#if (NMM_CORE == 1) MODULE module_diag_hailcast CONTAINS SUBROUTINE diag_hailcast_stub END SUBROUTINE diag_hailcast_stub END MODULE module_diag_hailcast #else MODULE module_diag_hailcast CONTAINS SUBROUTINE hailcast_diagnostic_driver ( grid , config_flags & , moist & , rho & , ids, ide, jds, jde, kds, kde & , ims, ime, jms, jme, kms, kme & , ips, ipe, jps, jpe, kps, kpe & , its, ite, jts, jte & , k_start, k_end ) USE module_domain, ONLY : domain , domain_clock_get USE module_configure, ONLY : grid_config_rec_type, model_config_rec USE module_state_description USE module_model_constants USE module_utility USE module_streams, ONLY: history_alarm, auxhist2_alarm #ifdef DM_PARALLEL USE module_dm, ONLY: wrf_dm_sum_real, wrf_dm_maxval #endif IMPLICIT NONE TYPE ( domain ), INTENT(INOUT) :: grid TYPE ( grid_config_rec_type ), INTENT(IN) :: config_flags INTEGER, INTENT(IN) :: ids, ide, jds, jde, kds, kde, & ims, ime, jms, jme, kms, kme, & ips, ipe, jps, jpe, kps, kpe INTEGER :: k_start , k_end, its, ite, jts, jte REAL, DIMENSION( ims:ime, kms:kme, jms:jme , num_moist), & INTENT(IN ) :: moist REAL, DIMENSION( ims:ime, kms:kme, jms:jme ), & INTENT(IN ) :: rho ! Local CHARACTER*512 :: message CHARACTER*256 :: timestr INTEGER :: i,j,k,nz INTEGER :: i_start, i_end, j_start, j_end REAL, DIMENSION( ims:ime, kms:kme, jms:jme ) :: qr & , qs & , qg & , qv & , qc & , qi & , ptot REAL, DIMENSION( ims:ime, jms:jme ) :: wup_mask_prev & , wdur_prev REAL :: dhail1,dhail2,dhail3,dhail4,dhail5 ! Timing TYPE(WRFU_Time) :: hist_time, aux2_time, CurrTime, StartTime TYPE(WRFU_TimeInterval) :: dtint, histint, aux2int LOGICAL :: is_after_history_dump, is_output_timestep, is_first_timestep ! Chirp the routine name for debugging purposes write ( message, * ) 'inside hailcast_diagnostics_driver' CALL wrf_debug( 100 , message ) ! Get timing info ! Want to know if when the last history output was ! Check history and auxhist2 alarms to check last ring time and how often ! they are set to ring CALL WRFU_ALARMGET( grid%alarms( HISTORY_ALARM ), prevringtime=hist_time, & ringinterval=histint) CALL WRFU_ALARMGET( grid%alarms( AUXHIST2_ALARM ), prevringtime=aux2_time, & ringinterval=aux2int) ! Get domain clock CALL domain_clock_get ( grid, current_time=CurrTime, & simulationStartTime=StartTime, & current_timestr=timestr, time_step=dtint ) ! Set some booleans for use later ! Following uses an overloaded .lt. is_after_history_dump = ( Currtime .lt. hist_time + dtint ) ! Following uses an overloaded .ge. is_output_timestep = (Currtime .ge. hist_time + histint - dtint .or. & Currtime .ge. aux2_time + aux2int - dtint ) write ( message, * ) 'is output timestep? ', is_output_timestep CALL wrf_debug( 100 , message ) ! Following uses an overloaded .eq. is_first_timestep = ( Currtime .eq. StartTime + dtint ) ! 3-D arrays for moisture variables DO i=ims, ime DO k=kms, kme DO j=jms, jme qv(i,k,j) = moist(i,k,j,P_QV) qr(i,k,j) = moist(i,k,j,P_QR) qs(i,k,j) = moist(i,k,j,P_QS) qg(i,k,j) = moist(i,k,j,P_QG) qc(i,k,j) = moist(i,k,j,P_QC) qi(i,k,j) = moist(i,k,j,P_QI) ENDDO ENDDO ENDDO ! Total pressure DO i=ims, ime DO k=kms, kme DO j=jms, jme ptot(i,k,j)=grid%pb(i,k,j)+grid%p(i,k,j) ENDDO ENDDO ENDDO ! After each history dump, reset max/min value arrays IF ( is_after_history_dump ) THEN DO j = jms, jme DO i = ims, ime grid%hailcast_dhail1(i,j) = 0. grid%hailcast_dhail2(i,j) = 0. grid%hailcast_dhail3(i,j) = 0. grid%hailcast_dhail4(i,j) = 0. grid%hailcast_dhail5(i,j) = 0. ENDDO ENDDO ENDIF ! is_after_history_dump ! We need to do some neighboring gridpoint comparisons for the updraft ! duration calculations; set i,j start and end values so we don't go off ! the edges of the domain. Updraft duration on domain edges will always be 0. i_start = its i_end = ite j_start = jts j_end = jte IF ( config_flags%open_xs .OR. config_flags%specified .OR. & config_flags%nested) i_start = MAX( ids+1, its ) IF ( config_flags%open_xe .OR. config_flags%specified .OR. & config_flags%nested) i_end = MIN( ide-1, ite ) IF ( config_flags%open_ys .OR. config_flags%specified .OR. & config_flags%nested) j_start = MAX( jds+1, jts ) IF ( config_flags%open_ye .OR. config_flags%specified .OR. & config_flags%nested) j_end = MIN( jde-1, jte ) IF ( config_flags%periodic_x ) i_start = its IF ( config_flags%periodic_x ) i_end = ite ! Make a copy of the updraft duration, mask variables wdur_prev(:,:) = grid%hailcast_wdur(:,:) wup_mask_prev(:,:) = grid%hailcast_wup_mask(:,:) ! Determine updraft mask (where updraft greater than some threshold) DO j = jts, jte DO i = its, ite grid%hailcast_wup_mask(i,j) = 0 grid%hailcast_wdur(i,j) = 