Changeset 12377 for NEMO/trunk/src/TOP/PISCES/P4Z/p4zche.F90
- Timestamp:
- 2020-02-12T15:39:06+01:00 (4 years ago)
- Location:
- NEMO/trunk
- Files:
-
- 2 edited
Legend:
- Unmodified
- Added
- Removed
-
NEMO/trunk
- Property svn:externals
-
old new 3 3 ^/utils/build/mk@HEAD mk 4 4 ^/utils/tools@HEAD tools 5 ^/vendors/AGRIF/dev @HEAD ext/AGRIF5 ^/vendors/AGRIF/dev_r11615_ENHANCE-04_namelists_as_internalfiles_agrif@HEAD ext/AGRIF 6 6 ^/vendors/FCM@HEAD ext/FCM 7 7 ^/vendors/IOIPSL@HEAD ext/IOIPSL
-
- Property svn:externals
-
NEMO/trunk/src/TOP/PISCES/P4Z/p4zche.F90
r10425 r12377 130 130 INTEGER :: niter_atgen = jp_maxniter_atgen 131 131 132 !! * Substitutions 133 # include "do_loop_substitute.h90" 132 134 !!---------------------------------------------------------------------- 133 135 !! NEMO/TOP 4.0 , NEMO Consortium (2018) … … 137 139 CONTAINS 138 140 139 SUBROUTINE p4z_che 141 SUBROUTINE p4z_che( Kbb, Kmm ) 140 142 !!--------------------------------------------------------------------- 141 143 !! *** ROUTINE p4z_che *** … … 145 147 !! ** Method : - ... 146 148 !!--------------------------------------------------------------------- 149 INTEGER, INTENT(in) :: Kbb, Kmm ! time level indices 147 150 INTEGER :: ji, jj, jk 148 151 REAL(wp) :: ztkel, ztkel1, zt , zsal , zsal2 , zbuf1 , zbuf2 … … 164 167 ! ------------------------------------------------------------- 165 168 IF (neos == -1) THEN 166 salinprac(:,:,:) = ts n(:,:,:,jp_sal) * 35.0 / 35.16504169 salinprac(:,:,:) = ts(:,:,:,jp_sal,Kmm) * 35.0 / 35.16504 167 170 ELSE 168 salinprac(:,:,:) = ts n(:,:,:,jp_sal)171 salinprac(:,:,:) = ts(:,:,:,jp_sal,Kmm) 169 172 ENDIF 170 173 … … 175 178 ! 0.04°C relative to an exact computation 176 179 ! --------------------------------------------------------------------- 177 DO jk = 1, jpk 178 DO jj = 1, jpj 179 DO ji = 1, jpi 180 zpres = gdept_n(ji,jj,jk) / 1000. 181 za1 = 0.04 * ( 1.0 + 0.185 * tsn(ji,jj,jk,jp_tem) + 0.035 * (salinprac(ji,jj,jk) - 35.0) ) 182 za2 = 0.0075 * ( 1.0 - tsn(ji,jj,jk,jp_tem) / 30.0 ) 183 tempis(ji,jj,jk) = tsn(ji,jj,jk,jp_tem) - za1 * zpres + za2 * zpres**2 184 END DO 185 END DO 186 END DO 180 DO_3D_11_11( 1, jpk ) 181 zpres = gdept(ji,jj,jk,Kmm) / 1000. 182 za1 = 0.04 * ( 1.0 + 0.185 * ts(ji,jj,jk,jp_tem,Kmm) + 0.035 * (salinprac(ji,jj,jk) - 35.0) ) 183 za2 = 0.0075 * ( 1.0 - ts(ji,jj,jk,jp_tem,Kmm) / 30.0 ) 184 tempis(ji,jj,jk) = ts(ji,jj,jk,jp_tem,Kmm) - za1 * zpres + za2 * zpres**2 185 END_3D 187 186 ! 188 187 ! CHEMICAL CONSTANTS - SURFACE LAYER … … 245 244 zplat = SIN ( ABS(gphit(ji,jj)*3.141592654/180.) ) 246 245 zc1 = 5.92E-3 + zplat**2 * 5.25E-3 247 zpres = ((1-zc1)-SQRT(((1-zc1)**2)-(8.84E-6*gdept _n(ji,jj,jk)))) / 4.42E-6246 zpres = ((1-zc1)-SQRT(((1-zc1)**2)-(8.84E-6*gdept(ji,jj,jk,Kmm)))) / 4.42E-6 248 247 zpres = zpres / 10.0 249 248 … … 448 447 END SUBROUTINE p4z_che 449 448 450 SUBROUTINE ahini_for_at(p_hini )449 SUBROUTINE ahini_for_at(p_hini, Kbb ) 451 450 !!--------------------------------------------------------------------- 452 451 !! *** ROUTINE ahini_for_at *** … … 462 461 !!--------------------------------------------------------------------- 463 462 REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: p_hini 463 INTEGER, INTENT(in) :: Kbb ! time level indices 464 464 INTEGER :: ji, jj, jk 465 465 REAL(wp) :: zca1, zba1 … … 471 471 IF( ln_timing ) CALL timing_start('ahini_for_at') 472 472 ! 473 DO jk = 1, jpk 474 DO jj = 1, jpj 475 DO ji = 1, jpi 476 p_alkcb = trb(ji,jj,jk,jptal) * 1000. / (rhop(ji,jj,jk) + rtrn) 477 p_dictot = trb(ji,jj,jk,jpdic) * 1000. / (rhop(ji,jj,jk) + rtrn) 478 p_bortot = borat(ji,jj,jk) 479 IF (p_alkcb <= 0.) THEN 480 p_hini(ji,jj,jk) = 1.e-3 481 ELSEIF (p_alkcb >= (2.*p_dictot + p_bortot)) THEN 482 p_hini(ji,jj,jk) = 1.e-10_wp 473 DO_3D_11_11( 1, jpk ) 474 p_alkcb = tr(ji,jj,jk,jptal,Kbb) * 1000. / (rhop(ji,jj,jk) + rtrn) 475 p_dictot = tr(ji,jj,jk,jpdic,Kbb) * 1000. / (rhop(ji,jj,jk) + rtrn) 476 p_bortot = borat(ji,jj,jk) 477 IF (p_alkcb <= 0.) THEN 478 p_hini(ji,jj,jk) = 1.e-3 479 ELSEIF (p_alkcb >= (2.*p_dictot + p_bortot)) THEN 480 p_hini(ji,jj,jk) = 1.e-10_wp 481 ELSE 482 zca1 = p_dictot/( p_alkcb + rtrn ) 483 zba1 = p_bortot/ (p_alkcb + rtrn ) 484 ! Coefficients of the cubic polynomial 485 za2 = aKb3(ji,jj,jk)*(1. - zba1) + ak13(ji,jj,jk)*(1.-zca1) 486 za1 = ak13(ji,jj,jk)*akb3(ji,jj,jk)*(1. - zba1 - zca1) & 487 & + ak13(ji,jj,jk)*ak23(ji,jj,jk)*(1. - (zca1+zca1)) 488 za0 = ak13(ji,jj,jk)*ak23(ji,jj,jk)*akb3(ji,jj,jk)*(1. - zba1 - (zca1+zca1)) 489 ! Taylor expansion around the minimum 490 zd = za2*za2 - 3.*za1 ! Discriminant of the quadratic equation 491 ! for the minimum close to the root 492 493 IF(zd > 0.) THEN ! If the discriminant is positive 494 zsqrtd = SQRT(zd) 495 IF(za2 < 0) THEN 496 zhmin = (-za2 + zsqrtd)/3. 483 497 ELSE 484 zca1 = p_dictot/( p_alkcb + rtrn ) 485 zba1 = p_bortot/ (p_alkcb + rtrn ) 486 ! Coefficients of the cubic polynomial 487 za2 = aKb3(ji,jj,jk)*(1. - zba1) + ak13(ji,jj,jk)*(1.-zca1) 488 za1 = ak13(ji,jj,jk)*akb3(ji,jj,jk)*(1. - zba1 - zca1) & 489 & + ak13(ji,jj,jk)*ak23(ji,jj,jk)*(1. - (zca1+zca1)) 490 za0 = ak13(ji,jj,jk)*ak23(ji,jj,jk)*akb3(ji,jj,jk)*(1. - zba1 - (zca1+zca1)) 491 ! Taylor expansion around the minimum 492 zd = za2*za2 - 3.*za1 ! Discriminant of the quadratic equation 493 ! for the minimum close to the root 494 495 IF(zd > 0.) THEN ! If the discriminant is positive 496 zsqrtd = SQRT(zd) 497 IF(za2 < 0) THEN 498 zhmin = (-za2 + zsqrtd)/3. 499 ELSE 500 zhmin = -za1/(za2 + zsqrtd) 501 ENDIF 502 p_hini(ji,jj,jk) = zhmin + SQRT(-(za0 + zhmin*(za1 + zhmin*(za2 + zhmin)))/zsqrtd) 503 ELSE 504 p_hini(ji,jj,jk) = 1.e-7 505 ENDIF 506 ! 