Select Git revision
mo_functions.f90
Code owners
Assign users and groups as approvers for specific file changes. Learn more.
mo_functions.f90 20.51 KiB
!>
!! Module houses functions which have no home :(.
!!
!! Created because I wanted to calculate the freeboard separately and didn't know where to put it.
!!
!!
!! @author Philipp Griewank
!!
!! COPYRIGHT
!!
!! This file is part of SAMSIM.
!!
!! SAMSIM is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
!!
!! SAMSIM 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 PARTICULAR PURPOSE. See the GNU General Public License for more details.
!!
!! You should have received a copy of the GNU General Public License along with SAMSIM. If not, see <http://www.gnu.org/licenses/>.
!
!!
!!
!! @par Revision History
!! Ribbon cut by Philipp Griewank 2011-01-07
!!
!!
!!
!!
!!
!!
MODULE mo_functions
USE mo_parameters
IMPLICIT NONE
PUBLIC
CONTAINS
!>
!! Calculates the physical density for given S and T.
!!
!!
!!
!! Although the model treats Salinity as a massless tracer, sometimes it is necessary to determine the exact density for specific purposes.
!! First implemented to calculate simple turbulence between liquid layer and ocean.
!! Uses following simplification of Frank J. Millero and Alain Poisson 1981:
!! Density = density_0 +A*S+B*S**1.5
!!
!!
!! @par Revision History
!! Started by Philipp Griewank (2011-02-24)
FUNCTION func_density(T, S) RESULT (density)
REAL(wp), INTENT(in) :: T, S
REAL(wp) :: density
REAL(wp) :: A, B, density_0
density_0 = 999.842594_wp + 6.8_wp / 100._wp * T
A = 0.825_wp
B = -5.7_wp / 1000._wp
density = density_0 + A * S + B * MAX(S, 0._wp)**1.5_wp
END FUNCTION func_density
!>
!! Calculates the freeboard of the 1d ice column.
!!
!!
!!
!! The freeboard is calculated by first finding out which layer is at water level, and then finding out how deep the layer is submerged. For the correct freeboard the mass above water equals the buoyancy of the submerged part. Since the density of each layer is constant, step two can be calculated explicitly.
!! The freeboard is the distance from the top of the ice to the water level.
!! If snow pushes the ice underwater the freeboard becomes negative
!!
!! @par Revision History
!! Built to spill by Philipp Griewank (2011-01-07) \n
!! Negative freeboard included by Philipp Griewank (2011-01-09) \n
!! Patched bug by Philipp Griewank (2011-03-10) \n
!! Add freeboard_snow_flag calculation of snow mass, check the code for further explanations by Niels Fuchs, MPIMET (2017-03-91) \n
FUNCTION func_freeboard(N_active, Nlayer, psi_s, psi_g, m, thick, m_snow, freeboard_snow_flag) RESULT (freeboard)
INTEGER, INTENT(in) :: N_active, Nlayer, freeboard_snow_flag
REAL(wp), INTENT(IN), DIMENSION(Nlayer) :: psi_s, psi_g, m, thick
REAL(wp), INTENT(in) :: m_snow
REAL(wp) :: freeboard, snowmass !< Niels, 2017 add: snowmass
REAL(wp) :: test1, test2, test3
INTEGER :: k
!< Niels, 2017 add: if loop, important for lab studies with large snow thickness only on a small area of the ice
IF (freeboard_snow_flag==0) THEN
snowmass = m_snow
ELSE
snowmass = 0._wp
END IF
!step 0.5, checking if the freeboard is negative (mass_snow greater then buoyancy of ice)
test3 = SUM(psi_s(1:N_active) * thick(1:N_active)) * (rho_l - rho_s) + SUM(psi_g(1:N_active) * thick(1:N_active)) * rho_l
IF(snowmass>test3) THEN
!snow underwater
test2 = SUM(psi_s(1:N_active) * thick(1:N_active)) * (rho_l - rho_s) + SUM(psi_g(1:N_active) * &
& thick(1:N_active)) * rho_l
freeboard = test2 - snowmass
freeboard = freeboard / rho_l
ELSE
!snow above water
!Step 1, finding the layer___________________________________________________
test1 = 0._wp
test2 = 1._wp
k = 0
DO WHILE(test1<test2)
k = k + 1
test2 = SUM(psi_s(k + 1:N_active) * thick(k + 1:N_active)) * (rho_l - rho_s) &
& + SUM(psi_g(k + 1:N_active) * thick(k + 1:N_active)) * rho_l
test1 = SUM(m(1:k)) + snowmass
END DO
!Step 2, find out where in the layer the waterline is________________________
test1 = SUM(m(1:k - 1)) + snowmass
test2 = test2 !stays the same
freeboard = test2 - test1 + (rho_l - m(k) / thick(k)) * thick(k)
freeboard = freeboard / rho_l
freeboard = freeboard + SUM(thick(1:k - 1))
END IF
END FUNCTION func_freeboard
!>
!! Calculates the albedo.
