The Tropical Rainfall Measuring Mission (TRMM) satellite began operating in December 1997 and was shut down on 8 April 2015. Over the oceans, the microwave (MW) sensor aboard TRMM measures sea surface temperature, wind speed, and rain rate as well as atmospheric columnar water vapor and cloud liquid water. Improved calibration methods are applied to the TRMM Microwave Imager (TMI), and a 17-yr climate record of these environmental parameters is produced so as to be consistent with the climate records from 13 other MW sensors. These TMI retrievals are validated relative to in situ observations over its 17-yr mission life. All indications point to TMI being an extremely stable sensor capable of providing satellite climate records of unprecedented length and accuracy.
The microwave (MW) imaging radiometer on the Tropical Rainfall Measuring Mission (TRMM) satellite operated from December 1997 to the end of the TRMM mission on 8 April 2015. This sensor is called TMI for TRMM Microwave Imager. Over the oceans, TMI provides a full suite of environmental parameters including sea surface temperature (SST or TS), wind speed (W), and rain rate (R), as well as atmospheric columnar water vapor (V) and cloud liquid water (L). The literature has many examples of the application of these satellite retrievals 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).
This paper describes the steps required to realize the full potential of TMI for climate applications. These include achieving proper geolocation, radio frequency interference (RFI) mitigation, and sensor calibration. With respect to calibration, the major challenge is to account for the slightly emissive TMI antenna, as discussed by Wentz et al. (2001). Some of the radiation received by TMI comes directly from the antenna and this component must be precisely removed. The results we show here indicate that TMI has been extremely stable over its 17-yr life.
An essential part of the analysis is to ensure the TMI calibration and the data processing algorithms are consistent with those used by Remote Sensing Systems (RSS) for the existing set of 13 MW sensors listed in Table 1. This table includes two MW scatterometers, for which the wind speed retrievals are consistent with the MW imagers. In 2010, RSS transitioned its Special Sensor Microwave Imager (SSM/I) processing from version 6 to version 7 (V7), which has become our common standard for all MW imagers (Wentz 2013). The V7 standard requires that the brightness temperature (TB) calibration reference for all sensors be the Meissner and Wentz (2012) ocean radiative transfer model (RTM). All sensors listed in Table 1 have been consistently processed and are at the V7 calibration standard. With the completion of the analyses present here, TMI has become the most recent addition to this set of intercalibrated sensors.
2. TMI basic characteristics
The TMI sensor is well described in the literature (Kummerow et al. 1998), and here we provide a few details relevant to this paper. TMI is a conically scanning radiometer that operates at five frequencies: 10.65, 19.35, 21.25, 37.0, and 85.5 GHz. For all frequencies except 21.25 GHz both vertical and horizontal polarization is measured. At 21.25 GHz only vertical polarization (v-pol) is measured. This gives nine channels. The cone angle for the antenna look direction is approximately 49° relative to the spacecraft nadir. The scanning azimuth angle is about ±65° relative to the spacecraft x axis. The spacecraft operates in two yaw modes. For the yaw = 0° (180°) mode, the spacecraft x axis points in the direction (opposite direction) of the spacecraft velocity vector. Spacecraft yaw maneuvers are performed every 15–30 days, depending on season, to ensure a proper thermal environment for the spacecraft. The yaw maneuvers produce an abrupt change in the solar radiation impinging on TMI, and this complicates the calibration procedure.
The TRMM orbit is inclined 35° relative to the equator and as a result the swath of Earth observations is limited to 40°S–40°N. The inclined orbit was intended to provide dense coverage of the tropics. Another advantage of the inclined orbit is that it facilitates intersatellite comparisons. During every orbit the TMI swath crosses those of all other polar-orbiting MW sensors and, using a collocation window of 1 h, provides a huge number of satellite intercomparisons. In this paper, we used intercomparisons with the F13 SSM/I, AMSR-E, and WindSat, which are three stable and well-calibrated sensors, to calibrate the TMI TB. These intercomparisons, as well as those coming from other sensors not used for the calibration, show that TMI is a very stable sensor.
3. TMI PPS 1B11 data
The starting point for our TMI analyses and data processing is the most recent version of the TMI brightness temperatures orbital data files (1B11, version 7.002) produced by the Precipitation Processing System (PPS) at NASA GSFC (NASA 2011; Precipitation Processing System 2012). The TB calibration for this PPS data is based on an RSS analysis of early TMI data from December 1997 through April 1998 (Wentz et al. 2001). The TMI calibration was adjusted to make the TMI TB agree with the RSS version 4 (V4) of F11, F13, and F14 SSM/I TB. Later, an empirical time-varying TB component was added to the 1B11 product to account for the varying temperature of the TMI antenna (Gopalan et al. 2009). This time-varying component has a zero mean and does not affect the overall absolute calibration based on the V4 SSM/I TB. Our objectives here are 1) to update the V4 TB calibration to the V7 calibration standard now used by all the other sensors and 2) to implement a more physical and exact method for dealing with the TMI antenna that is traceable back to the antenna’s surface emissivity. This update also has the advantage of using 17 yr of TMI observations as compared to the 4 months used in the initial Wentz et al. (2000) analysis.
