## 2 Materials and Methods  
### NUCAPS  
The NUCAPS environmental data record (EDR) is based on the Atmospheric Infrared Sounder (AIRS) algorithm version 5 [12]. NUCAPS retrieves the atmospheric geophysical state, surface properties, and cloud parameters using microwave (MW) and infrared (IR) satellite sounding observations. The NUCAPS Algorithm Theoretical Basis Document (ATBD) [13] contains a detailed description of the NUCAPS algorithm, but we discuss here parts that are relevant to this manuscript. NUCAPS utilizes a modified optimal-estimation technique [14], which uses prior information (first guess) to solve an inverse problem. For NUCAPS temperature and water vapor retrievals from the NOAA-20 satellite, the first guess is a global eigenvector regression [15] from cloud-cleared CrIS and ATMS radiances that are trained on the European Centre for Medium-Range Weather Forecasts (ECMWF)global model. Optimal-estimation techniques can also account for error propagation throughout the algorithm, such as instrument noise or other uncertainty in the employed techniques. NUCAPS retrievals include vertical profiles of temperature, water vapor, ozone, carbon monoxide, methane, carbon dioxide, nitric acid, nitrous oxide, sulfur dioxide, several cloud properties such as cloud top height and fraction, and surface properties. Each of these variables is retrieved in sequential order, using the previously solved variables and error characteristics to improve estimates of downstream variables. Each variable is retrieved using an optimal subset of the IR and MW channels, which is a method called channel selection [12; 16]. The channels are chosen so that (i) the variable being solved for has spectral sensitivity and (ii) other variables not being solved for have little or no sensitivity. Channel selection increases algorithm processing speed, which is imperative for time-sensitive operational distribution, and it reduces instrument noise in the final retrieval. While NUCAPS retrieves many variables, we will focus on the air temperature, water vapor, and cloud retrievals in this paper. NUCAPS uses cloud cleared radiances [12], which are constructed from a 3 \(\times\) 3 array of CrIS or AIRS or 2 \(\times\) 2 array of IASI collocated to ATMS, or AMSU, or AMSU + MHS observations on the same satellite, respectively. Cloud clearing infers the scene radiance if all clouds were removed, which eliminates the need for a complex (and possibly computationally slow and ill-posed) scattering model. Using this technique, robust retrievals are possible over clear to partly cloudy scenes with up to 80% cloud cover, thereby increasing the yield of successful observations. Since cloud clearing aggregates multiple sounder fields of view, implementing it results in a horizontal footprint that spans 50 km at nadir to 150 km at the scan edge. However, observations on these scales remain useful for operational forecasting on mesoscales (2-2000 km) and are within the normal horizontal drift ranges of rawinsondes. In addition to the combined MW and IR retrieval (hereon the IR + MW retrieval), NUCAPS retrieves temperature, water vapor, liquid water path, and surface emissivity using only MW channels. The MW-only retrieval has not been evaluated by forecasters but is part of the EDR file for research purposes. Unlike the IR + MW retrieval, the MW-only retrieval uses (i) all available MW channels, (ii) does not employ cloud clearing, (iii) solves for all variables simultaneously, and (iv) has a lower vertical resolution. Clouds have a much smaller effect on MW radiances, so MW-only estimates are possible when there are uniform clouds or fully cloudy scenes, whereas the IR + MW retrieval is degraded. MW-only retrievals are flagged as degraded over precipitating scenes, where NUCAPS-derived estimates of the liquid water amount are significant. This removes about 2-3% of MW-only retrievals a day. We evaluate the NUCAPS MW-only retrieval because it may be useful for increasing the yield of successful observations near tropical cyclones.