PARFIT 2.1 user`s manual - Istituto Nazionale di Geofisica e
Contents
1. N 5 E 4 0 0 25 0 5 0 75 1 Wind speed m s Figure 1 Wind profile generated by PARFIT 3 1 2 Block TURBULENCE e cdmin This parameter defines the minimum value of the atmospheric diffusion coefficient in m s The generated atmospheric diffusion coefficient starts from cdmin and increase by cdstep up to cdmax PARFIT 2 1 USER MANUAL 8 The wind direction is the direction towards the wind blows it starts from East direction 0 and increases counter clockwise eg a wind blowing from South has direction 90 and a wind from East has direction 180 e cdmax This parameter defines the maximum value of the atmospheric diffusion coefficient in m s The generated wind direction values start from cdmin and increase by cdstep up to cdmax If cdmin is equal to cdmax then only one wind direction is generated e cdstep This parameter defines the increase step of the atmospheric diffusion coefficient in m s The generated diffusion coefficient start from cdmin and increase by cdstep up to cdmax The value of cdstep should be equal to the difference cdmax cdmin divided by an integer number The generated sequence of atmospheric diffusion coefficients cd is cd cdmin i x cdstep i 0 ncd 10 where ncd is the number of generated wind directions ncd NINT ce FR cdstep and NINT represents the nearest integer 3 1 3 Block COLUMN e hcolmin This parameter defines the minimum value of the v2. zvent This parameter represents the elevation of the vent above sea level The generated column lies above the vent between zvent and hcol see 12 This parameter is not modified by PARFIT 3 1 5 Block FLAGS modew This parameter selects the x weighting factors w see 1 Flag modew 0 Constant weighting factor w 1 Flag modew 1 Proportional weighting factor w 1 Y3 Flag modew 2 Statistical weighting factor w 1 Yobs iflch This flag selects whether the maxima of the sub deposits generated by each grain size class must lie in the convex hull 0 NO 1 YES ifenl This flags allows the enlargement of the convex hull by the amount specified by parameter belthull 0 NO 1 YES It has effect if iflch 1 belthull This parameter specifies how much enlarge the convex hull in meters It has effect if both iflch 1 and ifenl 1 iflwgt In case some ground sections do not have associated a particle grain size distribution this flag allows the use of the grain size distrubution form the nearest point where it is available 0 NO 1 YES vmodel This flag selects the settling velocity model Flag vmodel 1 Model of Arastoopour et al 1982 Flag vmodel 2 Model of Ganser 1993 Flag vmodel 3 Model of Wilson and Huang 1979 Flag vmodel 4 Model of Dellino et al 2005 ifvofz This flag selects whether the settling velocity is allowed to vary with the altitude Flag ifvofz 0 The settling velocity is evalu
3. 1700 500 0e 6 2500 1 000e 3 2500 2 000e 3 2500 Table 2 Sample of file ground_thickness inp 4525476 4521650 4521538 4516330 4516554 4531112 4526071 4524904 4521504 4522298 4528885 4526648 4526671 4532304 o o o o ooo o o oo ooo 199 652 764 085 115 194 508 317 739 737 186 253 194 066 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Table 3 Sample of file column spectrum inp FS F p p p p p p p p o o 00000000 17 26 49 35 67 35 11 17 79 64 Diameter m Diameter m Diameter m Diameter m Diameter m Diameter m Diameter m Diameter m Diameter m Diameter m HHH HH HH HOH OH OF density density density density density density density density density density NTYPES number of particle types listed below shape wt shape wt shape wt shape wt shape wt shape wt shape wt shape wt shape wt shape wt 15 PARFIT 2 1 USER MANUAL 10 3 900e 6 7 800e 6 15 62e 6 31 25e 6 62 50e 6 125 0e 6 250 0e 6 500 0e 6 1 000e 3 2 000e 3 A02 0614 0712 0379 0242 0512 0702 1254 1462 1978 2146 13 1361 1477 0844 0581 4767 0953 0012 0002 0002 0003 gt 0000000000 Ooo0o00000000 Table 4 Sample of file ground spectra inp 1400 1400 1400 1400 1400 1700 1700 2500 2500 2500
