[Document Type] Speci.fication
[Title of the Invention] METHOD OF SEARCHING FOR UNSTEADY DUST
SOURCE POSITION OF DUSTFALL
[Technical Field]
The present invention relates to a technique for searching for a source of dustfall
in the atmosphere.
[Background Art]
[0002]
Dustfall is generated from various industries including agriculture and forestry.
In addition, dustfall which is generated from nature, such as sand dunes, is not negligible.
When there are a large number of dust sources, which are the sources of the dustfall, a
technique which analyzes the degree of contribution of the dust source as an influence on
the "measured value of the amount of dustfall" at the evaluation point of the dustfall is
15 important in managing the dustfall and taking a measure to the dustfall.
From this point of view, Patent Documents I to 4 disclose a technique which
evaluates the amount of dust generated from a plurality of emission sources from the
amount of dustfall measured at an evaluation point, that is, a technique which searches
for the main source of the dustfall.
[0003]
Patent Document I discloses a technique as follows, in which a model suitable
for simulations is selected from input conditions, such as atmospheric conditions,
meteoroIogica1 data, and topographical data of the evaluation range of the diffusion of air
pollutants, adjustment input parameters is selected from the measured values
25 corresponding to the input conditions in a database unit in order to improve the accuracy
2
of analysis, input data is created from the analysis conditions by the selected model and
the selected adjustment input parameters, performs simulations, the deviation between
the simulation result and data for the measured value of a discharge source is calculated,
and the discharge source corresponding to the data in which the calculated deviation is
5 the minimum is estimated.
[0004]
Patent Document 2 discloses a technique as follows, in which a normal emission
amount and the abnormal emission amount of chemical substance is obtained, the normal
emission amount discharged from an emission source for the period for which the
10 concentration of a chemical substance in the atmosphere preliminarily measured by an
atmosphere observation station is not abnormally high and the abnormal emission
amount of chemical substance discharged from the emission source for the period for
which the concentration of the chemical substance in the atmosphere is abnormally high
and finds a solution which minimizes the sum of the square of (the normal emission
15 amount-the abnormal emission amount) in the emission source to specify the emission
source which causes the abnormally high concentration of the chemical substance in the
atmosphere.
[0005]
Patent Document 3 discloses a technique as follows, which includes a first
20 process of measuring the amount of dispersed dust and the wind direction at
predetermined time intervals for an appropriate period of time at two or more arbitrary
measurement points A, B and C in the vicinity of a plurality of dust generation points a, b,
c, d, and e, a second process of calculating the average amount of dispersed dust in each
wind direction at each measurement point from the amount of dispersed dust and the
25 wind direction obtained in the first process, a third process of plotting a plurality ofwind
1 8 SEP 9011
3
directions in which the average amount of dispersed dust is large, centering on each
measurement point, on a map including the plurality of dust generation points a to e and
the measurement points A to C, and a fourth process of specifying, as the source of the
dispersed dust, the dust generation point disposed at the intersection of the wind
5 directions from each measurement point plotted in the third process or the dust
generation point in the wind direction on the map when the wind directions fiom each
measurement point are substantiaIly aligned with each other.
[0006]
Patent Document 4 discloses a technique as follows, which remotely controls
10 one or more independent-type portable multi-sensing terminal units that measure
multiple items of atmospheric pollution conditions through a wireless or wired nehvork
to measure the multiple items of atmospheric pollution conditions, collects the measured
data, and displays the collected data.
[0007]
15 When the concentration of dustfall at the evaluation point is evaluated from the
amount of dust generated from the emission source, a plume equation is generally used.
Patent Document 5 discloses a standard plume equation, as the following Expression (I),
as the atmosphere difision model of gas from a point emission source which is not
absorbed from the surface of the ground.
[Expression (I)]
C(x, Y, 2) =
(~pl2nc~,a,~~)ex~[-fl2x a{yex']p [-(~e-z)2/20~]+exp[-(~e+~)2/2~,} "]
[0008]
Here, the meaning of symbols in Expression (1) is as follows. The meaning of
25 the symbols holds ibr the following description. The following symbols are all based
1 8 SEP 7011
on the SI unit system:
x, y, z: three-dimensional rectangular coordinates of an evaluation point (a gas
source is the origin)
x: axoordinate value corresponding to a direction in which the central axis of a
plume extends on the horizontal plane
y: a coordinate value in a direction (in the following description, this direction is
referred to as a "horizontal direction", when necessary) perpendicular to the direction in
which the central axis of the plume extends on the horizontal plane
z: a coordinate value in a vertical direction
C: gas concentration at an evaluation point (x, y, z) pg/m3 or m3 / m3 ]
Qp: the amount of gas generated [kg/s or m3/s]
WS: a wind speed [mls]
He: the height of a gas source from the surface of the ground [m]
o,, 0,: a gas plume diffusion width [m] (a standard deviation of a gas
concentration distribution in a direction perpendicular to the flow of gas; ay is a gas
plume diffusion width in the horizontal direction and 0, is a gas plume diffusion width in
the vertical direction).
[0009]
Non-Patent Document 1 discloses the following Expression (2) as the plume
equation related to gas which is absorbed by the surface of the ground and a suspended
particulate matter (SPM) with a low fall velocity.
[Expression (2)]
C(x, Y, z) =
( ~ ~ ~ l r o ~ 0[-f~l2o~y2~] ){eexxpp [ - ( ~ e - z - ~ , x / ~ ~ ) ~ / 2 o , " ] + a e x ~ [ - ( ~ e + ~ - ~ ~ ~
1 0 SEP ')fill
5
In Expression (2), a is represented by the following Expression (3).
[Expression (3)]
a = 1 -2VdI{V,+Vd+(WS~He-Vs)/~z-(doJdx))
The meaning of the symbols in Expression (3) is as follows. The meaning of
5 the symbols holds for the following description.
Vd: a deposition velocity [m/s]
V,: a fall velocity [rn/s] (in the case of SPM; in the case of gas, the fall velocity
[OO 1 01
10 Here, o, and o, are characteristic values for representing a "plume difision
width" in the direction perpendicular to the central axis of the plume and are the distance
between the central axis of the plume and the point at which concentration is,a standard
deviation when the concentration distribution of the Gaussian distribution is assumed in
the direction perpendicular to the central axis of the plume.
15 The plume equation is not limited to Expression (1). For example, Non-Patent
Document.3 discloses a plume equation when the double Gaussian distribution of
concentration is assumed and a curve is used as the central axis of a plume.
A first common characteristic of the plume equations is that the concentration
value of a specific concentration evaluation point is represented by a functional formula
20 of, for example, the coordinate values of the evaluation point and the emission source, a
generation speed fiom the emission source, and weather conditions, such as the wind
direction and the wind speed, and the unique result is provided. A second common
characteristic of the plume equations is that, in the calculation of concentration, a central
axis is assumed and a "plume" in which a high-concentration region characterized by the
25 "plume diffusion widths" o, and a, is formed around the central axis is set. When the
1 8 SEP
6
plume equation is compared with other methods, a numerical analysis method which
numerically solves a plurality of simultaneous physical equations to calculate the
concentration value of a specific concentration evaluation point differs from the plume
equation in that it calculates concentration without assuming the plume and the
5 calculation result is not unique. In addition, a multi-regression equation which
calculates the concentration value of a specific concentration evaluation point using the
coordinate values of the evaluation point and the emission source, the generation speed
from the emission source, and weather conditions, such as the wind direction and the
wind speed, as variables does not assume the plume. Therefore, the multi-regression
10 equation is not the plume equation.
[OO 1 11
In Expression (2), the "term multiplied by a" represents the effect of gas or SPM
remaining above the surface of the ground, without being absorbed, when the shape of
the distribution of gas or SPM in the vertical direction is symmetrically inverted on the
15 surface of the ground. The absorption effect of gas or SPM to the surface of the ground
is adjusted by the magnitude of a. However, in the following description, the "term
multiplied by a" in Expression (23 is referred to as a "surface reflection term", if
necessary.
[00 121
In addition, Patent Document 6 discloses, as a technique which measures the
amount of dustfall at an evaluation point in a short cycle of about 10 minutes, a technique
in which continuous measurements of each of the mass of a coarse particle and the mass
of a fine pmicle is performed, using a particle collection port having a b e 1 shape with
the top open, an airflow path which circulates through the measurement device, and an
25 inertial classifier which is provided in the airflow path and calculates a change in the fall
1 8 SEP W!j
7
velocity of dustfall in the atmosphere from the measured value of the mass of the coarse
particle.
[00 131
However, the above-mentioned techniques according to the related art have the
5 following problems.
That is, the first problem is that a generated material, which is a search target
from the emission source, is not dustfall.
For example, in the techniques disclosed in Patent Documents 1 to 4, the search
target from the emission source is gas. In the technique disclosed in Patent Document 3,
10 SPM is included in the search target from the emission source. SPM is a particle which
is significantly smaller than dustfall (by definition, SPM is a particle with a diameter of
10 pm or less) and the diffusion behavior of SPM in the atmosphere is substantially the
same as that of gas except that fine particles are precipitated.
[OO 1 41
15 The dustfall is a dust particle which is significantly larger than SPM (a particle
has a diameter of about 10 pm or more) and the fall velocity thereof is very high.
Therefore, the diffusion behavior of the dustfall in the atmosphere is greatly affected by
the fall velocity of particles. Therefore, the diffusion behavior of the dustfall is very
different from that of gas.
