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  • View in gallery

    The earth minus cold count difference ΔCec (K) as measured during the deep-space maneuver as a function of scan position and scan number. These results are before removing the magnetic sensitivity error.

  • View in gallery

    As in Fig. 1, except the MSE has been removed.

  • View in gallery

    Results of the GMI deep-space maneuver during which the primary reflector and cold mirror simultaneously view cold space. Each column is a different frequency. The plots show ΔCec (K). The red and green curves show the v-pol and h-pol ΔCec, respectively. (top row) Results before adjusting the counts. (bottom) Results after applying offsets to Ce and Cc derived from the deep-space calibration. The black line shows ΔCec predicted by the MoM antenna pattern. The predicted values correspond to the average of v-pol and h-pol. For 24 GHz, the predicted ΔCec curve is the 11-GHz curve with a minus sign appended and slightly offset. We do this to show that the dominant Earth contamination at 24 GHz seems to be in Cc, not Ce.

  • View in gallery

    Histograms of the GMI’s second Stokes TA measurements for near-nadir observations.

  • View in gallery

    Results of the 20 May 2014 backlobe maneuver that occurred in the South Pacific. GMI TA measurement (red) compared to the simulated TA (blue). The time during which the pitch was between 177° and 183° is marked by the small black bar. During this time, the GMI backlobe is completely subtended by the earth, and this is the time period used to find ηbl.

  • View in gallery

    As in Fig. 5, except these results are from the 9 Dec 2014 backlobe maneuver that occurred over the Gulf of Alaska.

  • View in gallery

    Rain rate from the SSMIS flying on the DMSP F17 satellite taken within 1 h of the GMI backlobe observations during the 20 May 2014 maneuver. The 180° pitch point occurs at 23°S, 194°E.

  • View in gallery

    Geographic maps of the cold-count anomaly. Counts have been converted to TA (K) by multiplying by the typical gain for a given channel. The larger features are due to gain variation in the cold counts that persist even after averaging for 13 months and should not be interpreted as an error. The continents of South America and Australia are barely visible at 11 and 19 GHz, respectively.

  • View in gallery

    GMI TA minus RTM TA anomaly plotted vs the sun azimuth angle φsun and zenith angle θsun. The larger features at 89 GHz are attributed to the RTM mismodeling clouds. The dark blue area is the region of φsun, θsun not sampled by GMI. There is no evidence of hot-load problems.

  • View in gallery

    GMI TA minus RTM TA anomaly plotted vs the orbit number and intraorbit position. The results go up to orbit 6182. WindSat, TMI, and AMSR-2 are the reference sensors. The larger features at 89 GHz are attributed to the RTM mismodeling clouds. There is no evidence of residual MSE or other calibration problems.

  • View in gallery

    GMI TA minus RTM TA anomaly plotted vs the orbit number and intraorbit position. As in Fig. 10, except the GMI retrievals are used to compute the RTM TA rather than WindSat, TMI, and AMSR-2. Since there are GMI retrievals for all observations, there is complete coverage. There is no evidence of residual MSE or other calibration problems.

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On-Orbit Absolute Calibration of the Global Precipitation Measurement Microwave Imager

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  • 1 Remote Sensing Systems, Santa Rosa, California
  • | 2 Ball Aerospace and Technologies Corp., Boulder, Colorado
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Abstract

The Global Precipitation Measurement (GPM) Core Observatory was launched on 27 February 2014. One of the principal instruments on the spacecraft is the GPM Microwave Imager (GMI). This paper describes the absolute calibration of the GMI antenna temperature (TA) and the earth brightness temperature (TB). The deep-space observations taken on 20 May 2014, supplemented by nadir-viewing data, are used for the TA calibration. Data from two backlobe maneuvers are used to determine the primary reflector’s cold-space spillover, which is required to convert the TA into TB. The calibrated GMI observations are compared to predictions from an ocean radiative transfer model (RTM) using collocated WindSat ocean retrievals as input. The mean difference when averaged globally over 13 months does not exceed 0.1 K for any of the nine channels from 11 to 89 GHz. The RTM comparisons also show that there are no significant solar intrusion errors in the GMI hot load. The absolute accuracy of the GMI instrument is defined as the average ocean-viewing error of the measured TA or TB relative to the true TA or TB. Based on the analyses herein, the GMI absolute accuracy for TA is estimated to be about 0.1 K rms over all channels and 0.25 K rms over all channels for TB.

Denotes content that is immediately available upon publication as open access.

Publisher’s Note: This article was revised on 17 April 2017 to include the open access designation that was missing when originally published.

Corresponding author address: Frank J. Wentz, Remote Sensing Systems, 444 Tenth Street, Santa Rosa, CA 95401. E-mail: frank.wentz@remss.com

Abstract

The Global Precipitation Measurement (GPM) Core Observatory was launched on 27 February 2014. One of the principal instruments on the spacecraft is the GPM Microwave Imager (GMI). This paper describes the absolute calibration of the GMI antenna temperature (TA) and the earth brightness temperature (TB). The deep-space observations taken on 20 May 2014, supplemented by nadir-viewing data, are used for the TA calibration. Data from two backlobe maneuvers are used to determine the primary reflector’s cold-space spillover, which is required to convert the TA into TB. The calibrated GMI observations are compared to predictions from an ocean radiative transfer model (RTM) using collocated WindSat ocean retrievals as input. The mean difference when averaged globally over 13 months does not exceed 0.1 K for any of the nine channels from 11 to 89 GHz. The RTM comparisons also show that there are no significant solar intrusion errors in the GMI hot load. The absolute accuracy of the GMI instrument is defined as the average ocean-viewing error of the measured TA or TB relative to the true TA or TB. Based on the analyses herein, the GMI absolute accuracy for TA is estimated to be about 0.1 K rms over all channels and 0.25 K rms over all channels for TB.

Denotes content that is immediately available upon publication as open access.

Publisher’s Note: This article was revised on 17 April 2017 to include the open access designation that was missing when originally published.

Corresponding author address: Frank J. Wentz, Remote Sensing Systems, 444 Tenth Street, Santa Rosa, CA 95401. E-mail: frank.wentz@remss.com

1. Introduction

The Global Precipitation Measurement (GPM) Core Observatory (GPM Core Observatory) was launched on 27 February 2014. One of the principal instruments on the spacecraft is the GPM Microwave Imager (GMI). GMI is the follow-on instrument for the Tropical Rainfall Measuring Mission (TRMM) Microwave (MW) Imager (TMI), which provided continuous and stable observations for 17 years, until its scheduled end of mission in April 2015 (Wentz 2015). The combination of GMI and TMI provides the potential to acquire three decades of extraordinarily stable MW observations.

In addition to providing information on precipitation, over the oceans GMI provides a full suite of environmental parameters, including sea surface temperature (TS), wind speed (W), columnar water vapor (V), and columnar cloud liquid water (L). The literature has many examples of the importance of these variables to climate research (Wentz and Schabel 2000; Wentz et al. 2000; Trenberth et al. 2005; Chelton and Wentz 2005; Mears et al. 2007; Wentz et al. 2007). Three decades of these essential climate variables will provide a unique contribution to climate change research.

Climate applications are very demanding when it comes to sensor calibration. Here, we take a critical look at GMI on-orbit performance during the first year of operation (March 2014–March 2015). Typical climate applications require accuracies of about 0.1–0.2 K in the estimate of the earth’s MW brightness temperature (TB).

GMI represents a significant advancement in satellite MW imagers. The prelaunch characterization of the sensor was the most extensive ever and is thoroughly documented in a 221-page GMI calibration data book (GCDB) with an additional 25 appendixes (Draper 2015). GMI is the first MW imager to employ both external and internal calibration systems. This dual calibration provides the means, for the first time, to measure the nonlinear response of the electronics in orbit. The external hot load, used for the warm-end calibration, was carefully designed to eliminate problems due to solar intrusion and thermal gradients.

In addition to the well-designed, well-characterized sensor, GPM conducted several orbital maneuvers during the first year of operation that play an essential role in our analysis. These orbital maneuvers include the following:

  1. Deep-space maneuver for which the primary reflector and cold mirror view cold space.
  2. Backlobe maneuver for which the backlobe of the primary reflector sees the earth.
  3. Nadir maneuver for which the primary reflector views the earth at zero incidence angle.

Our long-standing method of calibrating satellite MW imagers is to use an ocean radiative transfer model (RTM) as a reference (Meissner and Wentz 2004, 2012; Wentz and Meissner 2016). This gives us a common reference for all sensors. Rather than using purely empirical offsets, the calibration to the RTM is done by adjusting physical parameters such as the hot-load temperature and the antenna pattern. For the purpose of doing geophysical retrievals, one important requirement is that the measurements agree with the RTM used to develop the retrieval algorithm, and our RTM calibration method accomplishes this. However, the question of absolute calibration has always been an issue. Until GMI, the uncertainty in characterization of the MW imagers was so large that we had considerable freedom (1–2 K) in adjusting the sensor parameters to match the observations to the RTM. This has changed with the advent of GMI and its orbital maneuvers. The absolute calibration can now be done using solely the GMI observations collected during the three maneuvers. The RTM comparisons can then be used to evaluate the cold-space calibration at warmer Earth temperatures.

2. Channel set and required datasets

GMI operates at eight frequencies from 11 to 183 GHz. Our analysis considers only the five lower channels: 10.6, 18.7, 23.8, 36.6, and 89.0 GHz. At all of these frequencies except 23.8 GHz, both vertical polarization (v-pol, V) and horizontal polarization (h-pol, H) observations are taken. At 23.8 GHz, there are only v-pol observations. This set of nine channels is denoted by 11V, 11H, 19V, 19H, 24V, 37V, 37H, 89V, and 89H.

The GMI data used herein are the V03C-Base-RSS data files obtained from NASA Goddard Precipitation Processing System (PPS) (GPM Science Team 2014). Unless otherwise noted, the calibration parameters we use are the same as reported in the GCDB. The ocean retrievals from the NRL WindSat on Coriolis, the Advanced Microwave Scanning Radiometer 2 (AMSR-2) on the Global Change Observation Mission for Water-1 (GCOM-W1), TMI, and the Special Sensor Microwave Imager/Sounders (SSMIS) on DMSP platforms are downloaded from Remote Sensing System (RSS) (www.remss.com). Two SSMIS are used in this study: one flying on the F16 spacecraft and the other on F17. All of these ocean retrievals are available as RSS version 7 products. The sea surface temperature dataset comes from the NOAA SST operational product (Reynolds et al. 2002a,b). For wind direction, we use the National Centers for Environmental Prediction (NCEP) Global Data Assimilation System 6-hourly wind fields (NOAA/NCEP 2000).

Much of the analysis is performed in terms of radiometer counts. To provide a more meaningful description of the sensitivities being considered, we note that between 35 and 45 counts is equivalent to a change of 1 K in antenna temperature (TA). Using a value of 40 counts = 1 K provides a simple means to translate counts to antenna temperature.

3. Antenna temperature equation

The antenna temperature is computed from
e1
e2
e3
where Ce, Cc, and Ch are the earth, cold, and hot counts; and Tc and Th are the temperatures for cold space and the hot load, respectively. We have introduced the abbreviated notation ΔCec and ΔChc for the two count differences—earth minus cold count and hot minus cold count, respectively—that govern TA. The earth-cold count difference ΔCec will play a central role in this paper. Equation (1) accounts for the quadratic term in the small nonlinearity in the radiometer output voltage relative to power coming into the feedhorn. It does not account for higher-order terms. This nonlinearity is characterized in terms of the temperature TNL, which has a typical value between 0.0 and 0.5 K, depending on the channel. Equation (3) provides a correction for errors related to the scan position and consists of two components: a fixed component g(α) that is a function of the scan angle α and an intrusion component that is proportional to the difference between the intrusion temperature Tinstru and the antenna temperature TA0. The proportional factor is h(α). The intrusion is most likely due to the cold-sky reflector and possibly other spacecraft components. The derivation of this along-scan correction is further discussed in section 11. The hot-load temperature Th is computed from an array of precision thermistors with correction for the thermal coupling with the hot-load tray (Draper 2015) and is further discussed in section 10.

It is customary to use the Rayleigh–Jeans approximation to Planck’s law at MW frequencies. The error due to the approximation can be made negligible by adding a small offset to the true cosmic microwave background temperature of 2.73 K. This modified cold-space temperature is called the Planck equivalent temperature TB,space. The cold-space temperature Tc in Eq. (1) is the same as TB,space except at the two lower frequencies of 11 and 19 GHz. Section 9 shows that there is a small amount of Earth radiation leaking into the cold-mirror observation during normal operation. To account for this, 0.2 and 0.1 K are added to TB,space at 11 and 19 GHz, respectively. Table 1 gives TB,space and Tc.

Table 1.

Planck equivalent temperature and cold-mirror temperature (K).

Table 1.

4. Magnetic sensitivity error

Soon after launch, an analysis of the radiometer counts collected during the deep-space maneuver revealed systematic errors correlated with the ambient magnetic field that consists of the earth’s magnetic field and a second component from the spacecraft and sensor, such as the magnetic reed switches on launch restraint (Draper 2015). The analysis clearly showed that the GMI receiver electronics are affected by the magnetic field. The magnetic sensitivity error (MSE) is modeled as (Draper 2015; Draper et al. 2015)
e4
e5
where C(α) are the radiometer count values after removing the MSE and C0(α) are the counts coming from the sensor. The term BE is the earth’s magnetic field vector in the spacecraft frame of reference, with the x axis in the direction of spacecraft velocity for zero yaw and the z axis in the direction opposite from the spacecraft nadir for zero pitch. The term is the rotation matrix for the spinning GMI sensor, and S is the electronics sensitivity vector: a constant to be found. The adjustments due to the spacecraft/sensor magnetic fields are represented by Γ(α) and ΔCk. The subscript k = c, h, or e denotes the segment of the scan during which the feedhorn views the cold-sky reflector, the hot load, and the primary reflector, respectively. In normal operation, the primary reflector views the earth, and hence we use the subscript e. The term Γ(α) is defined so that its mean value when averaged over the range of α for any of the three subscans (c, h, or e) is zero, and ΔCk is the overall count bias for the kth subscan.
The term Γ(α) is found using about 4 months of on-orbit count measurements. When averaged over several months, the term ST (α)BE in (4) averages to zero due to the variable scanning geometry. For the cold and hot subscan, Γ(α) is found by simply averaging the counts into α bins and then subtracting out the average value for all cells in the subscan being considered,
e6
where the brackets indicate a 4-month average and is the count average of all scan positions for the kth subscan. The calculation of C0(α) for the earth counts is more complicated because there are other factors (antenna-induced biases and scan-edge intrusions) that vary along the scan. The method for removing these other influences and isolating C0(α) is discussed in section 11. The values for C0(α) are given in the GCDB.
To find the sensitivity vector S, we use the observations from the deep-space maneuver. During this maneuver, both the primary reflector and the cold mirror viewed cold space simultaneously. Hence, the counts for the primary reflector C(αe) and the counts for the cold mirror C(αc) should be the same. Taking the difference of the earth and cold counts as given by Eq. (4) and assuming C(αe) = C(αc) gives
e7
e8
where the right-hand side is known and the unknowns are the three components of S and the bias term S0. Note that because the bottom row of the rotation matrix is independent α, the third component of S has no effect on Eq. (7). In other words, S3 has the same effect on all counts and hence does not affect CeCc. One can simply set S3 to zero with no effect on calibration.

