A concrete implementation of the glacier type, using a vertically integrated model of an ice shelf. This model is 1-dimensional only.
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| type(cheb1d_scalar_field), | private | :: | thickness | Thickness of ice shelf, |
|||
| type(cheb1d_vector_field), | private | :: | velocity | Flow velocity of ice shelf, |
|||
| type(cheb1d_scalar_field), | private | :: | eta | Viscosity of the ice, |
|||
| type(cheb1d_scalar_field), | private, | dimension(:), allocatable | :: | kappa | Taylor coefficients for the vertical structure of a Lagrangian tracer representing englacial layers/internal reflectors. |
||
| real(kind=r8), | private | :: | lambda | The dimensionless ratio $\lambda \equiv \frac{\rho_0m_0x_0}{\rho_iH-0u_0}$ |
|||
| real(kind=r8), | private | :: | chi | The dimensionless ratio |
|||
| real(kind=r8), | private | :: | zeta | The dimensionless ratio , corresponding to the Reynolds number. Currently unused. |
|||
| real(kind=r8), | private | :: | courant | The Courant number to use when calculating the time step. |
|||
| class(abstract_viscosity), | private, | allocatable | :: | viscosity_law | An object representing the model used for ice viscosity. |
||
| class(glacier_boundary), | private, | allocatable | :: | boundaries | An object specifying the boundary conditions for the ice shelf. |
||
| real(kind=r8), | private | :: | max_dt | The maximu allowable time step |
|||
| real(kind=r8), | private | :: | time | The time at which the ice shelf is in this state. |
|||
| integer, | private | :: | thickness_size | The number of data values in the thickness field. |
|||
| integer, | private | :: | velocity_size | The number of data values in the velocity field. |
|||
| integer, | private | :: | boundary_start | The number of data values needed to represent the boundary conditions. |
|||
| integer, | private | :: | thickness_lower_bound_size | The number of data values needed to represent the lower boundary conditions for thickness. |
|||
| integer, | private | :: | thickness_upper_bound_size | The number of data values needed to represent the upper boundary conditions for thickness. |
|||
| integer, | private | :: | velocity_lower_bound_size | The number of data values needed to represent the lower boundary conditions for velocity. |
|||
| integer, | private | :: | velocity_upper_bound_size | The number of data values needed to represent the upper boundary conditions for thickness. |
|||
| type(jacobian_block), | private | :: | thickness_jacobian | A representation of the Jacobian for the ice shelf thickness. |
|||
| type(jacobian_block), | private | :: | velocity_jacobian | A representation of the Jacobian for the ice shelf velocity. |
|||
| logical, | private | :: | stale_eta | Indicates whether the viscosity needs updating. |
|||
| logical, | private | :: | stale_jacobian | Indicates if the Jacobians are stale and in need of updating. |
Copies the data from one ice shelf into another. This is only needed due to a bug in gfortran which means that the intrinsic assignment for glacier types is not using the appropriate defined assignment for the field components.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(out) | :: | this | |||
| class(glacier), | intent(in) | :: | rhs | The ice shelf to be assigned to this one. |
Performs a time-step of the integration, taking the state of the glacier to the specified time using the provided melt-rate data.
