1 | MODULE bdylib |
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2 | !!====================================================================== |
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3 | !! *** MODULE bdylib *** |
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4 | !! Unstructured Open Boundary Cond. : Library module of generic boundary algorithms. |
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5 | !!====================================================================== |
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6 | !! History : 3.6 ! 2013 (D. Storkey) original code |
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7 | !! 4.0 ! 2014 (T. Lovato) Generalize OBC structure |
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8 | !!---------------------------------------------------------------------- |
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9 | !!---------------------------------------------------------------------- |
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10 | !! bdy_orlanski_2d |
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11 | !! bdy_orlanski_3d |
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12 | !!---------------------------------------------------------------------- |
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13 | USE oce ! ocean dynamics and tracers |
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14 | USE dom_oce ! ocean space and time domain |
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15 | USE bdy_oce ! ocean open boundary conditions |
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16 | USE phycst ! physical constants |
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17 | USE bdyini |
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18 | ! |
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19 | USE in_out_manager ! |
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20 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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21 | USE lib_mpp, ONLY: ctl_stop |
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22 | |
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23 | IMPLICIT NONE |
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24 | PRIVATE |
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25 | |
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26 | PUBLIC bdy_frs, bdy_spe, bdy_nmn, bdy_orl |
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27 | PUBLIC bdy_orlanski_2d |
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28 | PUBLIC bdy_orlanski_3d |
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29 | |
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30 | !!---------------------------------------------------------------------- |
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31 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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32 | !! $Id$ |
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33 | !! Software governed by the CeCILL license (see ./LICENSE) |
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34 | !!---------------------------------------------------------------------- |
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35 | CONTAINS |
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36 | |
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37 | SUBROUTINE bdy_frs( idx, phia, dta ) |
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38 | !!---------------------------------------------------------------------- |
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39 | !! *** SUBROUTINE bdy_frs *** |
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40 | !! |
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41 | !! ** Purpose : Apply the Flow Relaxation Scheme for tracers at open boundaries. |
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42 | !! |
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43 | !! Reference : Engedahl H., 1995, Tellus, 365-382. |
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44 | !!---------------------------------------------------------------------- |
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45 | TYPE(OBC_INDEX), INTENT(in) :: idx ! OBC indices |
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46 | REAL(wp), DIMENSION(:,:), POINTER, INTENT(in) :: dta ! OBC external data |
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47 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: phia ! tracer trend |
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48 | !! |
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49 | REAL(wp) :: zwgt ! boundary weight |
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50 | INTEGER :: ib, ik, igrd ! dummy loop indices |
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51 | INTEGER :: ii, ij ! 2D addresses |
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52 | !!---------------------------------------------------------------------- |
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53 | ! |
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54 | igrd = 1 ! Everything is at T-points here |
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55 | DO ib = 1, idx%nblen(igrd) |
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56 | DO ik = 1, jpkm1 |
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57 | ii = idx%nbi(ib,igrd) |
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58 | ij = idx%nbj(ib,igrd) |
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59 | zwgt = idx%nbw(ib,igrd) |
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60 | phia(ii,ij,ik) = ( phia(ii,ij,ik) + zwgt * (dta(ib,ik) - phia(ii,ij,ik) ) ) * tmask(ii,ij,ik) |
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61 | END DO |
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62 | END DO |
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63 | ! |
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64 | END SUBROUTINE bdy_frs |
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65 | |
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66 | |
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67 | SUBROUTINE bdy_spe( idx, phia, dta ) |
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68 | !!---------------------------------------------------------------------- |
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69 | !! *** SUBROUTINE bdy_spe *** |
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70 | !! |
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71 | !! ** Purpose : Apply a specified value for tracers at open boundaries. |
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72 | !! |
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73 | !!---------------------------------------------------------------------- |
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74 | TYPE(OBC_INDEX), INTENT(in) :: idx ! OBC indices |
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75 | REAL(wp), DIMENSION(:,:), POINTER, INTENT(in) :: dta ! OBC external data |
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76 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: phia ! tracer trend |
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77 | !! |
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78 | INTEGER :: ib, ik, igrd ! dummy loop indices |
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79 | INTEGER :: ii, ij ! 2D addresses |
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80 | !!---------------------------------------------------------------------- |
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81 | ! |
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82 | igrd = 1 ! Everything is at T-points here |
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83 | DO ib = 1, idx%nblenrim(igrd) |
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84 | ii = idx%nbi(ib,igrd) |
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85 | ij = idx%nbj(ib,igrd) |
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86 | DO ik = 1, jpkm1 |
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87 | phia(ii,ij,ik) = dta(ib,ik) * tmask(ii,ij,ik) |
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88 | END DO |
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89 | END DO |
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90 | ! |
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91 | END SUBROUTINE bdy_spe |
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92 | |
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93 | |
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94 | SUBROUTINE bdy_orl( idx, phib, phia, dta, lrim0, ll_npo ) |
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95 | !!---------------------------------------------------------------------- |
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96 | !! *** SUBROUTINE bdy_orl *** |
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97 | !! |
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98 | !! ** Purpose : Apply Orlanski radiation for tracers at open boundaries. |
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99 | !! This is a wrapper routine for bdy_orlanski_3d below |
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100 | !! |
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101 | !!---------------------------------------------------------------------- |
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102 | TYPE(OBC_INDEX), INTENT(in ) :: idx ! OBC indices |
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103 | REAL(wp), DIMENSION(:,:), POINTER, INTENT(in ) :: dta ! OBC external data |
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104 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: phib ! before tracer field |
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105 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: phia ! tracer trend |
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106 | LOGICAL , INTENT(in ) :: lrim0 ! indicate if rim 0 is treated |
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107 | LOGICAL , INTENT(in ) :: ll_npo ! switch for NPO version |
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108 | !! |
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109 | INTEGER :: igrd ! grid index |
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110 | !!---------------------------------------------------------------------- |
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111 | ! |
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112 | igrd = 1 ! Everything is at T-points here |
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113 | ! |
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114 | CALL bdy_orlanski_3d( idx, igrd, phib(:,:,:), phia(:,:,:), dta, lrim0, ll_npo ) |
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115 | ! |
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116 | END SUBROUTINE bdy_orl |
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117 | |
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118 | |
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119 | SUBROUTINE bdy_orlanski_2d( idx, igrd, phib, phia, phi_ext, lrim0, ll_npo ) |
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120 | !!---------------------------------------------------------------------- |
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121 | !! *** SUBROUTINE bdy_orlanski_2d *** |
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122 | !! |
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123 | !! - Apply Orlanski radiation condition adaptively to 2D fields: |
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124 | !! - radiation plus weak nudging at outflow points |
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125 | !! - no radiation and strong nudging at inflow points |
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126 | !! |
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127 | !! |
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128 | !! References: Marchesiello, McWilliams and Shchepetkin, Ocean Modelling vol. 3 (2001) |
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129 | !!---------------------------------------------------------------------- |
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130 | TYPE(OBC_INDEX), INTENT(in ) :: idx ! BDY indices |
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131 | INTEGER , INTENT(in ) :: igrd ! grid index |
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132 | REAL(wp), DIMENSION(:,:), INTENT(in ) :: phib ! model before 2D field |
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133 | REAL(wp), DIMENSION(:,:), INTENT(inout) :: phia ! model after 2D field (to be updated) |
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134 | REAL(wp), DIMENSION(: ), POINTER, INTENT(in ) :: phi_ext ! external forcing data |
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135 | LOGICAL , INTENT(in ) :: lrim0 ! indicate if rim 0 is treated |
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136 | LOGICAL , INTENT(in ) :: ll_npo ! switch for NPO version |
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137 | ! |
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138 | INTEGER :: jb ! dummy loop indices |
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139 | INTEGER :: ii, ij, iibm1, iibm2, ijbm1, ijbm2 ! 2D addresses |
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140 | INTEGER :: iijm1, iijp1, ijjm1, ijjp1 ! 2D addresses |
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141 | INTEGER :: iibm1jp1, iibm1jm1, ijbm1jp1, ijbm1jm1 ! 2D addresses |
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142 | INTEGER :: ii_offset, ij_offset ! offsets for mask indices |
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143 | INTEGER :: flagu, flagv ! short cuts |
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144 | INTEGER :: ibeg, iend ! length of rim to be treated (rim 0 or rim 1 or both) |
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145 | REAL(wp) :: zmask_x, zmask_y1, zmask_y2 |
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146 | REAL(wp) :: zex1, zex2, zey, zey1, zey2 |
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147 | REAL(wp) :: zdt, zdx, zdy, znor2, zrx, zry ! intermediate calculations |
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148 | REAL(wp) :: zout, zwgt, zdy_centred |
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149 | REAL(wp) :: zdy_1, zdy_2, zsign_ups |
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150 | REAL(wp), PARAMETER :: zepsilon = 1.e-30 ! local small value |
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151 | REAL(wp), POINTER, DIMENSION(:,:) :: zmask ! land/sea mask for field |
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152 | REAL(wp), POINTER, DIMENSION(:,:) :: zmask_xdif ! land/sea mask for x-derivatives |
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153 | REAL(wp), POINTER, DIMENSION(:,:) :: zmask_ydif ! land/sea mask for y-derivatives |
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154 | REAL(wp), POINTER, DIMENSION(:,:) :: pe_xdif ! scale factors for x-derivatives |
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155 | REAL(wp), POINTER, DIMENSION(:,:) :: pe_ydif ! scale factors for y-derivatives |
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156 | !!---------------------------------------------------------------------- |
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157 | ! |
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158 | ! ----------------------------------! |
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159 | ! Orlanski boundary conditions :! |
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160 | ! ----------------------------------! |
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161 | |
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162 | SELECT CASE(igrd) |
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163 | CASE(1) |
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164 | zmask => tmask(:,:,1) |
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165 | zmask_xdif => umask(:,:,1) |
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166 | zmask_ydif => vmask(:,:,1) |
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167 | pe_xdif => e1u(:,:) |
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168 | pe_ydif => e2v(:,:) |
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169 | ii_offset = 0 |
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170 | ij_offset = 0 |
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171 | CASE(2) |
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172 | zmask => umask(:,:,1) |
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173 | zmask_xdif => tmask(:,:,1) |
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174 | zmask_ydif => fmask(:,:,1) |
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175 | pe_xdif => e1t(:,:) |
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176 | pe_ydif => e2f(:,:) |
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177 | ii_offset = 1 |
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178 | ij_offset = 0 |
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179 | CASE(3) |
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180 | zmask => vmask(:,:,1) |
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181 | zmask_xdif => fmask(:,:,1) |
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182 | zmask_ydif => tmask(:,:,1) |
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183 | pe_xdif => e1f(:,:) |
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184 | pe_ydif => e2t(:,:) |
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185 | ii_offset = 0 |
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186 | ij_offset = 1 |
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187 | CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for igrd in bdy_orlanksi_2d' ) |
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188 | END SELECT |
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189 | ! |
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190 | IF( lrim0 ) THEN ; ibeg = 1 ; iend = idx%nblenrim0(igrd) ! rim 0 |
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191 | ELSE ; ibeg = idx%nblenrim0(igrd)+1 ; iend = idx%nblenrim(igrd) ! rim 1 |
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192 | ENDIF |
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193 | ! |
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194 | DO jb = ibeg, iend |
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195 | ii = idx%nbi(jb,igrd) |
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196 | ij = idx%nbj(jb,igrd) |
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197 | IF( ii == 1 .OR. ii == jpi .OR. ij == 1 .OR. ij == jpj ) CYCLE |
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198 | flagu = int( idx%flagu(jb,igrd) ) |
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199 | flagv = int( idx%flagv(jb,igrd) ) |
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200 | ! |
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201 | ! Calculate positions of b-1 and b-2 points for this rim point |
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202 | ! also (b-1,j-1) and (b-1,j+1) points |
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203 | iibm1 = ii + flagu ; iibm2 = ii + 2*flagu |
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204 | ijbm1 = ij + flagv ; ijbm2 = ij + 2*flagv |
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205 | ! |
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206 | iijm1 = ii - abs(flagv) ; iijp1 = ii + abs(flagv) |
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207 | ijjm1 = ij - abs(flagu) ; ijjp1 = ij + abs(flagu) |
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208 | ! |
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209 | iibm1jm1 = ii + flagu - abs(flagv) ; iibm1jp1 = ii + flagu + abs(flagv) |
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210 | ijbm1jm1 = ij + flagv - abs(flagu) ; ijbm1jp1 = ij + flagv + abs(flagu) |
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211 | ! |
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212 | ! Calculate scale factors for calculation of spatial derivatives. |
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213 | zex1 = ( abs(iibm1-iibm2) * pe_xdif(iibm1 +ii_offset,ijbm1 ) & |
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214 | & + abs(ijbm1-ijbm2) * pe_ydif(iibm1 ,ijbm1 +ij_offset) ) |
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215 | zex2 = ( abs(iibm1-iibm2) * pe_xdif(iibm2 +ii_offset,ijbm2 ) & |
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216 | & + abs(ijbm1-ijbm2) * pe_ydif(iibm2 ,ijbm2 +ij_offset) ) |
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217 | zey1 = ( (iibm1-iibm1jm1) * pe_xdif(iibm1jm1+ii_offset,ijbm1jm1 ) & |
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218 | & + (ijbm1-ijbm1jm1) * pe_ydif(iibm1jm1 ,ijbm1jm1+ij_offset) ) |
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219 | zey2 = ( (iibm1jp1-iibm1) * pe_xdif(iibm1 +ii_offset,ijbm1 ) & |
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220 | & + (ijbm1jp1-ijbm1) * pe_ydif(iibm1 ,ijbm1 +ij_offset) ) |
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221 | ! make sure scale factors are nonzero |
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222 | if( zey1 .lt. rsmall ) zey1 = zey2 |
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223 | if( zey2 .lt. rsmall ) zey2 = zey1 |
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224 | zex1 = max(zex1,rsmall); zex2 = max(zex2,rsmall) |
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225 | zey1 = max(zey1,rsmall); zey2 = max(zey2,rsmall); |
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226 | ! |
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227 | ! Calculate masks for calculation of spatial derivatives. |
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228 | zmask_x = ( abs(iibm1-iibm2) * zmask_xdif(iibm2 +ii_offset,ijbm2 ) & |
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229 | & + abs(ijbm1-ijbm2) * zmask_ydif(iibm2 ,ijbm2 +ij_offset) ) |
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230 | zmask_y1 = ( (iibm1-iibm1jm1) * zmask_xdif(iibm1jm1+ii_offset,ijbm1jm1 ) & |
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231 | & + (ijbm1-ijbm1jm1) * zmask_ydif(iibm1jm1 ,ijbm1jm1+ij_offset) ) |
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232 | zmask_y2 = ( (iibm1jp1-iibm1) * zmask_xdif(iibm1 +ii_offset,ijbm1 ) & |
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233 | & + (ijbm1jp1-ijbm1) * zmask_ydif(iibm1 ,ijbm1 +ij_offset) ) |
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234 | |
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235 | ! Calculation of terms required for both versions of the scheme. |
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236 | ! Mask derivatives to ensure correct land boundary conditions for each variable. |
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237 | ! Centred derivative is calculated as average of "left" and "right" derivatives for |
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238 | ! this reason. |
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239 | ! Note no rn_Dt factor in expression for zdt because it cancels in the expressions for |
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240 | ! zrx and zry. |
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241 | zdt = phia(iibm1 ,ijbm1 ) - phib(iibm1 ,ijbm1 ) |
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242 | zdx = ( ( phia(iibm1 ,ijbm1 ) - phia(iibm2 ,ijbm2 ) ) / zex2 ) * zmask_x |
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243 | zdy_1 = ( ( phib(iibm1 ,ijbm1 ) - phib(iibm1jm1,ijbm1jm1) ) / zey1 ) * zmask_y1 |
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244 | zdy_2 = ( ( phib(iibm1jp1,ijbm1jp1) - phib(iibm1 ,ijbm1 ) ) / zey2 ) * zmask_y2 |
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245 | zdy_centred = 0.5 * ( zdy_1 + zdy_2 ) |
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246 | !!$ zdy_centred = phib(iibm1jp1,ijbm1jp1) - phib(iibm1jm1,ijbm1jm1) |
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247 | ! upstream differencing for tangential derivatives |
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248 | zsign_ups = sign( 1.0_wp, zdt * zdy_centred ) |
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249 | zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) |
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250 | zdy = zsign_ups * zdy_1 + (1. - zsign_ups) * zdy_2 |
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251 | znor2 = zdx * zdx + zdy * zdy |
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252 | znor2 = max(znor2,zepsilon) |
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253 | ! |
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254 | zrx = zdt * zdx / ( zex1 * znor2 ) |
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255 | !!$ zrx = min(zrx,2.0_wp) |
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256 | zout = sign( 1.0_wp, zrx ) |
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257 | zout = 0.5*( zout + abs(zout) ) |
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258 | zwgt = 2.*rn_Dt*( (1.-zout) * idx%nbd(jb,igrd) + zout * idx%nbdout(jb,igrd) ) |
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259 | ! only apply radiation on outflow points |
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260 | if( ll_npo ) then !! NPO version !! |
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261 | phia(ii,ij) = (1.-zout) * ( phib(ii,ij) + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) & |
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262 | & + zout * ( phib(ii,ij) + zrx*phia(iibm1,ijbm1) & |
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263 | & + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) / ( 1. + zrx ) |
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264 | else !! full oblique radiation !! |
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265 | zsign_ups = sign( 1.0_wp, zdt * zdy ) |
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266 | zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) |
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267 | zey = zsign_ups * zey1 + (1.-zsign_ups) * zey2 |
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268 | zry = zdt * zdy / ( zey * znor2 ) |
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269 | phia(ii,ij) = (1.-zout) * ( phib(ii,ij) + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) & |
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270 | & + zout * ( phib(ii,ij) + zrx*phia(iibm1,ijbm1) & |
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271 | & - zsign_ups * zry * ( phib(ii ,ij ) - phib(iijm1,ijjm1 ) ) & |
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272 | & - (1.-zsign_ups) * zry * ( phib(iijp1,ijjp1) - phib(ii ,ij ) ) & |
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273 | & + zwgt * ( phi_ext(jb) - phib(ii,ij) ) ) / ( 1. + zrx ) |
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274 | endif |
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275 | phia(ii,ij) = phia(ii,ij) * zmask(ii,ij) |
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276 | END DO |
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277 | ! |
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278 | END SUBROUTINE bdy_orlanski_2d |
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279 | |
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280 | |
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281 | SUBROUTINE bdy_orlanski_3d( idx, igrd, phib, phia, phi_ext, lrim0, ll_npo ) |
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282 | !!---------------------------------------------------------------------- |
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283 | !! *** SUBROUTINE bdy_orlanski_3d *** |
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284 | !! |
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285 | !! - Apply Orlanski radiation condition adaptively to 3D fields: |
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286 | !! - radiation plus weak nudging at outflow points |
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287 | !! - no radiation and strong nudging at inflow points |
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288 | !! |
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289 | !! |
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290 | !! References: Marchesiello, McWilliams and Shchepetkin, Ocean Modelling vol. 3 (2001) |
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291 | !!---------------------------------------------------------------------- |
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292 | TYPE(OBC_INDEX), INTENT(in ) :: idx ! BDY indices |
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293 | INTEGER , INTENT(in ) :: igrd ! grid index |
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294 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: phib ! model before 3D field |
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295 | REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: phia ! model after 3D field (to be updated) |
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296 | REAL(wp), DIMENSION(:,: ), POINTER, INTENT(in ) :: phi_ext ! external forcing data |
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297 | LOGICAL , INTENT(in ) :: lrim0 ! indicate if rim 0 is treated |
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298 | LOGICAL , INTENT(in ) :: ll_npo ! switch for NPO version |
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299 | ! |
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300 | INTEGER :: jb, jk ! dummy loop indices |
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301 | INTEGER :: ii, ij, iibm1, iibm2, ijbm1, ijbm2 ! 2D addresses |
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302 | INTEGER :: iijm1, iijp1, ijjm1, ijjp1 ! 2D addresses |
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303 | INTEGER :: iibm1jp1, iibm1jm1, ijbm1jp1, ijbm1jm1 ! 2D addresses |
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304 | INTEGER :: ii_offset, ij_offset ! offsets for mask indices |
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305 | INTEGER :: flagu, flagv ! short cuts |
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306 | INTEGER :: ibeg, iend ! length of rim to be treated (rim 0 or rim 1 or both) |
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307 | REAL(wp) :: zmask_x, zmask_y1, zmask_y2 |
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308 | REAL(wp) :: zex1, zex2, zey, zey1, zey2 |
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309 | REAL(wp) :: zdt, zdx, zdy, znor2, zrx, zry ! intermediate calculations |
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310 | REAL(wp) :: zout, zwgt, zdy_centred |
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311 | REAL(wp) :: zdy_1, zdy_2, zsign_ups |
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312 | REAL(wp), PARAMETER :: zepsilon = 1.e-30 ! local small value |
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313 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zmask ! land/sea mask for field |
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314 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zmask_xdif ! land/sea mask for x-derivatives |
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315 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zmask_ydif ! land/sea mask for y-derivatives |
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316 | REAL(wp), POINTER, DIMENSION(:,:) :: pe_xdif ! scale factors for x-derivatives |
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317 | REAL(wp), POINTER, DIMENSION(:,:) :: pe_ydif ! scale factors for y-derivatives |
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318 | !!---------------------------------------------------------------------- |
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319 | ! |
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320 | ! ----------------------------------! |
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321 | ! Orlanski boundary conditions :! |
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322 | ! ----------------------------------! |
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323 | ! |
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324 | SELECT CASE(igrd) |
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325 | CASE(1) |
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326 | zmask => tmask(:,:,:) |
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327 | zmask_xdif => umask(:,:,:) |
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328 | zmask_ydif => vmask(:,:,:) |
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329 | pe_xdif => e1u(:,:) |
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330 | pe_ydif => e2v(:,:) |
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331 | ii_offset = 0 |
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332 | ij_offset = 0 |
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333 | CASE(2) |
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334 | zmask => umask(:,:,:) |
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335 | zmask_xdif => tmask(:,:,:) |
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336 | zmask_ydif => fmask(:,:,:) |
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337 | pe_xdif => e1t(:,:) |
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338 | pe_ydif => e2f(:,:) |
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339 | ii_offset = 1 |
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340 | ij_offset = 0 |
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341 | CASE(3) |
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342 | zmask => vmask(:,:,:) |
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343 | zmask_xdif => fmask(:,:,:) |
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344 | zmask_ydif => tmask(:,:,:) |
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345 | pe_xdif => e1f(:,:) |
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346 | pe_ydif => e2t(:,:) |
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347 | ii_offset = 0 |
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348 | ij_offset = 1 |
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349 | CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for igrd in bdy_orlanksi_2d' ) |
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350 | END SELECT |
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351 | ! |
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352 | IF( lrim0 ) THEN ; ibeg = 1 ; iend = idx%nblenrim0(igrd) ! rim 0 |
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353 | ELSE ; ibeg = idx%nblenrim0(igrd)+1 ; iend = idx%nblenrim(igrd) ! rim 1 |
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354 | ENDIF |
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355 | ! |
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356 | DO jk = 1, jpk |
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357 | ! |
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358 | DO jb = ibeg, iend |
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359 | ii = idx%nbi(jb,igrd) |
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360 | ij = idx%nbj(jb,igrd) |
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361 | IF( ii == 1 .OR. ii == jpi .OR. ij == 1 .OR. ij == jpj ) CYCLE |
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362 | flagu = int( idx%flagu(jb,igrd) ) |
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363 | flagv = int( idx%flagv(jb,igrd) ) |
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364 | ! |
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365 | ! calculate positions of b-1 and b-2 points for this rim point |
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366 | ! also (b-1,j-1) and (b-1,j+1) points |
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367 | iibm1 = ii + flagu ; iibm2 = ii + 2*flagu |
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368 | ijbm1 = ij + flagv ; ijbm2 = ij + 2*flagv |
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369 | ! |
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370 | iijm1 = ii - abs(flagv) ; iijp1 = ii + abs(flagv) |
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371 | ijjm1 = ij - abs(flagu) ; ijjp1 = ij + abs(flagu) |
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372 | ! |
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373 | iibm1jm1 = ii + flagu - abs(flagv) ; iibm1jp1 = ii + flagu + abs(flagv) |
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374 | ijbm1jm1 = ij + flagv - abs(flagu) ; ijbm1jp1 = ij + flagv + abs(flagu) |
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375 | ! |
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376 | ! Calculate scale factors for calculation of spatial derivatives. |
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377 | zex1 = ( abs(iibm1-iibm2) * pe_xdif(iibm1 +ii_offset,ijbm1 ) & |
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378 | & + abs(ijbm1-ijbm2) * pe_ydif(iibm1 ,ijbm1+ij_offset ) ) |
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379 | zex2 = ( abs(iibm1-iibm2) * pe_xdif(iibm2 +ii_offset,ijbm2 ) & |
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380 | & + abs(ijbm1-ijbm2) * pe_ydif(iibm2 ,ijbm2+ij_offset ) ) |
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381 | zey1 = ( (iibm1-iibm1jm1) * pe_xdif(iibm1jm1+ii_offset,ijbm1jm1 ) & |
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382 | & + (ijbm1-ijbm1jm1) * pe_ydif(iibm1jm1 ,ijbm1jm1+ij_offset) ) |
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383 | zey2 = ( (iibm1jp1-iibm1) * pe_xdif(iibm1 +ii_offset,ijbm1 ) & |
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384 | & + (ijbm1jp1-ijbm1) * pe_ydif(iibm1 ,ijbm1+ij_offset ) ) |
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385 | ! make sure scale factors are nonzero |
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386 | if( zey1 .lt. rsmall ) zey1 = zey2 |
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387 | if( zey2 .lt. rsmall ) zey2 = zey1 |
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388 | zex1 = max(zex1,rsmall); zex2 = max(zex2,rsmall); |
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389 | zey1 = max(zey1,rsmall); zey2 = max(zey2,rsmall); |
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390 | ! |
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391 | ! Calculate masks for calculation of spatial derivatives. |
