## 4 Retrieval of Atmospheric Water Vapor
Figure 1 displays the water vapor Jacobian for ATMS water vapor channels 1, 18, 19, 20, 21, and 22 at a scan angle of 30 degrees for a tropical standard atmosphere over land. The land surface emissivity of 0.971905 is chosen for obtaining a zero sensitivity on TPW at 23.8 GHz. The emissivity value is typical for vegetated land and forest [16; 17]. As one can see from the figure, the water vapor Jacobian for the ATMS channels 18 to 22 is negative because atmospheric emission is less than surface emission over the land for those channels. Similar to ATMS channels 18 to 22, the water vapor Jacobian for the ATMS channel 1 is negative above 820 hPa (red dashed line). However, the Jacobian for the ATMS channel 1 is positive below 820 hPa, where atmospheric emission is higher than the surface emission over the land because the land surface emissivity is less than one. The surface emission for the emissivity of 0.971905 and a surface temperature of 299.74 K is equivalent to the emission of a blackbody at a temperature of 293.30 K since from the surface, reflected atmospheric downwelling radiation under a clear-sky condition is small for the window channel at 23.8 GHz. The Jacobian value itself at each layer for ATMS channel 1 is meaningful and significant, in particular the good sensitivity in the surface boundary layer. Basically, the sum of the Jacobian values above and below 820 hPa is zero, which prevents one from deriving TPW via a method like Equation 7 using a single channel. Figure 1 shows that channel 1 has good sensitivity to a surface boundary layer while channel 18 (183.317 GHz) has very good sensitivity to the middle and upper troposphere. Figure 2 shows a case from an operational MiRS retrieval compared with an experimental retrieval performed without ATMS channel 1. It is for a single ECMWF profile. There is no obvious change in the temperature retrieval between the two experiments. However, without channel 1, the water vapor retrieval in the lower troposphere is significantly degraded, which affects the TPW retrieval. Table 2 shows the global statistics of the MiRS TPW retrieval against ECMWF analyses. We use the same operational settings and ATMS measurements in the MiRS for this study except for the switch on or off of the ATMS channel 1. The TPW derived from the ECMWF analysis data serves as the reference. In the operational MiRS retrieval, both the background and the first guess are interpolated by time and location from a dynamic climatological data set. The dynamic climatological data set was calculated from 60 days (5 days per month) of ECMWF data in 2015 and averaged for 5 (latitude) by 5 (longitude) degrees grids using a 10 by 10 degrees and 5-day moving window. In the ECMWF analysis, model prediction data and observations data \begin{table}
\begin{tabular}{c c c c c} \hline  & **Ocean** & \multicolumn{3}{c}{**Land**} \\ \hline Atmosphere\(\backslash\)Emissivity & 0.45470 & 0.93000 & 0.971905 & 1.00000 \\ \hline US Standard (TPW = 14.2 mm) & 1.4333 & 0.1146 & \(-\)0.0013 & \(-\)0.0796 \\ \hline Mid-latitude Summer (TPW = 29.2 mm) & 1.2492 & 0.1142 & 0.0133 & \(-\)0.0541 \\ \hline Topic (TPW = 41.1 mm) & 1.0870 & 0.0877 & 0.0000 & \(-\)0.0593 \\ \hline \end{tabular}
\end{table} 
Table 1: ATMS channel 1 brightness temperature sensitivity to total precipitable water (K/mm) for the U.S. standard atmospheric profile [15], mid-latitude summer and tropical atmospheric profiles. The values in the second row are ocean surface emissivity, and three land surface emissivities (unitless). The values between the second and the fifth columns, and between the third and the fifth rows are the brightness temperature sensitivity on TPW in unit of K/mm. For example, for the case of U.S. standard atmosphere over ocean here, one millimeter water vapor increment will result in a 1.4333 K increase on the ATMS channel 1 brightness temperature. are assimilated so that the analysis can serve as the \"best\" global reference. Over oceans, the degradation by removing channel 1 is more than 20% in standard deviation.