surface
viewed by the radiometer where much of solar intrusion occurs. Note that the gradient among three PRT temperatures is
very small (see Figures 3(b) and 4). This feature is different from that in WindSat
where a significant temperature gradient of more than 0.5 K exists among six
PRT temperatures due to solar radiation [20].Time series of three PRT temperatures (TW) during two orbits of observations for twelve days in 2005, where the black, red, and green represent three PRT temperatures. (a) January 5. (b) February 21. (c) March 20. (d) April 20. (e) May 18. (f) June 19. (g) July 18. (h) August 15. (i) September 15. (j) October 25. (k) November 7. (l) December 17.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)Due to the aforementioned mismatch, according to calibration (4), an error in the
antenna temperature (i.e., ΔTACAL)  may be caused, viz., (6)ΔTACAL=−[TA−TCCW−CC]ΔCW−[TW−TACW−CC]ΔCC+[CS−CCCW−CC]ΔTW.Table2
displays the error in the antenna temperature due to warm count anomalies over
several zones which are computed using the first term in (6). Results show that
the solar intrusion anomaly in CW can impart up to a maximum of 1.1 K depression in antenna temperatures near the
center of the intrusion period, while the error due to PRT temperature anomaly
is only about 0.1 K (not shown in table). This analysis is further confirmed by
consistency in magnitudes and positions of those warm count anomaly-caused
errors in antenna temperatures with the antenna temperature differences over
the same zones in Figure 2. Since the
anomaly of about 10 counts was sometimes detected in the cold space count for
some channels (figures are omitted), the effect of cold count anomaly (ΔCC) is included in (6).Table 2
Warm load count
anomaly zone identified from SSMIS data March 20, 2005.βL ~ βR denotes the latitudes of each anomaly zone width in the left and right
sides, respectively. (ΔCW)max is the maximum warm load count
anomaly for each zone and is estimatedaccording to Figure 3(a). (ΔTACAL)max  is the error in SSMIS radiance corresponding to (ΔCW)max, which is determined using the first term in (6), (i.e., −(TA−TC)/(CW−CC)ΔCW).
NamesZone 1
(ascending)Zone 2
(descending)Zone 3
(descending)Zone 4
(descending)Zone 5
(ascending)βL~βR40°N ~80°N56°N ~80°N3°S ~42°S42°S ~74°S56°S ~74°STime (minute)815121315(ΔCW)max3060203020(ΔTACAL)max   (K)−0.6−1.1−0.4-0.6−0.4A similar analysis can be applied to
other LAS channels. Besides the anomaly in 54.4 GHz, the anomaly of warm counts
also occurs at other LAS channels. Usually, the phase of the solar intrusion on
the warm load is dependent on channels. It is the location of the solar
illumination on the warm load tines and the relative position and timing of the
warm load calibration observations with respect to the series of feedhorns that
causes the phasing. However, for the LAS channels, the antenna temperatures
arrive at the feedhorn at nearly the same time, that is, the phase of the
anomaly is similar. Figure3(d) displays the times series of the warm counts at all
LAS channels (i.e., channels 1–7). These results indicate that while the
magnitude of each anomaly is variable with channel, the phase of each channel
anomaly is similar because their time difference is small.Furthermore, the features of the warm
count anomalies are investigated for various seasons. Figure3(e) displays time
series of CW of one orbit
of observations at 54.4 GHz for the first day of each month throughout the year
of 2005. It is observed that the solar intrusion to warm load always occurs and
the resulted warm count anomaly magnitude changes gradually with season. However,
several common features are noted from the
warm count anomaly distribution. The warm count anomaly lasts from 5 to
15 minutes every time the solar intrusion
occurs, and the locations of five zones are correlated to the positions
of the maximum/minimum warm counts in the time domain, that is, two of them
occur near CW maximum; two
prior to the CW minimum
and one after the CW minimum. In addition, the five solar
intrusion zones affect 30–40% of the entire orbital observations.Therefore, the radiance anomalies at the LAS
channels are characterized by both the antenna emission and warm count anomaly
and display regionally and
seasonally dependent features. These complicated features significantly increase
complexity and
difficulty of accurate corrections for such variable anomalies. However, those erroneous SSMIS radiances at the LAS
channels are inappropriate for assimilation into the numerical weather
prediction model. The reliable identification and correction of those anomalies
per orbit are thus mandatory for the utilization of SSMIS data in weather
prediction models. To remove these calibration anomalies in F16, three independent preprocessors for SSMIS radiances were
studied from 2005 on in NRL, UKMET, and NOAA National
Environmental Satellite, Data, and Information Service (NESDIS) and are currently available [8, 19, 21]. It is probably
fair to say that none of these preprocessors would be
described by their authors as definitive but represent their best efforts to date to correct the instrumental biases evident in F-16
SSMIS data. In what follows, the NOAA NESDIS preprocessor for SSMIS radiances
developed by Yan et al. [8] is introduced.


## 2.1. Brief Description of F16 SSMIS Instrument

The specifications of 24 SSMIS channels are
given in Table1. For reference purposes, the channels are grouped into four
subtypes corresponding to the lower atmospheric sounding (LAS) channels (e.g.,
channels 1–7), the upper atmospheric sounding (UAS) channels (e.g., channels
19–24), the imaging (IMA) channels (i.e., channels 8–11, and 17-18), and the
environmental (ENV) channels (e.g., channels 12–16), [1]. The
SSMIS consists of several major subsystems: antenna/calibration, receiver,
signal processing, scan drive, and deployment subsystems. The antenna/calibration subsystem includes the
main reflector, an array of feedhorns, a warm calibration load, and a cold
calibration reflector. The feedhorn array includes six corrugated
feedhorns.Table 1
Channel
characteristics of SSMIS sensor [1]. (1) Sampling refers to
along scan direction based on 833 km spacecraft altitude. (2) NEDT for
instrument temperature 0°C and calibration target 260 K with integration times of
8.4 msec for Channels 12–16; 12.6 msec for Channels 1–7, 24; and 25.2 msec for
Channels 19–23 and 4.2 msec for Channels 8–11, 17-18. (3) Number of subbands is
indicated by (n) next to individual 3-db width. (4) RCP denotes
right-hand circular polarization.)
ChannelCenter freq. (GHz)3-db width (MHz)Freq. stab. (MHz)Pol.NEDT (K)Sampling interval (km)150.338010V0.3437.5252.838910V0.3237.5353.59638010V0.3337.5454.438310V0.3337.5555.539110V0.3437.5657.2933010RCP0.4137.5759.423910RCP0.4037.581501642(2)200H0.8912.59183.31 ± 6.61526(2)200H0.9712.510183.31 ± 31019(2)200H0.6712.511183.31 ± 1513(2)200H0.8112.51219.3535575H0.33251319.3535775V0.31251422.23540175V0.43251537161675H0.25251637154575V0.20251791.6551418(2)100V0.3312.51891.6551411(2)100H0.3212.51963.283248 ± 0.2852711.35(2)0.08RCP2.7752060.792668 ± 0.3578921.35(2)0.08RCP2.7752160.792668 ± 0.357892 ± 0.0021.3(4)0.08RCP1.9752260.792668 ± 0.357892 ± 0.00552.6(4)0.12RCP1.3752360.792668 ± 0.357892 ± 0.0167.35(4)0.34RCP0.8752460.792668 ± 0.357892 ± 0.05026.5(4)0.84RCP0.937.5All SSMIS channels
are sampled every scan and a sampling period of 4.22 ms (corresponding to0.8°  azimuth scan increment)  is used for each channel. There
are 180 active sample positions where raw radiometric data of earth scenes are acquired
from each channel [2, 10]. These samples except for channels 8–11
and 17-18 are subjected to onboard flight software averaging in the along-scan
direction to improve the noise-equivalent difference temperature (NEDT) before
down-linking to the ground processing for final TDR calibration. For example,
for channels 1–7 and 24, three along-scan beams are averaged, resulting in 60
samples per scan; for channels 12–16, two adjacent along-scan beams are
averaged, resulting in 90 samples per scan; for channels 19–23, six along-scan
beams are averaged, resulting in 30 samples per scan, as summarized in Table 1.
For each scan, the feedhorns also pass beneath the stationary warm-load and
cold-space reflector calibration targets, where four samples of radiometric
counts for each calibration target are taken for all channels and are averaged
by the onboard flight software. The temperature of the warm load is provided by
three high-precision platinum resistance thermometer (PRT) probes.Once per rotation of the main reflector, the
energy from the Earth’s surface and atmosphere incident upon the reflector focuses on the feedhorn
assembly positioned in the reflector focal
plane. The receiver
subsystem accepts the energy from the six feedhorns and provided amplification,
filtering, and additional frequency multiplexing to output 24 discrete
frequency bands to the signal processing subsystem and then to the Operational Linescan System (OLS) under control of
the sensor signal processor and the flight software. The data are then
transmitted to the SSMIS ground processing by the OLS. Figure1 displays a block diagram of this process, which is
revised from Grumman [2]. In the SSMIS ground processing,
the TDR and SDR are further generated from the Sensor Data Records Processor  [2, 10]. Unfortunately, both main reflector emission and solar heating of
the warm calibration target occur in F16 SSMIS such that certain anomalies in
the SSMIS antenna temperatures are observed as illustrated next.Figure 1
SSMIS simplified block diagram [2].