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392 | zmask_x = ( abs(iibm1-iibm2) * zmask_xdif(iibm2 +ii_offset,ijbm2 ,jk) & |
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393 | & + abs(ijbm1-ijbm2) * zmask_ydif(iibm2 ,ijbm2 +ij_offset,jk) ) |
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394 | zmask_y1 = ( (iibm1-iibm1jm1) * zmask_xdif(iibm1jm1+ii_offset,ijbm1jm1 ,jk) & |
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395 | & + (ijbm1-ijbm1jm1) * zmask_ydif(iibm1jm1 ,ijbm1jm1+ij_offset,jk) ) |
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396 | zmask_y2 = ( (iibm1jp1-iibm1) * zmask_xdif(iibm1 +ii_offset,ijbm1 ,jk) & |
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397 | & + (ijbm1jp1-ijbm1) * zmask_ydif(iibm1 ,ijbm1 +ij_offset,jk) ) |
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398 | ! |
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399 | ! Calculate normal (zrx) and tangential (zry) components of radiation velocities. |
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400 | ! Mask derivatives to ensure correct land boundary conditions for each variable. |
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401 | ! Centred derivative is calculated as average of "left" and "right" derivatives for |
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402 | ! this reason. |
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403 | zdt = phia(iibm1 ,ijbm1 ,jk) - phib(iibm1 ,ijbm1 ,jk) |
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404 | zdx = ( ( phia(iibm1 ,ijbm1 ,jk) - phia(iibm2 ,ijbm2 ,jk) ) / zex2 ) * zmask_x |
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405 | zdy_1 = ( ( phib(iibm1 ,ijbm1 ,jk) - phib(iibm1jm1,ijbm1jm1,jk) ) / zey1 ) * zmask_y1 |
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406 | zdy_2 = ( ( phib(iibm1jp1,ijbm1jp1,jk) - phib(iibm1 ,ijbm1 ,jk) ) / zey2 ) * zmask_y2 |
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407 | zdy_centred = 0.5 * ( zdy_1 + zdy_2 ) |
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408 | !!$ zdy_centred = phib(iibm1jp1,ijbm1jp1,jk) - phib(iibm1jm1,ijbm1jm1,jk) |
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409 | ! upstream differencing for tangential derivatives |
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410 | zsign_ups = sign( 1.0_wp, zdt * zdy_centred ) |
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411 | zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) |
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412 | zdy = zsign_ups * zdy_1 + (1. - zsign_ups) * zdy_2 |
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413 | znor2 = zdx * zdx + zdy * zdy |
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414 | znor2 = max(znor2,zepsilon) |
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415 | ! |
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416 | ! update boundary value: |
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417 | zrx = zdt * zdx / ( zex1 * znor2 ) |
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418 | !!$ zrx = min(zrx,2.0_wp) |
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419 | zout = sign( 1.0_wp, zrx ) |
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420 | zout = 0.5*( zout + abs(zout) ) |
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421 | zwgt = 2.*rn_Dt*( (1.-zout) * idx%nbd(jb,igrd) + zout * idx%nbdout(jb,igrd) ) |
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422 | ! only apply radiation on outflow points |
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423 | if( ll_npo ) then !! NPO version !! |
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424 | phia(ii,ij,jk) = (1.-zout) * ( phib(ii,ij,jk) + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) & |
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425 | & + zout * ( phib(ii,ij,jk) + zrx*phia(iibm1,ijbm1,jk) & |
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426 | & + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) / ( 1. + zrx ) |
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427 | else !! full oblique radiation !! |
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428 | zsign_ups = sign( 1.0_wp, zdt * zdy ) |
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429 | zsign_ups = 0.5*( zsign_ups + abs(zsign_ups) ) |
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430 | zey = zsign_ups * zey1 + (1.-zsign_ups) * zey2 |
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431 | zry = zdt * zdy / ( zey * znor2 ) |
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432 | phia(ii,ij,jk) = (1.-zout) * ( phib(ii,ij,jk) + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) & |
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433 | & + zout * ( phib(ii,ij,jk) + zrx*phia(iibm1,ijbm1,jk) & |
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434 | & - zsign_ups * zry * ( phib(ii ,ij ,jk) - phib(iijm1,ijjm1,jk) ) & |
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435 | & - (1.-zsign_ups) * zry * ( phib(iijp1,ijjp1,jk) - phib(ii ,ij ,jk) ) & |
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436 | & + zwgt * ( phi_ext(jb,jk) - phib(ii,ij,jk) ) ) / ( 1. + zrx ) |
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437 | endif |
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438 | phia(ii,ij,jk) = phia(ii,ij,jk) * zmask(ii,ij,jk) |
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439 | END DO |
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440 | ! |
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441 | END DO |
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442 | ! |
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443 | END SUBROUTINE bdy_orlanski_3d |
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444 | |
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445 | SUBROUTINE bdy_nmn( idx, igrd, phia, lrim0 ) |
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446 | !!---------------------------------------------------------------------- |
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447 | !! *** SUBROUTINE bdy_nmn *** |
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448 | !! |
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449 | !! ** Purpose : Duplicate the value at open boundaries, zero gradient. |
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450 | !! |
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451 | !! |
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452 | !! ** Method : - take the average of free ocean neighbours |