507 ENDIF 508 END DO 509 END DO 510 END DO 498 zhmin = -za1/(za2 + zsqrtd) 499 ENDIF 500 p_hini(ji,jj,jk) = zhmin + SQRT(-(za0 + zhmin*(za1 + zhmin*(za2 + zhmin)))/zsqrtd) 501 ELSE 502 p_hini(ji,jj,jk) = 1.e-7 503 ENDIF 504 ! 505 ENDIF 506 END_3D 511 507 ! 512 508 IF( ln_timing ) CALL timing_stop('ahini_for_at') … … 516 512 !=============================================================================== 517 513 518 SUBROUTINE anw_infsup( p_alknw_inf, p_alknw_sup )514 SUBROUTINE anw_infsup( p_alknw_inf, p_alknw_sup, Kbb ) 519 515 520 516 ! Subroutine returns the lower and upper bounds of "non-water-selfionization" … … 525 521 REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: p_alknw_inf 526 522 REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: p_alknw_sup 527 528 p_alknw_inf(:,:,:) = -trb(:,:,:,jppo4) * 1000. / (rhop(:,:,:) + rtrn) - sulfat(:,:,:) & 523 INTEGER, INTENT(in) :: Kbb ! time level indices 524 525 p_alknw_inf(:,:,:) = -tr(:,:,:,jppo4,Kbb) * 1000. / (rhop(:,:,:) + rtrn) - sulfat(:,:,:) & 529 526 & - fluorid(:,:,:) 530 p_alknw_sup(:,:,:) = (2. * tr b(:,:,:,jpdic) + 2. * trb(:,:,:,jppo4) + trb(:,:,:,jpsil) ) &527 p_alknw_sup(:,:,:) = (2. * tr(:,:,:,jpdic,Kbb) + 2. * tr(:,:,:,jppo4,Kbb) + tr(:,:,:,jpsil,Kbb) ) & 531 528 & * 1000. / (rhop(:,:,:) + rtrn) + borat(:,:,:) 532 529 … … 534 531 535 532 536 SUBROUTINE solve_at_general( p_hini, zhi )533 SUBROUTINE solve_at_general( p_hini, zhi, Kbb ) 537 534 538 535 ! Universal pH solver that converges from any given initial value, … … 543 540 REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(IN) :: p_hini 544 541 REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: zhi 542 INTEGER, INTENT(in) :: Kbb ! time level indices 545 543 546 544 ! Local variables … … 565 563 IF( ln_timing ) CALL timing_start('solve_at_general') 566 564 567 CALL anw_infsup( zalknw_inf, zalknw_sup )565 CALL anw_infsup( zalknw_inf, zalknw_sup, Kbb ) 568 566 569 567 rmask(:,:,:) = tmask(:,:,:) … … 571 569 572 570 ! TOTAL H+ scale: conversion factor for Htot = aphscale * Hfree 573 DO jk = 1, jpk 574 DO jj = 1, jpj 575 DO ji = 1, jpi 576 IF (rmask(ji,jj,jk) == 1.) THEN 577 p_alktot = trb(ji,jj,jk,jptal) * 1000. / (rhop(ji,jj,jk) + rtrn) 578 aphscale = 1. + sulfat(ji,jj,jk)/aks3(ji,jj,jk) 579 zh_ini = p_hini(ji,jj,jk) 580 581 zdelta = (p_alktot-zalknw_inf(ji,jj,jk))**2 + 4.*akw3(ji,jj,jk)/aphscale 582 583 IF(p_alktot >= zalknw_inf(ji,jj,jk)) THEN 584 zh_min(ji,jj,jk) = 2.*akw3(ji,jj,jk) /( p_alktot-zalknw_inf(ji,jj,jk) + SQRT(zdelta) ) 585 ELSE 586 zh_min(ji,jj,jk) = aphscale*(-(p_alktot-zalknw_inf(ji,jj,jk)) + SQRT(zdelta) ) / 2. 587 ENDIF 588 589 zdelta = (p_alktot-zalknw_sup(ji,jj,jk))**2 + 4.*akw3(ji,jj,jk)/aphscale 590 591 IF(p_alktot <= zalknw_sup(ji,jj,jk)) THEN 592 zh_max(ji,jj,jk) = aphscale*(-(p_alktot-zalknw_sup(ji,jj,jk)) + SQRT(zdelta) ) / 2. 593 ELSE 594 zh_max(ji,jj,jk) = 2.