20 The amount of dustfall to be observed and managed is the deposition amount of
dustfall on the surface of the ground. In the techniques disclosed in Patent Documents 1
to 4, since the concentration of gas and SPM at the evaluation point is observed and
managed, it is difficult to directly know the deposition velocity of gas and SPM to the
surface of the ground. The deposition velocity Vd is reliably described in the
25 above-mentioned Expression (2). Therefore, when the deposition velocity Vd can be
1 8 SEP 'MI
8
accurately provided, it is possible to convert the concentration of gas and SPM at the
evaluation point into the deposition amount on the surface of the ground.
[OO 1 51
However, as disclosed in Non-Patent Document 1, the deposition velocity Vd of
5 SPM is affected by the state of the surface of the ground or air turbulence and varies
greatly due to the state of the surface of the ground or air turbulence. In addition, a
method of generally providing the deposition velocity Vd of gas has not been developed.
Therefore, it is very diff~cultto accurately give the value of the deposition velocity Va in
practice and it is difficult to at least quantitatively treat dustfall in the techniques
10 disclosed in Patent Documents 1 to 4.
[OO 1 61
The second problem is that a dust source search method for dustfall has not been
disclosed in the related art. As represented by Patent Document 3, the emission source
search method according to the related art premises the search of an emission source in
15 the horizontal plane (the surface of the ground). Therefore, in the emission source
search method according to the related art, it is difficult to three-dimensionally treat "the
source of the dustfall" which has a high particle fall velocity V, and the problem of the
deposition amount on the surface of the ground. In particular, in the method disclosed
in Patent Document 3 in which an emission source search line extends from the
20 evaluation point in the upwind direction, it is difficult to quantitatively and generally
treat the influence of the surface reflection term (~~~X~[-(H~+Z-V,~in~ WS)~/~CJ~~])
Expression (2). Therefore, in the related art, an effective method which associates the
emission source search line with the plume equation has not been proposed.
100 171
The third problem is that assume the position of the emission source and the
9
rough number of particles generated from the emission source in advance is unavoidable
when the emission source is searched for in the above-mentioned techniques according to
the related art.
For example, in the techniques disclosed in Patent Documents 1 and 2, first, for
5 all of the assumed emission sources and all evaluation points, the relationship between
the number of particles generated from an arbitrary emission source and concentration at
an arbitrary evaluation point is predicted as a weather condition function such as the
above-mentioned plume equation. Then, the parameters (for example, o, or Qp) of the
function are adjusted by an optimization method such that the difference between the
10 measured value of concentration at all evaluation points and the predicted value of
concentration is the minimum. Therefore, it is necessary to give at least the position of
all emission sources in advance. In addition, in order to ensure the validity of a
calculation process of the optimization method, it is generally desirable to give the rough
number of particles generated from each emission source as initial conditions in advance.
15 The reason is as follows. In the optimization problem, when the initial conditions
which are very different from the actual conditions are given, a solution is Iikely to
converge on a local stabilization point which is very different from the actual
stabilization point.
[00 181
20 FIG. 7 is a diagram schematically illustrating the dust source search method
according to the related art (Patent Document 3).
In the technique disclosed in Patent Document 3, as shown in FIG 7, a plurality
of dust (SPM) generation points a, by c, d, and e are assumed in advance and the
concentration of SPM is measured at a plurality of evaluation points ii, iz, and i3 around
25 the dust generation points for a long period. Then, the average value 1 (see a polygon
10
surrounding the evaluation points il, i2, and is) of the concentration of SPM in each wind
direction is calculated at each evaluation point for the period and emission source search
lines 2,3, and 4 extend from the evaluation points i,, i2, and i3 in the horizontal plane (the
surface of the ground) in the upwind direction of the wind direction in which the average
5 value of the concentration of SPM is the maximum. Among the intersection points 6,7,
and 8 between the emission source search lines, a point corresponding to any one of the
dust (SPM) generation points a, b, c, d, and e is determined to be a generation point
where a particularly large amount of dust (SPM) is generated.
[OO 191
10 In the technique disclosed in Patent Document 4, it is premised that the
measurement device is provided in the vicinity of the assumed emission source.
Therefore, the emission source needs to be known in advance.
However, when there are a large number of emission sources, in practice, it is
difficult to check the position of all of the emission sources and the rough amount of dust
15 generated from the emission sources. If possible, a large amount of resources is needed,
which is not preferable. Therefore, the techniques disclosed in Patent Documents 1 to 4
can be effectively applied only in an environment in which the number of emission
sources is very small or it is possible to sufficiently accurately check the amount of dust
generated from the emission source.
[0020]
The fourth problem is that the emission source, which is a search target, is
basically a steady emission source whose generation amount does not vary over time or a
quasi-steady dust source whose generation amount varies slightly over time in the
vicinity of an average time value.
For example, in the techniques disclosed in Patent Documents 1 and 2, the
11
optimization method is applied. Therefore, in general, the number of evaluation points
needs to be greater than the number of parameters which can be adjusted in the function
such as the applied plume equation. When the number of adjustable parameters is
substantially greater than the number of evaluation points, in general, the found solution
5 is not uniquely determined and the method fails.
[002 11
In addition, where there are a large number of emission sources, in many cases,
the number of evaluation points is set to be less than the number of emission sources in
terms of economic efficiency. In this case, when the emission source is limited to a
10 steady emission source (that is, when the amount of dust Qp is an adjustable parameter),
it is possible to ensure the measured value equal to or greater than the number of
emission sources by using the measured values at the evaluation points at a plurality of
different times and the optimization method can be applied. On the other hand, when
the techniques disclosed in Patent Documents 1 and 2 are applied to the unsteady
15 emission source whose generation amount Qp is unsteadily greatly changed, the amount
of dust QP needs to be an adjustable parameter. Therefore, when a large number of
emission sources are search targets, it is necessary to provide a very large number of
evaluation points more than the number of emission sources, which is not practical in
terms of economic efficiency.
[0022]
In the technique disclosed in Patent Document 3, data for the concentration of
SPM which is discretely collected at the evaluation point for a period of two months or
more is averaged to search for the emission source. Therefore, the emission source is
limited to a steady emission source.
In the technique disclosed in Patent Document 4, since the evaluation point is
12
arranged in the vicinity of the assumed emission source, it is possible, in principle, to
search for an unsteady emission source. I-Iowever, this technique does not disclose a
method of determining a prominent emission source among a plurality of emission
sources when the gases generated fiom the plurality of emission sources reach a specific
5 evaluation point at the same time and a method of arranging the evaluation points in the
vicinity of all of the assumed emission sources. Therefore, in this technique, it is
possible to search for the unsteady dust source only when the distance between the
emission sources is so great that the emission sources have no influence on each other.
That is, this technique can be applied only when the emission source is substantially in
10 one-to-one correspondence with the evaluation point.
I-Iowever, in practice, the amount of dust generated from the emission source is
generally large and varies over time. Therefore, the technique according to the related
art in which only the steady emission source or only the emission source which is in
one-to-one correspondence with the evaluation point is a search target cannot be
15 sufficiently applied to the actual search of the emission source.
[Related Art Documents]
[Patent Documents]
[0023]
[Patent Document 11 Japanese Unexamined Patent Application, First
20 Publication No. 2003-255055
[Patent Document 21 Japanese Unexamined Patent Application, First
Publication No. 2005-29204 1
[Patent Document 31 Japanese Unexamined Patent Application, First
Publication No. 2004- 170 11 2
[Patent Document 41 Japanese Unexamined Patent Application, First
Publication No. 2003-28 167 1
[Patent Document 51 Japanese Unexamined Patent Application, First
Publication No. 2007-122365
[Patent Document 61 Japanese Unexarnined Patent Application, First
5 Publication No. 2008-224332
[Non-Patent Documents]
[0024]
won-Patent Document 11 Suspended Particulate Matter Measure Conference
(Reviewed by Pollution Control Division, Nature Conservation Bureau, Ministry of the
10 Environment): Suspended Particulate Matter Pollution Forecast Manual, Toyokan
Publishing Co., Ltd., 1997
won-Patent Document 21 Shinichi Okamoto: Air Quality Forecast Lecture,
Gyosei, 2001
[Summary of the Invention]
15 [Problems to be Solved by the Invention]
[0025]
The present invention has been made in view of the above-mentioned problems
and an object of the present invention is to effectively search for a dustfall source that
generates dust, the amount of which is unsteadily changed, with high accuracy.
20 [Means for Solving the Problem]
[0026]
The inventors conducted a study in order to solve the problems and conceived
the following solution.
