PISM (a Parallel Ice Sheet Model) Reference Manual
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1. static const titlkeNname tn tnN 4 3 1 Detailed Description The base class for PISM Contains all essential variables parameters and flags for modelling an ice sheet FIXME add text about change of vertical variable Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 6 4 3 2 Member Function Documentation 4 3 2 1 PetscErrorCoderun virtual Do the time stepping for an evolution run This important routine can be replaced by derived classes it is virtual This procedure has the main loop The following actions are taken on each pass through the loop e the yield stress for the plastic till model is updated if appropriate the positive degree day model is invoked to compute the surface mass balance if appropriate a step of the bed deformation model is taken if appropriate the velocity field is updated in some cases the whole three dimensional field is updated and in some cases just the vertically averaged horizontal velocity is updated see velocity the time step is determined according to a variety of stability criteria see determineTimeStep the temperature field is updated according to the conservation of energy model based especially on the new velocity field see temperatureAgeStep the thickness of the ice is updated according to the mass conservation model see massBalExplicitStep there is various reporting to the user on2. e see updateNuViewers for nuView d i or d j and lognuView d n and NuView d N e see iceCompModel cc for compensatory Sigma viewer and redo of Sigma viewer d PS 4 3 3 Member Data Documentation 4 3 3 1 const titleNnametn static protected Holds variable names for NetCDF and Matlab files and short titles for graphical viewers This array of strings holds names and titles These names and titles are for views of the internal state of PISM That is they are not names and title for parts of the internal state of PISM Thus for example there is no one to one correspondence between the inter nal variables stored in PETSc Vecs and the entries in this array it is more complicated than that Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 4 IceParam Class Reference 20 This array is used for both variable names and short titles in writeMatlab Vars among other places It is accessed for short titles only in create Viewers This array is usually referenced by a single character Note that by the ASCII to integer conversion for instance the variable name corresponding to the single character name A is tn int A int 0 title Such indexing is facilitated by c Index 4 4 IceParam Class Reference Collects the parameters for the grid and computational domain 4 4 1 Detailed Description Collects the parameters for the grid and computat
3. 5 saveUVBarForSSA 16 setDefaults 6 setFromOptions 6 SigmaSIAToRegular 12 surfaceGradientSIA 11 temperatureAgeStep 16 temperatureStep 16 tn 19 updateSurfaceElevationAndMask 8 update Viewers 19 update YieldStressFromHmelt 9 velocities2DSIAToRegular 12 velocity 7 velocitySIAStaggered 11 velocitySSA 13 vert VelocityFromIncompressibility 18 writeFiles 7 writeMatlabVars 10 INDEX 22 writeSSAsystemMatlab 11 IceParam 20 initFromFile IceModel 7 initFromFile_netCDF IceModel 7 massBalExplicitStep IceModel 9 move Velocity ToDAVectors IceModel 15 putSavedU VBarInUVBar IceModel 16 rescale IceGrid 3 run IceModel 5 saveUVBarForSSA IceModel 16 setDefaults IceModel 6 setFromOptions IceModel 6 SigmaSIAToRegular IceModel 12 surfaceGradientSIA IceModel 11 temperatureAgeStep IceModel 16 temperatureStep IceModel 16 tn IceModel 19 updateSurfaceElevationAndMask IceModel 8 update Viewers IceModel 19 update YieldStressFromHmelt IceModel 9 velocities2 DSIAToRegular IceModel 12 velocity IceModel 7 velocitySIAStaggered IceModel 11 velocitySSA IceModel 13 vert VelocityFromIncompressibility IceModel 18 writeFiles IceModel 7 writeMatlab Vars IceModel 10 writeSSAsystemMatlab IceModel 11 Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen
4. 3 2 26 PetscErrorCode assembleSSARhs bool surfGradInward Vec rhs protected Computes the right hand side of the linear problem for the SSA equations The right side of the SSA equations is just pgHVh because in particular the basal stress is put on the left side of the system See com ment for assembleSSA Matrix The surface slope is computed by centered difference onto the regular grid which may use periodic ghosting Optionally the surface slope can be computed by only differencing into the grid for points at the edge see test I Note that the grid points with mask value MASK_SHEET correspond to the trivial equations uvbar O i ly uvbar O f 9 Uij 2 and similarly for v j That is the vertically averaged horizontal velocity is already known for these points because it was computed on the staggered grid using the SIA 4 3 2 27 PetscErrorCode moveVelocityToDAVectors Vec x protected Move the solution to the SSA system into a Vec which is DA distributed Since the parallel layout of the vector x in the KSP representation of the linear SSA system does not in general have anything to do with the DA based vectors for the rest of IceModel we must scatter the entire vector to all processors 4 3 2 28 PetscErrorCode broadcastSSAVelocity protected At all SSA points update the velocity field Once the vertically averaged velocity field is computed by the SSA this procedure updates the three
5. Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 8 4 3 2 9 PetscErrorCode createVecs protected virtual Allocate all Vecs defined in IceModel Initialization of an IceModel is confusing Here is a description of the intended order e 1 The constructor for IceModel Note IceModel has a member grid of class IceGrid Note grid p an IceParam is also constructed this sets defaults for grid p gt Mx My Mz Mbz Lx Ly Lz Lbz dx dy dz year e 1 5 derivedClass setFromOptions to get options special to derived class e 2 setFromOptions to get all options including Mx My Mz Mbz 2 5 initFromFile_netCDF which reads Mx My Mz Mbz from file and over writes previous if this represents a change the user is warned e 3 createDA which uses only Mx My Mz Mbz e 4 create Vecs uses DA to create allocate Vecs e 4 5 derivedClass create Vecs to create allocate Vecs special to derived class e 5 afterInitHook which changes Lx Ly Lz if set by user Note driver programs call only setFromOptions and initFromOptions for IceModel or derived class Note IceModel setFromOptions should be called at the end of derivedClass setFrom Options Note 2 5 3 and 4 are called from initFromFile in IceModel Note 3 and 4 are called from initFromOptions in some derived classes e g IceComp Model in cases where initFromFile is not called Note step 2 5 is ski
6. Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 18 Here T To We also apply the discretized conduction equation at z_0 These two combined equations yield a simplified form 2At 1 2KR To 2KT To G pcpAz where K kAt pcAz 7 4 3 2 35 PetscErrorCode ageStep PetscScalar x CFLviol protected Take an explicit time step for the age equation Also check the CFL for advection The age equation is I that is OT OF OF i OF 4 at dx Oy Oz where T t x y z is the age of the ice and u v w is the three dimensional velocity field This equation is hyperbolic purely advective The boundary condition is that when the ice fell as snow it had age zero That is T t x y h t x y 0 in accumu lation areas while there is no boundary condition elsewhere as the characteristics go outward elsewhere At this point the refreeze case either grounded basal ice or marine basal ice is not handled correctly The numerical method is first order upwind 4 3 2 36 PetscErrorCode excessToFromBasalMeltLayer PetscScalar rho_c PetscScalar z PetscScalar x Texcess PetscScalar x Hmelt protected Compute the melt water which should go to the base if T is above pressure melting 4 3 2 37 PetscErrorCode vertVelocityFromIncompressibility 0 protected Compute vertical velocity using basal conditions and incompressibility of the ice The original statement of incompressibility is w U
7. UV V De 0 This is immediately equivalent to the integral wanz f ain E E b x y t The basal kinematic equation is Ob w 5 Us Vb S Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 19 where S is the basal melt rate The inclusion of the basal melt rate is optional This equation determines the vertical velocity of the ice at the base w which is needed in the incompressibility integral Note we do a change of vertical coordinate Z z b x y t Thus all derivatives with respect to any variable x y z t change accordingly see elsewhere The revised form of the incompressibility integral is wan v u ve 2 d w x y t 0 z 2 The vertical integral is computed by the trapezoid rule 4 3 2 38 PetscErrorCode computeMax3DVelocities protected Compute the maximum velocities for time stepping and reporting to user 4 3 2 39 PetscErrorCode updateViewers protected Update the runtime graphical viewers At every time step the graphical viewers are updated The user specifies these viewers by the options d list or dbig list where list is a list of single character names of the viewers a list with no spaces See an appendix of the User s Manual for the names Most viewers are updated by this routing but some other are updated elsewhere e see computeMaxDiffusivity in iMutil cc for diffus View d D