*akw3(ji,jj,jk) /( p_alktot-zalknw_sup(ji,jj,jk) + SQRT(zdelta) ) 595 ENDIF 596 597 zhi(ji,jj,jk) = MAX(MIN(zh_max(ji,jj,jk), zh_ini), zh_min(ji,jj,jk)) 571 DO_3D_11_11( 1, jpk ) 572 IF (rmask(ji,jj,jk) == 1.) THEN 573 p_alktot = tr(ji,jj,jk,jptal,Kbb) * 1000. / (rhop(ji,jj,jk) + rtrn) 574 aphscale = 1. + sulfat(ji,jj,jk)/aks3(ji,jj,jk) 575 zh_ini = p_hini(ji,jj,jk) 576 577 zdelta = (p_alktot-zalknw_inf(ji,jj,jk))**2 + 4.*akw3(ji,jj,jk)/aphscale 578 579 IF(p_alktot >= zalknw_inf(ji,jj,jk)) THEN 580 zh_min(ji,jj,jk) = 2.*akw3(ji,jj,jk) /( p_alktot-zalknw_inf(ji,jj,jk) + SQRT(zdelta) ) 581 ELSE 582 zh_min(ji,jj,jk) = aphscale*(-(p_alktot-zalknw_inf(ji,jj,jk)) + SQRT(zdelta) ) / 2. 583 ENDIF 584 585 zdelta = (p_alktot-zalknw_sup(ji,jj,jk))**2 + 4.*akw3(ji,jj,jk)/aphscale 586 587 IF(p_alktot <= zalknw_sup(ji,jj,jk)) THEN 588 zh_max(ji,jj,jk) = aphscale*(-(p_alktot-zalknw_sup(ji,jj,jk)) + SQRT(zdelta) ) / 2. 589 ELSE 590 zh_max(ji,jj,jk) = 2.*akw3(ji,jj,jk) /( p_alktot-zalknw_sup(ji,jj,jk) + SQRT(zdelta) ) 591 ENDIF 592 593 zhi(ji,jj,jk) = MAX(MIN(zh_max(ji,jj,jk), zh_ini), zh_min(ji,jj,jk)) 594 ENDIF 595 END_3D 596 597 zeqn_absmin(:,:,:) = HUGE(1._wp) 598 599 DO jn = 1, jp_maxniter_atgen 600 DO_3D_11_11( 1, jpk ) 601 IF (rmask(ji,jj,jk) == 1.) THEN 602 zfact = rhop(ji,jj,jk) / 1000. + rtrn 603 p_alktot = tr(ji,jj,jk,jptal,Kbb) / zfact 604 zdic = tr(ji,jj,jk,jpdic,Kbb) / zfact 605 zbot = borat(ji,jj,jk) 606 zpt = tr(ji,jj,jk,jppo4,Kbb) / zfact * po4r 607 zsit = tr(ji,jj,jk,jpsil,Kbb) / zfact 608 zst = sulfat (ji,jj,jk) 609 zft = fluorid(ji,jj,jk) 610 aphscale = 1. + sulfat(ji,jj,jk)/aks3(ji,jj,jk) 611 zh = zhi(ji,jj,jk) 612 zh_prev = zh 613 614 ! H2CO3 - HCO3 - CO3 : n=2, m=0 615 znumer_dic = 2.*ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh*ak13(ji,jj,jk) 616 zdenom_dic = ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh*(ak13(ji,jj,jk) + zh) 617 zalk_dic = zdic * (znumer_dic/zdenom_dic) 618 zdnumer_dic = ak13(ji,jj,jk)*ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh & 619 *(4.*ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh*ak13(ji,jj,jk)) 620 zdalk_dic = -zdic*(zdnumer_dic/zdenom_dic**2) 621 622 623 ! B(OH)3 - B(OH)4 : n=1, m=0 624 znumer_bor = akb3(ji,jj,jk) 625 zdenom_bor = akb3(ji,jj,jk) + zh 626 zalk_bor = zbot * (znumer_bor/zdenom_bor) 627 zdnumer_bor = akb3(ji,jj,jk) 628 zdalk_bor = -zbot*(zdnumer_bor/zdenom_bor**2) 629 630 631 ! H3PO4 - H2PO4 - HPO4 - PO4 : n=3, m=1 632 znumer_po4 = 3.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & 633 & + zh*(2.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) + zh* ak1p3(ji,jj,jk)) 634 zdenom_po4 = ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & 635 & + zh*( ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) + zh*(ak1p3(ji,jj,jk) + zh)) 636 zalk_po4 = zpt * (znumer_po4/zdenom_po4 - 1.) ! Zero level of H3PO4 = 1 637 zdnumer_po4 = ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & 638 & + zh*(4.