According to a first aspect of the present invention, a method of searching for an
25 unsteady dust source position of dustfall includes: setting a measured value of an average
14
amount of dustfalf M for a period of Td(it) fiom a time Td(it-1) to a time Td(it), which is
an it-th time Td(iS in each time cycle Atd, at at least two different dustfall evaluation
points; deriving a representative wind direction WD(it) for the period of Td(id, based on a
wind direction that is continuously measured in a time cycle Atwint shorter than the time
5 cycle Atd for the period of Td(it) in the vicinity of the respective dustfall evaluation
points; deriving a representative wind speed WS(iS for the period of Td(iS, based on a
wind speed that is continuously measured in a time cycle Atwint shorter than the time
cycle Atd in the vicinity of the respective dustfall evaluation points and; deriving a
representative fall velocity V, of the dustfall, based on the measured value of the fall
10 velocity of the dustfall collected at the dustfall evaluation points for the period of Td(it);
setting, as a dustfall search region y(i, it) for the period OfTd(it) which is an arbitrary
period included in the period of t,(k) that is an evaluation period from a time t,(k-1) to a
time t,O when a k-th time in each time cycle Atg including two or more successive times
Td(it) is tg(k), first and second dustfall source search regions y ( i ~i,t) and y(i~i,t ), which
15 have central axes extending from two different dustfall evaluation points i~ and i~ as
starting points in an upwind direction of the representative wind direction WD and have
dustfall source search region widths around the central axes and distance ranges from the
central axes to the dustfall source search region widths in a vertical direction; deriving, at
the dustfall evaluation point i, an amount of dustfall M,,(i) at a time Td(id when the
20 maximum amount of dustfall M is obtained within a period of t,(k), i,,(i) which is it at
the time Td(it), and a representative wind direction WD,, and a representative wind
speed WS,, at the time Td(it); calculating distances Ld(iM)a nd Ld(iN)b etween a
coordinate point p which is included in both the first and second dustfall source search
regions y ( i ~L, ax)a nd y(i~i,t ) and the two dustfall evaluation points iMa nd iN;c alculating
15
each of first and second dust source search region central axis vertical cross-sectional
areas SP1 and Sp2, which are cross-sectional areas of the first and second dustfall source
search regions in vertical planes of the central axes of the first and second dustfall source
search regions including the coordinate point p, using the dustfall source search region
5 width; calculaiing assumed amounts of dust El and E2 which are proportional to the dust
source search region central axis vertical cross-sectional areas Spl and Sp2; and
determining that the coordinate point p is a main unsteady dust source with a time scale
equal to or more than the time cycle At, in the period of t,(k) when any ratio between the
assumed amounts of dust El and E2 which are calculated for a combination of all of
10 dustfall source search regions including the coordinate point p in the calculation of the
amount of dust is within a range of predetermined upper and lower limit threshold values,
determining that the coordinate point p is not the main unsteady dust source with the time
scale equal to or more than the time cycle At, in the period of t,(k) when any ratio
between the assumed amounts of dust El and E2 which are calculated in the calculation of
15 the amount of dust is beyond the range of the predetermined upper and lower limit
threshold values, and not determining the unsteady dust source of the dustfall at the
coordinate point p when the coordinate point p is not included in any of the dustfall
source search regions. The dustfall source search region width is a plume diffusion
width that is calculated at the distance on a central axis of a plume with the centrai axis
20 of the dustfall source search region as the central axis of the plume in a plume equation.
According to a second aspect of the present invention, in the method of
searching for an unsteady dust source position of dustfall according to the first aspect,
when the central axis of the dustfall source search region has a horizontal component as
an upwind direction of the wind direction and has a value V,/WS obtained by dividing
25 the representative fall velocity V, of the dustfall by the representative wind speed WS as
16
a vertical gradient, and in the plume equation, a plume diffusion width o, in a horizontal
direction and a plume diffusion width o, in a vertical direction are calculated as the
dustfall source search region width at the distance on the central axis of the plume with
the central axis of the dustfall source search region as the central axis of the plume, and
5 are used as a horizontal component and as a vertical component, respectively.
According to a third aspect of the present invention, in the method of searching
for an unsteady dust source position of dustfall according to the first aspect or the second
aspect, as the plume equation, the following Expressions (A) and (B) are used which
represent dust concentration C(x) at a distance x from an emission source on the central
10 axis of the plume using the plume diffusion widths o, and o,, the distance x from the
emission source on the central axis of the plume, a dustfall generation speed Qp, the
representative wind speed WS, a constant B, and a plume range defined by the plume
diffusion widths o, and a,:
[Expression (A)]
C(x) = B(Qp/2noyo,WS) (inside the plume range); and
[Expressions (B)]
C(x) = 0 (outside the plume range).
According to a fourth aspect of the present invention, in the method of searching
for an unsteady dust source position of dustfall according to the third aspect, an ellipse in
20 which a length of a major axis is two times the larger of the plume diffusion widths o,
and o, and a length of a minor axis is two times the smaller of the plume diffusion widths
o, and o, is a cross-sectional shape of the plume in a direction perpendicular to the
central axis of the plume, and the inside of the ellipse is the inside of the plume range and
then the plume range is calculated.
[Effect of the Lnvention]
[0027]
According to the present invention, dustfdl is measured at a small number of
evaluation points to effectively search for a dustfall source that generates dust, the
5 amount of which is unsteadily changed, with high accuracy.
[Brief Description of the Drawings]
[0028]
(Figure 11 FIG. 1 is a diagram illustrating an example of a plume which is
10 projected onto a horizontal plane.
[Figure 21 FIG. 2 is a diagram illustrating an example of a plume which is
projected onto a vertical plane.
[Figure 31 FIG. 3 is a flowchart illustrating an example of a process of a dust
source search device.
15 [Figure 41 FIG. 4 is a diagram illustrating an example of a dust source search
region.
[Figure 51 FIG. 5 is a diagram illustrating an example of a dust source search
method.
[Figure 63 FIG 6 is a diagram illustrating an example of a method of setting
20 the dust source search region in a direction other than a wind direction indicating a
maximum concentration value.
[Figure 71 FIG. 7 is a diagram illustrating a dust source search method
according to the related art.
[Embodiment of the Invention]
LO0291
18
(Characteristics of Embodiment of the Present Invention)
First, characteristics of an embodiment of the present invention will be
described.
A first characteristic of the embodiment of the present invention is that dustfall
5 is directly measured at a dustfall evaluation point to search for thc source of the dustfall.
[0030]
A second characteristic of the present invention is that, in the search of the
source of the dustfall, a dust source search region which extends from the dustfall
evaluation point in an upwind direction is associated with a plume equation to obtain
10 information about the amount of dust generated from dust source candidates.
To be specific, as described above, in the related art, it is difficult to treat the
ground reflection term (~-~X~[-(H~+~-V,X/WinS E)x~pr/es~sCioTn ~(2)]. ) Therefore, it
is difficult to associate a dust source search line which extends from the dustfall
evaluation point in the upwind direction with the plume equation. However, the
15 examination result of the inventors proved that the problem of the ground surface
reflection term occurred because the main target of the technique according to the related
art was gas or SPM. In the case of dustfall, since the fall velocity of particles is high, a
deposition velocity Vd is substantially equal to a fall velocity V,. Therefore, the
influence of the reflection of particles from the surface of the ground is small and a = 0 is
20 regarded to be established. Thus, an atmosphere diffusion formula (plume equation) for
the dustfall is the following Expression (4) obtained by substituting a = 0 into Expression
(2).
[Expressions 41
C(x, y, z) =(~r/2~cr,cr,~~)ex~[-~~l2~~]xex~[-(~e-z-~~~/~~)~/20~]
[003 11
Wen coordinates are converted by the following Expression (5), Expression (4)
becomes the following Expression (6).
[Expressions 41
Z = z+V,x/WS-He
[Expressions 61
C(x, y, 7,) = ( ~ p / 2 ~ ~ , o , ~ ~ ) x e x ~ [ - ~ ~ / 2 o ~ ] e x ~ [ - ~ ~ / 2 ~ ]
Here, the coordinate conversion of z into Z by Expression (5) corresponds to the
definition of concentration when the emission source (dust source) is the origin, the
10 central axis of a dust plume is set in the vertical plane at a depression angle of tan-'(V,
(particle fall velocity)/WS (wind speed)) in a downwind direction, and the central axis is
the Z-axis.
[0032]
The diffusion widths o; and o, are the standard deviation of the concentration
15 distribution in the y direction and in the z direction (in general, V, << WS is satisfied and
the z direction is regarded to be substantially equal to the Z direction under the condition
that V, << WS is satisfied), respectively. In many cases, when there is no influence of
reflection from the surface of the ground, the concentration distribution in the y direction
and the z direction is regarded as a normal distribution. In this case, while a
20 concentration value at y = ay and Z = o, is 60% of the maximum concentration value, a
concentration value at y = 20, and Z = 20, is 13% of the maximum concentration value.
That is, in the region in which y > o, and Z > o, are satisfied, concentration is rapidly
reduced. Therefore, in the embodiment of the present invention, the following
Expressions (7a) and (7b) are premised as the plume equation.
[Expressions (7a)l
2 0
C(x) = B(Qp/2.no,oZWS) (inside the plume range)
[Expressions (7b)l
C(x) = 0 (outside the plume range)
to0331
Here, the meaning of symbols in Expression (7a) is as follows:
B: a proportional constant.
In this method, since the only problem of Expression (7a) is a relative value, an
arbitrary value (for example, 1) may be given to the proportional constant B.
The inside of the plume range means a region in which, assuming that the
10 concentration distribution in the vertical direction of the plurne is a Gaussian distribution
as represented by Expression (4), concentration is closer to the central axis than to a
position indicating the value of the standard deviation of the concentration distribution.
Alternatively, sinlply, when the cross-section of the plume is an ellipse in which the
length of a major axis is two times the larger of o, and o, and the length of a minor axis
15 is two times the smaller of o, and o,, the inside of the ellipse may be the inside of the
plume range. In addition, more simply, the range may be represented by the following
Expression (8). On the other hand, the outside of the plume range is a range other than
the inside of the plurne range.
[Expression (S)]
a,> y>-oY and $2 ZL -0,
Here, o, and oZ are a function of a distance LO from the dust source and a time
period Atd (oy[Lo,A td] and o,[h, btd]). In addition, o, and s are the tabulated or
diagrammatized values which are calculated by fixing the period Atd (using the period Atd
as a reference period) and are calculated by empirically correcting the influence of the
2 1
period Atd using the Pasquill-Gifford formula or the Briggs formula disclosed in
Non-Patent Document I. As disclosed in Nan-Patent Document 2, a method of
empirically correcting the influence of the period Atd multiplies the plume difision
width 0, by ([Atd which is actually used]/[Atd of a reference net time])'.