Integrates the glacier's state to time. This is done using the
NITSOL package of iterative Krylov solvers. If a different
algorithm for the integration is desired, then this method may
be overridden in the concrete implementations of the glacier
type.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(glacier), | intent(inout) | :: | this | |||
| class(glacier), | intent(in), | dimension(:) | :: | old_states | Previous states of the glacier, with the most recent one first. |
|
| class(scalar_field), | intent(in) | :: | basal_melt | The melt rate that the bottom of the glacier experiences during this time step. |
||
| class(scalar_field), | intent(in) | :: | basal_drag | A paramter, e.g. coefficient of friction, needed to calculate the drag on basal surface of the glacier. |
||
| real(kind=r8), | intent(in) | :: | water_density | The density of the water below the glacier. |
||
| real(kind=r8), | intent(in) | :: | time | The time to which the glacier should be integrated |
||
| logical, | intent(out) | :: | success | True if the integration is successful, false otherwise |
Initialises an ice_shelf object with initial conditions provided by the arguments. At present only a 1D model is supported. If information is provided for higher dimensions then it will be ignored.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(out) | :: | this | |||
| real(kind=r8), | intent(in), | dimension(:,:) | :: | domain | An array containing the upper and lower limits of the domain for the ice shelf. The first index represents the dimension for which the boundaries apply. If the second index is 1 then it corresponds to the lower bound. If the second index is 2 then it corresponds to the upper bound. |
|
| integer, | intent(in), | dimension(:) | :: | resolution | The number of data points in each dimension. |
|
| procedure(thickness_func) | :: | thickness | A function which calculates the initial value of the thickness of the ice shelf at a given location. |
|||
| procedure(velocity_func) | :: | velocity | A function which calculates the initial value of the velocity (vector) of the ice at a given location in an ice shelf. |
|||
| real(kind=r8), | intent(in), | optional | :: | temperature | The temperature of the ice in the ice shelf. |
|
| class(abstract_viscosity), | intent(inout), | optional | allocatable | :: | viscosity_law | An object which calculates the viscosity of the ice. If not specified, then Glen's law will be used with $n=3$. Will be unallocated on return. |
| class(glacier_boundary), | intent(inout), | optional | allocatable | :: | boundaries | An object specifying the boundary conditions for the ice shelf. Will be unallocated on return. |
| real(kind=r8), | intent(in), | optional | :: | lambda | The dimensionless ratio $\lambda \equiv \frac{\rho_0m_0x_0}{\rho_ih_0u_0}$. |
|
| real(kind=r8), | intent(in), | optional | :: | chi | The dimensionless ratio $\chi \equiv \frac{\rho_igh_0x_x}{2\eta_0u_0}\left(1 - \frac{\rho_i}{\rho_0}\right)$. |
|
| real(kind=r8), | intent(in), | optional | :: | zeta | The dimensionless ratio $\zeta \equiv \frac{\rho_iu_0x_0}{\eta_0}$, corresponding to the Reynolds number. Currently this is unused and always treated as 0. |
|
| real(kind=r8), | intent(in), | optional | :: | courant | The Courant number to use when calculating the time step. Defaults to 100. Too large a value will pose difficulties for the nonlinear solver, while too small a value can be numerically unstable. Typically, smaller values are needed for lower resolution. |
|
| real(kind=r8), | intent(in), | optional | :: | max_dt | The maximum allowable time step. This defaults to (effectively no maximum). |
|
| procedure(kappa_init_func), | optional | :: | kappa | A function which specifies the initial values of the Taylor
coefficients describing the vertical distribution of internal
reflectors within the ice. The initial conditions at the
grounding line will provide the boundary conditions there
throughout the simulation. If this parameter is not provided
then these layers will not be included in the
integration. Both this parameter and |
||
| integer, | intent(in), | optional | :: | n_kappa | The number of Taylor coefficients used to describe internal
reflectors. If not provided then these reflectors will not be
included in the integration. Both this parameter and |
Returns the thickness of the ice shelf across its domain.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(in) | :: | this |
The ice thickness.
Returns the density of the ice in the shelf, which is assumed to be uniform across its domain.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(in) | :: | this |
The ice density.
Returns the density of the ice in the shelf, which is assumed to be uniform across its domain.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(in) | :: | this |
The ice density.
Returns the residual when the current state of the glacier is run through the system of equations describing it. The residual takes the form of a 1D array, with each element respresenting the residual for one of the equations in the system.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(in) | :: | this | |||
| class(glacier), | intent(in), | dimension(:) | :: | previous_states | The states of the glacier in the previous time steps. The first element of the array should be the most recent. The default implementation will only make use of the most recent state, but the fact that this is an array allows potential other implementations to use older states for higher-order integration methods. |
|
| class(scalar_field), | intent(in) | :: | melt_rate | Thickness of the ice above the glacier. |
||
| class(scalar_field), | intent(in) | :: | basal_drag_parameter | A paramter, e.g. coefficient of friction, needed to calculate the drag on basal surface of the glacier. |
||
| real(kind=r8), | intent(in) | :: | water_density | The density of the water below the glacier. |
The residual of the system of equations describing the glacier.
