PHi Mean and Phi Standard Deviation of Grain-size Distribution in Sediments: Method of Moments

Abstract. In this paper a new integral mathematical model for volcanic plumes, named PLUME-MoM, is presented. The model describes the steady-state dynamics of a plume in a 3-D coordinate system, accounting for continuous variability in particle size distribution of the pyroclastic mixture ejected at the vent. Volcanic plumes are composed of pyroclastic particles of many different sizes ranging from a few microns up to several centimeters and more. A proper description of such a multi-particle nature is crucial when quantifying changes in grain-size distribution along the plume and, therefore, for better characterization of source conditions of ash dispersal models. The new model is based on the method of moments, which allows for a description of the pyroclastic mixture dynamics not only in the spatial domain but also in the space of parameters of the continuous size distribution of the particles. This is achieved by formulation of fundamental transport equations for the multi-particle mixture with respect to the different moments of the grain-size distribution. Different formulations, in terms of the distribution of the particle number, as well as of the mass distribution expressed in terms of the Krumbein log scale, are also derived. Comparison between the new moments-based formulation and the classical approach, based on the discretization of the mixture in N discrete phases, shows that the new model allows for the same results to be obtained with a significantly lower computational cost (particularly when a large number of discrete phases is adopted). Application of the new model, coupled with uncertainty quantification and global sensitivity analyses, enables the investigation of the response of four key output variables (mean and standard deviation of the grain-size distribution at the top of the plume, plume height and amount of mass lost by the plume during the ascent) to changes in the main input parameters (mean and standard deviation) characterizing the pyroclastic mixture at the base of the plume. Results show that, for the range of parameters investigated and without considering interparticle processes such as aggregation or comminution, the grain-size distribution at the top of the plume is remarkably similar to that at the base and that the plume height is only weakly affected by the parameters of the grain distribution. The adopted approach can be potentially extended to the consideration of key particle–particle effects occurring in the plume including particle aggregation and fragmentation.

Download Full-text

Variation of the Descriptive Grain Size Distribution Along Cores From the Sebkha of Sidi El Hani, Eastern Tunisia

10.4018/978-1-7998-9498-8.ch012 ◽

2022 ◽

pp. 197-214

Author(s):

Elhoucine Essefi ◽

Soumaya Hajji

Keyword(s):

Grain Size ◽

Size Distribution ◽

Grain Size Distribution ◽

Method Of Moments ◽

Statistical Treatment ◽

Special Care ◽

Statistical Parameters ◽

Sedimentary Dynamics

In this chapter, cores were the object of descriptive classifications of the grain size distribution, which were meant to describe the grain size continuous variability within cores and to correlate between them. The statistical treatment of the crude data was done on the basis of two different methods (the method of moments statistics and the method of inclusive graphic statistics) to compute statistical parameters of the grain size distribution such as mean and median. The correlations between cores were done on the basis of sand/silt/clay percentages. Even though it has given special care to test different methods of studying the grain size distribution, this study has not deviated from its primary purpose of investigating the filling of the playa; correlations between different cores were meant to infer their sedimentary dynamics.

Download Full-text

PLUME-MoM 1.0: a new 1-D model of volcanic plumes based on the method of moments

Geoscientific Model Development Discussions ◽

10.5194/gmdd-8-3745-2015 ◽

2015 ◽

Vol 8 (5) ◽

pp. 3745-3790

Author(s):

M. de' Michieli Vitturi ◽

A. Neri ◽

S. Barsotti

Keyword(s):

Grain Size ◽

Size Distribution ◽

Grain Size Distribution ◽

Method Of Moments ◽

Computational Cost ◽

Sensitivity Analyses ◽

Plume Height ◽

New Model ◽

Volcanic Plumes ◽

Grain Distribution

Abstract. In this paper a new mathematical model for volcanic plumes, named PlumeMoM, is presented. The model describes the steady-state 1-D dynamics of the plume in a 3-D coordinate system, accounting for continuous variability in particle distribution of the pyroclastic mixture ejected at the vent. Volcanic plumes are composed of pyroclastic particles of many different sizes ranging from a few microns up to several centimeters and more. Proper description of such a multiparticle nature is crucial when quantifying changes in grain-size distribution along the plume and, therefore, for better characterization of source conditions of ash dispersal models. The new model is based on the method of moments, which allows description of the pyroclastic mixture dynamics not only in the spatial domain but also in the space of properties of the continuous size-distribution of the particles. This is achieved by formulation of fundamental transport equations for the multiparticle mixture with respect to the different moments of the grain-size distribution. Different formulations, in terms of the distribution of the particle number, as well as of the mass distribution expressed in terms of the Krumbein log scale, are also derived. Comparison between the new moments-based formulation and the classical approach, based on the discretization of the mixture in N discrete phases, shows that the new model allows the same results to be obtained with a significantly lower computational cost (particularly when a large number of discrete phases is adopted). Application of the new model, coupled with uncertainty quantification and global sensitivity analyses, enables investigation of the response of four key output variables (mean and standard deviation (SD) of the grain-size distribution at the top of the plume, plume height and amount of mass lost by the plume during the ascent) to changes in the main input parameters (mean and SD) characterizing the pyroclastic mixture at the base of the plume. Results show that, for the range of parameters investigated, the grain-size distribution at the top of the plume is remarkably similar to that at the base and that the plume height is only weakly affected by the parameters of the grain distribution.