A first-step requirement for all RSS data processing is that the TB coming from the satellite data provider (in this case PPS) be reversed back to the original sensor counts. Different data providers have different methodologies for converting radiometer counts to TB. Also, the various data providers can implement their own version changes to the counts-to-TB process, and these version changes are not always transparent to the users. By starting our analysis and data processing with the raw sensor counts, it is easier for us to maintain consistency, and we do not need to be concerned with the algorithm choices and changes of the data providers. For TMI, the counts-to-TB algorithm used by GSFC was supplied by RSS back in 1999. This algorithm is easily inverted to yield raw sensor counts.
Another component of the RSS processing is consistent geolocation. Rather than using the latitudes, longitudes, incidence angles, and such coming from the data provider, we use our own geolocation algorithm. The same tried-and-proven algorithm is used for all MW imagers. It is not uncommon to find errors in geolocation information provided by others. For the PPS TMI data, we find relatively large geolocation errors that are due to errors in the prelaunch sensor pointing angles.
4. Spacecraft roll error
Prior to version 7.002, the PPS 1B11 data had an error in specifying the spacecraft roll ϕ. This error revealed itself as a cross-track error in our SST retrievals. The roll error Δϕ repeats every orbit with a slow time dependence on a time scale of days to weeks and is modeled as
where ω is the orbit position angle going from 0° to 360° as the satellite goes through its orbit, starting at the southernmost point. The a coefficients are determined by a least squares fit based on the difference of the TMI SST retrieval TS,TMI and a reference SST given by the NOAA SST operational product TS,REY (Reynolds et al. 2002). The SST retrieval error resulting from the roll error is modeled as
where the first partial derivative is the error in the SST retrieval resulting from an error in specifying the Earth incidence angle θi and the second partial derivative is the change in θi produced by a change in roll. This second term is a function of the TMI scan position α. When TMI is looking forward (α = 0), the roll error has little effect on θi. The maximum effect is when TMI is looking to the side. The a coefficients in (1) are found so as to minimize, in a least squares sense, the difference of the SST retrieval error given by (2) and the observed TS,TMI − TS,REY difference. This fit is done for every TMI orbit using a moving ±15 orbit-averaging (±1 day) window. In this way, a table of a coefficients is found for every orbit.
The version 7.002 PPS 1B11 data files now have a roll correction applied, but only up to orbit 69 280. This roll correction is derived from the TRMM Precipitation Radar (PR) (Bilanow and Slojkowski 2006). The PR-derived roll correction is completely independent of our SST method. Figure 1 shows a0, a1, and a2 derived from the SST analysis plotted versus orbit number. Two sets of results are shown: one using PPS 1B11 data files without the PR roll correction and the other with the PR roll correction. The fact that the PR correction substantially reduces the size of a2 and to a lesser extent a1 indicates that the PR-derived and SST-derived roll corrections are consistent with each other. But note the abrupt increase in a2 after orbit 69 280 at which point the PR correction is no longer done. Also note the large roll errors that occurred right after TRMM’s orbit was boosted from 355 to 408 km near orbit 21 520. This was due to an attitude control problem, and both the SST-derived and PR-derived methods effectively correct this problem. For our analysis we use the SST-derived roll correction because it is available for the entire TMI mission.
5. Sensor pointing adjustment
After the spacecraft roll correction is applied, we evaluate the registration of the TMI antenna temperature TA imagery relative to coastlines, islands, lakes, and rivers. Errors in the TMI imagery are most obvious when one looks at the difference between observations taken when the spacecraft is at yaw = 0° and when it is at yaw = 180°. A pointing error in the spacecraft along-track direction will shift the yaw = 0° imagery one way and the yaw = 180° the other. Figure 2 shows an example of this. The difference of the 180° minus 0° yaw TA imagery of the Amazon basin for all nine TMI channels is shown. There is clearly a misregistration of the TA imagery as evidenced by the blue and red halos. We have done this type of analysis for many other MW imagers, and the misregistration error of TMI is larger than typical, being about 10 km at 11 GHz.
The panels in Fig. 2 are for orbits 80 001–85 000. We spent considerable time looking at many other time periods and other locations and concluded that the misregistration is constant in time and can be mostly corrected by simply adjusting the TMI nadir cone angle θn and azimuth angle α0 relative to the spacecraft x axis at the start of the scan. Table 2 gives the values of θn and α0 used for the PPS 1B11 processing and the new values that we derive. Figure 3 shows the improved registration resulting from using the revised θn and α0. There is obviously a big improvement in the registration but some small residual features remain. It is not clear if these features are lingering misregistration errors or if they are real differences resulting from the measurements from the two yaws being at different times. Since this set of figures only show the difference between the two yaws, we also present Fig. 4, which shows the TA imagery of the Hawaiian Islands just for yaw = 180°. The true location of the islands is shown in dark blue. A visual inspection of Fig. 4 suggests good absolute geolocation is now being achieved with the revised θn and α0. We estimate the geolocation error is now about 1–2 km.