0 DO k = k_start, k_end IF ( grid%w_2(i,k,j) .ge. 10. ) THEN grid%hailcast_wup_mask(i,j) = 1 ENDIF ENDDO ENDDO ENDDO ! Determine updraft duration; make sure not to call point outside the domain DO j = j_start, j_end DO i = i_start, i_end ! Determine updraft duration using updraft masks IF ( (grid%hailcast_wup_mask(i,j).eq.1) .OR. & (MAXVAL(wup_mask_prev(i-1:i+1,j-1:j+1)).eq.1) ) THEN grid%hailcast_wdur(i,j) = & MAXVAL(wdur_prev(i-1:i+1,j-1:j+1)) + grid%dt ENDIF ENDDO ENDDO ! Hail diameter in millimeters (HAILCAST) nz = k_end - k_start DO j = jts, jte DO i = its, ite ! Only call hailstone driver if updraft has been ! around longer than 15 min IF (grid%hailcast_wdur(i,j) .gt. 900) THEN CALL hailstone_driver ( grid%t_phy(i,kms:kme,j), & grid%z(i,kms:kme,j), & grid%ht(i, j), & ptot(i,kms:kme,j), & rho(i,kms:kme,j), & qv(i,kms:kme,j), & qi(i,kms:kme,j), & qc(i,kms:kme,j), & qr(i,kms:kme,j), & qs(i,kms:kme,j), & qg(i,kms:kme,j), & grid%w_2(i,kms:kme,j), & grid%hailcast_wdur(i,j), & nz, & dhail1, dhail2, & dhail3, dhail4, & dhail5 ) IF (dhail1 .gt. grid%hailcast_dhail1(i,j)) THEN grid%hailcast_dhail1(i,j) = dhail1 ENDIF IF (dhail2 .gt. grid%hailcast_dhail2(i,j)) THEN grid%hailcast_dhail2(i,j) = dhail2 ENDIF IF (dhail3 .gt. grid%hailcast_dhail3(i,j)) THEN grid%hailcast_dhail3(i,j) = dhail3 ENDIF IF (dhail4 .gt. grid%hailcast_dhail4(i,j)) THEN grid%hailcast_dhail4(i,j) = dhail4 ENDIF IF (dhail5 .gt. grid%hailcast_dhail5(i,j)) THEN grid%hailcast_dhail5(i,j) = dhail5 ENDIF ENDIF ENDDO ENDDO ! Calculate the mean and standard deviation of the hail diameter ! distribution over different embryo sizes DO j = jms, jme DO i = ims, ime !mean grid%hailcast_diam_mean(i,j)=(grid%hailcast_dhail1(i,j)+& grid%hailcast_dhail2(i,j) +grid%hailcast_dhail3(i,j)+& grid%hailcast_dhail4(i,j) +grid%hailcast_dhail5(i,j))/5. !sample standard deviation grid%hailcast_diam_std(i,j) = SQRT( ( & (grid%hailcast_dhail1(i,j)-grid%hailcast_diam_mean(i,j))**2.+& (grid%hailcast_dhail2(i,j)-grid%hailcast_diam_mean(i,j))**2.+& (grid%hailcast_dhail3(i,j)-grid%hailcast_diam_mean(i,j))**2.+& (grid%hailcast_dhail4(i,j)-grid%hailcast_diam_mean(i,j))**2.+& (grid%hailcast_dhail5(i,j)-grid%hailcast_diam_mean(i,j))**2.)& / 4.0) ENDDO ENDDO END SUBROUTINE hailcast_diagnostic_driver !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! Hailstone driver, adapted from hailstone subroutine in HAILCAST ! Inputs: ! 1-d (nz) ! TCA temperature (K) ! h1d height above sea level (m) ! PA total pressure (Pa) ! rho1d density (kg/m3) ! RA vapor mixing ratio (kg/kg) ! qi1d cloud ice mixing ratio (kg/kg) ! qc1d cloud water mixing ratio (kg/kg) ! qr1d rain water mixing ratio (kg/kg) ! qg1d graupel mixing ratio (kg/kg) ! qs1d snow mixing ratio (kg/kg) ! VUU updraft speed at each level (m/s) ! Float ! ht terrain height (m) ! wdur duration of any updraft > 10 m/s within 1 surrounding ! gridpoint ! Integer ! nz number of vertical levels ! ! Output: ! dhail hail diameter in mm ! 1st-5th rank-ordered hail diameters returned ! ! 13 Aug 2013 .................................Becky Adams-Selin AER ! adapted from hailstone subroutine in SPC's HAILCAST ! 18 Mar 2014 .................................Becky Adams-Selin AER ! added variable rime layer density, per Ziegler et al. (1983) ! 4 Jun 2014 ..................................Becky Adams-Selin AER ! removed initial embryo size dependency on microphysic scheme ! 5 Jun 2014 ..................................Becky Adams-Selin AER ! used smaller initial embryo sizes ! 25 Jun 2015..................................Becky Adams-Selin AER ! Significant revamping. Fixed units bug in HEATBUD that caused ! hailstone temperature instabilities. Similar issue fixed in BREAKUP ! subroutine. Removed graupel from ice content. Changed initial ! embryo size and location to better match literature. Added ! enhanced melting when hailstone collides with liquid water ! in regions above freezing. Final diameter returned is ice diameter ! only. Added hailstone temperature averaging over previous timesteps ! to decrease initial temperature instability at small embyro diameters. ! 3 Sep 2015...................................Becky Adams-Selin AER ! Insert embryos at -13C; interpret pressure and other variables to ! that exact temperature level. ! 16 Nov 2015...................................Becky Adams-Selin AER ! Hailstone travels horizontally through updraft instead of being ! locked in the center. ! ! See Adams-Selin and Ziegler 2016, MWR for further documentation. ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! SUBROUTINE hailstone_driver ( TCA, h1d, ht, PA, rho1d,& RA, qi1d,qc1d,qr1d,qs1d,qg1d, & VUU, wdur, & nz,dhail1,dhail2,dhail3,dhail4, & dhail5 ) IMPLICIT NONE INTEGER, INTENT(IN ) :: nz REAL, DIMENSION( nz ), & INTENT(IN ) :: TCA & ! temperature (K) , rho1d & , h1d & , PA & ! pressure (Pa) , RA & ! vapor mixing ratio (kg/kg) , VUU & ! updraft speed (m/s) , qi1d,qc1d,qr1d & , qs1d,qg1d REAL, INTENT(IN ) :: ht & , wdur !Output: 1st-5th rank-ordered hail diameters returned REAL, INTENT(INOUT) :: dhail1 & ! hail diameter (mm); , dhail2 & , dhail3 & , dhail4 & , dhail5 !Local variables REAL ZBAS, TBAS, WBASP ! height, temp, pressure of cloud base REAL RBAS ! mix ratio of cloud base REAL cwitot ! total cloud water, ice mix ratio INTEGER KBAS ! k of cloud base REAL tk_embryo ! temperature at which initial embryo is inserted REAL ZFZL, TFZL, WFZLP ! height, temp, pressure of embryo start point REAL RFZL ! mix ratio of embryo start point REAL VUFZL, DENSAFZL ! updraft speed, density of embryo start point INTEGER KFZL ! k of embryo start point INTEGER nofroze ! keeps track if hailstone has ever been frozen INTEGER CLOUDON ! use to zero out cloud water, ice once past updraft duration REAL RTIME ! real updraft duration (sec) REAL TAU, TAU_1, TAU_2 ! upper time limit of simulation (sec) REAL delTAU ! difference between TAU_2 and TAU_1 (sec) REAL g ! gravity (m/s) REAL r_d ! constant !hailstone parameters REAL*8 DD, D, D_ICE ! hail diameter (m) REAL VT ! terminal velocity (m/s) REAL V ! actual stone velocity (m/s) REAL TS ! hailstone temperature (K) !HAILSTONE temperature differencing REAL TSm1, TSm2 ! hailstone temperature at previous 3 timesteps REAL FW ! fraction of stone that is liquid REAL WATER ! mass of stone that is liquid REAL CRIT ! critical water mass allowed on stone surface REAL DENSE ! hailstone density (kg/m3) INTEGER ITYPE ! wet (2) or dry (1) growth regime !1-d column arrays of updraft parameters REAL, DIMENSION( nz ) :: & RIA, & ! frozen content mix ratio (kg/kg) RWA, & ! liquid content mix ratio (kg/kg) VUU_pert ! perturbed updraft profile (m/s) !in-cloud updraft parameters at location of hailstone REAL P ! in-cloud pressure (Pa) REAL RS ! in-cloud saturation mixing ratio REAL RI, RW ! ice, liquid water mix. ratio (kg/kg) REAL XI, XW ! ice, liquid water content (kg/m3 air) REAL PC ! in-cloud fraction of frozen water REAL TC ! in-cloud temperature (K) REAL VU ! in-cloud updraft speed (m/s) REAL VUMAX ! in-cloud updraft speed read from WRF (max allowed) REAL VUCORE ! perturbed in-cloud updraft speed REAL DENSA ! in-cloud updraft density (kg/m3) REAL Z ! height of hailstone (m) REAL DELRW ! diff in sat vap. dens. between hail and air (kg/m3) !variables to determine graupel size distribution REAL, DIMENSION(600) :: gd !graupel diameter REAL, DIMENSION(600) :: ng_d !number of graupel particles of that diameter REAL, DIMENSION(600) :: sum_ng_d !cumulative summation of # graupel particles of diam. D or less REAL lambdag !slope of the graupel size distribution REAL n0g !graupel distribution intercept REAL deng !graupel density REAL xslw1,ygra1,zans1 !Thompson graupel size dist parameters REAL pile !desired percentile REAL d02,d05,d10,d15,d20 !2,5,10,15,20th %ile graupel dsd diameters REAL n02,n05,n10,n15,n20 !#rank of each of the %iles REAL, DIMENSION(5) :: dhails !hail diameters with the 1st-15th %ile of graupel dsd !used as initial hail embryo size !mean sub-cloud layer variables REAL TLAYER,RLAYER,PLAYER ! mean sub-cloud temp, mix ratio, pres REAL TSUM,RSUM,PSUM ! sub-cloud layer T, R, P sums REAL LDEPTH ! layer depth !internal function variables REAL GM,GM1,GMW,GMI,DGM,DGMW,DGMI,DGMV,DI,ANU,RE,AE REAL dum REAL sec, secdel ! time step, increment in seconds INTEGER i, j, k, IFOUT, ind(1) CHARACTER*256 :: message !secdel = 0.05 secdel = 5.0 g=9.81 r_d = 287. ! Upper limit of simulation in seconds TAU = 7200. !simulation ends !Set initial updraft strength - reduce to simulate the embryo hovering ! around the edges of the updraft, as in Heymsfield and Musil (1982) DO i=1,nz VUU_pert(i) = VUU(i) * 1. ENDDO ! Initialize diameters to 0. DO i=1,5 dhails(i) = 0. ENDDO ! Cap updraft lifetime at 2000 sec. IF (wdur .GT. 2000) THEN RTIME = 2000. ELSE RTIME = wdur ENDIF !Sum frozen and liquid condensate. !Also find the cloud base for end-of-algorithm purposes. KBAS=nz !KFZL=nz DO k=1,nz cwitot = qi1d(k) + qc1d(k) !No longer include graupel in in-cloud ice amounts !RIA(k) = qi1d(k) + qs1d(k) + qg1d(k) RIA(k) = qi1d(k) + qs1d(k) !RWA(k) = qc1d(k) + qr1d(k) RWA(k) = qc1d(k) !IF ((RIA(k) .ge. 0.0001) .and. (TCA(k).lt.260.155) .and. & ! (k .lt. KFZL)) THEN ! KFZL = k !ENDIF IF ((cwitot .ge. 1.E-12) .and. (k .lt. KBAS)) THEN KBAS = k ENDIF ENDDO !QC - our embryo can't start below the cloud base. !IF (KFZL .lt. KBAS) THEN ! KFZL = KBAS !ENDIF !Pull heights, etc. of these levels out of 1-d arrays. !ZFZL = h1d(KFZL) !TFZL = TCA(KFZL) !WFZLP = PA(KFZL) !RFZL = RA(KFZL) ZBAS = h1d(KBAS) TBAS = TCA(KBAS) WBASP = PA(KBAS) RBAS = RA(KBAS) !Insert initial embryo at -13C tk_embryo = 260.155 TFZL = tk_embryo CALL INTERPP(PA, WFZLP, TCA, tk_embryo, IFOUT, nz) CALL INTERP(h1d, ZFZL, WFZLP, IFOUT, PA, nz) CALL INTERP(RA, RFZL, WFZLP, IFOUT, PA, nz) CALL INTERP(VUU_pert, VUFZL, WFZLP, IFOUT, PA, nz) CALL INTERP(rho1d, DENSAFZL, WFZLP, IFOUT, PA, nz) !!!!!!!!!!!!!!!! 0. INITIAL EMBRYO SIZE !!!!!!!!!!!!!!!!!!!!! ! SET CONSTANT RANGE OF INITIAL EMBRYO SIZES ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! See Adams-Selin and Ziegler 2016 MWR for explanation of why ! these sizes were picked. d02 = 9.E-4 d05 = 2.E-3 d10 = 5.E-3 d15 = 7.5E-3 d20 = 1.E-2 !Run each initial embryo size perturbation DO i=1,5 SELECT CASE (i) CASE (1) !Initial hail embryo diameter in m, at cloud base DD = d02 CASE (2) DD = d05 CASE (3) DD = d10 CASE (4) DD = d15 CASE (5) DD = d20 END SELECT !Begin hail simulation time (seconds) sec = 0. !Set initial values for parameters at freezing level P = WFZLP RS = RFZL TC = TFZL VU = VUFZL Z = ZFZL - ht LDEPTH = Z DENSA = DENSAFZL !Set initial hailstone parameters nofroze=1 !Set test for embryo: 0 for never been frozen; 1 frozen TS = TC TSm1 = TS TSm2 = TS D = DD !hailstone diameter in m FW = 0.0 DENSE = 500. !kg/m3 ITYPE=1. !Assume starts in dry growth. CLOUDON=1 !we'll eventually turn cloud "off" once updraft past time limit !Start time loop. DO WHILE (sec .lt. TAU) sec = sec + secdel !!!!!!!!!!!!!!!!!! 1. CALCULATE PARAMETERS !!!!!!!!!!!!!!!!! ! CALCULATE UPDRAFT PROPERTIES ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !Intepolate vertical velocity to our new pressure level CALL INTERP(VUU_pert,VUMAX,P,IFOUT,PA,nz) !print *, 'INTERP VU: ', VU, P !Outside pressure levels? If so, exit loop IF (IFOUT.EQ.1) GOTO 100 !Sine wave multiplier on updraft strength IF (SEC .GT. 0.0 .AND. SEC .LT. RTIME) THEN VUCORE = VUMAX * SIN( (3.14159 * SEC)/(RTIME) ) VU = VUCORE ELSEIF (SEC .GE. RTIME) THEN VU = 0.0 CLOUDON = 0 ENDIF !Calculate terminal velocity of the hailstone ! (use previous values) CALL TERMINL(DENSA,DENSE,D,VT,TC) !Actual velocity of hailstone (upwards positive) V = VU - VT !Use hydrostatic eq'n to calc height of next level P = P - DENSA*g*V*secdel Z = Z + V*secdel !Interpolate cloud temp, qvapor at new p-level CALL INTERP(TCA,TC,P,IFOUT,PA,nz) CALL INTERP(RA,RS,P,IFOUT,PA,nz) !New density of in-cloud air DENSA=P/(r_d*(1.+0.609*RS/(1.+RS))*TC) !Interpolate liquid, frozen water mix ratio at new level CALL INTERP(RIA,RI,P,IFOUT,PA,nz) CALL INTERP(RWA,RW,P,IFOUT,PA,nz) XI = RI * DENSA * CLOUDON XW = RW * DENSA * CLOUDON IF( (XW+XI).GT.0) THEN PC = XI / (XW+XI) ELSE PC = 1. ENDIF !!!!!!!!!!!!!!!!!! 2. TEST FOR WET/DRY GROWTH !!!!!!!!!!!!!!! ! WET GROWTH - STONE'S SFC >0; DRY GROWTH SFC < 0 ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !MOVED TEST INSIDE HEATBUD - JUST ASSIGN AFTER TS/FW CALC ! DENSITY OF HAILSTONE - DEPENDS ON FW ! ONLY WATER=1 GM/L=1000KG/M3; ONLY ICE =0.9 GM/L !DENSE=(FW*0.1+0.9) * 1000. !KG/M3 !RAS-density calc inside MASSAGR ! SATURATION VAPOUR DENSITY DIFFERENCE BETWTEEN STONE AND CLOUD CALL VAPORCLOSE(DELRW,PC,TS,TC,ITYPE) !!!!!!!!!!!!!!!!!! 3. STONE'S MASS GROWTH !!!!!!!!!!!!!!!!!!!! CALL MASSAGR(D,GM,GM1,GMW,GMI,DGM,DGMW,DGMI,DGMV,DI,ANU,RE,AE,& TC,TS,P,DENSE,DENSA,FW,VT,XW,XI,secdel,ITYPE,DELRW) !!!!!!!!!!!!!!!!!! 4. HEAT BUDGET OF HAILSTONE !!!!!!!!!!!!!!! CALL HEATBUD(TS,TSm1,TSm2,FW,TC,VT,DELRW,D,DENSA,GM1,GM,DGM,DGMW, & DGMV,DGMI,GMW,GMI,DI,ANU,RE,AE,secdel,ITYPE,P) !!!!! 5. TEST DIAMETER OF STONE AND HEIGHT ABOVE GROUND !!!!!!! ! TEST IF DIAMETER OF STONE IS GREATER THAN 9 MM LIMIT, IF SO ! BREAK UP !IF(D.GT.0.009) THEN ! CALL BREAKUP(DENSE,D,GM,FW) !ENDIF WATER=FW*GM !KG ! CRTICAL MASS CAPABLE OF BEING "SUPPORTED" ON THE STONE'S SURFACE CRIT = 1.0E-10 IF (WATER.GT.CRIT)THEN CALL BREAKUP(DENSE,D,GM,FW) ENDIF ! Has stone reached below cloud base? !IF (Z .LE. 0) GOTO 200 IF (Z .LE. ZBAS) GOTO 200 !calculate ice-only diameter size D_ICE = ( (6*GM*(1.-FW)) / (3.141592654*DENSE) )**0.33333333 !Has the stone entirely melted and it's below the freezing level? IF ((D_ICE .LT. 1.E-8) .AND. (TC.GT.273.155)) GOTO 300 !move values to previous timestep value TSm1 = TS TSm2 = TSm1 ENDDO !end cloud lifetime loop 100 CONTINUE !outside pressure levels in model 200 CONTINUE !stone reached surface 300 CONTINUE !stone has entirely melted and is below freezing level !!!!!!!!!!!!!!!!!! 