## 2.2. F16 SSMIS Radiance Error Assessment

A powerful approach of monitoring the onorbit satellite instrument performance in satellite
cal/val research fields is to compare satellite-observed radiances with radiative
transfer model- (RTM-) simulated radiances. At microwave frequencies, the global brightness temperature
for oxygen sounding channels between 54 to 59 GHz can be accurately simulated
due to our knowledge of the oxygen absorption spectrum. It is also due to the
fact that radiation for these channels originates mainly from the atmosphere,
not the surface. As a result, at oxygen channels of 54.4, 55.5, 57.3, and 59.4 GHz, the simulation accuracy is mainly dependent on the temperature accuracy in
regions where the weighting function peaks.  For example, an error of 1 K in physical
temperature where the weighting function peaks can result in an error of 0.1 K
in simulated brightness temperature [1]. In this study, the Community RTM developed by the Joint Center
for Satellite Data Assimilation (JCSDA)   [12]  is employed to
simulate the brightness temperatures at SSMIS channels using the absorption
model developed by Rosenkranz [13]. Inputs of the absorption model consist of
temperature and water vapor profiles obtained from the global data assimilation
system (GDAS)  analysis by the National Center for Environmental Prediction
(NCEP). The performance of the GDAS analysis products is continuously monitored by the NCEP Environmental Modeling Center
(http://www.emc.ncep.noaa.gov/modelperf/). The root mean square error of GDAS temperature
profiles against radiosonde
measurements below 10 mb is smaller than 2 K, which results in an uncertainty
of about 0.2 K in simulations from 54 to 59 GHz. Initially, the errors in
simulated brightness temperatures are significantly less affected by the errors
in GDAS water vapor profile because they are not sensitive to water vapor
absorption. Also, the effects of cloud and rain are not taken into account in
these simulations due to the lack of information. This is reasonable for the
54.4, 55.5, 57.3, and 59.4 GHz channels because their weighting functions
typically peak above the absorption layer that consists of clouds and
precipitation. Thus, any bias beyond an uncertainty of around 0.2 (resulting
from the temperature profile) can be attributed to calibration errors. Note that the brightness temperatures for F16 SSMIS instruments used
in this study are converted from their antenna temperatures using the coefficients provided by the instrument manufacturer to NRL.Shown in Figure2 is the longitudinal mean
difference between observed and simulated antenna temperatures for F-16 SSMIS
54.4 GHz on March 20,
2005. For
a direct comparison between simulation and observation, the simulated
brightness temperatures have been converted hereinafter to the antenna
temperatures. TARM
is the arm temperature
of the main reflector (more explanations are given in Section 2.3).  Results
in Figure 2 show that antenna brightness temperature biases have strong
geographical dependence along with obvious reductions over several latitudinal zones
labeled as “I~V.” Similar features are observed at 55.5, 57.3, and 59.4 GHz
channels (referring to Figures 8 and 10). After this analysis was extended to
other days throughout the seasons, we found similar conclusions except for
their variable magnitudes with regions (refer to Figure 10(b)). At other LAS
channels, brightness temperatures over cloud-free oceans can be accurately
simulated because of our knowledge of ocean emissivity [14]. Antenna
temperature differences between the SSMIS observations and simulations at 50.3,
52.8, and 53.6 GHz are thus investigated over cloud-free oceans. Results show
that the differences at these three channels have similar features to the above
four sounding channels except for slightly distinctive magnitudes (figures are
omitted here).Figure 2
The observed arm temperature and the longitudinally antenna temperature differences at 54.4 GHz between the SSMIS TDR measurements and radiative transfer simulations, on March 20, 2005, where the results from90°S to 90°N correspond to the ascending node observations and those from 90°N to 90°S correspond to the descending node observations.These geographically and seasonally
dependent biases in SSMIS radiances at the LAS channels are considered as
anomalies because we normally anticipate the bias for these sounding channels
to be relatively small and independent of location and season. Root causes of
the anomalies had been investigated which resulted from thermal emission by the
SSMIS main reflector and solar intrusion on warm calibration target [3, 7, 9, 10], as briefly
described in Sections 2.3 and 2.4 correspondingly.


## 2.3. Thermal Emission from SSMIS Main Reflector

The SSMIS
antenna consists of an offset parabolic main reflector and array of
feedhorns that work in concert to produce the antenna power patterns by a
combination of the radiation patterns of the feedhorn and the main reflector. As the antenna views earth, brightness temperature of the earth scene incident upon the
antenna is received and spatially filtered by the antenna to form antenna
temperature (TA) at the
input of the feedhorn. For a perfect reflector, this antenna temperature is only
an integral of the scene brightness temperature distribution incident on the
main reflector and the co- and cross-polarized far-field antenna power patterns
[15]. For an emissive reflector, the radiance arrived
at the feedhorn becomes (1−εR)TA, where εR denotes the emissivity of the main reflector.Ideally,
the reflector should be lossless, that is, its reflectivity is unity and its
emissivity is zero. However, according to the SSMIS instrument calibration team,
the F16 SSMIS main reflector is not a perfect reflector due to impurities in
the reflector coating such that its emissivity could vary from 0.01 to 0.04 for
frequencies between 19 and 183 GHz, respectively [3, 10].
Furthermore, the main reflector is heated periodically by incident solar
radiation and emits a variable radiation with space and time. As a result, the
“extra” radiation comes at the expense of reduced radiation from the scene
reflected into the feedhorns due to the reduced efficiency of the reflecting
surface (i.e., εRTR) where TR denotes the effective reflector temperature which is
based on the feed illumination convolved with the temperature field of the
reflector. In the rest of the paper, the effective reflector temperature is simply
named to be reflector temperature. Therefore, the antenna temperature focused
on the feedhorn including the main reflector emission contribution is given by (1)TA′=(1−εR)TA+εRTR, where the channel frequency
and polarization of each variable are omitted for simplicity. However (1)  is
rewritten to be (2)TA′=TA+εR(TR−TA),  which implies that the
antenna emission εR(TR−TA) must be accounted
for in order to obtain the antenna temperature of the earth scene.The magnitude of this antenna emission is
linearly proportional to the reflector emissivity and the difference between
the reflector temperature and the antenna temperature. At the current stage, a
set of SSMIS emissivty for frequencies between 19 and 183 GHz was simulated
using the NRL multilayer
antenna model [3, 10]. The reflector temperature is
not provided in F-16. Instead, there is a thermometer mounted on the antenna
arm to measure the arm temperature named as TARM,
as shown in Figure 2. The correlation of the antenna temperature anomaly to TARM is observed except for several latitudinal zones where the
solar intrusion results in certain discontinuity. However, the TARM does not respond as fast
as the antenna temperature anomaly. This is caused by a slower response of the
arm to solar heating than the reflector face since the thermometer measuring TARM is 0.3 meter away from
the center of the main reflector. The difference between the arm and reflector
temperatures is on the order of several tenths of Kelvin according to our
retrieved reflector temperature provided in Section 3.2, which leads to at most 1 K underestimate of the antenna emission according to (2).  Therefore, to derive reflector temperatures is
a key issue for antenna emission correction.


