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Difference between revisions of "TAU0"

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'''<code>TAU0</code>''' 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, <math>\tau_0</math>, 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 <code>TAU0</code> value in the fort.15 file and the <math>\tau_0</math> parameter more generally.  
 
'''<code>TAU0</code>''' 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, <math>\tau_0</math>, 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 <code>TAU0</code> value in the fort.15 file and the <math>\tau_0</math> parameter more generally.  
  
== TAU0 Values ==
+
== Parameter Summary ==
 
Because the <code>TAU0</code> value specified in the fort.15 file can be either a flag (indicating how ADCIRC should operate) or the actual <math>\tau_0</math> value used in solving the GWCE, it is important to distinguish between the two. All negative <code>TAU0</code> are flags, all positive <code>TAU0</code> are <math>\tau_0</math>. Furthermore, some values are overridden by the [[primitive weighting in continuity equation]] nodal attribute. The following table is a summary of possible <code>TAU0</code> values and their meaning. Note that for <code>TAU0 = -x.1</code> (where <code>x</code> is an integer), behavior is the same as <code>-x</code>, but the <math>\tau_0</math> values are written to the [[fort.90 file]]. More on this below in [[TAU0#Outputting|Outputting]].  
 
Because the <code>TAU0</code> value specified in the fort.15 file can be either a flag (indicating how ADCIRC should operate) or the actual <math>\tau_0</math> value used in solving the GWCE, it is important to distinguish between the two. All negative <code>TAU0</code> are flags, all positive <code>TAU0</code> are <math>\tau_0</math>. Furthermore, some values are overridden by the [[primitive weighting in continuity equation]] nodal attribute. The following table is a summary of possible <code>TAU0</code> values and their meaning. Note that for <code>TAU0 = -x.1</code> (where <code>x</code> is an integer), behavior is the same as <code>-x</code>, but the <math>\tau_0</math> values are written to the [[fort.90 file]]. More on this below in [[TAU0#Outputting|Outputting]].  
  
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|-
 
|-
 
! style="font-weight:bold;" | Varies in space
 
! style="font-weight:bold;" | Varies in space
| style="background-color:#fffc9e;" | no
+
| style="background-color:#fffc9e;" | no (mostly)
 
| style="background-color:#ffce93;" | yes
 
| style="background-color:#ffce93;" | yes
 
| style="background-color:#ffce93;" | yes
 
| style="background-color:#ffce93;" | yes
Line 50: Line 50:
 
| style="background-color:#ffce93;" | yes
 
| style="background-color:#ffce93;" | yes
 
|-
 
|-
! style="font-weight:bold;" | Expects nodal attribute
+
! style="font-weight:bold;" | [[primitive weighting in continuity equation]]
| style="background-color:#fffc9e;" | no
+
| yes
| style="background-color:#fffc9e;" | no
+
| discouraged
| style="background-color:#fffc9e;" | no
+
| discouraged
| style="background-color:#ffce93;" | yes
+
| yes
| style="background-color:#ffce93;" | yes
+
| discouraged
| style="background-color:#ffce93;" | yes
+
| yes
| style="background-color:#ffce93;" | yes
+
| yes
 +
|-
 +
! style="font-weight:bold;" | [[min and max primitive weighting in continuity equation]]
 +
| no
 +
| no
 +
| no
 +
| no
 +
| yes
 +
| no
 +
| no
 
|-
 
|-
 
! style="font-weight:bold;" | Minimum
 
! style="font-weight:bold;" | Minimum
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|}
 
|}
  
'''Positive values'''<br/>
+
=== Nodal Attributes ===
A positive value is ignored if the [[primitive weighting in continuity equation]] nodal attribute is specified in the fort.15 file. For all positive values, the value specified in the fort.15 file is spatially and temporally constant and applied directly, i.e. <code>TAU0 = <math>\tau_0</math></code>. Practical guidance on setting a constant <code>TAU0</code> is provided below in [[#Selecting Tau0|Selecting Tau0]]. Mathematically, the GWCE is a pure wave equation for <math>\tau_0=0</math>, and approaches a pure primitive equation as <math>\tau_0\rightarrow\infty</math>, however in practice, it behaves like a pure primitive equation once <math>\tau_0</math> reaches 1 or so.  
+
The [[primitive weighting in continuity equation]] nodal attribute permits a spatially variable <math>\tau_0</math> that is (at least initially) set equal to the nodal attribute values.
 +
*<code>TAU0 >= 0</code>, <math>\tau_0</math> is constant in time and equal to [[primitive weighting in continuity equation]] values
 +
*<code>TAU0 = -3, -6, or -7</code>, <math>\tau_0</math> varies in time and based on [[primitive weighting in continuity equation]] values
 +
The [[min and max primitive weighting in continuity equation]] only works with <code>TAU0 = -5</code>, details on it are below.
 +
 