!!
!!
!!
!! Calculates the albedo according to top conditions.
!! This is not a good albedo scheme! It is only a quick approach.
!! Non-continuous switching between wet and dry ice.
!! Linear change from wet ice to water.
!! Linear change from ice_dry snow for snow thinner than 30cm.
!!
!! psi_l(1)> 0.75 water
!! psi_l(1)> 0.6 linear change from wet ice to water
!! psi_l(1)> 0.2 wet ice
!! psi_l(1)< 0.2 -> dry ice
!! T_snow = 0 -> wet snow
!! T_snow < 0 -> dry snow
!!
!!
!!
!!
!! @par Revision History
!! Built to spill by Philipp Griewank (2011-02-12)
FUNCTION func_albedo(thick_snow, T_snow, psi_l, thick_min, albedo_flag) RESULT (albedo)
REAL(wp), INTENT(in) :: thick_snow, T_snow, psi_l, thick_min
INTEGER, INTENT(in) :: albedo_flag
REAL(wp) :: albedo
REAL(wp) :: ice_dry, ice_wet, snow_dry, snow_wet, water
ice_dry = 0.75
ice_wet = 0.6
snow_dry = 0.85
snow_wet = 0.75
water = 0.2
IF (thick_snow>thick_min) THEN
IF (T_snow<-0.01) THEN
albedo = snow_dry
ELSE
albedo = snow_wet
END IF
!snow depth approach
albedo = ice_dry + (albedo - ice_dry) * MIN(1._wp, thick_snow / 0.3_wp)
ELSE
IF (psi_l>0.9_wp) THEN
albedo = water
ELSE IF (psi_l>0.6_wp) THEN
albedo = ice_wet + (water - ice_wet) * ((psi_l - 0.6_wp) / 0.3_wp)
ELSE IF (psi_l>0.2_wp) THEN
albedo = ice_wet
ELSE
albedo = ice_dry
END IF
END IF
!Simple version
If (albedo_flag==1) then
IF (thick_snow>thick_min) THEN
IF (T_snow<-0.01) THEN
albedo = snow_dry
ELSE
albedo = snow_wet
END IF
ELSE
IF (psi_l<0.8) THEN
albedo = ice_dry
ELSE
albedo = water
END IF
END IF
END IF
END FUNCTION func_albedo
!>
!! Calculates the oxygen saturation as a function of salinity and temperature.
!!
!! Calculates the concentration of oxygen dissolved in freshwater and seawater in equilibrium with the atmosphere
!! The value should be umol/kg.
!! I switched to the solubility of nitrogen, oxygen and argon in water and sea wate from Weiss R.F. 1970 because I couldn't get the other one to work out
!! @par Revision History
!! Written by Dr. Philipp Griewank (2014-02-25)
FUNCTION func_sat_O2(T, S_bu) RESULT (sat_O2)
REAL(wp), INTENT(in) :: T, S_bu
REAL(wp) :: sat_O2, TT
TT = T + 273.16
sat_O2 = 1.42905_wp * EXP(-173.4292_wp + 24963.39_wp / TT + 143.3483 * LOG(TT / 100._wp) - 0.218492_wp * TT)
sat_O2 = sat_O2 * EXP(S_bu * (-0.033096_wp + 0.00014259_wp * TT - 0.0017_wp * TT**2 / 10000._wp))
sat_O2 = sat_O2 / 0.032
END FUNCTION func_sat_O2
!>
!! Calculates the freezing temperature.
!! Salt_flag determines if either ocean salt or NAcl is used.
!!
