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VORIS
A GIS-based tool for volcanic hazard assessment
USER’S GUIDE
Alicia Felpeto Observatorio Geofísico Central, IGN
VORIS 2.0.1
INDEX 1.- Introduction ................................................................................................... 1 2.- Copying Files ................................................................................................ 2
2.1.- Previous requirements............................................................................ 2 2.2.- Procedure ............................................................................................... 2
3.- Quick Start .................................................................................................... 4 4.- Hazard and Scenario Maps........................................................................... 6
4.1.- ASH FALLOUT ....................................................................................... 6 4.1.1.- Overview of the model ..................................................................... 6 4.1.2.- Operation ......................................................................................... 8 4.1.3.- Notes.............................................................................................. 10
4.1.3.1.- Stored files............................................................................... 10 4.1.3.2.- INI file ...................................................................................... 11
4.2.- LAVA FLOW ......................................................................................... 15 4.2.1.- Overview of the model ................................................................... 15 4.2.2.- Operation ....................................................................................... 16 4.2.3.- Notes.............................................................................................. 18
4.2.3.1.- Numeric values........................................................................ 18 4.2.3.2.- Stored files............................................................................... 18 4.2.3.3.- INI file ...................................................................................... 20
4.3.- ENERGY CONE ................................................................................... 23 4.3.1.- Overview of the model ................................................................... 23 4.3.2.- Operation ....................................................................................... 25 4.3.3.- Notes.............................................................................................. 26
4.3.3.1.- Stored files............................................................................... 26 4.3.3.2.- DAT file.................................................................................... 27
5.- Susceptibility Tools ..................................................................................... 28 5.1.- SUSCEPTIBILITY................................................................................. 28
5.1.1.- Overview of the computational procedure...................................... 28 5.1.2.- Operation........................................................................................... 29
5.1.3.- Notes.............................................................................................. 31 5.1.3.1.- Stored files............................................................................... 31 5.1.3.2.- Rounded values....................................................................... 31
5.2.- PDF CAUCHY/GAUSS......................................................................... 32 5.2.2.- Operation........................................................................................... 32
5.2.3.- Notes.............................................................................................. 34 5.2.3.1.- Stored files............................................................................... 34 5.2.3.2.- Rounded values....................................................................... 34
6.- Notes........................................................................................................... 35 6.1.- Decimal period...................................................................................... 35 6.1.- Formats tested...................................................................................... 35
References ....................................................................................................... 37 CONTACTS...................................................................................................... 38 Version 2.0.1 (February 2009)
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1.- INTRODUCTION VORIS (VOlcanic Risk Information System) is a GIS-based tool for volcanic hazard assessment. Its main objective is to provide the user the tools required for generating volcanic risk scenarios and hazard maps for different volcanic hazards, based on numerical simulations of those hazards. Up to this version, VORIS is able to simulate ash fallout, lava flows and pyroclastic density currents. VORIS 2.0.1 also includes tools for the computation of volcanic susceptibility. The tool has been mainly developed while the author worked at the Institute of Earth Sciences ‘Jaume Almera’, that belongs to the CSIC (Spanish National Council for Scientific Research), and in the framework of the European Projects AEGIS (Ability enlargement for geophysicists and information technology specialists, IST 2000-26450) and EXPLORIS (Explosive eruption risk and decision support for EU populations threatened by volcanoes,EVR1-2001-00047) and the Spanish project MAPASCAN (Elaboración de los mapas de peligros pasados y peligrosidad, y definición de escenarios eruptivos para las Islas Canarias, MEC, CGL2004-23200-E). Current developments are been realized in the Central Geophysical Observatory, belonging to the IGN (Spanish National Geographical Institute) A brief description of the objectives and structure of this tool has been published in the Journal of Volcanology and Geothermal Research (Felpeto et al., 2007).
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2.- COPYING FILES 2.1.- Previous requirements For this application to run, you need Windows XP (SP2) and ESRI© ArcViewTM 9.1 (SP2) with SpatialAnalyst Extension (activated). 2.2.- Procedure a) Copy the document VORIS_2_0_1.mxd anywhere. b) This document requires some extra files to be fully operative. The file structure needed is the following:
The folder ...\modGIS\ash\model should contain the files:
disper4.exe disper4.ini
The folder ...\modGIS\lava\model should contain the files: grapel4.exe grapel4.ini Those files can be extracted from the file VORIS_2_0_1_modGIS.rar. The folder modGIS can be directly copied in c:\ . If you prefer to copy it into another drive or directory, do the following:
Copy it where you want. Localize the folder where your Normal.mxt template is located (typically
in Windows XP in: c:\Documents and Settings\<YourUserName>\Application Data\ESRI\ArcMap\Templates
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or, if your operative system is in Spanish c:\Documents and Settings\<YourUserName>\Datos de programa\ESRI\ArcMap\Templates)
Create a text file named modGIS.txt containing the path where modGIS folder is located (e.g. if you have copied modGIS in the temp folder of your D: drive, the file modGIS.txt should contain: d:\temp )
Note that VORIS_2_0_1.mxd will first try to find modGIS folder directly in c: drive, and, only if it can’t find it, it will look for the modGIS.txt file to see where to find it
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3.- QUICK START
Open Voris_2_0_1.mxd
You will find a toolbar
The left icon is use for interactive vent selection (only for scenario maps)
Add any layer of the desired volcanic area (some tools require specific data, for example, if you want to simulate a lava flow or a pyroclastic density current –pdc-, you will need the topography of the area, therefore, you should add a DEM -Digital Elevation Model-). These data should be georeferenced in a UTM coordinate system, so that the numerical models can appropriately compute distances.
HAZARD AND SCENARIO MAPS
Click on “Volcanic Hazard” menu and then on “Hazard map/Scenario”
Select the hazard you want to simulate clicking on one of the buttons
A new window will appear for selecting the input parameters for the numerical model chosen. Select or enter the parameters required and click the Run button (see section 4 for a description of each model).
After the model computation finishes, the result of the simulation will
appear as a new layer in the current map.
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SUSCEPTIBILITY TOOLS
Click on “Susceptibility” menu.
Select the tool you want to use clicking on one of the buttons
A new window will appear for selecting the input parameters for the
chosen tool. Select or enter the parameters required and click the Run button (see the section 5 for a description of each tool).
After the computation finishes, the result will appear as a new layer in
the current map.
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4.- HAZARD AND SCENARIO MAPS
4.1.- ASH FALLOUT 4.1.1.- Overview of the model The model used for simulating ash fallout is an advection diffusion model that assumes that, far from the vent, the transport of the particles from a Plinian column is controlled by the advective effect of the wind, the diffusion due to atmospheric turbulence and the settling velocity of the particles. The main equation governing this process (Armienti et al., 1988), neglecting both the vertical wind and vertical diffusion is: where Cj is the concentration of particles of class j, (Wx, Wy, Wz) the wind field, vj the fall velocity of particles of class j , Kx , Ky and Ky the eddy diffusion coefficients and Sj is the source function, that represents the entrance of particles of class j into the system. To solve this equation, a few simplifications are adopted: all the mass is emitted at instant t=0, forming a vertical line over the vent, vertical wind and vertical diffusion are neglected, and horizontal diffusion coefficients are considered equal (Kx = Ky = K). From the numerical point of view, the computational domain is divided into N horizontal layers, in which one settling velocity of the particles of class j and horizontal winds are considered to be constant. This allows treating the 3D problem as a 2D one, increasing the computational speed. The granulometric distribution is computed in terms of parameter Φ, used to characterize the size of volcanic particles, defined by d=2- Φ (in millimetres). So, if V is the total volume of particles emitted in the eruption, the volume corresponding to size Φ, VΦ is: where Φm is the mean value of the distribution and σΦ is the standard deviation of the distribution.
jj
xj
xj
xjjj
zj
yj
xj S
zC
KyC
KxC
KzCv
zC
WyC
WxC
Wt
C+
∂∂
+∂∂
+∂∂
=∂
∂−
∂∂
+∂∂
+∂∂
+∂∂
2
2
2
2
2
2
⎟⎟⎠
⎞⎜⎜⎝
⎛ −−= 2
2
2)(exp
2 φφφ σ
φφσπ
mVV
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This material is distributed along a vertical line over the vent according to the approximation proposed by Suzuki (1983): where HT is the maximum height reached by the eruptive column and AΦ is a parameter that locates the maximum concentration of mass at a height HT(1-1/AΦ). This parameter is related to the size of the particles considered: where A is the column shape factor and vΦ0 is the terminal settling velocity of particles of size Φ at sea level. As stated previously, it is considered that all the material is emitted in instant t=0 forming a vertical “filament”, that is divided in N sections located at heights z1, z2 , …, zN. For every class of particles considered (Φ1, Φ2 , …, ΦM), and for every section of the column, the model computes the trajectory of the diffusion centre up to the ground, assuming that it translates horizontally through each layer and settles into the underlying layer till it reaches the ground surface. So, considered the vent located at (0,0), the location of each centre of diffusion the ground for particles of size Φ and the section initially located at height zj is: where ΔtΦi is the residence time of particles of size Φ in layer i: Once the location of the diffusion centre in the ground has been computed, its spreading is calculated for a time equal to the time spent by the considered particles (Φ) initially at section j to reach the ground (tfall Φj): So, assuming that the source function corresponding to each section has a square shape of size Δx, the thickness of the deposit corresponding to particles Φ initially at section j is (assuming perfect package):
) )1(1(
1)(
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φ
φ
φ
φ
φφ AT
HzA
T
eAH
eHzA
VzV
T
−
⎟⎟⎠
⎞⎜⎜⎝
⎛−
+−
⎟⎟⎠
⎞⎜⎜⎝
⎛−
=
0φφ v
AA =
iji
yij
iji
xij
tWy
tWx
φφ
φφ
Δ=
Δ=
∑
∑
=
=
1
0
1
0
i
iii v
zzt
1
φφ
−−=Δ
∑=
Δ=j
iifall tt
1j φφ
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Finally, the total thickness of the expected deposit is computed summing the contributions of every section and every class of particles considered: Terminal settling velocity In the model, the terminal settling velocity for particles falling at high Reynolds number is computed by: where ρp is the density of the particle, r its radius, g the gravity, ρa is the air density and D is the drag parameter, related to the shape of the particles. For low Reynolds numbers, the terminal settling velocity is calculated through Stokes law: where μa is the air viscosity. See Folch and Felpeto (2005) for a detailed description of the model. 4.1.2.- Operation Once the ashfall button is clicked, a small window for selecting the vent location appears. You can type the coordinates of the vent or click the button “Select Vent”. If you click this button, the previous window temporarily disappears to show the original map, where you should click to select the location of the vent.
( ) ( )
( ) ( )⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −+Δ+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −−Δ
⋅⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −+Δ+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −−ΔΔ
=
jfall
j
jfall
j
jfall
j
jfall
jjj
tKyyx
erftK
yyxerf
tKxxx
erftK
xxxerf
xV
yxT
φ
φ
φ
φ
φ
φ
φ
φφφ
0
0
0
02
2 2
2 24
),(
∑∑= =
=N
j
M
j yxTyxT1 1
),(),(φ
φ
Dgr
Va
p
3 8
0 ρρ
=
a
p grV
μρ9
2 2
0 =
9
When you have selected the vent, click on the “Run” button. A new window, corresponding to the numerical model, named DISPER4, will be opened. There you will see that the coordinates of the vent that you have selected appear in the corresponding boxes. The rest of the parameters are those by default, included in the disper4.ini file. You can modify most of the input parameters (except those in grey, which can only be modified editing the disper4.ini file). Refer to 4.3.1 section for a detailed description of the input parameters.
When all the input parameters have been introduced, click on Run button. A progress bar will appear that will show the progress of the computation in terms of the size of the particles already computed (e.g. if you have selected values for Φ between -2 and 2, and a Φ step of 0.5, then 9 classes of particles will be computed, so the progress bar will show 9 steps). Once the window named DISPER4 disappears, after a few seconds, a new layer will appear on your map, representing the thickness of the expected deposit, classified in eleven fixed classes.
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The result of every simulation is stored in ...\modGIS\ash\model\r folder, and named dep1, dep2, … etc. A text file containing the input parameters will be also saved into the same folder, with the corresponding name disper1.dat, disper2.dat, … etc. Note that in this version of VORIS, only scenarios can be computed for ash fallout, not hazard maps. 4.1.3.- Notes 4.1.3.1.- Stored files The result of every simulation is stored in the ...\modGIS\ash\model\r folder: depn.aux the auxiliary file of the GRID format by ESRI, with its
corresponding folder. n takes the first value between 1 and 1000 that is not present in ...\modGIS\ash\model\r folder. It is recommendable to delete these files periodically, as this directory can become really heavy!.
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dispern.dat it is a copy of the INI file used in the simulation that has generated depn, so it includes all the input parameters used.
Some extra files of the result are stored in the ...\modGIS\ash\model\temp folder:
depn.flt result in the format required by ArcToolBox-
ImportFromFloat tool. depn.hdr its corresponding header file. Note that perhaps you
will need to check the decimal period (. or ,) depending on your locale configuration.
depn.rdc documentation file for IDRISI32 GIS. To see the result in such system, you need to rename depn.flt to depn.rst.
depn.grd result for SURFER (Golden Software). It also include those values for thickness of the deposit lower than 1 mm.
4.1.3.2.- INI file The disper4.ini file has the following structure [Eruption] Volume=0.03 Column_Height=7000 X_Vent= 341614 Y_Vent= 3128598 Vent_Height=0 A_Parameter=3 [Particles] Fi_Mean=1 Fi_Standard_Deviation=1.5 Fi_Minimum=-2 Fi_Maximum=2 Fi_Density_Big=800 Fi_Density_Medium=1200 Fi_Density_Small=2300 D_Parameter=3.45 [Steps] Step_Vertical=100 Step_Horizontal=200 X_Cells=300 Y_Cells=300 X_Origin_Area=311614 Y_Origin_Area=3098598 Step_Fi=0.5 [Atmosphere] Difussion=1000 Tropopause=11300 Air_Density=1.2255
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Air_Temperature=288 Wind_Constant=1 [Wind1] Height=2000 Direction=270 Velocity=1.5 [Wind2] Height=4000 Direction=271 Velocity=2.5 [Wind3] Height=5000 Direction=272 Velocity=4 [Wind4] Height=7000 Direction=273 Velocity=5 [Eruption]Volume=0.03 Total volume emitted in km3 [Eruption]Column_Height=7000
Height of the eruptive column measured from the vent in metres
[Eruption]X_Vent= 341614 [Eruption]Y_Vent= 3128598
Coordinates of the vent [Eruption]Vent_Height=0
Height of the vent (in meters) if chimney effect is taken into account [Eruption]A_Parameter=3
Parameter that controls the shape of the eruptive column. The lower the value of the parameter, the higher the localization of the maximum of concentration.
[Particles]Fi_Mean=1
Mean value of the distribution of particle size, expressed in Φ units.
[Particles]Fi_Standard_Deviation=1.5
Standard deviation of the distribution of particle size, expressed in Φ units.
[Particles]Fi_Minimum=-2
Minimum value of Φ used in the computation. [Particles]Fi_Maximum=2
Maximum value of Φ used in the computation. It cannot be greater than 4 (characteristic dimension 0.0625 mm), as for higher values (smaller
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particles) effects such as electrostatic aggregation or ice/drop nucleation can occur.
[Particles]Fi_Density_Big=800
Density of the particles with Φ<1 (in kg/m3). [Particles]Fi_Density_Medium=1200
Density of the particles with 1≤Φ≤3 (in kg/m3). [Particles]Fi_Density_Small=2300
Density of the particles with Φ>3 (in kg/m3). [Particles]D_Parameter=3.45
Drag parameter. [Steps]Step_Vertical=100
Height of the vertical layers in which space will be divided. [Steps]Step_Horizontal=200
Cell size of the result grid. [Steps]X_Cells=300 [Steps]Y_Cells=300
Number of columns and rows of the grid for the result. [Steps]X_Origin_Area=311614 [Steps]Y_Origin_Area=3098598
Minimum values of the coordinates of the grid for the result. Try to adjust these values with [Steps]X_Cells and [Steps]Y_Cells to reduce the computation time (e.g. if your winds blow from the W, the values of [Steps]X_Origin_Area and [Steps]Y_Origin_Area could be very close to the vent location as the ashes will fall to the east). Although DISPER4 loads every parameter from its INI file, if the area defined by [Steps]X_Cells,[Steps]Y_Cells,[Steps]X_Origin_Area and [Steps]Y_Origin_Area does not contain the vent, the values of [Steps]X_Origin_Area and [Steps]Y_Origin_Area will be recalculated in such a way that the vent falls in the center of the result grid. Nevertheless, those values can be changed before clicking the “Run” button.
[Steps]Step_Fi=0.5 Precission in the classes of particles (e.g. if the value of [Steps]Step_Fi is 1, it means that the model will distribute the volumen between particle sizes as -2, -1, 0, 1, 2,… etc. If the value is 0.5, the classes considered will be -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2. …etc. Values typically used are 1 and 0.5.
[Atmosphere]Difussion=1000 Atmospheric horizontal diffusion, in m2/s. This value depends on the scale of the phenomena, ranging from
[Atmosphere]Tropopause=11300
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Height of the tropopause, in meters [Atmosphere]Air_Density=1.2255 Air density at sea level, in kg/m3 [Atmosphere]Air_Temperature=288 Air temperature at sea level, in Kelvin [Atmosphere]Wind_Constant=1 Must be 1 [Windn]Height=2000
Height (in meters) up to which the wind considered is that given by [Windn]Direction and [Windn]Velocity. There can be as many [Windn] blocks as necessary, numbered starting from 1 up to the number required, although in the main window of DISPER4 only the first five records will appear. The value of [Wind1]Height should be greater than 0, and the height value of the last block should be greater than the column height. [Windn] blocks must be ordered by height, from lower to higher altitudes (e.g. . [Windi]Height < [Windi+1]Height)
[Windn]Direction=270 Direction of the wind in degrees (starting from 0 –North- increasing clockwise).
[Windn]Velocity=1.5 Wind velocity in m/s.
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4.2.- LAVA FLOW 4.2.1.- Overview of the model The model used for simulating lava flow is a probabilistic model that assumes that topography plays the major role on determining the path that a lava flow will follow (see Felpeto, 2002; Felpeto et al., 2001). The model computes several possible paths for the flow, assuming two simple rules: the flow can only propagate from one cell to one of its eight neighbours if the difference of corrected topographic height between them is positive, and the probability for the flow to move from one cell to one its neighbours is proportional to that difference. The determination of the probability of each point being invaded by lava is performed by computing several random paths by means of a Monte Carlo algorithm. Let’s consider the topography represented by a mesh of squared cells whose value is the topographic height (h) of the cell (i.e. a DEM, Digital Elevation Model). If the flow is located in a cell (i=0), the probability (Pi ) that the flow enters into one of the eight surrounding cells (i = 1, 2,…, 8) is:
∑=
Δ
Δ= 8
1jj
ii
h
hP
where Δhi represents the difference in height between the cell where the flow is and each of its neighbours. In the estimation of this difference, a height correction (hc) is added to the height of the cell where the flow is currently located. This parameter simulates the effect of the height of the lava flow and allows it to propagate over small topographic barriers, that can be real or only small errors in the generation of the DEM. Therefore, Δhi is evaluated from:
( )( ) 0 0
0
0
00
≤−+=Δ
>−+−+=Δ
ici
icici
hhhifhhhhifhhhh
From those equations it is obvious that if the topographic height of cell i is higher than the corrected height of the cell where the flow is located, the probability of this flow to propagate to cell i is zero, implying the flow cannot propagate upwards. A Monte Carlo algorithm is used to compute the selection of the cell where the flow will propagate. It is necessary to note that the probability for the eight neighbour cells can be zero. This means that the flow has entered into a ‘sink’, a cell whose corrected height is lower than that of the eight neighbours, and then the flow will stop. In the case of a real lava flow, this ‘sink’ would probably be filled and the flow would continue. To avoid stopping the flow in such a situation, the model evaluates both prior equations for the sixteen cells which surround the original
16
eight ones (still considering that cell i= 0 is that where the flow is located). If any of these cells is accessible for the flow, it continues, otherwise it stops. In this scheme, the flow could propagate until it reaches the limits of the computational area. To avoid this, a parameter named maximum flow length (lmax) is included in the model and used to stop the flow when its length reaches lmax. Following this procedure, the computation of a possible path starts in the cell chosen as emission centre and its propagation is calculated with successive application of the method described, till the flow reaches lmax. When many paths have been computed, the probability of each cell to be invaded by lava is calculated as the ratio between the number of paths that have crossed the cell and the total number of paths computed. 4.2.2.- Operation Once the lava button is clicked, the input parameters form should appear. You should select the layer containing the topography (DEM), and type the maximum flow length (lmax), height correction (hc) and number of iterations (i.e. the number of possible paths that will be computed for each vent)
Then, select the vent(s). If you click on “single vent” option button, you could type the X and Y coordinates or click the button “Select Vent”. When this button is clicked, the input parameters window temporarily disappear to show the original map, where you should click to select the location of the vent. If you click on “Source Area” option button, a new combo box appears to select the raster layer containing the source area(s). This grid should have the same cell size, columns, rows and corners coordinates that the topography grid layer. All cells containing non-zero positive values will be considered as vents.
17
Then, you should select the susceptibility for each vent (i.e. spatial probability of the vents), selecting “Equal” (all the vents have the same probability) or “Map” and then select the raster layer containing values of relative probability. This grid should have the same cell size, columns, rows and corners coordinates that the topography grid layer. All non-zero positive values will be considered. Be careful not to assign zero probabilities to cells that do not appear as vents in the source area raster layer, because this means that possible paths will be computed for that vent, but they will be not taken into account in the final hazard map. When you have selected all the input parameters, click on the “Run” button. After a few seconds, a new window, corresponding to the numerical model, named GRAPEL4, will be opened. This window shows the input parameters previously selected. If you have selected a source area, a progress bar and a label on the estimated time for the computation may appear. If no progress bar is shown, it means that the expected time is less than 5 minutes.
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When the window named GRAPEL4 disappears, after a few seconds, a new layer will appear on your map, representing the logarithm of probability of each cell to be invaded by lava.