Updates the state of the ice shelf from its state vector. The state vector is a real array containing the value of each of the ice shelf's properties at each of the locations on the grid used in discretization.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(inout) | :: | this | |||
| real(kind=r8), | intent(in), | dimension(:) | :: | state_vector | A real array containing the data describing the state of the glacier. |
Provides a preconditioner for the nonlinear solver trying to bring the residual to zero. The Jacobian is approximated as a block matrix, where each block is a tridiagonal matrix using a finite difference method for differentiation.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(inout) | :: | this | |||
| class(glacier), | intent(in), | dimension(:) | :: | previous_states | The states of the glacier in the previous time steps. The first element of the array should be the most recent. The default implementation will only make use of the most recent state, but the fact that this is an array allows overriding methods to use older states for higher-order integration methods. |
|
| class(scalar_field), | intent(in) | :: | melt_rate | Thickness of the ice above the glacier |
||
| class(scalar_field), | intent(in) | :: | basal_drag_parameter | A paramter, e.g. coefficient of friction, needed to calculate the drag on basal surface of the glacier. |
||
| real(kind=r8), | intent(in) | :: | water_density | The density of the water below the glacier |
||
| real(kind=r8), | intent(in), | dimension(:) | :: | delta_state | The change to the state vector which is being preconditioned. |
The result of applying the preconditioner to delta_state.
Sets the time information held by the ice shelf object. This is the time at which the ice sheet is in its current state.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(inout) | :: | this | |||
| real(kind=r8), | intent(in) | :: | time | The time at which the glacier is in the present state. |
Returns the number of elements in the ice shelf's state vector. This is the size of the vector returned by residual and state_vector and taken as an argument by update.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(in) | :: | this |
The number of elements in the ice shelf's state vector.
Returns the state vector for the current state of the ice shelf. This takes the form of a 1D array.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(in) | :: | this |
The state vector describing the ice shelf.
Returns the a vector representing the current state of the internal reflectors in the ice shelf. This takes the form of a 1D array. The routien is only used for debugging purposes.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(in) | :: | this |
The state vector describing the ice shelf.
Reads the state of the ice shelf object from the specified group in an HDF5 file. This sets the thickness, the velocity, and parameter values.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(inout) | :: | this | |||
| integer(kind=hid_t), | intent(in) | :: | file_id | The identifier for the HDF5 file/group in which this data is meant to be written. |
||
| character(len=*), | intent(in) | :: | group_name | The name to give the group in the HDF5 file storing the ice shelf's data. |
||
| integer, | intent(out) | :: | error | Flag indicating whether routine ran without error. If no error occurs then has value 0. |
Writes the state of the ice shelf object to an HDF file in the specified group. This will consist of a thickness and a velocity dataset.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(in) | :: | this | |||
| integer(kind=hid_t), | intent(in) | :: | file_id | The identifier for the HDF5 file/group in which this data is meant to be written. |
||
| character(len=*), | intent(in) | :: | group_name | The name to give the group in the HDF5 file storing the ice shelf's data. |
||
| integer, | intent(out) | :: | error | Flag indicating whether routine ran without error. If no error occurs then has value 0. |
Calculates the time step for integrating the ice shelf, using the CFL condition.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(in) | :: | this |
The time-step to use
Computes the ice shelf velocity at the current time with the current ice thickness.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(inout) | :: | this | |||
| class(scalar_field), | intent(in) | :: | basal_drag | A paramter, e.g. coefficient of friction, needed to calculate the drag on basal surface of the glacier. |
||
| logical, | intent(out) | :: | success | True if the integration is successful, false otherwise |
Copies the data from one ice shelf into another. This is only needed due to a bug in gfortran which means that the intrinsic assignment for glacier types is not using the appropriate defined assignment for the field components.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(out) | :: | this | |||
| class(glacier), | intent(in) | :: | rhs | The ice shelf to be assigned to this one. |
Integrate the Taylor coefficients representing the vertical structure of internal reflectors forward to the specified time. This is done using an implicit method, with the resulting linear system solved using GMRES.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ice_shelf), | intent(inout) | :: | this | |||
| class(glacier), | intent(in), | dimension(:) | :: | old_states | Previous states of the ice_shelf, with the most recent one first. |
|
| real(kind=r8), | intent(in) | :: | time | The time to which the ice_shelf should be integrated |
||
| logical, | intent(out) | :: | success | True if the integration is successful, false otherwise |
type, extends(glacier), public :: ice_shelf
!* Author: Chris MacMackin
! Date: April 2016
!