 +
=== Positive TAU0 ===
 +
A positive value is ignored if the [[primitive weighting in continuity equation]] nodal attribute is specified in the fort.15 file. For all positive values, the value specified in the fort.15 file is spatially and temporally constant and applied directly, i.e. <code>TAU0 = <math>\tau_0</math></code>. Practical guidance on setting a constant <code>TAU0</code> is provided below in [[#Selecting Values|Selecting Values]]. Mathematically, the GWCE is a pure wave equation for <math>\tau_0=0</math>, and approaches a pure primitive equation as <math>\tau_0\rightarrow\infty</math>, however in practice, it behaves like a pure primitive equation once <math>\tau_0</math> reaches 1 or so.  
  
'''Negative Values'''<br/>
+
=== Negative TAU0 ===
 +
Unexpected behavior may arise if a mismatching nodal attribute is specified alongside one of these values, and this is discouraged. <br/>
 
''Spatially varying, temporally constant''<br/>
 
''Spatially varying, temporally constant''<br/>
Unexpected behavior may arise if nodal attributes are specified alongside one of these values, and this is discouraged.
 
*<code>TAU0 >= 0</code> and the [[primitive weighting in continuity equation]] nodal attribute is specified in the fort.15 file, <math>\tau_0</math> is set equal to the nodal attribute values.
 
 
*<code>TAU0 = -1</code>, <math>\tau_0</math> is computed as follows:  
 
*<code>TAU0 = -1</code>, <math>\tau_0</math> is computed as follows:  
 
**<code>If depth >= 10; then <math>\tau_0</math> = 0.005</code>
 
**<code>If depth >= 10; then <math>\tau_0</math> = 0.005</code>
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For <code>TAU0 = -3, -5, -6, or -7</code>, <math>\tau_0</math> is updated (via the <code>CalculateTimeVaryingTau0</code> subroutine) in space and in time. An initial "update" is done when the model starts. After this, updates are done only after a time step in which there is a change in wet/dry state somewhere in the model domain. For use cases that contain large number of nodes near the wet/dry boundary, this can be the equivalent of updating every time step. However, for use cases that have little or no wet/dry changes, '''there may be little or no updating'''. The rules listed above in [[TAU0#TAU0 Values|TAU0 Values]] are applied during the update. Each node's <math>\tau_0</math> is then spatially averaged with all immediate neighbors. Time-averaging (for <code>TAU0 = -6 or -7</code>) is applied last.  
 
For <code>TAU0 = -3, -5, -6, or -7</code>, <math>\tau_0</math> is updated (via the <code>CalculateTimeVaryingTau0</code> subroutine) in space and in time. An initial "update" is done when the model starts. After this, updates are done only after a time step in which there is a change in wet/dry state somewhere in the model domain. For use cases that contain large number of nodes near the wet/dry boundary, this can be the equivalent of updating every time step. However, for use cases that have little or no wet/dry changes, '''there may be little or no updating'''. The rules listed above in [[TAU0#TAU0 Values|TAU0 Values]] are applied during the update. Each node's <math>\tau_0</math> is then spatially averaged with all immediate neighbors. Time-averaging (for <code>TAU0 = -6 or -7</code>) is applied last.  
  
== Selecting Tau0 ==
+
== Selecting Values ==
For positive values (<code>TAU0=<math>\tau_0</math></code>), a good rule of thumb for setting <code>TAU0</code> is to set it equal to the largest value of an equivalent linear friction factor: for linear friction <code>TAU0 = [[TAU]]</code>; for quadratic friction <code>TAU0 = max(speed*Cd/depth)</code>. Typical values for <code>TAU0</code> are in the range of 0.005 – 0.1.
 
 
 
 
<code>TAU0 = -3</code>, paired with the [[primitive weighting in continuity equation]] nodal attribute is generally the most popular formulation. In this case, <code>TAU0Base</code> nodal attribute values can be generated with the ADCIRC utility program tau0_gen.f. The program bases generation on the following logic applied to each node individually:
 
<code>TAU0 = -3</code>, paired with the [[primitive weighting in continuity equation]] nodal attribute is generally the most popular formulation. In this case, <code>TAU0Base</code> nodal attribute values can be generated with the ADCIRC utility program tau0_gen.f. The program bases generation on the following logic applied to each node individually:
 
*<code>If the avg. dist. to neighboring nodes < 1750 m; then TAU0Base = 0.03</code>
 
*<code>If the avg. dist. to neighboring nodes < 1750 m; then TAU0Base = 0.03</code>
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**<code>If depth < 10m; then TAU0Base = 0.02</code> (<code>TAU0</code> is constant in time)
 
**<code>If depth < 10m; then TAU0Base = 0.02</code> (<code>TAU0</code> is constant in time)
 
**<code>If depth > 10m; then TAU0Base = 0.005</code> (<code>TAU0</code> is constant in time)
 
**<code>If depth > 10m; then TAU0Base = 0.005</code> (<code>TAU0</code> is constant in time)
 +
<math>\tau_0</math> needs to be smaller in deeper water where there is little dissipation, and can also be sensitive to mesh resolution. The spatial variation, spatial smoothing, and physics-driven time-updating typically allow for a good balance between stability and conservation.
 +
 +
For manually-specified positive values (<code>TAU0=<math>\tau_0</math></code>), a good rule of thumb for setting <code>TAU0</code> is to set it equal to the largest value of an equivalent linear friction factor: for linear friction <code>TAU0 = [[TAU]]</code>; for quadratic friction <code>TAU0 = max(speed*Cd/depth)</code>. Typical values for <code>TAU0</code> are in the range of 0.005 – 0.1.
  
 
== Outputting ==
 
== Outputting ==
 
For <code>TAU0</code> formulations that vary spatially or temporally, ADCIRC can output the internally-calculated nodal <math>\tau_0</math> values. They are written to the [[fort.90 file]], which has the same format and output frequency as the water surface elevation output file ([[fort.63]]). fort.90 output is activated by placing a 1 in the tenths place of <code>TAU0</code> in the fort.15 file. For example, if <code>TAU0 = -3.1</code>, the calculation of <math>\tau_0</math> is still carried out according to the description of <code>TAU0 = -3</code> above, and the fort.90 output file will also be produced.
 
For <code>TAU0</code> formulations that vary spatially or temporally, ADCIRC can output the internally-calculated nodal <math>\tau_0</math> values. They are written to the [[fort.90 file]], which has the same format and output frequency as the water surface elevation output file ([[fort.63]]). fort.90 output is activated by placing a 1 in the tenths place of <code>TAU0</code> in the fort.15 file. For example, if <code>TAU0 = -3.1</code>, the calculation of <math>\tau_0</math> is still carried out according to the description of <code>TAU0 = -3</code> above, and the fort.90 output file will also be produced.
 +
 +
[[Category:nodal attributes]]

Latest revision as of 11:55, 20 May 2019

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.

Parameter Summary

Because the TAU0 value specified in the fort.15 file can be either a flag (indicating how ADCIRC should operate) or the actual 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} value used in solving the GWCE, it is important to distinguish between the two. All negative TAU0 are flags, all positive TAU0 are 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} . Furthermore, some values are overridden by the primitive weighting in continuity equation nodal attribute. The following table is a summary of possible TAU0 values and their meaning. Note that for TAU0 = -x.1 (where x is an integer), behavior is the same as -x, but 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} values are written to the fort.90 file. More on this below in Outputting.

fort.15 TAU0 >= 0 -1 -2 -3 -5 -6 -7
Varies in space no (mostly) 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
primitive weighting in continuity equation yes discouraged discouraged yes discouraged yes yes
min and max primitive weighting in continuity equation no no no no yes no 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.

Nodal Attributes

The primitive weighting in continuity equation nodal attribute permits a spatially variable 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} that is (at least initially) set equal to the nodal attribute values.

  • TAU0 >= 0, 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 constant in time and equal to primitive weighting in continuity equation values
  • TAU0 = -3, -6, or -7, 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} varies in time and based on primitive weighting in continuity equation values

The min and max primitive weighting in continuity equation only works with TAU0 = -5, details on it are below.

Positive TAU0

A positive value is ignored if the primitive weighting in continuity equation nodal attribute is specified in the fort.15 file. For all positive values, the value specified in the fort.15 file is spatially and temporally constant and applied directly, i.e. TAU0 = 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} . Practical guidance on setting a constant TAU0 is provided below in Selecting Values. Mathematically, the GWCE is a pure wave equation for 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=0} , and approaches a pure primitive equation as 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\rightarrow\infty} , however in practice, it behaves like a pure primitive equation once 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} reaches 1 or so.

