# 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

Parameter Description Unit
Input directory path to input files
Site prefix Site prefix for Input/Output files
Case prefix Case prefix for Input/Output files
Parameter Description Unit
Model name name of the model -
Author name name of the model author -

## 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)
 $\Psi = \Phi =log_{2}D$ (1)
• Calculation of Dx
 $\psi_{x} = \phi_{b,i} + {\frac{\psi_{b,i+1} - \psi_{b,i}}{f_{f,i+1} - f_{f,i}}} \left ({\frac{x}{100} - f_{f,i}}\right )$ (2)
 $D_{x} = 2^ \left (\psi_{x}\right )$ (3)
• Calculation of geometric mean size and standard deviation
 $f_{i} = f_{f,i+1} - f_{f,i}$ (4)
 $D_{i} = \left (D_{b,i} - D_{b,i+1}\right )^ \left ({\frac{1}{2}}\right )$ (5)
 $\psi_{i} = {\frac{1}{2}}\left (\psi_{b,i} - \psi_{b,i+1}\right )$ (6)
 $\bar{\psi} = \sum\limits_{i=1}^N \psi_{i} f_{i}$ (7)
 $\sigma^2 = \sum\limits_{i=1}^N \left (\psi_{i} - \bar{\psi}\right )^2 f_{i}$ (8)
 $D_{g} = 2^ \left (\bar{\psi}\right )$ (9)
 $\sigma_{g} = 2^\left (\sigma\right )$ (10)

## Notes

Characteristic diameters is based on percent finer, Dx (i.e. size such that x percent of the sample is finer than Dx) can be computed if requested by the user.

If the inputted size distribution does not have a lower bound, DxL, such that xL = 0 and an upper bound, DxU, such that xU = 100, the program computes these bounds with a linear interpolation of the data using the following equation: Ψb,i-1 = log2 (Db,i+1)+(log2(Db,i)- log2(Db,i+1)) (0 - ff,i+1)/ (ff,i - ff,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, Dx, 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, Dg, the geometric standard deviation, σg, 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: