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limmp.F90 in branches/2016/dev_r6859_LIM3_meltponds/NEMOGCM/NEMO/LIM_SRC_3 – NEMO

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source: branches/2016/dev_r6859_LIM3_meltponds/NEMOGCM/NEMO/LIM_SRC_3/limmp.F90 @ 8098

Last change on this file since 8098 was 8098, checked in by vancop, 8 years ago
Further melt pond work
File size: 91.0 KB

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1	MODULE limmp
2	!!======================================================================
3	!! * MODULE limmp *
4	!! Melt ponds
5	!!======================================================================
6	!! history : ! Original code by Daniela Flocco and Adrian Turner
7	!! 1.0 ! 2012 (O. Lecomte) Adaptation for scientific tests (NEMO3.1)
8	!! 2.0 ! 2016 (O. Lecomte, C. Rousset, M. Vancoppenolle) Implementation in NEMO3.6
9	!!----------------------------------------------------------------------
10	#if defined key_lim3
11	!!----------------------------------------------------------------------
12	!! 'key_lim3' : LIM3 sea-ice model
13	!!----------------------------------------------------------------------
14	!! lim_mp_init : some initialization and namelist read
15	!! lim_mp : main calling routine
16	!! lim_mp_topo : main melt pond routine for the "topographic" formulation (FloccoFeltham)
17	!! lim_mp_area : ??? compute melt pond fraction per category
18	!! lim_mp_perm : computes permeability (should be a FUNCTION!)
19	!! calc_hpond : computes melt pond depth
20	!! permeability_phy : computes permeability
21
22	!!----------------------------------------------------------------------
23	USE phycst ! physical constants
24	USE dom_oce ! ocean space and time domain
25	! USE sbc_ice ! Surface boundary condition: ice fields
26	USE ice ! LIM-3 variables
27	USE lbclnk ! lateral boundary conditions - MPP exchanges
28	USE lib_mpp ! MPP library
29	USE wrk_nemo ! work arrays
30	USE in_out_manager ! I/O manager
31	USE lib_fortran ! glob_sum
32	USE timing ! Timing
33	! USE limcons ! conservation tests
34	! USE limctl ! control prints
35	! USE limvar
36
37	!OLI_CODE USE ice_oce, ONLY: rdt_ice, tatm_ice
38	!OLI_CODE USE phycst
39	!OLI_CODE USE dom_ice
40	!OLI_CODE USE dom_oce
41	!OLI_CODE USE sbc_oce
42	!OLI_CODE USE sbc_ice
43	!OLI_CODE USE par_ice
44	!OLI_CODE USE par_oce
45	!OLI_CODE USE ice
46	!OLI_CODE USE thd_ice
47	!OLI_CODE USE in_out_manager
48	!OLI_CODE USE lbclnk
49	!OLI_CODE USE lib_mpp
50	!OLI_CODE
51	!OLI_CODE IMPLICIT NONE
52	!OLI_CODE PRIVATE
53	!OLI_CODE
54	!OLI_CODE PUBLIC lim_mp_init
55	!OLI_CODE PUBLIC lim_mp
56
57	IMPLICIT NONE
58	PRIVATE
59
60	PUBLIC lim_mp_init ! routine called by sbcice_lim.F90
61	PUBLIC lim_mp ! routine called by sbcice_lim.F90
62
63	!! * Substitutions
64	# include "vectopt_loop_substitute.h90"
65	!!----------------------------------------------------------------------
66	!! NEMO/LIM3 4.0 , UCL - NEMO Consortium (2011)
67	!! $Id: limdyn.F90 6994 2016-10-05 13:07:10Z clem $
68	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
69	!!----------------------------------------------------------------------
70	CONTAINS
71
72	SUBROUTINE lim_mp_init
73	!!-------------------------------------------------------------------
74	!! * ROUTINE lim_mp_init *
75	!!
76	!! ** Purpose : Physical constants and parameters linked to melt ponds
77	!! over sea ice
78	!!
79	!! ** Method : Read the namicemp namelist and check the melt pond
80	!! parameter values called at the first timestep (nit000)
81	!!
82	!! ** input : Namelist namicemp
83	!!-------------------------------------------------------------------
84	INTEGER :: ios ! Local integer output status for namelist read
85	NAMELIST/namicemp/ ln_pnd, nn_pnd_scheme, nn_pnd_cpl, rn_apnd, rn_hpnd
86	!!-------------------------------------------------------------------
87
88	REWIND( numnam_ice_ref ) ! Namelist namicemp in reference namelist : Melt Ponds
89	READ ( numnam_ice_ref, namicemp, IOSTAT = ios, ERR = 901)
90	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namicemp in reference namelist', lwp )
91
92	REWIND( numnam_ice_cfg ) ! Namelist namicemp in configuration namelist : Melt Ponds
93	READ ( numnam_ice_cfg, namicemp, IOSTAT = ios, ERR = 902 )
94	902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namicemp in configuration namelist', lwp )
95	IF(lwm) WRITE ( numoni, namicemp )
96
97	IF(lwp) THEN ! control print
98	WRITE(numout,*)
99	WRITE(numout,*) 'lim_mp_init : ice parameters for melt ponds'
100	WRITE(numout,*) '~~~~~~~~~~~~'
101	WRITE(numout,*)' Activate melt ponds ln_pnd = ', ln_pnd
102	WRITE(numout,*)' Type of melt pond scheme =0 presc, =1 empirical = 2 topo nn_pnd_scheme = ', nn_pnd_scheme
103	WRITE(numout,*)' Type of melt pond coupling =0 pass., =1 full, =2 rad, 3=fw nn_pnd_cpl = ', nn_pnd_cpl
104	WRITE(numout,*)' Prescribed pond fraction rn_apnd = ', rn_apnd
105	WRITE(numout,*)' Prescribed pond depth rn_hpnd = ', rn_hpnd
106	ENDIF
107
108	IF ( .NOT. ln_pnd ) THEN
109	WRITE(numout,*) ' Melt ponds are not activated '
110	WRITE(numout,*) ' nn_pnd_scheme, nn_pnd_cpl, rn_apnd and rn_hpnd are set to zero '
111	nn_pnd_scheme = 0
112	nn_pnd_cpl = 0
113	rn_apnd = 0._wp
114	rn_hpnd = 0._wp
115	ENDIF
116
117	!
118	END SUBROUTINE lim_mp_init
119
120
121
122	SUBROUTINE lim_mp( kt )
123	!!-------------------------------------------------------------------
124	!! * ROUTINE lim_mp *
125	!!
126	!! ** Purpose : change melt pond fraction
127	!!
128	!! ** Method : brutal force
129	!!
130	!! ** Action : -
131	!! -
132	!!------------------------------------------------------------------------------------
133
134	INTEGER, INTENT(in) :: kt ! number of iteration
135	INTEGER :: ji, jj, jl ! dummy loop indices
136
137	! REAL(wp), POINTER, DIMENSION(:,:) :: zfsurf ! surface heat flux(obsolete, should be droped)
138	!
139	!!-------------------------------------------------------------------
140
141	IF( nn_timing == 1 ) CALL timing_start('limthd')
142
143	IF( nn_timing == 1 ) CALL timing_start('lim_mp')
144
145	SELECT CASE ( nn_pnd_scheme )
146
147	CASE (0)
148
149	CALL lim_mp_cstt ! staircase melt ponds
150
151	CASE (1)
152
153	CALL lim_mp_cesm ! empirical melt ponds
154
155	CASE (2)
156
157	CALL lim_mp_topo & ! topographic melt ponds
158	& (at_i, a_i, &
159	& vt_i, v_i, v_s, t_i, s_i, a_ip_frac, &
160	& h_ip, t_su)
161
162	END SELECT
163
164	! we should probably not aggregate here since we do it in lim_var_agg
165	! before output, unless we need the total volume and faction else where
166
167	! we should also make sure a_ip and v_ip are properly updated at the end
168	! of the routine
169
170	END SUBROUTINE lim_mp
171
172	SUBROUTINE lim_mp_cstt
173	!!-------------------------------------------------------------------
174	!! * ROUTINE lim_mp_cstt *
175	!!
176	!! ** Purpose : Compute melt pond evolution
177	!!
178	!! ** Method : Melt pond fraction and thickness are prescribed
179	!! to non-zero values when t_su = 0C
180	!!
181	!! ** Tunable parameters : pond fraction (rn_apnd), pond depth (rn_hpnd)
182	!!
183	!! ** Note : Coupling with such melt ponds is only radiative
184	!! Advection, ridging, rafting... are bypassed
185	!!
186	!! ** References : Bush, G.W., and Trump, D.J. (2017)
187	!!
188	!!-------------------------------------------------------------------
189	INTEGER :: ji, jj, jl
190	REAL(wp) :: z1_jpl ! 1/jpl
191	!!-------------------------------------------------------------------
192
193	z1_jpl = 1. / FLOAT(jpl)
194
195	WHERE ( ( a_i > epsi10 ) .AND. ( t_su >= rt0-epsi06 ) )
196	a_ip = rn_apnd * z1_jpl
197	h_ip = rn_hpnd
198	v_ip = a_ip * h_ip
199	a_ip_frac = a_ip / a_i
200	ELSE WHERE
201	a_ip = 0._wp
202	h_ip = 0._wp
203	v_ip = 0._wp
204	a_ip_frac = 0._wp
205	END WHERE
206
207	wfx_pnd(:,:) = 0._wp
208
209	END SUBROUTINE lim_mp_cstt
210
211	SUBROUTINE lim_mp_cesm
212	!!-------------------------------------------------------------------
213	!! * ROUTINE lim_mp_cesm *
214	!!
215	!! ** Purpose : Compute melt pond evolution
216	!!
217	!! ** Method : Empirical method. A fraction of meltwater is accumulated
218	!! in pond volume. It is then released exponentially when
219	!! surface is freezing.
220	!!
221	!! ** Tunable parameters : (no expertise yet)
222	!!
223	!! ** Note : Stolen from CICE for quick test of the melt pond
224	!! radiation and freshwater interfaces
225	!! Coupling can be radiative AND freshwater
226	!! Advection, ridging, rafting are called
227	!!
228	!! ** References : Holland, M. M. et al (J Clim 2012)
229	!!
230	!!-------------------------------------------------------------------
231
232	INTEGER, POINTER, DIMENSION(:) :: indxi ! compressed indices for cells with ice melting
233	INTEGER, POINTER, DIMENSION(:) :: indxj !
234
235	REAL(wp), POINTER, DIMENSION(:,:) :: zwfx_mlw ! available meltwater for melt ponding
236	REAL(wp), POINTER, DIMENSION(:,:,:) :: zrfrac ! fraction of available meltwater retained for melt ponding
237
238	REAL(wp), PARAMETER :: zrmin = 0.15_wp ! minimum fraction of available meltwater retained for melt ponding
239	REAL(wp), PARAMETER :: zrmax = 0.70_wp ! maximum '' '' '' '' ''
240	REAL(wp), PARAMETER :: zrexp = 0.01_wp ! rate constant to refreeze melt ponds
241	REAL(wp), PARAMETER :: zpnd_aspect = 0.8_wp ! pond aspect ratio
242
243	REAL(wp) :: zhi ! dummy ice thickness
244	REAL(wp) :: zhs ! dummy snow depth
245	REAL(wp) :: zTp ! reference temperature
246	REAL(wp) :: zdTs ! dummy temperature difference
247	REAL(wp) :: z1_rhofw ! inverse freshwater density
248	REAL(wp) :: z1_zpnd_aspect ! inverse pond aspect ratio
249	REAL(wp) :: zvpold ! dummy pond volume
250
251	INTEGER :: ji, jj, jl, ij ! loop indices
252	INTEGER :: icells ! size of dummy array
253
254	!!-------------------------------------------------------------------
255
256	CALL wrk_alloc( jpi*jpj, indxi, indxj)
257	CALL wrk_alloc( jpi,jpj, zwfx_mlw )
258	CALL wrk_alloc( jpi,jpj,jpl, zrfrac )
259
260	z1_rhofw = 1. / rhofw
261	z1_zpnd_aspect = 1. / zpnd_aspect
262	zTp = -2.
