1 | ! AeroBulk / 2020 / L. Brodeau |
---|
2 | ! |
---|
3 | ! When using AeroBulk to produce scientific work, please acknowledge with the following citation: |
---|
4 | ! |
---|
5 | ! Brodeau, L., B. Barnier, S. Gulev, and C. Woods, 2016: Climatologically |
---|
6 | ! significant effects of some approximations in the bulk parameterizations of |
---|
7 | ! turbulent air-sea fluxes. J. Phys. Oceanogr., doi:10.1175/JPO-D-16-0169.1. |
---|
8 | ! |
---|
9 | ! |
---|
10 | MODULE sbcblk_algo_ice_cdn |
---|
11 | !!==================================================================================== |
---|
12 | !! Author: Laurent Brodeau, January 2020 |
---|
13 | !!==================================================================================== |
---|
14 | USE par_kind, ONLY: wp |
---|
15 | USE par_oce, ONLY: jpi, jpj, Nis0, Nie0, Njs0, Nje0, nn_hls, ntsi, ntsj, ntei, ntej |
---|
16 | USE phycst ! physical constants |
---|
17 | USE sbc_phy ! Catalog of functions for physical/meteorological parameters in the marine boundary layer |
---|
18 | |
---|
19 | IMPLICIT NONE |
---|
20 | PRIVATE |
---|
21 | |
---|
22 | PUBLIC :: CdN10_f_LU12, CdN_f_LU12_eq36, CdN10_f_LU13, CdN_f_LG15, CdN_f_LG15_light |
---|
23 | |
---|
24 | REAL(dp), PARAMETER :: rCe_0 = 2.23E-3_wp !LOLO: this one can be more accurate when sea-ice data => Lupkes et al (2013), Eq.(1) |
---|
25 | REAL(dp), PARAMETER :: rNu_0 = 1._wp |
---|
26 | REAL(dp), PARAMETER :: rMu_0 = 1._wp |
---|
27 | REAL(dp), PARAMETER :: rbeta_0 = 1.4_wp ! (Eq.47) MIZ |
---|
28 | |
---|
29 | REAL(dp), PARAMETER :: rhmin_0 = 0.286_wp ! Eq.(25) |
---|
30 | REAL(dp), PARAMETER :: rhmax_0 = 0.534_wp ! Eq.(25) |
---|
31 | REAL(dp), PARAMETER :: rDmin_0 = 8._wp ! Eq.(27) |
---|
32 | REAL(dp), PARAMETER :: rDmax_0 = 300._wp ! Eq.(27) |
---|
33 | REAL(dp), PARAMETER :: rz0_w_0 = 3.27E-4 ! fixed roughness length over water (paragraph below Eq.36) |
---|
34 | |
---|
35 | !!============================================================ |
---|
36 | REAL(dp), PARAMETER :: rce10_i_0 = 3.46e-3_wp ! (Eq.48) MIZ |
---|
37 | |
---|
38 | REAL(dp), PARAMETER :: ralpha_0 = 0.2_wp ! (Eq.12) (ECHAM6 value) |
---|
39 | |
---|
40 | !! * Substitutions |
---|
41 | # include "do_loop_substitute.h90" |
---|
42 | !!---------------------------------------------------------------------- |
---|
43 | CONTAINS |
---|
44 | |
---|
45 | |
---|
46 | FUNCTION CdN10_f_LU12( pfrice, pz0w, pSc, phf, pDi ) |
---|
47 | !!---------------------------------------------------------------------- |
---|
48 | !! *** ROUTINE CdN10_f_LU12 *** |
---|
49 | !! |
---|
50 | !! GENERAL FORM OF EQUATION 22 of Lupkes et al. 2012 |
---|
51 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
52 | !! |
---|
53 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
---|
54 | !! drag referenced at 10m to make it dependent on edges at |
---|
55 | !! leads, melt ponds and flows (to be added to the "skin" |
---|
56 | !! contribution. After some |
---|
57 | !! approximations, this can be resumed to a dependency on |
---|
58 | !! ice concentration. |
---|
59 | !! |
---|
60 | !! ** References : Lupkes et al. JGR 2012 (theory) |
---|
61 | !! |
---|
62 | !!---------------------------------------------------------------------- |
---|
63 | REAL(dp), DIMENSION(jpi,jpj) :: CdN10_f_LU12 ! neutral FORM drag coefficient contribution over sea-ice |
---|
64 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc, phf and pDi all provided... |
---|
65 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pz0w ! roughness length over water [m] |
---|
66 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pSc ! shletering function [0-1] (Sc->1 for large distance between floes, ->0 for small distances) |
---|
67 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: phf ! mean freeboard of floes [m] |
---|
68 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pDi ! cross wind dimension of the floe (aka effective edge length for form drag) [m] |
---|
69 | !!---------------------------------------------------------------------- |
---|
70 | LOGICAL :: l_known_Sc=.FALSE., l_known_hf=.FALSE., l_known_Di=.FALSE. |
---|
71 | REAL(dp) :: ztmp, zrlog, zfri, zfrw, zSc, zhf, zDi |
---|
72 | INTEGER :: ji, jj |
---|
73 | !!---------------------------------------------------------------------- |
---|
74 | l_known_Sc = PRESENT(pSc) |
---|
75 | l_known_hf = PRESENT(phf) |
---|
76 | l_known_Di = PRESENT(pDi) |
---|
77 | |
---|
78 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
---|
79 | |
---|
80 | zfri = pfrice(ji,jj) |
---|
81 | zfrw = (1._wp - zfri) |
---|
82 | |
---|
83 | IF(l_known_Sc) THEN |
---|
84 | zSc = pSc(ji,jj) |
---|
85 | ELSE |
---|
86 | !! Sc parameterized in terms of A (ice fraction): |
---|
87 | zSc = zfrw**(1._wp / ( 10._wp * rBeta_0 )) ! Eq.(31) |
---|
88 | END IF |
---|
89 | |
---|
90 | IF(l_known_hf) THEN |
---|
91 | zhf = phf(ji,jj) |
---|
92 | ELSE |
---|
93 | !! hf parameterized in terms of A (ice fraction): |
---|
94 | zhf = rhmax_0*zfri + rhmin_0*zfrw ! Eq.(25) |
---|
95 | END IF |
---|
96 | |
---|
97 | IF(l_known_Di) THEN |
---|
98 | zDi = pDi(ji,jj) |
---|
99 | ELSE |
---|
100 | !! Di parameterized in terms of A (ice fraction): |
---|
101 | ztmp = 1._wp / ( 1._wp - (rDmin_0/rDmax_0)**(1._wp/rBeta_0) ) ! A* Eq.(27) |
---|
102 | zDi = rDmin_0 * ( ztmp/(ztmp - zfri) )**rBeta_0 ! Eq.(26) |
---|
103 | END IF |
---|
104 | |
---|
105 | ztmp = 1._wp/pz0w(ji,jj) |
---|
106 | zrlog = LOG(zhf*ztmp) / LOG(10._wp*ztmp) |
---|
107 | |
---|
108 | CdN10_f_LU12(:,:) = 0.5_wp* 0.3_wp * zrlog*zrlog * zSc*zSc * zhf/zDi * zfri ! Eq.(22) |
---|
109 | !! 1/2 Ce |
---|
110 | |
---|
111 | END_2D |
---|
112 | END FUNCTION CdN10_f_LU12 |
---|
113 | |
---|
114 | |
---|
115 | FUNCTION CdN_f_LU12_eq36( pzu, pfrice ) |
---|
116 | REAL(dp), DIMENSION(jpi,jpj) :: CdN_f_LU12_eq36 ! neutral FORM drag coefficient contribution over sea-ice |
---|
117 | REAL(wp), INTENT(in) :: pzu ! reference height [m] |
---|
118 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc, phf and pDi all provided... |
---|
119 | !!---------------------------------------------------------------------- |
