1 | MODULE icbthm |
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2 | !!====================================================================== |
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3 | !! *** MODULE icbthm *** |
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4 | !! Icebergs: thermodynamics routines for icebergs |
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5 | !!====================================================================== |
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6 | !! History : 3.3.1 ! 2010-01 (Martin&Adcroft) Original code |
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7 | !! - ! 2011-03 (Madec) Part conversion to NEMO form |
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8 | !! - ! Removal of mapping from another grid |
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9 | !! - ! 2011-04 (Alderson) Split into separate modules |
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10 | !! - ! 2011-05 (Alderson) Use tmask instead of tmask_i |
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11 | !!---------------------------------------------------------------------- |
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12 | !!---------------------------------------------------------------------- |
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13 | !! icb_thm : initialise |
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14 | !! reference for equations - M = Martin + Adcroft, OM 34, 2010 |
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15 | !!---------------------------------------------------------------------- |
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16 | USE par_oce ! NEMO parameters |
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17 | USE dom_oce ! NEMO domain |
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18 | USE in_out_manager ! NEMO IO routines, numout in particular |
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19 | USE lib_mpp ! NEMO MPI routines, ctl_stop in particular |
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20 | USE phycst ! NEMO physical constants |
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21 | USE sbc_oce |
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22 | USE lib_fortran, ONLY : DDPDD |
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23 | |
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24 | USE icb_oce ! define iceberg arrays |
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25 | USE icbutl ! iceberg utility routines |
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26 | USE icbdia ! iceberg budget routines |
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27 | |
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28 | IMPLICIT NONE |
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29 | PRIVATE |
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30 | |
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31 | PUBLIC icb_thm ! routine called in icbstp.F90 module |
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32 | |
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33 | !!---------------------------------------------------------------------- |
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34 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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35 | !! $Id$ |
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36 | !! Software governed by the CeCILL license (see ./LICENSE) |
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37 | !!---------------------------------------------------------------------- |
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38 | CONTAINS |
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39 | |
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40 | SUBROUTINE icb_thm( kt ) |
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41 | !!---------------------------------------------------------------------- |
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42 | !! *** ROUTINE icb_thm *** |
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43 | !! |
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44 | !! ** Purpose : compute the iceberg thermodynamics. |
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45 | !! |
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46 | !! ** Method : - See Martin & Adcroft, Ocean Modelling 34, 2010 |
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47 | !!---------------------------------------------------------------------- |
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48 | INTEGER, INTENT(in) :: kt ! timestep number, just passed to icb_utl_print_berg |
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49 | ! |
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50 | INTEGER :: ii, ij, jk, ikb |
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51 | REAL(wp) :: zM, zT, zW, zL, zSST, zVol, zLn, zWn, zTn, znVol, zIC, zDn, zD, zvb, zub, ztb |
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52 | REAL(wp) :: zMv, zMe, zMb, zmelt, zdvo, zdvob, zdva, zdM, zSs, zdMe, zdMb, zdMv |
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53 | REAL(wp) :: zMnew, zMnew1, zMnew2, zheat_hcflux, zheat_latent, z1_12 |
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54 | REAL(wp) :: zMbits, znMbits, zdMbitsE, zdMbitsM, zLbits, zAbits, zMbb |
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55 | REAL(wp) :: zxi, zyj, zff, z1_rday, z1_e1e2, zdt, z1_dt, z1_dt_e1e2, zdepw |
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56 | REAL(wp), DIMENSION(jpk) :: ztoce, zuoce, zvoce, ze3t, zzMv |
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57 | TYPE(iceberg), POINTER :: this, next |
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58 | TYPE(point) , POINTER :: pt |
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59 | ! |
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60 | COMPLEX(dp), DIMENSION(jpi,jpj) :: cicb_melt, cicb_hflx |
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61 | !!---------------------------------------------------------------------- |
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62 | ! |
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63 | !! initialiaze cicb_melt and cicb_heat |
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64 | cicb_melt = CMPLX( 0.e0, 0.e0, dp ) |
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65 | cicb_hflx = CMPLX( 0.e0, 0.e0, dp ) |
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66 | ! |
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67 | z1_rday = 1._wp / rday |
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68 | z1_12 = 1._wp / 12._wp |
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69 | zdt = berg_dt |
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70 | z1_dt = 1._wp / zdt |
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71 | ! |
