Microbial Sampling: Is It Better to Sample Many Times or Use Large Samples?

1993 ◽  
Vol 27 (3-4) ◽  
pp. 19-25 ◽  
Author(s):  
Charles N. Haas
Keyword(s):  
Small Volume ◽  
Negative Binomial ◽  
Dispersion Parameter ◽  
Microbial Quality ◽  
Large Samples ◽  
Repeated Sampling ◽  
Repeated Samples ◽  
Microbial Sampling

Repeated sampling of a water (raw, Ssished, recreational) is often used to assess microbial quality. Microbial distributions have often been found to be negative binomial distributed in such repeated samples. Under these conditions, it is shown that it is better to use a large number of small volume samples than vice versa, providing that the negative binomial dispersion parameter remains unaffected by volume. Further research is needed to determine if the latter assumption, which influences the conclusion proposed, is valid for various classes of microorganisms in various types of waters.

NUMERICAL SOLUTIONS OF SMOLUCHOWSKI'S EQUATIONS FOR THE COAGULATION OF UNCHARGED AEROSOLS

1965 ◽  
Vol 43 (8) ◽  
pp. 2312-2318 ◽  
Author(s):  
J. M. Beeckmans
Keyword(s):  
Particle Size ◽  
Numerical Solutions ◽  
Coagulation Factor ◽  
Dispersion Parameter ◽  
Particle Size Range ◽  
Mean Particle Size ◽  
A Value ◽  
Wide Range ◽  
Differential Sedimentation ◽  
Smoluchowski’S Equation

Smoluchowski's equations for the coagulation of uncharged aerosol particles were programmed for solution by electronic computer. Terms representing differential sedimentation, turbulence, and mean aggregate density in solid aerosols were included. The effect of heterogeneity in the particle-size distribution of the aerosols on their rate of coagulation was illustrated by means of a slip-corrected coagulation factor Fc, which assumes a value of unity in all non-turbulent homogeneous aerosols. Curves of Fc vs. σg, the geometrical standard deviation, were calculated for aerosols of various mean particle-size. The effects due to turbulence, and to differential sedimentation, were illustrated in a similar manner. It was also found that the process of coagulation gives rise to a degree of dispersion which is independent of the original dispersion parameter, and depends only slightly on the mean particle-size of the aerosol over a wide range of particle-sizes. In the particle-size range in which differential sedimentation is inappreciable, the relatively constant value of the dispersion parameter implies that heterogeneous aerosols must obey the simplified integrated form of Smoluchowski's equation, which is applicable to homogeneous aerosols. The coagulation constant exceeds that predicted by the simple theory by about 10% for liquid aerosols of 0.1 μ or less.

scholarly journals High-Precision Measurements of the Copolar Correlation Coefficient: Non-Gaussian Errors and Retrieval of the Dispersion Parameter μ in Rainfall

2016 ◽  
Vol 55 (7) ◽  
pp. 1615-1632 ◽  
Author(s):  
W. J. Keat ◽  
C. D. Westbrook ◽  
A. J. Illingworth
Keyword(s):  
Correlation Coefficient ◽  
Error Estimates ◽  
Dispersion Parameter ◽  
Rain Event ◽  
Error Statistics ◽  
Frequency Distributions ◽  
Ground Clutter ◽  
Gaussian Probability Distribution ◽  
Raindrop Size ◽  
Non Gaussian

AbstractThe copolar correlation coefficient ρhv has many applications, including hydrometeor classification, ground clutter and melting-layer identification, interpretation of ice microphysics, and the retrieval of raindrop size distributions (DSDs). However, the quantitative error estimates that are necessary if these applications are to be fully exploited are currently lacking. Previous error estimates of ρhv rely on knowledge of the unknown “true” ρhv and implicitly assume a Gaussian probability distribution function of ρhv samples. Frequency distributions of ρhv estimates are in fact shown to be highly negatively skewed. A new variable, = log10(1 − ρhv), is defined that does have Gaussian error statistics and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of ρhv. In addition, the manner in which the imperfect collocation of the horizontal and vertical polarization sample volumes may be accounted for is demonstrated. The possibility of using L to estimate the dispersion parameter μ in the gamma drop size distribution is investigated. Including drop oscillations is found to be essential for this application; otherwise, there could be biases in retrieved μ of up to approximately 8. Preliminary results in rainfall are presented. In a convective rain case study, the estimates presented herein show μ to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.

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