5 [0034]
When a dust species and a dust particle size are given, the particle fall velocity
V, is determined as a terminal velocity. Therefore, the amount of dustfall M(x) can be
represented by the following Expressions (9a) and (9b) in which concentration C(x) is
multiplied by the particle fall velocity V,.
10 Expression (9a)l
M(x) = V,B(Qp/2.noyozWS) (inside the plume range)
[Expression (9b)l
M(x) = 0 (outside the plume range).
[0035]
15 In Expression (9a), under the condition of a constant wind speed, the amount of
dustfall M(x) in a limited part of the plume range is determined only by the amount of
dust Qp and the plume diffusion widths o, and 0,. In addition, the values of the plume
diffusion widths o, and o, are a function of x and weather conditions and can be
represented by, for example, the Pasquill-Gifford equation disclosed in Non-Patent
20 Document 1. Therefore, under constant dust source conditions and constant weather
conditions, the amount of dustfall M(x) at a specific dustfall evaluation point can be
represented only by the distance x from a specific dust source.
Next, the existence range of the dust source at a specific dusgall evaluation
point is considered using Expression (9).
FIG. 1 is a diagram in which plumes a(iOla)n d a(i,t) that are generated on the
22
same horizontal plane as that including a dustfall evaluation point i~ are projected fiom
two dust sources iol and io2 disposed at a position x' = Lo onto the global coordinate
system x' and y' (the surface of the ground) in the horizontal plane having the specific
dustfall evaluation point i~ as the origin 0. In this case, a wind direction WD is the
5 positive direction of x'. The plumes a(iol) and a(io2) are arranged such that the central
axes 1 Oa and lob thereof are aligned with the surface of the ground at x' = 0 and the ends
of the plumes in the horizontal direction (the end of the plume a(iol) in the -yl direction
and the end of the plume a(io2) in the +y' direction) pass through the origin 0. The
arrangement positions of the plumes a(iol) and a(io2) are limit positions where the plumes
10 a(iol)a nd a(iO2)c an reach the dustfall evaluation point i~ from the dust sources iol and i,z
which are set at x - Lo. That is, the position of the dust source i0l is a limit position in
the +y' direction and the position of the dust source io2 is a limit position in the -y'
direction.
COO3 61
15 The diffusion width o, of the pl~uaesa (iol) and a(io2) at x' = 0 is o,(Lo).
Therefore, the half width of the distance between the dust sources iol and iO2 at x' = Lo is.
equal to o,(Lo), that is, the dieusion width o, of the plumes a(iol) and a(ioz) at x' = 0.
When the positions of the dust sources i0l and io2 are estimated during the measurement
of dustfall at the dustfall evaluation point iM, the dust sources iol and io2 are present in a
20 region y ( i ~it,) (a hatched region) interposed between a line which passes through the
origin 0 and the point of the dust source iOl and a line which passes through the origin 0
and the point of the dust source i02 in the horizontal plane. The region y(iM, it) is the
dust source search range.
[003 71
However, the value of x' = Lo where the dust sources ior and io2 are arranged is
23
arbitrary. Therefore, at the arbitrary position of x', the half width of the range of the
dust sources iol and io2 which can reach the dustfall evaluation point iM in the y' direction
is constantly o,(xl). That is, the half width of the dust source search range y(iM, id in the
y' direction is equal to a, on the same horizontal plane as that including the dust source in,
5 for example, the plume equation of Expression (6). Therefore, the dust source search
region y(iM, it) in the horizontal plane can be set by the width of the search region which
is represented by a function of only the distance from the dustfall evaluation point iM on a
central axis 1 I which extends from the dustfall evaluation poi$ i~ in the upwind
direction of the representative wind direction.
10 COO381
FIG. 2 is a diagram in which plumes a(iO3)a nd a(&) that are generated on the
same vertical plane as that including the dustfall evaluation point iM are projected fiom
two dust sources io3 and io4 which are disposed at a position x' = Lo onto the global
coordinate system x' and z in the vertical plane having the specific dustfdl evaluation
15 point i~ as the origin 0.
Specifically, the dust source search region y ( i ~i,d is set by the same method as
that described with reference to FIG. 1. At that time, the width of the dust source search
region y(iM, it) is represented by a diffusion width o,(x').
However, since dust falls, the central axes 1O a and lob of the plumes a(iO3)a nd
20 a(io4) and the central axis 11 of the dust source search region y(iM, it) are inclined at an
angle 0 (= tane'(v,/ws)) in the vertical cross-section. Therefore, only the dustfall
which is generated in a'portion of the region extending from the dustfall evaluation point
iM in the upwind direction can reach the dustfall evaluation point iM from the dust sources
io3 and i,4 among points in the upwind direction of the dustfall evaluation point iM. As
25 such, in the dust source search method in which the emission source search region y(iM,
24
it) extends from the dustfall evaluation point i~ in the upwind direction, the range of the
distance in the upwind direction is limited, which is not disclosed in the method
according to the related art. This method has the advantage over the method according
to the related art in that it is possible to limit the dust source search region y ( i ~i,t) .
5 [0039]
The simple and quantitative expression of the dust source search range y ( i ~i,d ,
which is a modification of the plume equation for the amount of dustfall, has not been
achieved by the plume equation according to the related art based on gas or SPM. The
inventors paid attention to the fact that the dust fall velocity V, was relatively high and
10 first achieved the simple and quantitative expression through a series of studies.
The present invention is not limited to the use of the plume equation of
Expression (9). For example, when precise measurement is performed in advance to
accurately express the influence of the ground surface reflection term, the term of o, in
Expression (9) may be appropriately corrected on the basis of the plume equation while
15 leaving the ground surface reflection term.
[0040]
A third characteristic of the embodiment of the present invention is that the dust
source or the amount of dust is not necessarily assumed in advance. In practice, in
many cases, the position of the dust source or the amount of dust generated therefrom is
20 not known. Therefore, the method according to the embodiment of the present
invention is advantageous because it practically searches for the dust source.
COO4 11
A fourth characteristic of the embodiment of the present invention is that an
unsteady dust source is specified. The method according to the embodiment of the
25 present invention can specify the main dust source for each acquisition cycle of the
25
measured value of the amount of dustfall or for the time corresponding to several
successive acquisition cycles of the measured value of the amount of dustfall.
Therefore, it is possible to check the unsteady dust source which varies in a time scale
equal to or more than several acquisition cycles of the measured value of the amount of
5 dustfall. In addition, the number of dustfall evaluation points required to specify the
unsteady dust source may be sufficiently less than the number of latent dust sources.
[0042]
Hereinafter, exemplary embodiments of the present invention will be described
in detail witb reference to the drawings. I-Iowever, in the specification and the drawings,
10 components having substantisllly the same functional structures are denoted by the same
reference numerals and the description thereof will not be repeated.
(First Embodiment)
First, a first embodiment will be described.
A dustfall amount measurement unit (device) measures the amount of dustfall in
15 each time cycle Atd (hereinafter, the "time cycle" is abbreviated to a "cycle" if necessary).
It is assumed that the time when the amount of dustfall is output is Td(id. The time
(period) from a time Td(it-1) to the time Td(it) is defined as a "period of Td(itY7. Here, it
is an integer that is increased by 1 from 0 which is the time when dustfall starts to be
measured. In addition, nt is a natural number equal to or greater than 2 and the time
20 including nt successive "periods of Td(it)" is defined as a "period of t,(k)". It is assumed
that the time of a starting point of the "period of t,(k)" is a time tg(k-1) and it is 0 at that
time. It is assumed that the time of an end point of the "period of t,(k)" is a time t,(k)
and it is nt at that time. In addition, k is an integer that is increased by 1 from 0 which is
the time when dustfall starts to be measured. In this embodiment, a dustfall source is
25 specified for each "period of tg(k)" and a dust source which has a time scale (that is, the
26
time when dust is continuously generated) equal to or more than the cycle At, (= nt. Atd)
is a search target.
LO0431
For example, a cycle corresponding to six cycles At4 can be used as the cycle At,
5 (when the cycle Atd is 10 minutes, the cycle At, is one hour). The dust source which can
be specified in this embodiment is an unsteady dust source with a time scale equal to or
more than the cycle At,. Therefore, it is not preferable to set the cycle Atg to a very
large value since the number of unsteady dust sources which can be specified is reduced.
In general, there is a large difference in weather conditions between day and night.
10 Therefore, sine many unsteady dust sources have a time scale equal to or more than a half
day, it is preferable that the cycle At, be equal to or less than 12 hours. When it is
determined in advance that the time scale of the unsteady dust source is equal to or more
than 12 hours, the cycle is not limited thereto.
[0044]
15 In addition, a rectangular coordinate system including x, y, and z is set in a
three-dimensional region in which the dust source can be searched for, n, coordinate
components, ny coordinate components, and n, coordinate components are provided on
each coordinate axis, and the three-dimensional space is represented by n,xn,xn,
coordinate points p. Here, the coordinate point p indicates a coordinate point with an
20 i,-th coordinate component, an i,-th coordinate component, and an izth coordinate
component. The position of each coordinate point is represented as Sc(i,, i,, i,) by a
position vector from the origin 0, using the orders i,, i,, and i, of the coordinate
components on each coordinate axis. Any one of three dust source determination
modes "dust source", "not dust source", and "undetermined" is set at each coordinate
25 point p.