263
264	!------------------------------------------------------------------
265	! Available melt water for melt ponding and corresponding fraction
266	!------------------------------------------------------------------
267
268	zwfx_mlw(:,:) = wfx_sum(:,:) + wfx_snw(:,:) ! available meltwater for melt ponding
269
270	zrfrac(:,:,:) = zrmin + ( zrmax - zrmin ) * a_i(:,:,:)
271
272	DO jl = 1, jpl
273
274	! v_ip(:,:,jl) ! Initialize things
275	! a_ip(:,:,jl)
276	! volpn(:,:) = hpnd(:,:) * apnd(:,:) * aicen(:,:)
277
278	!------------------------------------------------------------------------------
279	! Identify grid cells where ponds should be updated (can probably be improved)
280	!------------------------------------------------------------------------------
281
282	indxi(:) = 0
283	indxj(:) = 0
284	icells = 0
285
286	DO jj = 1, jpj
287	DO ji = 1, jpi
288	IF ( a_i(ji,jj,jl) > epsi10 ) THEN
289	icells = icells + 1
290	indxi(icells) = ji
291	indxj(icells) = jj
292	ENDIF
293	END DO ! ji
294	END DO ! jj
295
296	DO ij = 1, icells
297
298	ji = indxi(ij)
299	jj = indxj(ij)
300
301	zhi = v_i(ji,jj,jl) / a_i(ji,jj,jl)
302	zhs = v_s(ji,jj,jl) / a_i(ji,jj,jl)
303
304	IF ( zhi < rn_himin) THEN !--- Remove ponds on thin ice if ice is too thin
305
306	a_ip(ji,jj,jl) = 0._wp !--- Dump ponds
307	v_ip(ji,jj,jl) = 0._wp
308	a_ip_frac(ji,jj,jl) = 0._wp
309	h_ip(ji,jj,jl) = 0._wp
310
311	IF ( ( nn_pnd_cpl == 1 ) .OR. ( nn_pnd_cpl == 3 ) ) & !--- Give freshwater to the ocean
312	wfx_pnd(ji,jj) = wfx_pnd(ji,jj) + v_ip(ji,jj,jl)
313
314
315	ELSE !--- Update pond characteristics
316
317	!--- Add retained melt water to melt ponds
318	v_ip(ji,jj,jl) = v_ip(ji,jj,jl) + zrfrac(ji,jj,jl) * z1_rhofw * zwfx_mlw(ji,jj) * a_i(ji,jj,jl) * rdt_ice
319
320	!--- Shrink pond due to refreezing
321	zdTs = MAX ( zTp - t_su(ji,jj,jl) + rt0 , 0. )
322
323	zvpold = v_ip(ji,jj,jl)
324
325	v_ip(ji,jj,jl) = v_ip(ji,jj,jl) * EXP( zrexp * zdTs / zTp )
326
327	!--- Dump meltwater due to refreezing ( of course this is wrong
328	!--- but this parameterization is too simple )
329	IF ( ( nn_pnd_cpl == 1 ) .OR. ( nn_pnd_cpl == 3 ) ) THEN
330
331	wfx_pnd(ji,jj) = wfx_pnd(ji,jj) + rhofw * ( v_ip(ji,jj,jl) - zvpold ) * r1_rdtice
332
333	ENDIF
334
335	a_ip_frac(ji,jj,jl) = MIN( 1._wp , SQRT( v_ip(ji,jj,jl) * z1_zpnd_aspect / a_i(ji,jj,jl) ) )
336
337	h_ip(ji,jj,jl) = zpnd_aspect * a_ip_frac(ji,jj,jl)
338
339	a_ip(ji,jj,jl) = a_ip_frac(ji,jj,jl) * a_i(ji,jj,jl)
340
341	!-----------------------------------------------------------
342	! Limit pond depth
343	!-----------------------------------------------------------
344	! hpondn = min(hpondn, dpthhi*hi)
345
346	!--- Give freshwater to the ocean ?
347
348	ENDIF
349
350	END DO
351
352	END DO ! jpl
353
354	!--- Remove retained meltwater from surface fluxes
355
356	IF ( ( nn_pnd_cpl .EQ. 1 ) .OR. ( nn_pnd_cpl .EQ. 3 ) ) THEN
357
358	wfx_snw(:,:) = wfx_snw(:,:) * ( 1. - zrmin - ( zrmax - zrmin ) * at_i(:,:) )
359
360	wfx_sum(:,:) = wfx_sum(:,:) * ( 1. - zrmin - ( zrmax - zrmin ) * at_i(:,:) )
361
362	ENDIF
363
364	END SUBROUTINE lim_mp_cesm
365
366	SUBROUTINE lim_mp_topo (aice, aicen, &
367	vice, vicen, &
368	vsnon, &
369	ticen, salin, &
370	a_ip_frac, h_ip, &
371	Tsfc )
372	!!-------------------------------------------------------------------
373	!! * ROUTINE lim_mp_topo *
374	!!
375	!! ** Purpose : Compute melt pond evolution based on the ice
376	!! topography as inferred from the ice thickness
377	!! distribution.
378	!!
379	!! ** Method : This code is initially based on Flocco and Feltham
380	!! (2007) and Flocco et al. (2010). More to come...
381	!!
382	!! ** Tunable parameters :
383	!!
384	!! ** Note :
385	!!
386	!! ** References
387	!! Flocco, D. and D. L. Feltham, 2007. A continuum model of melt pond
388	!! evolution on Arctic sea ice. J. Geophys. Res. 112, C08016, doi:
389	!! 10.1029/2006JC003836.
390	!! Flocco, D., D. L. Feltham and A. K. Turner, 2010. Incorporation of
391	!! a physically based melt pond scheme into the sea ice component of a
392	!! climate model. J. Geophys. Res. 115, C08012,
393	!! doi: 10.1029/2009JC005568.
394	!!
395	!!-------------------------------------------------------------------
396
397	REAL (wp), DIMENSION (jpi,jpj), &
398	INTENT(IN) :: &
399	aice, & ! total ice area fraction
400	vice ! total ice volume (m)
401
402	REAL (wp), DIMENSION (jpi,jpj,jpl), &
403	INTENT(IN) :: &
404	aicen, & ! ice area fraction, per category
405	vsnon, & ! snow volume, per category (m)
406	vicen ! ice volume, per category (m)
407
408	REAL (wp), DIMENSION (jpi,jpj,nlay_i,jpl), &
409	INTENT(IN) :: &
410	ticen, & ! ice enthalpy, per category
411	salin
412
413	REAL (wp), DIMENSION (jpi,jpj,jpl), &
414	INTENT(INOUT) :: &
415	a_ip_frac , & ! pond area fraction of ice, per ice category
416	h_ip ! pond depth, per ice category (m)
417
418	REAL (wp), DIMENSION (jpi,jpj,jpl), &
419	INTENT(IN) :: &
420	Tsfc ! snow/sea ice surface temperature
421
422	! local variables
423	REAL (wp), DIMENSION (jpi,jpj,jpl) :: &
424	zTsfcn, & ! ice/snow surface temperature (C)
425	zvolpn, & ! pond volume per unit area, per category (m)
426	zvuin ! water-equivalent volume of ice lid on melt pond ('upper ice', m)
427
428	REAL (wp), DIMENSION (jpi,jpj,jpl) :: &
429	zapondn,& ! pond area fraction, per category
430	zhpondn ! pond depth, per category (m)
431
432	REAL (wp), DIMENSION (jpi,jpj) :: &
433	zvolp ! total volume of pond, per unit area of pond (m)
434
435	REAL (wp) :: &
436	zhi, & ! ice thickness (m)
437	zdHui, & ! change in thickness of ice lid (m)
438	zomega, & ! conduction
439	zdTice, & ! temperature difference across ice lid (C)
440	zdvice, & ! change in ice volume (m)
441	zTavg, & ! mean surface temperature across categories (C)
442	zTp, & ! pond freezing temperature (C)
443	zdvn ! change in melt pond volume for fresh water budget
444	INTEGER, DIMENSION (jpi*jpj) :: &
445	indxi, indxj ! compressed indices for cells with ice melting
446
447	INTEGER :: n,k,i,j,ij,icells,indxij ! loop indices
448
449	INTEGER, DIMENSION (jpl) :: &
450	kcells ! cells where ice lid combines with vice
451
452	INTEGER, DIMENSION (jpi*jpj,jpl) :: &
453	indxii, indxjj ! i,j indices for kcells loop
454
455	REAL (wp), parameter :: &
456	zhicemin = 0.1_wp , & ! minimum ice thickness with ponds (m)
457	zTd = 0.15_wp, & ! temperature difference for freeze-up (C)
458	zr1_rlfus = 1._wp / 0.334e+6 / 917._wp , & ! (J/m^3)
459	zmin_volp = 1.e-4_wp, & ! minimum pond volume (m)
460	z0 = 0._wp, &
461	zTimelt = 0._wp, &
462	z01 = 0.01_wp, &
463	z25 = 0.25_wp, &
464	z5 = 0.5_wp
465
466	!---------------------------------------------------------------
467	! Initialization
468	!---------------------------------------------------------------
469
470	zhpondn(:,:,:) = 0._wp
471	zapondn(:,:,:) = 0._wp
472	indxii(:,:) = 0
473	indxjj(:,:) = 0
474	kcells(:) = 0
475
476	zvolp(:,:) = wfx_sum(:,:) + wfx_snw(:,:) + vt_ip(:,:) ! Total available melt water, to be distributed as melt ponds
477	zTsfcn(:,:,:) = zTsfcn(:,:,:) - rt0 ! Convert in Celsius
478
479	! The freezing temperature for meltponds is assumed slightly below 0C,
480	! as if meltponds had a little salt in them. The salt budget is not
481	! altered for meltponds, but if it were then an actual pond freezing
482	! temperature could be computed.
483
484	! zTp = zTimelt - zTd ---> for lids
485
486	!-----------------------------------------------------------------
487	! Identify grid cells with ponds
488	!-----------------------------------------------------------------
489
490	icells = 0
491	DO j = 1, jpj
492	DO i = 1, jpi
493	zhi = z0
494	IF (aice(i,j) > epsi10 ) zhi = vice(i,j)/aice(i,j)
495	IF ( aice(i,j) > z01 .and. zhi > zhicemin .and. &
496	zvolp(i,j) > zmin_volp*aice(i,j)) THEN
497	icells = icells + 1
498	indxi(icells) = i
499	indxj(icells) = j
500	ELSE ! remove ponds on thin ice
501	!fpond(i,j) = fpond(i,j) - zvolp(i,j)
502	zvolpn(i,j,:) = z0
503	zvuin (i,j,:) = z0
504	zvolp (i,j) = z0
505	END IF
506	END DO ! i
507	END DO ! j
508
509	DO ij = 1, icells
510	i = indxi(ij)
511	j = indxj(ij)
512
513	!--------------------------------------------------------------
514	! calculate pond area and depth
515	!--------------------------------------------------------------
516	CALL lim_mp_area(aice(i,j),vice(i,j), &
517	aicen(i,j,:), vicen(i,j,:), vsnon(i,j,:), &
518	ticen(i,j,:,:), salin(i,j,:,:), &
519	zvolpn(i,j,:), zvolp(i,j), &
520	zapondn(i,j,:),zhpondn(i,j,:), zdvn)
521	! outputs are
522	! - zdvn
523	! - zvolpn
524	! - zvolp
525	! - zapondn
526	! - zhpondn
527
528	wfx_pnd(i,j) = wfx_pnd(i,j) + zdvn ! update flux from ponds to ocean
529
530	! mean surface temperature MV - why do we need that ? --> for the lid
531
532	! zTavg = z0
533	! DO n = 1, jpl
534	! zTavg = zTavg + zTsfcn(i,j,n)*aicen(i,j,n)
535	! END DO
536	! zTavg = zTavg / aice(i,j)
537
538	END DO ! ij
539
540	!---------------------------------------------------------------
541	! Update pond volume and fraction
542	!---------------------------------------------------------------
543
544	a_ip(:,:,:) = zapondn(:,:,:)
545	v_ip(:,:,:) = zapondn(:,:,:) * zhpondn(:,:,:)
546	a_ip_frac(:,:,:) = 0._wp
547	h_ip (:,:,:) = 0._wp
548
549	END SUBROUTINE lim_mp_topo
550
551	SUBROUTINE lim_mp_area(aice,vice, &
552	aicen, vicen, vsnon, ticen, &
553	salin, zvolpn, zvolp, &
554	zapondn,zhpondn,dvolp)
555
556	!!-------------------------------------------------------------------
557	!! * ROUTINE lim_mp_area *
558	!!
559	!! ** Purpose : Given the total volume of meltwater, update
560	!! pond fraction (a_ip) and depth (should be volume)
561	!!
562	!! **
563	!!
564	!!------------------------------------------------------------------
565
566	REAL (wp), INTENT(IN) :: &
567	aice,vice
568
569	REAL (wp), DIMENSION(jpl), INTENT(IN) :: &
570	aicen, vicen, vsnon
571
572	REAL (wp), DIMENSION(nlay_i,jpl), INTENT(IN) :: &
573	ticen, salin
574
575	REAL (wp), DIMENSION(jpl), INTENT(INOUT) :: &
576	zvolpn
577
578	REAL (wp), INTENT(INOUT) :: &
579	zvolp, dvolp
580
581	REAL (wp), DIMENSION(jpl), INTENT(OUT) :: &
582	zapondn, zhpondn
583
584	INTEGER :: &
585	n, ns, &
586	m_index, &
587	permflag
588
589	REAL (wp), DIMENSION(jpl) :: &
590	hicen, &
591	hsnon, &
592	asnon, &
593	alfan, &
594	betan, &
595	cum_max_vol, &
596	reduced_aicen
597
598	REAL (wp), DIMENSION(0:jpl) :: &
599	cum_max_vol_tmp
600
601	REAL (wp) :: &
602	hpond, &
603	drain, &
604	floe_weight, &
605	pressure_head, &
606	hsl_rel, &
607	deltah, &
608	perm, &
609	msno
610
611	REAL (wp), parameter :: &
612	viscosity = 1.79e-3_wp, & ! kinematic water viscosity in kg/m/s
613	z0 = 0.0_wp , &
614	c1 = 1.0_wp , &
615	p4 = 0.4_wp , &
616	p6 = 0.6_wp , &
617	epsi10 = 1.0e-11_wp
618
619	!-----------\|
620	! \|
621	! \|-----------\|
622	!___________\|___________\|______________________________________sea-level
623	! \| \|
624	! \| \|---^--------\|
625	! \| \| \| \|
626	! \| \| \| \|-----------\| \|-------
627	! \| \| \|alfan(n)\| \| \|
628	! \| \| \| \| \|--------------\|
629	! \| \| \| \| \| \|
630	!---------------------------v-------------------------------------------
631	! \| \| ^ \| \| \|
632	! \| \| \| \| \|--------------\|
633	! \| \| \|betan(n)\| \| \|
634	! \| \| \| \|-----------\| \|-------
635	! \| \| \| \|
636	! \| \|---v------- \|
637	! \| \|
638	! \|-----------\|
639	! \|
640	!-----------\|
641
642	!-------------------------------------------------------------------
643	! initialize
644	!-------------------------------------------------------------------
645
646	DO n = 1, jpl
647
648	zapondn(n) = z0
649	zhpondn(n) = z0
650
651	!----------------------------------------
652	! X) compute the effective snow fraction
653	!----------------------------------------
654	IF (aicen(n) < epsi10) THEN
655	hicen(n) = z0
656	hsnon(n) = z0
657	reduced_aicen(n) = z0
658	ELSE
659	hicen(n) = vicen(n) / aicen(n)
660	hsnon(n) = vsnon(n) / aicen(n)
661	reduced_aicen(n) = c1 ! n=jpl
662	IF (n < jpl) reduced_aicen(n) = aicen(n) &
663	* (-0.024_wp*hicen(n) + 0.832_wp)
664	asnon(n) = reduced_aicen(n) ! effective snow fraction (empirical)
665	! MV should check whether this makes sense to have the same effective snow fraction in here
666	END IF
667
668	! This choice for alfa and beta ignores hydrostatic equilibium of categories.
