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