[0045]
An example of the process (dust source search process) of the dust source search
device searching for a dust source will be described with reference to the flowchart
shown in FIG. 3. The dust source search device is implemented by an information
5 processing apparatus (for example, a commercial personal computer (PC)) including, for
example, an arithmetic device, such as a CPU, a memory, an HDD, and various interfaces.
For example, the flowchart shown in FIG. 3 is translated into an executable computer
program by a programming language, such as the C language, and is stored in the HDD
in advance. When the information processing apparatus performs the dust source search
10 process, the arithmetic device, such as a CPU, reads the executable computer program
stored in, for example, the HDD and starts the executable computer program. Then, the
arithmetic device, such as a CPU, sequentially performs operations based on the
commands of the executable computer program. The executable computer nogram
may be started manually, or periodically and automatically to start the dust source search
15 process. As described above, the dust source search device according to this
embodiment searches for a dustfall source for the "period of t,(k)" at a given time.
[0046]
Position information, such as a dustfall evaluation point and a coordinate point,
and necessary input information, such as the measured values of the amount of dustfall,
20 the wind direction, and the wind speed, or an analysis value related to a dust species, can
be manually input to the dust source search device through a keyboard or a console
screen connected to the information processing apparatus in advance. The input
information is stored in, for example, the HDD and is appropriately read with the
progress of the dust source search process.
In the dust source search device, for example, the determination result of the
28
unsteady dust source and the calculation result of the amount of dust at the calculated
specific coordinate point can be stored in the HDD and be displayed on the console
screen.
A portion of or the entire process of the dust source search device may be
5 replaced with other means such as manual calculation.
COO471
First, a first process will be described.
In Step 5201, the dust source search device initializes the dust source
determination mode to "undetermined" at a11 coordinate points p.
I0 Then, in Step S202, the dust source search device calculates the positions of all
dustfall evaluation points i (nM 2 i 2 1) in the horizontal plane (for example, a ground
height of 1.5 m) as a position vector P(i) indicating a position from the origin of the
coordinate system.
In Step S203, the dust source search device sets (inputs) "a representative wind
15 speed WD(it), a representative wind direction WS(it), the amount of dustfall M(i, it) at all
evaluation points, and the representative fall velocity V,(i, i3 of dustfall" for all "periods
Td(it)" included in the "period of t,(k)". In this embodiment, for example, in Step S202,
a dust amount setting process, a representative wind direction derivation process, a
representative wind speed derivation process, and a representative fall velocity derivation
20 process are performed.
The amount of dustfall M(i, i3 can be measured by, for example, the continuous
dustfall sampler disclosed in Patent Document 6 in a cycle Atd of 10 minutes. The
values ofthe wind direction and the wind speed can be measured by, for example, a
commercial propeller anemometer in a cycle Atwin, (for example, 1 second) shorter than
29
the cycle Atd. The spatial resolution of the wind direction is, for example, an interval of
1 ". For example, the average value of the "measured values of the wind direction and
the wind speed" for the corresponding "period of Td(it))) may be used as the
representative wind direction WD(it) and the representative wind speed WS(it). In
5 addition, the "vicinity of the dustfall evaluation point7' may be the range in which the
wind direction and the wind speed have high correlation with the wind direction and the
wind speed above the dustfall evaluation point and may be, for example, within a
horizontal distance of 1 krn from the dustfall evaluation point. In a region in which the
land is monotonous and the distribution of the wind direction and the wind speed is small,
10 the vicinity of the dustfall evaluation point may be a horizontal distance equal to or more
than 1 km. In addition, the height of the measurement point of the wind direction and
the wind speed may be, for example, a measurement height of 10 m from the surface of
the ground which is recommended by the meteorological agency. When the assumed
height of the dust source is sufficiently greater than 10 m, for example, an intermediate
15 value between the surface of the ground and the height of the dust source may be used as
the height of the measurement point.
lo0481
In addition, the average fall velocity of dustfall can be measured using a dustfall
sample which is collected at the evaluation point for all "periods of Td(iJ' included in the
20 "period of t,(k)" and can be used as the representative fall velocity V,(it) of dustfall
corresponding to each "period of Td(iJ". Alternatively, when a dustfall collection
sampling interval is longer than Td(it) due to, for example, restrictions in the
measurement device, all dustfall particles collected for the "period of tg(k)" may be used
as the dustfall samples and the average fall velocity of the dustfall samples may be used
25 as a representative fall velocity V, (= V,(iS = constant) common to all "periods of Td(it)"
3 0
included in the "period of t,(k)". For example, there is the following method as a
method of measuring the fall velocity of the dustfall sample. That is, the dustfall
scunple is discharged from the upper part of an airtight container, the time required for
each dustfall particle to reach the bottom of the container is measured, and the falling
5 distance is divided by the falling time to calculate the representative fall velocity V, of
the dustfall. In order to detect the arrival of each dustfall particle at the bottom of the
container, for example, a method can be used which continuously radiates a sheet-shaped
laser beam in the horizontal direction on the bottom of the container and detects
scattering light which is generated when dustfall passes through the laser beam using a
10 photodetector.
100491
As a method of calculating the representative fall velocity V, fi-om the fall
velocity of each dustfall particle, a method can be adopted which uses the falling time
corresponding to the time required for 50% of all dustfall particles to reach the bottom of
15 the container as the fall velocity of the dustfall particles related to the representative fall
velocity V, of the dustfall particles. Alternatively, when the density and shape of
dustfall are determined in advance, simply, the particle size distribution of the dustfall
samples can be measured to calculate the representative fall velocily V, of the dustfall
particles. As a method of calculating the representative fall velocity V, of the dustfall
20 particles from the dustfall particle size, for example, the following Stokes terminal
velocity Expression (10) can be used.
[Expression (I O)]
VS = (4g~p(pp-~f)/~3K R )' I 2
Here, the meaning of the symbols in Expression (1 0) is as follows (units are all
25 SI units):
g: gravity acceleration [mis2]
Dp: a particle size [m]
pp, pf: the density of particles and the density of a fluid mg/m3]
CR: a resistance coefficient [-I (various type of number tables are disclosed
5 depending on the shape of particles).
[0050]
Then, in Step 5204, the dust source search device sets "the dust source search
region y(i, it) related to each dustfall evaluation point" at all dustfall evaluation points i as
all times Td(it) in the "period of t,(k)". In this embodiment, for example, in Step S204, a
10 dustfill source search region setting process is performed.
FIG. 4 is a diagram illustrating an example of the dust source search range y(i, it).
An example of a method of setling the dust source search range y(i, it) will be described
with reference to FIG. 4.
In FIG. 4, y ( i ~i,t ) is another expression of a dust source search region y ( i ~i,d ,
15 which is decomposed for each coordinate component and shown in FIGS. 2 and 3, in one
diagram by isomeric projection. In FIG. 4, two dustfall evaluation points iM and iN are
arranged on a ground surface on the absolute coordinates (x', y', z) and the central axes of
dust source search regions ~(IMit,) and y(i~i,t ) are set at an elevation angle 8 (=
tan-'[vs(iM, it)/WS(it)] or tan-'p,(i~, it)/WS(it)]) in the upwind direction of the
20 representative wind direction WD(iJ, using the dustfall evaluation points iM and iN as
starting points. The dust source search regions y(iM, it) and y(iN, it) are set such that the
cross-section of an ellipse with a width 20, in the horizontal direction and a width 20, in
the vertical direction is formed around the central axis. As shown in FIG. 4, when there
are a plurality of dust source search regions y(i, it), a common region 41 between the
25 plurality of dust source search regions y(i, it) is generated in some cases.
[005 11
In Step S205, the dust source search device calculates "M,,(i), which is the
amount of dustfall at the time Td(it) when the amount of dustfall M(i, it) is the maximum
within the "period of tg(k)", imax(iw) hich is it at that time, and a representative wind
5 direction WD,, and a representative wind speed WS,, at the time Td(ity at the dustfall
evaluation point i. In this embodiment, for example, in Step S205, a maximum dustfall
information derivation process is performed.
[0052]
Next, a second process will be described.
10 First, in Step S206, the dust source search device selects a non-selected dustfall
evaluation point i as a dustfall evaluation point i ~ .
Then, in Step S207, the dust source search device selects a non-selected
coordinate point among the coordinate points p.
Then, in Step S208, the dust source search device calculates the position vector
15 Sc(i,, i,, i,) of the coordiilate point p. The position vector Sc of the coordinate point p is
set such that the origin of the coordinate axis is a starting point and the point (that is, the
point p) at which coordinate components are an i,-th coordinate axis division point, an
i,-th coordinate axis division point, and an i,th coordinate axis division point is an end
point. Here, a first unsteady dustfall search region y(iM, i,,) is "the only unsteady
20 dustfall search region related to the dustfall evaluation point iM" for the "period of t,Q",
[0053]
Then, in Step S209, the dust source search device selects another dustfall
evaluation point i~ different iiom the dustfall evaluation point iM. Here, a second
unsteady dustfall search region y(i~i,d is an "unsteady dustfall search region related to
25 the dustfall evaluation point i ~a"t a n "arbitrary time Td(it)o f the period of tp(k)".
Then, in Step S210, the dust source search device determines whether the
dustfall evaluation point iM selected in Step S206 and the dustfall evaluation point iN
selected in Step S209 are disposed at the same position. When it is determined that the
dustfall evaluation point iM selected in Step S206 and the dustfall evaluation point iN are
5 disposed at different positions, the process proceeds to Step S2 11. On the other hand,
when it is determined that the dustfall evaluation point iM selected in Step S206 and the
dustfall evaluation point iN are disposed at the same position, Steps S211 to S220 are
omitted and the process proceeds to Step S221, which will be described below.
