SCALE-RM
Data Types | Functions/Subroutines
scale_atmos_adiabat Module Reference

module atmosphere / adiabat More...

Functions/Subroutines

subroutine, public atmos_adiabat_setup
 Setup. More...
 
subroutine atmos_adiabat_cape_1d (KA, KS, KE, Kstr, DENS, TEMP, PRES, QV, QC, Qdry, Rtot, CPtot, CZ, FZ, CAPE, CIN, LCL, LFC, LNB, DENS_p, TEMP_p, BUOY_p, QV_p, converged)
 Calc CAPE and CIN Type of parcel method: Pseudo-adiabatic ascend from lowermost layer of the model Reference: Emanuel(1994) More...
 
subroutine atmos_adiabat_cape_3d (KA, KS, KE, IA, IS, IE, JA, JS, JE, Kstr, DENS, TEMP, PRES, QV, QC, Qdry, Rtot, CPtot, CZ, FZ, CAPE, CIN, LCL, LFC, LNB, DENS_p, TEMP_p, BUOY_p, QV_p)
 
subroutine atmos_adiabat_liftparcel_1d (KA, KS, KE, Kstr, DENS, TEMP, PRES, QV, QC, QDRY, Rtot, CPtot, DENS_p1D, TEMP_p1D, QV_p1D, kLCL, converged)
 Calc temperature profile with lifting parcel Method: Pseudo-adiabatic ascend from lowermost layer of the model Reference: Emanuel(1994) More...
 
subroutine atmos_adiabat_liftparcel_3d (KA, KS, KE, IA, IS, IE, JA, JS, JE, Kstr, DENS, TEMP, PRES, QV, QC, QDRY, Rtot, CPtot, DENS_p3D, TEMP_p3D, QV_p3D, kLCL, converged)
 

Detailed Description

module atmosphere / adiabat

Description
Moist adiabatic process for calculation of CAPE, CIN
Author
Team SCALE
NAMELIST
  • No namelist group
History Output
namedescriptionunitvariable
BUOY_parcel buoyancy profile in lifting parcel m/s2 P_BUOY
DENS_parcel density profile in lifting parcel kg/m3 P_DENS
QV_parcel humidity profile in lifting parcel kg/kg P_QV
TEMP_parcel temperature profile in lifting parcel K P_TEMP

Function/Subroutine Documentation

◆ atmos_adiabat_setup()

subroutine, public scale_atmos_adiabat::atmos_adiabat_setup ( )

Setup.

Definition at line 58 of file scale_atmos_adiabat.F90.

References scale_atmos_hydrometeor::atmos_hydrometeor_setup(), and scale_atmos_saturation::atmos_saturation_setup().

58  use scale_atmos_hydrometeor, only: &
59  atmos_hydrometeor_setup
60  use scale_atmos_saturation, only: &
61  atmos_saturation_setup
62 
63  call atmos_hydrometeor_setup
64  call atmos_saturation_setup
65 
66  return
scale_atmos_saturation
module atmosphere / saturation
Definition: scale_atmos_saturation.F90:12
scale_atmos_saturation::atmos_saturation_setup
subroutine, public atmos_saturation_setup
Setup.
Definition: scale_atmos_saturation.F90:211
scale_atmos_hydrometeor
module atmosphere / hydrometeor
Definition: scale_atmos_hydrometeor.F90:12
scale_atmos_hydrometeor::atmos_hydrometeor_setup
subroutine, public atmos_hydrometeor_setup
Setup.
Definition: scale_atmos_hydrometeor.F90:154
Here is the call graph for this function:

◆ atmos_adiabat_cape_1d()

subroutine scale_atmos_adiabat::atmos_adiabat_cape_1d ( integer, intent(in)  KA,
integer, intent(in)  KS,
integer, intent(in)  KE,
integer, intent(in)  Kstr,
real(rp), dimension (ka), intent(in)  DENS,
real(rp), dimension (ka), intent(in)  TEMP,
real(rp), dimension (ka), intent(in)  PRES,
real(rp), dimension (ka), intent(in)  QV,
real(rp), dimension (ka), intent(in)  QC,
real(rp), dimension (ka), intent(in)  Qdry,
real(rp), dimension (ka), intent(in)  Rtot,
real(rp), dimension(ka), intent(in)  CPtot,
real(rp), dimension ( ka), intent(in)  CZ,
real(rp), dimension (0:ka), intent(in)  FZ,
real(rp), intent(out)  CAPE,
real(rp), intent(out)  CIN,
real(rp), intent(out)  LCL,
real(rp), intent(out)  LFC,
real(rp), intent(out)  LNB,
real(rp), dimension(ka), intent(out)  DENS_p,
real(rp), dimension(ka), intent(out)  TEMP_p,
real(rp), dimension(ka), intent(out)  BUOY_p,
real(rp), dimension (ka), intent(out)  QV_p,
logical, intent(out)  converged 
)