The deep-space maneuver occurred on 20 May 2014, between 13.65 and 16.8 h UTC. In this maneuver the spacecraft is pitched 55° away from the earth, and both the main lobe and backlobe of the primary reflector view cold space. The cold mirror also views cold space during the first part of its scan segment (first 10 cold samples) except for 19 GHz, which has a small amount of Earth contamination even at the beginning of the scan. This determination of the 19-GHz Earth contamination is based on observing the change in cold counts as the spacecraft went from normal operation to the deep-space orientation. If only the first five observations of the cold scan are used, the 19-GHz Earth contamination is 0.07 K and 0.24 for v-pol and h-pol, respectively. These values are subtracted from Cc to obtain a value indicative of a true cold-space observation. For the other channels, we just average the first 10 observations in the cold scan and no other correction is necessary.

There are two orbits of deep-space observations (5947 scans), and for each scan there are 221 Earth scan positions αe. To avoid Earth contamination in Ce, we discard the first and last 20 scan positions (see Fig. 1). The 5947 scans × 181 scan positions gives 1 076 407 simultaneous linear equations corresponding to Eq. (7), from which S0 and the first two components of S (S1 and S2) are estimated via least squares. As discussed in section 7, a mild constraint is put on the estimation to maintain consistency between the spillover values obtained from the two backlobe maneuvers.

Fig. 1.
Fig. 1.

The earth minus cold count difference ΔCec (K) as measured during the deep-space maneuver as a function of scan position and scan number. These results are before removing the magnetic sensitivity error.

Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0212.1

The values for S0, S1, and S2 are given in Table 2 for each channel being considered here. Figure 1 shows ΔCec as measured during the deep-space maneuver as a fucntion of scan position and scan number before removing the MSE. Figure 2 show ΔCec after removing the MSE. The fact that the simple three-parameter model (S0, S1, S2) is so effective in removing the error is rather remarkable and clearly shows the effect is due to the changing magnetic field, as discovered by Draper shortly after launch (Draper 2015; Draper et al. 2015).

Table 2.

Count bias S0 (counts) and magnetic sensitivity vector components S1 and S2 (counts per μT).

Table 2.
Fig. 2.
Fig. 2.

As in Fig. 1, except the MSE has been removed.

Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0212.1

Figure 2 also shows 1) Earth contamination in Ce at the scan edges and 2) a zone of minimum ΔCec between scan positions 50 and 100. These zonal effects are mostly independent of the spacecraft position in orbit (i.e., scan number) and hence do not appear to be related to the MSE. We intrepret the zone of mininum ΔCec as “true” deep-space observations minimally affected by radiation from the earth.

5. Determination of the bias in ΔCec from deep-space observations

Figure 3 shows ΔCec averaged over scan positions 50–100 plotted versus spacecraft position in orbit (scan number). Two complete orbits are shown. For this figure we apply the dynamic part of the MSE (S1 and S2) but do not remove the bias (S0) because we want to examine the bias in ΔCec. We see biases ranging from 0 to 0.4 K depending on the channel. Figure 3 also shows Earth contamination in Ce as predicted by the on-orbit simulation using the method-of-moments (MoM) antenna patterns as discussed in section 7. This prediction is useful for marking those times during the deep-space maneuver that the earth field of view was over ocean versus land. The transition from ocean to land is marked by an increase in the predicted Ce contamination, which is about 0.1 K at 7 GHz and less for the higher frequencies. If the dominant portion of the earth contamination comes from Cc rather than Ce, the ocean–land transitions would have the opposite sign. Thus, these transitions provide a means to determine which contamination is dominant. If both Cc and Ce are equally contaminated, then the transitions will not appear and there will be no bias to remove.

Fig. 3.
Fig. 3.

Results of the GMI deep-space maneuver during which the primary reflector and cold mirror simultaneously view cold space. Each column is a different frequency. The plots show ΔCec (K). The red and green curves show the v-pol and h-pol ΔCec, respectively. (top row) Results before adjusting the counts. (bottom) Results after applying offsets to Ce and Cc derived from the deep-space calibration. The black line shows ΔCec predicted by the MoM antenna pattern. The predicted values correspond to the average of v-pol and h-pol. For 24 GHz, the predicted ΔCec curve is the 11-GHz curve with a minus sign appended and slightly offset. We do this to show that the dominant Earth contamination at 24 GHz seems to be in Cc, not Ce.

Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0212.1

The 11V ΔCec time series resembles the predicted Ce contamination, but the 11H ΔCec does not. The other channels show no obvious ocean–land transition except for 24V, which hints at an ocean–land transition of the opposite sign, indicating Cc is the dominant contamination. The predicted Earth contamination in Ce was also computed using a different set of antenna patterns: the physical optics (PO) model. The PO model gave about twice the earth contamination, which is not at all supported by the observations.

To determine the bias in ΔCec, we first look at its second Stokes component: vertical-minus-horizontal polarization, which we expect to be zero for deep-space observations. These biases range from about −0.1 to 0.2 K, depending on the channel and are shown in Table 3. We also give the results obtained from the nadir maneuver discussed in the next section. Removing the ΔCec second Stokes bias will affect the second Stokes TA, and we want to verify that any correction will not adversely affect the nadir observations. The nadir-observed second Stokes TA is given in Table 3 for land and ocean. Except at 89 GHz, we found that a good compromise to reduce the second Stokes bias in the deep-space observations, the nadir ocean observations, and the nadir land observations is to simply average the biases for these three types of observations and assume the error is in Ce. Table 3 shows the results after removing the bias in this manner. The second Stokes biases are now all at the 0.05-K level or smaller, except for the deep-space 11-GHz bias, which is 0.07 K. We think some—maybe all—of this is real Earth contamination of the 11V, and as such is real and should not be removed as a ΔCec bias. At 89 GHz, the deep-space second Stokes bias is −0.11 K, while the nadir ocean and land results show no appreciable bias. For this case the second Stokes bias is removed by assuming the error is in the cold counts Cc rather than Ce. In this way, the bias for deep space is removed with little effect on the ocean and land results, both of which are at the warm end of the calibration range and hence are insensitive to Cc.

Table 3.

Bias in the second Stokes component of ΔCec and TA (K).

Table 3.