669	! Hydrostatic equilibium of the entire ITD is accounted for below, assuming
670	! a surface topography implied by alfa=0.6 and beta=0.4, and rigidity across all
671	! categories. alfa and beta partition the ITD - they are areas not thicknesses!
672	! Multiplying by hicen, alfan and betan (below) are thus volumes per unit area.
673	! Here, alfa = 60% of the ice area (and since hice is constant in a category,
674	! alfan = 60% of the ice volume) in each category lies above the reference line,
675	! and 40% below. Note: p6 is an arbitrary choice, but alfa+beta=1 is required.
676
677	! MV:
678	! Note that this choice is not in the original FF07 paper and has been adopted in CICE
679	! No reason why is explained in the doc, but I guess there is a reason. I'll try to investigate, maybe
680
681	! Where does that choice come from
682
683	alfan(n) = 0.6 * hicen(n)
684	betan(n) = 0.4 * hicen(n)
685
686	cum_max_vol(n) = z0
687	cum_max_vol_tmp(n) = z0
688
689	END DO ! jpl
690
691	cum_max_vol_tmp(0) = z0
692	drain = z0
693	dvolp = z0
694
695	!----------------------------------------------------------
696	! x) Drain overflow water, update pond fraction and volume
697	!----------------------------------------------------------
698
699	!--------------------------------------------------------------------------
700	! the maximum amount of water that can be contained up to each ice category
701	!--------------------------------------------------------------------------
702
703	! MV
704	! If melt ponds are too deep to be sustainable given the ITD (OVERFLOW)
705	! Then the excess volume cum_max_vol(jl) drains out of the system
706	! It should be added to wfx_pnd
707	! END MV
708
709	DO n = 1, jpl-1 ! last category can not hold any volume
710
711	IF (alfan(n+1) >= alfan(n) .and. alfan(n+1) > z0) THEN
712
713	! total volume in level including snow
714	cum_max_vol_tmp(n) = cum_max_vol_tmp(n-1) + &
715	(alfan(n+1) - alfan(n)) * sum(reduced_aicen(1:n))
716
717	! subtract snow solid volumes from lower categories in current level
718	DO ns = 1, n
719	cum_max_vol_tmp(n) = cum_max_vol_tmp(n) &
720	- rhosn/rhofw * & ! free air fraction that can be filled by water
721	asnon(ns) * & ! effective areal fraction of snow in that category
722	max(min(hsnon(ns)+alfan(ns)-alfan(n), alfan(n+1)- &
723	alfan(n)), z0)
724	END DO
725
726	ELSE ! assume higher categories unoccupied
727	cum_max_vol_tmp(n) = cum_max_vol_tmp(n-1)
728	END IF
729	!IF (cum_max_vol_tmp(n) < z0) THEN
730	! call abort_ice('negative melt pond volume')
731	!END IF
732	END DO
733	cum_max_vol_tmp(jpl) = cum_max_vol_tmp(jpl-1) ! last category holds no volume
734	cum_max_vol (1:jpl) = cum_max_vol_tmp(1:jpl)
735
736	!----------------------------------------------------------------
737	! is there more meltwater than can be held in the floe?
738	!----------------------------------------------------------------
739	IF (zvolp >= cum_max_vol(jpl)) THEN
740	drain = zvolp - cum_max_vol(jpl) + epsi10
741	zvolp = zvolp - drain ! update meltwater volume available
742	dvolp = drain ! this is the drained water
743	IF (zvolp < epsi10) THEN
744	dvolp = dvolp + zvolp
745	zvolp = z0
746	END IF
747	END IF
748
749	! height and area corresponding to the remaining volume
750
751	! call calc_hpond(reduced_aicen, asnon, hsnon, rhos, alfan, &
752	! zvolp, cum_max_vol, hpond, m_index)
753
754	DO n=1, m_index
755	zhpondn(n) = hpond - alfan(n) + alfan(1) ! here oui choulde update
756	! volume instead, no ?
757	zapondn(n) = reduced_aicen(n)
758	! in practise, pond fraction depends on the empirical snow fraction
759	! so in turn on ice thickness
760	END DO
761
762	!------------------------------------------------------------------------
763	! Drainage through brine network (permeability)
764	!------------------------------------------------------------------------
765	!!! drainage due to ice permeability - Darcy's law
766
767	! sea water level
768	msno = z0
769	DO n=1,jpl
770	msno = msno + vsnon(n) * rhosn
771	END DO
772	floe_weight = (msno + rhoicvice + rau0zvolp) / aice
773	hsl_rel = floe_weight / rau0 &
774	- ((sum(betan(:)*aicen(:))/aice) + alfan(1))
775
776	deltah = hpond - hsl_rel
777	pressure_head = grav * rau0 * max(deltah, z0)
778
779	! drain IF ice is permeable
780	permflag = 0
781	IF (pressure_head > z0) THEN
782	DO n = 1, jpl-1
783	IF (hicen(n) /= z0) THEN
784	perm = 0. ! MV ugly dummy patch
785	CALL lim_mp_perm(ticen(:,n), salin(:,n), vicen(n), perm)
786	IF (perm > z0) permflag = 1
787
788	drain = permzapondn(n)pressure_head*rdt_ice / &
789	(viscosity*hicen(n))
790	dvolp = dvolp + min(drain, zvolp)
791	zvolp = max(zvolp - drain, z0)
792	IF (zvolp < epsi10) THEN
793	dvolp = dvolp + zvolp
794	zvolp = z0
795	END IF
796	END IF
797	END DO
798
799	! adjust melt pond DIMENSIONs
800	IF (permflag > 0) THEN
801	! recompute pond depth
802	! CALL calc_hpond(reduced_aicen, asnon, hsnon, rhos, alfan, &
803	! zvolp, cum_max_vol, hpond, m_index)
804	DO n=1, m_index
805	zhpondn(n) = hpond - alfan(n) + alfan(1)
806	zapondn(n) = reduced_aicen(n)
807	END DO
808	END IF
809	END IF ! pressure_head
810
811	!-------------------------------
812	! X) remove water from the snow
813	!-------------------------------
814	!------------------------------------------------------------------------
815	! total melt pond volume in category DOes not include snow volume
816	! snow in melt ponds is not melted
817	!------------------------------------------------------------------------
818
819	! Calculate pond volume for lower categories
820	DO n=1,m_index-1
821	zvolpn(n) = zapondn(n) * zhpondn(n) & ! what is not in the snow
822	- (rhosn/rhofw) * asnon(n) * min(hsnon(n), zhpondn(n))
823	END DO
824
825	! Calculate pond volume for highest category = remaining pond volume
826
827	! The following is completely unclear to Martin at least
828	! Could we redefine properly and recode in a more readable way ?
829
830	! m_index = last category with melt pond
831
832	IF (m_index == 1) zvolpn(m_index) = zvolp ! volume of mw in 1st category is the total volume of melt water
833
834	IF (m_index > 1) THEN
835	IF (zvolp > sum(zvolpn(1:m_index-1))) THEN
836	zvolpn(m_index) = zvolp - sum(zvolpn(1:m_index-1)) !
837	ELSE
838	zvolpn(m_index) = z0
839	zhpondn(m_index) = z0
840	zapondn(m_index) = z0
841	! If remaining pond volume is negative reduce pond volume of
842	! lower category
843	IF (zvolp+epsi10 < sum(zvolpn(1:m_index-1))) &
844	zvolpn(m_index-1) = zvolpn(m_index-1)-sum(zvolpn(1:m_index-1))&
845	+ zvolp
846	END IF
847	END IF
848
849	DO n=1,m_index
850	IF (zapondn(n) > epsi10) THEN
851	zhpondn(n) = zvolpn(n) / zapondn(n)
852	ELSE
853	dvolp = dvolp + zvolpn(n)
854	zhpondn(n) = z0
855	zvolpn(n) = z0
856	zapondn(n) = z0
857	end IF
858	END DO
859	DO n = m_index+1, jpl
860	zhpondn(n) = z0
861	zapondn(n) = z0
862	zvolpn (n) = z0
863	END DO
864
865	END SUBROUTINE lim_mp_area
866
867	!OLI_CODE
868	!OLI_CODE
869	!OLI_CODE SUBROUTINE calc_hpond(aicen, asnon, hsnon, rhos, alfan, &
870	!OLI_CODE zvolp, cum_max_vol, &
871	!OLI_CODE hpond, m_index)
872	!OLI_CODE !!-------------------------------------------------------------------
873	!OLI_CODE !! * ROUTINE calc_hpond *
874	!OLI_CODE !!
875	!OLI_CODE !! ** Purpose : Compute melt pond depth
876	!OLI_CODE !!-------------------------------------------------------------------
877	!OLI_CODE
878	!OLI_CODE REAL (wp), DIMENSION(jpl), INTENT(IN) :: &
879	!OLI_CODE aicen, &
880	!OLI_CODE asnon, &
881	!OLI_CODE hsnon, &
882	!OLI_CODE rhos, &
883	!OLI_CODE alfan, &
884	!OLI_CODE cum_max_vol
885	!OLI_CODE
886	!OLI_CODE REAL (wp), INTENT(IN) :: &
887	!OLI_CODE zvolp
888	!OLI_CODE
889	!OLI_CODE REAL (wp), INTENT(OUT) :: &
890	!OLI_CODE hpond
891	!OLI_CODE
892	!OLI_CODE INTEGER, INTENT(OUT) :: &
893	!OLI_CODE m_index
894	!OLI_CODE
895	!OLI_CODE INTEGER :: n, ns
896	!OLI_CODE
897	!OLI_CODE REAL (wp), DIMENSION(0:jpl+1) :: &
898	!OLI_CODE hitl, &
899	!OLI_CODE aicetl
900	!OLI_CODE
901	!OLI_CODE REAL (wp) :: &
902	!OLI_CODE rem_vol, &
903	!OLI_CODE area, &
904	!OLI_CODE vol, &
905	!OLI_CODE tmp, &
906	!OLI_CODE z0 = 0.0_wp, &
907	!OLI_CODE epsi10 = 1.0e-11_wp
908	!OLI_CODE
909	!OLI_CODE !----------------------------------------------------------------
910	!OLI_CODE ! hpond is zero if zvolp is zero - have we fully drained?
