A comprehensive review and extension of the theoretical bases for the measurement of the characteristics of rain and snow with vertically pointing Doppler radar are presented. The drop size distribution in rain can be computed from the Doppler spectrum, provided that the updraft can be estimated, but difficulties are involved in the case of snow. Doppler spectra and their moments are computed for rain by using various power law relations of fall speed υ versus particle diameter D and an exponential fit to the actual fall speed data. In the former case, there is no sharp upper bound to the spectra and all the spectral moments increase with rainfall rate R without limit; in the latter case, there is a sharp upper bound of the spectra corresponding to the limiting terminal velocity of raindrops, and the spectral moments approach an asymptote. Accordingly, the power laws are useful approximations over only limited ranges of precipitation rate. A comparison of theoretical and experimental mean Doppler velocity 〈υ〉 as a function of radar reflectivity factor Z shows that the empirical relation 〈υ〉 = 2.6Z0.107 of J. Joss and A. Waldvogel seems to be the only practical relation; even so, the scatter in 〈υ〉 is about ±1 m sec−1. This is also the kind of error to be expected in measuring updraft speeds by present methods. Such updraft errors result in unacceptably large errors in the drop number concentration estimated from Doppler spectra. In the absence of updrafts the mean Doppler velocity 〈υ〉 is uniquely related to Λ, the slope of the exponential drop size distribution. Simultaneous measurements of Z and 〈υ〉 can then be used to estimate N0, Λ, D0, M, and R, where N0 is the intercept of the exponential drop size distribution at D = 0, D0 is the median volume diameter, and M is the liquid‐water content.

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Recoverable manufacturing systems minimize the environmental impact of industry by reusing materials, reducing energy use, and reducing the need to landfill industrial products. These systems are widespread in the United States and are profitable, in addition to contributing to sustainable development. However, the management of supply-chain activities can differ greatly from management activities in traditional manufacturing supply chains. Seven complicating characteristics increase uncertainty. Managers must take actions to reduce uncertainty in the timing and quantity of returns, balance return rates with demand rates, and make material recovery more predictable. Managers must also plan for the collection of products from end-users. The use of information systems with new production-planning and control techniques makes management of these activities more predictable.

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