4. A05 A04 413 A11 46497 45590 45747 45901 47821 48044 3 0 4532304 6 0 4525476 0 0 4516554 5 0 4516330 5 0 4526671 3 0 4528885 0 0 0 0 o o ooo o Number of tests 1 FLAG CHI2 TOTMASS O VOL DRE 0 21788E 03 km3 HCOL CSUZ1 CSUZ2 CDIFF P TYPE 9 10 SUM B 0 20 4 1 4 wt 52 56 47 43 99421 56648E 09 000 0 000 000 000 0 Vset at sea level 3 6 7938 7 11 013 100 000 3 WARNING Min chi2 lies on parameters borders BDRY CSUZ1 4 00000000000000 BDRY CSUZ2 1 00000000000000 BDRY COLUMN HEIGHT 20000 0000000000 BDRY DIFF COEFF 4000 00000000000 PT Vset sealev X mass Y mass Distance OUT 1 0 64772E 03 291694979 4 134189328 5 318805492 5 OUT 2 0 25877E 02 73322233 5 36963382 6 79766707 5 OUT 3 0 10324E 01 18684857 3 12637221 6 19958639 5 OUT 4 0 40473E 01 5071057 4 6575958 9 5056476 8 DUT 5 0 14985 1670156 4 5061778 1 1333726 4 DUT 6 0 56111 757398 7 4655391 6 334588 4 DUT 7 1 3913 566784 6 4570524 6 125935 4 DUT 8 3 6853 492991 9 4537669 9 45159 2 IN 9 6 7938 473674 9 4529069 4 24014 0 IN 10 11 013 464440 6 4524958 0 13905 8 18
5. The first record defines the number of particles classes variable ntypes e The following ntypes records refer to each particle class Each record has four fields diameter of the particle metres density of the particle kg m particle shape factor adimensional for spheres 1 quantity of the particles weight A sample of file column spectrum inp is reported in Table 3 3 4 The input file ground spectra inp This file is used if the grain size distribution of the particles is specified in the deposit sections flag ifgsp 1 e The first record defines the number of particles types variable ntypes e The following ntypes records refer to each particle type Each record has three fields diameter of the particle metres density of the particle kg m particle shape factor adimensional for spheres 1 e Number of ground sections where the the particle type distribution is specified variable nsect e number of block equal to nsect follows Each block has the following structure Label of the section corresponding to the same label defined in file ground thickness inp List of ntypes records each containing the mass fraction of the corresponding particle type in the section These are specified in the same order as specified above A sample of file ground spectra inp is reported in Table 4 3 5 The optional input file wind dat The format of this file is the same as that used by HAZMAP e Number of
6. Z layers NZ e A list of NZ records each specifying the height of the Z layer above sea level in metres e A list of NZ records each corresponding to a different Z layer Each record has 6 fields year month day number of Z layer Vx Vy Where Vx and Vy are the components of the wind in the Z layer toward X East and Y North A sample of file winds dat is shown in Table 5 PARFIT 2 1 USER MANUAL 11 4 Output files 4 1 The output file parfit out File parfit out contains the results of PARFIT that is the parameters that minimize the discrepance between the simulated deposit and the field observation minimum x A sample of file parfit out is reported in Table 6 4 2 The output file chi2 out File chi2 out is generated when flag ifchi 1 in the input file parfit inp Thi file contains the complete list of x2 scanned by PARFIT during the search of its minimum This file has a number of records equal to the total combinations of parameters generated by PARFIT Each record has the following 9 fields Suzuki parameter A Suzuki parameter A column height wind intensity wind direction diffusion coefficient beta x number of particles types whose deposit has its baricenter inside the convex hull variable nctypes If flag iflch 0 ignore the convex hull then nctypes ntypes 4 3 The output file parfit wnd File parfit wnd contains the best wind found after minimizing the x It has the same structure of the input file winds