The first Stokes component of ΔCec before bias removal is shown in Table 4. The first Stokes component is defined as the sum of v-pol and h-pol divided by 2 (i.e., the average). At 24 GHz, there is no h-pol and the results for just v-pol are shown. As discussed above, at 19, 37, and 89 GHz we see no evidence of Earth contamination (i.e., no obvious ocean–land transitions), and we simply remove all the observed bias in the first Stokes ΔCec. At 11 GHz (24 GHz), we see some evidence of contamination in Ce (Cc) and do not remove all the observed bias because some of it appears to be real contamination. A small positive offset of 0.12 K is left at 11 GHz, and a small negative offset of −0.03 K is left at 24 GHz. The second row in Fig. 3 shows the ΔCec after the first and second Stokes bias removal. The earth contamination in 11V is now quite obvious, and the 11V ΔCec time series appears to be positioned properly with a small positive offset.

Table 4.

Bias in the first Stokes component of ΔCec (K).

Table 4.

Table 5 summarizes the results of this section. It gives the count offsets bc, be, and bec for the cold counts and Earth counts,
e9
e10
where the plus (minus) sign applies to v-pol (h-pol). Equation (4) is then used to remove the count bias. For the second Stokes offsets bc and be, we are able to separate the observed ΔCec bias into a cold-count bias and an Earth-count bias because we have results for cold space, moderate ocean, and warm land. For the first Stokes offset bec, we have only cold-space results and cannot tell how much of the ΔCec bias is due to Cc versus Ce. Thus, we have introduced the additional parameter κ that specifies the Cc versus Ce partitioning, and this parameter then becomes a degree of freedom that is discussed in section 8.
Table 5.

Offsets to cold and Earth counts that are subtracted to debias the counts.

Table 5.

6. Nadir observations

On 8 December 2014, between 20.8 and 23.9 h UTC, the GPM spacecraft was pitched 48.45° toward the earth so that the earth incidence angle θi at the center of the scan was near zero. We call this the nadir maneuver and use these nadir observations to evaluate the consistency between the v-pol and h-pol TA. For near-nadir observations, the second Stokes TB can be well approximated by
e11
The first term accounts for small (<5°) departures of θi from zero, where γ is the polarziation rotation angle. The second term is the influence of wind direction on the second Stokes TB, where W and φw are the wind speed and direction, respectively; and φυ is the direction of the v-pol vector. The b coefficients are estimated from ocean RTM to be 0.022, 0.021, 0.020, and 0.013 K for 11, 19, 37, and 89 GHz, respectively. The c coefficients also come from the RTM and are 0.1038, 0.1304, 0.1582, and 0.0671 K (m s−1)−1, respectively.

The polarization rotation angle γ accounts for the fact that the GMI-referenced v-pol and h-pol vectors are, in general, rotated relative to the earth v-pol and h-pol vectors, respectively, and that γ is the degree of rotation. For example, the observations near the center of the scan all have their v-pol vector pointing forward in the general direction of the spacecraft motion. For the observations to the left or right of center, this v-pol vector corresponds to the Earth reference h-pol vector and hence γ = ±90°. The wind direction effect at nadir is such that TB is larger when the wind direction is aligned with the polarization vector (Etkin et al. 1991). The wind speed and direction come from the NCEP 6-h wind fields collocated to the GMI observation.

Letting TAq,mea denote the GMI near-nadir second Stokes measurement, we define the TA nadir anomaly to be
e12
where 1 − η accounts for the antenna spillover effect discussed in the next section. Since (12) removes the θi and wind direction effects, ΔTAq should ideally be zero. Figure 4 shows histograms of ΔTAq. To construct these histograms, we used only the observation cells that are close to nadir (scan positions 107–115), which limits the incidence angle to a maximum of 4°. Histograms are done separately for land and ocean observations. Table 3 gives the mean values for the histograms for ocean and land separately. Figure 4 also shows the histogram of ΔTAq when the wind direction correction is not applied. Clearly, wind direction plays an important role in nadir observations, and if not accounted for it produces anomalous results.
Fig. 4.
Fig. 4.

Histograms of the GMI’s second Stokes TA measurements for near-nadir observations.

Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0212.1

The small biases in the second Stokes nadir TA are interpreted as biases in ΔCec, as discussed in the previous section. They could also be due to a difference between the v-pol and h-pol antenna spillover value or in ΔChc, but these factors would have a different effect on the three types of observations (deep space, ocean, and land). Because a small adjustment in ΔCec reduced the second Stokes error to the 0.05-K level simultaneously for deep space, ocean, and land, we conclude this is an appropriate approach.

7. Calculation of GMI antenna spillover

During normal operation of GMI (spacecraft pitch = 0°), the antenna temperature measured by the sensor can be expressed by
e13
where TB,earth is the gain-weighted Earth brightness temperature and η is called the cold-space spillover. Note that the notation η for spillover herein is the complement of that used in the GCDB. To determine TB,earth given the GMI TA measurement, the spillover component must be removed. The specification of η has always been a major challenge for satellite microwave radiometers. It is very difficult to measure directly in antenna chambers or on antenna ranges. Analyses of previous satellite MW radiometers indicate that errors of 1% in η are common and that this equates to 2-K errors in recovering TB,earth (Wentz 2013). In view of the uncertainty in the knowledge of η, the adjustment of this parameter has traditionally been our primary means to bring overall agreement between the satellite measurements and the RTM.

For GMI, we no longer allow η to be a degree of freedom. Rather, we directly compute it from the data acquired during the backlobe maneuver. This greatly constrains the calibration process. There were two backlobe maneuvers on 20 May 2014 and 9 December 2014. To accomplish these maneuvers, the spacecraft is put into an inertial hold mode, for which the spacecraft pitch relative to the earth varies from 0° to 360° around the orbit. At the point in the orbit where the pitch = 180°, the backlobe points directly down at the earth, and all the power in the backlobe is subtended by the earth. At the same time, the main lobe views cold space. Given the measured antenna temperature and the earth’s brightness temperature, one can estimate η.