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72 | ! we're either going to ignore berg fresh water melt flux and associated heat |
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73 | ! or we pass it into the ocean, so at this point we set them both to zero, |
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74 | ! accumulate the contributions to them from each iceberg in the while loop following |
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75 | ! and then pass them (or not) to the ocean |
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76 | ! |
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77 | berg_grid%floating_melt(:,:) = 0._wp |
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78 | ! calving_hflx re-used here as temporary workspace for the heat flux associated with melting |
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79 | berg_grid%calving_hflx(:,:) = 0._wp |
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80 | ! |
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81 | this => first_berg |
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82 | DO WHILE( ASSOCIATED(this) ) |
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83 | ! |
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84 | pt => this%current_point |
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85 | nknberg = this%number(1) |
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86 | |
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87 | CALL icb_utl_interp( pt%xi, pt%yj, & ! position |
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88 | & pssu=pt%ssu, pua=pt%ua, & ! oce/atm velocities |
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89 | & pssv=pt%ssv, pva=pt%va, & ! oce/atm velocities |
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90 | & psst=pt%sst, pcn=pt%cn ) |
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91 | |
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92 | IF ( nn_sample_rate > 0 .AND. MOD(kt-1,nn_sample_rate) == 0 ) THEN |
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93 | CALL icb_utl_interp( pt%xi, pt%yj, pe1=pt%e1, pe2=pt%e2, & |
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94 | & pui=pt%ui, pssh_i=pt%ssh_x, & |
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95 | & pvi=pt%vi, pssh_j=pt%ssh_y, & |
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96 | & phi=pt%hi, & |
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97 | & plat=pt%lat, plon=pt%lon ) |
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98 | END IF |
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99 | ! |
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100 | zSST = pt%sst |
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101 | zIC = MIN( 1._wp, pt%cn + rn_sicn_shift ) ! Shift sea-ice concentration !!gm ??? |
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102 | zM = pt%mass |
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103 | zT = pt%thickness ! total thickness |
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104 | zD = rho_berg_1_oce * zT ! draught (keel depth) |
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105 | ! F = zT - D ! freeboard |
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106 | zW = pt%width |
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107 | zL = pt%length |
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108 | zxi = pt%xi ! position in (i,j) referential |
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109 | zyj = pt%yj |
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110 | ii = INT( zxi + 0.5 ) ! T-cell of the berg |
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111 | ii = mi1( ii ) |
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112 | ij = INT( zyj + 0.5 ) |
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113 | ij = mj1( ij ) |
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114 | zVol = zT * zW * zL |
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115 | |
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116 | ! Environment |
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117 | ! default sst, ssu and ssv |
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118 | ! ln_M2016: use temp, u and v profile |
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119 | IF ( ln_M2016 ) THEN |
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120 | |
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121 | ! load t, u, v and e3 profile at icb position |
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122 | CALL icb_utl_interp( pt%xi, pt%yj, ptoce=ztoce, puoce=zuoce, pvoce=zvoce, pe3t=ze3t ) |
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123 | |
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124 | !compute bottom level |
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125 | CALL icb_utl_getkb( pt%kb, ze3t, zD ) |
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126 | |
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127 | ikb = MIN(pt%kb,mbkt(ii,ij)) |
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128 | ztb = ztoce(ikb) ! basal temperature |
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129 | zub = zuoce(ikb) |
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130 | zvb = zvoce(ikb) |
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131 | ELSE |
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132 | ztb = pt%sst |
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133 | zub = pt%ssu |
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134 | zvb = pt%ssv |
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135 | END IF |
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136 | |
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137 | zdvob = SQRT( (pt%uvel-zub)**2 + (pt%vvel-zvb)**2 ) ! relative basal velocity |
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138 | zdva = SQRT( (pt%ua -pt%ssu)**2 + (pt%va -pt%ssv)**2 ) ! relative wind |
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139 | zSs = 1.5_wp * SQRT( zdva ) + 0.1_wp * zdva ! Sea state (eqn M.A9) |
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140 | ! |
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141 | ! Melt rates in m/s (i.e. division by rday) |
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142 | IF ( ln_M2016 ) THEN |
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143 | ! Buoyant convection at sides (eqn M.A10) but averaging along all the iceberg draft |
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144 | zzMv(:) = MAX( 7.62d-3*ztoce(:)+1.29d-3*(ztoce(:)**2), 0._wp ) * z1_rday |
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145 | CALL icb_utl_zavg(zMv, zzMv, ze3t, zD, ikb ) |
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146 | ELSE |
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147 | zMv = MAX( 7.62d-3*zSST+1.29d-3*(zSST**2), 0._wp ) * z1_rday |
