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~~NOTOC~~
===== IntegrateVertically Solver =====

==== General Informations ====

  * **Solver Fortran File:** ''IntegrateVertically.f90'' 
  * **Solver Name:** ''IntegrateVertically'' 
  * **Required Output Variable(s):** given by the variable name
  * **Required Input Variable(s):** Name of the variable to be integrated in ''Integrated Variable Name'',  ''Depth'' or ''Height'' 
  * **Optional Output Variable(s):** None
  * **Optional Input Variable(s):** None


==== General Description ====
This solver compute the depth integrated value of a variable (sum_zb^zs D dz) or the mean value (1/H sum_zb^zs D dz). The resulting integrated value or mean can be computed on the upper surface or on the lower one. If the mean value is computed (''Compute Mean = Logical True''), the depth (if ''On Surface = Logical False'') or the height (if ''On Surface = Logical True'') has to be calculated. If the integrated variable is calculated on the upper surface (''On Surface = Logical True''), a Dirichlet BC has to be given at the bottom surface, and vice versa.  


==== SIF contents ====
<code>
Solver 2
  Equation = "IntegrateVertically"

   Procedure = File "ElmerIceSolvers" "IntegrateVertically"
   Variable = String "Mean Var"
   Variable DOFs = 1

   Exported Variable 1 = String "VarToBeIntegrated"
   Exported Variable 1 DOFs = 1

   ! We want it computed on the bed
   On Surface = Logical False
   ! We want the mean value
   ! We then need the Depth
   Compute Mean = Logical True
   Integrated Variable Name = String "VarToBeIntegrated"

   Linear System Solver = "Direct"
   Linear System Direct Method = umfpack
End

!!! free surface
Boundary Condition 2
  Target Boundaries = 6
  Mean Var = Real 0.0
  Depth = Real 0.0
End
</code>


==== Examples ====
An example using the ''IntegrateVertically'' Solver can be found in ''[ELMER_TRUNK]/elmerice/Tests/IntegrateVertically''.