---|
120 | REAL(dp) :: ztmp, zrlog, zfri, zhf, zDi |
---|
121 | INTEGER :: ji, jj |
---|
122 | !!---------------------------------------------------------------------- |
---|
123 | !zhf = 0.28 ! h_fc |
---|
124 | zhf = 0.41 ! h_fc |
---|
125 | zDi = rDmin_0 |
---|
126 | |
---|
127 | ztmp = 1._wp/rz0_w_0 |
---|
128 | zrlog = LOG(zhf*ztmp) / LOG(pzu*ztmp) |
---|
129 | |
---|
130 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
---|
131 | |
---|
132 | zfri = pfrice(ji,jj) |
---|
133 | |
---|
134 | CdN_f_LU12_eq36(:,:) = 0.5_wp* 0.3_wp * zrlog*zrlog * zhf/zDi * (1._wp - zfri)**rBeta_0 ! Eq.(35) & (36) |
---|
135 | !! 1/2 Ce |
---|
136 | END_2D |
---|
137 | END FUNCTION CdN_f_LU12_eq36 |
---|
138 | |
---|
139 | |
---|
140 | |
---|
141 | |
---|
142 | FUNCTION CdN10_f_LU13( pfrice ) |
---|
143 | !!---------------------------------------------------------------------- |
---|
144 | !! *** ROUTINE CdN10_f_LU13 *** |
---|
145 | !! |
---|
146 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
---|
147 | !! drag referenced at 10m to make it dependent on edges at |
---|
148 | !! leads, melt ponds and flows (to be added to the "skin" |
---|
149 | !! contribution. After some |
---|
150 | !! approximations, this can be resumed to a dependency on |
---|
151 | !! ice concentration. |
---|
152 | !! |
---|
153 | !! ** Method : The parameterization is taken from Lupkes et al. (2012) eq.(50) |
---|
154 | !! with the highest level of approximation: level4, eq.(59) |
---|
155 | !! The generic drag over a cell partly covered by ice can be re-written as follows: |
---|
156 | !! |
---|
157 | !! Cd = Cdw * (1-A) + Cdi * A + Ce * (1-A)**(nu+1/(10*beta)) * A**mu |
---|
158 | !! |
---|
159 | !! Ce = 2.23e-3 , as suggested by Lupkes (eq. 59) |
---|
160 | !! nu = mu = beta = 1 , as suggested by Lupkes (eq. 59) |
---|
161 | !! A is the concentration of ice minus melt ponds (if any) |
---|
162 | !! |
---|
163 | !! This new drag has a parabolic shape (as a function of A) starting at |
---|
164 | !! Cdw(say 1.5e-3) for A=0, reaching 1.97e-3 for A~0.5 |
---|
165 | !! and going down to Cdi(say 1.4e-3) for A=1 |
---|
166 | !! |
---|
167 | !! It is theoretically applicable to all ice conditions (not only MIZ) |
---|
168 | !! => see Lupkes et al (2013) |
---|
169 | !! |
---|
170 | !! ** References : Lupkes et al. JGR 2012 (theory) |
---|
171 | !! Lupkes et al. GRL 2013 (application to GCM) |
---|
172 | !! |
---|
173 | !!---------------------------------------------------------------------- |
---|
174 | REAL(dp), DIMENSION(jpi,jpj) :: CdN10_f_LU13 ! neutral FORM drag coefficient contribution over sea-ice |
---|
175 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b |
---|
176 | |
---|
177 | !!---------------------------------------------------------------------- |
---|
178 | REAL(dp) :: zcoef |
---|
179 | !!---------------------------------------------------------------------- |
---|
180 | zcoef = rNu_0 + 1._wp / ( 10._wp * rBeta_0 ) |
---|
181 | |
---|
182 | !! We are not an AGCM, we are an OGCM!!! => we drop term "(1 - A)*Cd_w" |