7. models are available for solving the direct problem that is to estimate the ash fall deposit starting from the total erupted mass grain size distribution of the particles wind field atmospheric conditions volcanic column height and shape eg FALL3D HAZMAP TEPHRA etc however few methods are available for solving the inverse problem eg Pyle 1989 Bonadonna et al 1998 PARFIT belongs to the category of the solvers of this inverse problem whose aim is to find the set of input parameters that minimize the difference between the simulated and the real deposits PARFIT was designed for searching the best parameters total mass column height the bulk granulometry the mass distribution inside the column wind profile and atmospheric diffusion coefficient required by the computer code HAZMAP for reconstructing the observed tephra deposits and granulometry spectra However the obtained results can be used also as input to other models PARFIT was applied for the reconstruction of ash fall deposits the Plinian eruption of Vesuvius occurred in A D 472 Bonasia et al 2010 2 Description of PARFIT PARFIT is FORTRAN code able to find the volcanic eruption parameters starting from field data On UNIX Linux machines PARFIT is executed by invoking the command parfit from the shell prompt The code reads the control file parfit inp where the user defines the domain of investigation of the eruption parameters and other computational flag
8. 2004 A numerical reconstruction of fall deposits from Agnano Montespina 4100 BP Plinian eruption in the Campi Flegrei area Tech Rep OV Prot N 4440 10 11 2004 Osservatorio Vesuviano INGV http www earth prints org handle 2122 2068 Pfeiffer T Costa A Macedonio G 2005 A model for the numerical simulation of tephra fall deposits J Volcanol Geotherm Res 140 273 294 Pyle D 1989 The thickness volume and grainsize of tephra fall deposits Bull Volcanol 51 1 15 Smithsonian Institution 1951 Smithsonian meteorological tables 6th edition Washington D C Suzuki T 1983 A theoretical model for dispersion of tephra In Shimozuru D Yokoyama I Eds Arc Volcanism Physics and Tectonics Terra Scientific Publishing Company TERRAPUB Tokyo pp 93 113 Wilson L Huang T 1979 The influence of shape on the atmospheric settling velocity of volcanic ash particles Earth Planet Sci Lett 44 311 324 PARFIT 2 1 USER MANUAL 14 Table 1 Sample of file parfit inp EXAMPLE OF FILE parfit inp Version 2 1 amp WIND rwindfile 1 htropo 11000 wndmin 40 wndmax 45 wndstep 5 dirmin 24 dirmax 26 dirstep 2 amp TURBULENCE cdmin 4000 cdmax 4000 cdstep 500 amp COLUMN hcolmin 20000 hcolmax 20000 hcolstep 500 suzimin suzimax suzistep suz2min suz2max suz2step amp VENT xvent yvent zvent amp
9. Blok FUAGS sro dla falli Se e a a ee Ge A GOR a aa 3 2 The input file ground thickness inp 2 2 020 000 0000 000000000 3 3 The input file column_spectrum inp 2 0 0000000000002 2a 3 4 The input file ground_spectra inp 0 0 2 0 0000000000 0004 3 5 The optional input file wind dat 2 2 0 0 0 0 0000 eee eee eee Output files 4 1 The output fileparfit out bse eG ate RES GN NESE ESS 4 2 The e o0utput file chi2 0ut s iso ae a eA Pee A E ed Bae 4 3 The output file parfit Wwhdi cirios hc pai ale elle babe ee eR E 44 The output file parfitscmp ie eea an be a ele Ee ee RT Men g Compiling and installing PARFIT 5 1 Floating Point precision e 5 2 2Thersuzukismodels a Rea er erates eaten e Dl ok be 4 NOTE List of Figures 1 Wind profile generated by PARFIT e List of Tables Sample of file parf itsinp si 2 bb aw Same ewe ee Ae e ee eG eat 8 Sample of file ground_thickness inp e Sample of file COLUMN Spectrum Imp Sample of file ground_spectra inp 00002 sample of file winds dat 505056444 aa a SARS Re OD CA ai Sample of file parfit OU os go we Beech A E ape Del ae ile en Ree de ea O UD QN A 11 11 dl 11 11 11 12 12 12 PARFIT 2 1 USER MANUAL 4 1 Introduction A common problem in volcanology is the description of the volcanic column and the ash transport mechanisms starting from the deposit generated by the eruption itself Different
