A concrete implementation of the basal_surface abstract data type, representing the buoyant plume beneath an ice shelf.
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| type(cheb1d_scalar_field), | private | :: | thickness | The thickness of the plume |
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| type(cheb1d_vector_field), | private | :: | velocity | The velocity of the plume |
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| type(cheb1d_vector_field), | private | :: | velocity_dx | The derivative of the velocity field |
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| type(cheb1d_scalar_field), | private | :: | temperature | The temperature of the plume |
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| type(cheb1d_scalar_field), | private | :: | temperature_dx | The derivative of the temperature of the plume |
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| type(cheb1d_scalar_field), | private | :: | salinity | The salinity of the plume |
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| type(cheb1d_scalar_field), | private | :: | salinity_dx | The derivative of the salinity of the plume |
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| class(abstract_entrainment), | private, | allocatable | :: | entrainment_formulation | An object which provides the parameterisation for entrainment of water into the plume. |
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| class(abstract_melt_relationship), | private, | allocatable | :: | melt_formulation | An object which provides the parameterisation for melting, salt, and heat fluxes from the plume to the ice. |
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| class(ambient_conditions), | private, | allocatable | :: | ambient_conds | An object specifying the temperature and salinity of the ambient ocean at its interface with the plume. |
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| class(equation_of_state), | public, | allocatable | :: | eos | An object specifying the equation of state relating the plume water's density to its temperature and salinity. |
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| class(plume_boundary), | private, | allocatable | :: | boundaries | An object specifying the boundary conditions for the plume. |
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| real(kind=r8), | private | :: | delta | The dimensionless ratio |
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| real(kind=r8), | public | :: | nu | The dimensionless ratio |
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| real(kind=r8), | private | :: | mu | The dimensionless ratio |
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| real(kind=r8), | private | :: | r_val | The dimensionless ratio of the ocean water density to the density of the overlying ice shelf. |
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| real(kind=r8), | public | :: | phi | The inverse Rossby number, |
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| real(kind=r8), | private | :: | time | The time at which the ice shelf is in this state |
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| integer, | private | :: | thickness_size | The number of data values in the thickness field |
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| integer, | private | :: | velocity_size | The number of data values in the velocity field |
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| integer, | private | :: | temperature_size | The number of data values in the temperature field |
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| integer, | private | :: | salinity_size | the number of data values in the salinity field |
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| logical, | private, | dimension(7) | :: | lower_bounds | = | .false. | Which variables have boundary conditions at the grounding line. |
| logical, | private, | dimension(7) | :: | upper_bounds | = | .false. | Which variables have boundary conditions at the calving front. |
| type(pseudospec_block), | private | :: | precond | A pseudospectral differentiation block which can be used for preconditioning. |
Instantiates a plume object with initial coniditions 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(plume), | intent(out) | :: | this | A plume object with its domain and initial conditions set according to the arguments of the constructor function. |
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| real(kind=r8), | intent(in), | dimension(:,:) | :: | domain | An array containing the upper and lower limits of the domain for the plume. 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. |
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| integer, | intent(in), | dimension(:) | :: | resolution | The number of data points in each dimension |
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| procedure(scalar_func) | :: | thickness | A function which calculates the initial value of the thickness of the plume at a given location. |
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| procedure(velocity_func) | :: | velocity | A function which calculates the initial value of the velocity (vector) of the water at a given location in a plume. |