In a more detailed expression, the antenna temperature measured by GMI is given by integrating the scene v-pol and h-pol brightness temperatures, TBv and TBh, respectively, weighted by the gain pattern over 4π sr (Piepmeier et al. 2008),
e14
where TBq is the second Stokes TB, Gvv is the copolarized complex gain amplitude, and Ghv is the cross-polarized complex gain amplitude. The angle φ is the rotation angle between the antenna-referenced polarization basis and the earth-based polarization basis. The h-pol TAh is given by switching the υ and h subscripts in Eq. (14). The TA measurements taken during the backlobe maneuver show very little polarization signature, with the differences between v-pol and h-pol being about 0.1 K or less. In view of this and the need to simplify the analysis, we assume that v-pol and h-pol backlobe patterns are the same. In addition, making the spillover the same preserves the second Stokes observations. We can then use the sum of the v-pol and h-pol measurements to calculate a single spillover for each frequency, independent of polarization. Assuming the v-pol and h-pol gain patterns are the same, Eq. (14) simplifies to be
e15
The sin2φ term is found to be very small (0.04 K) and is set to zero. Thus, the characterization of the backlobe gain reduces to specifying the copolarized and cross-polarized gain magnitudes |Gc|2 and |Gx|2, respectively. In addition to simplifying the problem, using the sum of v-pol and h-pol (i.e., the first Stokes TB) reduces the sensitivity of the calculation to the details of polarization rotation in the backlobe. The integral Eq. (15) is partitioned into the portion that is subtended by the earth (i.e., the backlobe portion) and the remaining portion that sees cold space,
e16
e17
where ηbl is the backlobe spillover, and we make use of the normalization property that the gain integrated over 4π sr is unity.
The prelaunch specification of the GMI antenna gain pattern was based on a hybrid method using both near-field feedhorn measurements and theoretical modeling as described in the GCDB. Two models were used: a physical optics (PO) model utilizing theoretical feed patterns and a method-of-moments (MoM) model using feed patterns measured by a near-field range. Although the spillover fraction differs when directly computed from each model, the backlobe spillover analysis is rather insensitive to the choice of model. We assume that the gain terms in Eqs. (14) and (15) can be represented by PO or MoM patterns with a simple scaling factor μ applied,
e18
e19
where the top hat indicates the gain is from either the PO model or the MoM model and the gain is the average value of the v-pol and h-pol model gain. One can then solve for ηbl:
e20
e21
Equation (21) shows the PO and MoM gain patterns are being used only as a weighting function to specify the effective Earth brightness temperature TB,eff seen by the backlobe. Even though the PO and MoM patterns have significantly different amplitudes, the calculation of ηbl is essentially the same (Δη = 0.0001) for the two patterns.
The backlobe spillover ηbl corresponds to that portion of the backlobe that is subtended by the earth when the sensor is pitched 180°. During normal operation (pitch = 0°), the portion of the antenna pattern seeing cold space is ηbl plus an additional annulus ηa that extends from the earth’s limb to the region corresponding to ηbl. Both the PO and MoM patterns indicate the power received by this region is very small, being about 0.2% or less of the total power. We use the PO values to account for this power, as shown in Table 6, and the total cold-sky spillover that is used for normal operation is
e22
This then gives the spillover value that is to be used in Eq. (13) to remove the contribution of cold space during normal operation.
Table 6.

Spillover computed from backlobe maneuver and theoretical models.

Table 6.

An on-orbit simulator is used to find TB,eff. The simulator performs the full 4π gain integration for each GMI observation taken during the backlobe maneuver. For 11–37 GHz, the scene brightness temperatures TBv and TBh come from the ocean RTM when the integration pixel is over the ocean. For 89 GHz, the scene brightness temperature comes from the temporally closest GMI data, adjusted appropriately for incidence angle. The TB for land pixels is simply set to 275 K. The pitch = 180° point of interest is in the open ocean, so the specification of the land pixels is not that important. The ocean RTM requires TS, W, wind direction φw, V, L, and rain rate R. The term TS comes from the NOAA SST operational product (Reynolds et al. 2002a,b), and φw comes the NCEP 6-h wind fields. The remaining environmental parameters (W, V, L, and R) come from other satellite MW radiometers that are coincident with the GMI observation. The collection of satellites used includes WindSat, AMSR-2, TMI, F16 SSMIS, and F17 SSMIS, all of which have been intercalibrated as described by Wentz (2015). The satellite closest in time is used, with the typical time difference between it and GMI being about 1 h.

Given TB,eff, ηbl is computed according to Eq. (20) for each GMI observation over the orbit segment for which the spacecraft pitch is between 177° and 183°. A simple average of all these values is then taken, and these values appear in Table 6 along with the annulus spillover ηa and the total spillover η. Separate values for ηbl are shown for the two maneuvers, and the consistency between the two maneuvers is at the 0.15-K level assuming a TA of 200 K. The average of these two maneuvers is used for η. Table 6 also shows the value of η predicted by the PO model and the MoM model. Except for 24 GHz, the PO values are close to the values we derive: 0–0.2 K for TA = 200 K. For 24 GHz there is no h-pol TA measurement, and we set TAh equal to TAv. For the other frequencies that have both polarizations, the difference between TAh and TAv is 0.1 K or less. So, setting TAh to TAv is a reasonable approximation, but it may partly explain the larger discrepancy in η at 24 GHz (0.39 K). The MoM η values are much larger, and we consider the MOM values spurious.

The satellite yaw for the first (second) backlobe maneuver was 0° (180°), and as a consequence magnetic sensitivity correction has opposite signs for the two maneuvers. We found the difference between the ηbl calculations for the two maneuvers fairly sensitive to S1. When doing the least squares estimation of S0S2, we put a mild constraint on S1 to keep the consistency of ηbl between the two maneuvers near the 0.2-K level. This constraint increased the 11-GHz S1 values by 0.05 and decreased the S1 values by 0.05 for the other channels. This constraint had very little impact on the quality of fit of Eq. (7) to the deep-space data. Also, by averaging the two maneuvers, the sensitivity to S1 is greatly reduced.

To further evaluate the method of computing spillover, Eq. (18) is used to compute TAv + TAh for an extended portion of the backlobe maneuver. This simulated TAv + TAh is then compared to the measured value in Fig. 5 (20 May maneuver) and Fig. 6 (9 December maneuver). The importance of using timely collocations from other satellites to specify the earth TB is shown in Fig. 5. On 20 May 2014, a fairly strong South Pacific storm shown in Fig. 7 had rapidly developed at the 180° pitch location. The GMI backlobe observed the storm at 23°S, 194°E at 17.3 h UTC. The high winds, vapor, and rain in the storm produce brightness temperatures considerably warmer than typical for that location. Both the simulated and measured TA show this increase at the storm location.

Fig. 5.
Fig. 5.

Results of the 20 May 2014 backlobe maneuver that occurred in the South Pacific. GMI TA measurement (red) compared to the simulated TA (blue). The time during which the pitch was between 177° and 183° is marked by the small black bar. During this time, the GMI backlobe is completely subtended by the earth, and this is the time period used to find ηbl.

Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0212.1

Fig. 6.
Fig. 6.

As in Fig. 5, except these results are from the 9 Dec 2014 backlobe maneuver that occurred over the Gulf of Alaska.

Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0212.1

Fig. 7.
Fig. 7.

Rain rate from the SSMIS flying on the DMSP F17 satellite taken within 1 h of the GMI backlobe observations during the 20 May 2014 maneuver. The 180° pitch point occurs at 23°S, 194°E.

Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0212.1

The 9 December maneuver shows the effect of land. Land observations are only encountered away from the 180° pitch point, and hence do not affect the spillover calculations. However, they do provide a good test for the simulation. As Fig. 6 shows, the simulation models the effect of the Aleutian Islands very well. The islands are seen as a small uptick in TA.

There is very good agreement between the simulated and measured TA over the range of pitch from 108° to 216° (144°–252°) for the 20 May (9 December) maneuver. The pitch ranges for the two maneuvers are different because the spacecraft yaw for the first maneuver was 0° and that for the second maneuver was 180°. This agreement, particularly with regard to modeling weather and land features, provides confidence in the spillover results. As the maneuver departs farther from the 180° point, the backlobe begins to leave the earth and the agreement degrades because the calculation of TA becomes much more sensitive to the detailed shape of the PO or MoM patterns. Toward the end of the maneuver, the mainlobe resumes viewing the earth and TA abruptly increases.