Calc CAPE and CIN Type of parcel method: Pseudo-adiabatic ascend from lowermost layer of the model Reference: Emanuel(1994)

Definition at line 83 of file scale_atmos_adiabat.F90.

References atmos_adiabat_liftparcel_1d(), and scale_const::const_grav.

Referenced by atmos_adiabat_cape_3d().

83  use scale_const, only: &
84  grav => const_grav
85  implicit none
86  integer, intent(in) :: ka, ks, ke
87 
88  integer, intent(in) :: kstr
89  real(RP), intent(in) :: dens (ka)
90  real(RP), intent(in) :: temp (ka)
91  real(RP), intent(in) :: pres (ka)
92  real(RP), intent(in) :: qv (ka)
93  real(RP), intent(in) :: qc (ka)
94  real(RP), intent(in) :: qdry (ka)
95  real(RP), intent(in) :: rtot (ka)
96  real(RP), intent(in) :: cptot(ka)
97  real(RP), intent(in) :: cz ( ka)
98  real(RP), intent(in) :: fz (0:ka)
99 
100  real(RP), intent(out) :: cape
101  real(RP), intent(out) :: cin
102  real(RP), intent(out) :: lcl
103  real(RP), intent(out) :: lfc
104  real(RP), intent(out) :: lnb
105  real(RP), intent(out) :: dens_p(ka)
106  real(RP), intent(out) :: temp_p(ka)
107  real(RP), intent(out) :: buoy_p(ka)
108  real(RP), intent(out) :: qv_p (ka)
109  logical, intent(out) :: converged
110 
111  real(RP) :: buoy_pf(ka)
112  integer :: klcl, klfc, klnb
113 
114  integer :: k
115  !---------------------------------------------------------------------------
116 
117  ! lift parcel
118  call atmos_adiabat_liftparcel_1d( ka, ks, ke, &
119  kstr, & ! [IN]
120  dens(:), temp(:), pres(:), & ! [IN]
121  qv(:), qc(:), & ! [IN]
122  qdry(:), rtot(:), cptot(:), & ! [IN]
123  dens_p(:), temp_p(:), qv_p(:), & ! [OUT]
124  klcl, converged ) ! [OUT]
125 
126  if ( .not. converged ) return
127 
128  ! parcel buoyancy
129  do k = ks, ke
130  buoy_p(k) = grav * ( dens(k) - dens_p(k) ) / dens_p(k)
131  end do
132 
133  do k = ks, ke-1
134  buoy_pf(k) = 0.5_rp * ( buoy_p(k+1) + buoy_p(k) )
135  end do
136  buoy_p(ke) = buoy_p(ke-1)
137 
138  lcl = 0.0_rp
139  lfc = 0.0_rp
140  lnb = 0.0_rp
141  cape = 0.0_rp
142  cin = 0.0_rp
143 
144  klfc = -1
145  klnb = -1
146 
147  do k = klcl, ke
148  if ( buoy_p(k) >= 0.0_rp ) then
149  klfc = k
150  exit
151  endif
152  enddo
153 
154  do k = ke, kstr, -1
155  if ( buoy_p(k) >= 0.0_rp ) then
156  klnb = k
157  exit
158  endif
159  enddo
160 
161  if ( klcl >= kstr ) then
162  lcl = cz(klcl)
163  endif
164 
165  if ( klfc >= kstr ) then
166  lfc = cz(klfc)
167  endif
168 
169  if ( klnb >= kstr ) then
170  lnb = cz(klnb)
171  endif
172 
173  if ( klfc >= kstr .AND. klnb > kstr ) then
174  do k = klfc, klnb
175  cape = cape + buoy_pf(k-1) * ( fz(k)-fz(k-1) )
176  enddo
177  endif
178 
179  if ( klfc >= kstr ) then
180  do k = kstr+1, klfc
181  cin = cin + buoy_pf(k-1) * ( fz(k)-fz(k-1) )
182  enddo
183  endif
184 
185  return
scale_const::const_grav
real(rp), public const_grav
standard acceleration of gravity [m/s2]
Definition: scale_const.F90:46
scale_const
module CONSTANT
Definition: scale_const.F90:11
Here is the call graph for this function:
Here is the caller graph for this function:

