**Welcome to the official ADCIRCWiki site! The site is currently under construction, with limited information. ---**

# TAU0

**TAU0** is an input in the fort.15 file that influences the degree of numerical diffusion in ADCIRC's governing equations. Specifically, it influences the weighting factor that determines the relative contribution of the primitive and wave portions of the the Generalized Wave-Continuity Equation (GWCE). The weighting factor, **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0}**
, is affected by values in both the fort.15 file and the fort.13 file, if the primitive weighting in continuity equation or min and max primitive weighting in continuity equation nodal attributes are specified. This page addresses both the TAU0 value in the fort.15 file and the **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0}**
parameter more generally.

## Contents

- 1 fort.15 TAU0 Values
- 2 Outputting
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0}** - 3 Selecting

## fort.15 TAU0 Values

Because the TAU0 value specified in the fort.15 file can be either a flag (indicating how ADCIRC should operate) or the actual

fort.15 TAU0 | >=0 | -1 | -2 | -3 | -5 | -6 | -7 |
---|---|---|---|---|---|---|---|

Varies in space | no | yes | yes | yes | yes | yes | yes |

Varies in time | no | no | no | yes | yes | yes | yes |

Space-averaged | no | no | no | yes | yes | yes | yes |

Time-averaged | no | no | no | no | no | yes | yes |

Requires nodal attribute | no | no | no | yes | no | yes | no |

Minimum | N/A | 0.002 | 0.002 | N/A | Tau0FullDomainMin | N/A | N/A |

Maximum | N/A | 0.005 | 1 | 0.2 | Tau0FullDomainMax | 0.2 | 0.2 |

Code Flags | |||||||

HighResTimeVaryingTau0 | .FALSE. | .FALSE. | .FALSE. | .TRUE. | .FALSE. | .TRUE. | .TRUE. |

FullDomainTimeVaryingTau0 | .FALSE. | .FALSE. | .FALSE. | .FALSE. | .TRUE. | .FALSE. | .FALSE. |

TimeAveragedTau0 | .FALSE. | .FALSE. | .FALSE. | .FALSE. | .FALSE. | .TRUE. | .FALSE. |

BackLoadedTimeAveragedTau0 | .FALSE. | .FALSE. | .FALSE. | .FALSE. | .FALSE. | .FALSE. | .TRUE. |

**Positive values**

For all positive values, the value specified in the fort.15 file is spatially and temporally constant and applied directly:

- = 0, the GWCE is a pure wave equation
- = 1, the GWCE behaves like a pure primitive continuity equation
- 0 < TAU0 < 1, the GWCE is a weighted sum of the primitive and wave portions of the equation

**Negative Values**

*Spatially varying, temporally constant*

- = -1,
- If the depth is >=10,
- If the depth is < 10,

- If the depth is >=10,
- = -2, TAU0 is spatially varying but constant in time; it is calculated according to depth as follows:
- If the depth is >=200
- If the depth is < 200 but > 1,
- If depth < 1,

- If the depth is >=200

*Spatially and temporally varying*

- = -3,
- If TAU0Base < 0.025;
- If TAU0Base >= 0.025;

- If TAU0Base < 0.025;
- = -5, FullDomainTimeVaryingTau0 is set to .True. and
- It is limited to a range specified by Tau0FullDomainMin and Tau0FullDomainMax, which are specified on the following line of the fort.15 file when TAU0 is -5

### Spatial and Temporal Updating

For `TAU0=-3, -5, -6, or -7`

,

## Outputting **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0}**

For TAU0 formulations that vary spatially or temporally, ADCIRC can output the internally-calculated nodal

## Selecting **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_0}**

For positive values (TAU0=

TAU0 = -3, paired with the primitive weighting in continuity equation nodal attribute is generally the most popular formulation. In this case, TAU0Base nodal attribute values can be generated with the ADCIRC utility program tau0_gen.f. The program bases generation on the following logic:

- If the avg. distance between a node and its neighbors < 1750 m TAU0Base = 0.03
- If the avg. distance between a node and its neighbors > 1750 m AND depth < 10m; TAU0Base = 0.02 (TAU0 is constant in time)
- If the avg. distance between a node and its neighbors > 1750 m AND depth > 10m; TAU0Base = 0.005 (TAU0 is constant in time)