!! @par Revision History
!! Written to procrastinate by Philipp Griewank (2011-05-05)
FUNCTION func_T_freeze(S_bu, salt_flag) RESULT (T_freeze)
REAL(wp), INTENT(in) :: S_bu
INTEGER, INTENT(in) :: salt_flag
REAL(wp) :: T_freeze
IF (salt_flag==2) THEN
T_freeze = -0.0592_wp * S_bu - 9.37 * S_bu**2.0 - 5.33 * 10.0**(-7.0) * S_bu**3.0
ELSE IF (salt_flag==1) THEN
T_freeze = -0.0575_wp * S_bu + 1.710523 * 1e-3 * S_bu**1.5 - 2.154996 * 1e-4 * S_bu**2.0
END IF
END FUNCTION func_T_freeze
!>
!! Calculates the incoming shortwave and other fluxes according to p. 193-194 PhD Notz.
!!
!!
!!
!! Simplified version of the Untersteiner Fluxes.
!! Returns only two fluxes as a function of time.
!! Simplified Year, 12 months of 30 days.
!! fl_sw is set to zero for November till February
!! Returns fluxes for day with day zero being 1. Jan.
!! Depending on when the run starts the time should be modified when calling
!!
!!
!!
!! @par Revision History
!! Ripped from Dirk by Philipp Griewank (2011-02-13)
SUBROUTINE sub_notzflux(time, fl_sw, fl_rest)
REAL(wp), INTENT(in) :: time
REAL(wp) :: day
REAL(wp), INTENT(out) :: fl_sw, fl_rest
day = time / 86400._wp
day = day
DO WHILE (day>360)
day = day - 360
END DO
fl_sw = 314._wp * EXP(-0.5_wp * ((day - 164._wp) / 47.9)**2._wp)
fl_rest = 118._wp * EXP(-0.5_wp * ((day - 206._wp) / 53.1)**2._wp) + 179._wp
IF (day<60. .OR. day>300.) THEN
fl_sw = 0.0_wp
END IF
END SUBROUTINE sub_notzflux
SUBROUTINE sub_init_state(H_abs, S_abs, m, thick)
REAL(wp), DIMENSION(:), INTENT(inout) :: H_abs, S_abs, m, thick
OPEN(1234, file = 'input/H_abs.txt', status = 'old')
READ(1234, *)H_abs
OPEN(1234, file = 'input/S_abs.txt', status = 'old')
READ(1234, *)S_abs
OPEN(1234, file = 'input/m.txt', status = 'old')
READ(1234, *)m
OPEN(1234, file = 'input/thick.txt', status = 'old')
READ(1234, *)thick
END SUBROUTINE sub_init_state
SUBROUTINE sub_initial_input(H_abs, S_abs, thick, m, N_active, Nlayer)
INTEGER, INTENT(in) :: N_active, Nlayer
REAL(wp), DIMENSION(Nlayer), INTENT(inout) :: H_abs, S_abs, thick, m
OPEN(1234,file='input/H_abs.txt',status='old')
READ(1234,*)H_abs(1:N_active)
CLOSE(1234)
OPEN(1234,file='input/S_abs.txt',status='old')
READ(1234,*)S_abs(1:N_active)
CLOSE(1234)
OPEN(1234,file='input/thick.txt',status='old')
READ(1234,*)thick(1:N_active)
CLOSE(1234)
OPEN(1234,file='input/m.txt',status='old')
READ(1234,*)m(1:N_active)
CLOSE(1234)
END SUBROUTINE sub_initial_input
!>
!! Reads in boundary value data if any should be used
!!
!!
!!