The result of every simulation is stored in ...\modGIS\lava\model\r folder, and named logp1, logp2, … etc. A text file containing the input parameters will be also saved into the same folder, with the corresponding name grapel1.dat, grapel2.dat, … etc. 4.2.3.- Notes 4.2.3.1.- Numeric values
Topography will be rounded to integer values.
Maximum flow length will be rounded to an integer value.
Height correction will be rounded to an integer value.
Number of iterations should obviously be an integer value.
Vent probability will be rounded to 32-bit floating-point values.
4.2.3.2.- Stored files
19
When you click the “Run” button in the input parameters window, the following files are stored in the ...\modGIS\lava\model\temp folder:
topo.rst contains the topography data (16-bit integers, binary).
topo.rdc its corresponding documentation file. vents.rst contains vents data (16-bit integers, binary), where
cells with value 1 will be considered as vents (only generated if source map is selected).
vents.rdc its corresponding documentation file prob.rst contains vent’s probability data (32-bit floating-point,
binary), where cells with value greater than zero will be considered (only generated if “source area” and “probability map” are selected).
prob.rdc its corresponding documentation file During and after the computation of the model, a few files are stored in the ...\modGIS\lava\model\temp folder:
__result.rst draft result of GRAPEL4 (32-bit floating point, binary). Contains the number of paths that have crossed each cell (multiply by the probability of each vent if a vent’s probability map has been selected).
__result.rdc its corresponding documentation file. __prob.rst probability of each cell to be covered by lava( 32-bit
floating point, binary). __prob.rdc its corresponding documentation file. __prob.flt same as __prob.rst (generated for easier importation
from ArcToolBox). __prob.hdr its corresponding header file. Note that perhaps you
will need to check the decimal period (. or ,) depending on your locale configuration.
__logprob.rst contains the logarithm (base 10) of the probability of each cell to be covered by lava (32-bit floating-point, binary).
__logprob.rdc its corresponding documentation file. __logprob.flt same as __logprob.rst (generated for easier
importation from ArcToolBox) __logprob.hdr its corresponding header file. Note that perhaps you
will need to check the decimal period (. or ,) depending on your locale configuration
__n.rst contains partially draft results (32-bit floating-point, binary) for the first x vents computed (__1.rst), the first 2x vents (__2.rst), … , nx vents (__n.rst),…etc. x value is typically 100, although it can be changed in the INI file. These files can be very useful in very long computations (days) when an error or a electrical power failure occurs.
__n.rdc its corresponding documentation file. centros.rst contains the vents already calculated, where the cell
value corresponds to the number of the __n.rst file
20
where the paths corresponding to that vent were first saved (16-bit integer, binary),
centros.rdc its corresponding documentation file.
Finally, in the ...\modGIS\lava\model\r folder, the result of every simulation is stored. logpn.aux the auxiliary file of the GRID format by ESRI, with its
corresponding folder. n takes the first value between 1 and 1000 that is not present in ...\modGIS\lava\model\r folder. It is recommendable to delete these files periodically, as this directory can become really heavy!.
grapeln.dat it is a copy of the INI file used in the simulation that has generated logpn, so it includes all the input parameters used.
4.2.3.3.- INI file The grapel4.ini file has the following structure [Vent] Single_map=0 X_Vent=331519.447210 Y_Vent=3128702.998043 File=notconsidered [Topography] Path=c:\myfolder\modGIS\lava\model\temp File=topo [Iterations] Num_iterations=1000 Save_File=100 [Hc] Value_map=0 Value=3 File=notconsidered [MaxFlowLenght] Value_map=0 Value=10000 File=notconsidered [Probability] Equal_map=0 File=notconsidered [Vent]Single_map=0
0 means single vent 1 means multiple vents (from map)
[Vent]X_Vent=331519.447210 [Vent]Y_Vent=3128702.998043
coordinates of the vent (only if [Vent]Single_map=0)
21
[Vent]File=notconsidered name of the vent file (no extension) (only if [Vent]Single_map=1). The files (both the .rst and the .rdc) should be located in the folder that appears on [Topography]Path= . This file should be of 16-bit integers, where every cell with value greater than 0 will be considered as vent.
[Topography]Path=c:\myfolder\modGIS\lava\model\temp
path where all the required input files should be located and where the result files will be stored
[Topography]File=topo
name of the DEM file (no extension). The files (both the .rst and the .rdc) should be located in the folder that appears on [Topography]Path= . This file should be of 16-bit integers.
[Iterations]Num_iterations=1000
number of iterations (paths) per vent [Iterations]Save_File=100
backup interval. It means that every 100 vents a copy of the draft result is stored in the disk (i.e. __1 conatins the result of the first 100 vents, __2 contains the result of the first 200 vents, ... etc).
[Hc]Value_map=0
must be 0 [Hc]Value=3
value for height correction. It should be a positive integer value in meters. [Hc]File=notconsidered
not used [MaxFlowLenght]Value_map=0
must be 0 [MaxFlowLenght]Value=10000
maximum flow length, in meters [MaxFlowLenght]File=notconsidered
not used [Probability]Equal_map=0
0 means that all the vents have the same probability 1 means the probability of each vent will be taken from [Probability]File= . It is only used if [Vent]Single_map=1 [Probability]File=notconsidered
name of the vent’s probability file (no extension). The files (both the .rst and the .rdc) should be located in the folder that appears on [Topography]Path= . This file should be of 16-bit integers. The values represent a probability index (e.g. if the value of a cell is 20.5 and the
22
value of another cell is 61.5 it means that the second one has three times the probability of becoming a vent than the first one).