6. RFI in the cold mirror
The TMI cold mirror is designed to look upward into deep space, which has a known brightness temperature of 2.7 K. This cold-space observation along with the observation of the blackbody hot load provides two calibration references for converting the radiometer counts to antenna temperatures. Unfortunately, sometimes the cold mirror observes the transmission from geostationary communication satellites orbiting above TMI. This is a common problem for MW imagers. The time period over which this type of interference occurs is relatively short: several minutes during an affected orbit. The calibration of the MW radiometers tend to be fairly stable over these short time intervals, and the problem of RFI in the cold mirror is solved by discarding the period of erroneous cold counts and bridging the resulting time gap via interpolation.
Since the offending geostationary satellites are at fixed positions, the interference problem occurs at specific geographical locations. Geographic maps of the TMI cold counts are made to identify these locations. Figure 5 shows the TMI cold counts plotted versus the spacecraft nadir latitude and longitude. Each panel in the figure represents an average over 1000 orbits for which the zonal mean value has been subtracted, thereby giving maps of the cold-count anomaly. These anomaly maps show cold-mirror RFI only occurs for yaw = 0°. Also, the cold-mirror interference only occurs for the descending segment of the orbit except for one case that occurs at the northernmost extent of TRMM’s orbit as the satellite is transitioning from ascending to descending. Table 3 gives the six types of cold-mirror RFI we identified by looking at the cold count anomaly maps. Figure 5 shows the anomaly maps corresponding to these six types. The RFI problem becomes greater in the latter part of the TMI mission. Bit masks are made of the anomaly areas shown in Fig. 5 and the cold counts in these areas and time periods are flagged as bad. To fill in gaps thus created, a linear interpolation of cold counts versus time is done using the good cold counts on either side of the gap.
7. Antenna temperature calibration equation for an emissive antenna
By definition, the antenna temperature is a measure of radiant power entering the feedhorn. It is the brightness temperature of the surrounding environment integrated over the gain pattern of the TMI parabolic antenna and feedhorn assembly. It is common practice to segment this integration into a component coming from Earth and another coming from cold space:
where η is the fraction of power coming from cold space having a brightness temperature TBspc of 2.7 K and is called the spillover coefficient; TAert is the component of radiation coming from Earth. The subscript A0 denotes this expression applies to a perfectly reflecting antenna (emissivity is 0). MW antennas tend to mix polarizations and the term TAert represents a combination of vertical and horizontal polarization. For example, the v-pol port of the feedhorn will primarily consist of v-pol Earth radiation but there will also be a small horizontal-polarization (h-pol) component. Thus TAert is specified as
where χ is the cross-polarization coupling coefficient, TBco is the copolarization brightness temperature, and TBx is the cross-polarization TB. For TMI we use the prelaunch antenna measurements to specify χ (given in Table 6).
For an emissive antenna like TMI some of the radiation comes from the antenna itself, and the radiation entering the feedhorn is
which provides the means to remove the emissivity effect. We note that (5) implicitly assumes all the cold-space radiation enters the feedhorn via the sidelobes of the antenna. In fact, some of the radiation may enter the feedhorn directly depending on the taper of the feedhorn pattern, and as such is not affected by ε. This is a subtle difference and amounts to about a 0.1-K difference in the modeling.
If the radiometer output has a linear response to TA, then the antenna temperature is given by
where Cc, Ch, and Ce are the radiometer counts when the radiometer is looking at the cold mirror, the hot load, and Earth scene, respectively. The temperatures Tc and Th are the effective temperatures of the cold and hot calibration targets. Equation (7) is simply expressing the assumption that the radiometer counts vary linearly as the scene temperature varies from Tc to Th. To account for nonlinearity in the radiometer’s response function, the usual method is to introduce the following quadratic term when estimating TA:
where β is a measure of the nonlinearity. The quadratic term accounts for the fact that the nonlinearity has no effect when the incoming radiation is at the same temperature as either the hot-load temperature Th or cold-load temperature Tc. Solving the quadratic equation gives
Equations (6), (7), and (9) provide the means to compute the antenna temperature TA0, free of emissivity effects, given the radiometer counts, the cold- and hot-load temperatures, Tc and Th, the antenna emissivity ε and temperature Tant, and the nonlinearity coefficient β. As a starting point, we use the emissivity values reported by Wentz et al. (2001) and assume a linear radiometer (β = 0). These values are later revised as discussed below. The remaining term that needs specifying is the physical temperature of the antenna Tant.
