| 1 | ! AeroBulk / 2020 / L. Brodeau |
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| 2 | ! |
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| 3 | ! When using AeroBulk to produce scientific work, please acknowledge with the following citation: |
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| 4 | ! |
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| 5 | ! Brodeau, L., B. Barnier, S. Gulev, and C. Woods, 2016: Climatologically |
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| 6 | ! significant effects of some approximations in the bulk parameterizations of |
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| 7 | ! turbulent air-sea fluxes. J. Phys. Oceanogr., doi:10.1175/JPO-D-16-0169.1. |
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| 8 | ! |
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| 9 | ! |
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| 10 | MODULE sbcblk_algo_ice_cdn |
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| 11 | !!==================================================================================== |
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| 12 | !! Author: Laurent Brodeau, January 2020 |
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| 13 | !!==================================================================================== |
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| 14 | USE par_kind, ONLY: wp |
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| 15 | USE par_oce, ONLY: jpi, jpj, Nis0, Nie0, Njs0, Nje0, nn_hls, ntsi, ntsj, ntei, ntej |
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| 16 | USE phycst ! physical constants |
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| 17 | USE sbc_phy ! Catalog of functions for physical/meteorological parameters in the marine boundary layer |
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| 18 | |
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| 19 | IMPLICIT NONE |
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| 20 | PRIVATE |
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| 21 | |
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| 22 | PUBLIC :: CdN10_f_LU12, CdN_f_LU12_eq36, CdN10_f_LU13, CdN_f_LG15, CdN_f_LG15_light |
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| 23 | |
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| 24 | REAL(wp), PARAMETER :: rCe_0 = 2.23E-3_wp !LOLO: this one can be more accurate when sea-ice data => Lupkes et al (2013), Eq.(1) |
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| 25 | REAL(wp), PARAMETER :: rNu_0 = 1._wp |
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| 26 | REAL(wp), PARAMETER :: rMu_0 = 1._wp |
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| 27 | REAL(wp), PARAMETER :: rbeta_0 = 1.4_wp ! (Eq.47) MIZ |
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| 28 | |
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| 29 | REAL(wp), PARAMETER :: rhmin_0 = 0.286_wp ! Eq.(25) |
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| 30 | REAL(wp), PARAMETER :: rhmax_0 = 0.534_wp ! Eq.(25) |
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| 31 | REAL(wp), PARAMETER :: rDmin_0 = 8._wp ! Eq.(27) |
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| 32 | REAL(wp), PARAMETER :: rDmax_0 = 300._wp ! Eq.(27) |
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| 33 | REAL(wp), PARAMETER :: rz0_w_0 = 3.27E-4 ! fixed roughness length over water (paragraph below Eq.36) |
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| 34 | |
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| 35 | !!============================================================ |
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| 36 | REAL(wp), PARAMETER :: rce10_i_0 = 3.46e-3_wp ! (Eq.48) MIZ |
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| 37 | REAL(wp), PARAMETER :: ralpha_0 = 0.2_wp ! (Eq.12) (ECHAM6 value) |
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| 38 | |
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| 39 | !! * Substitutions |
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| 40 | # include "do_loop_substitute.h90" |
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| 41 | !!---------------------------------------------------------------------- |
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| 42 | CONTAINS |
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| 43 | |
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| 44 | |
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| 45 | FUNCTION CdN10_f_LU12( pfrice, pz0w, pSc, phf, pDi ) |
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| 46 | !!---------------------------------------------------------------------- |
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| 47 | !! *** ROUTINE CdN10_f_LU12 *** |
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| 48 | !! |
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| 49 | !! GENERAL FORM OF EQUATION 22 of Lupkes et al. 2012 |
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| 50 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 51 | !! |
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| 52 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
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| 53 | !! drag referenced at 10m to make it dependent on edges at |
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| 54 | !! leads, melt ponds and flows (to be added to the "skin" |
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| 55 | !! contribution. After some |
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| 56 | !! approximations, this can be resumed to a dependency on |
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| 57 | !! ice concentration. |
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| 58 | !! |
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| 59 | !! ** References : Lupkes et al. JGR 2012 (theory) |
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| 60 | !! |
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| 61 | !!---------------------------------------------------------------------- |
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| 62 | REAL(wp), DIMENSION(jpi,jpj) :: CdN10_f_LU12 ! neutral FORM drag coefficient contribution over sea-ice |
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| 63 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc, phf and pDi all provided... |
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| 64 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0w ! roughness length over water [m] |
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| 65 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pSc ! shletering function [0-1] (Sc->1 for large distance between floes, ->0 for small distances) |
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| 66 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: phf ! mean freeboard of floes [m] |
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| 67 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pDi ! cross wind dimension of the floe (aka effective edge length for form drag) [m] |
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| 68 | !!---------------------------------------------------------------------- |
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| 69 | LOGICAL :: l_known_Sc=.FALSE., l_known_hf=.FALSE., l_known_Di=.FALSE. |