6. MELT STONE BELOW CLOUD !!!!!!!!!!!!!!!!!!!! !Did the stone shoot out the top of the storm? !Then let's assume it's lost in the murky "outside storm" world. IF (P.lt.PA(nz)) THEN D=0.0 !Is the stone entirely water? Then set D=0 and exit. ELSE IF(ABS(FW - 1.0).LT.0.001) THEN D=0.0 ELSE IF (Z.GT.0) THEN !If still frozen, then use melt routine to melt below cloud ! based on mean below-cloud conditions. !Calculate mean sub-cloud layer conditions TSUM = 0. RSUM = 0. PSUM = 0. DO k=1,KBAS TSUM = TSUM + TCA(k) PSUM = PSUM + PA(k) RSUM = RSUM + RA(k) ENDDO TLAYER = TSUM / KBAS PLAYER = PSUM / KBAS RLAYER = RSUM / KBAS !MELT is expecting a hailstone of only ice. At the surface !we're only interested in the actual ice diameter of the hailstone, !so let's shed any excess water now. D_ICE = ( (6*GM*(1.-FW)) / (3.141592654*DENSE) )**0.33333333 D = D_ICE CALL MELT(D,TLAYER,PLAYER,RLAYER,LDEPTH,VT) ENDIF !end check for melting call !assign hail size in mm for output dhails(i) = D * 1000 ENDDO !end embryo size loop !! Size-sort hail diameters for function output !! DO j=1,4 DO k=j+1,5 IF (dhails(j).lt.dhails(k)) THEN dum = dhails(j) dhails(j) = dhails(k) dhails(k) = dum ENDIF ENDDO ENDDO dhail1 = dhails(1) dhail2 = dhails(2) dhail3 = dhails(3) dhail4 = dhails(4) dhail5 = dhails(5) END SUBROUTINE hailstone_driver SUBROUTINE INTERPP(PA,PVAL,TA,TVAL,IFOUT,ITEL) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! INTERP: to linearly interpolate value of pval at temperature tval ! between two levels of pressure array pa and temperatures ta ! ! INPUT: PA 1D array of pressure, to be interpolated ! TA 1D array of temperature ! TVAL temperature value at which we want to calculate pressure ! IFOUT set to 0 if TVAL outside range of TA ! ITEL number of vertical levels ! OUTPUT: PVAL interpolated pressure variable at temperature tval ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IMPLICIT NONE REAL PVAL, TVAL REAL, DIMENSION( ITEL) :: TA, PA INTEGER ITEL, IFOUT !local variables INTEGER I REAL FRACT IFOUT=1 DO I=1,ITEL-1 IF ( (TVAL .LT. TA(I) .AND. TVAL .GE. TA(I+1)) .or. & ! dT/dz < 0 (TVAL .GT. TA(I) .AND. TVAL .LE. TA(I+1)) ) THEN ! dT/dz > 0 FRACT = (TA(I) - TVAL) / (TA(I) - TA(I+1)) !.... compute the pressure value pval at temperature tval PVAL = ((1.0 - FRACT) * PA(I)) + (FRACT * PA(I+1)) !End loop IFOUT=0 EXIT ENDIF ENDDO END SUBROUTINE INTERPP SUBROUTINE INTERP(AA,A,P,IFOUT,PA,ITEL) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! INTERP: to linearly interpolate values of A at level P ! between two levels of AA (at levels PA) ! ! INPUT: AA 1D array of variable ! PA 1D array of pressure ! P new pressure level we want to calculate A at ! IFOUT set to 0 if P outside range of PA ! ITEL number of vertical levels ! OUTPUT: A variable at pressure level P ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IMPLICIT NONE REAL A, P REAL, DIMENSION( ITEL) :: AA, PA INTEGER ITEL, IFOUT !local variables INTEGER I REAL PDIFF, VDIFF, RDIFF, VERH, ADIFF IFOUT=1 DO I=1,ITEL-1 IF (P.LE.PA(I) .AND. P.GT.PA(I+1)) THEN !Calculate ratio between vdiff and pdiff PDIFF = PA(I)-PA(I+1) VDIFF = PA(I)-P VERH = VDIFF/PDIFF !Calculate the difference between the 2 A values RDIFF = AA(I+1) - AA(I) !Calculate new value A = AA(I) + RDIFF*VERH !End loop IFOUT=0 EXIT ENDIF ENDDO END SUBROUTINE INTERP SUBROUTINE TERMINL(DENSA,DENSE,D,VT,TC) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! INTERP: Calculate terminal velocity of the hailstone ! ! INPUT: DENSA density of updraft air (kg/m3) ! DENSE density of hailstone ! D diameter of hailstone (m) ! TC updraft temperature (K) ! OUTPUT:VT hailstone terminal velocity (m/s) ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IMPLICIT NONE REAL*8 D REAL DENSA, DENSE, TC, VT REAL GMASS, GX, RE, W, Y REAL, PARAMETER :: PI = 3.141592654, G = 9.78956 REAL ANU !Mass of stone in kg GMASS = (DENSE * PI * (D**3.)) / 6. !Dynamic viscosity ANU = (0.00001718)*(273.155+120.)/(TC+120.)