8. Physical temperature of the antenna
There are no thermistors attached to the TMI antenna and hence other means are required to estimate its physical temperature Tant, which we express as
where is the mission-average reflector temperature and ΔTant is its variation. Because of other possible sources of biases in the TA calibration equation, it is difficult to uniquely specify . Previous results (Wentz et al. 2001) suggest a value near 290 K. During the course of this analysis, we experimented with two values: 280 and 290 K. The value for ε is between 0.025 and 0.050, and a 10-K change in represents a change from 0.25 to 0.50 K in the absolute bias of TA. The nature of the calibration process is such that any change in results in a compensating change in the spillover η (see next section). We found that using a value of = 280 K, as compared to 290 K, results in spillover values closer to prelaunch values. A colder value seems unreasonable in view of the Wentz et al. (2001) results, so 280 K is our choice for . The more important and difficult problem is specifying the variation in Tant over the mission life of TMI.
Our first approach to estimating ΔTant was to use a retrieval algorithm similar to the ones we use for geophysical retrievals (Wentz and Meissner 2007). Variations in Tant produce distinctive variations TA that have a specific spectral and polarimetric signature as dictated by (5). A simple linear retrieval algorithm is derived in the same manner that we derive the geophysical retrieval algorithm. A set of simulated antenna temperatures for a large ensemble of ocean scenes is generated using the RTM along with (5) to simulate the emissive antenna. For each scene, Tant is varied by ±50 K about its mean value. Using these scenes, an algorithm of the following form is trained in a least squares sense to estimate the variation ΔTant:
where subscript i denotes the seven lower TMI channels (from 11V to 37H), TAi is the TMI measurement, and is the antenna temperature for . For all channels other than the 21-GHz v-pol channel (21V), the function f is defined as f(x) = x − 150 and for 21V, f(x) = −ln(290 − x), which is a common method for removing the nonlinearity effects that occur near the 22.235-GHz water vapor line (Wentz and Meissner 2007). The algorithm’s p coefficients have a slight dependence on the Earth incidence angle θi, and Table 4 gives their values for θi = 53.3°.
Equation (11) is used to estimate Tant for every TMI ocean observation. The estimation error for a single observation is quite noisy, but by averaging over one day (15 orbits), the noise is substantially reduced. When doing the averaging we assume that, for a given local time and yaw (i.e., solar environment) within the orbit, ΔTant is nearly the same over the course of a day. Thus the averaging is stratified into 0.5-h local time bins. To specify , we use the daily mean TAi averaged over all local times.
We experimented with using to remove the emissive antenna effects. A good indicator of the algorithm’s performance is the veracity of the SST retrieval because this retrieval is quite sensitive to error in specifying ΔTant. When the SST retrievals were compared to the Reynolds SST, there were significant differences that were correlated with the local time (i.e., solar environment) of the TMI observations. It was clear that these differences were not due to true diurnal effects. Rather, they were as a result of deficiencies the estimate, which is just based on the TA observation. We decided to supplement the estimate of ΔTant with additional temperature information provided by the TMI thermistors. Although these thermistors are not attached to the antenna, they can be used as proxies of the thermal environment. There are three thermistors attached to the external hot load, one to the external top surface of the TMI drum enclosure, and one other attached to the 85-GHz receiver shelf. Let t1 (degree Celsius) denote the average of the three hot-load thermistors, and let t2 and t3 (degree Celsius) denote the drum temperature and the mixer temperature. Let , , and denote their average over a single orbit. These orbit-averaged values have the property that they slowly vary in time, having nearly the same value from one orbit to the next. As such, they provide information on the slowly varying component of ΔTant as the solar environment changes over days to weeks. Proxies for the rapidly changing part of ΔTant that occurs within each orbit are given by the change in thermistor readings relative to their orbital average, as is denoted by . This thermistor information is blended with the estimate from (11) by doing the following least squares fit to the TMI minus Reynolds SST differences (very similar to how roll errors were found in section 4):
This fit is done using TMI orbits 144–14 200, which is about 2.5 yr of data, thereby finding c0 through c11. The form for (12) that best represented the SST difference was determined by trial and error. A separate set of c coefficients is found for yaw = 0° and 180° and given in Table 5. The variation in the temperature of the antenna about its mean value is then given by
where Λ denotes the right-hand side of (12) and the sensitivity of TS to Tant is modeled as a constant value of −0.0617. Figure 6 shows ΔTant plotted versus local time and day of year for the entire TMI mission up to early 2014. The antenna reaches its maximum temperature for local time near 1900 for which ΔTant has a value near 25 K. The minimum value of about −25 K occurs near 0500 LT. The dependence of ΔTant on yaw is obvious from the vertical striping in Fig. 6.
