SICOPOLIS V5-dev  Revision 1105
calc_vz_m.F90
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1 !+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2 !
3 ! Module : c a l c _ v z _ m
4 !
5 !> @file
6 !!
7 !! Computation of the vertical velocity vz.
8 !!
9 !! @section Copyright
10 !!
11 !! Copyright 2009-2017 Ralf Greve, Tatsuru Sato
12 !!
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29 !<
30 !+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
31 
32 !-------------------------------------------------------------------------------
33 !> Computation of the vertical velocity vz.
34 !<------------------------------------------------------------------------------
35 module calc_vz_m
36 
37  use sico_types_m
39  use sico_vars_m
40 
41  implicit none
42 
43  private
45 
46 contains
47 
48 !-------------------------------------------------------------------------------
49 !> Computation of the vertical velocity vz for grounded ice.
50 !<------------------------------------------------------------------------------
51 subroutine calc_vz_grounded(dxi, deta, dzeta_c, dzeta_t)
52 
53 implicit none
54 
55 real(dp), intent(in) :: dxi, deta, dzeta_c, dzeta_t
56 
57 integer(i4b) :: i, j, kc, kt
58 real(dp) :: avz3(0:kcmax)
59 real(dp) :: cvz00, cvz0(0:ktmax), cvz1(0:ktmax), cvz2(0:ktmax), &
60  cvz3(0:kcmax), cvz4(0:kcmax), cvz5(0:kcmax)
61 real(dp) :: dxi_inv, deta_inv
62 
63 !-------- Term abbreviations --------
64 
65 dxi_inv = 1.0_dp/dxi
66 deta_inv = 1.0_dp/deta
67 
68 do kc=0, kcmax
69  if (flag_aa_nonzero) then
70  avz3(kc) = aa*eaz_c(kc)/(ea-1.0_dp)*dzeta_c
71  else
72  avz3(kc) = dzeta_c
73  end if
74 end do
75 
76 do i=1, imax-1
77 do j=1, jmax-1
78 
79  if (maske(j,i)==0) then ! grounded ice
80 
81 !-------- Abbreviations --------
82 
83  cvz00 = 0.5_dp*(vx_t(0,j,i)+vx_t(0,j,i-1))*dzb_dxi_g(j,i) &
84  +0.5_dp*(vy_t(0,j,i)+vy_t(0,j-1,i))*dzb_deta_g(j,i) &
85  +dzb_dtau(j,i)-q_b_tot(j,i)
86 
87  kt=0
88  cvz0(kt) = h_t(j,i)*insq_g11_g(j,i)*insq_g22_g(j,i) &
89  *( (vx_t(kt,j,i)*sq_g22_sgx(j,i) &
90  -vx_t(kt,j,i-1)*sq_g22_sgx(j,i-1))*dxi_inv &
91  +(vy_t(kt,j,i)*sq_g11_sgy(j,i) &
92  -vy_t(kt,j-1,i)*sq_g11_sgy(j-1,i))*deta_inv ) &
93  *dzeta_t
94  cvz1(kt) = (dzb_dxi_g(j,i)+zeta_t(kt)*dh_t_dxi_g(j,i)) &
95  *(vx_t(kt+1,j,i)+vx_t(kt+1,j,i-1) &
96  -vx_t(kt,j,i) -vx_t(kt,j,i-1))*0.5_dp
97  cvz2(kt) = (dzb_deta_g(j,i)+zeta_t(kt)*dh_t_deta_g(j,i)) &
98  *(vy_t(kt+1,j,i)+vy_t(kt+1,j-1,i) &
99  -vy_t(kt,j,i) -vy_t(kt,j-1,i))*0.5_dp
100 
101  do kt=1, ktmax-1
102  cvz0(kt) = h_t(j,i)*insq_g11_g(j,i)*insq_g22_g(j,i) &
103  *( (vx_t(kt,j,i)*sq_g22_sgx(j,i) &
104  -vx_t(kt,j,i-1)*sq_g22_sgx(j,i-1))*dxi_inv &
105  +(vy_t(kt,j,i)*sq_g11_sgy(j,i) &
106  -vy_t(kt,j-1,i)*sq_g11_sgy(j-1,i))*deta_inv ) &
107  *dzeta_t
108  cvz1(kt) = (dzb_dxi_g(j,i)+zeta_t(kt)*dh_t_dxi_g(j,i)) &
109  *(vx_t(kt+1,j,i)+vx_t(kt+1,j,i-1) &
110  -vx_t(kt-1,j,i)-vx_t(kt-1,j,i-1))*0.25_dp
111  cvz2(kt) = (dzb_deta_g(j,i)+zeta_t(kt)*dh_t_deta_g(j,i)) &
112  *(vy_t(kt+1,j,i)+vy_t(kt+1,j-1,i) &
113  -vy_t(kt-1,j,i)-vy_t(kt-1,j-1,i))*0.25_dp
114  end do
115 
116  kt=ktmax
117  cvz0(kt) = h_t(j,i)*insq_g11_g(j,i)*insq_g22_g(j,i) &
118  *( (vx_t(kt,j,i)*sq_g22_sgx(j,i) &
119  -vx_t(kt,j,i-1)*sq_g22_sgx(j,i-1))*dxi_inv &
120  +(vy_t(kt,j,i)*sq_g11_sgy(j,i) &
121  -vy_t(kt,j-1,i)*sq_g11_sgy(j-1,i))*deta_inv ) &
122  *dzeta_t
123  cvz1(kt) = (dzb_dxi_g(j,i)+zeta_t(kt)*dh_t_dxi_g(j,i)) &
124  *(vx_t(kt,j,i) +vx_t(kt,j,i-1) &
125  -vx_t(kt-1,j,i)-vx_t(kt-1,j,i-1))*0.5_dp
126  cvz2(kt) = (dzb_deta_g(j,i)+zeta_t(kt)*dh_t_deta_g(j,i)) &
127  *(vy_t(kt,j,i) +vy_t(kt,j-1,i) &
128  -vy_t(kt-1,j,i)-vy_t(kt-1,j-1,i))*0.5_dp
129 
130  kc=0
131  cvz3(kc) = avz3(kc)*h_c(j,i) &
132  *insq_g11_g(j,i)*insq_g22_g(j,i) &
133  *( (vx_c(kc,j,i)*sq_g22_sgx(j,i) &
134  -vx_c(kc,j,i-1)*sq_g22_sgx(j,i-1))*dxi_inv &
135  +(vy_c(kc,j,i)*sq_g11_sgy(j,i) &
136  -vy_c(kc,j-1,i)*sq_g11_sgy(j-1,i))*deta_inv )
137  cvz4(kc) = (dzm_dxi_g(j,i) &
138  +eaz_c_quotient(kc)*dh_c_dxi_g(j,i)) &
139  *(vx_c(kc+1,j,i)+vx_c(kc+1,j,i-1) &
140  -vx_c(kc,j,i) -vx_c(kc,j,i-1))*0.5_dp
141  cvz5(kc) = (dzm_deta_g(j,i) &
142  +eaz_c_quotient(kc)*dh_c_deta_g(j,i)) &
143  *(vy_c(kc+1,j,i)+vy_c(kc+1,j-1,i) &
144  -vy_c(kc,j,i) -vy_c(kc,j-1,i))*0.5_dp
145 
146  do kc=1, kcmax-1
147  cvz3(kc) = avz3(kc)*h_c(j,i) &
148  *insq_g11_g(j,i)*insq_g22_g(j,i) &
149  *( (vx_c(kc,j,i)*sq_g22_sgx(j,i) &
150  -vx_c(kc,j,i-1)*sq_g22_sgx(j,i-1))*dxi_inv &
151  +(vy_c(kc,j,i)*sq_g11_sgy(j,i) &
152  -vy_c(kc,j-1,i)*sq_g11_sgy(j-1,i))*deta_inv )
153  cvz4(kc) = (dzm_dxi_g(j,i) &
154  +eaz_c_quotient(kc)*dh_c_dxi_g(j,i)) &
155  *(vx_c(kc+1,j,i)+vx_c(kc+1,j,i-1) &
156  -vx_c(kc-1,j,i)-vx_c(kc-1,j,i-1))*0.25_dp
157  cvz5(kc) = (dzm_deta_g(j,i) &
158  +eaz_c_quotient(kc)*dh_c_deta_g(j,i)) &