8. the current state see summary and update Viewers Note that at the beginning and ends of the loop there is a chance for derived classes to do extra work See additionalAtStartTimestep and additionalAtEndTimestep 4 3 2 2 PetscErrorCode diagnosticRun virtual Calls the necessary routines to do a diagnostic calculation of velocity This important routine can be replaced by derived classes it is virtual This procedure has no loop but the following actions are taken e the yield stress for the plastic till model is updated if appropriate e the velocity field is updated in some cases the whole three dimensional field is updated and in some cases just the vertically averaged horizontal velocity is updated see velocity e there is various reporting to the user on the current state see summary and update Viewers Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 7 4 3 2 3 PetscErrorCode setDefaults virtual Assigns default values to the many parameters and flags in IceModel 4 3 2 4 PetscErrorCode setFromOptions virtual Read runtime command line options and set the corresponding parameter or flag This is called by a driver program assuming it would like to use command line options In fact this procedure only reads the majority of the options Some are read in initFrom Options writeFiles and setStartRunEnd YearsFromOptions
9. the value of the vertically averaged horizontal velocity U is known at all staggered grid points The surface slope Vh is needed on the staggered grid although the surface elevation h itself is known on the regular grid The scheme used for this is the one first proposed in the context of ice sheets by Mahaffy 1976 That is the method is type I in the classification described in Hindmarsh and Payne 1996 This routine also calls the part of the basal dynamical model applicable to the SIA see basalVelocity The basal sliding velocity is computed for all SIA points This routine also computes the basal frictional heating and the volume strain heating Note that the SIA is used at all points on the grid in this routine but that the resulting vertically averaged horizontal velocity is overwritten by different values at SSA points See correctBasalFrictionalHeating and correctSigma 4 3 2 19 PetscErrorCode frictionalHeatingSIAStaggered protected Compute the rate of frictional heating where the base is sliding by assuming the shear stress is from SIA 4 3 2 20 PetscErrorCode velocities2DSIAToRegular protected Average staggered grid vertically averaged horizontal velocity and basal velocity onto regular grid At the end of velocitySIAStaggered the vertically averaged horizontal velocity vuvbar 0 vuvbar 1 and the basal velocity ub vb is available on the staggered grid This procedure averages them onto the regular grid N
10. NO then the thickness is set to zero Note that the rate of thickness change 0H Ot is computed and saved as Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 10 is the rate of volume loss or gain Note updateSurfaceElevationAndMask is called at the end 4 3 2 13 PetscErrorCode update YieldStressFromHmelt protected Update the till yield stress for the plastic till model based on pressure and stored till water We implement formula 2 4 in C Schoof 2006 A variational approach to ice stream flow J Fluid Mech vol 556 pp 227 251 That formula is Te W pgH pw We modify it by 1 adding a small till cohesion cp see Paterson 3rd ed table 8 1 2 replacing py Apw where A Hmelt DEFAULT_MAX_HMELT thus 0 lt A lt 1 always while 0 when the bed is frozen and 3 computing porewater pressure pw as a fixed fraction y of the overburden pressure pg With these replacements our formula looks like Te Co u 1 Av pgH Note also that u tan where 0 is a friction angle The parameters co p 0 can be set by options till_cohesion till_pw_fraction and till_friction_angle respectively 4 3 2 14 PetscScalar basalVelocity const PetscScalar x const PetscScalar y const PetscScalar H const PetscScalar T const PetscScalar alpha const Petsc Scalar mu protected virtual Compute the coefficient for the basal veloci
11. PISM a Parallel Ice Sheet Model Reference Manual beta Generated by Doxygen 1 5 1 Fri Oct 5 14 38 34 2007 CONTENTS 1 Contents 1 PISM a Parallel Ice Sheet Model Main Page 1 2 PISM a Parallel Ice Sheet Model Hierarchical Index 2 3 PISM a Parallel Ice Sheet Model Class Index 2 4 PISM a Parallel Ice Sheet Model Class Documentation 2 1 PISM a Parallel Ice Sheet Model Main Page Author Ed Bueler This Reference Manual is a greatly shortened version of the complete HTML PISM source browser at pism doc doxy html index html As with the source browser this Manual was automatically generated by doxygen http www doxygen org from comments in the PISM source code This Manual documents the continuum models and the numerical methods in PISM It is restricted to documenting the three classes MaterialType and its derived classes IceGrid and its associated class IceParam and the main PISM class IceModel The source files from which this Manual is drawn are limited to files in the pism src base subdirectory Note that by contrast the source browser describes all classes and all class members and all source files in PISM Most users should start with the PISM User s Manual http www dms uaf edu bueler manual pdf or pism doc manual pdf for help with installing and using PISM Copyright C 2007 Ed Bueler This document is part of PISM PISM is free software you can redistribute it and or modify it unde