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148 | END IF |
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149 | |
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150 | ! Basal turbulent melting (eqn M.A7 ) but using the basal temperature |
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151 | zMb = MAX( 0.58_wp*(zdvob**0.8_wp)*(ztb+4.0_wp)/(zL**0.2_wp) , 0._wp ) * z1_rday |
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152 | |
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153 | ! Wave erosion (eqn M.A8 ) |
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154 | zMe = MAX( z1_12*(zSST+2.)*zSs*(1._wp+COS(rpi*(zIC**3))) , 0._wp ) * z1_rday |
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155 | |
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156 | IF( ln_operator_splitting ) THEN ! Operator split update of volume/mass |
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157 | zTn = MAX( zT - zMb*zdt , 0._wp ) ! new total thickness (m) |
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158 | znVol = zTn * zW * zL ! new volume (m^3) |
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159 | zMnew1 = ( znVol / zVol ) * zM ! new mass (kg) |
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160 | zdMb = zM - zMnew1 ! mass lost to basal melting (>0) (kg) |
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161 | ! |
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162 | zLn = MAX( zL - zMv*zdt , 0._wp ) ! new length (m) |
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163 | zWn = MAX( zW - zMv*zdt , 0._wp ) ! new width (m) |
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164 | znVol = zTn * zWn * zLn ! new volume (m^3) |
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165 | zMnew2 = ( znVol / zVol ) * zM ! new mass (kg) |
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166 | zdMv = zMnew1 - zMnew2 ! mass lost to buoyant convection (>0) (kg) |
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167 | ! |
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168 | zLn = MAX( zLn - zMe*zdt , 0._wp ) ! new length (m) |
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169 | zWn = MAX( zWn - zMe*zdt , 0._wp ) ! new width (m) |
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170 | znVol = zTn * zWn * zLn ! new volume (m^3) |
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171 | zMnew = ( znVol / zVol ) * zM ! new mass (kg) |
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172 | zdMe = zMnew2 - zMnew ! mass lost to erosion (>0) (kg) |
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173 | zdM = zM - zMnew ! mass lost to all erosion and melting (>0) (kg) |
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174 | ! |
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175 | ELSE ! Update dimensions of berg |
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176 | zLn = MAX( zL -(zMv+zMe)*zdt ,0._wp ) ! (m) |
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177 | zWn = MAX( zW -(zMv+zMe)*zdt ,0._wp ) ! (m) |
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178 | zTn = MAX( zT - zMb *zdt ,0._wp ) ! (m) |
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179 | ! Update volume and mass of berg |
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180 | znVol = zTn*zWn*zLn ! (m^3) |
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181 | zMnew = (znVol/zVol)*zM ! (kg) |
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182 | zdM = zM - zMnew ! (kg) |
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183 | zdMb = (zM/zVol) * (zW* zL ) *zMb*zdt ! approx. mass loss to basal melting (kg) |
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184 | zdMe = (zM/zVol) * (zT*(zW+zL)) *zMe*zdt ! approx. mass lost to erosion (kg) |
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185 | zdMv = (zM/zVol) * (zT*(zW+zL)) *zMv*zdt ! approx. mass loss to buoyant convection (kg) |
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186 | ENDIF |
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187 | |
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188 | IF( rn_bits_erosion_fraction > 0._wp ) THEN ! Bergy bits |
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189 | ! |
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190 | zMbits = pt%mass_of_bits ! mass of bergy bits (kg) |
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191 | zdMbitsE = rn_bits_erosion_fraction * zdMe ! change in mass of bits (kg) |
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192 | znMbits = zMbits + zdMbitsE ! add new bergy bits to mass (kg) |
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193 | zLbits = MIN( zL, zW, zT, 40._wp ) ! assume bergy bits are smallest dimension or 40 meters |
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194 | zAbits = ( zMbits / rn_rho_bergs ) / zLbits ! Effective bottom area (assuming T=Lbits) |
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195 | zMbb = MAX( 0.58_wp*(zdvo**0.8_wp)*(zSST+2._wp) / & |
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196 | & ( zLbits**0.2_wp ) , 0._wp ) * z1_rday ! Basal turbulent melting (for bits) |
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197 | zMbb = rn_rho_bergs * zAbits * zMbb ! in kg/s |
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198 | zdMbitsM = MIN( zMbb*zdt , znMbits ) ! bergy bits mass lost to melting (kg) |
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199 | znMbits = znMbits-zdMbitsM ! remove mass lost to bergy bits melt |
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200 | IF( zMnew == 0._wp ) THEN ! if parent berg has completely melted then |
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201 | zdMbitsM = zdMbitsM + znMbits ! instantly melt all the bergy bits |
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202 | znMbits = 0._wp |
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203 | ENDIF |
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204 | ELSE ! No bergy bits |
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205 | zAbits = 0._wp |
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206 | zdMbitsE = 0._wp |
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207 | zdMbitsM = 0._wp |
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208 | znMbits = pt%mass_of_bits ! retain previous value incase non-zero |
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209 | ENDIF |
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210 | |
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211 | ! use tmask rather than tmask_i when dealing with icebergs |
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212 | IF( tmask(ii,ij,1) /= 0._wp ) THEN ! Add melting to the grid and field diagnostics |
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213 | z1_e1e2 = r1_e1e2t(ii,ij) * this%mass_scaling |
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214 | z1_dt_e1e2 = z1_dt * z1_e1e2 |