10. FA f p p p p p p 9 p o o o oo oo o o ooo NTYPES Diameter m density shape Diameter m density shape Diameter m density shape Diameter m density shape Diameter m density shape Diameter m density shape Diameter m density shape Diameter m density shape Diameter m density shape Diameter m density shape NSECT number of ground sections LABEL Section 1 H HH HH HH HH H OH OF LABEL Section 2 16 PARFIT 2 1 USER MANUAL 40 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 19500 20000 1986 1986 1986 1986 1986 1986 1986 1986 1986 1986 1986 1986 1986 1986 Table 5 Sample of file winds dat 26 records deleted 821 1 1 661 0 740 821 2 3 322 1 479 821 3 4 983 2 219 821 4 6 644 2 958 821 5 8 305 3 698 8 21 6 9 966 4 437 8 21 7 11 627 5 177 8 21 8 13 288 5 916 8 21 9 14 949 6 656 8 21 10 16 610 7 395 8 21 11 18 271 8 135 8 21 12 19 932 8 874 26 records deleted 8 21 39 27 406 12 202 8 21 40 27 406 12 202 17 PARFIT 2 1 USER MANUAL Table 6 Sample of file parfit out Parfit version 2 1 Using wind file winds dat Number of ground sections 14 Using particles spectra from file ground spectra inp Number of Section A Section Section A Check for 02 Sum 1 00010 13 Sum 1 00020 14 Sum 0 99990 sections with spectrum maxima inside convex hull YES List of vertices of the convex hull A14 A01
11. FLAGS modew iflch Ork O AS A o 451737 4519302 0 I PRO Il o ifenl belthull 1000 iflwgt vmodel ifvofz ifchi ifgsp Il RORBRE OPEN WIND BLOCK Read file wind dat 0 NO 1 YES Height of the tropopause m Min wind intensity m s Max wind intensity m s Step of the wind intensity m s Min wind direction degrees Max wind direction degrees Step of wind direction degrees CLOSE WIND BLOCK OPEN TURBULENCE BLOCK Horizontal diffusion coefficient CLOSE TURBULENCE BLOCK OPEN COLUMN BLOCK Min column height Max column height Column height step Suzuki coefficient N 1 A Suzuki coefficient N 2 Lambda CLOSE COLUMN BLOCK VENT BLOCK Coordinates of the vent Elevation of the vent above sea level CLOSE VENT BLOCK FLAGS BLOCK Chi2 weighting mode 0 2 Check if gauss maxima are in convex hull 0 1 Enlarge the convex hull 0 NO 1 YES How much enlarge the convex hull m Use nearest points for spectra Settling velocity model Flag Vsettl is a function of Z Write file chi2 out 0 N0 1 YES Use file column spectrum inp ground spectra inp CLOSE FLAGS BLOCK PARFIT 2 1 USER MANUAL 14 A01 455906 A02 461855 A03 459513 A04 459015 AO5 457470 A06 469247 AO7 465646 AOS 471913 AO9 460309 A10 461577 A11 480443 A12 475851 A13 478215 A14 464973 10 3 900e 6 1400 7 800e 6 1400 15 62e 6 1400 31 25e 6 1400 62 50e 6 1400 125 0e 6 1700 250 0e 6
12. PARFIT 2 1 A tool for the parametrization of volcanic ash deposits G Macedonio A Costa Istituto Nazionale di Geofisica e Vulcanologia Osservatorio Vesuviano Napoli Italy Istituto Nazionale di Geofisica e Vulcanologia INGV Via Donato Creti 12 40128 Bologna Italy February 2014 PARFIT 2 1 USER MANUAL 2 PARFIT code Copyright C 2014 Giovanni Macedonio Antonio Costa This program is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 3 of the License or at your option any later version This program is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PUR POSE See the GNU General Public License for more details You should have received a copy of the GNU General Public License along with this program If not visit http www gnu org licenses PARFIT 2 1 USER MANUAL Contents 1 2 Introduction Description of PARFIT 21 How PARFIT Works du ph ob A ack nE SD a e dede Input files 3 1 The input file parfit inp ta ai pol e Sell Blok WIND 0045 2 Acne e Btu ja ea aa ak el a da ee 3 1 2 Block TURBULENCE cibi ah ths ge aie bee ae ee e had amp Ss 3 1 3 Block COLUMN sua aa oe Sak a His We ER Ae Oe ee Be we RE Sel Bloc VENT o sp puedo ae ee a be a Ake a ae de a DD Silo
13. Sec 3 5 e htropo This parameter is used when flag rwindfile 0 and specifies the height of the tropopause in meters In PARFIT htropo coincides with the height where the wind has its maximum intensity Fig 1 shows the wind profile generated by PARFIT According to Cornell et al 1983 we assume that the wind speed increases from zero at sea level up to its maximum at the height of the tropopause parameter htropo then its value is 75 of its maximum value The wind profile is then multiplied by the the factor wnd and rotated along the vertical axis towards direction dir see 6 and 8 e wndmin This parameter