Negative TAU0

Unexpected behavior may arise if a mismatching nodal attribute is specified alongside one of these values, and this is discouraged.
Spatially varying, temporally constant

  • TAU0 = -1, 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 computed as follows:
    • If depth >= 10; then 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} = 0.005
    • If depth < 10; then 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} = 0.020
    • This value is ignored if primitive weighting in continuity equation is specified in the fort.15 file.
  • TAU0 = -2, 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 is computed according to depth as follows:
    • If depth >= 200; then 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} = 0.005
    • If 1 < depth < 200; then 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} = 1/depth
    • If depth < 1; then 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 = 1}
    • This value is ignored if primitive weighting in continuity equation is specified in the fort.15 file.


Spatially and temporally varying
In the unlikely event that one of the below options not paired with its corresponding nodal attribute (the code will exit if this is done for some TAU0), then default values are set using the TAU0 = -1 logic.

  • TAU0 = -3, 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 computed from TAU0Base (read in from the nodal attribute) as follows:
    • If TAU0Base < 0.025; then 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} = TAU0Base (constant in time)
    • If TAU0Base >= 0.025; then 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} = TAU0Base+1.5*TK where TK=speed*Cd/depth
  • TAU0 = -5, 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 computed similar to TAU0 = -3 as follows:
    • 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} = Tau0Min+1.5*TK
    • It is limited by Tau0FullDomainMin <= 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} <= Tau0FullDomainMax, which are specified on the line following TAU0 in the fort.15 file (only when TAU0 = -5)
    • If the min and max primitive weighting in continuity equation nodal attribute is used, then the nodal minimum and maximum values replace the full-domain values in the above calculation.
  • TAU0 = -6, 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 defined using the rules for TAU0 = -3, and then is set equal to the time-average of the current and previous (time-averaged) values.
  • TAU0 = -7, 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 defined using the rules for TAU0 = -3, and then is set equal to the weighted time-average of the current and previous (time-averaged) values as follows:
    • 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} = AlphaTau0*TAU0VAR + (1.0-AlphaTau0)*LastTau0, where TAU0VAR is Tau0Base after spatial averaging, and AlphaTau0 = 0.25 is hard-coded into the model. This means that 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 weighted 75% toward older values.

Spatial and Temporal Updating

For TAU0 = -3, -5, -6, or -7, 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 updated (via the CalculateTimeVaryingTau0 subroutine) in space and in time. An initial "update" is done when the model starts. After this, updates are done only after a time step in which there is a change in wet/dry state somewhere in the model domain. For use cases that contain large number of nodes near the wet/dry boundary, this can be the equivalent of updating every time step. However, for use cases that have little or no wet/dry changes, there may be little or no updating. The rules listed above in TAU0 Values are applied during the update. Each node's 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 then spatially averaged with all immediate neighbors. Time-averaging (for TAU0 = -6 or -7) is applied last.

Selecting Values

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 applied to each node individually:

  • If the avg. dist. to neighboring nodes < 1750 m; then TAU0Base = 0.03
  • Otherwise
    • If depth < 10m; then TAU0Base = 0.02 (TAU0 is constant in time)
    • If depth > 10m; then TAU0Base = 0.005 (TAU0 is constant in time)

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} needs to be smaller in deeper water where there is little dissipation, and can also be sensitive to mesh resolution. The spatial variation, spatial smoothing, and physics-driven time-updating typically allow for a good balance between stability and conservation.

For manually-specified positive values (TAU0=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} ), a good rule of thumb for setting TAU0 is to set it equal to the largest value of an equivalent linear friction factor: for linear friction TAU0 = TAU; for quadratic friction TAU0 = max(speed*Cd/depth). Typical values for TAU0 are in the range of 0.005 – 0.1.

Outputting

For TAU0 formulations that vary spatially or temporally, ADCIRC can output the internally-calculated nodal 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} values. They are written to the fort.90 file, which has the same format and output frequency as the water surface elevation output file (fort.63). fort.90 output is activated by placing a 1 in the tenths place of TAU0 in the fort.15 file. For example, if TAU0 = -3.1, the calculation of 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 still carried out according to the description of TAU0 = -3 above, and the fort.90 output file will also be produced.