82 research outputs found

    Deep convective clouds at the tropopause

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    Data from the Atmospheric Infrared Sounder (AIRS) on the EOS Aqua spacecraft each day show tens of thousands of Cold Clouds (CC) in the tropical oceans with 10 μm window channel brightness temperatures colder than 225 K. These clouds represent a mix of cold anvil clouds and Deep Convective Clouds (DCC). This mix can be separated by computing the difference between two channels, a window channel and a channel with strong CO<sub>2</sub> absorption: for some cold clouds this difference is negative, i.e. the spectra for some cold clouds are inverted. We refer to cold clouds with spectra which are more than 2 K inverted as DCCi2. Associated with DCCi2 is a very high rain rate and a local upward displacement of the tropopause, a cold "bulge", which can be seen directly in the brightness temperatures of AIRS and Advanced Microwave Sounding Unit (AMSU) temperature sounding channels in the lower stratosphere. The very high rain rate and the local distortion of the tropopause indicate that DCCi2 objects are associated with severe storms. Significant long-term trends in the statistical properties of DCCi2 could be interesting indicators of climate change. While the analysis of the nature and physical conditions related to DCCi2 requires hyperspectral infrared and microwave data, the identification of DCCi2 requires only one good window channel and one strong CO<sub>2</sub> sounding channel. This suggests that improved identification of severe storms with future advanced geostationary satellites could be accomplished with the addition of one or two narrow band channels

    Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples

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    We develop a simple Quantile Spacing (QS) method for accurate probabilistic estimation of one-dimensional entropy from equiprobable random samples, and compare it with the popular Bin-Counting (BC) method. In contrast to BC, which uses equal-width bins with varying probability mass, the QS method uses estimates of the quantiles that divide the support of the data generating probability density function (pdf) into equal-probability-mass intervals. Whereas BC requires optimal tuning of a bin-width hyper-parameter whose value varies with sample size and shape of the pdf, QS requires specification of the number of quantiles to be used. Results indicate, for the class of distributions tested, that the optimal number of quantile-spacings is a fixed fraction of the sample size (empirically determined to be ~0.25-0.35), and that this value is relatively insensitive to distributional form or sample size, providing a clear advantage over BC since hyperparameter tuning is not required. Bootstrapping is used to approximate the sampling variability distribution of the resulting entropy estimate, and is shown to accurately reflect the true uncertainty. For the four distributional forms studied (Gaussian, Log-Normal, Exponential and Bimodal Gaussian Mixture), expected estimation bias is less than 1% and uncertainty is relatively low even for very small sample sizes. We speculate that estimating quantile locations, rather than bin-probabilities, results in more efficient use of the information in the data to approximate the underlying shape of an unknown data generating pdf.Comment: 23 pages, 12 figure
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