911	!OLI_CODE !----------------------------------------------------------------
912	!OLI_CODE
913	!OLI_CODE IF (zvolp < epsi10) THEN
914	!OLI_CODE hpond = z0
915	!OLI_CODE m_index = 0
916	!OLI_CODE ELSE
917	!OLI_CODE
918	!OLI_CODE !----------------------------------------------------------------
919	!OLI_CODE ! Calculate the category where water fills up to
920	!OLI_CODE !----------------------------------------------------------------
921	!OLI_CODE
922	!OLI_CODE !----------\|
923	!OLI_CODE ! \|
924	!OLI_CODE ! \|
925	!OLI_CODE ! \|----------\| -- --
926	!OLI_CODE !__________\|__________\|_________________________________________ ^
927	!OLI_CODE ! \| \| rem_vol ^ \| Semi-filled
928	!OLI_CODE ! \| \|----------\|-- -- -- - ---\|-- ---- -- -- --v layer
929	!OLI_CODE ! \| \| \| \|
930	!OLI_CODE ! \| \| \| \|hpond
931	!OLI_CODE ! \| \| \|----------\| \| \|-------
932	!OLI_CODE ! \| \| \| \| \| \|
933	!OLI_CODE ! \| \| \| \|---v-----\|
934	!OLI_CODE ! \| \| m_index \| \| \|
935	!OLI_CODE !-------------------------------------------------------------
936	!OLI_CODE
937	!OLI_CODE m_index = 0 ! 1:m_index categories have water in them
938	!OLI_CODE DO n = 1, jpl
939	!OLI_CODE IF (zvolp <= cum_max_vol(n)) THEN
940	!OLI_CODE m_index = n
941	!OLI_CODE IF (n == 1) THEN
942	!OLI_CODE rem_vol = zvolp
943	!OLI_CODE ELSE
944	!OLI_CODE rem_vol = zvolp - cum_max_vol(n-1)
945	!OLI_CODE END IF
946	!OLI_CODE exit ! to break out of the loop
947	!OLI_CODE END IF
948	!OLI_CODE END DO
949	!OLI_CODE m_index = min(jpl-1, m_index)
950	!OLI_CODE
951	!OLI_CODE !----------------------------------------------------------------
952	!OLI_CODE ! semi-filled layer may have m_index different snow in it
953	!OLI_CODE !----------------------------------------------------------------
954	!OLI_CODE
955	!OLI_CODE !----------------------------------------------------------- ^
956	!OLI_CODE ! \| alfan(m_index+1)
957	!OLI_CODE ! \|
958	!OLI_CODE !hitl(3)--> \|----------\| \|
959	!OLI_CODE !hitl(2)--> \|------------\| * * * * *\| \|
960	!OLI_CODE !hitl(1)--> \|----------\|* * * * * * \|* * * * * \| \|
961	!OLI_CODE !hitl(0)-->------------------------------------------------- \| ^
962	!OLI_CODE ! various snow from lower categories \| \|alfa(m_index)
963	!OLI_CODE
964	!OLI_CODE ! hitl - heights of the snow layers from thinner and current categories
965	!OLI_CODE ! aicetl - area of each snow depth in this layer
966	!OLI_CODE
967	!OLI_CODE hitl(:) = z0
968	!OLI_CODE aicetl(:) = z0
969	!OLI_CODE DO n = 1, m_index
970	!OLI_CODE hitl(n) = max(min(hsnon(n) + alfan(n) - alfan(m_index), &
971	!OLI_CODE alfan(m_index+1) - alfan(m_index)), z0)
972	!OLI_CODE aicetl(n) = asnon(n)
973	!OLI_CODE
974	!OLI_CODE aicetl(0) = aicetl(0) + (aicen(n) - asnon(n))
975	!OLI_CODE END DO
976	!OLI_CODE hitl(m_index+1) = alfan(m_index+1) - alfan(m_index)
977	!OLI_CODE aicetl(m_index+1) = z0
978	!OLI_CODE
979	!OLI_CODE !----------------------------------------------------------------
980	!OLI_CODE ! reorder array according to hitl
981	!OLI_CODE ! snow heights not necessarily in height order
982	!OLI_CODE !----------------------------------------------------------------
983	!OLI_CODE
984	!OLI_CODE DO ns = 1, m_index+1
985	!OLI_CODE DO n = 0, m_index - ns + 1
986	!OLI_CODE IF (hitl(n) > hitl(n+1)) THEN ! swap order
987	!OLI_CODE tmp = hitl(n)
988	!OLI_CODE hitl(n) = hitl(n+1)
989	!OLI_CODE hitl(n+1) = tmp
990	!OLI_CODE tmp = aicetl(n)
991	!OLI_CODE aicetl(n) = aicetl(n+1)
992	!OLI_CODE aicetl(n+1) = tmp
993	!OLI_CODE END IF
994	!OLI_CODE END DO
995	!OLI_CODE END DO
996	!OLI_CODE
997	!OLI_CODE !----------------------------------------------------------------
998	!OLI_CODE ! divide semi-filled layer into set of sublayers each vertically homogenous
999	!OLI_CODE !----------------------------------------------------------------
1000	!OLI_CODE
1001	!OLI_CODE !hitl(3)----------------------------------------------------------------
1002	!OLI_CODE ! \| * * * * * * * *
1003	!OLI_CODE ! \|* * * * * * * * *
1004	!OLI_CODE !hitl(2)----------------------------------------------------------------
1005	!OLI_CODE ! \| * * * * * * * * \| * * * * * * * *
1006	!OLI_CODE ! \|* * * * * * * * * \|* * * * * * * * *
1007	!OLI_CODE !hitl(1)----------------------------------------------------------------
1008	!OLI_CODE ! \| * * * * * * * * \| * * * * * * * * \| * * * * * * * *
1009	!OLI_CODE ! \|* * * * * * * * * \|* * * * * * * * * \|* * * * * * * * *
1010	!OLI_CODE !hitl(0)----------------------------------------------------------------
1011	!OLI_CODE ! aicetl(0) aicetl(1) aicetl(2) aicetl(3)
1012	!OLI_CODE
1013	!OLI_CODE ! move up over layers incrementing volume
1014	!OLI_CODE DO n = 1, m_index+1
1015	!OLI_CODE
1016	!OLI_CODE area = sum(aicetl(:)) - & ! total area of sub-layer
1017	!OLI_CODE (rhos(n)/rau0) * sum(aicetl(n:jpl+1)) ! area of sub-layer occupied by snow
1018	!OLI_CODE
1019	!OLI_CODE vol = (hitl(n) - hitl(n-1)) * area ! thickness of sub-layer times area
1020	!OLI_CODE
1021	!OLI_CODE IF (vol >= rem_vol) THEN ! have reached the sub-layer with the depth within
1022	!OLI_CODE hpond = rem_vol / area + hitl(n-1) + alfan(m_index) - &
1023	!OLI_CODE alfan(1)
1024	!OLI_CODE exit
1025	!OLI_CODE ELSE ! still in sub-layer below the sub-layer with the depth
1026	!OLI_CODE rem_vol = rem_vol - vol
1027	!OLI_CODE END IF
1028	!OLI_CODE
1029	!OLI_CODE END DO
1030	!OLI_CODE
1031	!OLI_CODE END IF
1032	!OLI_CODE
1033	!OLI_CODE END SUBROUTINE calc_hpond
1034	!OLI_CODE
1035	!OLI_CODE
1036	SUBROUTINE lim_mp_perm(ticen, salin, vicen, perm)
1037	!!-------------------------------------------------------------------
1038	!! * ROUTINE lim_mp_perm *
1039	!!
1040	!! ** Purpose : Determine the liquid fraction of brine in the ice
1041	!! and its permeability
1042	!!-------------------------------------------------------------------
1043	REAL (wp), DIMENSION(nlay_i), INTENT(IN) :: &
1044	ticen, & ! energy of melting for each ice layer (J/m2)
1045	salin
1046
1047	REAL (wp), INTENT(IN) :: &
1048	vicen ! ice volume
1049
1050	REAL (wp), INTENT(OUT) :: &
1051	perm ! permeability
1052
1053	REAL (wp) :: &
1054	Sbr ! brine salinity
1055
1056	REAL (wp), DIMENSION(nlay_i) :: &
1057	Tin, & ! ice temperature
1058	phi ! liquid fraction
1059
1060	INTEGER :: k
1061
1062	REAL (wp) :: &
1063	c2 = 2.0_wp
1064
1065	!-----------------------------------------------------------------
1066	! Compute ice temperatures from enthalpies using quadratic formula
1067	!-----------------------------------------------------------------
1068
1069	DO k = 1,nlay_i
1070	Tin(k) = ticen(k)
1071	END DO
1072
1073	!-----------------------------------------------------------------
1074	! brine salinity and liquid fraction
1075	!-----------------------------------------------------------------
1076
1077	IF (maxval(Tin-rtt) <= -c2) THEN
1078
1079	DO k = 1,nlay_i
1080	Sbr = - 1.2_wp &
1081	-21.8_wp * (Tin(k)-rtt) &
1082	- 0.919_wp * (Tin(k)-rtt)**2 &
1083	- 0.01878_wp * (Tin(k)-rtt)**3
1084	phi(k) = salin(k)/Sbr ! liquid fraction
1085	END DO ! k
1086
1087	ELSE
1088
1089	DO k = 1,nlay_i
1090	Sbr = -17.6_wp * (Tin(k)-rtt) &
1091	- 0.389_wp * (Tin(k)-rtt)**2 &
1092	- 0.00362_wp* (Tin(k)-rtt)**3
1093	phi(k) = salin(k)/Sbr ! liquid fraction
1094	END DO
1095
1096	END IF
1097
1098	!-----------------------------------------------------------------
1099	! permeability
1100	!-----------------------------------------------------------------
1101
1102	perm = 3.0e-08_wp * (minval(phi))**3 ! REFERENCE PLEASE (this fucking
1103	! bastard of Golden)
1104
1105	END SUBROUTINE lim_mp_perm
1106	!OLI_CODE
1107	!OLI_CODE #else
1108	!OLI_CODE !!----------------------------------------------------------------------
1109	!OLI_CODE !! Default option Dummy Module No LIM-3 sea-ice model
1110	!OLI_CODE !!----------------------------------------------------------------------
1111	!OLI_CODE CONTAINS
1112	!OLI_CODE SUBROUTINE lim_mp_init ! Empty routine
1113	!OLI_CODE END SUBROUTINE lim_mp_init
1114	!OLI_CODE SUBROUTINE lim_mp ! Empty routine
1115	!OLI_CODE END SUBROUTINE lim_mp
1116	!OLI_CODE SUBROUTINE compute_mp_topo ! Empty routine
1117	!OLI_CODE END SUBROUTINE compute_mp_topo
1118	!OLI_CODE SUBROUTINE pond_area ! Empty routine
1119	!OLI_CODE END SUBROUTINE pond_area
1120	!OLI_CODE SUBROUTINE calc_hpond ! Empty routine
1121	!OLI_CODE END SUBROUTINE calc_hpond
1122	!OLI_CODE SUBROUTINE permeability_phy ! Empty routine
1123	!OLI_CODE END SUBROUTINE permeability_phy
1124	!OLI_CODE #endif
1125	!OLI_CODE !!======================================================================
1126	!OLI_CODE END MODULE limmp_topo
1127
1128
1129	!OLI_CODE MODULE limmp_topo
1130	!OLI_CODE !!======================================================================
1131	!OLI_CODE !! * MODULE limmp_topo *
1132	!OLI_CODE !! LIM-3 sea-ice : computation of melt ponds' properties
1133	!OLI_CODE !!======================================================================
1134	!OLI_CODE !! History : Original code by Daniela Flocco and Adrian Turner
1135	!OLI_CODE !! ! 2012-09 (O. Lecomte) Adaptation for routine inclusion in
1136	!OLI_CODE !! NEMO-LIM3.1
1137	!OLI_CODE !! ! 2016-11 (O. Lecomte, C. Rousset, M. Vancoppenolle)
1138	!OLI_CODE !! Adaptation for merge with NEMO-LIM3.6
1139	!OLI_CODE !!----------------------------------------------------------------------
1140	!OLI_CODE #if defined key_lim3
1141	!OLI_CODE !!----------------------------------------------------------------------
1142	!OLI_CODE !! 'key_lim3' LIM-3 sea-ice model
1143	!OLI_CODE !!----------------------------------------------------------------------
1144	!OLI_CODE !! lim_mp_init : melt pond properties initialization
1145	!OLI_CODE !! lim_mp : melt pond routine caller
1146	!OLI_CODE !! compute_mp_topo : Actual melt pond routine
1147	!OLI_CODE !!----------------------------------------------------------------------
1148	!OLI_CODE USE ice_oce, ONLY: rdt_ice, tatm_ice
1149	!OLI_CODE USE phycst
1150	!OLI_CODE USE dom_ice
1151	!OLI_CODE USE dom_oce
1152	!OLI_CODE USE sbc_oce
1153	!OLI_CODE USE sbc_ice
1154	!OLI_CODE USE par_ice
1155	!OLI_CODE USE par_oce
1156	!OLI_CODE USE ice
1157	!OLI_CODE USE thd_ice
1158	!OLI_CODE USE in_out_manager
1159	!OLI_CODE USE lbclnk
1160	!OLI_CODE USE lib_mpp
1161	!OLI_CODE
1162	!OLI_CODE IMPLICIT NONE
1163	!OLI_CODE PRIVATE
1164	!OLI_CODE
1165	!OLI_CODE PUBLIC lim_mp_init
1166	!OLI_CODE PUBLIC lim_mp
1167	!OLI_CODE
1168	!OLI_CODE CONTAINS
1169	!OLI_CODE
1170	!OLI_CODE SUBROUTINE lim_mp_init
1171	!OLI_CODE !!-------------------------------------------------------------------
1172	!OLI_CODE !! * ROUTINE lim_mp_init *
1173	!OLI_CODE !!
1174	!OLI_CODE !! ** Purpose : Initialize melt ponds
1175	!OLI_CODE !!-------------------------------------------------------------------
1176	!OLI_CODE a_ip_frac(:,:,:) = 0._wp
1177	!OLI_CODE a_ip(:,:,:) = 0._wp
1178	!OLI_CODE h_ip(:,:,:) = 0._wp
1179	!OLI_CODE v_ip(:,:,:) = 0._wp
1180	!OLI_CODE h_il(:,:,:) = 0._wp
1181	!OLI_CODE v_il(:,:,:) = 0._wp
1182	!OLI_CODE
1183	!OLI_CODE END SUBROUTINE lim_mp_init
1184	!OLI_CODE
1185	!OLI_CODE
1186	!OLI_CODE SUBROUTINE lim_mp
1187	!OLI_CODE !!-------------------------------------------------------------------
1188	!OLI_CODE !! * ROUTINE lim_mp *
1189	!OLI_CODE !!
1190	!OLI_CODE !! ** Purpose : Compute surface heat flux and call main melt pond
1191	!OLI_CODE !! routine
1192	!OLI_CODE !!-------------------------------------------------------------------
1193	!OLI_CODE
1194	!OLI_CODE INTEGER :: ji, jj, jl ! dummy loop indices
1195	!OLI_CODE
1196	!OLI_CODE fsurf(:,:) = 0.e0
1197	!OLI_CODE DO jl = 1, jpl
1198	!OLI_CODE DO jj = 1, jpj
1199	!OLI_CODE DO ji = 1, jpi
1200	!OLI_CODE fsurf(ji,jj) = fsurf(ji,jj) + a_i(ji,jj,jl) * &
1201	!OLI_CODE (qns_ice(ji,jj,jl) + (1.0 - izero(ji,jj,jl)) &
1202	!OLI_CODE * qsr_ice(ji,jj,jl))
1203	!OLI_CODE END DO
1204	!OLI_CODE END DO
1205	!OLI_CODE END DO
1206	!OLI_CODE
1207	!OLI_CODE CALL compute_mp_topo(at_i, a_i, &
1208	!OLI_CODE vt_i, v_i, v_s, rhosn_glo, t_i, s_i, a_ip_frac, &
1209	!OLI_CODE h_ip, h_il, t_su, tatm_ice, diag_sur_me*rdt_ice, &
1210	!OLI_CODE fsurf, fwoc)
1211	!OLI_CODE
1212	!OLI_CODE at_ip(:,:) = 0.0
1213	!OLI_CODE vt_ip(:,:) = 0.0
1214	!OLI_CODE vt_il(:,:) = 0.0
1215	!OLI_CODE DO jl = 1, jpl
1216	!OLI_CODE DO jj = 1, jpj
1217	!OLI_CODE DO ji = 1, jpi
1218	!OLI_CODE a_ip(ji,jj,jl) = MAX(0.0_wp, a_ip_frac(ji,jj,jl) * &
1219	!OLI_CODE a_i(ji,jj,jl))
1220	!OLI_CODE v_ip(ji,jj,jl) = MAX(0.0_wp, a_ip_frac(ji,jj,jl) * &
1221	!OLI_CODE a_i(ji,jj,jl) * h_ip(ji,jj,jl))
1222	!OLI_CODE v_il(ji,jj,jl) = MAX(0.0_wp, a_ip_frac(ji,jj,jl) * &
1223	!OLI_CODE a_i(ji,jj,jl) * h_il(ji,jj,jl))
1224	!OLI_CODE at_ip(ji,jj) = at_ip(ji,jj) + a_ip(ji,jj,jl)
1225	!OLI_CODE vt_ip(ji,jj) = vt_ip(ji,jj) + v_ip(ji,jj,jl)
1226	!OLI_CODE vt_il(ji,jj) = vt_il(ji,jj) + v_il(ji,jj,jl)
1227	!OLI_CODE END DO
1228	!OLI_CODE END DO
1229	!OLI_CODE END DO
1230	!OLI_CODE
1231	!OLI_CODE END SUBROUTINE lim_mp
1232	!OLI_CODE
1233	!OLI_CODE
1234	!OLI_CODE SUBROUTINE compute_mp_topo(aice, aicen, &
1235	!OLI_CODE vice, vicen, &
1236	!OLI_CODE vsnon, rhos, &
1237	!OLI_CODE ticen, salin, &
1238	!OLI_CODE a_ip_frac, h_ip, &
1239	!OLI_CODE h_il, Tsfc, &
1240	!OLI_CODE potT, meltt, &
1241	!OLI_CODE fsurf, fwoc)
1242	!OLI_CODE !!-------------------------------------------------------------------
1243	!OLI_CODE !! * ROUTINE compute_mp_topo *
1244	!OLI_CODE !!