12. al box and the three dimensional PISM finite difference grid 4 2 2 Member Function Documentation 4 2 2 1 PetscErrorCode createDA Create the PETSc DAs for the grid specified in p a pointer to IceParam 4 2 2 2 PetscErrorCode rescale const PetscScalar lx const PetscScalar ly const PetscScalar lz Rescale IceGrid based on new values for Lx Ly Lz default version This method computes dx dy dz and Lbz based on the current values of Mx My Mz Mbz and the input values of Lx Ly and Lz Note that dz is the vertical spacing both in the ice and in bedrock Thus Loz Mbz x dz determines Lbz See the comment for rescale 1x ly 1z truelyPeriodic Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 4 4 2 2 3 PetscErrorCode rescale const PetscScalar lx const PetscScalar ly const PetscScalar lz const PetscTruth truely Periodic Rescale IceGrid based on new values for Lx Ly Lz but optionally allowing for peri odicity The grid used in PISM in particular the PETSc DAs used here are periodic in x and y This means that the ghosted values foo i 1 j foo i 1 j foo i j 1 foo li 4 1 for all 2D Vecs and similarly in the x and y di rections for 3D Vecs are always available That is they are available even if i j is a point at the edge of the grid On the other hand by default dx is the full width 2 x Lx divided by Mx 1 This means tha
13. among other places Note there are no options to directly set dx dy dz Lbz and year as the user should not directly set these grid parameters There are however options for directly setting Mx My Mz Mbz and also Lx Ly Lz 4 3 2 5 PetscErrorCode velocity bool update VelocityAtDepth Manage the computation of velocity and do the necessary communication This procedure calls the important routines velocitySIAStaggered velocitySSAQ and vertVelocityFromIncompressibility according to various flags 4 3 2 6 PetscErrorCode initFromFile const char fname Initialize from a saved PISM model state in NetCDF format Calls initFromFile_netCDFQ to do the actual work 4 3 2 7 PetscErrorCode writeFiles const char x defaultbasename const Petsc Truth forceFullDiagnostics Save model state in NetCDF format and save variables in Matlab format if desired Optionally allows saving of full velocity field Calls dumpToFile_netCDFQ dumpToFile_diagnostic_netCDFQ and writeMatlab Vars to do the actual work 4 3 2 8 PetscErrorCode initFromFile_netCDF const char fname Read a complete saved PISM model state for initialization of an evolution or diagnostic run When initializing from a NetCDF input file the file determines the number of grid points Mx My Mz Mbz and the dimensions of the computational box The user is warned when their command line options Mx My Mz Mbz are overrid den Generated on
14. aram Collects the parameters for the grid and computational domain 20 4 PISM a Parallel Ice Sheet Model Class Documenta tion 4 1 IceEISModel Class Reference This derived class does EISMINT II simplified geometry experiments Inherits IceModel Inherited by IceeRYANModel Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 2 IceGrid Class Reference 3 4 1 1 Detailed Description This derived class does EISMINT II simplified geometry experiments These experiments only involve the thermomechanically coupled shallow ice approx imation See A J Payne and ten others 200 Results from the EISMINT model inter comparison the effects of thermomechanical coupling J Glaciol 46 153 227 238 4 2 IceGrid Class Reference Describes the PISM grid and the distribution of data across processors Public Member Functions e PetscErrorCode createDA e PetscErrorCode rescale const PetscScalar Ix const PetscScalar ly const Petsc Scalar 1z e PetscErrorCode rescale const PetscScalar Ix const PetscScalar ly const Petsc Scalar 1z const PetscTruth truelyPeriodic 4 2 1 Detailed Description Describes the PISM grid and the distribution of data across processors This class creates and destroys the PETSc DAs distributed arrays which control how all PISM variables are distributed across multiple processors This class also contains the parameters which describe the PISM computation
