Estimation of TRMM Microwave Imager Antenna Temperature During Deep Space Calibration

Maneuvers Spencer Farrar, Student Member IEEE and Linwood Jones, Life Fellow IEEE

Central Florida Remote Sensing Lab (CFRSL) University of Central Florida

Orlando, USA

Abstract—In 1998, the Tropical Rainfall Measuring Mission observatory performed a set of maneuvers known as Deep Space Calibration (DSC) that allowed the TRMM Microwave Imager conically scanning antenna beam to view a known non-polarized calibration scene of 2.7 Kelvin. However, during this period the radiometric transfer function (radiometric counts-to-TA) was only valid for only a very short portion of main reflector deep space view. This paper discusses three methods of reconstructing the radiometric transfer function thereby providing a longer time series of Antenna Temperature (TA) for absolute calibration. Earth emission entering into the feed spillover region of the antenna pattern is acknowledged within this paper. The motivation of this work is for preparation of the Global Precipitation Measurement (GPM) Microwave Imager (GMI) DSC maneuvers set for May of 2014.

Keywords—TRMM; TMI; Deep Space Calibration; Antenna Temperature; Reconstruction; spillover; emissive reflector; GPM; GMI; radiometric counts

I. INTRODUCTION The Tropical Rainfall Measuring Mission (TRMM), a

collaboration between NASA and the Japan Aerospace Exploration Agency (JAXA), was launched on November 27, 1997 to study subtropical rainfall. The two primary instruments on TRMM are the Precipitation Radar (PR) and the TRMM Microwave Imager (TMI), the latter of which is the subject of this paper.

In January & September of 1998, the TRMM observatory performed a set of special maneuvers referred to as Deep Space Calibration (DSC) for calibration of the Clouds and Earth’s Radiant Energy System (CERES) instrument, and these set of maneuvers were also fruitful for calibrating TMI. In 2001 Remote Sensing Systems (RSS) [2] analyzed the TMI deep space observations to complement their work of calibrating TMI using collocated SSMI’s brightness temperature (TB) observations. However, due to the cold sky reflector (CSR) antenna beam intersecting the earth during DSC, the external two point (hot & cold) radiometric calibration was compromised, i.e., nullifying the radiometric transfer function for calculating the antenna temperature (TA). As a result, less than 16% of the deep space view (DSV) of the main reflector ( ) beam was available for calibration purposes.

This paper discusses three methods that reconstruct the TA during the DSVs for 2 TMI channels. Once reconstruction is performed it is obvious that one can characterize TMI feed spillover antenna region using the earth’s albedo & emission during the DSV.

II. TMI INSTRUMENT The TRMM Microwave Imager is a 9 channel conically

scanning total power radiometer with an 800 km swath and a nominal 52.8° EIA as depicted in Fig. 1. TMI’s heritage is of SSM/I and is only different in that it includes a 10.65 GHz feed horn and that the water vapor channel was shifted from 22.235 to 21.3 GHz; hence, the motivation of RSS for using SSM/I. Besides the water vapor channel being V-Pol only, the 10.65, 19.35, 37.00, and 85.5 GHz are linear dual-polarized frequencies, i.e., V- & H-Pol.

TMI is a two-point externally calibrated total power radiometer whereby the feed horns sequentially view a blackbody target (warm load microwave absorber) and a Cold Sky Reflector (CSR) that views space. An example of the calibration process, radiometric transfer function (radiometric counts-to-TA), is depicted in Fig. 2.

When the feed horn measures the warm load this is referred to as hot load counts (HLC) and when it views space cold sky counts (CSC). Hence, the HLC can be written as:

HLC = G × HLT + O (1)

where HLT is the hot load physical temp, G & O is the gain & offset (mathematical slope & y-intercept) between the two calibration points with units counts/Kelvin & counts, respectively. The linear radiometric transfer function is valid provided that nothing obscures the feed horn’s view of the two targets. However, this is not the case for the CSR view as will be discussed in Section III.

III. DEEP SPACE CALIBRATION MANEUVER

A. DSC Maneuver In 1998, a set of DSC maneuvers were performed, 6 in January & 1 in September, where the spacecraft’s attitude was put into an inertial hold, which allowed the spacecraft to perform a 360° pitch rotation relative to the normal geodetic earth pointing mode. This caused the TMI main reflector (MR) beam to view a non-polarized homogenous scene (deep space) of ~ 2.7 K. Unfortunately, during the majority

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Fig. 1. TMI Scanning Geometry (source: [1]).

of the DSC maneuver, the CSR beam was rotated and intercepted the earth; hence, the two-point calibration process was no longer valid, and the results could not be interpreted. An example of the DSC is depicted in Fig. 3 using AGI’s Systems Tool Kit (STK). Note that in both figures the earth is in the bottom of the each panel. In the left panel the MR (red beam) intersects earth while the CSR beam (green beam) views space. In the right panel the MR is now viewing cold space (DSV) while the CSR is partially intersecting the earth, with an uncertain TB.

B. Previous Work In 2001, RSS was first to use TMI DSC to calibrate the

radiometer [2]. Within their analysis, they used 300 scans to obtain an along scan error and ~100 scans for the calculation of the emissive reflector. As will be shown in section V, spillover must be accounted for so to properly address both of these analyses.

IV. ANTENNA TERMPERATURE RECONSTRUCTION Since the normal two point radiometric calibration is not

possible during most of the DSV, two alternate approaches have been developed that permit TMI counts to estimate TA from only a single warm calibration point and a few ancillary physical temperature measurements. One approach establishes a complex correlation coefficient between the radiometer gain, offset and receiver physical temperature. This robust relationship is established during normal (geodetic) pointing mode as a function of the receiver physical temperature, which is cyclical over a single orbit and has a seasonal mean temperature pattern. During the DSC maneuver, we use the warm load counts and physical temperature measurements, and other available instrument temperatures to estimate the receiver linear transfer function and thereby reconstruct the TA. The second approach reconstructs the cold sky counts based on multiple linear regression based on a combination of ancillary measurements that are valid during the DSV.

Fig. 2. Depiction of the two-point calibration radiometric transfer function.

A. Method 1: TA Reconstruction Using Gain & Offset As mentioned in Section II, during most of the DSV the

CSR beam is partially illuminating earth and the normal radiometer calibration process is corrupted. However, assuming that the relationship between the radiometric transfer function Gain & Offset (G & O) are linear, then it is possible to reconstruct TA from antenna counts.

Figure 4 depicts the approach for obtaining the linear relationship between G & O for 10 GHz V-Pol. The upper left panel shows a normalized gain & offset time series for 3 nominal (earth pointing) TMI orbits. The oscillation of the gain & offset are the result of cyclical orbital physical temperature variations of the TMI receiver. Note that the two curves exhibit an offset (phase difference) of 315 scans. The upper right panel shows a scatter diagram of G & O for multiple TMI orbits with the hysteresis present due to their phase difference. The lower left shows corresponding results after applying a 315 scan phase adjustment to align the two time series. Also, note the scatter plot (lower right panel) with the hysteresis collapsed, which allows a simple linear fit to be obtained.

This linear relationship between the Offset & Gain is:

O = m × G + b (2)

where m & b are the slope and y-intercept, respectively. These two parameters along with the phase shift applied are referred to as the reconstruction coefficients. An analysis of a large number of orbits reveals that these coefficients change with the thermal environment over time.

Unfortunately, during a DSC maneuver, the thermal changes are magnified (compared to a nominal orbit); therefore, the phase shift between the O & G signals is determined empirically through cross-correlation. The length of signal record to use for the cross-correlation is based on the metric of orbits; hence, six different lengths were chosen: 1, 3, 5, 7, 11, and 15 orbits, referred to as window size. It should be noted that the coefficients are determined only while the calibration process is valid, i.e., CSR views cold space.

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Fig. 3. Illustration of TMI during Earth Pointing Mode (left panel) & DSC Mode (right panel). The red beam represents MR beam and the green beam represents the CSR beam.

Once the linear relationship between G & O are obtained using (1) & (2), the reconstructed (estimated) gain (rGain) & offset (rOffset) are:

rGain = (HLC – b) / (HLT + m) (3)

rOffset = (m × HLC + b × HLT) / (HLT + m) (4)

Once the rGain & rOffset are determine the phase difference is reapplied to put them to their initial phase and TA is calculated using the MR counts.

B. A Post TA Reconstruction Correction The TA Reconstruction using Method-1 will have

residuals due to 1) imperfections in the simple linear relationship between G & O given by the reconstruction coefficients and 2) failure of the applied phase difference to align the G & O signals.