[0054]
10 When the process proceeds to Step S211, the dust source search device selects a
non-selected time Td(it) among the times Td(it) in the "period of t,(k)".
Then, in Step S212, the dust source search device determines whether the dust
source determination conditions that the coordinate point p selected in Step S207 is
included in both the first dust source search range y ( i ~i,d and the second dust source
15 search range y ( i ~i,t ) and the dust source determination mode is in the mode other than
"not dust source" are satisfied.
When it is determined that the dust source determination conditions are (all)
satisfied, the coordinate point p selected in Step S207 is likely to be a dust source. The
state in which the dust source determination conditions are satisfied corresponds to the
20 state in which the coordinale point p is in a common region 41 (a hatched region)
between the two dust source search regions y ( i ~i,m aanxd y)( i~i,t ) in FIG. 4. As such,
when the dust source determination conditions are satisfied, the process proceeds to Step
S213. On the other hand, when the dust source determination conditions are not
satisfied, Steps S213 to S220 are omitted and the process proceeds to Step S221, which
25 will be described below.
[OOSS]
When the process proceeds to Step S213, the dust source search device
calculates the (shortest) distance Ld(iM)b etween the coordinate point p selected in Step
S207 and the dustfall evaluation point iM selected in Step S206 and the (shortest) distance
5 Ld(iN)b etween the coordinate point p selected in Step S207 and the dustfall evaluation
point iN selected in Step S209.
The distance Ld(iM)b etween the coordinate point p and the dustfall evaluation
point iM is calculated, for example, as the norm of a vector connecting the end point of a
position vector P(iM) and the end point of the position vector Sc(i,, i,, i,). The second
10 distance Ld(iN)b etween the coordinate point p and the dustfall evaluation point i~ is
calculated by the same method as described above. In this embodiment, a distance
calculation process is performed in Step S213.
[0056]
Then, in Step S2 14, the dust source search device calculates "the central axis
15 vertical cross-sectional areas Spr and Sp2 of the dust source search regions y(iM, i3 and
y(i~i,t ) related to the dustfall evaluation points i~ and iN" at the coordinate point p
selected in Step S207. For example, a method of calculating the central axis vertical
cross-sectional areas SP1 and Sp2 of the dust source search regions y(iM, it) and y(iN, it) is
as follows. That is, the central axis vertical cross-sectional areas SP1 and Sp2 of the dust
20 source seasch regions y ( i ~i,t ) and y(i~i,t ) can be calculated as ihe area of an ellipse in
which the length of a major axis is two times the larger of the difision widths oy[Ld] and
~ z [ L d ] and the length of a minor axis is two times the smaller of the difision widths
(s~[L~an] d oz[Ld]. In this embodiment, for example, in Step S214, a cross-sectional area
calculation process is implemented.
[0057]
35
Then, in Step S215, the dust source search device calculates "the assumed
amounts of dust El and Ez at the coordinate point p selected in Step S207" which are
estimated Gom the dustfall evaluation points i~ and i ~ . The assumed amounts of dust
El and EZ are calculated by, for example, Expression (I 1 a) and Expression (1 1 b),
5 respectively.
[Expression (1 1 a)]
El = BIS,I
[Expression (I 1 b)]
E2 = BlS,2
10 1x1 Expression (1 1 a) and Expression (1 1 b), B1 is a coefficient. Expression (1 1 a)
and Expression (1 1 b) correspond to concentration at a limited par1 being proportional to
the amount of dust generated by the emission source and being inversely proportional to
the cross-sectional area of the plume at a limited part in the general plume equation.
That is, when the coordinate point p selected in Step 5207 is a dust source, concentration
15 which is inversely proportional to the cross-sectional area of the plume at the dustfall
evaluation points iM and iN is detected. In other words, as the assumed cross-sectional
of the plume increases with respect to constant detected concentration, the amount of
dust generated by the emission source corresponding thereto needs to increase.
Therefore, the amount of dust generated by the emission source is supposed to be
20 proportional to the cross-sectional area of the plume at the dustfall evaluation points iM
and i ~ .
[OOSS]
In Expression (1 la) and Expression (I 1 b), B1 is a coefficient which will be
originaIly changed by a large number of parameters, such as weather conditions.
25 However, in this embodiment, only the ratio of the assumed amounts of dust El and Ez is
36
used to determine the dust source, as will be described below. In addition, since the
assumed amounts of dust El and E:! are calculated on the basis of data at the same time,
the common weather conditions are premised. Therefore, in this embodiment, it is
possible to set B I as a constant using a simple method. In this embodiment, for example,
5 in Step S215, a dust amount calculation process is performed.
[0059]
Next, a third process will be described.
First, in Step S216, the dust source search device calculates a ratio R of the
assumed amounts of dust El and E2. The ratio R of the assumed amounts of dust El and
10 Ez may be or E2/E1.
Then, in Step S217, the dust source search device determines whether the
coordinate point p selected in Step S207 is the dust source. In this embodiment, the
dust source search device determines whether the ratio R of the assumed amounts of dust
El and E2 is in the range (R,,, 2 R 2 Rmino) f predetermined upper and lower limit
15 threshold values. When it is determined that the ratio R of the assumed amounts of dust
El and E2 is in the range of the predetermined upper and lower limit threshold values, it
is determined that the coordinate point p selected in Step S207 is the "dust source". On
the other hand, when it is determined that the ratio R of the assumed amounts of dust El
and E2 is beyond the range of the predetermined upper and lower limit threshold values,
20 it is determined that the coordinate point p selected in Step S207 is "not the dust source".
[0060]
The determination method is based on the following. A variation in the amount
of dust generated from the unsteady dust source with a time scale equal to or more than
the cycle Atg is sufficiently small in the "period of tg(k)" by definition. Therefore, it is
25 considered that, when a dust source which generates'a larger amount of dust than other
37
dust sources, that is, a main dust source is searched for, dustfall generated from the main
dust source is dominant at all evaluation points i which dust can reach for the "period of
t,(k)". In this case, when there are a plurality of dustfall evaluation points i which dust
can reach for the "period of t,(k)", the amounts 01dustfalI observed at the dustfall
5 evaluation points i have a constant ratio therebetween according to a function (that is, the
plume equation) of the distance between the dust source (coordinate point p) and each
dustfall evaluation point i. Therefore, the coordinate point p which satisfies this
condition is more likely to be the main dust source. Thus, when the ratio R of the
assumed amounts of dust El and E2 is within the range of the predetermined upper and
10 lower limit threshold values, the coordinate point p selected in Step S207 is determined
to be the "dust source".
[006l]
On the other hand, when the ratio of the amounts of dustfall observed at the
dustfall evaluation points i is very different from the value which is calculated from the
15 plume equation, the coordinate point p selected in Step S207 is likely to be a false dust
source even though the coordinate point p is disposed at the position where dustfall can
reach a plurality of evaluation points i during the "period of t,(k)". Therefore, when the
ratio R of the assumed amounts of dust El and EZ is beyond the range of the
predetermined upper and lower limit threshold values, the coordinate point p selected in
20 Step S207 is determined not to be the "dust source".
100621
When it is determined that the coordinate point p selected in Step S207 is the
dust source, the process proceeds to Step S218. On the other hand, when it is
determined that the coordinate point p selected in Step 5207 is not the dust source, the
25 process proceeds to Step S220, which will be described below.
38
In this embodiment, for example, in Step S212 and Step S217, a dust source
determination process is performed.
When the process proceeds to Step S218, the dust source search device sets the
dust source determination mode of the coordinate point p selected in Step S209 to "dust
5 source7'.
Then, in Step S219, dust source search device calculates the estimated amount
of dust at the coordinate point p which is determined to be the "dust source". For
example, the estimated amount of dust can be the average value of all of the assumed
amounts of dust E which are used in the determination of the dust source (Step S217) at
10 the coordinate point p which is determined to be the "dust source". Then, the process
proceeds to Step S22 1, which will be described below.
On the other hand, when the process proceeds to Step S220, the dust source
search device sets the dust source determination mode of the coordinate point p selected
in Step S207 to "not dust source". Then, the process proceeds to Step S221.
[0063]
When the process proceeds to Step S221, the dust sou& search device
determines whether all times Td(id in the "period of t,(k)" have been selected. When it
is determined that not all times Td(it) in the "period of t,(k)" have been selected, the
process returns to Step S211. On the other hand, when it is determined that all times
20 Td(it) in the "period of tg(k)" have been selected, the process proceeds to Step S222.
When the process proceeds to Step S222, the dust source search device
determines whether all dustfall evaluation points i have been selected as the dustfall
evaluation point i ~ . When it is determined that not all dustfall evaluation points i have
been selected as the dustfall evaluation point iN, the process returns to Step S209. On
25 the other hand, when it is determined that all dustfall evaluation points i have been
3 9
selected as the dustfall evaluation point i ~th,e process proceeds to Step S223.
When the process proceeds to Step S223, the dust source search device
determines whether all coordinate points p have been selected. When it is determined
that not all coordinate points p have been selected, the process returns to Step S207. On
5 the other hand, when it is determined that all coordinate points p have been selected, the
process proceeds to Step S224.
[0064]
When the process proceeds to Step S224, the dust source search device
determines whether all dustfall evaluation points i have been selected as the dustfall
10 evaluation point iM. When it is determined that not all dustfall evaluation points i have
been selected as the dustfall evaluation point iM, the process returns to Step S206. On
the other hand, when it is determined that not all dustfall evaluation points i have been
selected as the dustfall evaluation point i ~th,e p rocess proceeds to Step S225.