159  *(vy_c(kc+1,j,i)+vy_c(kc+1,j-1,i) &
160  -vy_c(kc-1,j,i)-vy_c(kc-1,j-1,i))*0.25_dp
161  end do
162 
163  kc=kcmax
164  cvz3(kc) = avz3(kc)*h_c(j,i) &
165  *insq_g11_g(j,i)*insq_g22_g(j,i) &
166  *( (vx_c(kc,j,i)*sq_g22_sgx(j,i) &
167  -vx_c(kc,j,i-1)*sq_g22_sgx(j,i-1))*dxi_inv &
168  +(vy_c(kc,j,i)*sq_g11_sgy(j,i) &
169  -vy_c(kc,j-1,i)*sq_g11_sgy(j-1,i))*deta_inv )
170  cvz4(kc) = (dzm_dxi_g(j,i) &
171  +eaz_c_quotient(kc)*dh_c_dxi_g(j,i)) &
172  *(vx_c(kc,j,i) +vx_c(kc,j,i-1) &
173  -vx_c(kc-1,j,i)-vx_c(kc-1,j,i-1))*0.5_dp
174  cvz5(kc) = (dzm_deta_g(j,i) &
175  +eaz_c_quotient(kc)*dh_c_deta_g(j,i)) &
176  *(vy_c(kc,j,i) +vy_c(kc,j-1,i) &
177  -vy_c(kc-1,j,i)-vy_c(kc-1,j-1,i))*0.5_dp
178 
179 !-------- Computation of vz_b --------
180 
181  vz_b(j,i) = cvz00
182 
183 !-------- Computation of vz --------
184 
185  if ((n_cts(j,i) == -1).or.(n_cts(j,i) == 0)) then
186  ! cold ice base, temperate ice base
187 
188  do kt=0, ktmax-1
189  vz_t(kt,j,i) = vz_b(j,i)
190  end do
191 
192  vz_m(j,i) = vz_b(j,i)
193 
194  vz_c(0,j,i) = vz_m(j,i) &
195  +0.5_dp*(-cvz3(0)+cvz4(0)+cvz5(0))
196 
197  do kc=1, kcmax-1
198  vz_c(kc,j,i) = vz_c(kc-1,j,i) &
199  -cvz3(kc)+cvz4(kc)+cvz5(kc)
200  end do
201 
202  else ! n_cts(j,i) == 1, temperate ice layer
203 
204  vz_t(0,j,i) = vz_b(j,i) &
205  +0.5_dp*(-cvz0(0)+cvz1(0)+cvz2(0))
206 
207  do kt=1, ktmax-1
208  vz_t(kt,j,i) = vz_t(kt-1,j,i) &
209  -cvz0(kt)+cvz1(kt)+cvz2(kt)
210  end do
211 
212  vz_m(j,i) = vz_t(ktmax-1,j,i) &
213  +0.5_dp*(-cvz0(ktmax)+cvz1(ktmax)+cvz2(ktmax))
214 
215  vz_c(0,j,i) = vz_m(j,i) &
216  +0.5_dp*(-cvz3(0)+cvz4(0)+cvz5(0))
217 
218  do kc=1, kcmax-1
219  vz_c(kc,j,i) = vz_c(kc-1,j,i) &
220  -cvz3(kc)+cvz4(kc)+cvz5(kc)
221  end do
222 
223  end if
224 
225 !-------- Computation of vz_s --------
226 
227  kc=kcmax
228 
229  vz_s(j,i) = vz_c(kc-1,j,i) &
230  +0.5_dp*(-cvz3(kc)+cvz4(kc)+cvz5(kc))
231 
232  else ! maske(j,i) /= 0 (not grounded ice)
233 
234  vz_b(j,i) = 0.0_dp
235 
236  do kt=0, ktmax-1
237  vz_t(kt,j,i) = 0.0_dp
238  end do
239 
240  vz_m(j,i) = 0.0_dp
241 
242  do kc=0, kcmax-1
243  vz_c(kc,j,i) = 0.0_dp
244  end do
245 
246  vz_s(j,i) = 0.0_dp
247 
248  end if
249 
250 end do
251 end do
252 
253 end subroutine calc_vz_grounded
254 
255 !-------------------------------------------------------------------------------
256 !> Computation of the vertical velocity vz for floating ice.
257 !<------------------------------------------------------------------------------
258 subroutine calc_vz_floating(z_sl, dxi, deta, dzeta_c)
260 implicit none
261 
262 real(dp), intent(in) :: z_sl
263 real(dp), intent(in) :: dxi, deta, dzeta_c
264 
265 integer(i4b) :: i, j, kt, kc
266 real(dp), dimension(0:JMAX,0:IMAX) :: vz_sl
267 real(dp), dimension(0:KCMAX) :: zeta_c_sgz, eaz_c_sgz, eaz_c_quotient_sgz
268 real(dp) :: dxi_inv, deta_inv
269 real(dp) :: dvx_dxi, dvy_deta
270 
271 dxi_inv = 1.0_dp/dxi
272 deta_inv = 1.0_dp/deta
273 
274 !-------- Abbreviations --------
275 
276 do kc=0, kcmax-1
277 
278  zeta_c_sgz(kc) = (kc+0.5_dp)*dzeta_c
279 
280  if (flag_aa_nonzero) then
281  eaz_c_sgz(kc) = exp(aa*zeta_c_sgz(kc))
282  eaz_c_quotient_sgz(kc) = (eaz_c_sgz(kc)-1.0_dp)/(ea-1.0_dp)
283  else
284  eaz_c_sgz(kc) = 1.0_dp
285  eaz_c_quotient_sgz(kc) = zeta_c_sgz(kc)
286  end if
287 
288 end do
289 
290 !-------- Computation of vz --------
291 
292 do i=1, imax-1
293 do j=1, jmax-1
294 
295  if (maske(j,i)==3_i2b) then ! floating ice
296 
297 ! ------ Derivatives of the horizontal velocity
298 
299  dvx_dxi = insq_g11_g(j,i)*insq_g22_g(j,i) &
300  *(vx_m(j,i)*sq_g22_sgx(j,i)-vx_m(j,i-1)*sq_g22_sgx(j,i-1)) &
301  *dxi_inv
302 
303  dvy_deta = insq_g11_g(j,i)*insq_g22_g(j,i) &
304  *(vy_m(j,i)*sq_g11_sgy(j,i)-vy_m(j-1,i)*sq_g11_sgy(j-1,i)) &
305  *deta_inv
306 
307 ! ------ Basal velocity vz_b
308 
309  vz_b(j,i) = 0.5_dp*(vx_m(j,i)+vx_m(j,i-1))*dzb_dxi_g(j,i) &
310  +0.5_dp*(vy_m(j,i)+vy_m(j-1,i))*dzb_deta_g(j,i) &
311  +dzb_dtau(j,i)-q_b_tot(j,i)
312  ! kinematic boundary condition at the ice base
313 
314 ! ------ Velocity at sea level vz_sl
315 
316  vz_sl(j,i) = vz_b(j,i) - (z_sl-zb(j,i))*(dvx_dxi+dvy_deta)
317 
318 ! ------ Surface velocity vz_s
319 
320  vz_s(j,i) = vz_sl(j,i) - (zs(j,i)-z_sl)*(dvx_dxi+dvy_deta)
321 
322 ! ------ Velocity vz_m at the interface between
323 ! the upper (kc) and the lower (kt) domain
324 
325  if ((n_cts(j,i) == -1).or.(n_cts(j,i) == 0)) then
326  ! cold ice base, temperate ice base
327 
328  vz_m(j,i) = vz_b(j,i)
329 
330  else ! n_cts(j,i) == 1, temperate ice layer
331 
332  vz_m(j,i) = vz_b(j,i) - h_t(j,i)*(dvx_dxi+dvy_deta)
333 
334  end if
335 
336 ! ------ 3-D velocity vz_c and vz_t
337 
338  do kc=0, kcmax-1
339  vz_c(kc,j,i) = vz_sl(j,i) &
340  -(zm(j,i)+eaz_c_quotient_sgz(kc)*h_c(j,i)-z_sl) &
341  *(dvx_dxi+dvy_deta)
342  end do
343 
344  if ((n_cts(j,i) == -1).or.(n_cts(j,i) == 0)) then
345  ! cold ice base, temperate ice base
346 
347  do kt=0, ktmax-1
348  vz_t(kt,j,i) = vz_b(j,i)
349  end do
350 
351  else ! n_cts(j,i) == 1, temperate ice layer
352 
353  do kt=0, ktmax-1
354  vz_t(kt,j,i) = vz_sl(j,i) &
355  -(zb(j,i) &
356  +0.5_dp*(zeta_t(kt)+zeta_t(kt+1))*h_t(j,i) &
357  -z_sl) &
358  *(dvx_dxi+dvy_deta)
359  end do
360 
361  end if
362 
363  end if
364 
365 end do
366 end do
367 
368 end subroutine calc_vz_floating
369 
370 !-------------------------------------------------------------------------------
371 !> Computation of the vertical velocity vz for static ice.
