# 1. General Model Information

### Name: Gas Diffusion Model

### Acronym: GDM

**Main medium:** terrestrial

**Main subject:** biogeochemistry

**Organization level:** ecosystem

**Type of model:** partial differential equations (finite differences)

**Main application:**

**Keywords:** gas diffusion, atmospheric-soil interactions

### Contact:

**Gordon Hutchinson**

USDA-ARS-NPA Soil Plant and Nutrient Research

P.O. Box E

Federal Building

Fort Collins, CO 80522

Phone: 970-490-8240

Fax: 970-490-8213

email: glhutch@lamar.colostate.edu

### Author(s):

Richard W. Healy
### Abstract:

The Gas Diffusion Model simulates the diffusion of various gases through the
soil. The model is based on a numerical solution of discrete-finite difference
approximations of a one or two dimensional diffusion equation. The model is
designed around a block center grid approach which results in a matrix equation
solved using the preconditioned conjugate gradients method. The model uses a 6
second time step executed over a 30 minute time period.

Validation Procedures: Model is verified by comparison of numerical and analytical solutions for
cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated
fluid flow.

** Author of the abstract:**
**CIESIN**

# II. Technical Information

### II.1 Executables:

**Operating System(s):** UNIX workstation or on a IBM PC (PC runtime is about two hours for a 30 minute time interval simulation)

### II.2 Source-code:

**Programming Language(s):** FORTRAN 77

### II.3 Manuals:

### II.4 Data:

# III. Mathematical Information

### III.1 Mathematics

### III.2 Quantities

Parameters for mass concentration, thermal gradients,

#### III.2.1 Input

Parameters for mass concentration, thermal gradients,constants of proportionality, constant-flux nodes, time step, and iteration Mass balance for each time step, including mass in and out of fixed
#### III.2.2 Output

Mass balance for each time step, including mass in and out of fixedconcentration nodes, mass in and out of fixed flux nodes, changes in storage, mass balance, andrelative error.
Temporal Scale: from one-tenth minute time step to 30 minute intervals.

Spatial Scale: Point

# IV. References

Initial model described in

**A.L. Ishii, R.W. Healy, K.G. Striegl. 1989 **A Numerical Solution for the Diffusion Equation in Hydrologic Systems. USGS Water-Resources Investigations Report. 89-4027.

# V. Further information in the World-Wide-Web

# VI. Additional remarks

This model is useful for the study of atmospheric-soil interactions. Itis a fairly complex model with respect to the mathematics employed. There areseveral unique features of the model that can be applied to otherdispersion/diffusion problems. The model uses a discrete finite-difference approximation method rather than the traditional linear diffusion equations. By employing a grid arrangement, calculations are made using linear algebra anda preconditioned conjugate gradient method which avoids the need to estimate iterative parameters.

Last review of this document by: T. Gabele: 9. 7. 1997 -

Status of the document:

* last modified by
Tobias Gabele Wed Aug 21 21:44:43 CEST 2002 *