1245	!OLI_CODE !! ** Purpose : Compute melt pond evolution based on the ice
1246	!OLI_CODE !! topography as inferred from the ice thickness
1247	!OLI_CODE !! distribution.
1248	!OLI_CODE !!
1249	!OLI_CODE !! ** Method : This code is initially based on Flocco and Feltham
1250	!OLI_CODE !! (2007) and Flocco et al. (2010). More to come...
1251	!OLI_CODE !!
1252	!OLI_CODE !! ** Tunable parameters :
1253	!OLI_CODE !!
1254	!OLI_CODE !! ** Note :
1255	!OLI_CODE !!
1256	!OLI_CODE !! ** References
1257	!OLI_CODE !! Flocco, D. and D. L. Feltham, 2007. A continuum model of melt pond
1258	!OLI_CODE !! evolution on Arctic sea ice. J. Geophys. Res. 112, C08016, doi:
1259	!OLI_CODE !! 10.1029/2006JC003836.
1260	!OLI_CODE !! Flocco, D., D. L. Feltham and A. K. Turner, 2010. Incorporation of
1261	!OLI_CODE !! a physically based melt pond scheme into the sea ice component of a
1262	!OLI_CODE !! climate model. J. Geophys. Res. 115, C08012,
1263	!OLI_CODE !! doi: 10.1029/2009JC005568.
1264	!OLI_CODE !!
1265	!OLI_CODE !!-------------------------------------------------------------------
1266	!OLI_CODE
1267	!OLI_CODE REAL (wp), DIMENSION (jpi,jpj), &
1268	!OLI_CODE INTENT(IN) :: &
1269	!OLI_CODE aice, & ! total ice area fraction
1270	!OLI_CODE vice ! total ice volume (m)
1271	!OLI_CODE
1272	!OLI_CODE REAL (wp), DIMENSION (jpi,jpj,jpl), &
1273	!OLI_CODE INTENT(IN) :: &
1274	!OLI_CODE aicen, & ! ice area fraction, per category
1275	!OLI_CODE vsnon, & ! snow volume, per category (m)
1276	!OLI_CODE rhos, & ! equivalent snow density, per category (kg/m^3)
1277	!OLI_CODE vicen ! ice volume, per category (m)
1278	!OLI_CODE
1279	!OLI_CODE REAL (wp), DIMENSION (jpi,jpj,nlay_i,jpl), &
1280	!OLI_CODE INTENT(IN) :: &
1281	!OLI_CODE ticen, & ! ice enthalpy, per category
1282	!OLI_CODE salin
1283	!OLI_CODE
1284	!OLI_CODE REAL (wp), DIMENSION (jpi,jpj,jpl), &
1285	!OLI_CODE INTENT(INOUT) :: &
1286	!OLI_CODE a_ip_frac , & ! pond area fraction of ice, per ice category
1287	!OLI_CODE h_ip , & ! pond depth, per ice category (m)
1288	!OLI_CODE h_il ! Refrozen ice lid thickness, per ice category (m)
1289	!OLI_CODE
1290	!OLI_CODE REAL (wp), DIMENSION (jpi,jpj), &
1291	!OLI_CODE INTENT(IN) :: &
1292	!OLI_CODE potT, & ! air potential temperature
1293	!OLI_CODE meltt, & ! total surface meltwater flux
1294	!OLI_CODE fsurf ! thermodynamic heat flux at ice/snow surface (W/m^2)
1295	!OLI_CODE
1296	!OLI_CODE REAL (wp), DIMENSION (jpi,jpj), &
1297	!OLI_CODE INTENT(INOUT) :: &
1298	!OLI_CODE fwoc ! fresh water flux to the ocean (from draining and other pond volume adjustments)
1299	!OLI_CODE ! (m)
1300	!OLI_CODE
1301	!OLI_CODE REAL (wp), DIMENSION (jpi,jpj,jpl), &
1302	!OLI_CODE INTENT(IN) :: &
1303	!OLI_CODE Tsfc ! snow/sea ice surface temperature
1304	!OLI_CODE
1305	!OLI_CODE ! local variables
1306	!OLI_CODE REAL (wp), DIMENSION (jpi,jpj,jpl) :: &
1307	!OLI_CODE zTsfcn, & ! ice/snow surface temperature (C)
1308	!OLI_CODE zvolpn, & ! pond volume per unit area, per category (m)
1309	!OLI_CODE zvuin ! water-equivalent volume of ice lid on melt pond ('upper ice', m)
1310	!OLI_CODE
1311	!OLI_CODE REAL (wp), DIMENSION (jpi,jpj,jpl) :: &
1312	!OLI_CODE zapondn,& ! pond area fraction, per category
1313	!OLI_CODE zhpondn ! pond depth, per category (m)
1314	!OLI_CODE
1315	!OLI_CODE REAL (wp), DIMENSION (jpi,jpj) :: &
1316	!OLI_CODE zvolp ! total volume of pond, per unit area of pond (m)
1317	!OLI_CODE
1318	!OLI_CODE REAL (wp) :: &
1319	!OLI_CODE zhi, & ! ice thickness (m)
1320	!OLI_CODE zdHui, & ! change in thickness of ice lid (m)
1321	!OLI_CODE zomega, & ! conduction
1322	!OLI_CODE zdTice, & ! temperature difference across ice lid (C)
1323	!OLI_CODE zdvice, & ! change in ice volume (m)
1324	!OLI_CODE zTavg, & ! mean surface temperature across categories (C)
1325	!OLI_CODE zTp, & ! pond freezing temperature (C)
1326	!OLI_CODE zdvn ! change in melt pond volume for fresh water budget
1327	!OLI_CODE INTEGER, DIMENSION (jpi*jpj) :: &
1328	!OLI_CODE indxi, indxj ! compressed indices for cells with ice melting
1329	!OLI_CODE
1330	!OLI_CODE INTEGER :: n,k,i,j,ij,icells,indxij ! loop indices
1331	!OLI_CODE
1332	!OLI_CODE INTEGER, DIMENSION (jpl) :: &
1333	!OLI_CODE kcells ! cells where ice lid combines with vice
1334	!OLI_CODE
1335	!OLI_CODE INTEGER, DIMENSION (jpi*jpj,jpl) :: &
1336	!OLI_CODE indxii, indxjj ! i,j indices for kcells loop
1337	!OLI_CODE
1338	!OLI_CODE REAL (wp), parameter :: &
1339	!OLI_CODE zhicemin = 0.1_wp , & ! minimum ice thickness with ponds (m)
1340	!OLI_CODE zTd = 0.15_wp, & ! temperature difference for freeze-up (C)
1341	!OLI_CODE zr1_rlfus = 1._wp / 0.334e+6 / 917._wp , & ! (J/m^3)
1342	!OLI_CODE zmin_volp = 1.e-4_wp, & ! minimum pond volume (m)
1343	!OLI_CODE z0 = 0._wp, &
1344	!OLI_CODE zTimelt = 0._wp, &
1345	!OLI_CODE z01 = 0.01_wp, &
1346	!OLI_CODE z25 = 0.25_wp, &
1347	!OLI_CODE z5 = 0.5_wp, &
1348	!OLI_CODE epsi10 = 1.0e-11_wp
1349	!OLI_CODE !---------------------------------------------------------------
1350	!OLI_CODE ! initialize
1351	!OLI_CODE !---------------------------------------------------------------
1352	!OLI_CODE
1353	!OLI_CODE DO j = 1, jpj
1354	!OLI_CODE DO i = 1, jpi
1355	!OLI_CODE zvolp(i,j) = z0
1356	!OLI_CODE END DO
1357	!OLI_CODE END DO
1358	!OLI_CODE DO n = 1, jpl
1359	!OLI_CODE DO j = 1, jpj
1360	!OLI_CODE DO i = 1, jpi
1361	!OLI_CODE ! load tracers
1362	!OLI_CODE zvolp(i,j) = zvolp(i,j) + h_ip(i,j,n) &
1363	!OLI_CODE * a_ip_frac(i,j,n) * aicen(i,j,n)
1364	!OLI_CODE zTsfcn(i,j,n) = Tsfc(i,j,n) - rtt ! convert in Celsius - Oli
1365	!OLI_CODE zvuin (i,j,n) = h_il(i,j,n) &
1366	!OLI_CODE * a_ip_frac(i,j,n) * aicen(i,j,n)
1367	!OLI_CODE
1368	!OLI_CODE zhpondn(i,j,n) = z0 ! pond depth, per category
1369	!OLI_CODE zapondn(i,j,n) = z0 ! pond area, per category
1370	!OLI_CODE END DO
1371	!OLI_CODE END DO
1372	!OLI_CODE indxii(:,n) = 0
1373	!OLI_CODE indxjj(:,n) = 0
1374	!OLI_CODE kcells (n) = 0
1375	!OLI_CODE END DO
1376	!OLI_CODE
1377	!OLI_CODE ! The freezing temperature for meltponds is assumed slightly below 0C,
1378	!OLI_CODE ! as if meltponds had a little salt in them. The salt budget is not
1379	!OLI_CODE ! altered for meltponds, but if it were then an actual pond freezing
1380	!OLI_CODE ! temperature could be computed.