372 !<------------------------------------------------------------------------------
373 subroutine calc_vz_static()
375 implicit none
376 
377 integer(i4b) :: i, j, kc, kt
378 
379 do i=0, imax
380 do j=0, jmax
381 
382  if ((maske(j,i)==0).or.(maske(j,i)==3)) then ! grounded or floating ice
383 
384  vz_b(j,i) = dzb_dtau(j,i)-q_b_tot(j,i)
385  ! kinematic boundary condition at the ice base
386 
387  do kt=0, ktmax-1
388  vz_t(kt,j,i) = vz_b(j,i)
389  end do
390 
391  vz_m(j,i) = vz_b(j,i)
392 
393  do kc=0, kcmax-1
394  vz_c(kc,j,i) = vz_b(j,i)
395  end do
396 
397  vz_s(j,i) = vz_b(j,i)
398 
399  else ! maske(j,i) == (1 or 2)
400 
401  vz_b(j,i) = 0.0_dp
402 
403  do kt=0, ktmax-1
404  vz_t(kt,j,i) = 0.0_dp
405  end do
406 
407  vz_m(j,i) = 0.0_dp
408 
409  do kc=0, kcmax-1
410  vz_c(kc,j,i) = 0.0_dp
411  end do
412 
413  vz_s(j,i) = 0.0_dp
414 
415  end if
416 
417 end do
418 end do
419 
420 end subroutine calc_vz_static
421 
422 !-------------------------------------------------------------------------------
423 
424 end module calc_vz_m
425 !
real(dp), dimension(0:kcmax, 0:jmax, 0:imax) vx_c
vx_c(kc,j,i): Velocity in x-direction in the upper (kc) ice domain (at (i+1/2,j,kc)) ...
integer(i2b), dimension(0:jmax, 0:imax) n_cts
n_cts(j,i): Mask for thermal conditions. -1: cold ice base, 0: temperate ice base with cold ice above...
real(dp), dimension(0:jmax, 0:imax) vz_m
vz_m(j,i): Velocity in z-direction at the position z=zm (interface between the upper (kc) and the low...
real(dp), dimension(0:kcmax) eaz_c
eaz_c(kc): Abbreviation for exp(aa*zeta(kc))
real(dp), dimension(0:jmax, 0:imax) vx_m
vx_m(j,i): Mean (depth-averaged) velocity in x-direction, at (i+1/2,j)
subroutine, public calc_vz_floating(z_sl, dxi, deta, dzeta_c)
Computation of the vertical velocity vz for floating ice.
Definition: calc_vz_m.F90:259
real(dp), dimension(0:jmax, 0:imax) vz_b
vz_b(j,i): Velocity in z-direction at the ice base, at (i,j)
real(dp), dimension(0:jmax, 0:imax) vz_s
vz_s(j,i): Velocity in z-direction at the ice surface, at (i,j)
real(dp), dimension(0:jmax, 0:imax) insq_g22_g
insq_g22_g(j,i): Inverse square root of g22 on grid point (i,j)
integer(i2b), dimension(0:jmax, 0:imax) maske
maske(j,i): Ice-land-ocean mask. 0: grounded ice, 1: ice-free land, 2: ocean, 3: floating ice ...
real(dp), dimension(0:jmax, 0:imax) sq_g22_sgx
sq_g22_sgx(j,i): Square root of g22, at (i+1/2,j)
real(dp), dimension(0:jmax, 0:imax) dh_c_dxi_g
(.)_g(j,i): Staggered-grid quantity (.) interpolated to grid point (i,j)
real(dp), dimension(0:ktmax, 0:jmax, 0:imax) vz_t
vz_t(kt,j,i): Velocity in z-direction in the lower (kt) ice domain (at (i,j,kt+1/2)) ...
real(dp), dimension(0:jmax, 0:imax) vy_m
vy_m(j,i): Mean (depth-averaged) velocity in y-direction, at (i,j+1/2)
Declarations of global variables for SICOPOLIS (for the ANT domain).