!! @par Revision History
!! Added by Jakob Deutloff in 2021
SUBROUTINE sub_input(length_input, timestep_data, T_top_input, T2m_input, T_bottom_input, S_bu_bottom_input, &
& fl_q_bottom_input, time_input,fl_sw_input, fl_lw_input, fl_lat_input, fl_sen_input, precip_l_input, &
& precip_s_input, boundflux_flag, precip_flag)
INTEGER, INTENT(in) :: length_input, boundflux_flag, precip_flag
REAL(wp), INTENT(in) :: timestep_data
INTEGER :: k
REAL(wp), DIMENSION(:), allocatable, INTENT(out) :: T_top_input, T2m_input, T_bottom_input, S_bu_bottom_input, &
& fl_q_bottom_input, time_input, fl_sw_input, fl_lw_input, fl_lat_input, fl_sen_input, &
& precip_l_input, precip_s_input
ALLOCATE(T_top_input(Length_Input), time_input(Length_Input), T2m_input(Length_Input), &
& T_bottom_input(Length_Input), S_bu_bottom_input(Length_Input), &
& fl_q_bottom_input(Length_Input), fl_sw_input(Length_Input), fl_lw_input(Length_Input), &
& fl_lat_input(Length_Input), fl_sen_input(Length_Input), precip_l_input(Length_Input), &
& precip_s_input(Length_Input))
IF (boundflux_flag == 1) THEN
OPEN(1234, file = 'input/T_top.txt', status = 'old')
READ(1234, *)T_top_input
CLOSE(1234)
ELSE IF (boundflux_flag == 2) THEN
OPEN(1234, file = 'input/fl_lw.txt', status = 'old')
READ(1234, *)fl_lw_input
CLOSE(1234)
OPEN(1234, file = 'input/fl_sw.txt', status = 'old')
READ(1234, *)fl_sw_input
CLOSE(1234)
OPEN(1234, file = 'input/fl_lat.txt', status = 'old')
READ(1234, *)fl_lat_input
CLOSE(1234)
OPEN(1234, file = 'input/fl_sen.txt', status = 'old')
READ(1234, *)fl_sen_input
CLOSE(1234)
IF (precip_flag == 1) THEN
OPEN(1234, file = 'input/T2m.txt', status = 'old')
READ(1234, *)T2m_input
CLOSE(1234)
END IF
ELSE IF (boundflux_flag == 3) THEN
OPEN(1234, file = 'input/T_top.txt', status = 'old')
READ(1234, *)T_top_input
CLOSE(1234)
OPEN(1234, file = 'input/T2m.txt', status = 'old')
READ(1234, *)T2m_input
CLOSE(1234)
END IF
OPEN(1234, file = 'input/T_bottom.txt', status = 'old')
READ(1234, *)T_bottom_input
CLOSE(1234)
OPEN(1234, file = 'input/S_bu_bottom.txt', status = 'old')
READ(1234, *)S_bu_bottom_input
CLOSE(1234)
OPEN(1234, file = 'input/fl_q_bottom.txt', status = 'old')
READ(1234, *)fl_q_bottom_input
CLOSE(1234)
OPEN(1234, file = 'input/precip_l.txt', status = 'old')
READ(1234, *)precip_l_input
CLOSE(1234)
OPEN(1234, file = 'input/precip_s.txt', status = 'old')
READ(1234, *)precip_s_input
CLOSE(1234)
DO k = 1, Length_Input
time_input(k) = REAL(k - 1) * timestep_data
END DO
END SUBROUTINE sub_input
!>
!! Calculates salt and tracer mixing between lowest layer and underlying water.
!!
!!
!!Very simple turbulence assumption which mixes the lowest layer with the underlying water.
!!Based on assumption that there is a constant amount of turbulence A.
!!This turbulence is amplified when the lowest layer is denser then the ocean mixed layer.
!!And also dampened when the lowest layer is less dense then the mixed layer.
!!Assumption; turb=A*exp(B(density_layer-density_ocean))
!!A and B set in parameters.i
!!A = turb_A , B = turb_B
!!
!!
!!
!! @par Revision History
!! Moved from grotz by Philipp Griewank (2014-04-2)
SUBROUTINE sub_turb_flux(T_bottom, S_bu_bottom, T, S_abs, m, dt, N_bgc, bgc_bottom, bgc_abs)
REAL(wp), INTENT(in) :: T_bottom, S_bu_bottom, T, m, dt
INTEGER, INTENT(in) :: N_bgc
REAL(wp), INTENT(inout) :: S_abs
REAL(wp), INTENT(inout), DIMENSION(N_bgc), OPTIONAL :: bgc_abs
REAL(wp), INTENT(in), DIMENSION(N_bgc), OPTIONAL :: bgc_bottom
REAL(wp) :: turb !< mass flow between lowest layer and underlying water over the timestep
turb = turb_A * EXP(turb_B * (-func_density(T_bottom, S_bu_bottom) + func_density(T, S_abs / m))) * dt
S_abs = S_abs - turb * (S_abs / m - S_bu_bottom)
IF(PRESENT(bgc_bottom)) THEN
bgc_abs(:) = bgc_abs(:) - turb * (bgc_abs(:) / m - bgc_bottom(:))
END IF
END SUBROUTINE sub_turb_flux
!>
!! Calculates the thickness of the meltwater film.
!!
!!
!!
!! If the top ice layer is being melted (T_top>T_freeze) it is assumed that a thin meltwater film appears at the top.
!! The thickness of this film is determined by the amount of incoming heat and diffusive transport.
!! The incoming heat is an input (fl_q(1)) and the diffusive heat is (T(1)-T_freeze)/R.