23
4.3.- ENERGY CONE 4.3.1.- Overview of the model The model used for simulating the maximum potential extent affected by pyroclastic density currents (PDC) is a very simple model proposed by Malin and Sheridan (1982). The principle is that the height of the starting point of the flow (Hc) ratios to the length of the runout (L) as a type of friction parameter termed the Heim coefficient. The inclination of the energy cone is an angle (αc) defined by arctan (Hc/L). The intersection of the energy cone, originating at the eruptive source, with the ground surface defines the distal limits of the flow.
So, the model is applied calculating the energy cone defined by Hc , αc and the vent coordinates and intersecting it with the topography of the area. So, the cell ij can be affected by the flow if hij>0, where hij is: hij = H0 + Hc- tg αc dij - h0ij where H0 is the topographic height of the vent, Hc the collapse equivalent height, dij the distance from the vent to the cell ij and h0ij the topographic height of the cell ij. After this computation, an accessibility algorithm is applied to avoid the flow accessing areas that are protected by topographic barriers. The algorithm is an iterative process through n=0,1,2,…, where only the cells with hij>0 are considered:
H0
Hc
h0
h αc
d
24
0 0
1 2 3 2 3 2
0
21111
/
0
1
2 2
3 3 12
2
0 0 0
1
1
11
00
1
1
1
1
00
00
00
==
===∨===
=
+>+=
+≤≤−+≤≤−
∃
=
=
==
==−=
=≠≠>
===
−
−
−−
−
−
−
−
mij
mij
mij
mij
mij
mij
mij
mij
ijijklkl
mkl
mij
mij
mij
mij
mij
mij
ji
ij
ij
AifA
AifAAAifAnm
otherwiseA
hhhhA
jljiki
kl
A
ifA
AifA
AifAnm
Ajjii
hifAnm
where i0j0 corresponds to the vent cell. The last iteration will be an m=2n step when no cell changes its value from 1 to 2. The accessible cells are those with Aij=3. The following figure shows on the left the result of one simulation and on the right the same simulation after applying the accessibility algorithm (vent located at black dot).
See a detailed description of the model in Toyos et al. (2007).
25
4.3.2.- Operation Once the PDC button is clicked, the input parameters form should appear. You should select the layer containing the topography (DEM), and type the collapse equivalent height (Hc) and the collapse equivalent angle (αc).
Then, select the vent(s). If you click on “Single vent” option button, you could type the X and Y coordinates or click the button “Select Vent”. When this button is clicked, the input parameters window temporarily disappear to show the original map, where you should click to select the location of the vent. If you click on “Source Area” option button, a new combo box appears to select the raster layer containing the source area(s). This grid should have the same cell size, columns, rows and corners coordinates that the DEM grid layer. All cells containing non-zero positive values will be considered as vents.
Then, you should select the susceptibility for each vent (i.e. spatial probability of the vents), selecting “Equal” (all the vents have the same probability) or “Map” and then select the raster layer containing values of relative probability. This
26
grid should have the same cell size, columns, rows and corners coordinates that the topography grid layer. All non-zero positive values will be considered. Be careful not to assign zero probabilities to cells that do not appear as vents in the source area raster layer, because this means that the model be computed for that vent, but it will be not taken into account in the final hazard map. When you have selected all the input parameters, click on the “Run” button. If you have selected a source area, a progress bar will appear. After the computation finishes, a new layer named “Probability. Energy Cone model” will appear on your map, representing the probability of each cell being covered by the PDC. Obviously, if you have selected a single vent, the result will show an unique color (red), as it represent the area potentially affected by the flows.
The result of every simulation is stored in ...\modGIS\econe\r folder, and named ec1, ec2, … etc. A text file containing the input parameters will be also saved into the same folder, with the corresponding name ec1.dat, ec2.dat, … etc. 4.3.3.- Notes 4.3.3.1.- Stored files The result of every simulation is stored in the ...\modGIS\econe\r folder:
27
ecn.aux the auxiliary file of the GRID format by ESRI, with its
corresponding folder. n takes the first value between 1 and 1000 that is not present in ...\modGIS\econe\r folder. It is recommendable to delete these files periodically, as this directory can become really heavy!.
ecn.dat a text file that include all the input parameters used in the simulation that has generated ecn.
4.3.3.2.- DAT file The structure of the DAT file that is stored for each simulation is the following: Topography : dem_50m_w hc : 200 ac : 11 Vent : single x= 341775 y= 3128534 Topography Name of the layer containing the DEM. hc
Collapse equivalent height in meters. Sheridan and Malin (1983) proposed values ranging from about 100 m up to about 1000 m (for very big eruptions).
ac
Collapse equivalent angle (degrees). Sheridan and Malin (1983) proposed values ranging from about 4º to 27º (low values for surge eruptions and high values for phreatomagmatic eruptions).
Vent
If “Single Vent” has been selected, the rest of the line contains the coordinates of the vent: single x= 341775 y= 3128534 If “Source map” has been selected, the rest of the line will be: From map <the name of the vents layer> and another line on the susceptibility that will look like Vents probability: Equal or Vents probability : From map <the name of the corresponding layer>
28
5.- SUSCEPTIBILITY TOOLS Volcanic susceptibility can be defined as the spatial probability for the opening of a future vent. The quantification of such probability is a rather complicated problem, as it would imply knowledge about the easiest paths for the magma to reach the surface. Ideally, volcanic susceptibility should be computed considering all the available data that can provide information on the stress field, which is the main factor controlling the path that the magma will follow. These data can come from very different sources, as structural data measured in the field (vents, alignments, faults, dikes … etc.), geophysical data or numerical modelling. From each data source, a probability density function (PDF) should be generated in order to be able to combine al the available data. Once all the PDFs are generated, they are combined for the computation of the final probability map. 5.1.- SUSCEPTIBILITY 5.1.1.- Overview of the computational procedure If the spatial distribution of volcanoes in a region is completely random, a homogeneous Poisson process can be used for estimating the probability of a point containing one or more new vents. However, in many volcanic regions, the distribution of events is clearly not random, as vents tend to cluster. In these cases, non-homogeneous Poisson process is the simplest alternative to model clustered random data. Considering a non-homogeneous Poisson process, the probability (P) of a new event occurring in a grid area of size Δx2 centred on point (x,y) is given by:
( ) ( )x x exp11NP xyxy ΔΔλ−−=≥ where N is the number of events to occur in that area and λxy is a probability density function (PDF) that represents the spatial intensity of volcanism. The computation of this PDF is the key point for assessing the susceptibility, and it should include all the available information regarding the propensity of each point to contain a future vent. For each available dataset (k=1,…,M), three data are required: a probability density function should ( k
xyPDF ), relevance (Rvk) and the reliability (Rbk).