## 2.4. Calibration Target Anomalies by Solar Intrusions

The SSMIS measurements are calibrated by
passing the feedhorns through two fixed reference targets: a warm load and a
cold space reflector. LetCS, CC, and CW denote the radiometric counts
of earth scene, cold space, and warm load,
respectively. Also, TC is
the deep space cosmic background temperature, and TW is the PRT-measured brightness temperature of the
warm load (PRT temperature). Generally, the scene counts are converted to the antenna temperature TA using the
warm load and cold space counts along with their corresponding brightness
temperatures, (3)TA=F(CS,CW,CC,TW,TC), where F is the calibration function.Obviously, the accuracy ofTA is affected by the selection of a calibration function F, which can be a linear or nonlinear
function. The nonlinearity can result from an imperfect square
law detector and/or intermediate frequency amplifier compression in the
receiver subsystem. Generally speaking, the calibration accuracy for a
microwave radiometer through a linear algorithm is not adequate [16–18]. However, the SSMIS nonlinear contribution at the LAS channels is not
investigated in this study. Instead, F  in (3) is assumed to be linearly related
to the antenna temperature and calibration parameters. Thus, we have (4)TA=TC+S(CS−CC),  where (5)S=TW−TCCW−CC.Obviously, accuracy of antenna temperature
relies on accuracy of calibration target information such as warm count, PRT temperature,
and cold count. Unfortunately, soon after launch of the SSMIS, solar radiation
impinges upon the surfaces of the warm load tines and results in rapid heating
of warm load tines over several geometric scenarios [19]. Detailed analyses are referred to Swadley
et al. [19]  and omitted here. A
direct result of this heating of warm load tines is a sudden short-term positive jump in warm counts which is named as
warm count anomaly or ΔCW (ΔCW > 0). Figure 3(a)
displays the time series of warm counts at channel 4 (54.4 GHz) for one orbit
of observations in Figure 2. The warm count anomalies are clearly seen in the
zones labeled as “I~V,” and
each zone is accompanied with short-term jumps in warm counts whose maximum
distributes between 20 and 60 counts.Time series ofCW, TW, gain, during one orbit of observations, on March 20, 2005 for (a)~(d) and on the first day of twelve months 2005 for (e), where a constant (orbital mean of corresponding counts) has been subtracted from the warm count to emphasize characteristics of warm count anomaly. (a) CW  at 54.4 GHz. (b) TW. (c) gain at 54.4 GHz. (d) CW  at 50.3, 52.8, 53.6, 54.4, 55.5, 57.3, 59.4 GHz. (e) Time series of CW at 54.4 GHz during one orbit in twelve months in 2005, where the numbers from 1 to 12 denote the month of data.
(a)(b)(c)(d)(e)However, this
solar intrusion does not cause obvious temperature anomaly and gradient in three warm load PRT temperatures.
Figure3(b) displays the time series of
three warm load PRT temperatures for the same orbit. More examples are given in Figures 4(a)–4(l), where the times series of three PRT
temperatures are shown during two orbits of observations for one day each month
in 2005. The maximum fluctuation in three PRT temperatures due to solar
intrusion is only around 0.2 K and the
affected region is also smaller than warm counts. According to the estimate of
the channel gain (Figure 3(c)), there is a variation of about 37 counts per 1 K. Thus,
the magnitude and phase of fluctuations in TW do not match with these of the fluctuations in CW. This
phenomenon is attributed primarily to the thermal inertia of the warm load and
the fact that the PRTs are imbedded deep enough inside the substrate of
the warm load and not at the surface
viewed by the radiometer where much of solar intrusion occurs. Note that the gradient among three PRT temperatures is
very small (see Figures 3(b) and 4). This feature is different from that in WindSat
where a significant temperature gradient of more than 0.5 K exists among six
PRT temperatures due to solar radiation [20].Time series of three PRT temperatures (TW) during two orbits of observations for twelve days in 2005, where the black, red, and green represent three PRT temperatures. (a) January 5. (b) February 21. (c) March 20. (d) April 20. (e) May 18. (f) June 19. (g) July 18. (h) August 15. (i) September 15. (j) October 25. (k) November 7. (l) December 17.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)Due to the aforementioned mismatch, according to calibration (4), an error in the
antenna temperature (i.e., ΔTACAL)  may be caused, viz., (6)ΔTACAL=−[TA−TCCW−CC]ΔCW−[TW−TACW−CC]ΔCC+[CS−CCCW−CC]ΔTW.Table2
displays the error in the antenna temperature due to warm count anomalies over
several zones which are computed using the first term in (6). Results show that
the solar intrusion anomaly in CW can impart up to a maximum of 1.1 K depression in antenna temperatures near the
center of the intrusion period, while the error due to PRT temperature anomaly
is only about 0.1 K (not shown in table). This analysis is further confirmed by
consistency in magnitudes and positions of those warm count anomaly-caused
errors in antenna temperatures with the antenna temperature differences over
the same zones in Figure 2. Since the
anomaly of about 10 counts was sometimes detected in the cold space count for
some channels (figures are omitted), the effect of cold count anomaly (ΔCC) is included in (6).Table 2
Warm load count
anomaly zone identified from SSMIS data March 20, 2005.βL ~ βR denotes the latitudes of each anomaly zone width in the left and right
sides, respectively. (ΔCW)max is the maximum warm load count
anomaly for each zone and is estimatedaccording to Figure 3(a). (ΔTACAL)max  is the error in SSMIS radiance corresponding to (ΔCW)max, which is determined using the first term in (6), (i.e., −(TA−TC)/(CW−CC)ΔCW).
NamesZone 1
(ascending)Zone 2
(descending)Zone 3
(descending)Zone 4
(descending)Zone 5
(ascending)βL~βR40°N ~80°N56°N ~80°N3°S ~42°S42°S ~74°S56°S ~74°STime (minute)815121315(ΔCW)max3060203020(ΔTACAL)max   (K)−0.6−1.1−0.4-0.6−0.4A similar analysis can be applied to
other LAS channels. Besides the anomaly in 54.4 GHz, the anomaly of warm counts
also occurs at other LAS channels. Usually, the phase of the solar intrusion on
the warm load is dependent on channels. It is the location of the solar
illumination on the warm load tines and the relative position and timing of the
warm load calibration observations with respect to the series of feedhorns that
causes the phasing. However, for the LAS channels, the antenna temperatures
arrive at the feedhorn at nearly the same time, that is, the phase of the
anomaly is similar. Figure3(d) displays the times series of the warm counts at all
LAS channels (i.e., channels 1–7). These results indicate that while the
magnitude of each anomaly is variable with channel, the phase of each channel
anomaly is similar because their time difference is small.Furthermore, the features of the warm
count anomalies are investigated for various seasons. Figure3(e) displays time
series of CW of one orbit
of observations at 54.4 GHz for the first day of each month throughout the year
of 2005. It is observed that the solar intrusion to warm load always occurs and
the resulted warm count anomaly magnitude changes gradually with season. However,
several common features are noted from the
warm count anomaly distribution. The warm count anomaly lasts from 5 to
15 minutes every time the solar intrusion
occurs, and the locations of five zones are correlated to the positions
of the maximum/minimum warm counts in the time domain, that is, two of them
occur near CW maximum; two
prior to the CW minimum
and one after the CW minimum. In addition, the five solar
intrusion zones affect 30–40% of the entire orbital observations.Therefore, the radiance anomalies at the LAS
channels are characterized by both the antenna emission and warm count anomaly
and display regionally and
seasonally dependent features. These complicated features significantly increase
complexity and
difficulty of accurate corrections for such variable anomalies. However, those erroneous SSMIS radiances at the LAS
channels are inappropriate for assimilation into the numerical weather
prediction model. The reliable identification and correction of those anomalies
per orbit are thus mandatory for the utilization of SSMIS data in weather
prediction models. To remove these calibration anomalies in F16, three independent preprocessors for SSMIS radiances were
studied from 2005 on in NRL, UKMET, and NOAA National
Environmental Satellite, Data, and Information Service (NESDIS) and are currently available [8, 19, 21]. It is probably
fair to say that none of these preprocessors would be
described by their authors as definitive but represent their best efforts to date to correct the instrumental biases evident in F-16
SSMIS data. In what follows, the NOAA NESDIS preprocessor for SSMIS radiances
developed by Yan et al. [8] is introduced.


## 3. Methodology of F16 SSMIS Radiance Anomaly Correction Algorithm

### 3.1. Correction of Calibration Warm Count Anomaly

Correction of calibration warm count anomaly relies primarily on fast Fourier transform
(FFT) analysis of warm counts due to a distinctive feature of warm count
anomaly from major components of warm counts in frequency domain. The solar intrusion-caused
anomaly is readily evident in the time series of warm counts, where several areas of sudden short-term
positive jumps are observed in warm counts. In the domain of frequency,
those anomalies represent a set of higher-frequency components superimposed onCW in comparison to its primary
frequency component. Figure 5(a) displays the energy spectrum of observed warm
counts (CWObs) at channel 4 for an orbit (around 102 minutes),
while Figure 5(b) displays time series of both CWObs and a few orders of
harmonic components (i.e., CW1~CW4), which are
calculated using FFT analysis. According to SSMIS satellite period (about 102
minutes), the primary frequency component of CWObs is approximately 1/102
(min−1) or 0.00016 Hz. Thus, the solar intrusion-caused components
are distributed primarily beyond the frequency range of the first few harmonic
components of the FFT spectrum of CWObs. By assessing the antenna temperature differences using
the reconstructed warm count time series, it is found that the first four or
five harmonic components can capture the major
features of the solar intrusion-corrected CW over the first two (strong) solar intrusion-contaminated zones in Figure 5(b),
while the first six or higher harmonic components may be needed to correct warm
count anomaly over zones 3–5 where the solar intrusion is relatively weak. Therefore,
initially, we can filter out major high-frequency components in CW related to solar
contamination by replacing CWObs with its respective
order of harmonic components, and further construct solar intrusion-corrected warm
counts (CWCor). Finally, in principle, regions where ΔCW (CWObs−CWCor)  exceeds a certain threshold are identified and the
calibration correction is calculated using (6)   there.(a) FFT energy spectrum ofCWObs at channel 4 (54.4 GHz) during one orbit of observations on March 20, 2006. (b) Time series of CWObs, CW1~CW4 at 54.4 GHz for the same orbit as in (a). (c) Comparisons of CWObs,  CWExt and its periodically extended warm counts at 54.4 GHz. In the figures, an orbital mean of corresponding counts has been subtracted from the warm counts in each orbit of observations.
(a)(b)(c)In this process, it is important to
reduce truncating effect on FFT spectrum of SSMIS data (e.g.,CWObs). When we use FFT
to measure the frequency content of a time series of data, we have to base the
analysis on a finite set of data (e.g., one orbit of observations in our study).
The FFT transform assumes that the finite dataset is one period of a periodic
signal, that is, the two endpoints of the data are interpreted as though they
were connected together. However, satellite-measured data in an orbit may
deviate from this feature. As a result, the finiteness of one orbit of data may
result in a truncated waveform nearby two edges of time-finite signal. In this
study, this effect can be significantly reduced by a periodical extension of
the observed data, that is, artificially extending observations from one orbit (approximate
one period) to about two orbits (approximate two periods). According to our
analysis, the warm counts in SSMIS observations show good stability and
consistency from one orbit to its neighboring orbits. This allows us to extend
original warm counts (CWObs) into a new dataset (CWExt) of about two periods (orbits), where the first half
orbit of data in CWExt is constructed by
using the second half orbit of CWObs, the last half orbit of data in CWExt is constructed by
using the first half orbit of CWObs, the rest of CWExt consists of the
observed warm counts. As a result, the FFT analysis is applied to a periodically
extended CWExt instead of CWObs.
In this way, the truncating effect occurs only during
the extended data part instead of the original data part, as shown in Figure 5(c).
Thus, the spectral characteristics of CWObs with less truncating
effect can be extracted from the FFT spectrum of artificially extending warm
counts (CWExt).In addition, the quality check of the
reconstructed warm counts is also important to avoid over-correcting the effect
of solar intrusions on warm counts.  It
has been known that solar intrusions are always related to regions nearby the
positions of the maximum/minimum ofCWObs and each intrusion occurs between 5 and 15
minutes in different seasons, based on our statistical analysis throughout one
year of data (Figure 3(e)). This feature may help identify rough locations of
several solar intrusions on warm counts in different season. Then, the reconstructed
warm counts only replace the observed warm counts over these regions. Figure 6 shows CWObs and corresponding CWCor at channel 4 for all orbits of observations on
August 15, 2006,
where CWCor in each orbit is generated by applying the
above procedures. The reconstructed warm counts in the figure effectively correct
most of the anomalies from solar intrusion. A similar analysis can be applied
to other observations and channels in a year. By assessing corresponding
antenna temperature differences based on the reconstructed warm counts, the
residual antenna temperature errors are usually smaller than 0.1 K (the figures
are omitted).Figure 6
Time series ofCWObs and corresponding CWCor at 54.4 GHz for all orbits on August 15, 2006. In the figures, an orbital mean of corresponding counts has been subtracted from the warm counts in each orbit of observations.


### 3.2. Removal of Antenna Emission

From the
linear calibration equation (4) and the reconstructed calibration counts, the
antenna temperatures can be obtained. This antenna temperature (TA′), however,
includes the contribution of the antenna emission. Theoretically, we can derive
the antenna temperature from the earth scene’s radiance by removing antenna
emission using (2), that is, (7)TA=TA′−εRTR1−εR.Obviously, the variables required to
perform this calculation are the reflector
temperature and emissivity. Unfortunately,
neither of them is available from measurements. For the reflector emissivity, a
set of reflector emissivity at
frequencies from 19.35 GHz to 183 GHz are given from the NRL emissivity model simulations.
With this reflector emissivity, the remaining issue is to find reflector
temperature (TR).Estimate
of reflector temperatures are made from the arm temperature of the main
reflector (i.e.,TARM). As
discussed in Section 2, TARM
is an important indicator because it displays a similar orbital feature to the
radiance difference (antenna emission) except for its response lag to solar
heating (see Figure 2). So, the reflector temperature can be calculated in terms
of TARM with a proper
adjustment [7, 9],
that is,
(8)TR(ti)=TARM(ti)+ΔTR(ti),  where ΔTR represents an adjustment corresponding to the difference between TR and TARM
due to the response lag of the arm to solar
heating, t the time of each scan line
corresponding to a specific latitude,
and the subscript “i” the ith scan line per orbit.In
this study,ΔTR is determined by using a group of polynomial expressions
for latitude. The fitting coefficients of polynomial expressions are derived
from the training datasets of TR  (and TARM), and this TR is
generated by solving (7) with the RTM simulations, that is, (9)TR,ich=TA,ich′−(1−εR,ich)TA,ichεR,ich, where εR,ich  is the
emissivity at the ith channel, and i=4,5,6,7, corresponding for 54.4,
55.5, 57.3, 59.4 GHz. However, TA in (9) is obtained approximately from
the RTM simulated antenna temperature.After the training dataset of the
retrievedTR and observed  TARM
is obtained, ΔTR is
further derived as an equation in terms of latitude (β), which is expressed as (10)ΔTR,ich=a0i+∑j=1Najiβ.As an example, Figure7 shows the
reflector arm temperature, the retrieved and fitted reflector temperatures at
54.4 GHz, on March 20, 2006,
where the retrieved reflector temperature is calculated using (9) and the
fitted reflector temperature is calculated using (8) and (10). It is found that
the retrieved reflector temperature can be fitted well from (8) and (10). In
comparison to the observed TARM,
the TR
at channel 4 responds
to the solar heating faster than TARM
and the most significant adjustment (i.e., a maximum ΔTR) is made
when the spacecraft is out of the Earth’s eclipse (around 20°N in
the ascending node). Consequently, the reflector temperature captures more closely
the trend of the bias than the arm temperature. The reflector temperature does
show a significant orbital cycle where it varies between 220 and 330 K. This
large variation in TR (100 K) can explain a maximum error of 2 K in SSMIS antenna temperature at oxygen
channels. So-estimated emission magnitude at 54.4 GHz agrees well with the
observed anomaly.Figure 7
Comparisons of the observed arm temperature, the retrieved and fitted reflector temperatures at 54.4 GHz during one orbit of observations on March 20, 2006.Global distribution of antenna temperature bias between SSMIS TDR measurements and radiative transfer simulations  on March 20, 2006 for (a) 54.4 GHz, and (b) 55.5 GHz.
(a)
SSMIS observations-simulations at 54.4 GHz, 2006-03-20(b)
SSMIS observations-simulations at 55.5 GHz, 2006-03-20According to the results of the reflector
temperatures at the four channels retrieved using (9), some similar orbital features
are observed from the four retrieved reflector temperatures (the figures are
omitted here) although their magnitudes vary slightly with channel with a
difference of about 10 K. For simplicity, the reflector temperatures at the other
three channels are produced from the reconstructed reflector temperatures at
channel 4 with some constant offsets from 10 to 15 K. Currently, we are unable
to accurately simulate the global brightness temperatures at channels 1~3 due
to lack in information of accurate clouds and land surface emissivity. It has
been known that the observations from channels 1~5 are received through the A4
antenna feed. Also, the difference in the retrieved reflector temperatures at
the four channels between 4 and 7 is below 15 K over most of areas. So, in this
study, the reflector temperatures at channels 1~3 are assumed to be
equivalent approximately to that at  channel 4.


## 3.1. Correction of Calibration Warm Count Anomaly

Correction of calibration warm count anomaly relies primarily on fast Fourier transform
(FFT) analysis of warm counts due to a distinctive feature of warm count
anomaly from major components of warm counts in frequency domain. The solar intrusion-caused
anomaly is readily evident in the time series of warm counts, where several areas of sudden short-term
positive jumps are observed in warm counts. In the domain of frequency,
those anomalies represent a set of higher-frequency components superimposed onCW in comparison to its primary
frequency component. Figure 5(a) displays the energy spectrum of observed warm
counts (CWObs) at channel 4 for an orbit (around 102 minutes),
while Figure 5(b) displays time series of both CWObs and a few orders of
harmonic components (i.e., CW1~CW4), which are
calculated using FFT analysis. According to SSMIS satellite period (about 102
minutes), the primary frequency component of CWObs is approximately 1/102
(min−1) or 0.00016 Hz. Thus, the solar intrusion-caused components
are distributed primarily beyond the frequency range of the first few harmonic
components of the FFT spectrum of CWObs. By assessing the antenna temperature differences using
the reconstructed warm count time series, it is found that the first four or
five harmonic components can capture the major
features of the solar intrusion-corrected CW over the first two (strong) solar intrusion-contaminated zones in Figure 5(b),
while the first six or higher harmonic components may be needed to correct warm
count anomaly over zones 3–5 where the solar intrusion is relatively weak. Therefore,
initially, we can filter out major high-frequency components in CW related to solar
contamination by replacing CWObs with its respective
order of harmonic components, and further construct solar intrusion-corrected warm
counts (CWCor). Finally, in principle, regions where ΔCW (CWObs−CWCor)  exceeds a certain threshold are identified and the
calibration correction is calculated using (6)   there.(a) FFT energy spectrum ofCWObs at channel 4 (54.4 GHz) during one orbit of observations on March 20, 2006. (b) Time series of CWObs, CW1~CW4 at 54.4 GHz for the same orbit as in (a). (c) Comparisons of CWObs,  CWExt and its periodically extended warm counts at 54.4 GHz. In the figures, an orbital mean of corresponding counts has been subtracted from the warm counts in each orbit of observations.
(a)(b)(c)In this process, it is important to
reduce truncating effect on FFT spectrum of SSMIS data (e.g.,CWObs). When we use FFT
to measure the frequency content of a time series of data, we have to base the
analysis on a finite set of data (e.g., one orbit of observations in our study).
The FFT transform assumes that the finite dataset is one period of a periodic
signal, that is, the two endpoints of the data are interpreted as though they
were connected together. However, satellite-measured data in an orbit may
deviate from this feature. As a result, the finiteness of one orbit of data may
result in a truncated waveform nearby two edges of time-finite signal. In this
study, this effect can be significantly reduced by a periodical extension of
the observed data, that is, artificially extending observations from one orbit (approximate
one period) to about two orbits (approximate two periods). According to our
analysis, the warm counts in SSMIS observations show good stability and
consistency from one orbit to its neighboring orbits. This allows us to extend
original warm counts (CWObs) into a new dataset (CWExt) of about two periods (orbits), where the first half
orbit of data in CWExt is constructed by
using the second half orbit of CWObs, the last half orbit of data in CWExt is constructed by
using the first half orbit of CWObs, the rest of CWExt consists of the
observed warm counts. As a result, the FFT analysis is applied to a periodically
extended CWExt instead of CWObs.
In this way, the truncating effect occurs only during
the extended data part instead of the original data part, as shown in Figure 5(c).
Thus, the spectral characteristics of CWObs with less truncating
effect can be extracted from the FFT spectrum of artificially extending warm
counts (CWExt).In addition, the quality check of the
reconstructed warm counts is also important to avoid over-correcting the effect
of solar intrusions on warm counts.  It
has been known that solar intrusions are always related to regions nearby the
positions of the maximum/minimum ofCWObs and each intrusion occurs between 5 and 15
minutes in different seasons, based on our statistical analysis throughout one
year of data (Figure 3(e)). This feature may help identify rough locations of
several solar intrusions on warm counts in different season. Then, the reconstructed
warm counts only replace the observed warm counts over these regions. Figure 6 shows CWObs and corresponding CWCor at channel 4 for all orbits of observations on
August 15, 2006,
where CWCor in each orbit is generated by applying the
above procedures. The reconstructed warm counts in the figure effectively correct
most of the anomalies from solar intrusion. A similar analysis can be applied
to other observations and channels in a year. By assessing corresponding
antenna temperature differences based on the reconstructed warm counts, the
residual antenna temperature errors are usually smaller than 0.1 K (the figures
are omitted).Figure 6
Time series ofCWObs and corresponding CWCor at 54.4 GHz for all orbits on August 15, 2006. In the figures, an orbital mean of corresponding counts has been subtracted from the warm counts in each orbit of observations.


