Model help:GSDCalculator: Difference between revisions

Revision as of 12:21, 1 July 2011

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)

[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}} }[/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)

Nomenclature

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 = log₂ (D_b,i+1)+(log₂(D_b,i)- log₂(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: http://csdms.colorado.edu/wiki/Special:Upload
Create link to the file on your page: [[Image:<file name>]].

Developer(s)

Gary Parker

References

Key papers

Links

Model:GSDCalculator

@@ Line 64: / Line 64: @@
 * Linearly interpolated grain size (in Ψ scale)
 ::::{|
-|width=800px|<math>\Psi =log_{2}D </math>
+|width=800px|<math>\Psi = \Phi =log_{2}D </math>
 |width=50px align="right"|(1)
+|}
+* Calculation of D<sub>x</sub>
+::::{|
+|width=800px|<math>\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}} </math>
+|width=50px align="right"|(2)
+|}
+::::{|
+|width=800px|<math> D_{x} = 2^ \left (\psi_{x}\right ) </math>
+|width=50px align="right"|(3)
+|}
+* Calculation of geometric mean size and standard deviation
+::::{|
+|width=800px|<math> f_{i} = f_{f,i+1} - f_{f,i} </math>
+|width=50px align="right"|(4)
+|}
+::::{|
+|width=800px|<math> D_{i} = \left (D_{b,i} - D_{b,i+1}\right )^ \left ({\frac{1}{2}}\right ) </math>
+|width=50px align="right"|(5)
+|}
+::::{|
+|width=800px|<math> \psi_{i} = {\frac{1}{2}}\left (\psi_{b,i} - \psi_{b,i+1}\right ) </math>
+|width=50px align="right"|(6)
+|}
+::::{|
+|width=800px|<math> \bar{\psi} = \sum\limits_{i=1}^N \psi_{i} f_{i} </math>
+|width=50px align="right"|(7)
+|}
+::::{|
+|width=800px|<math> \sigma^2 = \sum\limits_{i=1}^N \left (\psi_{i} - \bar{\psi}\right )^2 f_{i} </math>
+|width=50px align="right"|(8)
+|}
+::::{|
+|width=800px|<math> D_{g} = 2^ \left (\bar{\psi}\right ) </math>
+|width=50px align="right"|(9)
+|}
+::::{|
+|width=800px|<math> \sigma_{g} = 2^\left (\sigma\right ) </math>
+|width=50px align="right"|(10)
 |}
@@ Line 75: / Line 113: @@
 |-
 | D
-| sedimwent size
+| sediment size
-| L
-|-
-| D<sub>x</sub>
-| characteristic diameter of the size diameter based on the percent finer
 | L
 |-
@@ Line 89: / Line 123: @@
 | lower bound of the size distribution based on the percent finer
 | L
+|-
+| D<sub>b,i</sub>
+| the ith grain size diameter
+| L
+|-
+| f<sub>f,i</sub>
+| mass fraction in the sample that is finer than size D<sub>b,i</sub>
+| -
+|-
+| ψ<sub>i</sub>
+| characteristic size of ith grain size range
+| L
+|-
+| f<sub>i</sub>
+| fraction of sample in ith grain size range
+| -
 |-
 | xU
@@ Line 100: / Line 150: @@
 | Ψ
 | sediment size in the psi-scale
+| -
+|-
+| bar{Ψ}
+| mean grain size on psi scale
+| L
+|-
+| σ
+| standard deviation on psi scale
 | -
 |-
@@ Line 115: / Line 173: @@
 | geometric standard deviation of the size distribution
 | -
+|-
+| D<sub>x</sub>
+| characteristic diameter of the size diameter based on the percent finer
+| L
 |-
 |}
@@ Line 124: / Line 186: @@
 Characteristic diameters is based on percent finer, D<sub>x</sub> (i.e. size such that x percent of the sample is finer than D<sub>x</sub>) can  be computed if requested by the user.
-If the inputted size distribution does not have a lower bound, D<sub>xL</sub>, such that xL = 0 and an upper bound, D<sub>xU</sub>, such that xU = 100, the program computes these bounds with a linear interpolation of the data.
+If the inputted size distribution does not have a lower bound, D<sub>xL</sub>, such that xL = 0 and an upper bound, D<sub>xU</sub>, such that xU = 100, the program computes these bounds with a linear interpolation of the data using the following equation:
+Ψ<sub>b,i-1</sub> = log<sub>2</sub> (D<sub>b,i+1</sub>)+(log<sub>2</sub>(D<sub>b,i</sub>)- log<sub>2</sub>(D<sub>b,i+1</sub>)) (0 - f<sub>f,i+1</sub>)/ (f<sub>f,i</sub> - f<sub>f,i</sub>).
-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.
+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.