Due to these shortcomings, an Post-Reconstruction Correction (PRC) was applied to mitigate the effects of these residuals. Recognizing that residuals are a function of the thermal environment and hence, satellite orientation relative to the sun vector, it was decided the proper response should be a function of solar angles, i.e., solar azimuth and elevation within the ECI coordinates. The PRC is essentially a lookup table of the residuals between the true and reconstructed gain and offset as a function of azimuth and elevation. The table is created using residuals during valid calibrated scans, i.e., non-DSV portions of the orbit. An example of the correction is shown in Fig. 5. As one can see the residual without the PCR is ±1 Kelvin (blue) and after (red) is less than 0.25 Kelvin. The different window sizes can differ up to 0.6 Kelvin during DSV for 10V.

C. Method 2: Cold Sky Count Reconstruction Method-2 is a more recent and independent method of

obtaining TA during the DSC calibration. Essentially, it is a multiple linear regression using a combination of TMI temperature sensors that are valid during the DSV but are trained using nominal (non-DSV) scans. It reconstructs the cold sky reflector counts as a function of the HLT, HLC, Antenna Deployment Mechanism Physical Temperature Sensor (ADM), and Top of Radiator Physical Temperature Sensor (TR) and is of form:

Fig. 4. Upper Left: Shows normalized gain and offset with difference of 315 scans phase shift. Upper Right: Scatter plot of the non-normalized gain & offset with the phase shift with hysteresis present. Lower Left: Applying a 315 phase so gain & offset are in phase. Lower Right: Scatter plot of the non-normalized gain & offset with phase shift applied and collapsed hysteresis.

CSC = c1 + c2×HLC + c3×HLT + c4×ADM + c5×TR (5)

where c1-5 are the regression coefficients. As can be seen in Fig. 5, Method-2 (green curve) during non-DSV scans performs better than the previous methods.

V. RESULTS

A. Comparing Methods The common factors between all reconstruction methods

are 1) the algorithms are trained using nominal (non-DSV) scans and 2) the HLC and other ancillary data that is obtainable during non-DSV & DSV scans is used to reconstruct TA. In both panels the solid black curve is the calibrated TA, which is not valid between the dashed black lines. Between the green dashed lines, the TMI is in eclipse thus the physical temperatures are cooling down. Note that the first black line occurs simulatously with the TRMM goes into eclipse (1st green line) in left panel. The curves with different colors are the average of all window sizes and scan positions 1-4 (left edge of swath) for a simplistic comparison between the three methods: Method-1 (blue),

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Fig. 5. TA Residuals for Method 1 before (blue) and after (red) PCR. Method 2 is represented by the green curve. In between the black lines are regions/scans where the normal calibration technique is not valid.

Fig. 6. Reconstructed TA during DSV 1 for 10 (left panel) & 19 GHz (right panel). Solid Black line is the calibrated TA, within the green dashed lines TRMM is within eclipse.

Method-1 + PCR (red), and Method-2 (green). Note for the 10V case that the disagreements between the methods are up to 0.6 Kelvin and for the 19V case less than 0.25 Kelvin. This is because the signal of the HLC & CSC is noisier for the 10V case then 19V.

B. Feed Spillover During DSV When the main reflector views deep space at 10 & 19

GHz, the brightness temperature should be a constant 2.7 kelvin. However, as seen in Fig. 6, not only does TA never reach 2.7, but the reconstructed time series varies by 4 & 7 kelvin peak-to-peak for 10V & 19V, respectively.

This can be rationalized by two reasons: 1) as is suggested in [1] and corrected in [3] an emissive main reflector would produce an additive time varying bias to the TA signal, and 2) earth’s emission entering feed spillover region causes additive biases that are dependent on earth’s surface (e.g., ocean or land). For Fig. 6 between scans 3000-3500, for both channels exhibit a large jump in TA then a gradual decrease to scan 4250. When associating scan position 52 for the 10V with the sub-satellite point (SSP), there appears to be a strong correlation with the earth surface (land or ocean) as is

shown in Fig. 7 for DSV 1 to 6. Note that when the spacecraft is over land, the TA jumps depending on area of the land mass and ratio of land and ocean that is present. When the main reflector starts to view space for DSV 1 & 4, TRMM is located over Australia, and the TA is between 16 &17 kelvin but then drops when the spacecraft moves over ocean. Hence, the jumps in Fig. 6 are due to Australia entering into the feed spillover region. For the rest of the DSVs, it is obvious when over land the signal is warmer than when over ocean.

