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Difference between revisions of "TAU0"

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(Added new info about -6, -7, and the updating, reorganized)
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== <code>TAU0</code> Values ==
 
== <code>TAU0</code> Values ==
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>. 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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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>. 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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*<code>TAU0 = -5</code>, <math>\tau_0</math> is computed similar to <code>TAU0 = -3</code> as follows:
 
*<code>TAU0 = -5</code>, <math>\tau_0</math> is computed similar to <code>TAU0 = -3</code> as follows:
 
**<code><math>\tau_0</math> = Tau0Min+1.5*TK</code>
 
**<code><math>\tau_0</math> = Tau0Min+1.5*TK</code>
**It is limited by <code>[[Tau0FullDomainMin]] <= <math>\tau_0</math> <= [[Tau0FullDomainMax]]</code>, which are specified on the following line of the fort.15 file (only when <code>TAU0 = -5</code>)
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**It is limited by <code>[[Tau0FullDomainMin]] <= <math>\tau_0</math> <= [[Tau0FullDomainMax]]</code>, which are specified on the line following <code>TAU0</code> in the fort.15 file (only when <code>TAU0 = -5</code>)
 
**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.  
 
**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.  
 
*<code>TAU0 = -6</code>, <math>\tau_0</math> is defined using the rules for <code>TAU0 = -3</code>, and then is set equal to the time-average of the current and previous (time-averaged) values.  
 
*<code>TAU0 = -6</code>, <math>\tau_0</math> is defined using the rules for <code>TAU0 = -3</code>, and then is set equal to the time-average of the current and previous (time-averaged) values.  
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== Spatial and Temporal Updating ==
 
== Spatial and Temporal Updating ==
For <code>TAU0 = -3, -5, -6, or -7</code>, <math>\tau_0</math> is updated 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.  
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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.  
  
 
== Selecting <math>\tau_0</math> ==
 
== Selecting <math>\tau_0</math> ==
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 (e.g, for linear friction <code>TAU0 = [[TAU]]</code>; for quadratic friction <code>TAU0</code> = maximum (speed*Cd/depth)</code>. Typical values for <code>TAU0</code> are in the range of 0.005 – 0.1.
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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:
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<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:
*If the avg. distance between a node and its neighbors < 1750 m TAU0Base = 0.03
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*<code>If the avg. dist. to neighboring nodes < 1750 m; then TAU0Base = 0.03</code>
*If the avg. distance between a node and its neighbors > 1750 m AND depth < 10m; TAU0Base = 0.02  (TAU0 is constant in time)
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*Otherwise
*If the avg. distance between a node and its neighbors > 1750 m AND depth > 10m; TAU0Base = 0.005 (TAU0 is constant in time)
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**<code>If depth < 10m; then TAU0Base = 0.02</code> (<code>TAU0</code> is constant in time)
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**<code>If depth > 10m; then TAU0Base = 0.005</code> (<code>TAU0</code> is constant in time)
  
 
== Outputting <math>\tau_0</math> ==
 
== Outputting <math>\tau_0</math> ==
For TAU0 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 TAU0 in the fort.15 file. For example, if TAU0=-3.1, the calculation of <math>\tau_0</math> is still carried out according to the description of TAU0 = -3 above, and the fort.90 output file will also be produced.
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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.

Revision as of 23:25, 18 February 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, , 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 parameter more generally.

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 value used in solving the GWCE, it is important to distinguish between the two. All negative TAU0 are flags, all positive TAU0 are . 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 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 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, i.e. TAU0 = , so:

  • TAU0 = 0, the GWCE is a pure wave equation
  • TAU0 = 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

  • TAU0 = -1, is computed as follows:
    • If depth >= 10; then = 0.005
    • If depth < 10; then = 0.020
  • TAU0 = -2, is is computed according to depth as follows:
    • If depth >= 200; then = 0.005
    • If 1 < depth < 200; then = 1/depth
    • If depth < 1; then

Spatially and temporally varying

  • TAU0 = -3, is computed from TAU0Base (read in from the nodal attribute file) as follows:
    • If TAU0Base < 0.025; then = TAU0Base (constant in time)
    • If TAU0Base >= 0.025; then = TAU0Base+1.5*TK where TK=speed*Cd/depth
  • TAU0 = -5, is computed similar to TAU0 = -3 as follows:
  • TAU0 = -6, 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, 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:
    • = AlphaTau0*TAU0VAR + (1.0-AlphaTau0)*LastTau0, where AlphaTau0 = 0.25 is hard-coded into the model, this means that is weighted 75% toward older values

Spatial and Temporal Updating

For TAU0 = -3, -5, -6, or -7, 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 is then spatially averaged with all immediate neighbors. Time-averaging (for TAU0 = -6 or -7 is applied last.

Selecting

For positive values (TAU0=), 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.

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)

Outputting

For TAU0 formulations that vary spatially or temporally, ADCIRC can output the internally-calculated nodal 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 is still carried out according to the description of TAU0 = -3 above, and the fort.90 output file will also be produced.