29
The probability density function ( k
xyPDF ) represents the spatial recurrence rate if only dataset k is considered. The relevance (Rvk) of one item describes the relative significance of the data considered in the evaluation of the susceptibility. The value of the relevance of each item should be assessed by specialists and, probably, through an elicitation procedure. It is necessary to note that this values are assessed to the data itself, without taking into account the quality of these data or even if they are available or not. The reliability (Rbk) of one item reflects somehow the quality of the available data, in terms of their use on the assessment of the volcanic susceptibility. So, final PDF for the evaluation of the susceptibility is computed by means of:
∑
∑=
=
=
== Nk
k
kk
Mk
k
kxy
kk
xy
RbRv
PDFRbRv
1
1
λ
5.1.2.- Operation Once the susceptibility button is clicked, the input parameters form should appear.
Click on “Select layers” and a new window containing all available raster layers will appear.
30
Click on the checkboxes of the layers you want to include in the computation of the susceptibility. In this version, only up to six layers can be considered.
Then, introduce the values for the relevance and the reliability for each layer. Note that, by default, the value of reliability is 1 for all the layers. The sum of all relevance values should be 1. This can be easily accomplished by clicking on one of the option buttons on the left column (named “Aut”). Selecting one of those option buttons means that the relevance value for its corresponding layer will be computed as the difference between 1 and the sum of the rest of relevance values. Nevertheless, all the relevance values can be introduced manually. The system will check if the sum is 1 or not. Click on the “Run” button and, when the computation finishes, three new raster layers will be added to the map: “Final PDF”, which shows the spatial intensity
31
λxy ; “Susceptibility” that obviously shows the susceptibility, and “Susceptibility (log)”, which shows the logarithm of the susceptibility.
Note that in this version of VORIS, monitoring data can not be used for the computation of short term susceptibility. 5.1.3.- Notes 5.1.3.1.- Stored files No files are stored with the use of this tool. The final result can be saved at any desired location with the desired name making a right mouse click on the result layer and selecting “Make Permanent”. 5.1.3.2.- Rounded values The lowest value that will appear in the susceptibility map is 10-15. This is due to the fact that for values below around 10-15, the result of the exponential function of ArcMap is 1 (and, then, the computed susceptibility is 0). As, strictly speaking, the susceptibility cannot be 0 for any cell with non zero values on every PDF considered, the system replace those 0 values with 10-15 value. This means that a cell value of 10-15 should be read as “equal or lower that 10-15 “
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5.2.- PDF CAUCHY/GAUSS One of the most common methods for the estimation of the spatial probability for the opening of future vents is the kernel technique. A kernel function is used to obtain the intensity of volcanic events at a sampling point, calculated as a function of the distance to nearby volcanoes and a smoothing factor (h). The most used kernel functions are Gaussian and Cauchy kernels (see Martin et al., 2004) For the two-dimensional Gaussian kernel, the spatial recurrence rate λGxy at the point (x,y) is :
∑= ⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ −
+⎟⎠⎞
⎜⎝⎛ −
−π
=λM
1i
2vi
2vi
2xy hyy
hxx
21exp
Mh21G
where (xvi,yvi) are the coordinates of the ith volcanic vent used in the calculation, M the total number of volcanic vents used and h the smoothing factor. The resulting PDF is normalized dividing by the integral across the whole area of study. For the two-dimensional Cauchy kernel, λCxy at the point (x,y) is :
∑=
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ −
+⎟⎠⎞
⎜⎝⎛ −
+π
=λM
1i2
vi2
vi2xy
hyy
hxx1
1Mh
1C
For the evaluation of which of the kernels better describes the spatial distribution of past vents, a nearest-neighbour test can be applied by plotting the distance to the nearest neighbour versus the fraction of volcanic events considered. This test is also useful for choosing the appropriate smoothing factor for the selected kernel, by plotting the theoretical curves for different values of the smoothing factor (Martin et al., 2004). The “PDF Cauchy/Gauss” tool allows calculating the PDF for Gauss or Cauchy kernels, both for points datasets and straight lines datasets. In the second case, the value of the smoothing parameter can be estimated by a nearest neighbour test, considering the central point of each line. 5.2.2.- Operation Once the PDF Cauchy/Gauss button is clicked, the input parameters form should appear.
33
Select a Base Raster Layer. The characteristics of this raster will determine those of the output (cell size, extent, reference system and NoData cells).The cell values of this raster will not be used in the computation of the PDF. Select a Point or Polyline layer, that are the input parameter for the computation of the PDF. Select Cauchy or Gauss kernel and introduce, in meters, the value for the smoothing parameter. Click on the “Run” button. A progress bar will appear with a label that indicates the total number of features in the file and the features already computed. When the computation finishes, two new raster layers will be added to the map: one with the Resulting PDF and another one with its logarithm. In both titles the value of the smoothing factor and the selected kernel are included.