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453 | !! |
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454 | !! ___ ! |_____| ! ___| ! __|x o ! |_ _| ! | |
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455 | !! __|x ! x ! x o ! o ! |_| ! |x o |
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456 | !! o ! o ! o ! ! o x o ! |x_x_ |
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457 | !! ! o |
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458 | !!---------------------------------------------------------------------- |
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459 | INTEGER, INTENT(in ) :: igrd ! grid index |
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460 | REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: phia ! model after 3D field (to be updated), must be masked |
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461 | TYPE(OBC_INDEX), INTENT(in ) :: idx ! OBC indices |
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462 | LOGICAL , INTENT(in ) :: lrim0 ! indicate if rim 0 is treated |
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463 | !! |
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464 | REAL(wp) :: zweight |
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465 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zmask ! land/sea mask for field |
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466 | INTEGER :: ib, ik ! dummy loop indices |
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467 | INTEGER :: ii, ij ! 2D addresses |
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468 | INTEGER :: ipkm1 ! size of phia third dimension minus 1 |
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469 | INTEGER :: ibeg, iend ! length of rim to be treated (rim 0 or rim 1 or both) |
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470 | INTEGER :: ii1, ii2, ii3, ij1, ij2, ij3, itreat |
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471 | !!---------------------------------------------------------------------- |
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472 | ! |
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473 | ipkm1 = MAX( SIZE(phia,3) - 1, 1 ) |
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474 | ! |
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475 | SELECT CASE(igrd) |
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476 | CASE(1) ; zmask => tmask(:,:,:) |
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477 | CASE(2) ; zmask => umask(:,:,:) |
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478 | CASE(3) ; zmask => vmask(:,:,:) |
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479 | CASE DEFAULT ; CALL ctl_stop( 'unrecognised value for igrd in bdy_nmn' ) |
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480 | END SELECT |
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481 | ! |
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482 | IF( lrim0 ) THEN ; ibeg = 1 ; iend = idx%nblenrim0(igrd) ! rim 0 |
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483 | ELSE ; ibeg = idx%nblenrim0(igrd)+1 ; iend = idx%nblenrim(igrd) ! rim 1 |
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484 | ENDIF |
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485 | ! |
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486 | DO ib = ibeg, iend |
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487 | ii = idx%nbi(ib,igrd) |
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488 | ij = idx%nbj(ib,igrd) |
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489 | itreat = idx%ntreat(ib,igrd) |
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490 | CALL find_neib( ii, ij, itreat, ii1, ij1, ii2, ij2, ii3, ij3 ) ! find free ocean neighbours |
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491 | SELECT CASE( itreat ) |
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492 | CASE( 1:8 ) |
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493 | IF( ii1 < 1 .OR. ii1 > jpi .OR. ij1 < 1 .OR. ij1 > jpj ) CYCLE |
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494 | DO ik = 1, ipkm1 |
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495 | IF( zmask(ii1,ij1,ik) /= 0. ) phia(ii,ij,ik) = phia(ii1,ij1,ik) |
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496 | END DO |
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497 | CASE( 9:12 ) |
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498 | IF( ii1 < 1 .OR. ii1 > jpi .OR. ij1 < 1 .OR. ij1 > jpj ) CYCLE |
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499 | IF( ii2 < 1 .OR. ii2 > jpi .OR. ij2 < 1 .OR. ij2 > jpj ) CYCLE |
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500 | DO ik = 1, ipkm1 |
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501 | zweight = zmask(ii1,ij1,ik) + zmask(ii2,ij2,ik) |
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502 | IF( zweight /= 0. ) phia(ii,ij,ik) = ( phia(ii1,ij1,ik) + phia(ii2,ij2,ik) ) / zweight |
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503 | END DO |
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504 | CASE( 13:16 ) |
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505 | IF( ii1 < 1 .OR. ii1 > jpi .OR. ij1 < 1 .OR. ij1 > jpj ) CYCLE |
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506 | IF( ii2 < 1 .OR. ii2 > jpi .OR. ij2 < 1 .OR. ij2 > jpj ) CYCLE |
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507 | IF( ii3 < 1 .OR. ii3 > jpi .OR. ij3 < 1 .OR. ij3 > jpj ) CYCLE |
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508 | DO ik = 1, ipkm1 |
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509 | zweight = zmask(ii1,ij1,ik) + zmask(ii2,ij2,ik) + zmask(ii3,ij3,ik) |
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510 | IF( zweight /= 0. ) phia(ii,ij,ik) = ( phia(ii1,ij1,ik) + phia(ii2,ij2,ik) + phia(ii3,ij3,ik) ) / zweight |
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511 | END DO |
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512 | END SELECT |
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513 | END DO |
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514 | ! |
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515 | END SUBROUTINE bdy_nmn |
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516 | |
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517 | !!====================================================================== |
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518 | END MODULE bdylib |
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