*ak1p3(ji,jj,jk)*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & 639 & + zh*(9.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & 640 & + ak1p3(ji,jj,jk)*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) & 641 & + zh*(4.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) + zh * ak1p3(ji,jj,jk) ) ) ) 642 zdalk_po4 = -zpt * (zdnumer_po4/zdenom_po4**2) 643 644 ! H4SiO4 - H3SiO4 : n=1, m=0 645 znumer_sil = aksi3(ji,jj,jk) 646 zdenom_sil = aksi3(ji,jj,jk) + zh 647 zalk_sil = zsit * (znumer_sil/zdenom_sil) 648 zdnumer_sil = aksi3(ji,jj,jk) 649 zdalk_sil = -zsit * (zdnumer_sil/zdenom_sil**2) 650 651 ! HSO4 - SO4 : n=1, m=1 652 aphscale = 1.0 + zst/aks3(ji,jj,jk) 653 znumer_so4 = aks3(ji,jj,jk) * aphscale 654 zdenom_so4 = aks3(ji,jj,jk) * aphscale + zh 655 zalk_so4 = zst * (znumer_so4/zdenom_so4 - 1.) 656 zdnumer_so4 = aks3(ji,jj,jk) 657 zdalk_so4 = -zst * (zdnumer_so4/zdenom_so4**2) 658 659 ! HF - F : n=1, m=1 660 znumer_flu = akf3(ji,jj,jk) 661 zdenom_flu = akf3(ji,jj,jk) + zh 662 zalk_flu = zft * (znumer_flu/zdenom_flu - 1.) 663 zdnumer_flu = akf3(ji,jj,jk) 664 zdalk_flu = -zft * (zdnumer_flu/zdenom_flu**2) 665 666 ! H2O - OH 667 aphscale = 1.0 + zst/aks3(ji,jj,jk) 668 zalk_wat = akw3(ji,jj,jk)/zh - zh/aphscale 669 zdalk_wat = -akw3(ji,jj,jk)/zh**2 - 1./aphscale 670 671 ! CALCULATE [ALK]([CO3--], [HCO3-]) 672 zeqn = zalk_dic + zalk_bor + zalk_po4 + zalk_sil & 673 & + zalk_so4 + zalk_flu & 674 & + zalk_wat - p_alktot 675 676 zalka = p_alktot - (zalk_bor + zalk_po4 + zalk_sil & 677 & + zalk_so4 + zalk_flu + zalk_wat) 678 679 zdeqndh = zdalk_dic + zdalk_bor + zdalk_po4 + zdalk_sil & 680 & + zdalk_so4 + zdalk_flu + zdalk_wat 681 682 ! Adapt bracketing interval 683 IF(zeqn > 0._wp) THEN 684 zh_min(ji,jj,jk) = zh_prev 685 ELSEIF(zeqn < 0._wp) THEN 686 zh_max(ji,jj,jk) = zh_prev 687 ENDIF 688 689 IF(ABS(zeqn) >= 0.5_wp*zeqn_absmin(ji,jj,jk)) THEN 690 ! if the function evaluation at the current point is 691 ! not decreasing faster than with a bisection step (at least linearly) 692 ! in absolute value take one bisection step on [ph_min, ph_max] 693 ! ph_new = (ph_min + ph_max)/2d0 694 ! 695 ! In terms of [H]_new: 696 ! [H]_new = 10**(-ph_new) 697 ! = 10**(-(ph_min + ph_max)/2d0) 698 ! = SQRT(10**(-(ph_min + phmax))) 699 ! = SQRT(zh_max * zh_min) 700 zh = SQRT(zh_max(ji,jj,jk) * zh_min(ji,jj,jk)) 701 zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below 702 ELSE 703 ! dzeqn/dpH = dzeqn/d[H] * d[H]/dpH 704 ! = -zdeqndh * LOG(10) * [H] 705 ! \Delta pH = -zeqn/(zdeqndh*d[H]/dpH) = zeqn/(zdeqndh*[H]*LOG(10)) 706 ! 707 ! pH_new = pH_old + \deltapH 708 ! 