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| 70 | REAL(wp) :: ztmp, zrlog, zfri, zfrw, zSc, zhf, zDi |
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| 71 | INTEGER :: ji, jj |
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| 72 | !!---------------------------------------------------------------------- |
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| 73 | l_known_Sc = PRESENT(pSc) |
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| 74 | l_known_hf = PRESENT(phf) |
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| 75 | l_known_Di = PRESENT(pDi) |
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| 76 | |
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| 77 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
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| 78 | |
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| 79 | zfri = pfrice(ji,jj) |
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| 80 | zfrw = (1._wp - zfri) |
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| 81 | |
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| 82 | IF(l_known_Sc) THEN |
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| 83 | zSc = pSc(ji,jj) |
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| 84 | ELSE |
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| 85 | !! Sc parameterized in terms of A (ice fraction): |
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| 86 | zSc = zfrw**(1._wp / ( 10._wp * rBeta_0 )) ! Eq.(31) |
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| 87 | END IF |
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| 88 | |
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| 89 | IF(l_known_hf) THEN |
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| 90 | zhf = phf(ji,jj) |
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| 91 | ELSE |
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| 92 | !! hf parameterized in terms of A (ice fraction): |
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| 93 | zhf = rhmax_0*zfri + rhmin_0*zfrw ! Eq.(25) |
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| 94 | END IF |
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| 95 | |
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| 96 | IF(l_known_Di) THEN |
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| 97 | zDi = pDi(ji,jj) |
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| 98 | ELSE |
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| 99 | !! Di parameterized in terms of A (ice fraction): |
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| 100 | ztmp = 1._wp / ( 1._wp - (rDmin_0/rDmax_0)**(1._wp/rBeta_0) ) ! A* Eq.(27) |
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| 101 | zDi = rDmin_0 * ( ztmp/(ztmp - zfri) )**rBeta_0 ! Eq.(26) |
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| 102 | END IF |
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| 103 | |
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| 104 | ztmp = 1._wp/pz0w(ji,jj) |
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| 105 | zrlog = LOG(zhf*ztmp) / LOG(10._wp*ztmp) |
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| 106 | |
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| 107 | CdN10_f_LU12(ji,jj) = 0.5_wp* 0.3_wp * zrlog*zrlog * zSc*zSc * zhf/zDi * zfri ! Eq.(22) |
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| 108 | !! 1/2 Ce |
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| 109 | |
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| 110 | END_2D |
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| 111 | END FUNCTION CdN10_f_LU12 |
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| 112 | |
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| 113 | |
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| 114 | FUNCTION CdN_f_LU12_eq36( pzu, pfrice ) |
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| 115 | !!---------------------------------------------------------------------- |
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| 116 | REAL(wp), DIMENSION(jpi,jpj) :: CdN_f_LU12_eq36 ! neutral FORM drag coefficient contribution over sea-ice |
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| 117 | REAL(wp), INTENT(in) :: pzu ! reference height [m] |
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| 118 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc, phf and pDi all provided... |
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| 119 | !!---------------------------------------------------------------------- |
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| 120 | REAL(wp) :: ztmp, zrlog, zfri, zhf, zDi |
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| 121 | INTEGER :: ji, jj |
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| 122 | !!---------------------------------------------------------------------- |
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| 123 | !zhf = 0.28 ! h_fc |
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| 124 | zhf = 0.41 ! h_fc |
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| 125 | zDi = rDmin_0 |
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| 126 | |
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| 127 | ztmp = 1._wp/rz0_w_0 |
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| 128 | zrlog = LOG(zhf*ztmp) / LOG(pzu*ztmp) |
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| 129 | |
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| 130 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
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| 131 | zfri = pfrice(ji,jj) |
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| 132 | CdN_f_LU12_eq36(ji,jj) = 0.5_wp* 0.3_wp * zrlog*zrlog * zhf/zDi * (1._wp - zfri)**rBeta_0 ! Eq.(35) & (36) |
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| 133 | !! 1/2 Ce |
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| 134 | END_2D |
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| 135 | END FUNCTION CdN_f_LU12_eq36 |
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| 136 | |
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| 137 | |
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| 138 | FUNCTION CdN10_f_LU13( pfrice ) |
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| 139 | !!---------------------------------------------------------------------- |
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| 140 | !! *** ROUTINE CdN10_f_LU13 *** |
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| 141 | !! |
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| 142 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
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| 143 | !! drag referenced at 10m to make it dependent on edges at |
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| 144 | !! leads, melt ponds and flows (to be added to the "skin" |
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| 145 | !! contribution. After some |
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| 146 | !! approximations, this can be resumed to a dependency on |
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| 147 | !! ice concentration. |
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| 148 | !! |
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| 149 | !! ** Method : The parameterization is taken from Lupkes et al. (2012) eq.(50) |
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| 150 | !! with the highest level of approximation: level4, eq.(59) |