defines the minimum value of the wind intensity at tropopause in m s The generated wind intensity values start from wndmin and increase by wndstep up to wndmax e wndmax This parameter defines the maximum value of the wind intensity at tropopause in m s The generated wind intensity values start from wndmin and increase by wndstep up to wndmax If wndmin is equal to wndmax then only one wind intensity is generated e wndstep This parameter defines the increase step of the wind intensity at tropopause in m s The generated wind intensity values start from wndmin and increase by wndstep up to wndmax The value of wndstep should be equal to the difference wndmax wndmin divided by an integer number the number of steps 1 The generated sequence of wind intensities at tropopause wnd is wnd wndmin wndstep
14. Thus among all the possible choices we focus on a restricted number of grain size classes for which the inverse problem results better constrained In fact in a first step the program identifies the area enclosed by the measured ground sections that is delimited by a convex hull The calculation of the total mass at the ground is performed by summing the contribution of each particle type that leads to a Gaussian centre placed inside the convex hull of the measured ground sections This procedure allows for estimating the total mass relative to these classes only In order to obtain the total mass over a wider range of grain sizes in a second step we repeat the inversions fixing the values of column height wind direction wind speed and diffusion coefficients as they were obtained in the previous step and extend the computation of the bulk particle spectrum to the particles classes previously neglected thus leading to the final estimation of the effective total mass and of the total bulk velocity class distribution The ash load at the ground is given by Mif x aci y Yi M x y gt dro exp 202 2 1 9 1 9 1 3 where o2 is the thickness of the Gaussian relative to the particles that fall from the height z with the settling velocity v It is related to the settling time and the diffusion coefficient by the relation od 2Kti The particles settling velocity varies with the height In ord
15. UAL 6 3 Input files 3 1 The input file parfit inp File parfit inp contains information for performing the search of the eruptions parameters and for controlling the output generated by parfit This file is structured in blocks following the FORTRAN NAMELISTS easily readable from FORTRAN codes These blocks are WIND TURBULENCE COLUMN VENT and FLAGS Each block begins with the directive amp block name and ends with a slash where block name is the name of the block The blocks must be written in the same order as specified before see also Table 1 Each block contains a list of variables with associated their value Comments start with the symbol and are ignored The name of the variables reflect the same name of the variable used in the FORTRAN code sample of this file is reported in Table 1 3 1 1 Block WIND This is the first block of file parfit inp It begins with the directive amp WIND and ends with a slash see also Table 1 In this block data referring to the generated wind profile are specified The user may specify a single wind profile read from a file or specify some parameters used to generate a sequence of wind profiles for best fitting the deposit data e rwindfile This flag selects weather a wind profile is read from file wind dat flag rwindfile 0 or the wind profiles are generated using the other parameters defined below flag rwindfile 0 The structure of file wind dat is specified in