709 ! [H]_new = 10**(-pH_new) 710 ! = 10**(-pH_old - \Delta pH) 711 ! = [H]_old * 10**(-zeqn/(zdeqndh*[H]_old*LOG(10))) 712 ! = [H]_old * EXP(-LOG(10)*zeqn/(zdeqndh*[H]_old*LOG(10))) 713 ! = [H]_old * EXP(-zeqn/(zdeqndh*[H]_old)) 714 715 zh_lnfactor = -zeqn/(zdeqndh*zh_prev) 716 717 IF(ABS(zh_lnfactor) > pz_exp_threshold) THEN 718 zh = zh_prev*EXP(zh_lnfactor) 719 ELSE 720 zh_delta = zh_lnfactor*zh_prev 721 zh = zh_prev + zh_delta 598 722 ENDIF 599 END DO 600 END DO 601 END DO 602 603 zeqn_absmin(:,:,:) = HUGE(1._wp) 604 605 DO jn = 1, jp_maxniter_atgen 606 DO jk = 1, jpk 607 DO jj = 1, jpj 608 DO ji = 1, jpi 609 IF (rmask(ji,jj,jk) == 1.) THEN 610 zfact = rhop(ji,jj,jk) / 1000. + rtrn 611 p_alktot = trb(ji,jj,jk,jptal) / zfact 612 zdic = trb(ji,jj,jk,jpdic) / zfact 613 zbot = borat(ji,jj,jk) 614 zpt = trb(ji,jj,jk,jppo4) / zfact * po4r 615 zsit = trb(ji,jj,jk,jpsil) / zfact 616 zst = sulfat (ji,jj,jk) 617 zft = fluorid(ji,jj,jk) 618 aphscale = 1. + sulfat(ji,jj,jk)/aks3(ji,jj,jk) 619 zh = zhi(ji,jj,jk) 620 zh_prev = zh 621 622 ! H2CO3 - HCO3 - CO3 : n=2, m=0 623 znumer_dic = 2.*ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh*ak13(ji,jj,jk) 624 zdenom_dic = ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh*(ak13(ji,jj,jk) + zh) 625 zalk_dic = zdic * (znumer_dic/zdenom_dic) 626 zdnumer_dic = ak13(ji,jj,jk)*ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh & 627 *(4.*ak13(ji,jj,jk)*ak23(ji,jj,jk) + zh*ak13(ji,jj,jk)) 628 zdalk_dic = -zdic*(zdnumer_dic/zdenom_dic**2) 629 630 631 ! B(OH)3 - B(OH)4 : n=1, m=0 632 znumer_bor = akb3(ji,jj,jk) 633 zdenom_bor = akb3(ji,jj,jk) + zh 634 zalk_bor = zbot * (znumer_bor/zdenom_bor) 635 zdnumer_bor = akb3(ji,jj,jk) 636 zdalk_bor = -zbot*(zdnumer_bor/zdenom_bor**2) 637 638 639 ! H3PO4 - H2PO4 - HPO4 - PO4 : n=3, m=1 640 znumer_po4 = 3.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & 641 & + zh*(2.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) + zh* ak1p3(ji,jj,jk)) 642 zdenom_po4 = ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & 643 & + zh*( ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) + zh*(ak1p3(ji,jj,jk) + zh)) 644 zalk_po4 = zpt * (znumer_po4/zdenom_po4 - 1.) ! Zero level of H3PO4 = 1 645 zdnumer_po4 = ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & 646 & + zh*(4.*ak1p3(ji,jj,jk)*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & 647 & + zh*(9.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) & 648 & + ak1p3(ji,jj,jk)*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) & 649 & + zh*(4.*ak1p3(ji,jj,jk)*ak2p3(ji,jj,jk) + zh * ak1p3(ji,jj,jk) ) ) ) 650 zdalk_po4 = -zpt * (zdnumer_po4/zdenom_po4**2) 651 652 ! H4SiO4 - H3SiO4 : n=1, m=0 653 znumer_sil = aksi3(ji,jj,jk) 654 zdenom_sil = aksi3(ji,jj,jk) + zh 655 zalk_sil = zsit * (znumer_sil/zdenom_sil) 656 zdnumer_sil = aksi3(ji,jj,jk) 657 zdalk_sil = -zsit * (zdnumer_sil/zdenom_sil**2) 658 659 ! HSO4 - SO4 : n=1, m=1 660 aphscale = 1.0 + zst/aks3(ji,jj,jk) 661 znumer_so4 = aks3(ji,jj,jk) * aphscale 662 zdenom_so4 = aks3(ji,jj,jk) * aphscale + zh 663 zalk_so4 = zst * (znumer_so4/zdenom_so4 - 1.) 