1381	!OLI_CODE
1382	!OLI_CODE zTp = zTimelt - zTd
1383	!OLI_CODE
1384	!OLI_CODE !-----------------------------------------------------------------
1385	!OLI_CODE ! Identify grid cells with ponds
1386	!OLI_CODE !-----------------------------------------------------------------
1387	!OLI_CODE
1388	!OLI_CODE icells = 0
1389	!OLI_CODE DO j = 1, jpj
1390	!OLI_CODE DO i = 1, jpi
1391	!OLI_CODE zhi = z0
1392	!OLI_CODE IF (aice(i,j) > epsi10) zhi = vice(i,j)/aice(i,j)
1393	!OLI_CODE IF ( aice(i,j) > z01 .and. zhi > zhicemin .and. &
1394	!OLI_CODE zvolp(i,j) > zmin_volp*aice(i,j)) THEN
1395	!OLI_CODE icells = icells + 1
1396	!OLI_CODE indxi(icells) = i
1397	!OLI_CODE indxj(icells) = j
1398	!OLI_CODE ELSE ! remove ponds on thin ice
1399	!OLI_CODE !fpond(i,j) = fpond(i,j) - zvolp(i,j)
1400	!OLI_CODE zvolpn(i,j,:) = z0
1401	!OLI_CODE zvuin (i,j,:) = z0
1402	!OLI_CODE zvolp (i,j) = z0
1403	!OLI_CODE END IF
1404	!OLI_CODE END DO ! i
1405	!OLI_CODE END DO ! j
1406	!OLI_CODE
1407	!OLI_CODE DO ij = 1, icells
1408	!OLI_CODE i = indxi(ij)
1409	!OLI_CODE j = indxj(ij)
1410	!OLI_CODE
1411	!OLI_CODE !--------------------------------------------------------------
1412	!OLI_CODE ! calculate pond area and depth
1413	!OLI_CODE !--------------------------------------------------------------
1414	!OLI_CODE CALL pond_area(aice(i,j),vice(i,j),rhos(i,j,:), &
1415	!OLI_CODE aicen(i,j,:), vicen(i,j,:), vsnon(i,j,:), &
1416	!OLI_CODE ticen(i,j,:,:), salin(i,j,:,:), &
1417	!OLI_CODE zvolpn(i,j,:), zvolp(i,j), &
1418	!OLI_CODE zapondn(i,j,:),zhpondn(i,j,:), zdvn)
1419	!OLI_CODE
1420	!OLI_CODE fwoc(i,j) = fwoc(i,j) + zdvn ! -> Goes to fresh water budget
1421	!OLI_CODE
1422	!OLI_CODE ! mean surface temperature
1423	!OLI_CODE zTavg = z0
1424	!OLI_CODE DO n = 1, jpl
1425	!OLI_CODE zTavg = zTavg + zTsfcn(i,j,n)*aicen(i,j,n)
1426	!OLI_CODE END DO
1427	!OLI_CODE zTavg = zTavg / aice(i,j)
1428	!OLI_CODE
1429	!OLI_CODE DO n = 1, jpl-1
1430	!OLI_CODE
1431	!OLI_CODE IF (zvuin(i,j,n) > epsi10) THEN
1432	!OLI_CODE
1433	!OLI_CODE !----------------------------------------------------------------
1434	!OLI_CODE ! melting: floating upper ice layer melts in whole or part
1435	!OLI_CODE !----------------------------------------------------------------
1436	!OLI_CODE ! IF (zTsfcn(i,j,n) > zTp) THEN
1437	!OLI_CODE IF (zTavg > zTp) THEN
1438	!OLI_CODE
1439	!OLI_CODE zdvice = min(meltt(i,j)*zapondn(i,j,n), zvuin(i,j,n))
1440	!OLI_CODE IF (zdvice > epsi10) THEN
1441	!OLI_CODE zvuin (i,j,n) = zvuin (i,j,n) - zdvice
1442	!OLI_CODE zvolpn(i,j,n) = zvolpn(i,j,n) + zdvice
1443	!OLI_CODE zvolp (i,j) = zvolp (i,j) + zdvice
1444	!OLI_CODE !fwoc(i,j) = fwoc(i,j) + zdvice
1445	!OLI_CODE
1446	!OLI_CODE IF (zvuin(i,j,n) < epsi10 .and. zvolpn(i,j,n) > puny) THEN
1447	!OLI_CODE ! ice lid melted and category is pond covered
1448	!OLI_CODE zvolpn(i,j,n) = zvolpn(i,j,n) + zvuin(i,j,n)
1449	!OLI_CODE !fwoc(i,j) = fwoc(i,j) + zvuin(i,j,n)
1450	!OLI_CODE zvuin(i,j,n) = z0
1451	!OLI_CODE END IF
1452	!OLI_CODE zhpondn(i,j,n) = zvolpn(i,j,n) / zapondn(i,j,n)
1453	!OLI_CODE END IF
1454	!OLI_CODE
1455	!OLI_CODE !----------------------------------------------------------------
1456	!OLI_CODE ! freezing: existing upper ice layer grows
1457	!OLI_CODE !----------------------------------------------------------------
1458	!OLI_CODE ELSE IF (zvolpn(i,j,n) > epsi10) THEN ! zTavg <= zTp
1459	!OLI_CODE
1460	!OLI_CODE ! dIFferential growth of base of surface floating ice layer
1461	!OLI_CODE zdTice = max(-zTavg, z0) ! > 0
1462	!OLI_CODE zomega = rcdiczdTice zr1_rlfus
1463	!OLI_CODE zdHui = sqrt(zomegardt_ice + z25(zvuin(i,j,n)/ &
1464	!OLI_CODE aicen(i,j,n))*2)- z5 zvuin(i,j,n)/aicen(i,j,n)
1465	!OLI_CODE
1466	!OLI_CODE zdvice = min(zdHui*zapondn(i,j,n), zvolpn(i,j,n))
1467	!OLI_CODE IF (zdvice > epsi10) THEN
1468	!OLI_CODE zvuin (i,j,n) = zvuin (i,j,n) + zdvice
1469	!OLI_CODE zvolpn(i,j,n) = zvolpn(i,j,n) - zdvice
1470	!OLI_CODE zvolp (i,j) = zvolp (i,j) - zdvice
1471	!OLI_CODE !fwoc(i,j) = fwoc(i,j) - zdvice
1472	!OLI_CODE zhpondn(i,j,n) = zvolpn(i,j,n) / zapondn(i,j,n)
1473	!OLI_CODE END IF
1474	!OLI_CODE
1475	!OLI_CODE END IF ! zTavg
1476	!OLI_CODE
1477	!OLI_CODE !----------------------------------------------------------------
1478	!OLI_CODE ! freezing: upper ice layer begins to form
1479	!OLI_CODE ! note: albedo does not change
1480	!OLI_CODE !----------------------------------------------------------------
1481	!OLI_CODE ELSE ! zvuin < epsi10
1482	!OLI_CODE
1483	!OLI_CODE ! thickness of newly formed ice
1484	!OLI_CODE ! the surface temperature of a meltpond is the same as that
1485	!OLI_CODE ! of the ice underneath (0C), and the thermodynamic surface
1486	!OLI_CODE ! flux is the same
1487	!OLI_CODE zdHui = max(-fsurf(i,j)rdt_icezr1_rlfus, z0)
1488	!OLI_CODE zdvice = min(zdHui*zapondn(i,j,n), zvolpn(i,j,n))
1489	!OLI_CODE IF (zdvice > epsi10) THEN
1490	!OLI_CODE zvuin (i,j,n) = zdvice
1491	!OLI_CODE zvolpn(i,j,n) = zvolpn(i,j,n) - zdvice
1492	!OLI_CODE zvolp (i,j) = zvolp (i,j) - zdvice
1493	!OLI_CODE !fwoc(i,j) = fwoc(i,j) - zdvice
1494	!OLI_CODE zhpondn(i,j,n)= zvolpn(i,j,n) / zapondn(i,j,n)
1495	!OLI_CODE END IF
1496	!OLI_CODE
1497	!OLI_CODE END IF ! zvuin
1498	!OLI_CODE
1499	!OLI_CODE END DO ! jpl
1500	!OLI_CODE
1501	!OLI_CODE END DO ! ij
1502	!OLI_CODE
1503	!OLI_CODE !---------------------------------------------------------------
1504	!OLI_CODE ! remove ice lid if there is no liquid pond
1505	!OLI_CODE ! zvuin may be nonzero on category jpl due to dynamics
1506	!OLI_CODE !---------------------------------------------------------------
1507	!OLI_CODE
1508	!OLI_CODE DO j = 1, jpj
1509	!OLI_CODE DO i = 1, jpi
1510	!OLI_CODE DO n = 1, jpl
1511	!OLI_CODE IF (aicen(i,j,n) > epsi10 .and. zvolpn(i,j,n) < puny &
1512	!OLI_CODE .and. zvuin (i,j,n) > epsi10) THEN
1513	!OLI_CODE kcells(n) = kcells(n) + 1
1514	!OLI_CODE indxij = kcells(n)
1515	!OLI_CODE indxii(indxij,n) = i
1516	!OLI_CODE indxjj(indxij,n) = j
1517	!OLI_CODE END IF
1518	!OLI_CODE END DO
1519	!OLI_CODE END DO ! i
1520	!OLI_CODE END DO ! j
1521	!OLI_CODE
1522	!OLI_CODE DO n = 1, jpl
1523	!OLI_CODE
1524	!OLI_CODE IF (kcells(n) > 0) THEN
1525	!OLI_CODE DO ij = 1, kcells(n)
1526	!OLI_CODE i = indxii(ij,n)
1527	!OLI_CODE j = indxjj(ij,n)
1528	!OLI_CODE fwoc(i,j) = fwoc(i,j) + rhoic/rauw * zvuin(i,j,n) ! Completely refrozen lid goes into ocean (to be changed)
1529	!OLI_CODE zvuin(i,j,n) = z0
1530	!OLI_CODE END DO ! ij
1531	!OLI_CODE END IF
1532	!OLI_CODE
1533	!OLI_CODE ! reload tracers
1534	!OLI_CODE DO j = 1, jpj
1535	!OLI_CODE DO i = 1, jpi
1536	!OLI_CODE IF (zapondn(i,j,n) > epsi10) THEN
1537	!OLI_CODE h_il(i,j,n) = zvuin(i,j,n) / zapondn(i,j,n)
1538	!OLI_CODE ELSE
1539	!OLI_CODE zvuin(i,j,n) = z0
1540	!OLI_CODE h_il(i,j,n) = z0
1541	!OLI_CODE END IF
1542	!OLI_CODE IF (aicen(i,j,n) > epsi10) THEN
1543	!OLI_CODE a_ip_frac(i,j,n) = zapondn(i,j,n) / aicen(i,j,n) * &
1544	!OLI_CODE (1.0_wp - MAX(z0, SIGN(1.0_wp, -zvolpn(i,j,n))))
1545	!OLI_CODE h_ip(i,j,n) = zhpondn(i,j,n)
1546	!OLI_CODE ELSE
1547	!OLI_CODE a_ip_frac(i,j,n) = z0
1548	!OLI_CODE h_ip(i,j,n) = z0
1549	!OLI_CODE h_il(i,j,n) = z0
1550	!OLI_CODE END IF
1551	!OLI_CODE END DO ! i
1552	!OLI_CODE END DO ! j
1553	!OLI_CODE
1554	!OLI_CODE END DO ! n
1555	!OLI_CODE
1556	!OLI_CODE END SUBROUTINE compute_mp_topo
1557	!OLI_CODE
1558	!OLI_CODE
1559	!OLI_CODE SUBROUTINE pond_area(aice,vice,rhos, &
1560	!OLI_CODE aicen, vicen, vsnon, ticen, &
1561	!OLI_CODE salin, zvolpn, zvolp, &
1562	!OLI_CODE zapondn,zhpondn,dvolp)
1563	!OLI_CODE !!-------------------------------------------------------------------
1564	!OLI_CODE !! * ROUTINE pond_area *
1565	!OLI_CODE !!
1566	!OLI_CODE !! ** Purpose : Compute melt pond area, depth and melting rates
1567	!OLI_CODE !!------------------------------------------------------------------
1568	!OLI_CODE REAL (wp), INTENT(IN) :: &
1569	!OLI_CODE aice,vice
1570	!OLI_CODE
1571	!OLI_CODE REAL (wp), DIMENSION(jpl), INTENT(IN) :: &
1572	!OLI_CODE aicen, vicen, vsnon, rhos
1573	!OLI_CODE
1574	!OLI_CODE REAL (wp), DIMENSION(nlay_i,jpl), INTENT(IN) :: &
1575	!OLI_CODE ticen, salin
1576	!OLI_CODE
1577	!OLI_CODE REAL (wp), DIMENSION(jpl), INTENT(INOUT) :: &
1578	!OLI_CODE zvolpn
1579	!OLI_CODE
1580	!OLI_CODE REAL (wp), INTENT(INOUT) :: &
1581	!OLI_CODE zvolp, dvolp
1582	!OLI_CODE
1583	!OLI_CODE REAL (wp), DIMENSION(jpl), INTENT(OUT) :: &
1584	!OLI_CODE zapondn, zhpondn
1585	!OLI_CODE
1586	!OLI_CODE INTEGER :: &
1587	!OLI_CODE n, ns, &
1588	!OLI_CODE m_index, &
1589	!OLI_CODE permflag
1590	!OLI_CODE
1591	!OLI_CODE REAL (wp), DIMENSION(jpl) :: &
1592	!OLI_CODE hicen, &
1593	!OLI_CODE hsnon, &
1594	!OLI_CODE asnon, &
1595	!OLI_CODE alfan, &
1596	!OLI_CODE betan, &
1597	!OLI_CODE cum_max_vol, &
1598	!OLI_CODE reduced_aicen
1599	!OLI_CODE
1600	!OLI_CODE REAL (wp), DIMENSION(0:jpl) :: &
1601	!OLI_CODE cum_max_vol_tmp
1602	!OLI_CODE
1603	!OLI_CODE REAL (wp) :: &
1604	!OLI_CODE hpond, &
1605	!OLI_CODE drain, &
1606	!OLI_CODE floe_weight, &
1607	!OLI_CODE pressure_head, &
1608	!OLI_CODE hsl_rel, &
1609	!OLI_CODE deltah, &
1610	!OLI_CODE perm, &
1611	!OLI_CODE apond, &
1612	!OLI_CODE msno
1613	!OLI_CODE
1614	!OLI_CODE REAL (wp), parameter :: &
1615	!OLI_CODE viscosity = 1.79e-3_wp, & ! kinematic water viscosity in kg/m/s
1616	!OLI_CODE z0 = 0.0_wp , &
1617	!OLI_CODE c1 = 1.0_wp , &
1618	!OLI_CODE p4 = 0.4_wp , &
1619	!OLI_CODE p6 = 0.6_wp , &
1620	!OLI_CODE epsi10 = 1.0e-11_wp
1621	!OLI_CODE
1622	!OLI_CODE !-----------\|
1623	!OLI_CODE ! \|
1624	!OLI_CODE ! \|-----------\|
1625	!OLI_CODE !___________\|___________\|______________________________________sea-level
1626	!OLI_CODE ! \| \|
1627	!OLI_CODE ! \| \|---^--------\|
1628	!OLI_CODE ! \| \| \| \|
1629	!OLI_CODE ! \| \| \| \|-----------\| \|-------
1630	!OLI_CODE ! \| \| \|alfan(n)\| \| \|
1631	!OLI_CODE ! \| \| \| \| \|--------------\|
1632	!OLI_CODE ! \| \| \| \| \| \|
1633	!OLI_CODE !---------------------------v-------------------------------------------
1634	!OLI_CODE ! \| \| ^ \| \| \|
1635	!OLI_CODE ! \| \| \| \| \|--------------\|
1636	!OLI_CODE ! \| \| \|betan(n)\| \| \|
1637	!OLI_CODE ! \| \| \| \|-----------\| \|-------
1638	!OLI_CODE ! \| \| \| \|
1639	!OLI_CODE ! \| \|---v------- \|
1640	!OLI_CODE ! \| \|
1641	!OLI_CODE ! \|-----------\|
1642	!OLI_CODE ! \|
1643	!OLI_CODE !-----------\|
1644	!OLI_CODE
1645	!OLI_CODE !-------------------------------------------------------------------
1646	!OLI_CODE ! initialize
1647	!OLI_CODE !-------------------------------------------------------------------
1648	!OLI_CODE
1649	!OLI_CODE DO n = 1, jpl
1650	!OLI_CODE
1651	!OLI_CODE zapondn(n) = z0
1652	!OLI_CODE zhpondn(n) = z0
1653	!OLI_CODE
1654	!OLI_CODE IF (aicen(n) < epsi10) THEN
1655	!OLI_CODE hicen(n) = z0
1656	!OLI_CODE hsnon(n) = z0
1657	!OLI_CODE reduced_aicen(n) = z0
1658	!OLI_CODE ELSE
1659	!OLI_CODE hicen(n) = vicen(n) / aicen(n)
1660	!OLI_CODE hsnon(n) = vsnon(n) / aicen(n)
1661	!OLI_CODE reduced_aicen(n) = c1 ! n=jpl
1662	!OLI_CODE IF (n < jpl) reduced_aicen(n) = aicen(n) &
1663	!OLI_CODE * (-0.024_wp*hicen(n) + 0.832_wp)
1664	!OLI_CODE asnon(n) = reduced_aicen(n)
1665	!OLI_CODE END IF
1666	!OLI_CODE
1667	!OLI_CODE ! This choice for alfa and beta ignores hydrostatic equilibium of categories.