16. ated at sea level and is assumed constant with height Flag ifvofz 1 The settling velocity is allowed to vary with the altitude assuming that the variations of the density and viscosity of the atmosphere follow the International Standard Atmosphere Smithsonian Institution 1951 ifchi This flag specifies whether the list of evaluated is printed in file chi2 out 0 NO 1 YES ifgsp This file selects the method for handling the bulk grain size distribution in the column ifgsp 0 The whole grain size distribution in the column is read from file column spectrum inp PARFIT 2 1 USER MANUAL 10 ifgsp 1 The grain size distribution in the column is estimated from best fitting the grain size distributions in the deposit sections defined in file ground spectra inp 3 2 The input file ground_thickness inp This file defines the deposit sections e The first record defines the number of ground sections specified below variable npts e npts records each corresponding to a different ground section Each record has the following fields label of the section X and Y UTM coordinates of the section thickness of the deposit metres density of the deposit A sample of file ground thickness inp is reported in Table 2 3 3 The input file column spectrum inp This file is used if the bulk grain size distribution of the eruption column is known flag ifgsp 0 This is equivalent to the bulk grain size distribution of the deposit e
17. be adapted to the user 5 1 Floating Point precision PARFIT 2 1 allows the complilation of subroutines and functions either assuming that floating point reals ar single or double precision To switch between these edit file src kindtype f90 and set the integer parameter SP as SINGLE or DOUBLE Then issue the command make 5 2 The Suzuki model PARFIT may be compiled using the standard Suzuki model subroutine suzuki 90 or its integrated ver sion subroutine isuzuki f90 function igamma f90 To switch between the two versions uncomment the corresponding list of linked object s in file src Makefile parameter SUZUKIMODEL 6 NOTE PARFIT 2 1 uses the following public domain routines e To define the properties of the U S Standard Atmosphere 1977 PARFITuses subroutine atmo sphere written by Ralph Carmichael Public Domain Aeronautical Software 2009 freely available at http www pdas com e To define the convex hull of the sampled ground points parfit uses algorithm 523 by W F Eddy ACM TOMS 3 1977 411 412 available at URL http www netlib org TOMS algorithm 523 Here algorithm 523 was translated in F90 and is contained into subroutines convex f90 and split f90 Acknowledgments We thank R Bonasia for testing the code and suggestions that greatly improved the code This work was partially supported by the Italian Department of Civil Protection INGV DPC Agreement 2007 2009 Project V5 SPeeD Referenc
18. dat see Sec 3 5 However the date of the wind is set to day 0 month 0 year 0 If the the input wind file is used flag rwindfile 1 then parfit wnd becomes a duplicate of file winds dat 4 4 The output file parfit cmp 5 Compiling and installing PARFIT PARFIT version 2 1 is written in FORTRAN 90 To install parfit uncompress and unpack the tar file parfit 2 1 tar gz then go to the parfit 2 1 src directory gunzip parfit 2 1 tar gz tar xf parfit 2 1 tar cd parfit 2 4 src Now you should select the FORTRAN compiler edit the Makefile and set the variable FC must to the proper compiler For example FC ifort FCFLAGS In this case the Intel FORTRAN compiler ifort is specified Another choice could be the gfortran compiler FC gfortran FCFLAGS Additional compilation flags can specified by the variable FCFLAGS For example to activate the optimizer of the ifort compiler flag 0 insert FC ifort FCFLAGS 0 Now you are ready to compile parfit just issue the command make PARFIT 2 1 USER MANUAL 12 This generates the binary files parfit By default the executable is installed in the directory src To check the installation change directory to example under the directory parfit 2 1 andrun src parfit The executable binary file parfit may be moved in your preferred PATH Moreover the input files parfit inp ground_thickness inp ground spectra inp and the optional file wind dat can be mod ified to