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| 151 | !! The generic drag over a cell partly covered by ice can be re-written as follows: |
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| 152 | !! |
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| 153 | !! Cd = Cdw * (1-A) + Cdi * A + Ce * (1-A)**(nu+1/(10*beta)) * A**mu |
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| 154 | !! |
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| 155 | !! Ce = 2.23e-3 , as suggested by Lupkes (eq. 59) |
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| 156 | !! nu = mu = beta = 1 , as suggested by Lupkes (eq. 59) |
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| 157 | !! A is the concentration of ice minus melt ponds (if any) |
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| 158 | !! |
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| 159 | !! This new drag has a parabolic shape (as a function of A) starting at |
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| 160 | !! Cdw(say 1.5e-3) for A=0, reaching 1.97e-3 for A~0.5 |
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| 161 | !! and going down to Cdi(say 1.4e-3) for A=1 |
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| 162 | !! |
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| 163 | !! It is theoretically applicable to all ice conditions (not only MIZ) |
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| 164 | !! => see Lupkes et al (2013) |
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| 165 | !! |
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| 166 | !! ** References : Lupkes et al. JGR 2012 (theory) |
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| 167 | !! Lupkes et al. GRL 2013 (application to GCM) |
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| 168 | !! |
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| 169 | !!---------------------------------------------------------------------- |
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| 170 | REAL(wp), DIMENSION(jpi,jpj) :: CdN10_f_LU13 ! neutral FORM drag coefficient contribution over sea-ice |
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| 171 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b |
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| 172 | !!---------------------------------------------------------------------- |
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| 173 | INTEGER :: ji, jj |
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| 174 | REAL(wp) :: zcoef |
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| 175 | !!---------------------------------------------------------------------- |
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| 176 | zcoef = rNu_0 + 1._wp / ( 10._wp * rBeta_0 ) |
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| 177 | |
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| 178 | !! We are not an AGCM, we are an OGCM!!! => we drop term "(1 - A)*Cd_w" |
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| 179 | !! => so we keep only the last rhs terms of Eq.(1) of Lupkes et al, 2013 that we divide by "A": |
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| 180 | !! (we multiply Cd_i_s and Cd_i_f by A later, when applying ocean-ice partitioning... |
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| 181 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
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| 182 | CdN10_f_LU13(ji,jj) = rCe_0 * pfrice(ji,jj)**(rMu_0 - 1._wp) * (1._wp - pfrice(ji,jj))**zcoef |
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| 183 | END_2D |
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| 184 | !! => seems okay for winter 100% sea-ice as second rhs term vanishes as pfrice == 1.... |
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| 185 | |
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| 186 | END FUNCTION CdN10_f_LU13 |
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| 187 | |
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| 188 | |
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| 189 | FUNCTION CdN_f_LG15( pzu, pfrice, pz0i, pSc, phf, pDi ) |
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| 190 | !!---------------------------------------------------------------------- |
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| 191 | !! *** ROUTINE CdN_f_LG15 *** |
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| 192 | !! |
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| 193 | !! GENERAL FORM OF EQUATION 21 of Lupkes & Gryanik (2015) |
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| 194 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 195 | !! |
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| 196 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
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| 197 | !! drag referenced at 10m to make it dependent on edges at |
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| 198 | !! leads, melt ponds and flows (to be added to the "skin" |
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| 199 | !! contribution. After some |
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| 200 | !! approximations, this can be resumed to a dependency on |
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| 201 | !! ice concentration. |
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| 202 | !! |
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| 203 | !! ** References : Lupkes & Gryanik (2015) |
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| 204 | !! |
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| 205 | !!---------------------------------------------------------------------- |
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| 206 | REAL(wp), DIMENSION(jpi,jpj) :: CdN_f_LG15 ! neutral FORM drag coefficient contribution over sea-ice |
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| 207 | REAL(wp), INTENT(in ) :: pzu ! reference height [m] |
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| 208 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc, phf and pDi all provided... |
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| 209 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0i ! roughness length over ICE [m] (in LU12, it's over water ???) |
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| 210 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pSc ! shletering function [0-1] (Sc->1 for large distance between floes, ->0 for small distances) |
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| 211 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: phf ! mean freeboard of floes [m] |
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| 212 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pDi ! cross wind dimension of the floe (aka effective edge length for form drag) [m] |
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| 213 | !!---------------------------------------------------------------------- |
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| 214 | LOGICAL :: l_known_Sc=.FALSE., l_known_hf=.FALSE., l_known_Di=.FALSE. |
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| 215 | REAL(wp) :: ztmp, zrlog, zfri, zfrw, zSc, zhf, zDi |
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| 216 | INTEGER :: ji, jj |
