Model help:GSDCalculator
GSDCalculator
This model is a Grain Size Distribution Statistics Calculator.
Model introduction
This model is used to calculate statistical characteristics of grain size distributions. Given a grain size distribution, the program computes the geometric mean diameter, and the geometric standard deviation.
Model parameters
Uses ports
This will be something that the CSDMS facility will add
Provides ports
This will be something that the CSDMS facility will add
Main equations
- Linearly interpolated grain size (in Ψ scale)
[math]\displaystyle{ \Psi = \Phi =log_{2}D }[/math] (1)
- Calculation of D_{x}
[math]\displaystyle{ \psi_{x} = \phi_{b,i} + {\frac{\psi_{b,i+1} - \psi_{b,i}}{f_{f,i+1} - f_{f,i}}} \left ({\frac{x}{100} - f_{f,i}}\right ) }[/math] (2)
[math]\displaystyle{ D_{x} = 2^ \left (\psi_{x}\right ) }[/math] (3)
- Calculation of geometric mean size and standard deviation
[math]\displaystyle{ f_{i} = f_{f,i+1} - f_{f,i} }[/math] (4)
[math]\displaystyle{ D_{i} = \left (D_{b,i} - D_{b,i+1}\right )^ \left ({\frac{1}{2}}\right ) }[/math] (5)
[math]\displaystyle{ \psi_{i} = {\frac{1}{2}}\left (\psi_{b,i} - \psi_{b,i+1}\right ) }[/math] (6)
[math]\displaystyle{ \bar{\psi} = \sum\limits_{i=1}^N \psi_{i} f_{i} }[/math] (7)
[math]\displaystyle{ \sigma^2 = \sum\limits_{i=1}^N \left (\psi_{i} - \bar{\psi}\right )^2 f_{i} }[/math] (8)
[math]\displaystyle{ D_{g} = 2^ \left (\bar{\psi}\right ) }[/math] (9)
[math]\displaystyle{ \sigma_{g} = 2^\left (\sigma\right ) }[/math] (10)
Symbol | Description | Unit |
---|---|---|
D | sediment size | L |
D_{xU} | upper bound of the size distribution based on the percent finer | L |
D_{xL} | lower bound of the size distribution based on the percent finer | L |
D_{b,i} | the ith grain size diameter | L |
f_{f,i} | mass fraction in the sample that is finer than size D_{b,i} | - |
ψ_{i} | characteristic size of ith grain size range | L |
f_{i} | fraction of sample in ith grain size range | - |
xU | percent finer of the upper bound of the size distribution | - |
xL | percent finer of the lower bound of the size distribution | - |
Ψ | sediment size in the psi-scale | - |
bar{Ψ} | mean grain size on psi scale | L |
σ | standard deviation on psi scale | - |
Output
Symbol | Description | Unit |
---|---|---|
D_{g} | geometric mean diameter of the size distribution | L |
σ_{g} | geometric standard deviation of the size distribution | - |
D_{x} | characteristic diameter of the size diameter based on the percent finer | L |
Notes
Characteristic diameters is based on percent finer, D_{x} (i.e. size such that x percent of the sample is finer than D_{x}) can be computed if requested by the user.
If the inputted size distribution does not have a lower bound, D_{xL}, such that xL = 0 and an upper bound, D_{xU}, such that xU = 100, the program computes these bounds with a linear interpolation of the data using the following equation: Ψ_{b,i-1} = log_{2} (D_{b,i+1})+(log_{2}(D_{b,i})- log_{2}(D_{b,i+1})) (0 - f_{f,i+1})/ (f_{f,i} - f_{f,i}).
Input data may be entered either from the finer to the coarser size or from the coarser to the finer. The program will automatically reorder the data.
Data may be on either a 0.00-1.00 scale or a 0-100 scale. The program will always use a 0-1 scale to do the calculations.
The program will prompt users if they want to calculate characteristic diameters based on percent finer, D_{x}, and what diameters they would like to know.
The program can calculate up to 10 characteristic diameters based on percent finer.
The geometric mean diameter, D_{g}, the geometric standard deviation, σ_{g}, and the user-defined characteristic diameters based on percent finer will be appended to a file with the reorganized, scaled, and bounded grain size distribution.
Examples
An example run with input parameters, BLD files, as well as a figure / movie of the output
Follow the next steps to include images / movies of simulations:
- Upload file: https://csdms.colorado.edu/wiki/Special:Upload
- Create link to the file on your page: [[Image:<file name>]].
See also: Help:Images or Help:Movies
Developer(s)
References
Key papers