1668	!OLI_CODE ! Hydrostatic equilibium of the entire ITD is accounted for below, assuming
1669	!OLI_CODE ! a surface topography implied by alfa=0.6 and beta=0.4, and rigidity across all
1670	!OLI_CODE ! categories. alfa and beta partition the ITD - they are areas not thicknesses!
1671	!OLI_CODE ! Multiplying by hicen, alfan and betan (below) are thus volumes per unit area.
1672	!OLI_CODE ! Here, alfa = 60% of the ice area (and since hice is constant in a category,
1673	!OLI_CODE ! alfan = 60% of the ice volume) in each category lies above the reference line,
1674	!OLI_CODE ! and 40% below. Note: p6 is an arbitrary choice, but alfa+beta=1 is required.
1675	!OLI_CODE
1676	!OLI_CODE alfan(n) = p6 * hicen(n)
1677	!OLI_CODE betan(n) = p4 * hicen(n)
1678	!OLI_CODE
1679	!OLI_CODE cum_max_vol(n) = z0
1680	!OLI_CODE cum_max_vol_tmp(n) = z0
1681	!OLI_CODE
1682	!OLI_CODE END DO ! jpl
1683	!OLI_CODE
1684	!OLI_CODE cum_max_vol_tmp(0) = z0
1685	!OLI_CODE drain = z0
1686	!OLI_CODE dvolp = z0
1687	!OLI_CODE
1688	!OLI_CODE !--------------------------------------------------------------------------
1689	!OLI_CODE ! the maximum amount of water that can be contained up to each ice category
1690	!OLI_CODE !--------------------------------------------------------------------------
1691	!OLI_CODE
1692	!OLI_CODE DO n = 1, jpl-1 ! last category can not hold any volume
1693	!OLI_CODE
1694	!OLI_CODE IF (alfan(n+1) >= alfan(n) .and. alfan(n+1) > z0) THEN
1695	!OLI_CODE
1696	!OLI_CODE ! total volume in level including snow
1697	!OLI_CODE cum_max_vol_tmp(n) = cum_max_vol_tmp(n-1) + &
1698	!OLI_CODE (alfan(n+1) - alfan(n)) * sum(reduced_aicen(1:n))
1699	!OLI_CODE
1700	!OLI_CODE
1701	!OLI_CODE ! subtract snow solid volumes from lower categories in current level
1702	!OLI_CODE DO ns = 1, n
1703	!OLI_CODE cum_max_vol_tmp(n) = cum_max_vol_tmp(n) &
1704	!OLI_CODE - rhos(ns)/rauw * & ! fraction of snow that is occupied by solid ??rauw
1705	!OLI_CODE asnon(ns) * & ! area of snow from that category
1706	!OLI_CODE max(min(hsnon(ns)+alfan(ns)-alfan(n), alfan(n+1)- &
1707	!OLI_CODE alfan(n)), z0)
1708	!OLI_CODE ! thickness of snow from ns layer in n layer
1709	!OLI_CODE END DO
1710	!OLI_CODE
1711	!OLI_CODE ELSE ! assume higher categories unoccupied
1712	!OLI_CODE cum_max_vol_tmp(n) = cum_max_vol_tmp(n-1)
1713	!OLI_CODE END IF
1714	!OLI_CODE !IF (cum_max_vol_tmp(n) < z0) THEN
1715	!OLI_CODE ! call abort_ice('negative melt pond volume')
1716	!OLI_CODE !END IF
1717	!OLI_CODE END DO
1718	!OLI_CODE cum_max_vol_tmp(jpl) = cum_max_vol_tmp(jpl-1) ! last category holds no volume
1719	!OLI_CODE cum_max_vol (1:jpl) = cum_max_vol_tmp(1:jpl)
1720	!OLI_CODE
1721	!OLI_CODE !----------------------------------------------------------------
1722	!OLI_CODE ! is there more meltwater than can be held in the floe?
1723	!OLI_CODE !----------------------------------------------------------------
1724	!OLI_CODE IF (zvolp >= cum_max_vol(jpl)) THEN
1725	!OLI_CODE drain = zvolp - cum_max_vol(jpl) + epsi10
1726	!OLI_CODE zvolp = zvolp - drain
1727	!OLI_CODE dvolp = drain
1728	!OLI_CODE IF (zvolp < epsi10) THEN
1729	!OLI_CODE dvolp = dvolp + zvolp
1730	!OLI_CODE zvolp = z0
1731	!OLI_CODE END IF
1732	!OLI_CODE END IF
1733	!OLI_CODE
1734	!OLI_CODE ! height and area corresponding to the remaining volume
1735	!OLI_CODE
1736	!OLI_CODE call calc_hpond(reduced_aicen, asnon, hsnon, rhos, alfan, &
1737	!OLI_CODE zvolp, cum_max_vol, hpond, m_index)
1738	!OLI_CODE
1739	!OLI_CODE DO n=1, m_index
1740	!OLI_CODE zhpondn(n) = hpond - alfan(n) + alfan(1)
1741	!OLI_CODE zapondn(n) = reduced_aicen(n)
1742	!OLI_CODE END DO
1743	!OLI_CODE apond = sum(zapondn(1:m_index))
1744	!OLI_CODE
1745	!OLI_CODE !------------------------------------------------------------------------
1746	!OLI_CODE ! drainage due to ice permeability - Darcy's law
1747	!OLI_CODE !------------------------------------------------------------------------
1748	!OLI_CODE
1749	!OLI_CODE ! sea water level
1750	!OLI_CODE msno = z0
1751	!OLI_CODE DO n=1,jpl
1752	!OLI_CODE msno = msno + vsnon(n) * rhos(n)
1753	!OLI_CODE END DO
1754	!OLI_CODE floe_weight = (msno + rhoicvice + rau0zvolp) / aice
1755	!OLI_CODE hsl_rel = floe_weight / rau0 &
1756	!OLI_CODE - ((sum(betan(:)*aicen(:))/aice) + alfan(1))
1757	!OLI_CODE
1758	!OLI_CODE deltah = hpond - hsl_rel
1759	!OLI_CODE pressure_head = grav * rau0 * max(deltah, z0)
1760	!OLI_CODE
1761	!OLI_CODE ! drain IF ice is permeable
1762	!OLI_CODE permflag = 0
1763	!OLI_CODE IF (pressure_head > z0) THEN
1764	!OLI_CODE DO n = 1, jpl-1
1765	!OLI_CODE IF (hicen(n) /= z0) THEN
1766	!OLI_CODE CALL permeability_phi(ticen(:,n), salin(:,n), vicen(n), perm)
1767	!OLI_CODE IF (perm > z0) permflag = 1
1768	!OLI_CODE drain = permzapondn(n)pressure_head*rdt_ice / &
1769	!OLI_CODE (viscosity*hicen(n))
1770	!OLI_CODE dvolp = dvolp + min(drain, zvolp)
1771	!OLI_CODE zvolp = max(zvolp - drain, z0)
1772	!OLI_CODE IF (zvolp < epsi10) THEN
1773	!OLI_CODE dvolp = dvolp + zvolp
1774	!OLI_CODE zvolp = z0
1775	!OLI_CODE END IF
1776	!OLI_CODE END IF
1777	!OLI_CODE END DO
1778	!OLI_CODE
1779	!OLI_CODE ! adjust melt pond DIMENSIONs
1780	!OLI_CODE IF (permflag > 0) THEN
1781	!OLI_CODE ! recompute pond depth
1782	!OLI_CODE CALL calc_hpond(reduced_aicen, asnon, hsnon, rhos, alfan, &
1783	!OLI_CODE zvolp, cum_max_vol, hpond, m_index)
1784	!OLI_CODE DO n=1, m_index
1785	!OLI_CODE zhpondn(n) = hpond - alfan(n) + alfan(1)
1786	!OLI_CODE zapondn(n) = reduced_aicen(n)
1787	!OLI_CODE END DO
1788	!OLI_CODE apond = sum(zapondn(1:m_index))
1789	!OLI_CODE END IF
1790	!OLI_CODE END IF ! pressure_head
1791	!OLI_CODE
1792	!OLI_CODE !------------------------------------------------------------------------
1793	!OLI_CODE ! total melt pond volume in category DOes not include snow volume
1794	!OLI_CODE ! snow in melt ponds is not melted
1795	!OLI_CODE !------------------------------------------------------------------------
1796	!OLI_CODE
1797	!OLI_CODE ! Calculate pond volume for lower categories
1798	!OLI_CODE DO n=1,m_index-1
1799	!OLI_CODE zvolpn(n) = zapondn(n) * zhpondn(n) &
1800	!OLI_CODE - (rhos(n)/rauw) * asnon(n) * min(hsnon(n), zhpondn(n))!
1801	!OLI_CODE END DO
1802	!OLI_CODE
1803	!OLI_CODE ! Calculate pond volume for highest category = remaining pond volume
1804	!OLI_CODE IF (m_index == 1) zvolpn(m_index) = zvolp
1805	!OLI_CODE IF (m_index > 1) THEN
1806	!OLI_CODE IF (zvolp > sum(zvolpn(1:m_index-1))) THEN
1807	!OLI_CODE zvolpn(m_index) = zvolp - sum(zvolpn(1:m_index-1))
1808	!OLI_CODE ELSE
1809	!OLI_CODE zvolpn(m_index) = z0
1810	!OLI_CODE zhpondn(m_index) = z0
1811	!OLI_CODE zapondn(m_index) = z0
1812	!OLI_CODE ! If remaining pond volume is negative reduce pond volume of
1813	!OLI_CODE ! lower category
1814	!OLI_CODE IF (zvolp+epsi10 < sum(zvolpn(1:m_index-1))) &
1815	!OLI_CODE zvolpn(m_index-1) = zvolpn(m_index-1)-sum(zvolpn(1:m_index-1))&
1816	!OLI_CODE + zvolp
1817	!OLI_CODE END IF
1818	!OLI_CODE END IF
1819	!OLI_CODE
1820	!OLI_CODE DO n=1,m_index
1821	!OLI_CODE IF (zapondn(n) > epsi10) THEN
1822	!OLI_CODE zhpondn(n) = zvolpn(n) / zapondn(n)
1823	!OLI_CODE ELSE
1824	!OLI_CODE dvolp = dvolp + zvolpn(n)
1825	!OLI_CODE zhpondn(n) = z0
1826	!OLI_CODE zvolpn(n) = z0
1827	!OLI_CODE zapondn(n) = z0
1828	!OLI_CODE end IF
1829	!OLI_CODE END DO
1830	!OLI_CODE DO n = m_index+1, jpl
1831	!OLI_CODE zhpondn(n) = z0
1832	!OLI_CODE zapondn(n) = z0
1833	!OLI_CODE zvolpn (n) = z0
1834	!OLI_CODE END DO
1835	!OLI_CODE
1836	!OLI_CODE END SUBROUTINE pond_area
1837	!OLI_CODE
1838	!OLI_CODE
1839	!OLI_CODE SUBROUTINE calc_hpond(aicen, asnon, hsnon, rhos, alfan, &
1840	!OLI_CODE zvolp, cum_max_vol, &
1841	!OLI_CODE hpond, m_index)
1842	!OLI_CODE !!-------------------------------------------------------------------
1843	!OLI_CODE !! * ROUTINE calc_hpond *
1844	!OLI_CODE !!
1845	!OLI_CODE !! ** Purpose : Compute melt pond depth
1846	!OLI_CODE !!-------------------------------------------------------------------
1847	!OLI_CODE
1848	!OLI_CODE REAL (wp), DIMENSION(jpl), INTENT(IN) :: &
1849	!OLI_CODE aicen, &
1850	!OLI_CODE asnon, &
1851	!OLI_CODE hsnon, &
1852	!OLI_CODE rhos, &
1853	!OLI_CODE alfan, &
1854	!OLI_CODE cum_max_vol
1855	!OLI_CODE
1856	!OLI_CODE REAL (wp), INTENT(IN) :: &
1857	!OLI_CODE zvolp
1858	!OLI_CODE
1859	!OLI_CODE REAL (wp), INTENT(OUT) :: &
1860	!OLI_CODE hpond
1861	!OLI_CODE
1862	!OLI_CODE INTEGER, INTENT(OUT) :: &
1863	!OLI_CODE m_index
1864	!OLI_CODE
1865	!OLI_CODE INTEGER :: n, ns
1866	!OLI_CODE
1867	!OLI_CODE REAL (wp), DIMENSION(0:jpl+1) :: &
1868	!OLI_CODE hitl, &
1869	!OLI_CODE aicetl
1870	!OLI_CODE
1871	!OLI_CODE REAL (wp) :: &
1872	!OLI_CODE rem_vol, &
1873	!OLI_CODE area, &
1874	!OLI_CODE vol, &
1875	!OLI_CODE tmp, &
1876	!OLI_CODE z0 = 0.0_wp, &
1877	!OLI_CODE epsi10 = 1.0e-11_wp
1878	!OLI_CODE
1879	!OLI_CODE !----------------------------------------------------------------
1880	!OLI_CODE ! hpond is zero if zvolp is zero - have we fully drained?