◆ atmos_adiabat_cape_3d()

subroutine scale_atmos_adiabat::atmos_adiabat_cape_3d ( integer, intent(in)  KA,
integer, intent(in)  KS,
integer, intent(in)  KE,
integer, intent(in)  IA,
integer, intent(in)  IS,
integer, intent(in)  IE,
integer, intent(in)  JA,
integer, intent(in)  JS,
integer, intent(in)  JE,
integer, intent(in)  Kstr,
real(rp), dimension (ka,ia,ja), intent(in)  DENS,
real(rp), dimension (ka,ia,ja), intent(in)  TEMP,
real(rp), dimension (ka,ia,ja), intent(in)  PRES,
real(rp), dimension (ka,ia,ja), intent(in)  QV,
real(rp), dimension (ka,ia,ja), intent(in)  QC,
real(rp), dimension (ka,ia,ja), intent(in)  Qdry,
real(rp), dimension (ka,ia,ja), intent(in)  Rtot,
real(rp), dimension(ka,ia,ja), intent(in)  CPtot,
real(rp), dimension ( ka,ia,ja), intent(in)  CZ,
real(rp), dimension (0:ka,ia,ja), intent(in)  FZ,
real(rp), dimension(ia,ja), intent(out)  CAPE,
real(rp), dimension (ia,ja), intent(out)  CIN,
real(rp), dimension (ia,ja), intent(out)  LCL,
real(rp), dimension (ia,ja), intent(out)  LFC,
real(rp), dimension (ia,ja), intent(out)  LNB,
real(rp), dimension(ka,ia,ja), intent(out), optional, target  DENS_p,
real(rp), dimension(ka,ia,ja), intent(out), optional, target  TEMP_p,
real(rp), dimension(ka,ia,ja), intent(out), optional, target  BUOY_p,
real(rp), dimension (ka,ia,ja), intent(out), optional, target  QV_p 
)

Definition at line 196 of file scale_atmos_adiabat.F90.

References atmos_adiabat_cape_1d(), and scale_prc::prc_abort().