*(TC/273.155)**(1.5) !CALC THE BEST NUMBER, X AND REYNOLDS NUMBER, RE GX=(8.0*GMASS*G*DENSA)/(PI*(ANU*ANU)) RE=(GX/0.6)**0.5 !SELECT APPROPRIATE EQUATIONS FOR TERMINAL VELOCITY DEPENDING ON !THE BEST NUMBER IF (GX.LT.550) THEN W=LOG10(GX) Y= -1.7095 + 1.33438*W - 0.11591*(W**2.0) RE=10**Y VT=ANU*RE/(D*DENSA) ELSE IF (GX.GE.550.AND.GX.LT.1800) THEN W=LOG10(GX) Y= -1.81391 + 1.34671*W - 0.12427*(W**2.0) + 0.0063*(W**3.0) RE=10**Y VT=ANU*RE/(D*DENSA) ELSE IF (GX.GE.1800.AND.GX.LT.3.45E08) THEN RE=0.4487*(GX**0.5536) VT=ANU*RE/(D*DENSA) ELSE RE=(GX/0.6)**0.5 VT=ANU*RE/(D*DENSA) ENDIF END SUBROUTINE TERMINL SUBROUTINE VAPORCLOSE(DELRW,PC,TS,TC,ITYPE) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! VAPORCLOSE: CALC THE DIFFERENCE IN SATURATION VAPOUR DENSITY ! BETWEEN THAT OVER THE HAILSTONE'S SURFACE AND THE IN-CLOUD ! AIR, DEPENDS ON THE WATER/ICE RATIO OF THE UPDRAFT, ! AND IF THE STONE IS IN WET OR DRY GROWTH REGIME ! ! INPUT: PC fraction of updraft water that is frozen ! TS temperature of hailstone (K) ! TC temperature of updraft air (K) ! ITYPE wet (2) or dry (1) growth regime ! OUTPUT: DELRW difference in sat vap. dens. between hail and air ! (kg/m3) ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IMPLICIT NONE REAL DELRW, PC, TS, TC INTEGER ITYPE !local variables REAL RV, ALV, ALS, RATIO DATA RV/461.48/,ALV/2500000./,ALS/2836050./ REAL ESAT, RHOKOR, ESATW, RHOOMGW, ESATI, RHOOMGI, RHOOMG ! FOR HAILSTONE: FIRST TEST IF STONE IS IN WET OR DRY GROWTH RATIO = 1./273.155 IF(ITYPE.EQ.2) THEN !!WET GROWTH ESAT=611.*EXP(ALV/RV*(RATIO-1./TS)) ELSE !!DRY GROWTH ESAT=611.*EXP(ALS/RV*(RATIO-1./TS)) ENDIF RHOKOR=ESAT/(RV*TS) ! NOW FOR THE AMBIENT/IN-CLOUD CONDITIONS ESATW=611.*EXP(ALV/RV*(RATIO-1./TC)) RHOOMGW=ESATW/(RV*TC) ESATI=611.*EXP(ALS/RV*(RATIO-1./TC)) RHOOMGI=ESATI/(RV*TC) !RHOOMG=PC*(RHOOMGI-RHOOMGW)+RHOOMGW RHOOMG = RHOOMGI !done as in hailtraj.f ! CALC THE DIFFERENCE(KG/M3): <0 FOR CONDENSATION, ! >0 FOR EVAPORATION DELRW=(RHOKOR-RHOOMG) END SUBROUTINE VAPORCLOSE SUBROUTINE MASSAGR(D,GM,GM1,GMW,GMI,DGM,DGMW,DGMI,DGMV,DI,ANU,RE,AE,& TC,TS,P,DENSE,DENSA,FW,VT,XW,XI,SEKDEL,ITYPE,DELRW) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! CALC THE STONE'S INCREASE IN MASS !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IMPLICIT NONE REAL*8 D REAL GM,GM1,GMW,GMI,DGM,DGMW,DGMI,DI,ANU,RE,AE, & TC,TS,P,DENSE,DENSA,FW,VT,XW,XI,SEKDEL,DELRW INTEGER ITYPE !local variables REAL PI, D0, GMW2, GMI2, EW, EI,DGMV REAL DENSEL, DENSELI, DENSELW REAL DC !MEAN CLOUD DROPLET DIAMETER (MICRONS, 1E-6M) REAL VOLL, VOLT !VOLUME OF NEW LAYER, TOTAL (M3) REAL VOL1, DGMW_NOSOAK, SOAK, SOAKM REAL DENSAC, E PI=3.141592654 ! CALCULATE THE DIFFUSIVITY DI (m2/s) D0=0.226*1.E-4 ! change to m2/s, not cm2/s DI=D0*(TC/273.155)**1.81*(100000./P) ! COLLECTION EFFICIENCY FOR WATER AND ICE !EW=1.0 ! IF TS WARMER THAN -5C THEN ACCRETE ALL THE ICE (EI=1.0) ! OTHERWISE EI=0.21 !IF(TS.GE.268.15)THEN ! EI=1.00 !ELSE ! EI=0.21 !ENDIF ! COLLECTION EFFICIENCY FOR WATER AND ICE EW=1.0 ! Linear function for ice accretion efficiency IF (TC .GE. 273.155) THEN EI=1.00 ELSE IF (TC.GE.233.155) THEN EI= 1.0 - ( (273.155 - TS) / 40. ) ELSE !cooler than -40C EI = 0.0 ENDIF ! CALCULATE THE VENTILATION COEFFICIENT - NEEDED FOR GROWTH FROM VAPOR !The coefficients in the ventilation coefficient equations have been !experimentally derived, and are expecting cal-C-g units. Do some conversions. DENSAC = DENSA * (1.E3) * (1.E-6) !dynamic viscosity ANU=1.717E-4*(393.0/(TC+120.0))*(TC/273.155)**1.5 ! CALCULATE THE REYNOLDS NUMBER - unitless RE=D*VT*DENSAC/ANU E=(0.60)**(0.333333333)*(RE**0.50) !ventilation coefficient vapor (fv) ! SELECT APPROPRIATE VALUES OF AE ACCORDING TO RE IF(RE.LT.6000.0)THEN AE=0.78+0.308*E ELSEIF(RE.GE.6000.0.AND.RE.LT.20000.0)THEN AE=0.76*E ELSEIF(RE.GE.20000.0) THEN AE=(0.57+9.0E-6*RE)*E ENDIF ! CALC HAILSTONE'S MASS (GM), MASS OF WATER (GMW) AND THE ! MASS OF ICE IN THE STONE (GMI) GM=PI/6.*(D**3.)*DENSE GMW=FW*GM GMI=GM-GMW ! STORE THE MASS GM1=GM ! NEW MASS GROWTH CALCULATIONS WITH VARIABLE RIME ! LAYER DENSITY BASED ON ZIEGLER ET AL. (1983) ! CALCULATE INCREASE IN MASS DUE INTERCEPTED CLD WATER, USE ! ORIGINAL DIAMETER GMW2=GMW+SEKDEL*(PI/4.*D**2.*VT*XW*EW) DGMW=GMW2-GMW GMW=GMW2 ! CALCULATE THE INCREASE IN MASS DUE INTERCEPTED CLOUD ICE GMI2=GMI+SEKDEL*(PI/4.*D**2.*VT*XI*EI) DGMI=GMI2-GMI GMI=GMI2 ! CALCULATE INCREASE IN MASS DUE TO SUBLIMATION/CONDENSATION OF ! WATER VAPOR DGMV = SEKDEL*2*PI*D*AE*DI*DELRW IF (DGMV .LT. 0) DGMV=0 ! CALCULATE THE TOTAL MASS CHANGE DGM=DGMW+DGMI+DGMV ! CALCULATE DENSITY OF NEW LAYER, DEPENDS ON FW AND ITYPE IF (ITYPE.EQ.1) THEN !DRY GROWTH !If hailstone encountered supercooled water, calculate new layer density ! using Macklin form IF ((DGMW.GT.0).OR.(DGMV.GT.0)) THEN !MEAN CLOUD DROPLET RADIUS, ASSUME CLOUD DROPLET CONC OF 3E8 M-3 (300 CM-3) DC = (0.74*XW / (3.14159*1000.