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Ryan Lagerquist, Amy McGovern, Cameron R. Homeyer, David John Gagne II, and Travis Smith

except the last follow this linear transformation with leaky ReLU and batch normalization, like the convolutional layers. The last dense layer uses the sigmoid activation function (section 6.2.2.2 of Goodfellow et al. 2016 ), which forces the output to range over [0, 1], allowing it to be interpreted as a probability. The last dense layer does not use batch normalization, because this would force the outputs to a Gaussian distribution, which permits values outside [0, 1] and is therefore invalid for

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Sid-Ahmed Boukabara, Vladimir Krasnopolsky, Jebb Q. Stewart, Eric S. Maddy, Narges Shahroudi, and Ross N. Hoffman

final section concludes with a summary and outlook. SATELLITE REMOTE SENSING AND NWP CHALLENGES AND ML. The many challenges to satellite remote sensing and NWP are grouped here by forcing mechanism—Big Data, advanced models and applications, and user demands. In the sections that follow we show that recent advances in ML in terms of efficiency, capability, and ease of implementation, can help to meet these challenges. First, NWP is failing to exploit the growing diversity and volume of observations

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Eric D. Loken, Adam J. Clark, Amy McGovern, Montgomery Flora, and Kent Knopfmeier

with the proper value of σ , spatially smoothing ensemble probabilities reduces sharpness (e.g., Sobash et al. 2011 , 2016 ; Loken et al. 2017 , 2019 ) and potentially sacrifices resolution if too much smoothing is required. Moreover, the “best” value of σ may vary based on geographic location and time of year (e.g., Fig. 3 ), as precipitation uncertainty is reduced where stronger and/or more predictable forcing is present, such as near high terrain (e.g., Blake et al. 2018 ) or during the

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