## 3 Results
### Double Differences
#### 3.2.2 Stratification of DD  
One metric for the DD biases, is the stability of the mean value when data are sorted in various ways. Besides using GDAS as environmental data to derive DD biases, another dataset called European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis Interim (ERA-I) [22] was also used to increase our confidence in the results. Therefore, four cases of radiometric intercalibration of TMI relative to GMI are implemented to evaluate the TMI V8 dataset with respect to V7. Case 1 refers to the intercalibration of TMI V7 relative to GMI, using GDAS as ancillary data. Case 2 is also TMI V7 but with ERA-I. Case 3 is TMI V8 with GDAS, and Case 4 is TMI V8 with ERA-I. The mean and standard deviation (STD) values of DD's over the 13-month period of all the channels are listed in Table 2. The results between using GDAS and ERA-I are extremely close to each other (Case 1 compared to Case 2, and Case 3 compared to Case 4). When Case 1 is compared to Case 3 or Case 2 compared to Case 4, it is noticeable that the average values of DD's changed from V7 to V8. The minimum change is 0.8 K for the 89 GHz H-pol and the maximum is 2.41 K for the 10 GHz V-pol. The STD values changed slightly from V7 to V8, where 19 GHz V- and H-pol have the maximum changes, \(\geq\)0.1 K.  
Ideally, when the DD's are separated into two yaw orientations, they should be identical. To examine this, the difference between DD\({}_{\text{yaw-0}}\) and DD\({}_{\text{yaw-180}}\) are calculated and presented in Figure 12 for all the 9 channels. For both V7 & V8, the change in DD's between the two yaw flips is small for all channels with largest difference being \(-0.4\) K & \(-0.3\) K respectively at 23 GHz V channel. For all channels, V8 appears to be \(<\)0.1 K smaller than V7. Continuing the analysis (see Figure 13), it was noticed that the DD anomaly from V7 shows a systematic dependence, when sorted on latitude for the 19V, 19H and 23V channels. It is noted that similar results have been previously presented by [PERSON] et al. [23]. While the reason for this is not fully understood, it is believed that this is related to the water vapor absorption line at 22 GHz; and moreover in V8, the DD latitude dependence is evidently improved. Figure 11: Monthly intercalibration double differences (DD) for TMI relative to GMI for four cases. Red line indicates monthly averaged DD using TMI V7 Tb and GDAS environmental data; blue is TMI V7 but with ERA-I; green is TMI V8 with GDAS and black is TMI V8 but with ERA-I data. Figure 12: Mean double difference (DD) between Yaw 0\({}^{\circ}\) and 180\({}^{\circ}\) of each channel for both V7 (red dots) and V8 (blue squares). Since the correction of the emissive antenna and the sun intrusion to the hot load were based on the solar coordinates, it was important to assess the change in DD anomaly (CDDA) from V7 and V8 which is calculated as follows:  
\[\mathrm{CDDA}(\beta,\mathrm{phase})=(\mathrm{DD_{8}}-<\mathrm{DD_{8}}>)-(\mathrm{ DD_{7}}-<\mathrm{DD_{7}}>) \tag{3}\]  
where \(<\mathrm{DD_{7}}>\) and \(<\mathrm{DD_{8}}>\) are the averaged DD for V7 and V8 respectively. The resulting CDDA was stratified based on the solar coordinates, which are the sun beta angle and the phase from orbit midnight. The scattered DD for channel 19.35 V and 0\({}^{\circ}\) yaw orientation is shown in Figure 14, which includes relatively large differences (\(>\)\(\pm\)0.4 K), especially in the region of the solar intrusion into the hot load. This verifies the improvement of the hot load correction procedure. Furthermore, a scatter plot between the GMI earth scene brightness temperatures and the values of DD \(>\pm\)0.4 K at 19.35 GHz V channel is shown in Figure 15. It is apparent that V8 DD's appear to be independent of the scene brightness with a slope close to zero, while V7 DD's have a perceptible positive linear dependence with a slope of +0.04 K/K.