196  use scale_prc, only: &
197  prc_abort
198  use scale_file_history, only: &
199  file_history_in
200  implicit none
201  integer, intent(in) :: ka, ks, ke
202  integer, intent(in) :: ia, is, ie
203  integer, intent(in) :: ja, js, je
204 
205  integer, intent(in) :: kstr
206  real(RP), intent(in) :: dens (ka,ia,ja)
207  real(RP), intent(in) :: temp (ka,ia,ja)
208  real(RP), intent(in) :: pres (ka,ia,ja)
209  real(RP), intent(in) :: qv (ka,ia,ja)
210  real(RP), intent(in) :: qc (ka,ia,ja)
211  real(RP), intent(in) :: qdry (ka,ia,ja)
212  real(RP), intent(in) :: rtot (ka,ia,ja)
213  real(RP), intent(in) :: cptot(ka,ia,ja)
214  real(RP), intent(in) :: cz ( ka,ia,ja)
215  real(RP), intent(in) :: fz (0:ka,ia,ja)
216 
217  real(RP), intent(out) :: cape(ia,ja)
218  real(RP), intent(out) :: cin (ia,ja)
219  real(RP), intent(out) :: lcl (ia,ja)
220  real(RP), intent(out) :: lfc (ia,ja)
221  real(RP), intent(out) :: lnb (ia,ja)
222 
223  real(RP), intent(out), optional, target :: dens_p(ka,ia,ja)
224  real(RP), intent(out), optional, target :: temp_p(ka,ia,ja)
225  real(RP), intent(out), optional, target :: buoy_p(ka,ia,ja)
226  real(RP), intent(out), optional, target :: qv_p (ka,ia,ja)
227 
228  logical :: converged, error
229 
230  real(RP), pointer :: p_dens(:,:,:), p_temp(:,:,:), p_buoy(:,:,:), p_qv(:,:,:)
231 
232  integer :: i, j
233  !---------------------------------------------------------------------------
234 
235  error = .false.
236 
237  if ( present(dens_p) ) then
238  p_dens => dens_p
239  else
240  allocate( p_dens(ka,ia,ja) )
241  end if
242  if ( present(temp_p) ) then
243  p_temp => temp_p
244  else
245  allocate( p_temp(ka,ia,ja) )
246  end if
247  if ( present(buoy_p) ) then
248  p_buoy => buoy_p
249  else
250  allocate( p_buoy(ka,ia,ja) )
251  end if
252  if ( present(qv_p) ) then
253  p_qv => qv_p
254  else
255  allocate( p_qv(ka,ia,ja) )
256  end if
257 
258 
259  !$omp parallel do OMP_SCHEDULE_ collapse(2) &
260  !$omp private(converged)
261  do j = js, je
262  do i = is, ie
263 
264  call atmos_adiabat_cape_1d( ka, ks, ke, &
265  kstr, &
266  dens(:,i,j), temp(:,i,j), pres(:,i,j), & ! [IN]
267  qv(:,i,j), qc(:,i,j), qdry(:,i,j), & ! [IN]
268  rtot(:,i,j), cptot(:,i,j), & ! [IN]
269  cz(:,i,j), fz(:,i,j), & ! [IN]
270  cape(i,j), cin(i,j), & ! [OUT]
271  lcl(i,j), lfc(i,j), lnb(i,j), & ! [OUT]
272  p_dens(:,i,j), p_temp(:,i,j), & ! [OUT]
273  p_buoy(:,i,j), p_qv(:,i,j), & ! [OUT]
274  converged ) ! [OUT]
275 
276  if ( .not. converged ) then
277  log_error("ATMOS_ADIABAT_cape_3D",*) '[liftparcel] not converged! ', i, j
278  error = .true.
279  end if
280 
281  end do
282  end do
283 
284  if ( error ) call prc_abort
285 
286  call file_history_in( p_dens(:,:,:), 'DENS_parcel', 'density profile in lifting parcel', 'kg/m3' )
287  call file_history_in( p_temp(:,:,:), 'TEMP_parcel', 'temperature profile in lifting parcel', 'K' )
288  call file_history_in( p_buoy(:,:,:), 'BUOY_parcel', 'buoyancy profile in lifting parcel', 'm/s2' )
289  call file_history_in( p_qv(:,:,:), 'QV_parcel', 'humidity profile in lifting parcel', 'kg/kg' )
290 
291  if ( .not. present(dens_p) ) deallocate( p_dens )
292  if ( .not. present(temp_p) ) deallocate( p_temp )
293  if ( .not. present(buoy_p) ) deallocate( p_buoy )
294  if ( .not. present(qv_p ) ) deallocate( p_qv )
295 
296  return
scale_prc
module PROCESS
Definition: scale_prc.F90:11
scale_prc::prc_abort
subroutine, public prc_abort
Abort Process.
Definition: scale_prc.F90:338
scale_file_history
module file_history
Definition: scale_file_history.F90:15
Here is the call graph for this function:

◆ atmos_adiabat_liftparcel_1d()

subroutine scale_atmos_adiabat::atmos_adiabat_liftparcel_1d ( integer, intent(in)  KA,
integer, intent(in)  KS,
integer, intent(in)  KE,
integer, intent(in)  Kstr,
real(rp), dimension (ka), intent(in)  DENS,
real(rp), dimension (ka), intent(in)  TEMP,
real(rp), dimension (ka), intent(in)  PRES,
real(rp), dimension (ka), intent(in)  QV,
real(rp), dimension (ka), intent(in)  QC,
real(rp), dimension (ka), intent(in)  QDRY,
real(rp), dimension (ka), intent(in)  Rtot,
real(rp), dimension(ka), intent(in)  CPtot,
real(rp), dimension(ka), intent(out)  DENS_p1D,
real(rp), dimension(ka), intent(out)  TEMP_p1D,
real(rp), dimension (ka), intent(out)  QV_p1D,
integer, intent(out)  kLCL,
logical, intent(out)  converged 
)

Calc temperature profile with lifting parcel Method: Pseudo-adiabatic ascend from lowermost layer of the model Reference: Emanuel(1994)

Definition at line 311 of file scale_atmos_adiabat.F90.

References scale_atmos_hydrometeor::cp_water.

Referenced by atmos_adiabat_cape_1d(), and atmos_adiabat_liftparcel_3d().

311  use scale_atmos_hydrometeor, only: &
312  hydrometeor_entr => atmos_hydrometeor_entr, &
313  cp_water
314  use scale_atmos_saturation, only: &
315  atmos_saturation_moist_conversion_pres_liq
316  implicit none
317  integer, intent(in) :: ka, ks, ke
318 
319  integer, intent(in) :: kstr
320  real(RP), intent(in) :: dens (ka)
321  real(RP), intent(in) :: temp (ka)
322  real(RP), intent(in) :: pres (ka)
323  real(RP), intent(in) :: qv (ka)
324  real(RP), intent(in) :: qc (ka)
325  real(RP), intent(in) :: qdry (ka)
326  real(RP), intent(in) :: rtot (ka)
327  real(RP), intent(in) :: cptot(ka)
328 
329  real(RP), intent(out) :: dens_p1d(ka)
330  real(RP), intent(out) :: temp_p1d(ka)
331  real(RP), intent(out) :: qv_p1d (ka)
332  integer, intent(out) :: klcl
333  logical, intent(out) :: converged
334 
335  real(RP) :: entr_p
336  real(RP) :: qv_p, qc_p, qdry_p
337  real(RP) :: rtot_p, cptot_p
338  real(RP) :: temp_p
339 
340  real(RP) :: fact
341 
342  integer :: k
343  !---------------------------------------------------------------------------
344 
345  do k = 1, kstr
346  dens_p1d(k) = dens(k)
347  temp_p1d(k) = temp(k)
348  qv_p1d(k) = qv(k)
349  enddo
350 
351  ! vapor + liquid water at the start point
352  qv_p = qv(kstr)
353  qc_p = qc(kstr)
354  qdry_p = qdry(kstr)
355  rtot_p = rtot(kstr)
356  cptot_p = cptot(kstr)
357 
358  call hydrometeor_entr( temp(kstr), pres(kstr), & ! [IN]
359  qv_p, qc_p, qdry_p, & ! [IN]
360  rtot_p, cptot_p, & ! [IN]
361  entr_p ) ! [OUT]
362 
363  klcl = -1
364  do k = kstr, ke
365 
366  call atmos_saturation_moist_conversion_pres_liq( &
367  pres(k), entr_p, qdry_p, & ! [IN]
368  qv_p, qc_p, rtot_p, cptot_p, & ! [INOUT]
369  temp_p, & ! [OUT]
370  converged ) ! [OUT]
371 
372  if ( .NOT. converged ) then
373  exit
374  endif
375 
376  if ( qc_p > 0.0_rp .and. klcl == -1 ) klcl = k
377 
378  ! remove condensed water
379  fact = 1.0_rp / ( 1.0_rp - qc_p )
380  cptot_p = ( cptot_p - cp_water * qc_p ) * fact
381  rtot_p = rtot_p * fact
382  qdry_p = qdry_p * fact
383  qv_p = qv_p * fact
384  ! Entr_p = Entr_p - QC_p * CP_WATER * log( TEMP_p / TEM00 )
385  qc_p = 0.0_rp
386 
387  dens_p1d(k) = pres(k) / ( rtot_p * temp_p )
388  temp_p1d(k) = temp_p
389  qv_p1d(k) = qv_p
390 
391  enddo
392 
393  return
scale_atmos_saturation
module atmosphere / saturation
Definition: scale_atmos_saturation.F90:12
scale_atmos_hydrometeor
module atmosphere / hydrometeor
Definition: scale_atmos_hydrometeor.F90:12
scale_atmos_hydrometeor::cp_water
real(rp), public cp_water
CP for water [J/kg/K].
Definition: scale_atmos_hydrometeor.F90:133
Here is the caller graph for this function:

◆ atmos_adiabat_liftparcel_3d()

subroutine scale_atmos_adiabat::atmos_adiabat_liftparcel_3d ( integer, intent(in)  KA,
integer, intent(in)  KS,
integer, intent(in)  KE,
integer, intent(in)  IA,
integer, intent(in)  IS,
integer, intent(in)  IE,
integer, intent(in)  JA,
integer, intent(in)  JS,
integer, intent(in)  JE,
integer, intent(in)  Kstr,
real(rp), dimension (ka,ia,ja), intent(in)  DENS,
real(rp), dimension (ka,ia,ja), intent(in)  TEMP,
real(rp), dimension (ka,ia,ja), intent(in)  PRES,
real(rp), dimension (ka,ia,ja), intent(in)  QV,
real(rp), dimension (ka,ia,ja), intent(in)  QC,
real(rp), dimension (ka,ia,ja), intent(in)  QDRY,
real(rp), dimension (ka,ia,ja), intent(in)  Rtot,
real(rp), dimension(ka,ia,ja), intent(in)  CPtot,
real(rp), dimension(ka,ia,ja), intent(out)  DENS_p3D,
real(rp), dimension(ka,ia,ja), intent(out)  TEMP_p3D,
real(rp), dimension (ka,ia,ja), intent(out)  QV_p3D,
integer, dimension(ia,ja), intent(out)  kLCL,
logical, intent(out)  converged 
)

Definition at line 403 of file scale_atmos_adiabat.F90.

References atmos_adiabat_liftparcel_1d(), and scale_prc::prc_abort().

403  use scale_prc, only: &
404  prc_abort
405  use scale_atmos_hydrometeor, only: &
406  hydrometeor_entr => atmos_hydrometeor_entr
407  use scale_atmos_saturation, only: &
408  atmos_saturation_moist_conversion_pres_liq
409  implicit none
410 
411  integer, intent(in) :: ka, ks, ke
412  integer, intent(in) :: ia, is, ie
413  integer, intent(in) :: ja, js, je
414 
415  integer, intent(in) :: kstr
416  real(RP), intent(in) :: dens (ka,ia,ja)
417  real(RP), intent(in) :: temp (ka,ia,ja)
418  real(RP), intent(in) :: pres (ka,ia,ja)
419  real(RP), intent(in) :: qv (ka,ia,ja)
420  real(RP), intent(in) :: qc (ka,ia,ja)
421  real(RP), intent(in) :: qdry (ka,ia,ja)
422  real(RP), intent(in) :: rtot (ka,ia,ja)
423  real(RP), intent(in) :: cptot(ka,ia,ja)
424 
425  real(RP), intent(out) :: dens_p3d(ka,ia,ja)
426  real(RP), intent(out) :: temp_p3d(ka,ia,ja)
427  real(RP), intent(out) :: qv_p3d (ka,ia,ja)
428  integer, intent(out) :: klcl(ia,ja)
429  logical, intent(out) :: converged
430 
431  logical :: error
432 
433  integer :: i, j
434  !---------------------------------------------------------------------------
435 
436  error = .false.
437 
438  !$omp parallel do OMP_SCHEDULE_ collapse(2)
439  do j = js, je
440  do i = is, ie
441 
442  call atmos_adiabat_liftparcel_1d( ka, ks, ke, &
443  kstr, & ! [IN]
444  dens(:,i,j), temp(:,i,j), pres(:,i,j), & ! [IN]
445  qv(:,i,j), qc(:,i,j), & ! [IN]
446  qdry(:,i,j), rtot(:,i,j), cptot(:,i,j), & ! [IN]
447  dens_p3d(:,i,j), temp_p3d(:,i,j), qv_p3d(:,i,j), & ! [OUT]
448  klcl(i,j), converged ) ! [OUT]
449  if ( .not. converged ) then
450  log_error("ATMOS_ADIABAT_liftparcel_3D",*) '[liftparcel] not converged! ', i, j
451  error = .true.
452  end if
453 
454  enddo
455  enddo
456 
457  if ( error ) call prc_abort
458 
459  return
scale_atmos_saturation
module atmosphere / saturation
Definition: scale_atmos_saturation.F90:12
scale_atmos_hydrometeor
module atmosphere / hydrometeor
Definition: scale_atmos_hydrometeor.F90:12
scale_prc
module PROCESS
Definition: scale_prc.F90:11
scale_prc::prc_abort
subroutine, public prc_abort
Abort Process.
Definition: scale_prc.F90:338
Here is the call graph for this function:
Generated by   doxygen 1.8.13