15. dimensional horizontal velocities u and v Note that w gets update later by vert VelocityFromIncompressibility The three dimensional velocity field is needed for example so that the temperature equation can include advection Basal velocities also get updated Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 16 Here is where the flag doSuperpose controlled by option super is relevant If do Superpose is true then the result of the SIA computation already done is added to the result of SSA This procedure also computes the maximum horizontal speed in the SSA areas so that the CFL condition for the upwinding in massBalExplicitStep and only for SSA points can be computed 4 3 2 29 PetscErrorCode correctSigma protected At SSA points correct the previously computed volume strain heating 4 3 2 30 PetscErrorCode correctBasalFrictionalHeating protected At SSA points correct the previously computed basal frictional heating 4 3 2 31 PetscErrorCode saveUVBarForSSA const PetscTruth firstTime protected Save the values of vertically averaged horizontal velocity for the first guess in the SSA iteration 4 3 2 32 PetscErrorCode putSavedUVBarInUVBar protected For all SSA points put previous SSA velocities in vubar vvbar 4 3 2 33 PetscErrorCode temperatureAgeStep protected Manages the time stepping and parallel communication for
16. e velocity field is computed by vert VelocityFromIncompressibility 4 3 2 23 PetscErrorCode velocitySSA protected Compute the vertically averaged horizontal velocity from the shallow shelf approxi mation SSA This is the main procedure implementing the SSA The outer loop over index k is the nonlinear iteration In this loop the effective viscosity is computed by computeEffectiveViscosity and then the linear system is set up and solved This procedure creates a PETSC KSP it calls assembleSSAMatrix and assemble SSARhs to store the linear system in the KSP and calls the PETSc procedure KSP Solve to solve the linear system Solving the linear system is also a loop an iteration but it occurs inside KSPSolve This inner loop is controlled by PETSc but the user can set the option ksp_rtol in particular and that tolerance controls when the inner loop terminates The outer loop terminates when the effective viscosity is no longer changing much ac cording to the tolerance set by the option ssa_rtol The outer loop also terminates when a maximum number of iterations is exceeded In truth there is an outer outer loop over index 1 This one manages an attempt to over regularize the effective viscosity so that the nonlinear iteration the outer loop over k has a chance to converge 4 3 2 24 PetscErrorCode computeEffectiveViscosity Vec vNu 2 PetscReal ep silon protected virtual Compute the product
17. elocity field and the surface and basal mass balance The partial differential equation describing the conservation of mass in the map plane parallel to the geoid is OH SN gN DE S V q where E q UH In these equations H is the ice thickness M is the surface mass balance accumulation or ablation S is the basal mass balance e g basal melt and U is the vertically averaged horizontal velocity of the ice Note U u 0 in the notation used here The map plane flux of the ice q is defined by the above formula This procedure massBalExplicitStep uses this conservation of mass equation to up date the ice thickness This method is first order explicit in time The derivatives in V q are computed by centered finite difference methods In the case of the SIA the value of U is already stored on the staggered grid by velocitySIAStaggered and it is differenced in the obvious centered manner with averaging of the thickness onto the staggered grid In the case of SSA locations the V q term is computed by upwinding after expanding V q U VH V U H That is the mass conservation equation is regarded as an advection equation with source term OH p tU VH M 85S V U H The product of velocity and the gradient of thickness on the left is computed by first order upwinding Note that the CFL condition for this advection scheme is checked see determineTimeStep Note that if the point is flagged as MASK_FLOATING_OCEA
18. ional domain Note that the default choices made when constructing an instance of IceParam will be overridden by PISM runtime options by the input file if an input file is used and frequently by derived classes of IceModel Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen Index ageStep IceModel 18 assembleSSA Matrix IceModel 14 assembleSSARhs IceModel 15 basalVelocity IceModel 10 broadcastSS AVelocity IceModel 15 computeEffective Viscosity IceModel 13 computeMax3DVelocities IceModel 19 correctBasalFrictional Heating IceModel 16 correctSigma IceModel 16 createDA IceGrid 3 create Vecs IceModel 7 destroy Vecs IceModel 8 diagnosticRun IceModel 6 excess ToFromBasalMeltLayer IceModel 18 frictionalHeatingSIAStaggered IceModel 12 horizontal VelocitySIARegular IceModel 12 IceEISModel 2 IceGrid 3 IceGrid createDA 3 rescale 3 IceModel 4 IceModel ageStep 18 assembleSSAMatrix 14 assembleSSARhs 15 basal Velocity 10 broadcastSSAVelocity 15 computeEffectiveViscosity 13 computeMax3DVelocities 19 correctBasalFrictionalHeating 16 correctSigma 16 create Vecs 7 destroy Vecs 8 diagnosticRun 6 excessToFromBasalMeltLayer 18 frictionalHeatingSIAStaggered 12 horizontal VelocitySIARegular 12 initFromFile 7 initFromFile_netCDF 7 massBalExplicitStep 9 move VelocityToDAVectors 15 putSavedUVBarInUVBar 16 run