19. er to take into account the variability of the particles velocity with height it is defined the coefficient 1 1 dz Atij 4 pcg Ub where dzi j is the thickness of the layer k and vz j the settling velocity of the particle of the class j into the layer k The ground load is then given by b i j 3 M0 D EP exp e aco u vol 4 The mass distribution in real eruption columns is governed by complex physical processes that the model cannot account for In order to consider a mushroom like shape for the column it is used an empirical formula modified from the original Suzuki formula Suzuki 1983 z z Sle yz t So 1 explA DI x d t to d a xo y yo where Sy is the normalisation constant o yo are the coordinates of the vent H is the column height and A and are two empirical parameters introduced in Pfeiffer et al 2005 5 The user defines the range and step of the eruption parameters This defines a multidimensional grid generated by all the combinations of the parameters PARFIT performs a search on the grid for the minimum x between the simulated deposit simulated and the field data Simulations are performed using the HAZMAP model embedded in PARFIT is based on HAZMAP a computer program for simulat ing the ground deposit generated by the sedimentation of volcanic particles from an explosive eruption Macedonio et al 2005 Pfeiffer et al 2005 PARFIT 2 1 USER MAN
20. es Arastoopour H Lin S Weil S 1982 Analysis of vertical pneumatic conveying of solids using multi phase flow models AIChE J 28 467 473 Bonadonna C Ernst G Sparks R 1998 Thickness variations and volume estimates of tephra fall deposits the importance of particle Reynolds number J Volcanol Geotherm Res 81 173 187 Bonasia R Macedonio G Costa A Mele D Sulpizio R 2010 Numerical inversion and analysis of tephra fallout deposits from the 472 AD sub Plinian eruption at vesuvius Italy through a new best fit procedure J Volcanol Geotherm Res 189 238 246 Cornell W Carey S Sigurdsson H 1983 Computer simulation and transport of the Campanian Y 5 ash J Volcanol Geotherm Res 17 89 109 Costa A Dell Erba F Di Vito M Isaia R Macedonio G Orsi G Pfeiffer T Apr 2009 Tephra fallout hazard assessment at the campi flegrei caldera italy Bull Volcanol 71 3 259 273 PARFIT 2 1 USER MANUAL 13 Dellino P Mele D Bonasia R Braia L La Volpe R 2005 The analysis of the influence of pumice shape on its terminal velocity Geophys Res Lett 32 L21306 Ganser G 1993 A rational approach to drag prediction of spherical and nonspherical particles Powder Technol 77 143 152 Macedonio G Costa A Longo A 2005 A computer model for volcanic ash fallout and assessment of subsequent hazard Comput Geosci 31 837 845 Pfeiffer T Costa A
21. i 0 nwnd 6 where nwnd is the number of generated wind directions nwnd NINT aan wndstep and NINT represents the nearest integer PARFIT 2 1 USER MANUAL 7 e dirmin This parameter defines the minimum value of the wind direction at tropopause in degrees_east The generated wind direction values start from dirmin and increase by dirstep up to dirmax The wind direction is the direction towards the wind blows it starts from East direction 0 and increases counter clockwise eg a wind blowing from South has direction 90 and a wind from East has direction 180 e dirmax This parameter defines the maximum value of the wind direction at tropopause in degrees_east The generated wind direction values start from dirmin and increase by dirstep up to dirmax If dirmin is equal to dirmax then only one wind direction is generated e dirstep This parameter defines the increase step of the wind direction at tropopause in degrees The generated wind direction values start from dirmin and increase by dirstep up to dirmax The value of dirstep should be equal to the difference dirmax dirmin divided by an integer number the number of steps 1 The generated sequence of wind directions dir is dir dirmin x dirstep i 0 ndir 8 where ndir is the number of generated wind directions ndir NINT dirmax dirstep and NINT represents the nearest integer 20 15 E 104