When the process proceeds to Step S225, the dust source search device displays
15 the position of the dust source and the estimated amount of dust from the dust source.
Then, the process of the flowchart shown in FIG 3 ends. However, all coordinate
points p may not be determined to be the dust source. In this case, in Step 5225, the
dust source search device displays information indicating that all coordinate points p may
not be determined to be the dust source.
[0065)
As described above, the second and third processes can be performed for all
times Td(it) in the "period of t,(k)". The determination result indicating whether a
specific coordinate point p is the dust source at a specific time Td(it) can be the
determination result indicating whether the specific coordinate point p is the dust source
25 representing the "period of t,(k)". When it is determined that the coordinate point p
40
selected in Step S207 is "not the dust source" at a given time Td(it), the coordinate point p
is determined not to be the main dust source for the "period of tg(k)". When it is
determined that the coordinate point p is the "dust source" at a given time Td(it) and is
"not the dust source" at any time other than the given time, the coordinate point p
5 determines to be the "main dust source for the period oft,".
COO661
The second and third processes may change the dustfall evaluation points i~ and
iN or the coordinate point p and independently determine whether the changed points are
the dust source, if necessary. At the coordinate point p which has not been used to
10 determine the dust source, the initial value "undetermined" remains as the dust source
determination mode. In addition, the process may end when the dust source is obtained.
The second and third processes determine whether a specific coordinate point p
is the dust source at a specific dustfall dustfall evaluation point i (= iM) (sets any one of
the dust source determination modes). If necessary, the dustfall evaluation point i and
15 the coordinate point p are changed and the same determination process as described
above is performed.
As such, in the this embodiment, since the concept of the plume equation is
applied to the emission source search region which extends from the evaluation point p in
the upwind direction, it is possible to accurately specify the position of the dustfall source
20 with a time scale equal to or more than the cycle Atg and the amount of dust generated by
the emission source. Therefore, dustfall is measured at a small number of evaluation
points and it is possible to effectively search for the dust sources including an unsteady
dust source with high accuracy.
[0067]
(Second Embodiment)
4 1
Next, a second embodiment of the present invention will be described.
When it is determined that the height of a dust source is limited lo a value in the
vicinity of the surface of the ground, a dust source search region is not set in a
three-dimensional region unlike in the first embodiment, but is set in the horizontal plane
5 (in a two-dimensional region). Therefore, it is possible to simplify a process of
searching for the dust source and reduce the possibility that the dust source will not be
searched for.
[0068]
Specifically, in Step S204 of FIG. 3, a dust source search device omits the
10 inclination of the central axes of dust source search regions y ( i ~i,d and y(i~i,t) with
respect to the vertical direction and a diffusion width o, in the vertical direction (an
elevation angle 0 is 0" and the difision width o, is 0) and forms two-dimensional dust
source search regions y ( i ~i,t ) and y(i~i,t) .
In addition, position vectors P and Sc in Steps S202 and S208 are
15 two-dimensional vectors without a vertical component.
[0069]
However, as such, even when the two-dimensional dust source search regions
y ( i ~i,d and y(i~i,d are formed, it is necessary to consider the influence of the diffusion
of a dust plume in the vertical direction in the calculation of the amount of dust at a
20 coordinate point p. Therefore, in Step 3214, the dust source search device needs to
calculate "the cenbal axis vertical cross-sectional areas Spl and Spz of the dust source
search regions y ( i ~i,t) and y(i~i,J related to dustfall evaluation points iMa nd iNna t the
coordinate point p selected in Step S207. The central axis vertical cross-sectional areas
S,I and Sp2 of the dust source search regions y ( i ~i,t) and y(i~i,t ) related to the dustfall
25 evaluation points i~ and i~ can be the cross-sectional area of a circle having, as its radius,
42
the "diffusion width oy[Ld] of dustfall particles in the horizontal direction" at the
calculated distances Ld(iM) and Ld(i~)". Alternatively, the "difTusion width oz[Ld] of
dustfall particles in the vertical direction at the distances Ld(iM) and Ld(iN))'
corresponding to the "diffusion width oy[Ld] of dustfall particles in the horizontal
5 direction at the distances Ld(iM) and Ld(iN)" may be used and the cross-sectional area of
an ellipse having 2x0~or 2x02 as the major axis and the minor axis may be the central
axis vertical cross-sectional areas.
[0070]
In this embodiment, in general, the wind direction and the wind speed are
10 changed at each time Td(it) included in a "period of tg(k)". In this embodiment, since
the main dust source related to a specific dustfall evaluation point i~ is searched for, it is
natural to set the first dust source search range y ( i ~i,d in the upwind direction of a wind
direction WD,,(iM) in which the amount of dustfall is the maximum for the "period of
t,(k)". In order to specifj the dust source in the first dust source search range y(iM, it),
15 the second dust source search region y(i~i,t ) at another evaluation point i~ needs to
intersect the first dust source. In this embodiment, "the measured value M(iN, id of the
amount of dustfall at a dustfall evaluation point i ~a"t the time when a wind direction
WD(iN, it) different from a wind direction WD,,(iM) is formed for the "period of t,(k)"
is used. Therefore, it is easy for the iirst and second dust source search regions y(iM, id
20 and y(iN, it) to intersect each other and it is possible to determine whether a dust source is
present at a large number of coordinate points p. It is possible to reduce the number of
"undetermined" coordinate points p.
[007 1 ]
In this case, the wind direction wD(i~i,t) may not be the wind direction when
25 the maximum amount of dustfall is measured at the dustfall evaluation point iN, unlike
43
the related art. The reason is as follows. In the embodiment of the present invention,
since there is an estimated value of the amount of dust in the dust source search region
based on the plume equation, it is possible to determine whether a dust source is present,
using information about the absolute value of the measured value of the amount of
5 dustfall in a specific wind direction (that is, not information about the relative value of
the amount of dustfall in other wind direction conditions), in addition to information
indicating the wind direction in which the amount of dustfall is the maximum, unlike in
the related art.
[0072]
10 The advantages of the embodiment of the present invention will be described
using the same target system as that in FIG. 7 which is a schematic diagram illustrating
an emission source search method according to the related art. As described above, in
the related art, in FIG. 7, intersection points 6,7, and 8 between emission source search
lines 2,3, and 4 are regarded as dust sources. However, in the technique according to
15 the related art, there is no information about a generation amount on the emission source
search lines 2,3, and 4. Therefore, it is difficult to Wher obtain information about
whether the intersection points 6,7, and 8 are valid as the dust sources. For example,
the intersection point 6 is actually likely to be the main emission source. However, it
may be that the emission source search lines 2 and 3 intersect each other at the
20 intersection point 6 due to the influence of another main dust source on the dustfall
evaluation points i l and i2 (for example, it may be that the main emission source related
to the dustfall evaluation point il is the intersection point 7 and the main dust source
related to the dustfall evaluation point i2 is the intersection point 8 or an unknown
emission source disposed at the position that is closer to the dustfall evaluation point i2
25 than to a facility (dust (SPM) generation point) c). In the related art, it is difficult to
44
determine a true dust source among the dust sources. In particular, when the emission
source search lines 2,3, and 4 intersect each other at points which are not assumed as the
emission sources (for example, at the intersection points 7 and 8), it is difficult to
determine whether the intersection point is an unknown dust source or an apparent
5 intersection between the emission source search lines (that is, the intersection point is not
the emission source). Therefore, the error that an excessive number of dust sources are
detected (all intersection points are determined to be the emission sources) or it is
difficult to detect an unknown dust source (all intersections between the emission source
search lines at the points which are not assumed as the emission sources in advance are
10 determined to be false emission sources) is inevitable.
[0073]
FIG. 5 is a diagram schematically illustrating an example of the dust source
search method according to the embodiment of the present invention.
As shown in FIG. 5, when the embodiment of the present invention is applied, it
15 is possible to examine whether the intersection point is valid as the dust source in the
intersection region between the dust source search regions. That is, for example, in FIG,
5, it is assumed that coordinate points pl, p2, and p3 in the common regions between dust
source search regions y(i1, it,,), y(i2, itmax)a, nd y(i3, itmaua)r e obtained as the dustfall
evaluation points corresponding to the intersection points 6,7, and 8 shown in FIG. 7.
20 In this case, for example, in order to evaluate the validity of the coordinate point p, as the
dust source, the estimated amounts of dust E(p1, il) and E@I, iz) at the coordinate point
pl with respect to the dustfall evaluation points il and i2 are compared to quantitatively
determine the dust source.
[0074]
In the related art, theoretically, only the emission source in the direction in
45
which the detected concentration for each wind direction is the maximum is searched.
When an unsteady dust source is searched for, a measurement period is relatively short
and a variation in the wind direction for the measurement period is generally limited.
Therefore, in practice, it is difficult to obtain the measured value of concentration under
5 all wind direction conditions at each dustfall evaluation point. Therefore, since the
wind direction which should show the maximum concentration value is not generated for
the measurement period, in some cases, it is difficult to search for the emission source (or
to determine whether the emission source is a true emission source or a false emission
source) at a specific dustfall evaluation point, depending on combinations of the wind
10 direction ranges capable of obtaining the main emission source, the dustfall evaluation
point, and the measured value. Originally, there is some information about the emission
source even at the measured value of concentration under limited wind direction
conditions. Therefore, when the dust source can be searched for in the direction in
which wind direction data is present (for example, when an emission source search line,
15 such as the emission source search line 5 shown in FIG. 7, can be set), it is possible to
provide at least information which is useful to identiijr the emission source at another
dustfall evaluation point. However, in the related art, there is no method of setting
various emission source search lines including the emission source search line 5 shown
in FIG. 7. Therefore, it is difficult to use concentration measurement data in the
20 direction other than the wind direction showing the maximum value of concentration.