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| 217 | !!---------------------------------------------------------------------- |
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| 218 | l_known_Sc = PRESENT(pSc) |
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| 219 | l_known_hf = PRESENT(phf) |
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| 220 | l_known_Di = PRESENT(pDi) |
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| 221 | |
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| 222 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
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| 223 | |
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| 224 | zfri = pfrice(ji,jj) |
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| 225 | zfrw = (1._wp - zfri) |
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| 226 | |
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| 227 | IF(l_known_Sc) THEN |
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| 228 | zSc = pSc(ji,jj) |
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| 229 | ELSE |
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| 230 | !! Sc parameterized in terms of A (ice fraction): |
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| 231 | zSc = zfrw**(1._wp / ( 10._wp * rBeta_0 )) ! Eq.(31) |
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| 232 | END IF |
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| 233 | |
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| 234 | IF(l_known_hf) THEN |
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| 235 | zhf = phf(ji,jj) |
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| 236 | ELSE |
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| 237 | !! hf parameterized in terms of A (ice fraction): |
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| 238 | zhf = rhmax_0*zfri + rhmin_0*zfrw ! Eq.(25) |
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| 239 | END IF |
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| 240 | |
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| 241 | IF(l_known_Di) THEN |
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| 242 | zDi = pDi(ji,jj) |
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| 243 | ELSE |
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| 244 | !! Di parameterized in terms of A (ice fraction): |
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| 245 | ztmp = 1._wp / ( 1._wp - (rDmin_0/rDmax_0)**(1._wp/rBeta_0) ) ! A* Eq.(27) |
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| 246 | zDi = rDmin_0 * ( ztmp/(ztmp - zfri) )**rBeta_0 ! Eq.(26) |
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| 247 | END IF |
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| 248 | |
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| 249 | ztmp = 1._wp/pz0i(ji,jj) |
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| 250 | zrlog = LOG(zhf*ztmp/2.718_wp) / LOG(pzu*ztmp) !LOLO: adding number "e" !!! |
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| 251 | |
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| 252 | CdN_f_LG15(ji,jj) = 0.5_wp* 0.4_wp * zrlog*zrlog * zSc*zSc * zhf/zDi * zfri ! Eq.(21) Lukes & Gryanik (2015) |
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| 253 | !! 1/2 Ce |
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| 254 | |
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| 255 | END_2D |
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| 256 | END FUNCTION CdN_f_LG15 |
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| 257 | |
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| 258 | |
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| 259 | FUNCTION CdN_f_LG15_light( pzu, pfrice, pz0w ) |
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| 260 | !!---------------------------------------------------------------------- |
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| 261 | !! *** ROUTINE CdN_f_LG15_light *** |
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| 262 | !! |
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| 263 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
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| 264 | !! drag referenced at 10m to make it dependent on edges at |
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| 265 | !! leads, melt ponds and flows (to be added to the "skin" |
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| 266 | !! contribution. After some |
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| 267 | !! approximations, this can be resumed to a dependency on |
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| 268 | !! ice concentration. |
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| 269 | !! |
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| 270 | !! ** References : Lupkes & Gryanik (2015) |
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| 271 | !! |
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| 272 | !!---------------------------------------------------------------------- |
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| 273 | REAL(wp), DIMENSION(jpi,jpj) :: CdN_f_LG15_light ! neutral FORM drag coefficient contribution over sea-ice |
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| 274 | REAL(wp), INTENT(in) :: pzu ! reference height [m] |
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| 275 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b |
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| 276 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0w ! roughness length over water [m] |
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| 277 | !!---------------------------------------------------------------------- |
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| 278 | REAL(wp) :: ztmp, zrlog, zfri |
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| 279 | INTEGER :: ji, jj |
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| 280 | !!---------------------------------------------------------------------- |
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| 281 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
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| 282 | |
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| 283 | zfri = pfrice(ji,jj) |
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| 284 | |
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| 285 | ztmp = 1._wp / pz0w(ji,jj) |
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| 286 | zrlog = LOG( 10._wp * ztmp ) / LOG( pzu * ztmp ) ! part of (Eq.46) |
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| 287 | |
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| 288 | CdN_f_LG15_light(ji,jj) = rce10_i_0 *zrlog*zrlog * zfri * (1._wp - zfri)**rbeta_0 ! (Eq.46) [ index 1 is for ice, 2 for water ] |
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| 289 | |
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| 290 | END_2D |
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| 291 | END FUNCTION CdN_f_LG15_light |
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| 292 | |
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| 293 | |
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| 294 | !!====================================================================== |
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| 295 | END MODULE sbcblk_algo_ice_cdn |
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