*3.E8))**0.33333333 * 1.E6 !MICRONS !RIME LAYER DENSITY, MACKLIN FORM DENSELW = 0.11*(DC*VT / (273.16-TS))**0.76 !G CM-3 DENSELW = DENSELW * 1000. !KG M-3 !BOUND POSSIBLE DENSITIES IF (DENSELW.LT.100) DENSELW=100 IF (DENSELW.GT.900) DENSELW=900 ENDIF IF (DGMI.GT.0) THEN !Ice collection main source of growth, so set new density layer ! to value calculated from Thompson et al. 2008 snow-diameter relation !Mean cloud ice/snow radius, assume concentration of 1E3 M-3 ! Chose 1E3 because median cloud ice concentration in ! look up table in Thompson mp code in WRF DI = (0.74*XI / (3.14159*1000.*1.E3))**0.33333333 !M DENSELI = 0.13 / DI !kg m-3 IF (DENSELI .LT. 100) THEN DENSELI = 100. ENDIF IF (DENSELI .GT. 900) THEN DENSELI = 900. ENDIF ENDIF !All liquid water contributes to growth, none is soaked into center. DGMW_NOSOAK = DGMW !All liquid water contributes to growth, ! none of it is soaked into center. ELSE !WET GROWTH !Collected liquid water can soak into the stone before freezing, ! increasing mass and density but leaving volume constant. !Volume of current drop, before growth VOL1 = GM/DENSE !Difference b/w mass of stone if density is 900 kg/m3, and ! current mass SOAK = 900*VOL1 - GM !Liquid mass available SOAKM = DGMW !Soak up as much liquid as we can, up to a density of 900 kg/m3 IF (SOAKM.GT.SOAK) SOAKM=SOAK GM = GM+SOAKM !Mass of current drop, plus soaking !New density of current drop, including soaking but before growth DENSE = GM/VOL1 !Mass increment of liquid water growth that doesn't ! include the liquid water we just soaked into the stone. DGMW_NOSOAK = DGMW - SOAKM !Whatever growth does occur has high density DENSELW = 900. !KG M-3 DENSELI = 900. ENDIF !VOLUME OF NEW LAYER !VOLL = (DGM) / DENSEL !VOLL = (DGMI+DGMV+DGMW_NOSOAK) / DENSEL !VOLL = (DGMI) / DENSELI + (DGMW_NOSOAK+DGMV) / DENSELW IF (DGMI.LE.0) THEN VOLL = (DGMW_NOSOAK+DGMV) / DENSELW ELSE IF (DGMW.LE.0) THEN VOLL = (DGMI) / DENSELI ELSE VOLL = (DGMI) / DENSELI + (DGMW_NOSOAK+DGMV) / DENSELW ENDIF !NEW TOTAL VOLUME, DENSITY, DIAMETER VOLT = VOLL + GM/DENSE !DENSE = (GM+DGM) / VOLT DENSE = (GM+DGMI+DGMV+DGMW_NOSOAK) / VOLT !D=D+SEKDEL*0.5*VT/DENSE*(XW*EW+XI*EI) GM = GM+DGMI+DGMW_NOSOAK+DGMV D = ( (6*GM) / (PI*DENSE) )**0.33333333 END SUBROUTINE MASSAGR SUBROUTINE HEATBUD(TS,TSm1,TSm2,FW,TC,VT,DELRW,D,DENSA,GM1,GM,DGM,DGMW, & DGMV,DGMI,GMW,GMI,DI,ANU,RE,AE,SEKDEL,ITYPE,P) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! CALCULATE HAILSTONE'S HEAT BUDGET ! See Rasmussen and Heymsfield 1987; JAS ! Original Hailcast's variable units ! TS - Celsius ! FW - unitless, between 0 and 1 ! TC - Celsius ! VT - m/s ! D - m ! DELRW - g/cm3 (per comment) ! DENSA - g/cm3 (per comment) ! GM1, DMG, DGMW, DGMV, DGMI, GMW, GMI - should all be kg ! DI - cm2 / sec ! P - hPa ! Original HAILCAST HEATBUD subroutine uses c-g-s units, so do some conversions !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IMPLICIT NONE REAL*8 D REAL TS,TSm1,TSm2,FW,TC,VT,DELRW,DENSA,GM1,GM,DGM,DGMW,DGMV, & DGMI,GMW,GMI,DI,ANU,RE,AE,SEKDEL,P INTEGER ITYPE REAL RV, RD, G, PI, ALF, ALV, ALS, CI, CW, AK REAL H, AH, TCC, TSC, DELRWC, DENSAC, TDIFF REAL DMLT REAL TSCm1, TSCm2 DATA RV/461.48/,RD/287.04/,G/9.78956/ DATA PI/3.141592654/,ALF/79.7/,ALV/597.3/ DATA ALS/677.0/,CI/0.5/,CW/1./ !Convert values to non-SI units here TSC = TS - 273.155 TSCm1 = TSm1 - 273.155 TSCm2 = TSm2 - 273.155 TCC = TC - 273.155 DELRWC = DELRW * (1.E3) * (1.E-6) DENSAC = DENSA * (1.E3) * (1.E-6) !DI still in cm2/sec ! CALCULATE THE CONSTANTS AK=(5.8+0.0184*TCC)*1.E-5 !thermal conductivity - cal/(cm*sec*K) !dynamic viscosity - calculated in MASSAGR !ANU=1.717E-4*(393.0/(TC+120.0))*(TC/273.155)**1.5 ! CALCULATE THE REYNOLDS NUMBER - unitless !RE=D*VT*DENSAC/ANU - calculated in MASSAGR H=(0.71)**(0.333333333)*(RE**0.50) !ventilation coefficient heat (fh) !E=(0.60)**(0.333333333)*(RE**0.50) !ventilation coefficient vapor (fv) ! SELECT APPROPRIATE VALUES OF AH AND AE ACCORDING TO RE IF(RE.LT.6000.0)THEN AH=0.78+0.308*H !AE=0.78+0.308*E ELSEIF(RE.GE.6000.0.AND.RE.LT.20000.0)THEN AH=0.76*H !AE=0.76*E ELSEIF(RE.GE.20000.0) THEN AH=(0.57+9.0E-6*RE)*H !AE=(0.57+9.0E-6*RE)*E calculated in MASSAGR ENDIF ! FOR DRY GROWTH FW=0, CALCULATE NEW TS, ITIPE=1 ! FOR WET GROWTH TS=0, CALCULATE NEW FW, ITIPE=2 IF(ITYPE.EQ.1) THEN ! DRY GROWTH; CALC NEW TEMP OF THE STONE !Original Hailcast algorithm (no time differencing) !TSC=TSC-TSC*DGM/GM1+SEKDEL/(GM1*CI)* & ! (2.*PI*D*(AH*AK*(TCC-TSC)-AE*ALS*DI*DELRWC)+ & ! DGMW/SEKDEL*(ALF+CW*TCC)+DGMI/SEKDEL*CI*TCC) TSC=0.6*(TSC-TSC*DGM/GM1+SEKDEL/(GM1*CI)* & (2.*PI*D*(AH*AK*(TCC-TSC)-AE*ALS*DI*DELRWC)+ & DGMW/SEKDEL*(ALF+CW*TCC)+DGMI/SEKDEL*CI*TCC)) + & 0.2*TSCm1 + 0.2*TSCm2 TS = TSC+273.155 IF (TS.GE.273.155) THEN TS=273.155 TDIFF = ABS(TS-273.155) ENDIF TDIFF = ABS(TS-273.155) IF (TDIFF.LE.1.E-6) ITYPE=2 !NOW IN WET GROWTH ELSE IF (ITYPE.EQ.2) THEN ! WET GROWTH; CALC NEW FW IF (TCC.LT.0.) THEN !Original Hailcast algorithm FW=FW-FW*DGM/GM1+SEKDEL/(GM1*ALF)* & (2.