## IntegrateVertically Solver

**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

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

### Examples

An example using the `IntegrateVertically`

Solver can be found in `[ELMER_TRUNK]/elmerice/Tests/IntegrateVertically`

.