## 3.2. Removal of Antenna Emission

From the
linear calibration equation (4) and the reconstructed calibration counts, the
antenna temperatures can be obtained. This antenna temperature (TA′), however,
includes the contribution of the antenna emission. Theoretically, we can derive
the antenna temperature from the earth scene’s radiance by removing antenna
emission using (2), that is, (7)TA=TA′−εRTR1−εR.Obviously, the variables required to
perform this calculation are the reflector
temperature and emissivity. Unfortunately,
neither of them is available from measurements. For the reflector emissivity, a
set of reflector emissivity at
frequencies from 19.35 GHz to 183 GHz are given from the NRL emissivity model simulations.
With this reflector emissivity, the remaining issue is to find reflector
temperature (TR).Estimate
of reflector temperatures are made from the arm temperature of the main
reflector (i.e.,TARM). As
discussed in Section 2, TARM
is an important indicator because it displays a similar orbital feature to the
radiance difference (antenna emission) except for its response lag to solar
heating (see Figure 2). So, the reflector temperature can be calculated in terms
of TARM with a proper
adjustment [7, 9],
that is,
(8)TR(ti)=TARM(ti)+ΔTR(ti),  where ΔTR represents an adjustment corresponding to the difference between TR and TARM
due to the response lag of the arm to solar
heating, t the time of each scan line
corresponding to a specific latitude,
and the subscript “i” the ith scan line per orbit.In
this study,ΔTR is determined by using a group of polynomial expressions
for latitude. The fitting coefficients of polynomial expressions are derived
from the training datasets of TR  (and TARM), and this TR is
generated by solving (7) with the RTM simulations, that is, (9)TR,ich=TA,ich′−(1−εR,ich)TA,ichεR,ich, where εR,ich  is the
emissivity at the ith channel, and i=4,5,6,7, corresponding for 54.4,
55.5, 57.3, 59.4 GHz. However, TA in (9) is obtained approximately from
the RTM simulated antenna temperature.After the training dataset of the
retrievedTR and observed  TARM
is obtained, ΔTR is
further derived as an equation in terms of latitude (β), which is expressed as (10)ΔTR,ich=a0i+∑j=1Najiβ.As an example, Figure7 shows the
reflector arm temperature, the retrieved and fitted reflector temperatures at
54.4 GHz, on March 20, 2006,
where the retrieved reflector temperature is calculated using (9) and the
fitted reflector temperature is calculated using (8) and (10). It is found that
the retrieved reflector temperature can be fitted well from (8) and (10). In
comparison to the observed TARM,
the TR
at channel 4 responds
to the solar heating faster than TARM
and the most significant adjustment (i.e., a maximum ΔTR) is made
when the spacecraft is out of the Earth’s eclipse (around 20°N in
the ascending node). Consequently, the reflector temperature captures more closely
the trend of the bias than the arm temperature. The reflector temperature does
show a significant orbital cycle where it varies between 220 and 330 K. This
large variation in TR (100 K) can explain a maximum error of 2 K in SSMIS antenna temperature at oxygen
channels. So-estimated emission magnitude at 54.4 GHz agrees well with the
observed anomaly.Figure 7
Comparisons of the observed arm temperature, the retrieved and fitted reflector temperatures at 54.4 GHz during one orbit of observations on March 20, 2006.Global distribution of antenna temperature bias between SSMIS TDR measurements and radiative transfer simulations  on March 20, 2006 for (a) 54.4 GHz, and (b) 55.5 GHz.
(a)
SSMIS observations-simulations at 54.4 GHz, 2006-03-20(b)
SSMIS observations-simulations at 55.5 GHz, 2006-03-20According to the results of the reflector
temperatures at the four channels retrieved using (9), some similar orbital features
are observed from the four retrieved reflector temperatures (the figures are
omitted here) although their magnitudes vary slightly with channel with a
difference of about 10 K. For simplicity, the reflector temperatures at the other
three channels are produced from the reconstructed reflector temperatures at
channel 4 with some constant offsets from 10 to 15 K. Currently, we are unable
to accurately simulate the global brightness temperatures at channels 1~3 due
to lack in information of accurate clouds and land surface emissivity. It has
been known that the observations from channels 1~5 are received through the A4
antenna feed. Also, the difference in the retrieved reflector temperatures at
the four channels between 4 and 7 is below 15 K over most of areas. So, in this
study, the reflector temperatures at channels 1~3 are assumed to be
equivalent approximately to that at  channel 4.


## 4. Evaluations of SSMIS Anomaly Correction Algorithms

### 4.1. Comparisons with RTM Simulations and AMSU-A Observations

Performance of the SSMIS antenna
temperature anomaly correction algorithm is assessed using the observed and RTM-simulated
brightness temperatures at all LAS channels. For demonstration, Figures8(a)-8(b) display the global distributions of the
bias at 54.4 and 55.5 GHz for March
20, 2006, which are computed using the SSMIS TDR data; Figures 9(a)-9(b)
display the global distributions of the bias at the same frequencies, which are
computed using the antenna temperatures after the SSMIS anomaly correction
(known as CTDR). In comparison to results for SSMIS TDR data in Figures 8(a)-8(b), the
antenna temperature biases caused by antenna emission and warm count anomaly are
mostly corrected in Figures 9(a)-9(b). The absolute biases in CTDR data are
typically smaller than 0.5 K over most of the global areas. A similar
comparison may be applied to channels 1–3, but the regions are limited to cloud-free
oceans due to lack of accurate information about clouds and land emissivity.
Results also show that antenna temperature differences by using CTDR data are
typically within 0.5 K (figures are omitted). This conclusion is also valid for
longer sets of SSMIS TDR data throughout 2006. As an example, Figure 10(a) shows
the mean bias for a few SSMIS sounding channels plotted against latitude on June
19, 2006, whereas Figure 10(b) displays a time series of the mean bias at
latitude of 50°N in descending node throughout 2006. Note that the antenna
temperature anomalies at certain latitudes show a strong seasonal feature. For
example, the antenna temperature anomalies at 50°N from March to September
vary around 1.8 K, but they gradually reduce to around 0.5 K beyond this
period. Also, the gradual shifts
in phase and magnitude of the biases are observed. This is presumably a result
of the change in satellite to sun’s position from season to season. Overall, the
results in Figure 10 demonstrate that the antenna temperature differences after
anomaly correction throughout a year are usually smaller than 0.5 K. Therefore,
a stable performance of the SSMIS CTDR radiances at the LAS channels can be
produced from the newly developed SSMIS anomaly correction algorithm.Global distributions of antenna temperature bias between F16 CTDR measurements and radiative transfer simulations where “Cal.” denotes the calibrated antenna temperatures using the newly developed calibration algorithm for (a) 54.4 GHz and (b) 55.5 GHz.
(a)
Cal. SSMIS observations-simulations at 54.4 GHz, 2006-03-20(b)
Cal. SSMIS observations-simulations at 55.5 GHz, 2006-03-20(a) Longitudinally averaged antenna temperature biases between F16 SSMIS TDR (CTDR) measurements and simulations at 54.4, 55.5, 57.3, and 59.4 GHz on June 19, 2006, and (b)  time series of the longitudinally averaged antenna temperature biases at latitude of50°N. In the figures, red is for newly calibrated while blue for original TDR results.
(a)(b)Furthermore, for monitoring the onorbit
instrument performance and for achieving the calibration consistency and
traceability, the intersatellite comparison among various satellite-borne
radiometers is very important. Since SSMIS and AMSU-A have several
channels in common, the measurements at 53.6, 54.4, 55.5, and 57.3 GHz from
both instruments can be compared directly for calibration consistency check-up.
To match the data together, we developed the simultaneous conical overpass (SCO)
which is a slight revision of the simultaneous Nadir overpass (SNO) algorithm
[18, 22]. When two satellites at different
altitudes cross each other at the same earth location, an SCO match pair is
generated. The distance window from
two sensor observations is set to be equal to an earth ground distance of 50 km; the time window is set to 60 seconds; the viewing angle window is about 2°.There are a total of 347 SCO events found
for F-16 SSMIS and NOAA-16 AMSU from January 2005 to December 2006, which are
located usually at high latitudes. The brightness temperatures of these
SCO-observations at 53.6, 54.4, 55.5, and 57.3 GHz are displayed in Figures11(a)–11(d), respectively. For convenience of comparison, the SCO observations of
SSMIS brightness temperatures (SDR data) before and after our new calibration
are plotted against AMSU measurements. The mean brightness temperature difference
and the standard deviation of the brightness temperature differences are shown
in the figures. It is recognized that the original SSMIS brightness
temperatures are larger than these from NOAA-16 AMSU by a positive value from 1
and 2 K depending upon channel, which is consistent with the previous analyses.
The mean differences in brightness temperatures between calibrated SSMIS and
NOAA-16 AMSU measurements are usually around 0.5 K at 54.4, 55.5, and 57.3 GHz.
At 53.6 GHz, the mean differences for both TDR and CTDR SSMIS data are
relatively large, which might imply a large systematic bias in F16 SSMIS data at
this frequency.Intersatellite comparisons of brightness temperatures (TB) between F16 SSMIS TDR (CTDR) and NOAA-16 measurements at (a) 53.6 GHz, (b) 54.4 GHz, (c) 55.5 GHz, and (d) 57.3 GHz. In the figures, red is for newly calibrated while blue for original TDR results.
(a)(b)(c)(d)As shown in Figures11(a)–11(d), the standard
deviation of CTDR at each of the four channels is between 0.3 and 0.5, which is
usually smaller than that of TDR data except for 53.6 GHz. This implies that
the aforementioned SSMIS recalibration algorithm corrects the major effects of
the antenna emission and the solar intrusion on the warm counts, but at the
same time, it adds some noises into the CTDR data at 53.6 GHz. The noise
sources associated are investigated by two experiments, turning on/off emission
and warm count anomaly correction prior SCO collocation. Table 3 displays the
mean brightness temperature biases and standard deviation between AMSU-A and
SSMIS brightness temperatures. Here, three F16 datasets are used including original
TDR data, TDR data with only emission anomaly correction, and the TDR data
including both emission and warm count anomaly corrections. It is found that
the emission correction contributes some extra noises to the data (i.e., a
larger standard deviation compared to the TDR data) at 53.6 and 55.5 GHz. The warm
count anomaly correction reduces the standard  deviation. An increase in the
standard deviation from the antenna emission correction may be due to
inaccurate reflector temperatures (see Section 4.3 for details).Table 3
Biases and standard deviation (STD) characteristics of brightness
temperature differences between F16 SSMIS and NOAA 16 AMSU from SCO
measurements at four frequencies.
TDR typeBIAS/STD53.6 GHz54.4 GHz55.5 GHz57.2 GHzNo recalibrationBIAS2.6231.8161.3200.741STD0.4470.7100.4230.785Emission only correctionBIAS1.4330.4580.1170.622STD0.7220.4710.4790.551Emission plus warm count anomaly correctionsBIAS1.4600.6480.1800.357STD0.6610.4320.3780.566