---|
183 | !! => so we keep only the last rhs terms of Eq.(1) of Lupkes et al, 2013 that we divide by "A": |
---|
184 | !! (we multiply Cd_i_s and Cd_i_f by A later, when applying ocean-ice partitioning... |
---|
185 | |
---|
186 | CdN10_f_LU13(:,:) = rCe_0 * pfrice(:,:)**(rMu_0 - 1._wp) * (1._wp - pfrice(:,:))**zcoef |
---|
187 | !! => seems okay for winter 100% sea-ice as second rhs term vanishes as pfrice == 1.... |
---|
188 | |
---|
189 | END FUNCTION CdN10_f_LU13 |
---|
190 | |
---|
191 | |
---|
192 | FUNCTION CdN_f_LG15( pzu, pfrice, pz0i, pSc, phf, pDi ) |
---|
193 | !!---------------------------------------------------------------------- |
---|
194 | !! *** ROUTINE CdN_f_LG15 *** |
---|
195 | !! |
---|
196 | !! GENERAL FORM OF EQUATION 21 of Lupkes & Gryanik (2015) |
---|
197 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
198 | !! |
---|
199 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
---|
200 | !! drag referenced at 10m to make it dependent on edges at |
---|
201 | !! leads, melt ponds and flows (to be added to the "skin" |
---|
202 | !! contribution. After some |
---|
203 | !! approximations, this can be resumed to a dependency on |
---|
204 | !! ice concentration. |
---|
205 | !! |
---|
206 | !! ** References : Lupkes & Gryanik (2015) |
---|
207 | !! |
---|
208 | !!---------------------------------------------------------------------- |
---|
209 | REAL(dp), DIMENSION(jpi,jpj) :: CdN_f_LG15 ! neutral FORM drag coefficient contribution over sea-ice |
---|
210 | REAL(wp), INTENT(in ) :: pzu ! reference height [m] |
---|
211 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b ! NOT USED if pSc, phf and pDi all provided... |
---|
212 | REAL(dp), DIMENSION(jpi,jpj), INTENT(in) :: pz0i ! roughness length over ICE [m] (in LU12, it's over water ???) |
---|
213 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pSc ! shletering function [0-1] (Sc->1 for large distance between floes, ->0 for small distances) |
---|
214 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: phf ! mean freeboard of floes [m] |
---|
215 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in), OPTIONAL :: pDi ! cross wind dimension of the floe (aka effective edge length for form drag) [m] |
---|
216 | !!---------------------------------------------------------------------- |
---|
217 | LOGICAL :: l_known_Sc=.FALSE., l_known_hf=.FALSE., l_known_Di=.FALSE. |
---|
218 | REAL(dp) :: ztmp, zrlog, zfri, zfrw, zSc, zhf, zDi |
---|
219 | INTEGER :: ji, jj |
---|
220 | !!---------------------------------------------------------------------- |
---|
221 | l_known_Sc = PRESENT(pSc) |
---|
222 | l_known_hf = PRESENT(phf) |
---|
223 | l_known_Di = PRESENT(pDi) |
---|
224 | |
---|
225 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
---|
226 | |
---|
227 | zfri = pfrice(ji,jj) |
---|
228 | zfrw = (1._wp - zfri) |
---|
229 | |
---|
230 | IF(l_known_Sc) THEN |
---|
231 | zSc = pSc(ji,jj) |
---|
232 | ELSE |
---|
233 | !! Sc parameterized in terms of A (ice fraction): |
---|
234 | zSc = zfrw**(1._wp / ( 10._wp * rBeta_0 )) ! Eq.(31) |