*PI*D*(AH*AK*TCC-AE*ALV*DI*DELRWC)+ & DGMW/SEKDEL*(ALF+CW*TCC)+DGMI/SEKDEL*CI*TCC) ELSE !Calculate decrease in ice mass due to melting DMLT = (2.*PI*D*AH*AK*TCC + 2.*PI*D*AE*ALV*DI*DELRWC + & DGMW/SEKDEL*CW*TCC) / ALF FW = (FW*GM + DMLT) / GM ENDIF IF(FW.GT.1.)FW=1. IF(FW.LT.0.)FW=0. !IF ALL OUR ACCRETED WATER WAS FROZEN, WE ARE BACK IN DRY GROWTH IF(FW.LE.1.E-6) THEN ITYPE=1 ENDIF ENDIF END SUBROUTINE HEATBUD SUBROUTINE BREAKUP(DENSE,D,GM,FW) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! INVOKE SHEDDING SCHEME !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IMPLICIT NONE REAL*8 D REAL DENSE, GM, FW !local variables REAL WATER, GMI, CRIT, WAT, PI DATA PI/3.141592654/ WATER=FW*GM !KG !GMI=(GM-WATER) !KG ! CALC CRTICAL MASS CAPABLE OF BEING "SUPPORTED" ON THE STONE'S ! SURFACE !CRIT=0.268+0.1389*GMI !CRIT=0.268*1.E-3 + 0.1389*1.E-3*GMI !mass now in kg instead of g CRIT = 1.0E-10 !IF (WATER.GT.CRIT)THEN - test now occurs outside function WAT=WATER-CRIT GM=GM-WAT FW=(CRIT)/GM IF(FW.GT.1.0) FW=1.0 IF(FW.LT.0.0) FW=0.0 ! RECALCULATE DIAMETER AFTER SHEDDING ! Assume density remains the same !DENSE=(FW*(0.1)+0.9) * 1000. D=(6.*GM/(PI*DENSE))**(0.333333333) !ENDIF END SUBROUTINE BREAKUP SUBROUTINE MELT(D,TLAYER,PLAYER,RLAYER,LDEPTH,VT) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! This is a spherical hail melting estimate based on the Goyer ! et al. (1969) eqn (3). The depth of the warm layer, estimated ! terminal velocity, and mean temperature of the warm layer are ! used. DRB. 11/17/2003. ! ! INPUT: TLAYER mean sub-cloud layer temperature (K) ! PLAYER mean sub-cloud layer pressure (Pa) ! RLAYER mean sub-cloud layer mixing ratio (kg/kg) ! VT terminal velocity of stone (m/s) ! OUTPUT: D diameter (m) ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IMPLICIT NONE REAL*8 D REAL TLAYER, PLAYER, RLAYER, LDEPTH, VT REAL eenv, delta, ewet, de, der, wetold, wetbulb, wetbulbk REAL tdclayer, tclayer, eps, b, hplayer REAL*8 a REAL sd, lt, ka, lf, lv, t0, dv, pi, rv, rhoice, & tres, re, delt, esenv, rhosenv, essfc, rhosfc, dsig, & dmdt, mass, massorg, newmass, gamma, r, rho INTEGER wcnt !Convert temp to Celsius, calculate dewpoint in celsius tclayer = TLAYER - 273.155 a = 2.53E11 b = 5.42E3 tdclayer = b / LOG(a*eps / (rlayer*player)) hplayer = player / 100. !Calculate partial vapor pressure eps = 0.622 eenv = (player*rlayer) / (rlayer+eps) eenv = eenv / 100. !convert to mb !Estimate wet bulb temperature (C) gamma = 6.6E-4*player delta = (4098.0*eenv)/((tdclayer+237.7)*(tdclayer+237.7)) wetbulb = ((gamma*tclayer)+(delta*tdclayer))/(gamma+delta) !Iterate to get exact wet bulb wcnt = 0 DO WHILE (wcnt .lt. 11) ewet = 6.108*(exp((17.27*wetbulb)/(237.3 + wetbulb))) de = (0.0006355*hplayer*(tclayer-wetbulb))-(ewet-eenv) der= (ewet*(.0091379024 - (6106.396/(273.155+wetbulb)**2))) & - (0.0006355*hplayer) wetold = wetbulb wetbulb = wetbulb - de/der wcnt = wcnt + 1 IF ((abs(wetbulb-wetold)/wetbulb.gt.0.0001)) THEN EXIT ENDIF ENDDO wetbulbk = wetbulb + 273.155 !convert to K ka = .02 ! thermal conductivity of air lf = 3.34e5 ! latent heat of melting/fusion lv = 2.5e6 ! latent heat of vaporization t0 = 273.155 ! temp of ice/water melting interface dv = 0.25e-4 ! diffusivity of water vapor (m2/s) pi = 3.1415927 rv = 1004. - 287. ! gas constant for water vapor rhoice = 917.0 ! density of ice (kg/m**3) r = D/2. ! radius of stone (m) !Compute residence time in warm layer tres = LDEPTH / VT !Calculate dmdt based on eqn (3) of Goyer et al. (1969) !Reynolds number...from pg 317 of Atmo Physics (Salby 1996) !Just use the density of air at 850 mb...close enough. rho = 85000./(287.*TLAYER) re = rho*r*VT*.01/1.7e-5 !Temperature difference between environment and hailstone surface delt = wetbulb !- 0.0 !assume stone surface is at 0C !wetbulb is in Celsius !Difference in vapor density of air stream and equil vapor !density at the sfc of the hailstone esenv = 610.8*(exp((17.27*wetbulb)/ & (237.3 + wetbulb))) ! es environment in Pa rhosenv = esenv/(rv*wetbulbk) essfc = 610.8*(exp((17.27*(t0-273.155))/ & (237.3 + (t0-273.155)))) ! es environment in Pa rhosfc = essfc/(rv*t0) dsig = rhosenv - rhosfc !Calculate new mass growth dmdt = (-1.7*pi*r*(re**0.5)/lf)*((ka*delt)+((lv-lf)*dv*dsig)) IF (dmdt.gt.0.) dmdt = 0 mass = dmdt*tres !Find the new hailstone diameter massorg = 1.33333333*pi*r*r*r*rhoice newmass = massorg + mass if (newmass.lt.0.0) newmass = 0.0 D = 2.*(0.75*newmass/(pi*rhoice))**0.333333333 END SUBROUTINE MELT END MODULE module_diag_hailcast #endif