### 4.2. Impacts of Anomaly-Reduced SSMIS Measurements on NCEP NWP Model

Direct benefits from improved cal/val algorithms will be more satellite data used in NWP models, which is directly related to quality of satellite data. So, it is important to demonstrate if the anomaly-corrected SSMIS data at the LAS channels is of good quality for operational applications in weather and climate models. The anomalies in F16 SSMIS radiances at the LAS channels can be mostly corrected using the algorithm as shown in Section3. However, there remain certain scan-dependent biases in F16 SSMIS measurements which are irrelevant to calibration anomaly [10, 23]. Figures 12(a)–12(d) display mean biases of antenna temperatures against scan beam position at four LAS channels, which is a difference between antenna temperature at a given beam position and that at a central beam position. The results in Figure 12 represent an average based on one year of data in ascending node over cloud-free oceans. An obvious decrease of around a couple of Kevin depending on channel is detected at each channel. Since the scan-dependent bias feature is relatively stable, this scan bias can be corrected in terms of scan position from the SSMIS measurements. NWP model is based on an assumption that the used data is no bias. A bias correction including SSMIS scan bias is thus needed as the SSMIS data is applied to NWP (the description of the bias correction is omitted here). Figure 13(a) displays the utilization rate of the SSMIS data with a bias correction at channels 1–4 for three orbits of observations which are assimilated into the NCEP global forecast model after a set of quality controls (QCs) (seeing explanations in the figure for details). For comparison, the data recalibrated using UK SSMIS recalibration algorithm (UKMO SSMIS CTDR data) [21] is assimilated into the NCEP global forecast model and the data usage is also shown in the figure. It is found that NESDIS TDR anomaly correction algorithms result in more SSMIS data assimilated into NWP models than the UK SSMIS recalibration algorithm. For instance, about 40 to 70% of NESDIS SSMIS CTDR data at channels 2 and 4 can be assimilated into the NCEP global forecast system, comparing to only 15 and 60% if UKMO SSMIS CTDR data are used.SSMIS antenna temperature (TA) scan-dependent bias in ascending node at several LAS channels [23]. (a) 50.3 GHz. (b) 52.8 GHz. (c) 53.6 GHz. (d) 54.4 GHz.
(a)(b)(c)(d)(a) Number of the SSMIS data from channel 1 to channel 4 for three orbits of observations used in the NCEP global forecast model, on August 9, 2006. (b) Vertical distribution of root mean square error (RMSE) difference in the predicted geopotential height along latitude between the five days of assimilation experiments of “Cntl” and “Test” by using the NCEP global forecast model (Courtesy to Masahiro Kazumori).
(a)(b)With those SSMIS CTDR data, the positive
impact is also observed in predicting the NWP analysis fields such as
geopotential height. Figure13(b) is the distribution of difference of root mean square
error (RMSE) of two geopotential heights versus latitude, where two
geopotential heights are predicted by using “Test” and “Cntl” assimilation
experiments correspondingly. In “Cntl” assimilation experiment, only
operational global dataset including AMSU data is used in NCEP gridpoint statistical
interpolation (GSI) global data assimilation system, whereas in “Test” experiment,
NESDIS SSMIS CTDR data is also added into the GSI system in addition to the
operational and AMSU datasets. Results in the figure do show that a negative difference
in the RMSE of the geopotential height at various latitudes in the
stratosphere, which implies that the use of NESDIS SSMIS CTDR data improves the
accuracy of the geopotential height. In the lower atmosphere, the obvious
improvement is also detected as the NESDIS SSMIS CTDR data is used in the GSI
system. These results further demonstrated the good performance of the NESDIS
SSMIS CTDR data at the LAS channels. For comparison, a similar assimilation
experiment to the NESDIS SSMIS CTDR data experiment except for UKMO SSMIS CTDR
data is carried out. The corresponding RMSE vertical distribution in comparison
with the control experiment is also displayed in Figure 13(b).


### 4.3. Error Discussion

The
above anomaly-corrected SSMIS antenna temperatures at the LAS channels show a
good agreement with the corresponding RTM simulations and AMSU-A observations,
and produce some positive impact on numerical weather prediction analysis
fields. However, since some approximations are assumed in the derived anomaly
correction algorithm, it is still important to investigate any possible errors
in the algorithm.One error source may stem from the used
main reflector emissivity. Since the onboard F16 SSMIS main reflector
emissivity at the LAS channels is not available, the SSMIS main reflector emissivity in this
study relies on the NRL multilayer antenna model simulations. Some studies have shown that the
NRL multilayer antenna model
simulations are imperfect  [24]. According to definition of
antenna emission (see Section 2.3), for an emissivity error of δεR, the error of antenna
emission equals to (TR−TA)δεR when an
accurate reflector temperature is used. Fortunately, in
this study, the training set of reflector temperatures at several LAS channels is
determined using (9) for known reflector emissivity and antenna emission (see
Section 3.2). Thus, (9) is rewritten to be (11)εR(TR−TA)=TAE, where TAE
is antenna emission defined in Section 2.3 and also equals
to TA′−TA. Note that the
channel frequency and polarization of each variable are omitted here. For the
antenna emissions at channels 4–7, that is, TA′−TA, they are obtained by
differences between SSMIS measured and RTM simulated brightness temperatures. This
implies that the error in used antenna emission at each of channels 4–7 is only related to RTM simulation accuracy, but it is irrelevant to the errors in εR and TR. At channels 1–3, the
reflector temperatures are assumed to be the same as that at channel 4. A
certain error can be caused by this inaccurate assumption or the difference
between the reflector temperature at channels 1–3 and that at channel 4.
According to our analysis over oceans, this difference is relatively small and
so-caused effect on antenna temperature is also small (an estimate of this
effect is given below). Thus, the accuracies of the antenna emissions and
anomaly-corrected antenna temperatures at the LAS channels are less affected by
the error in the reflector emissivity in this study.However, the error inεR can be transferred to TR such that the
reflector temperature derived using (9) may be not real reflector temperature
if the NRL emissivity simulations deviate obviously from real F16 reflector
properties. This can be seen by applying an operator of derivative to (11), that
is, (12)δTR=−(TR−TA)δεRεR+δεR. Thus, there would remain some uncertainty in derived reflector
temperatures at LAS channels. In addition, potential error in reflector
temperature due to emissivity error implies that the antenna emission
correction algorithm shown in Section 3.2  is inapplicable for window channels
because an accurate reflector emissivity is always needed for accurate antenna
emission simulations and corrections at window channels. For example, at 19.35,
23.8, 31.4, 91.655 GHz, the accurate RTM simulations over global areas are at
least difficult if not impossible due to our limited knowledge of emissivity
simulation over land. These channels also use different feedhorns from LAS
channels, so the approximation of the reflector temperature at channel 4 to
these window channels would be invalid. It becomes very important to have
accurate reflector emissivity and temperature for reliable assessment of
antenna emission there using definition of antenna emission.Another error source may result from the
reflector temperature error caused by other three possible error sources: (1) the
assumption thatTR,CH1–3≈TR,CH4; (2) the  assumption that the RTM simulations are equal to realistic
anomaly-free radiances; (3) the reflector temperature bias due to the inaccurate
fitting (see Figure 7). This error can be expressed to be (13)δTA=εRδTR′.Note that this reflector temperature
error (δTR′) is different from that defined by (12) because this
error is not correlated to the emissivity error. The reflector temperature error
due to RTM simulation error is usually smaller than 10 K because RTM simulation
error is about 0.2 K, while the reflector temperature error due to other
factors are also relatively small. As shown in Sections 4.1 and 4.2, the total
residual error in anomaly-corrected antenna temperatures is about 0.5 K. Therefore, the SSMIS CTDR data is of
sufficient accuracy to be used operationally for input to numerical weather
prediction and climate models.