19. of the effective viscosity v and ice thickness H In PISM the product vH can be i constant ii can be computed with a constant ice hardness B temperature independent but with dependence of the viscosity on the strain rates or iii it can depend on the strain rates and have a vertically averaged ice hardness The flow law in ice stream and ice shelf regions must for now be a temperature dependent Glen law That is more general forms like Goldsby Kohlstedt are not yet inverted Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 14 The effective viscosity is bu 3N dudv 1 du dv Ox Oy Ox Oy 4 O0y Ox where in the temperature dependent case B v 2 i 1 n 2n B FIXME SOME INTEGRAL In the temperature dependent case the ice hardness is computed by the trapezoid rule 4 3 2 25 PetscErrorCode assembleSSAMatrix Vec vNu 2 Mat A protected Assemble the matrix left hand side for the numerical approximation of the SSA equa tions The SSA equations are in their clearest form aT where 7 j range over x y I is a depth integrated viscous stress tensor i e equation 2 6 in Schoof 2006 and following Morland 1987 and Tgp are the components of the basal shear stress Also f is the driving shear stress f pgH These equations determine velocity in a more or less elliptic equation manner Here H i
20. omputation There are two methods for computing the surface gradient The default is to transform the thickness to something more regular and differentiate that In particular as shown in Calvo et al 2002 for the flat bed and n 3 case if we define n pp 2nt2 n then 7 is more regular near the margin than H So the default method for computing the surface gradient is to compute n n Vh ETE 2 2 2 Vb recalling that h H b This method is only applied when 7 gt 0 at a given point otherwise Vh Vb We are computing this gradient by finite differences onto a staggered grid We do so by centered differences using roughly the same method for 7 and b that Mahaffy 1976 applies directly to the surface elevation h The optional method is to directly differentiate the surface elevation h by the Mahaffy 1976 method 4 3 2 18 PetscErrorCode velocitySIAStaggered bool faststep protected Compute the vertically averaged horizontal velocity according to the SIA See the comment for massBalExplicitStep before reading the rest of this comment Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 12 Note that one may write q UH DVh U H in shallow ice approximation SIA areas Here A is the surface elevation of the ice U is the basal sliding velocity and D is the diffusivity which is computed in this method At the end of this routine
21. ote that communication of ghosted values must occur between velocitySIAStaggered and this procedure for the averaging to work Only two dimensional regular grid velocities are updated here The full three dimensional velocity field is not updated here but instead in horizontal VelocitySIARegular and in vert VelocityFromIncompressibility 4 3 2 21 PetscErrorCode SigmaSIAToRegular protected Put the basal frictional heating and the volume strain heating onto the regular grid At the end of velocitySIAStaggered the basal frictional heating and the volume strain heating are available on the staggered grid This procedure averages them onto the regular grid Note that communication of ghosted values must occur between velocity SIAStaggered and this procedure for the averaging to work Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 13 4 3 2 22 PetscErrorCode horizontalVelocitySIARegular protected Update regular grid horizontal velocities u v at depth for SIA regions In the current scheme the procedure velocitySIAStaggered computes several scalar quantities at depth the details of which are too complicated to explain That is these quantities correspond to three dimensional arrays This procedure takes those quanti ties and computes the three dimensional arrays for the horizontal components u and v of the velocity field The vertical component w of th
22. pped when bootstrapping bif and bootstrapFromFile_netCDF or in those derived classes which can start with no input files e g IceCompModel and IceEISModel That is 2 5 is only done when starting from a saved model state 4 3 2 10 PetscErrorCode destroyVecs protected virtual De allocate all Vecs defined in IceModel Undoes the actions of create Vecs 4 3 2 11 PetscErrorCode updateSurfaceElevationAndMask protected Update the surface elevation and the flow type mask when the geometry has changed Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 9 This procedure should be called whenever necessary to maintain consistency of ge ometry For instance it should be called when either ice thickness or bed elevation change In particular we always want h H b to apply at grounded points and on the other hand we want the mask to reflect that the ice is floating if the floatation criterion applies at a point There is one difficult case When a point was floating and becomes grounded we gen erally do not know whether to mark it as MASK_SHEET so that the SIA applies or MASK_DRAGGING so that the SSA applies For now there is a vote by neighbors scheme among the grounded neighbors When the MASK_DRAGGING points have plastic till bases this is not an issue 4 3 2 12 PetscErrorCode massBalExplicitStep protected Update the thickness from the v