34
5.2.3.- Notes 5.2.3.1.- Stored files No result files are stored with the use of this tool. The final results can be saved at any desired location with the desired name making a right mouse click on the result layer and selecting “Make Permanent”. If the source dataset is a polyline, a temporal shape file is created in the same folder were the original dataset is stored and named “tempoly”. After the computation finishes, all the files corresponding to this temporal dataset are deleted. Nevertheless, if a problem occurs maybe any of the “tempoly” files can not be deleted. This will result in an error on successive launches of the tool. If this occurs, delete manually those files. 5.2.3.2.- Rounded values As it is obvious from equations in section 5.2.1, no cell on the result can have zero value. Nevertheless, the lowest value that will appear is 10-40. This is due to the fact that ArcMap when working with GRID format cannot work in double precision, so, when computing logarithms it return 0 for input values below 10-40. So, the tool substitutes values under 10-40 by 10-40.This means that a cell value of 10-40 should be read as “equal or lower that 10-40 “
35
6.- NOTES 6.1.- Decimal period Effort has been made in designing VORIS 2.0.1 in such a way that it can run whatever the locale numerical configuration is. Although this issue had been achieved in previous versions that run on ArcGIS 8.2, in ArcGIS 9.1 things have changed and the system works except when the settings for the decimal separator are customized. For example, if your system has been configured in Español(España) the decimal separator is “,”; if you customize it from the Control Panel->Regional Settings->Numbers->Decimal Separator changing to a “.” some of the tools of VORIS 2.0.1 may not work properly. Specifically, those that use import functions (lava and ashfall numerical simulations). This is due to the fact that the tool rewrites the header files (.hdr) to the locale decimal separator (“.” in this example), BUT ArcMap do not recognize locale customizations (so, in this example, ArcMap consider that if your configuration is Spanish, the decimal separator is “,”). We have not found any solution to this problem. In fact, it is an intrinsic problem of ArcGIS. In general, we have decided to use period (.) as decimal separator. So, when you write an input parameter, try to use always the period and not the comma (although the system will accept in most cases both period and comma as decimal separator). If you change your regional settings, close ArcMap and launch it again so it can recognize the new configuration (and even better, shut down your computer and turn it on again). 6.1.- Formats tested The whole application has been tested with the most common formats used in ArcMap: GRID for raster data and Shapefile for vector data (in fact, only for point and polyline data). Many of the tools of VORIS tool extract values from raster GRID data programmatically through Visual Basic for Applications. There are some pixel type for this kind of data that are not supported in Visual Basic (for example PT_USHORT, unsigned16 bit integers or PT_ULONG, unsigned 32 bit integers). VORIS has been tested for PT_SHORT (16 bits integers), PT_LONG (32 bit integers) and PT_FLOAT (32 bit floating point). If you find problems with
36
your GRID data, try converting them to any of those three types. This can be easily done with ArcToolBox->Data Management Tools->Copy Raster, specifying the pixel type, or with the great Hawth’s Tools (http://www.spatialecology.com/htools/) using Raster tools->Raster Data Type Conversion.
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REFERENCES Armienti, P.; Macedonio, G.; Pareschi, M.T., (1988). A numerical model for
simulation of tephra transport and deposition: applications to May18, 1980, Mount St. Helens eruption. J. Geophys. Res., 93(B6): 6463-6476.
Felpeto, A. (2002). Modelización física y simulación numérica de procesos
eruptivos para la generación de mapas de peligrosidad volcánica. Ph. D. Thesis. Universidad Complutense, Madrid, 250 pp.
Felpeto, A.; Araña, V.; Ortiz, R.; Astiz, M.; García, A., (2001). Assesment and
modelling of lava flow hazard on Lanzarote (Canary Islands). Natural Hazards, 23: 247-257.
Felpeto, A.; Martí, J.; Ortiz, R. (2007) Automatic GIS-based system for volcanic
hazard assessment. J. Volcanol. Geotherm. Res., 166:106-116. Folch, A.; Felpeto, A. (2005) A coupled model for dispersal of tephra during
sustained explosive eruptions. J. Volcanol. Geotherm. Res., 145:337-349.
Malin, MC.; Sheridan, MF. (1982). Computer-assisted mapping of pyroclastic
surges. Science 217:637-639. Martin, A. J., K. Umeda, C. B. Connor, J. N. Weller, D. Zhao, and M. Takahashi
(2004), Modeling long-term volcanic hazards through Bayesian inference: An example from the Tohoku volcanic arc, Japan, J. Geophys. Res., 109, B10208.
Sheridan, MF.; Malin, MC. (1983). Application of computer-assisted mapping to
volcanic hazard evaluation of surge eruption: Vulcano, Lipari, Vesuvius. Explosive Volcanism. J. Volcanol. Geotherm. Res. 17:187-202.
Suzuki, T., (1983). A theoretical model for dispersion of tephra. En: D.
Shimozuru y I. Yokoyama (Ed.) Arc Volcanism: Physics and Tectonics. Terra Scientific Publishing Company,Tokyo, 95-113.
Toyos, G.; Cole, P.; Felpeto, A.; Martí, J. (2007) A GIS-based methodology for
hazard mapping of small volume pyroclastic density currents. Natural Hazards,41-1, 99-112.
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CONTACTS Alicia Felpeto Observatorio Geofísico Central, IGN c/Alfonso XII, 3 28014 Madrid, SPAIN [email protected]
Joan Martí Instituto de Ciencias de la Tierra ‘Jaume Almera’ c/Lluis Sole i Sabaris s/n 08028 Barcelona, SPAIN [email protected]
http://www.gvb-csic.es
