**Solver Fortran File:**`SurfaceBoundaryEnthalpy.f90`

**Solver Name:**`SurfEnthBoundarySolver`

**Required Output Variable(s):**`Surf Enth`

**Optional Output Variable(s):**`Mass Balance`

,`Densi`

,`Firn`

,`Melting`

,`Refreeze`

,`Accu`

,`Rad_Fact`

,`Rain`

,`PotRad`

**Required Input Variable(s):**`Depth`

and`SurfGrad`

from the FlowDepth Solver**Input Data:**Daily air temperature timeserie**Optional Input Data:**Daily precipitation timeserie

For vertically structured 3D mesh only. Works in serial and parallel.

SurfEnthBoundarySolver is a pseudo-solver which compute surface mass balance and Dirichlet surface boundary condition for the Enthalpy solver. It takes into account firn heating processes by solving vertical melt-water percolation and refreezing.

The solver uses the provided air temperature (and precipitation) daily record to compute the associated mean surface characteristic of the glacier over the time period covered by the provided data time-serie. It can output the following variables:

`Mass Balance`

(m w.eq./yr): Mean surface mass balance`Surf Enth`

(J/kg) : Enthalpy value bellow active layer. Can be use as a Dirichlet condition in the Enthalpy Solver`Densi`

(kg/m3): Density field in 3D`Firn`

(m w. eq.) : Firn thickness`Melting`

(m w.eq./yr) : Surface melting`Refreeze`

(m w.eq./yr) : Amount of refreezing (superimposed ice)`Accu`

(m w.eq./yr) : Snow accumulation`Rad_fact`

(m w.eq./(W/m2)) : Melting factor for radiation`Rain`

(m w.eq./yr) : Amount of rain`PotRad`

(W/m2) : Potential solar radiation

The mass balance model is based on a degree day model that takes into account potential solar radiation. Mean Enthalpy at 10m-depth (bellow active layer), is computed by solving the heat equation on a 1D vertical profile forced by a mean annual cycle of air temperature and precipitation determined from the data. This is done for each surface nodes using a Crank-Nicholson scheme on a 6 cm resolution grid at daily time-step. It takes into account of seasonal change of the density profile and allow percolation of water only where density is lower than 800 kg/m3. More details about the model can be found in:

Gilbert, A., Sinisalo, A., Gurung, T. R., Fujita, K., Maharjan, S. B., Sherpa, T. C., & Fukuda, T. (2020). The influence of water percolation through crevasses on the thermal regime of a Himalayan mountain glacier. The Cryosphere, 14(4), 1273–1288. https://doi.org/10.5194/tc-14-1273-2020

The parameters are set in the constant section of the sif file :

Constants rho_surf = real 350.0 ! Snow surface density rho_ice = real 917.0 ! Ice density rho_w = real 1000.0 ! Water density Sr = real 0.005 ! Residual water saturation in Snow/Firn T_ref_enthalpy = real 200.0 ! Use to compute Surf Enth (see Enthalpy solver) L_heat = real 334000.0 ! Latent heat of fusion AirTemperatureFile = File "YourTempFile.dat" ! Contain daily temperature data PrecipFile = File "YourPrecipFile.dat" ! Contain daily precipitation data (optional) Precip = real 0.300 !Mean annual precipitation if PrecipFile not provided TempCorrec= real -0.12 !Possibility of shifting temperature to get steady state mass balance for example (optional) PrecipCorrec = real 1.0 !Possibility of adding a correcting factor on precipitation if PrecipFile provided (optional) GradTemp = real 0.0065 !Air temperature Lapse Rate (K m^-1) GradPrecip= real 0.001 !Precipitation Lapse Rate (% m^-1) z_temp = real 5310.0 !Elevation of temperature measurement from AirTemperatureFile (m) z_precip = real 5310.0 !Elevation of Precipitation measurement (m) RadFact_ice = real 0.0000925 ! Melting factor for ice from radiation RadFact_snow = real $0.0000925/2.0 ! Melting factor for snow from radiation Deg_jour = real 0.0114 ! Melting factor from air temperature seuil_precip = real 2.0 !Rain/Snow air temperature threshold (degree C) seuil_fonte = real 0.0 !Melting air temperature threshold (degree C) firn_param = real 30.0 ! Firn densification factor (yr) super_ice = real 0.15 ! Superimposed ice factor Latitude = real 28.82 !Latitude (degree) to compute Potential Solar Radiation !Possibility to export 1D profile simulation at one node of coordinate (X_output1D,Y_output1D) (optional) X_output1D = real x_coordinate Y_output1D = real y_coordinate End

The solver needs output from the FlowDepth Solver :

Solver 1 Equation = "Flowdepth" Procedure = File "ElmerIceSolvers" "FlowDepthSolver" Variable = String "Depth" Variable DOFs = 1 Linear System Solver = "Direct" ! this sets the direction ! -1 is negative z-direction (upside down) ! +1 is positive (downside up) Gradient = Real -1.0E00 Calc Free Surface = Logical True Freesurf Name = String "Surf" End

The solver is called with the following:

Solver 2 Equation = SurfBoundary Variable = Surf Enth Variable DOFs = 1 procedure = "ElmerIceSolvers" "SurfEnthBoundarySolver" ! The following variables declaration are optional: Exported Variable 1 = String "Mass Balance" Exported Variable 1 DOFs = 1 Exported Variable 2 = String "Densi" Exported Variable 2 DOFs = 1 Exported Variable 3 = String "Firn" Exported Variable 3 DOFs = 1 Exported Variable 4 = String "Melting" Exported Variable 4 DOFs = 1 Exported Variable 5 = String "Refreeze" Exported Variable 5 DOFs = 1 Exported Variable 6 = String "Accu" Exported Variable 6 DOFs = 1 Exported Variable 7 = String "Rad_Fact" Exported Variable 7 DOFs = 1 Exported Variable 8 = String "Rain" Exported Variable 8 DOFs = 1 Exported Variable 9 = String "PotRad" Exported Variable 9 DOFs = 1 End

Boundary Condition to setup Dirichlet condition for the Enthalpy Solver:

! Upper Surface Boundary Condition 2 Target Boundaries = 2 Depth = real 0.0 Enthalpy_h = Equals Surf Enth End

An example solving for the enthalpy within the Rika Samba Glacier using the SurfEnthBoundarySolver can be found in `[ELMER_TRUNK]/elmerice/examples/Test_SurfaceBoundaryEnth`

.

Gilbert, A., Sinisalo, A., Gurung, T. R., Fujita, K., Maharjan, S. B., Sherpa, T. C., & Fukuda, T. (2020). The influence of water percolation through crevasses on the thermal regime of a Himalayan mountain glacier. The Cryosphere, 14(4), 1273–1288. https://doi.org/10.5194/tc-14-1273-2020