[0075]
FIG. 6 is a diagram schematically illustrating an example of a method of setting
the dust source search region in the direction other than the wind direction showing the
maximum concentration value.
In the embodiment of the present invention, as shown in FIG. 6, it is possible to
46
set the dust source search region (for example, a dust source search region y(i3, it2)) in the
direction other than the wind direction showing the maximum concentration value. As
a result, it is possible to determine whether a dust source is present in the region in which
the dust source cannot be evaluated in the related art, such as a coordinate point p4 in a
5 common region between the dust source search regions y(i1, itm,) and y(i3, it2). As a
result, it is possible to significaitly increase the number of coordinate points p where it is
possible to determine whether a dust source is present, as compared to the related art, and
to search for the dust source with high accuracy.
LO0761
10 The related art shown in FIG. 7 has the problem that all of the intersection points
6,7, and 8 between the dust source search lines 2,3, and 4 are regarded as dust sources in
order to determine whether a dust source is present on the two-dimensional plane. In
contrast, in the first embodiment of the present invention, the dust source search region
y(i, it) is expanded in the three-dimensional space, using the analysis result of the particle
I5 size of the dustfall sample obtained at the dustfall evaluation point i. Therefore, in the
related art, even though it seems that the dust source search ranges intersect each other in
the plan view shown in FIG. 5, in many cases, there is no common region between the
dust source search ranges in a space including the vertical direction. Therefore, in the
embodiment of the present invention, among specific points corresponding to the
20 intersection points 6,7, and 8 on the plane shown in FIG. 7, a point which cannot actually
be the dust source (that is, a point which is not included in the common region between
the dust source search regions in the three-dimensional space) can be excluded from dust
source candidates. As a result, it is possible to search for a dust source with high
accuracy.
As such, according to the embodiment of the present invention, it is possible to
47
set a large number of coordinate points p which can be dust source candidates while
excluding the coordinate point p which cannot be the dust source. It is possible to
specify the position of the dust source and the amount of dust generated from the dust
source at the set coordinate point p with high accuracy.
5 [0077]
However, a computer can execute a program to implement the above-described
embodiment of the present invention. In addition, the embodiment of the present
invention can be applied to a computer-readable recording medium having the program
recorded thereon and a computer program product such as the program. Examples of
10 the recording medium may include a flexible disk, a hard disk, an optical disk, a
magneto-optical disk, a CD-ROM, a magnetic tape, a non-volatile memory card, and a
ROM.
While the preferred embodiments of the present invention have been described
and illustrated above, it should be understood that these are exemplary of the present
15 invention and are not to be considered as limiting. That is, various modifications and
changes of the present invention can be made without departing from the technical spirit
or main characteristics of the present invention.
fDescription of the Reference Symbols]
[0078]
i: DUSTFALL EVALUATION POINT
i,: DUST SOURCE
a, b, c, d, e: ASSUMED EMISSION SOURCE
p: COORDINATE POINT
a: PLUME
y: DUST SOURCE SEARCH RANGE
48
10: CENTRAL AXIS OF PLUME
11 : CENTRAL AXIS OF DUST SOURCE SEARCH REGION
41 : COMMON REGION BETWEEN DUST SOURCE SEARCH REGIONS
[Document Type] Claims
[Claim I]
A method of searching for an unsteady dust source position of dustfall, the
method comprising:
5 setting a measured value of an average amount of dustfall M for a period of
Td(it) fiom a time Td(it-1) to a time Td(it), which is an it-th time Td(it) in each time cycle
Atd, at at least two different dustfall evaluation points;
deriving a representative wind direction WD(iJ for the period of Td(it), based on
a wind direction that is continuously measured in a time cycle Atwint shorter than the time
10 cycle Atd for the period of Td(it) in the vicinity of the respective dustfall evaluation
points;
deriving a representative wind speed WS(il) for the period of Td(it), based on a
wind speed that is continuously measured in a time cycle Atwin, shorter than the time
cycle Ad in the vicinity of the respective dustfall evaluation points and;
deriving a representative fall velocity V, of the dustfall, based on the measured
value of the fall velocity of the dustfall collected at the dustfall evaluatioi~p oints for the
period of Td(it);
setting, as a dustfall search region y(i, id for the period of Td(it) which is an
arbitrary period included in the period of t,(k) that is an evaluation period from a time
t,(k-1) to a time t,(k) when a k-th time in each time cycle Atg inchding two or more
successive times Td(iS is t,(k), first and second dustfall source search regions y(iM, it) and
y(i~i,t ), which have central axes extending from two different dustfall evaluation points
i~ and i~ as starting points in an upwind direction of the representative wind direction
WD and have dustfall source search region widths around the central axes and distance
5 0
ranges from the central axes to the dustfall source search region widths in a vertical
direction;
deriving, at the dnstfall evaluation point i, an amount of dustfall M,,(i) at a
time Td(iS when the maximum amount of dustfall M is obtained within a period of t,(k),
5 i,,(i) which is it at the time Td(it), and a representative wind direction WD,, and a
representative wind speed WS,,, at the time Td(it);
calculating distances Ld(iM) and Ld(iN) between the two dusifall evaluation
points iM and iN and a coordinate point p which is included in both the first dustfall
source search region y(iM, i,) that is the only unsteady dustfall search region related to
10 the dustfall evaluation point iM for the period of tg(k) and the second dustfall source
search region y(iN, id related to the dustfall evaluation point i~ different from the dustfall
evaluation point iM at the time Td(it) which is an arbitrary time included in the period of
tgf k);
calculating each of first and second dust source search region central axis
15 vertical cross-sectional areas Sp1 and Sp2, which are cross-sectional areas of the first and
second dustfall source search regions in vertical planes of the central axes of the first and
second dustfall source search regions including the coordinate point p, using the dustfall
source search region width;
calculating assumed amounts of dust El and E2 which are proportional to the
20 dust source search region central axis vertical cross-sectional areas SP1 and Sp2; and
determining that the coordinate point p is a main unsteady dust source with a
time scale equal to or more than the time cycle Atg in the period of tg(k) when any ratio
between the assumed amounts of dust El and E2 which are calculated for a combination
of all of dustfall source search regions including the coordinate point p in the calculation
25 of the amount of dust is within a range of predetermined upper and lower limit threshold
5 1
values, determining that the coordinate point p is not the main unsteady dust source with
the time scale equal to or more than the time cycle At, in the period of tg(k) when any
ratio of the assumed amounts of dust El and EZ which are calculated in the calculation of
the amount of dust is beyond the range of the predetermined upper and lower limit
5 threshold values, and not determining the unsteady dust source of the dustfall at the
coordinate point p when the coordinate point p is not included in any of the dustfall
source search regions,
wherein, the dustfall source search region width is a plume diffusion width that
is calculated at the distance on a central axis of a plume with the central axis of the
10 dustfall source search region as the central axis of the plume in a plume equation.
[Claim 21
The method of searching for an unsteady dust source position of dustfall
according to Claim 1,
wherein the central axis of the dustfall source search region has a horizontal
15 component as an upwind direction of the wind direction and has a value V,/WS obtained
by dividing the representative fall velocity V, of the dustfall by the representative wind
speed WS as a vertical gradient, and
in the plume equation, a plume diffusion width o, in a horizontal direction and a
plume diffusion width o, in a vertical direction are calculated as the dustfall source
20 search region width at the distance on the central axis of the plume with the central axis
of the dustfall source search region as the central axis of the plume, and are used as a
horizontal component and as a vertical component, respectively.
[Claim 31
The method of searching for an unsteady dust source position of dustfall
25 according to Claim 1 or 2,
52
wherein, as the plume equation, the following Expressions (A) and (B) are used
which represent dust concentration C(x) at a distance x fiom an emission source on the
central axis of the plume using the plume diffusion widths ay and a,, the distance x from
the emission source on the central axis of the plume, a dustfall generation speed Qp, the
5 representative wind speed WS, a constant B, and a plume range defined by the plume
diffusion widths oy and a,:
[Expression (A)]
C(x) = B(Q~/~ZO~CJ,(WinSsi)d e the plume range); and
[Expressions (B)]
10 C(x) = 0 (outside the plume range).
[Claim 41
The method of searching for an unsteady dust source position of dustfall
according to Claim 3,
wherein an ellipse in which a length of a major axis is two times the larger of the
15 plume diffusion widths cr, and a, and a length of a minor axis is two times the smaller of
the plume difhsion widths o; and o, is a cross-sectional shape of the plume in a direction
perpendicular to the central axis of the plume, and
the inside of the ellipse is the inside of the plume range and then the plume
range is calculated.
[Document Type] Abstract
[Abstract]
[Problem to be Solved by the Invention] A search for a dustfall source w-hich generates
dust, and the amount of which is unsteadily changed, is performed with high efficiency
5 and accuracy.
[Means for Solving the Problem] A coefficient Bl is multiplied by dust source search
region central axis vertical cross-sectional areas Spl and Sp2 related to evaluation points
iM and iN at a coordinate point p in first and second emission source search regions y(iM,
it) and y ( ii,t ), which have central axes that extend from the evaluation points iMa nd iN
10 as a starting point in the upwind direction of a representative wind direction WD, to
calculate the assumed amounts of dust El and Ez and it is determined whether the ratio of
the assumed amounts of dust El and E2 is within a predetermined range.