9. Amazon forest calibration
When calibrating the set of 11 MW imagers listed in Table 1, our usual approach is to calibrate to the ocean RTM and then verify the calibration over land targets. For the most part, the radiometers are sufficiently linear that no further calibration is needed over land. For TMI, the calibration problem becomes more complex because of the emissive antenna. To simplify the problem and separate the estimation of the various calibration parameters, we use an area in the northern Amazon basin as a calibration reference in addition to the ocean. The antenna temperature of the Amazon forest is near 275 K, which is similar to the physical temperature of the antenna Tant, and as a result the sensitivity of TA to ε is very small, as is shown by its partial derivative derived from (5):
This property helps to separate the derivation of η from the derivation of ε. The emission from the Amazon forest is nearly unpolarized, and as a result TAert given by (4) equals TBco to within 0.02K. Inverting (3) to yield η and setting TAert = TBco gives
where TA0 is the TMI measurement, corrected for emissivity effects according to (6), and TBco is the “true” brightness temperature of the Amazon forest. To specify TBco, we use the region 1°S–3°N, 301°–308°E as our calibration target. This region has been used by other investigators (Brown and Ruf 2005; Meissner and Wentz 2010). It is heavily forested and has remained stable for the last couple of decades. We have a large database of Amazon TB measurements collected from the all the MW imagers listed in Table 1. We only used observations from 0100 to 0500 local time to avoid diurnal warming problems, and a diurnal model (Mo 2007) is used to normalize all observations to 0130 LT. We average the results from all sensors to obtain a reference TB value for the TMI calibration. Table 6 gives this sensor-averaged TB value and the standard deviation of the TB values for the individual sensors. These sensor-averaged values are used to specify TBco, and (15) is used to compute postlaunch spillover values. The prelaunch and Amazon-derived values of η are given in Table 6. Values are given for each of the nine TMI channels. In some cases, the frequencies of the reference sensors are not quite the same as the TMI channels, but these differences are small and are not a real issue.
10. Ocean calibration
To find the other terms in the TA calibration equation, we use the ocean as a calibration reference. The Meissner and Wentz (2012) ocean RTM is used to generate a simulated TA. The RTM requires the specification of SST, wind speed W, and direction φ, as well as columnar water vapor V and cloud liquid water L. We only use observations that are free of rain as determined by the TMI rain algorithm. For the frequencies we are considering, the atmospheric component of TA is primarily a function of the columnar amount of vapor and liquid water rather than the detailed shape of the vertical profiles (Wentz 1997). Furthermore, SST and V serve as proxies for the air temperature profile. Variations in the profile shape and temperature from typical values will produce errors in the RTM, but these errors are small and by design have a zero mean.
Recently, the accuracy of the RTM was tested by comparing its predicted TB with the measurements from the Global Precipitation Measurement (GPM) Microwave Imager (GMI) launched in February 2014. The RTM predates GMI, and hence GMI provides an independent assessment of the RTM. Much effort was put into GMI’s prelaunch calibration because GMI is to serve as a calibration standard for current and future MW imagers. For all channels from 11 to 89 GHz, the difference between the GMI measured TB and the RTM was always less than 0.8 K (Draper et al. 2015). Considering that the GMI absolute accuracy requirement is 1.3 K, these GMI minus RTM differences may be mostly due to small calibration errors with GMI rather than the RTM.
The inputs to the ocean RTM are as follows. SST comes from the Reynolds optimum interpolation (OI) product (Reynolds et al. 2002, 2007a,b) interpolated to the location of the TMI footprint. For W, V, and L we use the geophysical retrievals from the F13, AMSR-E, and WindSat. These three sensors cover the entire mission life of TMI. We require the retrievals be within 1 h and 25 km from the TMI observation. For wind direction, we use the National Centers for Environmental Prediction Global Data Assimilation System 6-hourly wind fields (NCEP 2000). A large database of TMI and RTM TA pairs (TA,TMI, TA,RTM) is thus constructed and analyzed in several different ways.
We first determine the nonlinearity coefficients β and find optimum values of the antenna emissivities ε now that the antenna physical temperature has been specified. Values for β and ε are found so as to minimize the least squares variance of TA,TMI − TA,RTM, and these values are shown in Table 7. Also shown is the change in the ocean TA that occurs when β is applied. The Wentz et al. (2001) values of ε ranged from 0.027 to 0.040 and showed no obvious spectral dependence. In comparison, the rederived emissivity values range from 0.025 to 0.049 with a clear spectral dependence of increasing with frequency. This tendency for the emissivity to increase with frequency is similar to that observed for the F16 SSM/IS, which also has an emissive antenna (Kunkee et al. 2008).
