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Neural networks (NNs) are developed for estimating the error variances of individual infrared and microwave atmospheric temperature and humidity profile retrievals, thus potentially significantly improving their assimilation into numerical weather prediction models. Currently, most assimilation processes require error covariance matrices that are typically estimated over diverse profile ensembles. In addition to these “ensemble error variances,” this work explores the estimation of “sample error variances” that are relevant to a single sample of the ensemble (that is, an individual profile retrieval and its error at each pressure level). This analysis is facilitated by considering an individual profile retrieval as the most likely sample from a distribution of retrievals, given an individual sensor observation vector. The sample error variance is defined as the variance of this distribution. The approach described in this paper does not attempt to compute these retrieval distributions explicitly, as this is computationally prohibitive for hyperspectral sounders. Instead, NNs are trained to estimate the variances of these distributions directly. Examples over ocean utilizing AIRS/AMSU soundings on the NASA Aqua satellite and those from a proposed hyperspectral microwave sounder show that the predicted sample error variances agree well with the true sample error variances as determined by European Centre for Medium-Range Weather Forecasts analyzes colocated to the sensor observations. Furthermore, simple quality indicators derived using thresholding of the sample variance estimates compare favorably to AIRS Level-2 Version-5 quality flags.