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| procedure(scalar_func) | :: | temperature | A function which calculates the initial value of the temperature of the plume at a given location. |
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| procedure(scalar_func) | :: | salinity | A function which calculates the initial value of the salinity of the plume at a given location. |
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| class(abstract_entrainment), | intent(inout), | optional | allocatable | :: | entrainment_formulation | An object which calculates entrainment into the plume. Will be unallocated on exit. Defaults to that used by Jenkins (1991) with the coefficient $E_0 = 1$. |
| class(abstract_melt_relationship), | intent(inout), | optional | allocatable | :: | melt_formulation | An object which calculates melting and the resulting thermal transfer into/out of the plume. Will be unallocated on exit. Defaults to that used by Dallaston et al. (2015), scaled to be consistent with the nondimensionalisation used here. |
| class(ambient_conditions), | intent(inout), | optional | allocatable | :: | ambient_conds | An object specifying the salinity and temperature of the ambient ocean. Will be unallocated on exit. Defaults to uniform ambient salinity and temperature, both of which are set to 0 (as temperature and salinity are measured relative to some reference value). |
| class(equation_of_state), | intent(inout), | optional | allocatable | :: | eos | An object specifying the equation of state for the water in the plume. Will be unallocated on exit. Defaults to linearised equation of state with no temperature dependence and a haline contraction coefficient of 1. The reference density is set to be 1 in the dimensionless units when salinity and temeprature are 0. |
| class(plume_boundary), | intent(inout), | optional | allocatable | :: | boundaries | An object providing the boundary conditions for the plume. Will be unallocated on exit. Defaults to those used by Dallaston et al. (2015). |
| real(kind=r8), | intent(in), | optional | :: | delta | The dimensionless ratio . Defaults to 0.036. |
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| real(kind=r8), | intent(in), | optional | :: | nu | The dimensionless ratio . Defaults to 0. |
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| real(kind=r8), | intent(in), | optional | :: | mu | The dimensionless ratio . Defaults to 0. |
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| real(kind=r8), | intent(in), | optional | :: | r_val | The dimensionless ratio of the water density to the ice shelf density, Defaults to 1.12. |
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| real(kind=r8), | intent(in), | optional | :: | phi | The inverse Rossby number, . Defaults to 0. |
Computes and returns the melt rate at the bottom of the ice shelf due to interaction with the plume.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(plume), | intent(in) | :: | this |
The melt rate at the base of the ice shelf.
Computes and returns a quantity which may be necessary to determine the frictional drag the plume exerts on the bottom of the ice shelf. The plume would actually tend to exert no drag on the bottom of the ice shelf, but this method is present so that there is a consistent interface with the ground data type.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(plume), | intent(in) | :: | this |
The melt rate at the base of the ice sheet.
Computes and returns the density of the plume water beneath the ice shelf. The density of this water would vary depending on how much saline ambient water has been entrained into the plume versus how much fresh water has been released due to melting. However, the Boussinesq approximation is used here and only a single reference density is returned.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(plume), | intent(in) | :: | this |
The density of the water at the base of the ice sheet.
Updates the state of the plume from its state vector. The state vector is a real array containing the value of each of the plume's properties at each of the locations on the grid used in discretization.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(plume), | intent(inout) | :: | this | |||
| real(kind=r8), | intent(in), | dimension(:) | :: | state_vector | A real array containing the data describing the state of the plume. |
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| class(scalar_field), | intent(in), | optional | :: | ice_thickness | The ice thickness which, if present, will be used to update the calculation of the melt rate. |
Returns the number of elements in the plume's state vector. This is the size of the vector returned by state_vector and taken as an argument by update.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(plume), | intent(in) | :: | this |
The number of elements in the plume's state vector.
Returns the state vector for the current state of the plume. This takes the form of a 1D array.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(plume), | intent(in) | :: | this |
The state vector describing the plume.
Reads the state of the plume object from an HDF file in the specified group. This sets the thickness, velocity, temperature, salinity dataset, and parameter values.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(plume), | 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. |
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| character(len=*), | intent(in) | :: | group_name | The name to give the group in the HDF5 file storing the ice shelf's data. |
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| integer, | intent(out) | :: | error | Flag indicating whether routine ran without error. If no error occurs then has value 0. |
Writes the state of the plume object to an HDF file in the specified group. This will consist of a thickness, a velocity, a temperature, and a salinity dataset.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(plume), | 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. |
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| character(len=*), | intent(in) | :: | group_name | The name to give the group in the HDF5 file storing the ice shelf's data. |
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| integer, | intent(out) | :: | error | Flag indicating whether routine ran without error. If no error occurs then has value 0. |
Solves the state of the plume for the specified ice properties, at the specified time. This is done using the a quasilinearisation method and a GMRES iterative linear solver.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(plume), | intent(inout) | :: | this | |||
| class(scalar_field), | intent(in) | :: | ice_thickness | Thickness of the ice above the basal surface |
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| real(kind=r8), | intent(in) | :: | ice_density | The density of the ice above the basal surface, assumed uniform |
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| real(kind=r8), | intent(in) | :: | ice_temperature | The temperature of the ice above the basal surface, assumed uniform |
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| real(kind=r8), | intent(in) | :: | time | The time to which the basal surface should be solved |
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| logical, | intent(out) | :: | success | True if the solver is successful, false otherwise |
type, extends(basal_surface), public :: plume
!* Author: Christopher MacMackin
! Date: April 2016
!
! A concrete implementation of the [[basal_surface(type)]]
! abstract data type, representing the buoyant plume beneath an
! ice shelf.
!
private
type(cheb1d_scalar_field) :: thickness
!! The thickness of the plume
type(cheb1d_vector_field) :: velocity
!! The velocity of the plume
type(cheb1d_vector_field) :: velocity_dx
!! The derivative of the velocity field
type(cheb1d_scalar_field) :: temperature
!! The temperature of the plume
type(cheb1d_scalar_field) :: temperature_dx
!! The derivative of the temperature of the plume
type(cheb1d_scalar_field) :: salinity
!! The salinity of the plume
type(cheb1d_scalar_field) :: salinity_dx
!! The derivative of the salinity of the plume
class(abstract_entrainment), allocatable :: entrainment_formulation
!! An object which provides the parameterisation for entrainment
!! of water into the plume.
class(abstract_melt_relationship), allocatable :: melt_formulation
!! An object which provides the parameterisation for melting,
!! salt, and heat fluxes from the plume to the ice.
class(ambient_conditions), allocatable :: ambient_conds
!! An object specifying the temperature and salinity of the
!! ambient ocean at its interface with the plume.
class(equation_of_state), allocatable, public :: eos
!! An object specifying the equation of state relating the plume
!! water's density to its temperature and salinity.
class(plume_boundary), allocatable :: boundaries
!! An object specifying the boundary conditions for the plume.
real(r8) :: delta
!! The dimensionless ratio \(\delta \equiv \frac{D_0}{h_0}\)
real(r8), public :: nu
!! The dimensionless ratio \(\nu \equiv \frac{\kappa_0}{x_0U_o}\)
real(r8) :: mu
!! The dimensionless ratio \(\mu \equiv \frac{C_dx_0}{D_0}\)
real(r8) :: r_val
!! The dimensionless ratio of the ocean water density to the
!! density of the overlying ice shelf.
real(r8), public :: phi
!! The inverse Rossby number, \(\Phi \equiv \frac{fx_0}{U_0}\)
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 :: temperature_size
!! The number of data values in the temperature field
integer :: salinity_size
!! the number of data values in the salinity field
logical, dimension(7) :: lower_bounds = .false.
!! Which variables have boundary conditions at the grounding
!! line.
logical, dimension(7) :: upper_bounds = .false.
!! Which variables have boundary conditions at the calving
!! front.
type(pseudospec_block) :: precond
!! A pseudospectral differentiation block which can be used for
!! preconditioning.
contains
procedure :: initialise => plume_initialise
procedure :: basal_melt => plume_melt
procedure :: basal_drag_parameter => plume_drag_parameter
procedure :: water_density => plume_water_density
procedure :: update => plume_update
procedure :: data_size => plume_data_size
procedure :: state_vector => plume_state_vector
procedure :: read_data => plume_read_data
procedure :: write_data => plume_write_data
procedure :: solve => plume_solve
end type plume