## 2 Materials and Methods  
### TMI 1B11 V8 (Gpm05)  
#### 2.1.1 Algorithm Development  
In this section, the changes of the final legacy TMI product will be described. The purpose of these changes are to make the final revision more robust than previous versions that were based on ad-hoc corrections. The main modifications in the final version are the following: TRMM's geolocation correction, scan bias correction, reducing the effect of the noise equivalent delta-Tb (NEDT), Radio Frequency Interference (RFI) in the Cold Sky Reflector (CSR) correction, hot load correction, and the Main Reflector (MR) emissive antenna correction. The first change in 1B11 V8 is the geolocation calculation, which provides the geodetic latitude and longitude for each observation, has been improved. There are three components that are responsible for the geolocation data: TRMM orbit ephemeris, TRMM attitude and TMI's antenna pointing alignment. The ephemeris information, which includes the Greenwich Hour Angle (GHA), was provided by the NASA Goddard Space Flight Center (GSFC), and some errors in the ephemeris GHA were identified in 2013. These errors have been corrected in V8 by using the latest information from the U.S. Naval Observatory. The geolocation accuracy after correcting the ephemeris increased to 0.1 km instead of 0.45 km from previous versions [7]. In previous versions, errors were identified in the spacecraft attitude for yaw and roll, which were subsequently corrected based on the PR measurements [8]. The correction was only applied from the beginning of the mission to 15 January 2010. For V8, the spacecraft attitude was recomputed using new ground-definitive attitude computation software that uses spacecraft gyro and sun sensor data along with the measurements of the spacecraft roll derived using the PR science data for the entire mission. The V8 attitudes improve the accuracy from tenths of a degree range to hundredths of a degree range [7]. Furthermore, the TMI antenna boresight pointing offset (spin axis misalignment) was reanalyzed in V8 for each channel. The nominal value of the antenna boresight offset from the spin axis was 49\({}^{\circ}\) for all channels. However, better values were found for each feed horn: 49.45\({}^{\circ}\) for the 10 GHz feed horn and 49.28\({}^{\circ}\) for the high-frequency feed horns. In addition, the 10 GHz feed horn showed different value for each polarization: 49.4\({}^{\circ}\) for the vertical (V-pol) polarization and 49.5\({}^{\circ}\) for the horizontal polarization (H-pol). Moreover, the starting azimuth angle for observations was found to be \(-63.91^{\circ}\) for the 10 GHz feed horn and \(-64.36^{\circ}\) for the high-frequency feed horns. Since the 10 GHz feed horn was directed to the main reflector earlier than the other feed horn, it was estimated to make its observations ahead by about 0.2 s. Finally, an overall alignment offset relative to TRMM spacecraft inertial coordinate system axes was estimated as \(-0.08^{\circ}\) in pitch angle and 0.08\({}^{\circ}\) in roll [7; 9]. The second main change applied to V8 was the scan Tb bias correction. In 2001, a Tb bias was found that was dependent upon the azimuth scan position, and it was reported that this bias also changed, based on the scene temperature [2]. However, in V7, the bias temperature was calculated for each channel based on the average ocean temperature. This was changed in V8, when the scan bias correction was updated to be dependent on the scene temperature, as seen in Figure 1[9]. The third improvement in V8 was to average hot and cold load calibration samples from consecutive scans to reduce the effect of the NEDT during the calibration process. The true gain and offset should vary slowly on-orbit with changes in the physical temperature of the receiver.