664 zdnumer_so4 = aks3(ji,jj,jk) 665 zdalk_so4 = -zst * (zdnumer_so4/zdenom_so4**2) 666 667 ! HF - F : n=1, m=1 668 znumer_flu = akf3(ji,jj,jk) 669 zdenom_flu = akf3(ji,jj,jk) + zh 670 zalk_flu = zft * (znumer_flu/zdenom_flu - 1.) 671 zdnumer_flu = akf3(ji,jj,jk) 672 zdalk_flu = -zft * (zdnumer_flu/zdenom_flu**2) 673 674 ! H2O - OH 675 aphscale = 1.0 + zst/aks3(ji,jj,jk) 676 zalk_wat = akw3(ji,jj,jk)/zh - zh/aphscale 677 zdalk_wat = -akw3(ji,jj,jk)/zh**2 - 1./aphscale 678 679 ! CALCULATE [ALK]([CO3--], [HCO3-]) 680 zeqn = zalk_dic + zalk_bor + zalk_po4 + zalk_sil & 681 & + zalk_so4 + zalk_flu & 682 & + zalk_wat - p_alktot 683 684 zalka = p_alktot - (zalk_bor + zalk_po4 + zalk_sil & 685 & + zalk_so4 + zalk_flu + zalk_wat) 686 687 zdeqndh = zdalk_dic + zdalk_bor + zdalk_po4 + zdalk_sil & 688 & + zdalk_so4 + zdalk_flu + zdalk_wat 689 690 ! Adapt bracketing interval 691 IF(zeqn > 0._wp) THEN 692 zh_min(ji,jj,jk) = zh_prev 693 ELSEIF(zeqn < 0._wp) THEN 694 zh_max(ji,jj,jk) = zh_prev 695 ENDIF 696 697 IF(ABS(zeqn) >= 0.5_wp*zeqn_absmin(ji,jj,jk)) THEN 698 ! if the function evaluation at the current point is 699 ! not decreasing faster than with a bisection step (at least linearly) 700 ! in absolute value take one bisection step on [ph_min, ph_max] 701 ! ph_new = (ph_min + ph_max)/2d0 702 ! 723 724 IF( zh < zh_min(ji,jj,jk) ) THEN 725 ! if [H]_new < [H]_min 726 ! i.e., if ph_new > ph_max then 727 ! take one bisection step on [ph_prev, ph_max] 728 ! ph_new = (ph_prev + ph_max)/2d0 703 729 ! In terms of [H]_new: 704 730 ! [H]_new = 10**(-ph_new) 705 ! = 10**(-(ph_min + ph_max)/2d0) 706 ! = SQRT(10**(-(ph_min + phmax))) 707 ! = SQRT(zh_max * zh_min) 708 zh = SQRT(zh_max(ji,jj,jk) * zh_min(ji,jj,jk)) 709 zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below 710 ELSE 711 ! dzeqn/dpH = dzeqn/d[H] * d[H]/dpH 712 ! = -zdeqndh * LOG(10) * [H] 713 ! \Delta pH = -zeqn/(zdeqndh*d[H]/dpH) = zeqn/(zdeqndh*[H]*LOG(10)) 714 ! 715 ! pH_new = pH_old + \deltapH 716 ! 717 ! [H]_new = 10**(-pH_new) 718 ! = 10**(-pH_old - \Delta pH) 719 ! = [H]_old * 10**(-zeqn/(zdeqndh*[H]_old*LOG(10))) 720 ! = [H]_old * EXP(-LOG(10)*zeqn/(zdeqndh*[H]_old*LOG(10))) 721 ! = [H]_old * EXP(-zeqn/(zdeqndh*[H]_old)) 722 723 zh_lnfactor = -zeqn/(zdeqndh*zh_prev) 724 725 IF(ABS(zh_lnfactor) > pz_exp_threshold) THEN 726 zh = zh_prev*EXP(zh_lnfactor) 727 ELSE 728 zh_delta = zh_lnfactor*zh_prev 729 zh = zh_prev + zh_delta 730 ENDIF 731 732 IF( zh < zh_min(ji,jj,jk) ) THEN 733 ! if [H]_new < [H]_min 734 ! i.e., if ph_new > ph_max then 735 ! take one bisection step on [ph_prev, ph_max] 736 ! ph_new = (ph_prev + ph_max)/2d0 737 ! In terms of [H]_new: 738 ! [H]_new = 10**(-ph_new) 739 ! = 10**(-(ph_prev + ph_max)/2d0) 740 ! = SQRT(10**(-(ph_prev + phmax))) 741 ! = SQRT([H]_old*10**(-ph_max)) 742 ! = SQRT([H]_old * zh_min) 743 zh = SQRT(zh_prev * zh_min(ji,jj,jk)) 744 zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below 745 ENDIF 746 747 