The feed spillover region is defined as the angular region that the feed horn pattern goes beyond the main reflector, which is defined as 38-90 degrees off the rotation axis of TMI. To understand the correlation of the jumps in TA during DSV, the spillover region (footprint on the earth surface) is geolocated with the land coastline map for several different times as shown in Fig. 8. Fig. 8 (a) is similar to Fig. 7 but only shows DSV 1 & 3 and is for 19 V-Pol. The middle panels (b & c) represent the time series of TA (blue) and the projection of the spillover region on earth multiplied by the land percentage that is present within this spillover field of view (SFOV) (green). The panel (b) represents DSV 1 and

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Fig. 7. Reconstructed TA for Beam 52 at 10 GHz V-Pol with the associated sub-satellite point for that given scan.

panel (c) for DSV 3. Reconstructed TA for Beam 52 10 GHz V-Pol with the associated sub-satellite point for that given scan. Next, panel (d) represents the SFOV for three points in time during DSV 3, where the SFOV illuminates a portion of Africa, Madagascar, and the Indian Ocean as it is leaving space and starting to illuminate the earth. The second SFOV is in mid-DSV and fully illuminates the Indian Ocean. For the last point in time, as the SFOV is leaving earth, it illuminates the mainland of south east Asia and the China Sea.

For the time series of DSV 1 in (b) there is a large amount of land present in the SFOV for scans 300 – 600 where there is a sudden increase in the TA signal which corresponds to Australia. For scans 1200 – 1700 even though the green curve is reporting a large amount of land, the TA does not because at this time most of SFOV is actually being obscured by the back part the spacecraft (Dog House structure of TRMM) and backside of the cold sky reflector but is not removed for the SFOV geolocation; hence, significantly less radiation enters the feed spillover region. For DSV 3, the associated SFOV (d) is shown over the earth and the jumps in TA are directly proportional to the amount of land that is present, this is obvious for time 3 where the green and blue curves between scans 700 – 1100 have the same envelope characteristics. It should be noted that this analysis does not include feed horn gain & EIA of the signal entering the spillover region, which are contributors to additive amount of TA.

VI. CONCLUSION & FUTURE WORK In this paper, the 1998 DSC maneuvers for TMI were

explained and three techniques of reconstructing the radiometric antenna temperature during the DSV were discussed. The first technique (Method-1) uses the cyclical characteristics of the radiometric transfer function gain & offset that was characterized as a function of time. The second is the former Method-1 but with a post reconstruction correction (Method-1+PRC) that uses the solar angles relative to the spacecraft’s orbit in ECI to mitigate the residuals. The third (Method-2) is a multiple linear regression as a function of ancillary data that is obtainable during the DSV. The three techniques proposed show satisfactory agreement between each other where differences are less than ¾ of kelvin at the end of the DSV.

As stated in the initial DSC analysis on TMI [2], there was disagreement between the two methods where the DSC results had unexpected larger variability and warmer bias compared to the SSM/I comparisons. This work now justifies this disagreement because of feed spillover effects, i.e., the earth’s emission radiating into the feed spillover lobes.

Future missions that require the satellite DSC should utilize this fact of feed spillover so to characterize this parameter during post launch. Our future work will consist of calculating the spillover so to remove this signal from TMI DSV so to estimate the main reflector emissivity. Similar analysis done in this paper will be applied to the GMI DSC maneuvers planned in Mid-May of this year

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Fig. 8. Reconstructed TA beam 52 19GHz V-Pol DSV1 & 3. Panel a) same as Fig 7 but for DSV 1 & 3, b& c) depicts the reconstructed TA for with the SFOV multiplied by land percentage, and d) shows where the SFOV for three time stamps.

ACKNOWLEDGMENT Steve Bilanow for helping in the understanding of the

TRMM inertial hold & TMI geolocation code. Yimin Ji for providing the 1A11 data set and literature so we may do this analysis. This research was sponsored under a grant with the NASA Goddard Space Flight Center’s Precipitation Measurement Mission.

REFERENCES [1] C. Kummerow, W. Barnes, T. Kozu, J. Shiue, J. Simpson, “The

Tropical Rainfall Measuring Mission (TRMM) Sensor Package,” Journal of Atmospheric and Oceanic Technology, vol 15, pp 809-817, June 1998.

[2] F. Wentz, P. Ashcroft, C. Gentemann, “Post-Launch Calibration of the TRMM Microwave Imager,” IEEE Trans. Geosci. Remote Sensing, vol. 39, pp 415-422, Feb 2001

[3] K. Gopalan, L. Jones, S. Biswas, S. Bilanow, T. Wilheit, T. Kasparis, “A Time-Varying Radiometric Bias Correction for the TRMM Microwave Imager,” IEEE Trans. Geosci. Remote Sensing, col. 47, pp 3722-3730, Nov 2009

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