Another possible source of error for MW imagers is mispecification of the effective hot-load temperature Th. The temperature of the TMI hot load is measured by three thermistors, which are averaged together to obtain Th. However, thermal gradients in the load will cause the effective temperature of the load, as seen by the feedhorn, to be different from the thermistor readings. To assess this potential problem, we stratify the TA,TMI − TA,RTM difference according to 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. These (φsun, θsun) binned values are averaged over the TMI mission. The TA difference is converted to an error ΔTh in specifying the hot-load temperature using
This expression comes from the TA calibration equations and expresses the fact that the error in TA resulting from an error in Th decreases linearly to zero as TA goes from Th to Tc. The leading minus sign is applied because ΔTh is added to the thermistor-inferred Th. Figure 7 shows ΔTh plotted versus the sun angles φsun and θsun for the nine TMI channels. There is a good deal of interchannel consistency in the ΔTh plots. The small interchannel differences in ΔTh could be due to any number of small residual errors in the analysis. Or, the differences may be an indication of varying penetration depths and horizontal sampling of the load by the feedhorn. We found small but systematic differences in the ΔTh(φsun, θsun) plots when stratified according to the two yaws and separate corrections are applied for each yaw. Figure 7 shows the results for yaw = 180°.
We also look at the effect of the TRMM’s orbit being boosted from 355 to 408 km in August 2001. The F13 observations bridge this change in the TRMM altitude and provide the means to evaluate the pre- versus postboost TMI TA. The increase in altitude increases the Earth incidence angle θi, but this effect is accounted for when computing TA,RTM. The TA,TMI − TA,RTM difference was computed before the boost and 20 000 orbits after the boost. Small differences on the order of 0.1–0.2 K are found and are given in Table 7 for each channel. These small offsets are subtracted from the preboost TA. It is not clear what causes these biases. They do not have the signature of an error related to θi. Possibly the difference in the pre- versus postboost thermal environment is not being modeled quite correctly.
Wentz et al. (2001) reported along-scan errors in the TMI observations related to the scan angle α and derived a correction based on both cold-space observations and ocean observations. We revisited this problem using the technique just described for finding ΔTh. In this case, the TA,TMI − TA,RTM differences are stratified according to α. The along-scan errors found by this new analysis, which uses 17 yr of TMI observations, are within 0.1 K of that found by Wentz et al. (2001). This demonstrates that the along-scan errors are very stable in time. For the V7 TMI calibration, we use the new values.
11. Analysis of calibrated antenna temperatures
All of the calibration adjustments discussed above are applied to the TMI observations, and calibrated TA are found. Figure 8 shows the difference of the TMI-calibrated TA minus the RTM TA computed using F13, AMSR-E, or WindSat geophysical retrievals. The differences are plotted versus orbit number and orbit position angle ω, and this is called a mission plot because it is useful for looking at the entire mission of a given sensor. A moving window of ±300 orbits is used for averaging. Table 8 gives the mean and standard deviations of the TA differences preaveraged over ±300 orbits in time and 3.6° in ω. By design, the mean TA,TMI − TA,RTM is near zero (0.00–0.02 K). For the lower frequencies (11–37 GHz) the standard deviation of TA,TMI − TA,RTM is between 0.07 and 0.18 K. The standard deviations are somewhat higher at 85 GHz, where the influence of clouds, which have high spatial/temporal variability, dominates the statistics. For some channels the geographic variation of TA is about 50 K, and a standard deviation of 0.1 K represents a 0.2% modeling and calibration error. There is some slight vertical banding in Fig. 8 that is related to transitioning to and from the three calibration sensors. The F13 overlap is from the beginning of the TMI mission to orbit 68 200. The AMSR-E overlap is for orbits 25 915–79 089, and the WindSat overlap is for orbit 29 793 to the end of the TMI mission.
For perspective, we also include the results we obtain when using the brightness temperature values in the PPS 1B11 data files. The 1B11 results are shown in Fig. 9 and Table 8. The 1B11 TB show large biases (1–2 K) relative to the RTM. To stay within the ±1-K color bar, these large overall biases have been removed when making Fig. 9. Still there are relatively large residual features (±1 K) in the 1B11 mission plot, which manifest themselves as higher standard deviations in Table 8. The PPS statistics are in terms of TB rather than TA, but the difference is negligible: ΔTA ≈ 0.98ΔTB.
12. Intersatellite comparisons of environmental parameters
In this section, we compare the TMI retrievals of SST, wind speed, water vapor, cloud liquid water, and rain rate (Wentz et al. 2015) with similar retrievals from other MW sensors. The differences of these environmental parameters (other MW sensor minus TMI) are denoted by ΔTS, ΔW, ΔV, ΔL, and ΔR. A collocation window of ±1 h and ±25 km is used in the analyses. These comparisons are done globally over all ocean regions observed by TMI (40°S–40°N).
For all MW imagers, we use the same type of retrieval algorithm, and this helps to achieve consistency among the retrievals from different sensors. The retrieval algorithm is described by Wentz and Spencer (1998), Chelton and Wentz (2005), and Wentz and Meissner (2007). The rain retrieval part of the algorithm is further detailed in Wentz and Spencer (1998) and Hilburn and Wentz (2008a). The retrieval algorithm is designed to be, as much as possible, the inverse of the RTM. By inverse we mean the following:
where Γ represents the retrieval algorithm with the input being the set TBrtm of brightness temperatures computed from the ocean RTM assuming a set Ep of environmental parameters. The desired property is that the retrieved environmental parameters equal the ones used to compute TBrtm. Equation (17) in effect defines the retrieval algorithm in terms of the RTM. This inverse property (17) helps to ensure that the TB calibration results in a proper Ep calibration, as is shown in this section. It also greatly facilitates the overall calibration process by reducing the problem to a function of four variables (TS, W, V, and L). The retrieval algorithm uses all TMI channels except for two 85-GHz channels. The rain rate retrieval uses a separate algorithm (Wentz and Spencer 1998), for which the W, V, and L retrievals serve as input.
