Search Results

You are looking at 1 - 10 of 27 items for :

  • Author or Editor: Paul L. Smith x
  • Journal of Applied Meteorology and Climatology x
  • Refine by Access: All Content x
Clear All Modify Search
Paul L. Smith

Abstract

No abstract available.

Full access
Paul L. Smith Jr.

Abstract

Full access
Paul L. Smith

Abstract

Gamma functions are widely used in an effort to represent characteristics of observed raindrop size distributions, especially at the small-particle end. However, available instruments do not agree about the character of the small-drop region, and for many purposes that part of the spectrum is unimportant. At the large-drop end, sampling limitations impede reliable measurements. Thus, when moment methods are used to determine parameters for the fitted functions, the experimental uncertainties tend to be greater than the differences in important bulk quantities, such as rainfall rate or radar reflectivity factor, between the resulting gamma distributions and corresponding, simpler exponential distribution functions. It consequently makes little practical difference whether exponential or gamma functions are employed, and the exponential model is appropriate for many purposes.

Full access
Paul L. Smith
Full access
Paul L. Smith
Full access
Paul L. Moore
and
Daniel L. Smith

Abstract

An objective technique has been developed for modifying precipitation probability guidance forecasts received from the National Meteorological Center by means of radar information which becomes available subsequent to receipt of the guidance forecasts. Tests show improvement with respect to both the centralized guidance and the official subjective forecasts. The findings also carry implications as to the resolution necessary in radar data used in such a procedure.

Full access
Paul L. Smith
and
Albert Waldvogel

Abstract

Reports of hailstones larger than those indicated by hailpad observations being found on the ground around the hailpad sites raise questions about the validity of maximum-size determinations. Data from the Grossversuch IV hailpad network demonstrate this characteristic behavior. An analysis of the hailstone sampling process shows this to be an expected consequence, which interferes with reliable determinations of maximum hail-stone sizes.

Full access
Paul L. Smith
and
Donna V. Kliche

Abstract

The moment estimators frequently used to estimate parameters for drop size distribution (DSD) functions being “fitted” to observed raindrop size distributions are biased. Consequently, the fitted functions often do not represent well either the raindrop samples or the underlying populations from which the samples were taken. Monte Carlo simulations of the process of sampling from a known exponential DSD, followed by the application of a variety of moment estimators, demonstrate this bias. Skewness in the sampling distributions of the DSD moments is the root cause of this bias, and this skewness increases with the order of the moment. As a result, the bias is stronger when higher-order moments are used in the procedures. Correlations of the sample moments with the size of the largest drop in a sample (D max) lead to correlations of the estimated parameters with D max, and, in turn, to spurious correlations between the parameters. These things can lead to erroneous inferences about characteristics of the raindrop populations that are being sampled. The bias, and the correlations, diminish as the sample size increases, so that with large samples the moment estimators may become sufficiently accurate for many purposes.

Full access
Paul L. Smith
and
Donna V. Kliche
Full access
Paul L. Smith
,
Zhong Liu
, and
Jurg Joss

Abstract

Because of the randomness associated with sampling from a population of raindrops, variations in the data reflect some undetermined mixture of sampling variability and inhomogeneity in the precipitation. Better understanding of the effects of sampling variability can aid in interpreting drop size observations. This study begins with a Monte Carlo simulation of the sampling process and then evaluates the resulting estimates of the characteristics of the underlying drop population. The characteristics considered include the liquid water concentration and the reflectivity factor; the maximum particle size in each sample is also determined. The results show that skewness in the sampling distributions when the samples are small (which is the usual case in practice) produces a propensity to underestimate all of the characteristic quantities. In particular, the distribution of the sample maximum drop sizes suggests that it may be futile to try to infer an upper truncation point for the size distribution on the basis of the maximum observed particle size.

Resulting paired values, for example, of Z and W for repeated sampling, were plotted on the usual type of log–log scatterplots. This yielded quite plausible-looking Z–R and Z–W relationships even though the parent drop population (and, hence, the actual values of the quantities) was unchanging; the “relationships” arose entirely from the sampling variability. Moreover, if the sample size is small, the sample points are shown to be necessarily displaced from the point corresponding to the actual population values of the variables. Consequently, any assessment of the “accuracy” of a Z–R relationship based on drop size data should include some consideration of the numbers of drops involved in the samples making up the scatterplot.

Full access