Definition: sico_vars_m.F90:35
real(dp) ea
ea: Abbreviation for exp(aa)
logical flag_aa_nonzero
flag_aa_nonzero: Flag for the exponential stretch parameter aa. .true.: aa greater than zero (non-equ...
subroutine, public calc_vz_grounded(dxi, deta, dzeta_c, dzeta_t)
Computation of the vertical velocity vz for grounded ice.
Definition: calc_vz_m.F90:52
real(dp) aa
aa: Exponential stretch parameter of the non-equidistant vertical grid in the upper (kc) ice domain ...
Declarations of kind types for SICOPOLIS.
real(dp), dimension(0:jmax, 0:imax) zs
zs(j,i): Coordinate z of the surface topography
real(dp), dimension(0:jmax, 0:imax) dh_c_deta_g
(.)_g(j,i): Staggered-grid quantity (.) interpolated to grid point (i,j)
real(dp), dimension(0:jmax, 0:imax) h_c
H_c(j,i): Thickness of ice in the upper (kc) domain (thickness of the cold-ice layer for POLY...
Computation of the vertical velocity vz.
Definition: calc_vz_m.F90:35
real(dp), dimension(0:jmax, 0:imax) sq_g11_sgy
sq_g11_sgy(j,i): Square root of g11, at (i,j+1/2)
real(dp), dimension(0:jmax, 0:imax) dzb_deta_g
(.)_g(j,i): Staggered-grid quantity (.) interpolated to grid point (i,j)
subroutine, public calc_vz_static()
Computation of the vertical velocity vz for static ice.
Definition: calc_vz_m.F90:374
real(dp), dimension(0:kcmax, 0:jmax, 0:imax) vz_c
vz_c(kc,j,i): Velocity in z-direction in the upper (kc) ice domain (at (i,j,kc+1/2)) ...
real(dp), dimension(0:jmax, 0:imax) zm
zm(j,i): Coordinate z of the bottom of the upper (kc) ice domain = top of the lower (kt) ice domain (...
real(dp), dimension(0:jmax, 0:imax) q_b_tot
Q_b_tot(j,i): Sum of Q_bm and Q_tld.
real(dp), dimension(0:kcmax) eaz_c_quotient
eaz_c_quotient(kc): Abbreviation for (eaz_c(kc)-1.0)/(ea-1.0)
real(dp), dimension(0:jmax, 0:imax) dh_t_deta_g
(.)_g(j,i): Staggered-grid quantity (.) interpolated to grid point (i,j)
real(dp), dimension(0:jmax, 0:imax) dh_t_dxi_g
(.)_g(j,i): Staggered-grid quantity (.) interpolated to grid point (i,j)
real(dp), dimension(0:jmax, 0:imax) dzm_dxi_g
(.)_g(j,i): Staggered-grid quantity (.) interpolated to grid point (i,j)
real(dp), dimension(0:ktmax, 0:jmax, 0:imax) vy_t
vy_t(kt,j,i): Velocity in y-direction in the lower (kt) ice domain (at (i,j+1/2,kt)) ...
real(dp), dimension(0:jmax, 0:imax) dzm_deta_g
(.)_g(j,i): Staggered-grid quantity (.) interpolated to grid point (i,j)
real(dp), dimension(0:jmax, 0:imax) insq_g11_g
insq_g11_g(j,i): Inverse square root of g11 on grid point (i,j)
real(dp), dimension(0:kcmax, 0:jmax, 0:imax) vy_c
vy_c(kc,j,i): Velocity in y-direction in the upper (kc) ice domain (at (i,j+1/2,kc)) ...
real(dp), dimension(0:ktmax) zeta_t
zeta_t(kt): Sigma coordinate zeta_t of grid point kt
real(dp), dimension(0:jmax, 0:imax) zb
zb(j,i): Coordinate z of the ice base
real(dp), dimension(0:jmax, 0:imax) dzb_dtau
dzb_dtau(j,i): Derivative of zb by tau (time)
real(dp), dimension(0:jmax, 0:imax) h_t
H_t(j,i): Thickness of ice in the lower (kt) domain (thickness of the temperate layer for POLY...
Declarations of global variables for SICOPOLIS.
real(dp), dimension(0:ktmax, 0:jmax, 0:imax) vx_t
vx_t(kt,j,i): Velocity in x-direction in the lower (kt) ice domain (at (i+1/2,j,kt)) ...
real(dp), dimension(0:jmax, 0:imax) dzb_dxi_g
(.)_g(j,i): Staggered-grid quantity (.) interpolated to grid point (i,j)