! A concrete implementation of the [[glacier]] type, using a vertically
! integrated model of an ice shelf. This model is 1-dimensional only.
!
private
type(cheb1d_scalar_field) :: thickness
!! Thickness of ice shelf, \(h\)
type(cheb1d_vector_field) :: velocity
!! Flow velocity of ice shelf, \(\vec{u}\)
type(cheb1d_scalar_field) :: eta
!! Viscosity of the ice, \(\eta\)
type(cheb1d_scalar_field), dimension(:), allocatable :: kappa
!! Taylor coefficients for the vertical structure of a
!! Lagrangian tracer representing englacial layers/internal
!! reflectors.
real(r8) :: lambda
!! The dimensionless ratio
!! $\lambda \equiv \frac{\rho_0m_0x_0}{\rho_iH-0u_0}$
real(r8) :: chi
!! The dimensionless ratio \(\chi \equiv
!! \frac{\rho_igh_0x_0}{2\eta_0u_0} \left(1 -
!! \frac{\rho_i}{\rho_o}\right)\)
real(r8) :: zeta
!! The dimensionless ratio \(\zeta \equiv
!! \frac{\rho_iu_0x_0}{\eta_0}\), corresponding to the Reynolds
!! number. Currently unused.
real(r8) :: courant
!! The Courant number to use when calculating the time step.
class(abstract_viscosity), allocatable :: viscosity_law
!! An object representing the model used for ice viscosity.
class(glacier_boundary), allocatable :: boundaries
!! An object specifying the boundary conditions for the ice
!! shelf.
real(r8) :: max_dt
!! The maximu allowable time step
real(r8) :: time
!! The time at which the ice shelf is in this state.
integer :: thickness_size
!! The number of data values in the thickness field.
integer :: velocity_size
!! The number of data values in the velocity field.
integer :: boundary_start
!! The number of data values needed to represent the boundary
!! conditions.
integer :: thickness_lower_bound_size
!! The number of data values needed to represent the lower
!! boundary conditions for thickness.
integer :: thickness_upper_bound_size
!! The number of data values needed to represent the upper
!! boundary conditions for thickness.
integer :: velocity_lower_bound_size
!! The number of data values needed to represent the lower
!! boundary conditions for velocity.
integer :: velocity_upper_bound_size
!! The number of data values needed to represent the upper
!! boundary conditions for thickness.
type(jacobian_block) :: thickness_jacobian
!! A representation of the Jacobian for the ice shelf thickness.
type(jacobian_block) :: velocity_jacobian
!! A representation of the Jacobian for the ice shelf velocity.
logical :: stale_eta
!! Indicates whether the viscosity needs updating.
logical :: stale_jacobian
!! Indicates if the Jacobians are stale and in need of updating.
contains
procedure :: initialise => shelf_initialise
procedure :: ice_thickness => shelf_thickness
!$ procedure :: ice_velocity => shelf_velocity
procedure :: ice_density => shelf_density
procedure :: ice_temperature => shelf_temperature
procedure :: residual => shelf_residual
procedure :: update => shelf_update
procedure :: precondition => shelf_precondition
procedure :: set_time => shelf_set_time
procedure :: data_size => shelf_data_size
procedure :: state_vector => shelf_state_vector
procedure :: kappa_vector => shelf_kappa_vector
procedure :: read_data => shelf_read_data
procedure :: write_data => shelf_write_data
procedure :: time_step => shelf_time_step
procedure :: solve_velocity => shelf_solve_velocity
! procedure :: integrate => shelf_integrate
procedure, private :: assign => shelf_assign
procedure :: integrate_layers => ice_shelf_integrate_layers
end type ice_shelf