One complication of doing the spillover computation is that the GMI cold mirror views the earth, rather than cold space, at the 180° pitch point. Thus, the standard cold-mirror/hot-load calibration cannot be used. Instead, we use the count difference of the hot load with noise diode minus hot load without noise diode, ChnCh, to specify the radiometer gain G:
e23
e24
where ΔTN is the excess temperature produced by the noise diode. There is some uncertainty in specifying ΔTN simply as a function of the physical temperature of the noise diode. A better approach is to specify ΔTN so that the gain G is the same as the standard cold-mirror/hot-load gain while the cold mirror is still seeing cold space, that is, before the pitch exceeds about 55°,
e25

The brackets denote a 12-min average done right before the cold mirror ceases to have a clear view of cold space. The second term in Eq. (25) accounts for the change in ΔTN due to the physical temperature of the noise diode that varies during the course of the maneuver. The receiver temperature TR is used to model the temperature variation. The sensitivity coefficient a is found from the ΔTN versus TR plots in the GCDB. Combining Eqs. (24) and (25), one can see that the gain G for the 12-min initialization period is the standard cold-mirror/hot-load gain (ThTc)/(ChCc). Because the 89-GHz channels do not have noise diodes, the 89-GHz TA is calibrated from Eq. (23) using G = bTR + c. The coefficients b and c are derived from a least squares fit of the gain to receiver temperature during the portion of the maneuver where the cold target is valid.

When computing TA0 from Eq. (23), the counts offsets given by Eqs. (9) and (10) must be applied. We found that the specification of κ mattered little. Three cases were run for κ = 0 (all the error is in Cc), κ = 1 (all the error is in Ce), and κ = 0.5 (equal error in Ce and Cc). The choice of κ had a negligible effect on η (0.000 04 or less) because TA for the backlobe measurements, which is 9 K or less, is very close the temperature of cold space (2.7 K), and changing Ce versus Cc has essentially the same effect. This is fortunate because it allows us to determine η without having to be concerned with specifying κ.

For the 9 December maneuver, the spacecraft transitions immediately from normal operation to the backlobe maneuver. However, the 20 May backlobe maneuver is preceded by a deep-space maneuver lasting over 3 h. We did not want to use a gain initialization period that was 4 h before the 180° pitch point because ΔTN could have significant variation over this long of a time period that is not captured by (23). Instead, we chose the initialization period to be the 12 min right before the spacecraft transitioned from the deep-space maneuver to the backlobe maneuver, which occurred at 16.8 h UTC.

8. GMI antenna temperatures compared to the RTM

In this section we compare the GMI TA measurements with simulated TA from the ocean RTM. The simulated v-pol antenna temperature is given by
e26
The h-pol TA is also given by (26), but with the v and h subscripts reversed. Equation (26) is the same as Eq. (13) except that we explicitly show the polarization mixing, which is represented by the cross-polarization coefficient χ. The term η comes from the backlobe analysis discussed in section 7. Equation (26) is an often used approximation for the full TA integral equation as depicted by Eq. (14).
The coefficient χ is found by integrating the cross-polarized gain over the antenna pattern
e27
where Ω0 is the solid angle of integration. It is typical to reference χ to an integration over just the main lobe (more specifically, over a solid angle 2.5 times larger than the 3-dB beamwidth). However, there is additional polarization mixing outside the main lobe that should be considered. Table 7 gives χ values for Ω0 equal to 2.5 times and 25 times the 3-dB beamwidth (BW). We use the 25BW values for our analysis. The results are nearly identical for the PO and MoM patterns. For a given frequency, there are very small differences between the v-pol and h-pol patterns, and we use the average values, as shown in Table 7.
Table 7.

Cross-polarization coupling.

Table 7.

The specification of the earth brightness temperatures TBv and TBh in Eq. (26) is done in the same way as described for the backlobe analysis in section 7. The only differences are 1) rainy observations are excluded and 2) a collocation window of 1 h and 25 km is used. Separate calculations are done using WindSat, TMI, and AMSR-2 to specify the environmental parameters W, V, L, and R. Table 8 shows the mean values of TATA,rtm averaged over the 13 months of collocation and averaged over the world’s oceans. The first five rows in Table 8 show various results using the WindSat retrievals. Rows 1 and 2 show results using the method-of-moments spillover and the physical optics spillover, respectively, and with no offsets applied to the counts, that is, no bias removal. The MoM biases are quite large (2 K), and as mentioned earlier the MOM spillover appears to be spurious. The PO results show much better agreement between the GMI TA and the RTM, with differences of the order of 0–0.3 K. When Eqs. (9) and (10) are used to remove the bias in Ce and Cc, respectively, the TATA,rtm difference is further reduced (rows 3–5). We show results for κ = 0 (all the error is in Cc) and κ = 1 (all the error is in Ce). The choice of κ can make a 0.1–0.2-K difference depending on the channel. We also show results of an optimum choice of κ, where we use κ = 1 at 11 GHZ, and κ = 0.5 for all other channels. The bottom two rows show the TMI and AMSR-2 TATA,rtm, respectively, using this optimum κ.

Table 8.

TATA,rtm (K) from WindSat, TMI, and AMSR-2.

Table 8.

We think WindSat is probably the best calibrated sensor that is collocated with GMI, and the WindSat TATA,rtm biases do not exceed 0.1 K. The WindSat ocean retrievals have been thoroughly validated by us and many others (Wentz 2012; Meissner et al. 2011; Mears et al. 2015; De Biasio and Zecchetto 2013; Huang et al. 2014; Wentz 2015) against buoy measurements, GPS vapor measurements, and geophysical retrievals for other satellites. WindSat has proven to be a very stable sensor. Comparisons of WindSat SST and winds with ocean buoys and WindSat vapor with GPS-derived vapor show no obvious evidence of drift. Comparisons with TMI also verify the stability of WindSat (Wentz 2015). We use a tight 1-h GMI–WindSat collocation window to avoid diurnal issues.

The high level of agreement between the GMI TA and the RTM is partly due to some adjustments made to the RTM based on an early analysis of GMI observations. This is discussed by Wentz and Meissner (2016). For example, at 37 and 89 GHz, the atmospheric absorption was decreased to match the second Stokes GMI observation. This decrease in absorption brought the model closer to laboratory measurements. Other small changes were made related to vapor and wind sensitivities, but there were no adjustments to force the first Stokes RTM to match GMI. See Wentz and Meissner (2016) for the details.

9. Cold-sky mirror

Cold calibration observations are taken during the portion of the scan during which the cold-sky mirror is seen by the feedhorn. At this point in the scan, the cold mirror is between the underlying feedhorn and the primary reflector above. A problem that has occurred with previous MW imagers is that the feedhorn sees a small amount of radiation coming from the primary reflector around the outer edge of the cold mirror. This effect is called cold-mirror spillover. The MW imagers AMSR-E and AMSR-2 have a cold-mirror spillover near 0.4%, that is, 0.4% of the cold calibration observation comes from the earth (Imaoka 2010). When specifying the temperature of cold-space Tc in Eq. (4), this Earth radiation needs to be considered, and Tc will have a value greater than the Planck-equivalent TB,space.

To examine this problem for GMI, we make geographic maps of the cold counts. When doing the mapping, the latitudes and longitudes of where the main reflector is looking at the time of the cold observations are used. Anomaly Cc maps are then made averaging over 13 months (March 2014–March 2015) and subtracting the zonal average (average over all longitudes) for 1° latitude bands. Figure 8 shows the resulting Cc anomaly maps for each GMI channel being considered. Any significant cold-mirror spillover will manifest itself as a contrast between the cold oceans and the warmer continents. For 11 and 19 GHz, a careful inspection reveals South America and Australia, respectively, but these features are very faint. The largest features in Fig. 8 are due to gain variations in Cc that persist even after averaging for 13 months. The GMI cold-mirror spillover features are much less distinct than those observed with AMSR-E and AMSR-2. It is clear that for GMI cold-mirror spillover is a very small problem. Still, there is a little Earth radiation leaking in, and Tc is a little greater than the minimum value given by TB,space. Since the ocean TB (average of v-pol and h-pol) is about halfway between 0 K and the land TB, the average earth contamination for land and ocean is about 1.5 times the ocean–land contrast shown in Fig. 8.

Fig. 8.
Fig. 8.

Geographic maps of the cold-count anomaly. Counts have been converted to TA (K) by multiplying by the typical gain for a given channel. The larger features are due to gain variation in the cold counts that persist even after averaging for 13 months and should not be interpreted as an error. The continents of South America and Australia are barely visible at 11 and 19 GHz, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0212.1

Since some continents show up and others do not, the estimate of the land–ocean contrast is uncertain. We use an approximate value of 0.1 K for 11 GHz. For 19 GHz, for which the features are fainter, we use half this value. This gives an increase of 0.15 and 0.075 K for the increase in Tc due to Earth contamination (TA ≈ 200), and the corresponding cold-mirror spillover values are 0.08% and 0.04%. The GCDB predicts the spillover values of 0.17% and 0.04%. The GCDB also predicts some additional contamination coming from the spacecraft, and we slightly increase the contamination values to 0.2 and 0.1 K, which are the values shown in Table 1. If we assume the error in Tc is 0.06 K, then according to Eq. (1) the error in the v-pol and h-pol TA is 0.03 and 0.04 K, respectively.

The deep-space analysis in section 5 does not show Earth contamination in Cc at 11 and 19 GHz. This is probably because of the different pointing geometry of the cold mirror and the fact that we use only the first part of the cold scan for the deep-space analysis.

10. Hot load

Hot calibration observations are taken during the portion of the scan during which the hot load is seen by the feedhorn. At this point in the scan, the hot load is between the underlying feedhorn and the primary reflector above. A problem with previous MW imagers has been large thermal gradients in the hot load. Because of these gradients, the effective temperature of the hot load, as seen by the feedhorn, is not well represented by the precision thermistors that are attached to the hot load. The thermal gradients are mostly due to the varying sun–spacecraft geometry that occurs over every orbit. At some points in the orbit, the sun either directly shines or reflects into the hot load, thereby producing the thermal gradients (Twarog et al. 2006). The GMI design utilizes very tight shrouding around the hot load, which is intended to eliminate direct and reflected solar loading onto the load’s radiating surface (Draper 2015). Although most previous MW imager designs include hot-load shrouding, nearly all of them have experienced hot-load problems from solar intrusion to one extent or another (Wentz 2013).

These hot-load problems can be seen by making plots of measured-minus-predicted TA anomalies, TATA,rtm, versus the sun’s azimuth angle φsun and zenith angle θsun as measured in the spacecraft coordinate system for which the z axis points up away from nadir and the x axis is the spacecraft velocity vector. The TA anomalies are denoted by
e28
where TA comes from Eq. (1) and TA,rtm is computed as described above. Figure 9 shows ΔTA plotted versus φsun, θsun. To produce this figure, we use ocean retrievals from three MW images: WindSat, AMSR-2, and TMI for the period from the beginning of the GMI mission 4 March 2014–31 March 2015. Using just one satellite would not capture the full extent of the φsun, θsun-space seen by GMI. For a given imager and a given channel, there are small overall biases in ΔTA as listed in Table 8. In Fig. 9, these small biases are removed to more clearly show features just related to the sun angles. We see no evidence at all that the GMI hot load has an error associated with the sun angle. The 89-GHz images do show features reaching 0.5 K, but we attribute this to mismodeling of the radiative properties of clouds at 89 GHz. It is an RTM problem, not a sensor problem. Clouds strongly affect the 89-GHz observations, and factors such as air temperature, cloud height, and drop size distribution play a much stronger role than at the lower frequencies. Errors on the order of 0.5 K are probably to be expected. Note there are few observations for sun–azimuth angles between 350° and 360°, and that is why the results look noisy in this region. Comparing Fig. 9 to similar figures for other MW imagers shows how well the GMI hot load is performing (Wentz 2013, 2015).
Fig. 9.
Fig. 9.

GMI TA minus RTM TA anomaly plotted vs the sun azimuth angle φsun and zenith angle θsun. The larger features at 89 GHz are attributed to the RTM mismodeling clouds. The dark blue area is the region of φsun, θsun not sampled by GMI. There is no evidence of hot-load problems.

Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0212.1

The algorithm for computing Th from the thermistor values is given in the GCDB. The algorithm first performs a simple average of either four or five thermistors, depending on the channel, and then does a correction that accounts for the temperature difference between the hot-load temperature and the hot-load tray temperature. In view of the results show here, we see no need to adjust this Th value coming from this algorithm.

11. Along-scan biases

For the earth subscan, the derivation of the along-scan correction terms and g(α), h(α), and Γ(α) in Eqs. (3) and (4) is also based on the measured-minus-predicted TA anomalies ΔTA. In this case, ΔTA is binned and averaged according to the scan angle α rather than φsun, θsun. The term ΔTA(α) is found from a 4-month average of ocean observations (March–June 2014). The average value of ΔTA(α) for all α is subtracted out, thereby making ΔTA(α) an unbiased correction that does not affect the absolute calibration of GMI. This along-scan anomaly is then partitioned into a count anomaly Γ(α) resulting from the spacecraft/sensor fixed magnetic field, an additive portion g(α) that most likely comes from the antenna sidelobes and backlobe, and a multiplicative term h(α) due to the intrusion of the cold-sky mirror at the end of the earth scan. The method for partitioning the three terms is given in the GCDB. The scan bias correction terms g(α) and h(α) have been derived to remove scan biases both at cold ocean temperatures and over warm land scenes (Yang et al. 2015). We have verified that extending data from March 2014 through March 2015 has no appreciable effect on ΔTA(α); that is to say, the along-scan anomaly is stable with time. We refer the reader to the GCDB for more information on the along-scan biases.

12. Mission and closure plots

Next we present what we call mission plots because they provide a summary of the entire GMI mission. These plots show the anomaly ΔTA plots versus orbit number and intraorbit position ω, which is the angular position of the spacecraft relative to its southernmost position. Hence ω = 0°, 90°, 180°, and 270° correspond to the minimum latitude near 60°S, the ascending node, the maximum latitude near 60°N, and the descending node. Figure 10 shows the results. For the lower frequencies from 11 to 37 GHz, the variation of ΔTA is mostly within ±0.2 K. At 89 GHz there is higher variability due to clouds as already discussed in section 10. We see no residual MSE or other problems, at least at the 0.1–0.2-K level.

Fig. 10.
Fig. 10.