Download Full-text

Grain-Size Distribution of Surface Sediments in the Chanthaburi Coast, Thailand and Implications for the Sedimentary Dynamic Environment

Journal of Marine Science and Engineering ◽

10.3390/jmse8040242 ◽

2020 ◽

Vol 8 (4) ◽

pp. 242 ◽

Cited By ~ 2

Author(s):

Chengtao Wang ◽

Min Chen ◽

Hongshuai Qi ◽

Wichien Intasen ◽

Apichai Kanchanapant

Keyword(s):

Grain Size ◽

Standard Deviation ◽

Trend Analysis ◽

Size Distribution ◽

Grain Size Distribution ◽

Surface Sediments ◽

Sedimentary Environment ◽

Hydrodynamic Conditions ◽

Deviation Analysis ◽

Grain Size Trend Analysis

This paper analyzes the grain-size distribution of surface sediments of the Chanthaburi coast of Thailand to investigate the sedimentary environment and its evolution to better use and protect the coast. The Flemming triangle method, the grade-standard deviation method, and the Gao–Collins grain-size trend analysis method (GSTA model) were used to study the dynamic sedimentary environment of the area and provide preliminary identification of source materials. There are seven types of surface sediments on this coast, with grain sizes (φ) generally consisting of sand and silt. Sorting is generally poor, and becomes gradually poorer with distance offshore. Skewness is generally positive. The study area is mainly composed of sand and silt, indicating that the hydrodynamics are strong. The results of grade-standard deviation analysis indicate that sediment grain size b (3.25–4.5φ) is a sensitive indicator of environmental change. This sediment type exhibits a relatively complex transport trend, mainly characterized by northwestward and northeastward transport from sea to land. Sediments at the mouth of the Chanthaburi Estuary and the Welu River fluctuate under the influence of tidal currents. Based on the results of grade-standard deviation analysis and grain-size trend analysis, the study area was divided into three provinces, representing different sedimentary environments and material sources. Compared with tidal-controlled estuaries in the temperate regions of eastern China, the two tropical estuaries examined in this study exhibited smaller suspended sediment loads, runoff amounts, and tidal ranges. However, hydrodynamic conditions were generally stronger. The main reasons for the similarities and differences in the transport trends of sediments in these estuaries were differences in hydrodynamic conditions and the specifics of regional topography.

Download Full-text

Variability of suspended sediment grain size distribution in winter floods

Annals of Warsaw University of Life Sciences – SGGW Land Reclamation ◽

10.1515/sggw-2016-0011 ◽

2016 ◽

Vol 48 (2) ◽

pp. 141-151

Author(s):

Agnieszka Hejduk ◽

Leszek Hejduk

Keyword(s):

Particle Size ◽

Grain Size ◽

Standard Deviation ◽

Size Distribution ◽

Suspended Sediment ◽

Grain Size Distribution ◽

Sediment Grain Size ◽

Mean Values ◽

Average Value ◽

Sediment Size

Abstract Variability of suspended sediment grain size distribution in winter floods. The work presents the results of research concern variability of suspended sediment grain size, transported during the winter floods in agricultural catchment, in the period of hydrological years 2012-2015. The information about grain size distribution from nine winter flood events were collected over the study period, which allowed to analyze the variability of suspended sediment particle size during the various events. Grain size of sediment was determined using a laser particle size analyzer Mastersizer Microplus from Malvern Instruments Ltd. Variability of individual particle size classes were observed in each flood. Sand fraction dominated in seven of nine measured events. There was no significant increase of suspended sediment size in relation to the maximum of discharge. It can be explain by a relatively low discharge of recorded events. The percentage of material classified as clay (<4 μm) ranged from 0.08 to 1.01%, silt-sized material (>4 and <63 μm) ranged between 9.31 and 67.17% and sand-size material (>63 μm) ranged from 32.01 to 90.61%. The relationship between the particle size and the discharge requires further studies. The diameter d10, d50 and d90 and a standard deviation were calculated for each flood. Mean values of d50 for individual flood ranged between 41.05 and 191.32 μm with average value of 99.01 μm and average standard deviation of 32.57.

Download Full-text

Grain-size distribution analysis of Quaternary sediments from the southern part of the Lodz region in Poland: a computational-methods approach

Geologos ◽

10.2478/v10118-011-0012-7 ◽

2011 ◽

Vol 17 (4) ◽

pp. 205-219 ◽

Cited By ~ 5

Author(s):

Lucyna Wachecka-Kotkowska ◽

Paweł Kotkowski

Keyword(s):

Grain Size ◽

Size Distribution ◽

Grain Size Distribution ◽

Computational Methods ◽

Method Of Moments ◽

Linear Interpolation ◽

Unconsolidated Sediments ◽

Distribution Analysis ◽

Quaternary Sediments ◽

Average Grain Size

Grain-size distribution analysis of Quaternary sediments from the southern part of the Lodz region in Poland: a computational-methods approachEighteen samples of Quaternary unconsolidated sediments from the Piotrków Plateau and the Radomsko Hills in central Poland have been analysed for their average grain size, sorting, skewness and kurtosis. The analysis was carried out by seven computational methods of interpolation and nine extrapolation methods. It appears that linear interpolation, the traditional method (DOS), and the Josek and Gradistat Programs give comparable results, but that quadratic interpolation and the method of moments should not be applied since they yield unreliable results. The method of moments gives unduly high or unduly low parameter values because of the application of different, i.e. incomparable measures in the applied formulae. It should be stressed that only extrapolation provides, if performed under the right conditions, the possibility to determine some parameters, in particular skewness values.

Download Full-text