Paul L. Smith

Equivalent radar reflectivity factors for snow and ice particles

Expression analytique reliant le coefficient de reflectivite radar au coefficient equivalent exprime en fonction de la taille des particules

The area-time integral as an indicator for convective rain volumes

Abstract Digital radar data are used to investigate further a simple technique for estimating rainfall amounts on the basis of area coverage information. The basis of the technique is the existence of a strong correlation between a measure of the rain area coverage and duration called the Area-Time Integral (ATI) and the rain volume. This strong correlation is again demonstrated using echo cluster data from the North Dakota Cloud Modification Project 5 cm radars. Integration on a scan-by-scan basis proved to be superior for determining ATI values to the hour-by-hour integration used previously. A 25 dB(z) reflectivity threshold was found suitable for the ATI calculation. The correlation coefficient on log-log plots of cluster rain volume versus ATI is approximately 0.98, indicating a power-law relationship between the variables. The exponent of that relationship is just a little higher than one, which indicates that the cluster average rainfall rate is almost independent of the storm size and duration. A ...

Radar Reflectivity Factor Calculations in Numerical Cloud Models Using Bulk Parameterization of Precipitation

Abstract This paper describes and compares various methods for calculating radar reflectivity factors in numerical cloud models that use bulk methods to characterize the precipitation processes. Equations sensitive to changes in the parameters of the particle size distributions are favored because they allow simulation of phenomena causing such changes. Marshall-Palmer-type functions are established to represent hailstone size distributions because the previously available distributions lead to implausibly large reflectivity factors. Simplified equations are developed for calculating reflectivity factors for both dry and wet hail. Some examples are given of the use of the various equations in numerical cloud models.

A study of sampling-variability effects in raindrop size observations

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...

Microphysical Characteristics of a Well-Developed Weak Echo Region in a High Plains Supercell Thunderstorm

Abstract Microphysical measurements in and near the weak echo region of a supercell thunderstorm are discussed. The observations were made in southeastern Montana with an armored T-28 aircraft, which has the capability to measure hydrometeors over almost the entire spectrum between about 3 μm and 5 cm diameter. The storm exhibited many of the classic supercell characteristics, such as a well-developed weak echo region, overhang, persistent hook echo, and a large high-reflectivity core. Peak updrafts in the weak echo region exceeded 50 m s−1, and a continuous region of updraft extending over a horizontal distance of more than 14 km was observed. The updraft core appeared to be undiluted, but the edges of the updraft were clearly mixed with air from other regions of the storm. Virtually no ice particles were observed in the weak echo region, but the cloud liquid water concentrations exceeded 6 g m−3. Hail larger than 4 cm was encountered in several locations to the west of the weak echo region. The observat...

Raindrop Size Distributions: Exponential or Gamma—Does the Difference Matter?

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.

The Bias in Moment Estimators for Parameters of Drop Size Distribution Functions: Sampling from Exponential Distributions

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 (Dmax) lead to correlations of the estimated parameters with Dmax, and, in turn, to spurious correlations between the parameters. These things can lead to erroneous inferences about characteristics of...

An Observational Examination of Long-Lived Supercells. Part I: Characteristics, Evolution, and Demise

Observations of supercells and their longevity across the central and eastern United States are examined, with the primary focus on understanding the properties of long-lived supercells (defined as supercells lasting 4 h). A total of 224 long-lived supercells, occurring in 184 separate events, are investigated. These properties are compared with those of short-lived supercells (lifetimes 2 h) to determine the salient differences between the two classifications. A key finding is that long-lived supercells are considerably more isolated and discrete than short-lived supercells; as a result, the demise of a long-lived supercell (i.e., the end of the supercell phase) is often signaled by a weakening of the storm’s circulation and/or a rapid dissipation of the thunderstorm. In contrast, short-lived supercells commonly experience a demise linked to storm mergers and convective transitions (e.g., evolution to a bow echo). Also noteworthy, 36% of the long-lived supercell events were associated with strong or violent tornadoes (F2–F5), compared with only 8% for the short-lived supercell events. Evolutionary characteristics of long-lived supercells vary geographically across the United States, with the largest contrasts between the north-central United States and the Southeast. For example, 86% of the long-lived supercells across the north-central United States were isolated for most of their lifetime, whereas only 35% of those in the Southeast displayed this characteristic. Not surprisingly, the convective mode was discrete for 70% of the long-lived supercell events across the north-central United States, compared with 39% for the Southeast.

The Bias and Error in Moment Estimators for Parameters of Drop Size Distribution Functions: Sampling from Gamma Distributions

Abstract This paper complements an earlier one that demonstrated the bias in the method-of-moments (MM) estimators frequently used to estimate parameters for drop size distribution (DSD) functions being “fitted” to observed raindrop size distributions. Here the authors consider both the bias and the errors in MM estimators applied to samples from known gamma DSDs (of which the exponential DSD treated in the earlier paper is a special case). The samples were generated using a similar Monte Carlo simulation procedure. The skewness in the sampling distributions of the DSD moments that causes this bias is less pronounced for narrower population DSDs, and therefore the bias problems (and also the errors) diminish as the gamma shape parameter increases. However, the bias still increases with the order of the moments used in the MM procedures; thus it is stronger when higher-order moments (such as the radar reflectivity) are used. The simulation results also show that the errors of the estimates of the DSD param...

The North Dakota Thunderstorm Project: A Cooperative Study of High Plains Thunderstorms

Abstract The North Dakota Thunderstorm Project was conducted in the Bismarck, North Dakota, area from 12 June through 22 July 1989. The project deployed Doppler radars, cloud physics aircraft, and supporting instrumentation to study a variety of aspects of convective clouds. These included transport and dispersion; entrainment; cloud-ice initiation and evolution; storm structure, dynamics, and kinematics; atmospheric chemistry; and electrification. Of primary interest were tracer experiment that identified and tracked specific regions within evolving clouds as a means of investigating the transport, dispersion, and activation of ice-nucleating agents as well as studying basic transport and entrainment processes. Tracers included sulfur hexafluoride (SF6), carbon monoxide, ozone, radar chaff, and silver iodide. Doppler radars were used to perform studies of all scales of convection, from first-echo cases to a mesoscale convective system. An especially interesting dual-Doppler study of two splitting thunder...