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215 | ! |
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216 | ! iceberg melt |
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217 | !! the use of DDPDD function for the cumulative sum is needed for reproducibility |
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218 | zmelt = ( zdM - ( zdMbitsE - zdMbitsM ) ) * z1_dt ! kg/s |
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219 | CALL DDPDD( CMPLX( zmelt * z1_e1e2, 0.e0, dp ), cicb_melt(ii,ij) ) |
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220 | ! |
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221 | ! iceberg heat flux |
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222 | !! the use of DDPDD function for the cumulative sum is needed for reproducibility |
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223 | !! NB. The src_calving_hflx field is currently hardwired to zero in icb_stp, which means that the |
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224 | !! heat density of the icebergs is zero and the heat content flux to the ocean from iceberg |
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225 | !! melting is always zero. Leaving the term in the code until such a time as this is fixed. DS. |
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226 | zheat_hcflux = zmelt * pt%heat_density ! heat content flux : kg/s x J/kg = J/s |
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227 | zheat_latent = - zmelt * rLfus ! latent heat flux: kg/s x J/kg = J/s |
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228 | CALL DDPDD( CMPLX( ( zheat_hcflux + zheat_latent ) * z1_e1e2, 0.e0, dp ), cicb_hflx(ii,ij) ) |
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229 | ! |
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230 | ! diagnostics |
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231 | CALL icb_dia_melt( ii, ij, zMnew, zheat_hcflux, zheat_latent, this%mass_scaling, & |
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232 | & zdM, zdMbitsE, zdMbitsM, zdMb, zdMe, & |
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233 | & zdMv, z1_dt_e1e2 ) |
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234 | ELSE |
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235 | WRITE(numout,*) 'icb_thm: berg ',this%number(:),' appears to have grounded at ',narea,ii,ij |
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236 | CALL icb_utl_print_berg( this, kt ) |
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237 | WRITE(numout,*) 'msk=',tmask(ii,ij,1), e1e2t(ii,ij) |
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238 | CALL ctl_stop('icb_thm', 'berg appears to have grounded!') |
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239 | ENDIF |
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240 | |
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241 | ! Rolling |
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242 | zDn = rho_berg_1_oce * zTn ! draught (keel depth) |
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243 | IF( zDn > 0._wp .AND. MAX(zWn,zLn) < SQRT( 0.92*(zDn**2) + 58.32*zDn ) ) THEN |
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244 | zT = zTn |
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245 | zTn = zWn |
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246 | zWn = zT |
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247 | ENDIF |
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248 | |
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249 | ! Store the new state of iceberg (with L>W) |
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250 | pt%mass = zMnew |
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251 | pt%mass_of_bits = znMbits |
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252 | pt%thickness = zTn |
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253 | pt%width = MIN( zWn , zLn ) |
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254 | pt%length = MAX( zWn , zLn ) |
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255 | |
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256 | next=>this%next |
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257 | |
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258 | !!gm add a test to avoid over melting ? |
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259 | !!pm I agree, over melting could break conservation (more melt than calving) |
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260 | |
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261 | IF( zMnew <= 0._wp ) THEN ! Delete the berg if completely melted |
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262 | CALL icb_utl_delete( first_berg, this ) |
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263 | ! |
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264 | ELSE ! Diagnose mass distribution on grid |
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265 | z1_e1e2 = r1_e1e2t(ii,ij) * this%mass_scaling |
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266 | CALL icb_dia_size( ii, ij, zWn, zLn, zAbits, & |
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267 | & this%mass_scaling, zMnew, znMbits, z1_e1e2 ) |
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268 | ENDIF |
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269 | ! |
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270 | this=>next |
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271 | ! |
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272 | END DO |
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273 | ! |
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274 | berg_grid%floating_melt = REAL(cicb_melt,dp) ! kg/m2/s |
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275 | berg_grid%calving_hflx = REAL(cicb_hflx,dp) |
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276 | ! |
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277 | ! now use melt and associated heat flux in ocean (or not) |
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278 | ! |
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279 | IF(.NOT. ln_passive_mode ) THEN |
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280 | emp (:,:) = emp (:,:) - berg_grid%floating_melt(:,:) |
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281 | qns (:,:) = qns (:,:) + berg_grid%calving_hflx (:,:) |
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282 | ENDIF |
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283 | ! |
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284 | END SUBROUTINE icb_thm |
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285 | |
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286 | !!====================================================================== |
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287 | END MODULE icbthm |
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