23. r the terms of the GNU General Public License as published by the Free Software Foundation either version 2 of the License or at your option any later version PISM is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PAR TICULAR PURPOSE See the GNU General Public License for more details You should have received a copy of the GNU General Public License along with PISM if not write to the Free Software Foundation Inc 51 Franklin St Fifth Floor Boston MA 02110 1301 USA Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 2 PISM a Parallel Ice Sheet Model Hierarchical Index 2 2 PISM a Parallel Ice Sheet Model Hierarchical In dex 2 1 PISM a Parallel Ice Sheet Model Class Hierarchy This inheritance list is sorted roughly but not completely alphabetically IceGrid 3 IceModel 4 IceEISModel 2 IceParam 20 3 PISM a Parallel Ice Sheet Model Class Index 3 1 PISM a Parallel Ice Sheet Model Class List Here are the classes structs unions and interfaces with brief descriptions IceEISModel This derived class does EISMINT II simplified geometry ex periments 2 IceGrid Describes the PISM grid and the distribution of data across pro cessors 3 IceModel The base class for PISM Contains all essential variables pa rameters and flags for modelling an ice sheet 4 IceP
24. ressFromHmelt virtual PetscScalar basal Velocity const PetscScalar x const PetscScalar y const PetscScalar H const PetscScalar T const PetscScalar alpha const PetscScalar mu PetscErrorCode writeMatlab Vars const char fname PetscErrorCode writeSS AsystemMatlab Vec vNu 2 PetscErrorCode surfaceGradientSIA PetscErrorCode velocitySIAStaggered bool faststep PetscErrorCode frictionalHeatingSIAStaggered PetscErrorCode velocities2DSIAToRegular PetscErrorCode SigmaSIAToRegular PetscErrorCode horizontal VelocitySIARegular PetscErrorCode velocitySSA virtual PetscErrorCode computeEffective Viscosity Vec vNu 2 PetscReal ep silon PetscErrorCode assembleSSAMatrix Vec vNu 2 Mat A PetscErrorCode assembleSSARhs bool surfGradInward Vec rhs PetscErrorCode move VelocityToDAVectors Vec x PetscErrorCode broadcastSSAVelocity PetscErrorCode correctSigma PetscErrorCode correctBasalFrictionalHeating PetscErrorCode saveUVBarForSSA const PetscTruth firstTime PetscErrorCode putSavedUVBarInUVBar PetscErrorCode temperatureAgeStep virtual PetscErrorCode temperatureStep PetscErrorCode ageStep PetscScalar CFLviol PetscErrorCode excessToFromBasalMeltLayer PetscScalar rho_c PetscScalar Z PetscScalar Texcess PetscScalar Hmelt PetscErrorCode vert VelocityFromIncompressibility PetscErrorCode computeMax3DVelocities PetscErrorCode update Viewers Static Protected Attributes
25. s the ice thickness and h is the elevation of the surface of the ice More specifically the SSA equations are o u v o u Ov h 2 fast ay ay P Gp ae FR OG o u Ov o Ou Ov Oh za ay ae a a tro Moh where u is the z component of the velocity and v is the y component of the velocity Note v is the vertically averaged effective viscosity of the ice For ice shelves T 0 MacAyeal et al 1996 For ice streams with a basal till modelled as a plastic material T 7 u u where u u v u u v cor and 7 is the yield stress of the till Schoof 2006 For ice streams with a basal till modelled as a linearly viscous material Tg Gu where is the basal drag friction parameter Hulbe amp MacAyeal 1999 Note that the basal shear stress appears on the left side of the above system We believe this is crucial because of its effect on the spectrum of the linear approximations of each stage The effect on spectrum is clearest in the linearly viscous till case i e Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 15 Hulbe amp MacAyeal 1999 but there seems to be an analogous effect in the plastic till case Schoof 2006 This method assembles the matrix for the left side of the SSA equations The numerical method is finite difference In particular FIXME explain f d approxs esp mixed derivatives 4
