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Richard E. Passarelli Jr.

Abstract

The theory of parametric techniques for the recovery of Doppler spectral moments from ground-clutter-contaminated measurements of the radar autocorrelation function is presented. Seven algorithms for the mean velocity are given as examples, and evaluated using simulated Gaussian weather and measured ground clutter signals. Some algorithms can provide accurate estimates of the mean velocity at clutter-to-signal power ratios of > 10 dB and one performs well at 20 dB. An example in actual precipitation is also presented.

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Richard E. Passarelli Jr.

Abstract

Mean snowflake collection efficiencies can be estimated by studying the height evolution of snow-size spectra in natural precipitation. This was done using coordinated aircraft and Doppler radar measurements of snow-size spectra and analytical and numerical techniques to model the stochastic collection process. For aggregating stellar and dendritic crystals in the temperature range −15 to −12°C the estimated mean collection efficiency was 1.4±0.6.

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Richard E. Passarelli Jr.

Abstract

It is well known that snowflakes tend to distribute exponentially with respect to their melted diameter. This fact is used to formulate an approximate analytical model of the deposition and aggregation growth of snow in stratiform clouds. The model predicts the height evolution in a steady-state, vertically heterogeneous cloud of the slope and intercept parameters, N(h) and λ (h), of the size distribution of snowflakes which is assumed to be given by n(D,h)=N(h) exp[−λ(h)D], where h is the height in the cloud and D the snowflake diameter. Solutions for N(t) and λ(t) for a time-dependent spatially homogeneous cloud are also presented. Results from this technique compare well with numerical integrations for the case of perfect geometric coalescence of raindrops. This stratiform snow model predicts the existence of radar reflectivity-snowfall rate relations although, for this first-order model, there is fair agreement between theoretical and observed values. The model suggests that “equilibrium” snow size spectra owe their existence to the counteracting effects of deposition and aggregation growth.

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Richard E. Passarelli Jr.

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Richard E. Passarelli Jr. and Ramesh C. Srivastava

Abstract

Unlike raindrops, ice particles of the same mass can have different fallspeeds, due to variations in the particle shape and bulk density. (This is an extension of the popular axiom that no two snowflakes are alike.) This is an additional source of variance for vertical incidence Doppler (VID) spectra taken in snow that has been neglected in previous studies which assume a one-to-one fallspeed-mass relationship. The total VID spectral variance due to the dispersion of ice particle fallspeeds can be broken down into two components, i.e., that due to the mean fallspeed-mass relationship and that due to fluctuations about the mean. Existing data on ice particle fallspeeds are not adequate for a thorough evaluation, but do indicate that these two sources of fallspeed variance can be of the same order. These results suggest that the task of deducing snow-size spectra from VID measurements is more difficult than has been recognized.

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Richard E. Passarelli Jr. and Ramesh C. Srivastava

Abstract

A new theoretical approach to snowflake aggregation is presented which accounts for the fact that snowflakes of the same mass can have a spectrum of fallspeeds. The essence of the approach is to define a modified kernel which can be used in the stochastic collection equation exactly as one would use a standard kernel computed by assuming that snowflakes of the same mass have a unique fallspeed. The modified kernel approach predicts more rapid aggregation than the standard kernel approach, the degree of enhancement being critically dependent on the width of the fallspeed spectrum. For the case of aggregates of dendrites, measurements made by a number of investigators suggest that the width of the fallspeed spectrum is of the same order as the variation in the mean fallspeed over the typical range of snowflake sites. Thus the effect of including the fallspeed spectrum in calculations of aggregation is large, and may even dominate the aggregation process.

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Richard E. Passarelli Jr. and Hannah Boehme

Abstract

Topographic forcing over the hills and small mountains of southern New England plays an important role in determining the distribution of pre-warm-front precipitation from winter cyclones. Upslope regions receive 20–60% more precipitation than do nearby downslope or coastal regions. Both the intensity and duration of precipitation contribute to the positive upslope anomalies. The magnitude of the upslope anomalies, the details of the precipitation intensity distributions at proximal upslope and downslope gauges, and the results of simple models indicate that precipitation scavenging in orographic clouds can explain the orographic enhancement. Also, the existence of a positive precipitation anomaly over the coastal plain suggests that frictional convergence may be generating weak, but persistent vertical motions.

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K. Kenneth Lo and Richard E. Passarelli Jr.

Abstract

In studies of precipitation growth, comparisons between theory and observation are difficult because of the problem in obtaining a complete 4-dimensional (space and time) description of the kinematic, thermodynamic and microphysical properties of the atmosphere. A new flight plan has been devised which permits one to observe the height evolution of snow-size spectra in a reference frame where the effects of horizontal gradients and temporal changes are minimized. The flight plan, termed the advecting spiral descent (ASD), requires an aircraft to start aloft in a mesoscale precipitation area and then spiral downward in a constant bank angle, descending at approximately the mean fallspeed of snow. Qualitative comparisons between ASD observations and particle growth theory suggest that snow evolves through at least three stages characterized by deposition, aggregation and breakup. The breakup process serves to limit the number of large snow particles and interacts with aggregation to produce a limiting value of the slope of the snow-size spectrum.

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Richard E. Passarelli Jr. and Alan D. Siggia

Abstract

The relationships between the Doppler spectrum of velocities and the autocorrelation function can be studied via simple geometric and power series expansion relations. The asymptotic expansion of the autocorrelation function in terms of the central moments of the Doppler spectrum provides a new theoretical framework for time-domain spectral moment estimation and illustrates the trade-offs in optimal moment estimation. A number of new moment estimators are derived via this general approach and evaluations of three new spectral width estimators demonstrate that the implementation of a single spectral width estimator is generally not the best approach.

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Bernard Vonnegut and Richard E. Passarelli Jr.

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