### 5. Summary and Conclusions

F16
SSMIS radiances at LAS channels show certain anomalies approximately between−1 K and 2 K due to both antenna emission and solar heating of warm load tines. The
antenna emission occurs globally and results in a strong geographical
dependence with obvious peaks frequently near the mid- and high-latitudes,
which can result in either positive or negative error in observed antenna
temperatures depending on difference between reflector temperature and
earth-viewing antenna temperature. The warm load count anomaly occurs over
several latitudinal zones whose coverage is around 30~40% of each orbit of
observations, which always results in a negative error in observed antenna
temperatures.An algorithm for SSMIS antenna
temperature anomaly correction has been developed using the F16 SSMIS TDR data
based on FFT analysis and calibration equation associated with reflector
temperature. With this SSMIS anomaly correction
algorithm based on the SSMIS TDR data, most of the effects from the warm count
and antenna anomalies can be removed from the SSMIS observations at the LAS
channels with a residual error smaller than 0.5 K. The produced SSMIS CTDR data is much
encouraging and is also of sufficient accuracy to be used operationally for
input to numerical weather prediction and climate models. A direct benefit from
this SSMIS CTDR data is more SSMIS data being used in NWP models, resulting in
improved NWP analysis fields. The F16 CTDR data is archived in NOAA STAR and
available under request through fuzhong.weng@noaa.gov and banghua.yan@noaa.gov.However, there remain some weaknesses in
this study. For example, the NRL-modeled emissivity used in this study has certain
errors [24]. This error would not obviously affect the
accuracy of the SSMIS antenna temperatures with anomaly correction at several
LAS channels. However, this error can result in some errors in the derived
reflector temperatures and can affect an accurate assessment of antenna
emission at window channels. Therefore, more studies are needed in our future
research activities about the best estimates of F16 main reflector emissivity
and temperatures at various channels.


## 4.1. Comparisons with RTM Simulations and AMSU-A Observations

Performance of the SSMIS antenna
temperature anomaly correction algorithm is assessed using the observed and RTM-simulated
brightness temperatures at all LAS channels. For demonstration, Figures8(a)-8(b) display the global distributions of the
bias at 54.4 and 55.5 GHz for March
20, 2006, which are computed using the SSMIS TDR data; Figures 9(a)-9(b)
display the global distributions of the bias at the same frequencies, which are
computed using the antenna temperatures after the SSMIS anomaly correction
(known as CTDR). In comparison to results for SSMIS TDR data in Figures 8(a)-8(b), the
antenna temperature biases caused by antenna emission and warm count anomaly are
mostly corrected in Figures 9(a)-9(b). The absolute biases in CTDR data are
typically smaller than 0.5 K over most of the global areas. A similar
comparison may be applied to channels 1–3, but the regions are limited to cloud-free
oceans due to lack of accurate information about clouds and land emissivity.
Results also show that antenna temperature differences by using CTDR data are
typically within 0.5 K (figures are omitted). This conclusion is also valid for
longer sets of SSMIS TDR data throughout 2006. As an example, Figure 10(a) shows
the mean bias for a few SSMIS sounding channels plotted against latitude on June
19, 2006, whereas Figure 10(b) displays a time series of the mean bias at
latitude of 50°N in descending node throughout 2006. Note that the antenna
temperature anomalies at certain latitudes show a strong seasonal feature. For
example, the antenna temperature anomalies at 50°N from March to September
vary around 1.8 K, but they gradually reduce to around 0.5 K beyond this
period. Also, the gradual shifts
in phase and magnitude of the biases are observed. This is presumably a result
of the change in satellite to sun’s position from season to season. Overall, the
results in Figure 10 demonstrate that the antenna temperature differences after
anomaly correction throughout a year are usually smaller than 0.5 K. Therefore,
a stable performance of the SSMIS CTDR radiances at the LAS channels can be
produced from the newly developed SSMIS anomaly correction algorithm.Global distributions of antenna temperature bias between F16 CTDR measurements and radiative transfer simulations where “Cal.” denotes the calibrated antenna temperatures using the newly developed calibration algorithm for (a) 54.4 GHz and (b) 55.5 GHz.
(a)
Cal. SSMIS observations-simulations at 54.4 GHz, 2006-03-20(b)
Cal. SSMIS observations-simulations at 55.5 GHz, 2006-03-20(a) Longitudinally averaged antenna temperature biases between F16 SSMIS TDR (CTDR) measurements and simulations at 54.4, 55.5, 57.3, and 59.4 GHz on June 19, 2006, and (b)  time series of the longitudinally averaged antenna temperature biases at latitude of50°N. In the figures, red is for newly calibrated while blue for original TDR results.
(a)(b)Furthermore, for monitoring the onorbit
instrument performance and for achieving the calibration consistency and
traceability, the intersatellite comparison among various satellite-borne
radiometers is very important. Since SSMIS and AMSU-A have several
channels in common, the measurements at 53.6, 54.4, 55.5, and 57.3 GHz from
both instruments can be compared directly for calibration consistency check-up.
To match the data together, we developed the simultaneous conical overpass (SCO)
which is a slight revision of the simultaneous Nadir overpass (SNO) algorithm
[18, 22]. When two satellites at different
altitudes cross each other at the same earth location, an SCO match pair is
generated. The distance window from
two sensor observations is set to be equal to an earth ground distance of 50 km; the time window is set to 60 seconds; the viewing angle window is about 2°.There are a total of 347 SCO events found
for F-16 SSMIS and NOAA-16 AMSU from January 2005 to December 2006, which are
located usually at high latitudes. The brightness temperatures of these
SCO-observations at 53.6, 54.4, 55.5, and 57.3 GHz are displayed in Figures11(a)–11(d), respectively. For convenience of comparison, the SCO observations of
SSMIS brightness temperatures (SDR data) before and after our new calibration
are plotted against AMSU measurements. The mean brightness temperature difference
and the standard deviation of the brightness temperature differences are shown
in the figures. It is recognized that the original SSMIS brightness
temperatures are larger than these from NOAA-16 AMSU by a positive value from 1
and 2 K depending upon channel, which is consistent with the previous analyses.
The mean differences in brightness temperatures between calibrated SSMIS and
NOAA-16 AMSU measurements are usually around 0.5 K at 54.4, 55.5, and 57.3 GHz.
At 53.6 GHz, the mean differences for both TDR and CTDR SSMIS data are
relatively large, which might imply a large systematic bias in F16 SSMIS data at
this frequency.Intersatellite comparisons of brightness temperatures (TB) between F16 SSMIS TDR (CTDR) and NOAA-16 measurements at (a) 53.6 GHz, (b) 54.4 GHz, (c) 55.5 GHz, and (d) 57.3 GHz. In the figures, red is for newly calibrated while blue for original TDR results.
(a)(b)(c)(d)As shown in Figures11(a)–11(d), the standard
deviation of CTDR at each of the four channels is between 0.3 and 0.5, which is
usually smaller than that of TDR data except for 53.6 GHz. This implies that
the aforementioned SSMIS recalibration algorithm corrects the major effects of
the antenna emission and the solar intrusion on the warm counts, but at the
same time, it adds some noises into the CTDR data at 53.6 GHz. The noise
sources associated are investigated by two experiments, turning on/off emission
and warm count anomaly correction prior SCO collocation. Table 3 displays the
mean brightness temperature biases and standard deviation between AMSU-A and
SSMIS brightness temperatures. Here, three F16 datasets are used including original
TDR data, TDR data with only emission anomaly correction, and the TDR data
including both emission and warm count anomaly corrections. It is found that
the emission correction contributes some extra noises to the data (i.e., a
larger standard deviation compared to the TDR data) at 53.6 and 55.5 GHz. The warm
count anomaly correction reduces the standard  deviation. An increase in the
standard deviation from the antenna emission correction may be due to
inaccurate reflector temperatures (see Section 4.3 for details).Table 3
Biases and standard deviation (STD) characteristics of brightness
temperature differences between F16 SSMIS and NOAA 16 AMSU from SCO
measurements at four frequencies.
TDR typeBIAS/STD53.6 GHz54.4 GHz55.5 GHz57.2 GHzNo recalibrationBIAS2.6231.8161.3200.741STD0.4470.7100.4230.785Emission only correctionBIAS1.4330.4580.1170.622STD0.7220.4710.4790.551Emission plus warm count anomaly correctionsBIAS1.4600.6480.1800.357STD0.6610.4320.3780.566