22. noa i the values predicted by the model The choice of the weighting factors w depends upon the distribution of the errors Costa et al 2009 In order to well constrain the input parameters it is necessary to know thickness and grain size values in a large number N of stratigraphic sections such as N gt gt p For example Pfeiffer and Costa 2004 showed that a good reliable inversion is given by at least 40 50 well distributed stratigraphic sections and at least 3 5 sections with individual granulometry and particle component distributions However especially for ancient eruptions finding enough outcrops with a good exposure is often very arduous There is a risk of finding parameters that result physically incorrect especially when we deal with portions of the deposit which represent the tail of the distribution relative to a particle class In order to avoid these problems in the scientific literature other techniques for the calculation of the particles spectrum in terms of the total grain size distribution were adopted allowing the reduction of the degrees of freedom PARFIT 2 1 USER MANUAL 5 PARFIT 2 0 uses a new procedure which allows for fitting also the bulk grain size distributions even when only few stratigraphic sections are available We assume that the best fitted parameters such as column height column shape coefficients wind velocity and diffusion coefficient do not vary with the choice of the grain size classes
23. olcanic column height in meters The generated column height start from hcolmin and increase by hcolstep up to hcolmax The column height is the height of the top of the column respect to the sea level e hcolmax This parameter defines the maximum value of the volcanic column height in meters The generated column heights start from hcolmin and increase by hcolstep up to hcolmax If hcolmin is equal to hcolmax then only one column height is generated The column height is the height of the top of the column respect to the sea level e hcolstep This parameter defines the increase step of the eruptive column height in meters The generated column heights start from hcolmin and increase by hcolstep up to colmax The value of hcolstep should be equal to the difference hcolmax hcolmin divided by an integer number The generated sequence of volcanic column heights hcol is hcol hcolmin i x hcolstep i 0 nhcol 12 where nhcol is the number of generated column heights 13 hcolmax hcolmin nhcol NINT soe hcolstep and NINT represents the nearest integer 3 1 4 Block VENT e xvent This parameter represents the X coordinate of the vent Usually it is the East UTM coordinate of the vent This parameter is not modified by PARFIT PARFIT 2 1 USER MANUAL 9 yvent This parameter represents the Y coordinate of the vent Usually it is the North UTM coordinate of the vent This parameter is not modified by PARFIT
24. s see Sec 3 1 then it loads the thickness of the ground deposit measured in different stratigraphic sections file ground_thickness inp and performs a search on grid for finding the best parameters that fit the deposit using the model HAZMAP Macedonio et al 2005 Pfeiffer et al 2005 If the bulk grain size distribution ie the grain size distribution in the eruption column is known it may be specified in the optional input file column spectrum inp Alternatively the bulk grain size distribution is estimated by parfit starting from the size distributions at ground defined in file ground_spectra inp Results are printed on the screen and in file parfit out 2 1 How PARFIT works Input parameters required by HAZMAP for reconstructing an ash fallout deposit produced by an explosive volcanic eruption can be obtained solving an inverse problem Fitting is performed using a least squares method which compares measured and calculated deposits thickness and grain sizes Because of the inherent limitation of the model to medium range and distal parts of a deposit only available data at a distance of at least few km from the eruption vent are considered The function to be minimised e g Pfeiffer et al 2005 Costa et al 2009 is N 1 2 5 Wi Yoos i Fi mos 1 i 1 X N p where w are weighting factors N is the number of observed data p is the number of free parameters Yobs i denote the observed ground load kg m and Yi
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