GMI TA minus RTM TA anomaly plotted vs the orbit number and intraorbit position. The results go up to orbit 6182. WindSat, TMI, and AMSR-2 are the reference sensors. The larger features at 89 GHz are attributed to the RTM mismodeling clouds. There is no evidence of residual MSE or other calibration problems.

Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0212.1

As a final consistency check, we do a closure analysis, which is the same as the mission plots except that the environmental parameters W, V, and L used to compute TA,rtm come directly from the GMI ocean retrieval algorithm. Thus, collocation is no longer a problem, and we have a value of TA,rtm for every GMI observation over the ocean, thereby giving us a full uninterrupted set of ΔTA anomalies. Since there are only three retrievals for the nine channels, there is no guarantee that ΔTA will be zero. A single anomalous channel will be quite apparent. With previous MW imagers, this closure analysis proved effective in detecting small problems (Wentz 2013). Figure 11 shows the results for GMI. There is slight zonal banding at the ±0.1-K level, but this is likely due to small inconsistencies in the retrieval algorithm not being a perfect inverse of the RTM, particularly with respect to the 70-K variation in 24V TA due to changing water vapor. The larger, cloud-related features in the 89-GHz images are similar to those shown in the previous section and again are attributed to RTM problems. We see no evidence of sensor calibration problems with GMI.

Fig. 11.
Fig. 11.

GMI TA minus RTM TA anomaly plotted vs the orbit number and intraorbit position. As in Fig. 10, except the GMI retrievals are used to compute the RTM TA rather than WindSat, TMI, and AMSR-2. Since there are GMI retrievals for all observations, there is complete coverage. There is no evidence of residual MSE or other calibration problems.

Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0212.1

13. Error analysis

In this section we present an uncertainty analysis for the GMI TA and TB. The analysis computes the rms error over all GMI channels and should be considered as representative of any one of the channels. The analysis results are shown in Table 9. For each term, we define a static bias and time-varying error term applicable to ocean conditions. The static bias is unsigned and provides an estimate of the error’s magnitude based on observations, analysis, or conservative engineering judgment. The time-varying error represents a 1σ excursion from the static bias typically induced by changes in the scene brightness temperature, along-scan position, or on-orbit thermal conditions. Error terms are combined in a statistical root-sum-squared sense to provide a top-level estimate of the TA and TB error.

Table 9.

On-orbit error analysis for GMI over ocean scenes. The results show an rms of all GMI channels. DSC stands for deep space calibration.

Table 9.

For the TA error, the primary error drivers are the earth’s magnetic field correction and the hot load. The error in the earth’s magnetic field correction arises mainly from uncertainty in the knowledge of the magnetic sensitivity vector for the receivers. Other minor sources of error include the magnetic field model and interfering fields from the onboard observatory magnetic torque bars. Based on experience generating the magnetic sensitivity vectors and working to correct the data with different sources for the magnetic fields, we conservatively estimate that there is no more than 20% uncertainty in this term, which translates to less than 0.08-K rms error.

For the hot load, thermal gradients on the load are the primary driver of error. Thermal gradients arise as the hot-load surface is heated and cooled by the surfaces immediately facing the load. The thermal gradients are corrected on orbit, but they likely leave a residual temperature-varying error. We estimate the error to be within 0.1 K (1σ) with a small residual bias. Based on this analysis, we estimate that the radiometric bias in TA for ocean scenes is within 0.1-K rms with a time-varying error of 0.13 K.

The largest error contributing to TB error is the spillover correction. The on-orbit spillover correction is derived from the inertial hold data and consists of three main terms: the estimate of the earth TB in the antenna backlobe, the TA calibration during the inertial hold, and the use of modeled antenna patterns for the spillover annular region not subtended by the earth during the inertial hold. Of these terms, the analysis is most sensitive to the TA calibration. The error arises due to the lack of good cold swath data while the spacecraft is pitched 180° and the need to use noise diodes or other means to calibrate the data. We estimate the TA calibration error to be about 0.2-K rms based on trial and error with various calibration schemes.

Overall, the absolute rms calibration error over all GMI channels is 0.25 K for ocean scenes. This same analysis may be performed also for land scenes, resulting in an error of about 0.34-K rms over all GMI channels.

14. Conclusions

GMI’s only significant calibration problem appears to be its sensitivity to the ambient magnetic field. Fortunately, the deep-space observations provide the means to characterize and remove the magnetic sensitivity error (MSE), both its variable part and its bias. The nadir observations give us additional calibration points for the second Stokes TA at ocean and land temperatures. This allows us to precisely calibrate the ΔCec term in the TA in Eq. (1). The other terms in the TA equation are the cold-space temperature Tc, the hot-load temperature Th, and the difference between the hot count and the cold count ΔChc. With respect to Tc, we did detect a small amount of cold-mirror spillover (0.2 K at 11 GHz, 0.1 K at 19 GHz), but this was expected based on prelaunch analyses. With respect to Th, we found no evidence of sun intrusion into the hot load. There could be an overall bias in Th, but the fact that the first Stokes GMI TA matches the RTM to better than 0.1 K suggests any bias in Th must be small. We were not able to examine ΔChc, but again the RTM comparisons indicate any bias in ΔChc must be around the 0.1-K level. We conclude that the accuracy of the GMI TA is near 0.1 K, which is typical of the discrepancies shown in our various analyses. None of our analyses showed discrepancies larger than 0.2 K.

The second part of the calibration problem is the specification of the primary reflector’s cold-space spillover η, which is needed to convert TA to TB. The backlobe maneuvers provided the means to directly compute η rather than relying on prelaunch measurements. The agreement between η derived from the backlobe maneuvers and the ones computed from the physical optics antenna pattern is 0.1–0.2 K (TA =200 K) except for 24V, which is somewhat higher (0.4 K). The agreement between η for the two maneuvers is at the 0.15-K level, and by averaging the two maneuvers the sensitivity of η to the MSE is greatly reduced. We conclude the error in specifying η is about 0.1 K. Considering other small additional errors, the total error in estimating the earth brightness temperature is estimated to be about 0.25 K. This error estimate is supported by the WindSat RTM comparisons, for which the globally averaged TATA,rtm does not exceed 0.1 K.

GMI marks a milestone in satellite microwave radiometry. GMI is the first microwave imager that has been independently calibrated (i.e., without resorting to the RTM) to an absolute accuracy near 0.25 K. Furthermore, the inclusion of the noise diodes, which measure the radiometer’s nonlinearity, directly provides the means to maintain this calibration over the full range of TB, from the cold oceans at 80 K to the hot deserts at 300 K. By establishing reference temperatures for the oceans and for stable land targets, such as the Amazon rain forest, GMI’s precision calibration can be extended both forward and backward in time to create highly accurate multidecadal records of our planet’s changing climate as seen in the microwave spectrum.

Acknowledgments

This investigation was supported by NASA’s Earth Science Division. We thank Tom Wilheit, Linwood Jones, Spencer Ferrar, Rachael Kroodsma, Darren Mckague, Wes Berg, and other members of the GPM Intersatellite Calibration (X-CAL) Working Group for their critical role in formulating many of the calibration maneuvers performed by the GPM Core Observatory that made this analysis possible. We also thank Sergey Krimchansky at Goddard Space Flight Center for advocating for the maneuvers and the GPM operations flight team for performing them. We would also like to thank Dr. Erich F. Stocker and his team at the NASA Goddard PPS for all the help they provided during the course of this investigation.

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