IF( zh > zh_max(ji,jj,jk) ) THEN 748 ! if [H]_new > [H]_max 749 ! i.e., if ph_new < ph_min, then 750 ! take one bisection step on [ph_min, ph_prev] 751 ! ph_new = (ph_prev + ph_min)/2d0 752 ! In terms of [H]_new: 753 ! [H]_new = 10**(-ph_new) 754 ! = 10**(-(ph_prev + ph_min)/2d0) 755 ! = SQRT(10**(-(ph_prev + ph_min))) 756 ! = SQRT([H]_old*10**(-ph_min)) 757 ! = SQRT([H]_old * zhmax) 758 zh = SQRT(zh_prev * zh_max(ji,jj,jk)) 759 zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below 760 ENDIF 761 ENDIF 762 763 zeqn_absmin(ji,jj,jk) = MIN( ABS(zeqn), zeqn_absmin(ji,jj,jk)) 764 765 ! Stop iterations once |\delta{[H]}/[H]| < rdel 766 ! <=> |(zh - zh_prev)/zh_prev| = |EXP(-zeqn/(zdeqndh*zh_prev)) -1| < rdel 767 ! |EXP(-zeqn/(zdeqndh*zh_prev)) -1| ~ |zeqn/(zdeqndh*zh_prev)| 768 769 ! Alternatively: 770 ! |\Delta pH| = |zeqn/(zdeqndh*zh_prev*LOG(10))| 771 ! ~ 1/LOG(10) * |\Delta [H]|/[H] 772 ! < 1/LOG(10) * rdel 773 774 ! Hence |zeqn/(zdeqndh*zh)| < rdel 775 776 ! rdel <-- pp_rdel_ah_target 777 l_exitnow = (ABS(zh_lnfactor) < pp_rdel_ah_target) 778 779 IF(l_exitnow) THEN 780 rmask(ji,jj,jk) = 0. 781 ENDIF 782 783 zhi(ji,jj,jk) = zh 784 785 IF(jn >= jp_maxniter_atgen) THEN 786 zhi(ji,jj,jk) = -1._wp 787 ENDIF 788 731 ! = 10**(-(ph_prev + ph_max)/2d0) 732 ! = SQRT(10**(-(ph_prev + phmax))) 733 ! = SQRT([H]_old*10**(-ph_max)) 734 ! = SQRT([H]_old * zh_min) 735 zh = SQRT(zh_prev * zh_min(ji,jj,jk)) 736 zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below 789 737 ENDIF 790 END DO 791 END DO 792 END DO 738 739 IF( zh > zh_max(ji,jj,jk) ) THEN 740 ! if [H]_new > [H]_max 741 ! i.e., if ph_new < ph_min, then 742 ! take one bisection step on [ph_min, ph_prev] 743 ! ph_new = (ph_prev + ph_min)/2d0 744 ! In terms of [H]_new: 745 ! [H]_new = 10**(-ph_new) 746 ! = 10**(-(ph_prev + ph_min)/2d0) 747 ! = SQRT(10**(-(ph_prev + ph_min))) 748 ! = SQRT([H]_old*10**(-ph_min)) 749 ! = SQRT([H]_old * zhmax) 750 zh = SQRT(zh_prev * zh_max(ji,jj,jk)) 751 zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below 752 ENDIF 753 ENDIF 754 755 zeqn_absmin(ji,jj,jk) = MIN( ABS(zeqn), zeqn_absmin(ji,jj,jk)) 756 757 ! Stop iterations once |\delta{[H]}/[H]| < rdel 758 ! <=> |(zh - zh_prev)/zh_prev| = |EXP(-zeqn/(zdeqndh*zh_prev)) -1| < rdel 759 ! |EXP(-zeqn/(zdeqndh*zh_prev)) -1| ~ |zeqn/(zdeqndh*zh_prev)| 760 761 ! Alternatively: 762 ! |\Delta pH| = |zeqn/(zdeqndh*zh_prev*LOG(10))| 763 ! ~ 1/LOG(10) * |\Delta [H]|/[H] 764 ! < 1/LOG(10) * rdel 765 766 ! Hence |zeqn/(zdeqndh*zh)| < rdel 767 768 ! rdel <-- pp_rdel_ah_target 769 l_exitnow = (ABS(zh_lnfactor) < pp_rdel_ah_target) 770 771 IF(l_exitnow) THEN 772 rmask(ji,jj,jk) = 0. 773 ENDIF 774 775 zhi(ji,jj,jk) = zh 776 777 IF(jn >= jp_maxniter_atgen) THEN 778 zhi(ji,jj,jk) = -1._wp 779 ENDIF 780 781 ENDIF 782 END_3D 793 783 END DO 794 784 !
Note: See TracChangeset
for help on using the changeset viewer.