## 4.2. Impacts of Anomaly-Reduced SSMIS Measurements on NCEP NWP Model

Direct benefits from improved cal/val algorithms will be more satellite data used in NWP models, which is directly related to quality of satellite data. So, it is important to demonstrate if the anomaly-corrected SSMIS data at the LAS channels is of good quality for operational applications in weather and climate models. The anomalies in F16 SSMIS radiances at the LAS channels can be mostly corrected using the algorithm as shown in Section3. However, there remain certain scan-dependent biases in F16 SSMIS measurements which are irrelevant to calibration anomaly [10, 23]. Figures 12(a)–12(d) display mean biases of antenna temperatures against scan beam position at four LAS channels, which is a difference between antenna temperature at a given beam position and that at a central beam position. The results in Figure 12 represent an average based on one year of data in ascending node over cloud-free oceans. An obvious decrease of around a couple of Kevin depending on channel is detected at each channel. Since the scan-dependent bias feature is relatively stable, this scan bias can be corrected in terms of scan position from the SSMIS measurements. NWP model is based on an assumption that the used data is no bias. A bias correction including SSMIS scan bias is thus needed as the SSMIS data is applied to NWP (the description of the bias correction is omitted here). Figure 13(a) displays the utilization rate of the SSMIS data with a bias correction at channels 1–4 for three orbits of observations which are assimilated into the NCEP global forecast model after a set of quality controls (QCs) (seeing explanations in the figure for details). For comparison, the data recalibrated using UK SSMIS recalibration algorithm (UKMO SSMIS CTDR data) [21] is assimilated into the NCEP global forecast model and the data usage is also shown in the figure. It is found that NESDIS TDR anomaly correction algorithms result in more SSMIS data assimilated into NWP models than the UK SSMIS recalibration algorithm. For instance, about 40 to 70% of NESDIS SSMIS CTDR data at channels 2 and 4 can be assimilated into the NCEP global forecast system, comparing to only 15 and 60% if UKMO SSMIS CTDR data are used.SSMIS antenna temperature (TA) scan-dependent bias in ascending node at several LAS channels [23]. (a) 50.3 GHz. (b) 52.8 GHz. (c) 53.6 GHz. (d) 54.4 GHz.
(a)(b)(c)(d)(a) Number of the SSMIS data from channel 1 to channel 4 for three orbits of observations used in the NCEP global forecast model, on August 9, 2006. (b) Vertical distribution of root mean square error (RMSE) difference in the predicted geopotential height along latitude between the five days of assimilation experiments of “Cntl” and “Test” by using the NCEP global forecast model (Courtesy to Masahiro Kazumori).
(a)(b)With those SSMIS CTDR data, the positive
impact is also observed in predicting the NWP analysis fields such as
geopotential height. Figure13(b) is the distribution of difference of root mean square
error (RMSE) of two geopotential heights versus latitude, where two
geopotential heights are predicted by using “Test” and “Cntl” assimilation
experiments correspondingly. In “Cntl” assimilation experiment, only
operational global dataset including AMSU data is used in NCEP gridpoint statistical
interpolation (GSI) global data assimilation system, whereas in “Test” experiment,
NESDIS SSMIS CTDR data is also added into the GSI system in addition to the
operational and AMSU datasets. Results in the figure do show that a negative difference
in the RMSE of the geopotential height at various latitudes in the
stratosphere, which implies that the use of NESDIS SSMIS CTDR data improves the
accuracy of the geopotential height. In the lower atmosphere, the obvious
improvement is also detected as the NESDIS SSMIS CTDR data is used in the GSI
system. These results further demonstrated the good performance of the NESDIS
SSMIS CTDR data at the LAS channels. For comparison, a similar assimilation
experiment to the NESDIS SSMIS CTDR data experiment except for UKMO SSMIS CTDR
data is carried out. The corresponding RMSE vertical distribution in comparison
with the control experiment is also displayed in Figure 13(b).


## 4.3. Error Discussion

The
above anomaly-corrected SSMIS antenna temperatures at the LAS channels show a
good agreement with the corresponding RTM simulations and AMSU-A observations,
and produce some positive impact on numerical weather prediction analysis
fields. However, since some approximations are assumed in the derived anomaly
correction algorithm, it is still important to investigate any possible errors
in the algorithm.One error source may stem from the used
main reflector emissivity. Since the onboard F16 SSMIS main reflector
emissivity at the LAS channels is not available, the SSMIS main reflector emissivity in this
study relies on the NRL multilayer antenna model simulations. Some studies have shown that the
NRL multilayer antenna model
simulations are imperfect  [24]. According to definition of
antenna emission (see Section 2.3), for an emissivity error of δεR, the error of antenna
emission equals to (TR−TA)δεR when an
accurate reflector temperature is used. Fortunately, in
this study, the training set of reflector temperatures at several LAS channels is
determined using (9) for known reflector emissivity and antenna emission (see
Section 3.2). Thus, (9) is rewritten to be (11)εR(TR−TA)=TAE, where TAE
is antenna emission defined in Section 2.3 and also equals
to TA′−TA. Note that the
channel frequency and polarization of each variable are omitted here. For the
antenna emissions at channels 4–7, that is, TA′−TA, they are obtained by
differences between SSMIS measured and RTM simulated brightness temperatures. This
implies that the error in used antenna emission at each of channels 4–7 is only related to RTM simulation accuracy, but it is irrelevant to the errors in εR and TR. At channels 1–3, the
reflector temperatures are assumed to be the same as that at channel 4. A
certain error can be caused by this inaccurate assumption or the difference
between the reflector temperature at channels 1–3 and that at channel 4.
According to our analysis over oceans, this difference is relatively small and
so-caused effect on antenna temperature is also small (an estimate of this
effect is given below). Thus, the accuracies of the antenna emissions and
anomaly-corrected antenna temperatures at the LAS channels are less affected by
the error in the reflector emissivity in this study.However, the error inεR can be transferred to TR such that the
reflector temperature derived using (9) may be not real reflector temperature
if the NRL emissivity simulations deviate obviously from real F16 reflector
properties. This can be seen by applying an operator of derivative to (11), that
is, (12)δTR=−(TR−TA)δεRεR+δεR. Thus, there would remain some uncertainty in derived reflector
temperatures at LAS channels. In addition, potential error in reflector
temperature due to emissivity error implies that the antenna emission
correction algorithm shown in Section 3.2  is inapplicable for window channels
because an accurate reflector emissivity is always needed for accurate antenna
emission simulations and corrections at window channels. For example, at 19.35,
23.8, 31.4, 91.655 GHz, the accurate RTM simulations over global areas are at
least difficult if not impossible due to our limited knowledge of emissivity
simulation over land. These channels also use different feedhorns from LAS
channels, so the approximation of the reflector temperature at channel 4 to
these window channels would be invalid. It becomes very important to have
accurate reflector emissivity and temperature for reliable assessment of
antenna emission there using definition of antenna emission.Another error source may result from the
reflector temperature error caused by other three possible error sources: (1) the
assumption thatTR,CH1–3≈TR,CH4; (2) the  assumption that the RTM simulations are equal to realistic
anomaly-free radiances; (3) the reflector temperature bias due to the inaccurate
fitting (see Figure 7). This error can be expressed to be (13)δTA=εRδTR′.Note that this reflector temperature
error (δTR′) is different from that defined by (12) because this
error is not correlated to the emissivity error. The reflector temperature error
due to RTM simulation error is usually smaller than 10 K because RTM simulation
error is about 0.2 K, while the reflector temperature error due to other
factors are also relatively small. As shown in Sections 4.1 and 4.2, the total
residual error in anomaly-corrected antenna temperatures is about 0.5 K. Therefore, the SSMIS CTDR data is of
sufficient accuracy to be used operationally for input to numerical weather
prediction and climate models.


## 5. Summary and Conclusions

F16
SSMIS radiances at LAS channels show certain anomalies approximately between−1 K and 2 K due to both antenna emission and solar heating of warm load tines. The
antenna emission occurs globally and results in a strong geographical
dependence with obvious peaks frequently near the mid- and high-latitudes,
which can result in either positive or negative error in observed antenna
temperatures depending on difference between reflector temperature and
earth-viewing antenna temperature. The warm load count anomaly occurs over
several latitudinal zones whose coverage is around 30~40% of each orbit of
observations, which always results in a negative error in observed antenna
temperatures.An algorithm for SSMIS antenna
temperature anomaly correction has been developed using the F16 SSMIS TDR data
based on FFT analysis and calibration equation associated with reflector
temperature. With this SSMIS anomaly correction
algorithm based on the SSMIS TDR data, most of the effects from the warm count
and antenna anomalies can be removed from the SSMIS observations at the LAS
channels with a residual error smaller than 0.5 K. The produced SSMIS CTDR data is much
encouraging and is also of sufficient accuracy to be used operationally for
input to numerical weather prediction and climate models. A direct benefit from
this SSMIS CTDR data is more SSMIS data being used in NWP models, resulting in
improved NWP analysis fields. The F16 CTDR data is archived in NOAA STAR and
available under request through fuzhong.weng@noaa.gov and banghua.yan@noaa.gov.However, there remain some weaknesses in
this study. For example, the NRL-modeled emissivity used in this study has certain
errors [24]. This error would not obviously affect the
accuracy of the SSMIS antenna temperatures with anomaly correction at several
LAS channels. However, this error can result in some errors in the derived
reflector temperatures and can affect an accurate assessment of antenna
emission at window channels. Therefore, more studies are needed in our future
research activities about the best estimates of F16 main reflector emissivity
and temperatures at various channels.



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*Source: 420985-2009-04-16.xml*