!! See the thermodynamics section for R.
!! The thickness of the meltlayer is determined by dividing the heat intake of the meltwater film by the amount of latent heat needed to melt the solid fraction of the top layer.
!! If the solid fractions sinks below a given threshold (psi_s_top_min) a different approach is used.
!! The melt thickness is then calculated by assuming that the ice below the meltwater film has a solid fraction of psi_s_top_min.
!! Although the thickness can be reduced, variations of mass, salinity and enthalpy are calculated in the flushing subroutine.
!!
!!
!!
!! @par Revision History
!! Introduced by Philipp Griewank (2011-05-09)
SUBROUTINE sub_melt_thick(psi_l, psi_s, psi_g, T, T_freeze, T_top, fl_Q, thick_snow, dt, melt_thick, thick, thick_min)
REAL(wp), INTENT(in) :: psi_l, psi_s, psi_g, T, T_freeze, T_top, fl_Q, thick_snow, dt, thick_min
REAL(wp), INTENT(out) :: melt_thick
REAL(wp), INTENT(inout) :: thick
melt_thick = 0.0_wp
!Assumption Q flux from film to layer fl_mid = 2._wp*(psi_l(1)*k_l+psi_s(1)*k_s)/thick*(T_freeze-T(1)).
!The energy different between fl_Q(1) and fl_mid is the amount of energy that goes to melt the meltwater film.
!This only applies when the snow thickness is thin
IF (thick_snow<thick_min .AND. T_top>=T_freeze) THEN
melt_thick = -fl_Q - 2._wp * (psi_l * k_l + psi_s * k_s) / thick * (T_freeze - T)
melt_thick = melt_thick * dt / MAX((latent_heat * rho_s * psi_s), 0.000000000000001_wp)
melt_thick = MIN(psi_l * thick, melt_thick)
END IF
!The other way that top meltwater is formed is when the solid fraction of the top layer is less then
!a prescribed value (psi_s_top_min).
!The melt layer is assigned so that the rest of the layer achieves a solid fraction that equals
!the prescribed (psi_s_top_min)
!When snow is present meltwater floods the snow layer..
!At the moment this melt_thick assignment has higher priority then the T_top method.
IF (psi_s<psi_s_top_min) THEN
melt_thick = thick * (1._wp - psi_s / psi_s_top_min)
END IF
!Making sure that air percentage is kept to gas_snow_ice2
IF(melt_thick>0.0_wp .AND. psi_g>gas_snow_ice2) THEN
IF(melt_thick>(psi_g - gas_snow_ice2) * thick) THEN
melt_thick = melt_thick - (psi_g - gas_snow_ice2) * thick
thick = thick * (1._wp - (psi_g - gas_snow_ice2))
ELSE
thick = thick - melt_thick
melt_thick = 0._wp
END IF
END IF
END SUBROUTINE sub_melt_thick
!>
!! Calculates how the meltwater film interacts with snow.
!!
!!
!! Is activated when a thin snow layer (thinner then thick_min) is on top of meltwater.
!! The snow is flooded and turned into ice.
!!
!!
!!
!!
!! @par Revision History
!! Put together by Philipp Griewank (2011-10-17)
SUBROUTINE sub_melt_snow(melt_thick, thick, thick_snow, H_abs, H_abs_snow, m, m_snow, psi_g_snow)
REAL(wp), INTENT(inout) :: melt_thick, thick, thick_snow, H_abs, H_abs_snow, m, m_snow, psi_g_snow
REAL(wp) :: shift
shift = 1._wp / MAX(psi_g_snow, 0.01_wp) * melt_thick
IF (shift>=thick_snow) THEN
melt_thick = melt_thick - thick_snow * psi_g_snow
H_abs = H_abs + H_abs_snow
m = m + m_snow
thick = thick + (1._wp - psi_g_snow) * thick_snow
thick_snow = 0.0_wp
m_snow = 0.0_wp
H_abs_snow = 0.0_wp
ELSE
H_abs = H_abs + shift / thick_snow * H_abs_snow
H_abs_snow = H_abs_snow - shift / thick_snow * H_abs_snow
m = m + shift / thick_snow * m_snow
m_snow = m_snow - shift / thick_snow * m_snow
thick = thick + shift - melt_thick
thick_snow = thick_snow - shift
melt_thick = 0.0_wp
END IF
END SUBROUTINE sub_melt_snow
end module mo_functions