1881	!OLI_CODE !----------------------------------------------------------------
1882	!OLI_CODE
1883	!OLI_CODE IF (zvolp < epsi10) THEN
1884	!OLI_CODE hpond = z0
1885	!OLI_CODE m_index = 0
1886	!OLI_CODE ELSE
1887	!OLI_CODE
1888	!OLI_CODE !----------------------------------------------------------------
1889	!OLI_CODE ! Calculate the category where water fills up to
1890	!OLI_CODE !----------------------------------------------------------------
1891	!OLI_CODE
1892	!OLI_CODE !----------\|
1893	!OLI_CODE ! \|
1894	!OLI_CODE ! \|
1895	!OLI_CODE ! \|----------\| -- --
1896	!OLI_CODE !__________\|__________\|_________________________________________ ^
1897	!OLI_CODE ! \| \| rem_vol ^ \| Semi-filled
1898	!OLI_CODE ! \| \|----------\|-- -- -- - ---\|-- ---- -- -- --v layer
1899	!OLI_CODE ! \| \| \| \|
1900	!OLI_CODE ! \| \| \| \|hpond
1901	!OLI_CODE ! \| \| \|----------\| \| \|-------
1902	!OLI_CODE ! \| \| \| \| \| \|
1903	!OLI_CODE ! \| \| \| \|---v-----\|
1904	!OLI_CODE ! \| \| m_index \| \| \|
1905	!OLI_CODE !-------------------------------------------------------------
1906	!OLI_CODE
1907	!OLI_CODE m_index = 0 ! 1:m_index categories have water in them
1908	!OLI_CODE DO n = 1, jpl
1909	!OLI_CODE IF (zvolp <= cum_max_vol(n)) THEN
1910	!OLI_CODE m_index = n
1911	!OLI_CODE IF (n == 1) THEN
1912	!OLI_CODE rem_vol = zvolp
1913	!OLI_CODE ELSE
1914	!OLI_CODE rem_vol = zvolp - cum_max_vol(n-1)
1915	!OLI_CODE END IF
1916	!OLI_CODE exit ! to break out of the loop
1917	!OLI_CODE END IF
1918	!OLI_CODE END DO
1919	!OLI_CODE m_index = min(jpl-1, m_index)
1920	!OLI_CODE
1921	!OLI_CODE !----------------------------------------------------------------
1922	!OLI_CODE ! semi-filled layer may have m_index different snow in it
1923	!OLI_CODE !----------------------------------------------------------------
1924	!OLI_CODE
1925	!OLI_CODE !----------------------------------------------------------- ^
1926	!OLI_CODE ! \| alfan(m_index+1)
1927	!OLI_CODE ! \|
1928	!OLI_CODE !hitl(3)--> \|----------\| \|
1929	!OLI_CODE !hitl(2)--> \|------------\| * * * * *\| \|
1930	!OLI_CODE !hitl(1)--> \|----------\|* * * * * * \|* * * * * \| \|
1931	!OLI_CODE !hitl(0)-->------------------------------------------------- \| ^
1932	!OLI_CODE ! various snow from lower categories \| \|alfa(m_index)
1933	!OLI_CODE
1934	!OLI_CODE ! hitl - heights of the snow layers from thinner and current categories
1935	!OLI_CODE ! aicetl - area of each snow depth in this layer
1936	!OLI_CODE
1937	!OLI_CODE hitl(:) = z0
1938	!OLI_CODE aicetl(:) = z0
1939	!OLI_CODE DO n = 1, m_index
1940	!OLI_CODE hitl(n) = max(min(hsnon(n) + alfan(n) - alfan(m_index), &
1941	!OLI_CODE alfan(m_index+1) - alfan(m_index)), z0)
1942	!OLI_CODE aicetl(n) = asnon(n)
1943	!OLI_CODE
1944	!OLI_CODE aicetl(0) = aicetl(0) + (aicen(n) - asnon(n))
1945	!OLI_CODE END DO
1946	!OLI_CODE hitl(m_index+1) = alfan(m_index+1) - alfan(m_index)
1947	!OLI_CODE aicetl(m_index+1) = z0
1948	!OLI_CODE
1949	!OLI_CODE !----------------------------------------------------------------
1950	!OLI_CODE ! reorder array according to hitl
1951	!OLI_CODE ! snow heights not necessarily in height order
1952	!OLI_CODE !----------------------------------------------------------------
1953	!OLI_CODE
1954	!OLI_CODE DO ns = 1, m_index+1
1955	!OLI_CODE DO n = 0, m_index - ns + 1
1956	!OLI_CODE IF (hitl(n) > hitl(n+1)) THEN ! swap order
1957	!OLI_CODE tmp = hitl(n)
1958	!OLI_CODE hitl(n) = hitl(n+1)
1959	!OLI_CODE hitl(n+1) = tmp
1960	!OLI_CODE tmp = aicetl(n)
1961	!OLI_CODE aicetl(n) = aicetl(n+1)
1962	!OLI_CODE aicetl(n+1) = tmp
1963	!OLI_CODE END IF
1964	!OLI_CODE END DO
1965	!OLI_CODE END DO
1966	!OLI_CODE
1967	!OLI_CODE !----------------------------------------------------------------
1968	!OLI_CODE ! divide semi-filled layer into set of sublayers each vertically homogenous
1969	!OLI_CODE !----------------------------------------------------------------
1970	!OLI_CODE
1971	!OLI_CODE !hitl(3)----------------------------------------------------------------
1972	!OLI_CODE ! \| * * * * * * * *
1973	!OLI_CODE ! \|* * * * * * * * *
1974	!OLI_CODE !hitl(2)----------------------------------------------------------------
1975	!OLI_CODE ! \| * * * * * * * * \| * * * * * * * *
1976	!OLI_CODE ! \|* * * * * * * * * \|* * * * * * * * *
1977	!OLI_CODE !hitl(1)----------------------------------------------------------------
1978	!OLI_CODE ! \| * * * * * * * * \| * * * * * * * * \| * * * * * * * *
1979	!OLI_CODE ! \|* * * * * * * * * \|* * * * * * * * * \|* * * * * * * * *
1980	!OLI_CODE !hitl(0)----------------------------------------------------------------
1981	!OLI_CODE ! aicetl(0) aicetl(1) aicetl(2) aicetl(3)
1982	!OLI_CODE
1983	!OLI_CODE ! move up over layers incrementing volume
1984	!OLI_CODE DO n = 1, m_index+1
1985	!OLI_CODE
1986	!OLI_CODE area = sum(aicetl(:)) - & ! total area of sub-layer
1987	!OLI_CODE (rhos(n)/rau0) * sum(aicetl(n:jpl+1)) ! area of sub-layer occupied by snow
1988	!OLI_CODE
1989	!OLI_CODE vol = (hitl(n) - hitl(n-1)) * area ! thickness of sub-layer times area
1990	!OLI_CODE
1991	!OLI_CODE IF (vol >= rem_vol) THEN ! have reached the sub-layer with the depth within
1992	!OLI_CODE hpond = rem_vol / area + hitl(n-1) + alfan(m_index) - &
1993	!OLI_CODE alfan(1)
1994	!OLI_CODE exit
1995	!OLI_CODE ELSE ! still in sub-layer below the sub-layer with the depth
1996	!OLI_CODE rem_vol = rem_vol - vol
1997	!OLI_CODE END IF
1998	!OLI_CODE
1999	!OLI_CODE END DO
2000	!OLI_CODE
2001	!OLI_CODE END IF
2002	!OLI_CODE
2003	!OLI_CODE END SUBROUTINE calc_hpond
2004	!OLI_CODE
2005	!OLI_CODE
2006	!OLI_CODE SUBROUTINE permeability_phi(ticen, salin, vicen, perm)
2007	!OLI_CODE !!-------------------------------------------------------------------
2008	!OLI_CODE !! * ROUTINE permeability_phi *
2009	!OLI_CODE !!
2010	!OLI_CODE !! ** Purpose : Determine the liquid fraction of brine in the ice
2011	!OLI_CODE !! and its permeability
2012	!OLI_CODE !!-------------------------------------------------------------------
2013	!OLI_CODE REAL (wp), DIMENSION(nlay_i), INTENT(IN) :: &
2014	!OLI_CODE ticen, & ! energy of melting for each ice layer (J/m2)
2015	!OLI_CODE salin
2016	!OLI_CODE
2017	!OLI_CODE REAL (wp), INTENT(IN) :: &
2018	!OLI_CODE vicen ! ice volume
2019	!OLI_CODE
2020	!OLI_CODE REAL (wp), INTENT(OUT) :: &
2021	!OLI_CODE perm ! permeability
2022	!OLI_CODE
2023	!OLI_CODE REAL (wp) :: &
2024	!OLI_CODE Sbr ! brine salinity
2025	!OLI_CODE
2026	!OLI_CODE REAL (wp), DIMENSION(nlay_i) :: &
2027	!OLI_CODE Tin, & ! ice temperature
2028	!OLI_CODE phi ! liquid fraction
2029	!OLI_CODE
2030	!OLI_CODE INTEGER :: k
2031	!OLI_CODE
2032	!OLI_CODE REAL (wp) :: &
2033	!OLI_CODE c2 = 2.0_wp
2034	!OLI_CODE
2035	!OLI_CODE !-----------------------------------------------------------------
2036	!OLI_CODE ! Compute ice temperatures from enthalpies using quadratic formula
2037	!OLI_CODE !-----------------------------------------------------------------
2038	!OLI_CODE
2039	!OLI_CODE DO k = 1,nlay_i
2040	!OLI_CODE Tin(k) = ticen(k)
2041	!OLI_CODE END DO
2042	!OLI_CODE
2043	!OLI_CODE !-----------------------------------------------------------------
2044	!OLI_CODE ! brine salinity and liquid fraction
2045	!OLI_CODE !-----------------------------------------------------------------
2046	!OLI_CODE
2047	!OLI_CODE IF (maxval(Tin-rtt) <= -c2) THEN
2048	!OLI_CODE
2049	!OLI_CODE DO k = 1,nlay_i
2050	!OLI_CODE Sbr = - 1.2_wp &
2051	!OLI_CODE -21.8_wp * (Tin(k)-rtt) &
2052	!OLI_CODE - 0.919_wp * (Tin(k)-rtt)**2 &
2053	!OLI_CODE - 0.01878_wp * (Tin(k)-rtt)**3
2054	!OLI_CODE phi(k) = salin(k)/Sbr ! liquid fraction
2055	!OLI_CODE END DO ! k
2056	!OLI_CODE
2057	!OLI_CODE ELSE
2058	!OLI_CODE
2059	!OLI_CODE DO k = 1,nlay_i
2060	!OLI_CODE Sbr = -17.6_wp * (Tin(k)-rtt) &
2061	!OLI_CODE - 0.389_wp * (Tin(k)-rtt)**2 &
2062	!OLI_CODE - 0.00362_wp* (Tin(k)-rtt)**3
2063	!OLI_CODE phi(k) = salin(k)/Sbr ! liquid fraction
2064	!OLI_CODE END DO
2065	!OLI_CODE
2066	!OLI_CODE END IF
2067	!OLI_CODE
2068	!OLI_CODE !-----------------------------------------------------------------
2069	!OLI_CODE ! permeability
2070	!OLI_CODE !-----------------------------------------------------------------
2071	!OLI_CODE
2072	!OLI_CODE perm = 3.0e-08_wp * (minval(phi))**3
2073	!OLI_CODE
2074	!OLI_CODE END SUBROUTINE permeability_phi
2075	!OLI_CODE
2076	!OLI_CODE #else
2077	!OLI_CODE !!----------------------------------------------------------------------
2078	!OLI_CODE !! Default option Dummy Module No LIM-3 sea-ice model
2079	!OLI_CODE !!----------------------------------------------------------------------
2080	!OLI_CODE CONTAINS
2081	!OLI_CODE SUBROUTINE lim_mp_init ! Empty routine
2082	!OLI_CODE END SUBROUTINE lim_mp_init
2083	!OLI_CODE SUBROUTINE lim_mp ! Empty routine
2084	!OLI_CODE END SUBROUTINE lim_mp
2085	!OLI_CODE SUBROUTINE compute_mp_topo ! Empty routine
2086	!OLI_CODE END SUBROUTINE compute_mp_topo
2087	!OLI_CODE SUBROUTINE pond_area ! Empty routine
2088	!OLI_CODE END SUBROUTINE pond_area
2089	!OLI_CODE SUBROUTINE calc_hpond ! Empty routine
2090	!OLI_CODE END SUBROUTINE calc_hpond
2091	!OLI_CODE SUBROUTINE permeability_phy ! Empty routine
2092	!OLI_CODE END SUBROUTINE permeability_phy
2093	!OLI_CODE #endif
2094	!OLI_CODE !!======================================================================
2095	!OLI_CODE END MODULE limmp_topo
2096	!OLI_CODE
2097	#else
2098	!!----------------------------------------------------------------------
2099	!! Default option Empty module NO LIM sea-ice model
2100	!!----------------------------------------------------------------------
2101	CONTAINS
2102	SUBROUTINE lim_mp_init ! Empty routine
2103	END SUBROUTINE lim_mp_init
2104	SUBROUTINE lim_mp ! Empty routine
2105	END SUBROUTINE lim_mp
2106	SUBROUTINE lim_mp_topo ! Empty routine
2107	END SUBROUTINE lim_mp_topo
2108	SUBROUTINE lim_mp_cesm ! Empty routine
2109	END SUBROUTINE lim_mp_cesm
2110	SUBROUTINE lim_mp_area ! Empty routine
2111	END SUBROUTINE lim_mp_area
2112	SUBROUTINE lim_mp_perm ! Empty routine
2113	END SUBROUTINE lim_mp_perm
2114	#endif
2115
2116	!!======================================================================
2117	END MODULE limmp

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