# Evaluating Satellite Sounding Temperature Observations for Cold Air Aloft Detection
## 2 Data and Methods
### NUCAPS Technical Description  
NUCAPS is a system that retrieves temperature, water vapor, and trace gases from both microwave and infrared sounders on low earth orbiting (LEO) satellites. For this paper, we only examine the NUCAPS temperature profiles as other retrieved products are not relevant to CAA forecasting. To evaluate the skill in detecting CAA and rather than focus on algorithm improvements, we will only use those profiles where both the combined infrared and microwave retrieval have passed NUCAPS quality control [6; 15]. NUCAPS also retrieves temperature from water vapor from microwave-only channels. However, we will not examine microwave-only profiles because they have not yet been evaluated for use in NWS operation. For a complete discussion of the NUCAPS algorithm, see [4; 5; 6; 9; 10]. Apart from quality control flags, NUCAPS has two retrieval metrics that can be useful for evaluating NUCAPS temperature retrieval skill, namely uncertainty due to clouds and retrieval information content. NUCAPS employs a technique known as \"cloud clearing\" that removes the radiative effects of clouds from top of atmosphere instrument measurements to enable retrievals in partly cloudy scenes. Cloud clearing ingests the measured IR spectra from each \(3\times 3\) array of IR sounder fields of view (FOV; ~14 km at nadir) and derives a single cloud-free spectrum for this aggregate spatial footprint, also known as field of regard (FOR; ~50 km at nadir). NUCAPS retrieves soundings from cloud cleared spectra, which means that within each FOR footprint, a NUCAPS temperature profile depicts the clear state around clouds, not through clouds. This is an important distinction, especially when comparing against radiosondes that measure the atmosphere inside clouds. Cloud clearing is a robust, linear technique that is advantageous in operational, global sounding systems because it (1) does not require any prior knowledge of cloud types or their microphysical properties, and (2) does not require complex cloud radiative transfer calculations, which can be computationally expensive and significantly increase data latency [4]. NUCAPS produces several diagnostic parameters alongside its retrievals to help evaluate the uncertainty cloud clearing introduces. We will describe these parameters further in Section 3.2. Like all sounding retrieval algorithms, NUCAPS solves an inverse problem to derive a dependent variable (e.g., air temperature as a function of pressure) from an independent variable (radiances). NUCAPS utilizes the Bayesian Optimal-Estimation technique [16] to retrieve atmospheric state variables that meets NOAA operational requirements [17]. The Bayesian retrieval method combines an a priori estimate (a reasonable first guess of the atmospheric state variable) with the observed radiances into the final retrieval. The degree to which the observed radiance can improve upon the a priori is represented by the averaging kernel matrix (AKM). An AKM quantifies the degree to which the observed state (retrieval) relates to the \"true\" state (as embedded in the measured radiances). The AKM is calculated as a function of the covariances of the signal and the noise and thus varies from scene to scene as described in [16]. Inside the AKM, values range between 0 and 1. In practice, averaging kernel values are always less than 1 because retrieval noise is never zero, while they can approximate 0 where the measured radiances have very little sensitivity to the variable in question, in which case the retrieval will approximate the a priori estimate. In NUCAPS, the a priori for temperature is a regression retrieval that uses coefficients calculated as the covariance between ECMWF and observed radiances from four global focus days. The regression uses four global days to capture sufficient diurnal and seasonal variability of IR and MW spectral combinations for the state variable [6]. Since NUCAPS is a global product, the regression was designed to not be regional or application specific.