Figures 10–14 show the time series of the monthly averages of ΔTS, ΔW, ΔV, ΔL, and ΔR, respectively. For each time series, these figures show the mean values of ΔEp, called offset, and the drift in ΔEp. The drift is defined as the least squares slope of the time series times the duration of the time series and hence is a measure of the change in ΔEp over the period of overlap. For Fig. 10, which shows SST, there are only three other sensors that provide SST retrievals: WindSat, AMSR-E, and Advanced Microwave Scanning Radiometer 2 (AMSR-2). For the other figures, there are a total of nine MW imagers that can be compared to TMI. Furthermore for Fig. 11, which shows wind speed, there are two additional sensors: the scatterometers QuikScat and Advanced Scatterometer (ASCAT).
Given this many comparisons, certain problems with some of the MW imagers become obvious. These problems are listed in Table 9. The most notable problems are with the F15 SSM/I and the F16 SSM/IS. On 14 August 2006, a radar calibration beacon (RADCAL) was activated on the F15 satellite. Although we have taken measures to correct this problem (Hilburn and Wentz 2008b; Hilburn 2009), the retrievals are still quite noisy during the RADCAL period, which is shown in red in Figs. 11–14. Also shown in red is the time period starting in 2009 for F16, during which the F16 retrievals significantly degrade. The F16 SSM/IS is our most problematic sensor. It has an emissive antenna, sun intrusion into the hot load, and an orbit with a rapidly drifting ascending node time. Clearly, we need to revisit our calibration of F16. Of minor note is that the last year (2008) of the F14 SSM/I seems anomalous and is marked red in the figures. Those portions of the time series that are marked red are excluded when computing the offset and drift.
Remarkably, in no instance do we find any problems with TMI, which by all indications is an extremely stable sensor. The one caveat is that in this analysis we are looking at monthly averages, and problems associated with the emissive antenna tend to average out. The comparisons of SST (Fig. 10) show excellent agreement as do the wind comparisons (Fig. 11) with the scatterometers and WindSat. Apart from the issues listed in Table 9, the vapor, cloud, and rain comparisons (Figs. 12–14) also look very good. There is no suggestion of a disconnect between the preboost TMI retrievals and the postboost retrievals (boost occurred August 2001). A close inspection reveals a very small upturn in the wind time series in 2014 for WindSat and AMSR-2 compared to TMI. We believe this is due to the rapidly decaying TRMM orbit that started in mid-2014. This change in altitude from 405 to 360 km is showing a spurious decrease the TMI wind retrievals of up to 0.05–0.1 m s−1. However, the ASCAT comparison does not show this for some reason.
13. Validation using in situ observations
In this section we compare the TMI retrievals with in situ observations. These observations include SST, wind speed, and rain measurements from moored buoys as well as island GPS measurements of columnar water vapor (Wang et al. 2007). The moored buoys include those operated by National Buoy Data Center (NBDC; Gower 2002; Portmann 2009) and by the Pacific Marine Environmental Laboratory (PMEL; McPhaden et al. 1998, 2009; Bourles et al. 2008). In addition to moored buoys, SST comparisons also include drifting buoys. The method used for the GPS vapor comparisons is described by Mears et al. (2015).
None of these in situ measurements was directly used during the TMI calibration process and hence represent a withheld dataset. Of course, the F13, WindSat, and AMSR-E geophysical retrievals, which were used for the TA calibration, have been validated against similar in situ observations. We can now see if the closure requirement (17) successfully translates the TA calibration into a precise Ep calibration.
The TMI SSTs are compared with drifting and moored buoy data. At low wind speeds during the day, the skin surface temperature, which is measured by TMI, can be significantly different from the at-depth temperature recorded by the in situ instruments. To avoid this diurnal warming problem, daytime wind speeds below 6 m s−1 are excluded from the comparisons. Figure 15 shows the 17-yr time series of the TMI SST minus in situ SST. The red line in Fig. 15a is the mean moored buoy/drifter SST and the black line is the collocated TMI SST. The mean difference and the standard deviation between the two are shown in Fig. 15b. These results are extremely consistent over the 17 yr. The overall TMI minus in situ bias is nearly the same for day and night: −0.01° and +0.02°C, respectively. Given the fact that the SST retrieval is quite sensitive to the emissive antenna problem, this consistency in the day versus night SST bias is strong evidence that the emissive antenna is being modeled correctly. The SST differences are also plotted versus SST, W, V, and L (not shown) to verify the TMI retrievals have the proper dynamic range and no crosstalk with the other Ep.