---|
235 | END IF |
---|
236 | |
---|
237 | IF(l_known_hf) THEN |
---|
238 | zhf = phf(ji,jj) |
---|
239 | ELSE |
---|
240 | !! hf parameterized in terms of A (ice fraction): |
---|
241 | zhf = rhmax_0*zfri + rhmin_0*zfrw ! Eq.(25) |
---|
242 | END IF |
---|
243 | |
---|
244 | IF(l_known_Di) THEN |
---|
245 | zDi = pDi(ji,jj) |
---|
246 | ELSE |
---|
247 | !! Di parameterized in terms of A (ice fraction): |
---|
248 | ztmp = 1._wp / ( 1._wp - (rDmin_0/rDmax_0)**(1._wp/rBeta_0) ) ! A* Eq.(27) |
---|
249 | zDi = rDmin_0 * ( ztmp/(ztmp - zfri) )**rBeta_0 ! Eq.(26) |
---|
250 | END IF |
---|
251 | |
---|
252 | ztmp = 1._wp/pz0i(ji,jj) |
---|
253 | zrlog = LOG(zhf*ztmp/2.718_wp) / LOG(pzu*ztmp) !LOLO: adding number "e" !!! |
---|
254 | |
---|
255 | CdN_f_LG15(:,:) = 0.5_wp* 0.4_wp * zrlog*zrlog * zSc*zSc * zhf/zDi * zfri ! Eq.(21) Lukes & Gryanik (2015) |
---|
256 | !! 1/2 Ce |
---|
257 | |
---|
258 | END_2D |
---|
259 | END FUNCTION CdN_f_LG15 |
---|
260 | |
---|
261 | |
---|
262 | |
---|
263 | FUNCTION CdN_f_LG15_light( pzu, pfrice, pz0w ) |
---|
264 | !!---------------------------------------------------------------------- |
---|
265 | !! *** ROUTINE CdN_f_LG15_light *** |
---|
266 | !! |
---|
267 | !! ** Purpose : Computes the "form" contribution of the neutral air-ice |
---|
268 | !! drag referenced at 10m to make it dependent on edges at |
---|
269 | !! leads, melt ponds and flows (to be added to the "skin" |
---|
270 | !! contribution. After some |
---|
271 | !! approximations, this can be resumed to a dependency on |
---|
272 | !! ice concentration. |
---|
273 | !! |
---|
274 | !! ** References : Lupkes & Gryanik (2015) |
---|
275 | !! |
---|
276 | !!---------------------------------------------------------------------- |
---|
277 | REAL(dp), DIMENSION(jpi,jpj) :: CdN_f_LG15_light ! neutral FORM drag coefficient contribution over sea-ice |
---|
278 | REAL(wp), INTENT(in) :: pzu ! reference height [m] |
---|
279 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in) :: pfrice ! ice concentration [fraction] => at_i_b |
---|
280 | REAL(dp), DIMENSION(jpi,jpj), INTENT(in) :: pz0w ! roughness length over water [m] |
---|
281 | !!---------------------------------------------------------------------- |
---|
282 | REAL(dp) :: ztmp, zrlog, zfri |
---|
283 | INTEGER :: ji, jj |
---|
284 | !!---------------------------------------------------------------------- |
---|
285 | DO_2D( nn_hls, nn_hls, nn_hls, nn_hls ) |
---|
286 | |
---|
287 | zfri = pfrice(ji,jj) |
---|
288 | |
---|
289 | ztmp = 1._wp / pz0w(ji,jj) |
---|
290 | zrlog = LOG( 10._wp * ztmp ) / LOG( pzu * ztmp ) ! part of (Eq.46) |
---|
291 | |
---|
292 | CdN_f_LG15_light(:,:) = rce10_i_0 *zrlog*zrlog * zfri * (1._wp - zfri)**rbeta_0 ! (Eq.46) [ index 1 is for ice, 2 for water ] |
---|
293 | |
---|
294 | END_2D |
---|
295 | END FUNCTION CdN_f_LG15_light |
---|
296 | |
---|
297 | |
---|
298 | |
---|
299 | !!====================================================================== |
---|
300 | END MODULE sbcblk_algo_ice_cdn |
---|