## 3 Results
### Retrieval Diagnostics  
NUCAPS retrievals are color coded to help forecasters quickly assess the retrieval quality and are a function of numerous internal statistical checks. The diagnostic parameters are written to the NUCAPS-EDR file for researchers to understand why a particular retrieval was successful or rejected. The degrees of freedom (DOF; Figure 3a) are calculated from the trace of the averaging kernel matrix (AKM) and a measure of the retrieval information content. The DOF are interpreted as the number of fully independent levels in the retrieved profile, where higher values indicate greater measurement skill. Temperature can have up to 7 DOFs in the tropics [23], although more recent work showed typical temperature DOF values between 4 and 5 over the tropical Atlantic [32]. For the 8 September 2019 flight, the temperature DOFs were closer to 4. The bars in Figure 3 are again color coded using the same scheme as Figures 1 and 2 to indicate retrieval quality. Note that there are fewer DOFs for temperature profiles when the IR + MW retrieval had a rejection flag (yellow or red). Figure 2: The top row shows the vertical pressure cross-sections (mb) for the (**a**) dropsonde temperature, (**b**) the NUCAPS temperature IR + MW retrieval from NOAA-20, and (**c**) the difference between (**a,b**). The bottom row shows (**d**) the dropsonde water vapor mixing ratio, (**e**) the NUCAPS water vapor IR + MW retrieval from NOAA-20, and (**f**) the difference between (**d,e**). Profiles shown are for the dropsonde collocations in Figure 1. The squares at the bottom of each plot represent the quality flag, as described in Figure 1.  
The water vapor DOFs (Figure 3b) range from 2.5 to 3.0, which are fewer than the average of 5 DOFs in past studies on the vertical resolution of satellite sounder retrievals [23]. The chi-squared of a variable is the residual from observed and estimated values normalized by the instrument and geophysical noise. Chi-squared values at or below 1.0 indicate high signal-to-noise. For this flight, successful IR + MW had a chi-squared temperature statistic of less than 1.0, and the rejected IR + MW temperature retrievals had a chi-squared value greater than 1.1 (Figure 3c). For water vapor, most of the successful IR + MW retrievals had a chi-squared value less than 1.0, although sondes 15-16 were less than 2.0 (Figure 3d). The rejected water vapor retrievals had chi-squared values greater than 3.0. NUCAPS automatically rejects retrievals when the chi-squared of temperature exceeds 4 or the chi-squared of water vapor exceeds 5, which are 2.0 and 2.2 more noise than signal, respectively. Figure 3e,f show the total cloud fraction and the chi-squared of the cloud clearing. Cloud fraction and height are retrieved variables in NUCAPS and not diagnostic parameters, but they show where retrievals may have less skill in the column. The total cloud fraction in Figure 3e shows that the IR + MW retrieval was successful over partly cloudy scenes, while the MW-only retrieval was successful over cloudy conditions. Scenes where the retrieved total cloud fraction exceeds 80% are rejected. Figure 3f shows the chi-squared of the cloud clearing. Retrievals where this value exceeds 3.0 are automatically rejected, even if the total cloud fraction is below 80%. Examining the statistics above and rejection criteria, no single metric was the cause of failure. Instead, these retrievals were likely rejected due to a combination of smaller checks. This is apparent from visually inspecting the airmass RGB in Figure 1, but NUCAPS makes no a priori assumptions on the underlying cloud scenes. This demonstrates that the rejection criteria are performing as expected for this tropical cyclone case. Given the number of diagnostics generated from NUCAPS, it is possible to tailor a new quality control scheme for tropical cyclone applications. However, our results here show that the existing method adequately flags unrealistic profiles, and at this point, we do not recommend a change.