The TMI wind speeds are compared with those from the NDBC and PMEL moored arrays. All buoy wind measurements are normalized to a height of 10 m above the surface. The collocation window is 30 min and 25 km, and the comparisons go from the beginning of the TMI mission up through 2011. We omit data after 2011 from the analysis because of reduced buoy data availability. Figure 16 shows the wind difference plotted versus mean wind speed. There are few buoy observations above 15 m s−1, and at these higher winds the buoys tend to underestimate the winds (Howden et al. 2008). The wind speed differences are also plotted versus SST, V, and L (not shown) to verify the TMI retrievals have no crosstalk with the other Ep.
The TMI vapor retrievals are compared to those from GPS stations located on small remote islands. For this analysis, a 5 × 5 gridcell box is centered on the location of the GPS station and a local gradient is removed from the satellite field before comparison, as described by Mears et al. (2015). The comparison consisted of over 67 000 collocations for 26 stations. Figure 17 shows a scatterplot of the TMI vapor retrievals versus the GPS values. The overall mean difference of TMI minus GPS is 0.45 mm, which is large enough to be of some concern. We examined the GPS results for WindSat and found a similar bias. The original absolute calibration of the vapor retrieval was based on radiosonde comparisons (Wentz 1997) and now we see an inconsistency relative to GPS. Both radiosondes and GPS measurements are subject to their own particular bias problems, and we need to study this issue better to determine what the absolute vapor reference should be.
Figure 18 shows a scatterplot comparing collocated TMI rain rate retrievals with daily rain rates from PMEL tropical buoys located between 25°S and 21°N, with most of the buoys being within 10° of the equator. In the figure, each point represents a particular buoy for which the rain rates have been averaged over all time. We require a minimum record length of one year, which provides 78 buoys. There are a total of 238 924 individual collocations. Averaging over all buoys and all times gives a TMI value of 1576 mm yr−1 and a buoy value of 1572 mm yr−1. This 4 mm yr−1 difference is remarkably small. The standard deviation of the 78 individual buoys in Fig. 18 is 287 mm yr−1 (18.3%), and the linear slope is 0.969 with an R2 correlation of 0.936.
14. Trends from TMI
Figure 19 shows trend maps for the five TMI environmental parameters. These trends are found from a linear least squares fit of the Ep over the 17 yr of data with the seasonal cycle being removed. Trends are found for every 2° latitude–longitude cells from 40°S to 40°N. It should be emphasized that these trends are specific to the TMI period of operation (1998–2014), and 1998 was the warmest year of the last century (Trenberth and Fasullo 2013; Trenberth et al. 2014). The displayed trends consist of a cyclic component associated with various climate oscillations [e.g., ENSO, the Pacific decadal oscillation (PDO), and the Indian Ocean dipole (IOD)] and an underlying component associated with long-term climate change. The separation of the two components is a major challenge for climate research. One obvious feature that does occur during the 1998–2014 period is a substantial moistening of the intertropical convergence zone accompanied by a drying in the tropical South Pacific. Although the regional trends can be quite large, the globally average trends (40°S–40°N, oceans only), which are given in Fig. 19, are small.
TMI is a very stable sensor as evidenced by comparisons with many other MW sensors. Table 10 gives a summary of these intersatellite relative drifts, where F17 has been excluded because of an obvious drift problem. The table lists the mean and standard deviation of the drifts of the 10 sensors relative to TMI. In addition to demonstrating the stability of TMI, these comparisons also reveal obvious problems with some of the other sensors, most notably F15 after the RADCAL was turned on, F16 starting in 2009, and a persistent drift in F17. Also, AMSR-E may have a small shift that occurs around 2008. Table 10 also provides a summary of the TMI geophysical retrievals versus in situ comparisons. Close agreement is found with the exception of the 0.45-mm bias relative to the columnar vapor derived from GPS measurements. This bias is related to the difference between the GPS measurements and the radiosonde measurements used in the original calibration, and further study is required to resolve this difference.
The TMI TB and Ep datasets, along with datasets from all the other MW sensors discussed here, are available from RSS. These datasets extend back to 1987 and provide nearly three decades of direct satellite observations of climate variability over the oceans. These observations should help clarify interannual and decadal climate oscillations, which will lead to building better climate indices.
This work was supported by NASA’s Earth Science Division. The TMI 1B11 dataset used in this effort was made available by NASA’s Science Mission Directorate, and are archived and distributed by the Goddard Earth Sciences (GES) Data and Information Services Center (DISC). We gratefully acknowledge the providers of data used to validate the TMI data: NOAA/PMEL TAO Project Office and the NOAA/National Data Buoy Center for moored buoy wind and rain data, NCDC for the Reynolds OI SST data, and Junhong Wang for GPS-derived TPW data.