26. t a fraction of this melt water is transported to the base according to the scheme in excessToFromBasalMeltLayer Here is a more complete discussion and derivation Consider a column of a slowly flowing and heat conducting material as shown in the left side of the next figure The left side shows a general column of flowing and heat conduction material showing a small segment V The right side shows a more specific column of ice flowing and sliding over bedrock This is an Eulerian view so the material flows through a column which remains fixed and is notional The column is vertical We will assume when needed that it is rectangular in cross section with cross sectional area ArAy sliding at ice rock interface a bedrock Figure Left a general column of material Right ice over bedrock FIXME CONTINUE TO MINE egqns3D tex FOR MORE The application of the geothermal flux at the base of a column is a special case for which we give a finite difference argument This scheme follows the equation 2 114 in Morton and Mayers 2005 We have the boundary condition T where G t x y is the applied geothermal flux and it is applied at level z Bo in the bedrock which is the only case considered here We add a virtual lower grid point z 1 zo Az and we approximate the above boundary condition at z_0 by the centered difference T T 2Az G Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel
27. t we conceive of the computational domain as starting at the i 0 grid location and ending at the i Mx 1 grid location in particular This idea is not quite compatible with the periodic nature of the grid The upshot is that if one computes in a truely periodic way then the gap between the i Qandi Mx 1 grid points should also have width dx Thus we compute dx 2 x Lx Mx 4 3 IceModel Class Reference The base class for PISM Contains all essential variables parameters and flags for modelling an ice sheet Inherited by IceCompModel IceDragYieldModel IceEISModel IceExactSSAModel IceGRNModel IceHEINOModel IceROSSModel and ShelfModel Public Member Functions virtual PetscErrorCode run virtual PetscErrorCode diagnosticRun virtual PetscErrorCode setDefaults virtual PetscErrorCode setFromOptions PetscErrorCode velocity bool updateSIAVelocity AtDepth PetscErrorCode initFromFile const char PetscErrorCode writeFiles const char xdefaultbasename const PetscTruth forceFullDiagnostics PetscErrorCode initFromFile_netCDF const char fname Protected Member Functions e virtual PetscErrorCode create Vecs e virtual PetscErrorCode destroyVecs e PetscErrorCode updateSurfaceElevationAndMask e PetscErrorCode massBalExplicitStep Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 5 PetscErrorCode update YieldSt
28. the temperature and age equations Note that both the temperature equation and the age equation involve advection and have a CFL condition Morton amp Mayers 1994 By being slightly conservative we use the same CFL condition for both Bueler and others 2007 Exact solutions thermomechanically coupled J Glaciol We also report any CFL violations these can only occur when using the tempskip option 4 3 2 34 PetscErrorCode temperatureStep O protected virtual Takes a semi implicit time step for the temperature equation In summary the conservation of energy equation is dT T k Pe i T g TA where T t x y z is the temperature of the ice This equation is the shallow approx imation of the full three dimensional conservation of energy Note dT dt stands for Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 17 the material derivative so advection is included Here p is the density of ice c is its specific heat and k is its conductivity Also X is the volume strain heating In summary the numerical method is first order upwind for advection and centered differences with semi implicitness for the vertical conduction term Note that we work from the bottom of the column upward in building the system to solve in the semi implicit time stepping scheme Note that the excess energy above pressure melting is converted to melt water and tha
29. ty in SIA regions In SIA regions a basal sliding law of the form U up Vp CVh is allowed Here U is the horizontal velocity of the base of the ice the sliding velocity and h is the elevation of the ice surface This procedure returns the positive coefficient C in this relationship This coefficient can depend of the thickness the basal temperature and the horizontal location This procedure is virtual and can be replaced by any derived class The default version for IceModel here is location independent pressure melting temperature activated linear sliding Generated on Fri Oct 5 14 38 34 2007 for PISM a Parallel Ice Sheet Model by Doxygen 4 3 IceModel Class Reference 11 4 3 2 15 PetscErrorCode writeMatlabVars const char gt fname protected Write out selected variables in Matlab m format Writes out the independent variables year x and y Then writes out variables se lected with option mat v using single character names See Appendix C of the User s Manual Writes these to foo mif option mato foo is given 4 3 2 16 PetscErrorCode writeSSAsystemMatlab Vec vNu 2 protected Write out the linear system of equations for the last nonlinear iteration for SSA Writes out the matrix the right hand side and the solution vector in a Matlab readable format a m file 4 3 2 17 PetscErrorCode surfaceGradientSIA protected Compute the surface gradient in advance of the SIA velocity c
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PISM (a Parallel Ice Sheet Model) Reference Manual