PISM, A Parallel Ice Sheet Model
pism::energy::BedThermalUnit Class Referenceabstract

Given the temperature of the top of the bedrock, for the duration of one time-step, provides upward geothermal flux at that interface at the end of the time-step. More...

#include <BedThermalUnit.hh>

Inheritance diagram for pism::energy::BedThermalUnit:

Public Types

typedef std::shared_ptr< BedThermalUnitPtr

typedef std::shared_ptr< const BedThermalUnitConstPtr

Public Member Functions

BedThermalUnit (IceGrid::ConstPtr g)

virtual ~BedThermalUnit ()=default

void init (const InputOptions &opts)

const IceModelVec2Sflux_through_top_surface () const
Return the upward heat flux through the top surface of the bedrock thermal layer. More...

const IceModelVec2Sflux_through_bottom_surface () const
Return the upward heat flux through the bottom surface of the bedrock thermal layer. More...

void update (const IceModelVec2S &bedrock_top_temperature, double t, double dt)

double vertical_spacing () const

double depth () const

unsigned int Mz () const

Public Member Functions inherited from pism::Component
Component (IceGrid::ConstPtr g)

virtual ~Component ()=default

DiagnosticList diagnostics () const

TSDiagnosticList ts_diagnostics () const

IceGrid::ConstPtr grid () const

void define_model_state (const File &output) const
Define model state variables in an output file. More...

void write_model_state (const File &output) const
Write model state variables to an output file. More...

MaxTimestep max_timestep (double t) const
Reports the maximum time-step the model can take at time t. More...

Static Public Member Functions

static BedThermalUnitFromOptions (IceGrid::ConstPtr g, std::shared_ptr< const Context > ctx)

Protected Member Functions

virtual void initialize_bottom_surface_flux ()

virtual void init_impl (const InputOptions &opts)
Initialize the bedrock thermal unit. More...

virtual void update_impl (const IceModelVec2S &bedrock_top_temperature, double t, double dt)=0

virtual double vertical_spacing_impl () const =0

virtual double depth_impl () const =0

virtual unsigned int Mz_impl () const =0

virtual void define_model_state_impl (const File &output) const
The default (empty implementation). More...

virtual void write_model_state_impl (const File &output) const
The default (empty implementation). More...

virtual DiagnosticList diagnostics_impl () const

Protected Member Functions inherited from pism::Component
virtual MaxTimestep max_timestep_impl (double t) const

virtual TSDiagnosticList ts_diagnostics_impl () const

virtual void regrid (const std::string &module_name, IceModelVec &variable, RegriddingFlag flag=NO_REGRID_WITHOUT_REGRID_VARS)

Protected Attributes

IceModelVec2S m_bottom_surface_flux
upward heat flux through the bottom surface of the bed thermal layer More...

IceModelVec2S m_top_surface_flux
upward heat flux through the top surface of the bed thermal layer More...

Protected Attributes inherited from pism::Component
const IceGrid::ConstPtr m_grid
grid used by this component More...

const Config::ConstPtr m_config
configuration database used by this component More...

const units::System::Ptr m_sys
unit system used by this component More...

const Logger::ConstPtr m_log
logger (for easy access) More...

Protected Types inherited from pism::Component
enum  RegriddingFlag { REGRID_WITHOUT_REGRID_VARS , NO_REGRID_WITHOUT_REGRID_VARS }
This flag determines whether a variable is read from the -regrid_file file even if it is not listed among variables in -regrid_vars. More...

Detailed Description

Given the temperature of the top of the bedrock, for the duration of one time-step, provides upward geothermal flux at that interface at the end of the time-step.

The geothermal flux actually applied to the base of an ice sheet is dependent, over time, on the temperature of the basal ice itself. The purpose of a bedrock thermal layer in an ice sheet model is to implement this dependency by using a physical model for the temperature within that layer, the upper lithosphere. Because the upper part of the lithosphere stores or releases energy into the ice, the typical lithosphere geothermal flux rate is not the same thing as the geothermal flux applied to the base of the ice. This issue has long been recognized by ice sheet modelers [e.g. RitzFabreLetreguilly].

For instance, suppose the ice sheet is in a balanced state in which the geothermal flux deep in the crust is equal to the heat flux into the ice base. If the near-surface ice cools from this state then, because the ice temperature gradient is now greater in magnitude, between the warm bedrock and the cooler ice, the ice will for some period receive more than the deep geothermal flux rate. Similarly, if the ice warms from the balanced state then the temperature difference with the bedrock has become smaller and the magnitude of the ice basal heat flux will be less than the deep geothermal rate.

We regard the lithosphere geothermal flux rate, which is applied in this model to the base of the bedrock thermal layer, as a time-independent quantity. This concept is the same as in all published ice sheet models, to our knowledge.

Because the relevant layer of bedrock below an ice sheet is typically shallow, modeling the bedrock temperature is quite simple. Let $$T_b(t,x,y,z)$$ be the temperature of the bedrock layer, for elevations $$-L_b \le z \le 0$$. In this routine, $$z=0$$ refers to the top of the bedrock, the ice/bedrock interface. (Note $$z=0$$ is the base of the ice in IceModel, and thus a different location if ice is floating.) Let $$G$$ be the lithosphere geothermal flux rate, namely the PISM input variable bheatflx; see Related Page std_names . Let $$k_b$$ = bedrock_thermal_conductivity in pism_config.cdl) be the constant thermal conductivity of the upper lithosphere. In these terms the actual upward heat flux into the ice/bedrock interface is the quantity,

$G_0 = -k_b \frac{\partial T_b}{\partial z}.$

This is the output of the method top_heat_flux() in this class.

The evolution equation solved in this class, for which a timestep is done by the update() method, is the standard 1D heat equation

$\rho_b c_b \frac{\partial T_b}{\partial t} = k_b \frac{\partial^2 T_b}{\partial z^2}$

where $$\rho_b$$ = bedrock_thermal_density and $$c_b$$ = bedrock_thermal_specific_heat_capacity in pism_config.cdl.

If n_levels >= 3 then everything is the general case. The lithospheric temperature in temp is saved in files as litho_temp. The top_heat_flux() method uses second-order differencing to compute the values of $$G_0$$.

If n_levels <= 1 then this object becomes very simplified: there is no internal state in IceModelVec3 temp. The update() and allocate() methods are null, and the top_heat_flux() method does nothing other than to copy the field $$G$$ = bheatflx into result.

If n_levels == 2 then everything is the general case except that top_heat_flux() method uses first-order differencing to compute the values of $$G_0$$.

Definition at line 101 of file BedThermalUnit.hh.

The documentation for this class was generated from the following files: