Description
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This function calculates the distribution of vertical velocities (dh_dt) into respective bins based on height (h). It separates velocities into positive and negative components, computes their absolute values, and then calculates the weighted average of absolute, positive, and negative velocities for each bin. Additionally, it computes the uncertainty of the weighted averages. This function also provides counts of positive, negative, and absolute velocities for each bin, as well as shaded areas representing the uncertainty for the weighted averages.
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