# Airborne Measurement in the Ash Plume from Mount Sakurajima: Analysis of Gravitational Effects on Dispersion and Fallout

Authors: Jonas Eliasson; Junichi Yoshitani; Konradin Weber; Nario Yasuda; Masato Iguchi; Andreas Vogel
Journal: International Journal of Atmospheric Sciences
 (2014)

---

## Abstract

Volcanic ash concentrations in the plume from Sakurajima volcano in Japan are observed from airplanes equipped with optical particle counters and GPS tracking devices. The volcano emits several puffs a day. The puffs are also recorded by the Sakurajima Volcanological Observatory. High concentrations are observed in the puffs and fallout driven by vertical air current, called streak fallout. Puffs dispersion is analyzed by the classical diffusion-advection method and a new gravitational dispersion method. The fluid mechanic of the gravitational dispersion, streak fallout, and classical diffusion-advection theory is described in three separate appendices together with methods to find the time gravitational dispersion constant and the diffusion coefficient from satellite photos. The diffusion-advection equation may be used to scale volcanic eruptions so the same eruption plumes can be scaled to constant flux and wind conditions or two eruptions can be scaled to each other. The dispersion analyses show that dispersion of volcanic plumes does not follow either theories completely. It is most likely diffusion in the interface of the plume and the ambient air, together with gravitational flattening of the plumes core. This means larger boundary concentration gradients and smaller diffusion coefficients than state of the art methods can predict.


---

## Body

## 1. Introduction

Airborne observations of volcanic ash concentrations with optical particle counters and GPS tracking have recently been taken in use to study volcanic plumes [1–7].Three campaigns of airborne observations of volcanic ash and gas content of the plume from the Sakurajima volcano in Japan were performed in 2013, in cooperation between the Universities of Kyoto, University of Iceland, and University of Applied Sciences in Düsseldorf, Germany. The Sakurajima volcano has been in constant eruption since 1955; it does not emit a continuous plume but produces a series of explosion puffs, sometimes many each day [8]. The preliminary results of the first campaign were described in presentations to the IAVCEI conference July 2013 in Kagoshima, Japan [9–12].The staggering economic disaster [13, 14], inflicted upon the aviation industry by the Eyjafjallajökull eruption in 2010 and the Grimsvötn eruption in 2011, made clear the importance of ash cloud predictions. These events sparked the research program that produced the Sakurajima campaigns. It is hoped they may help to increase the accuracy of ash cloud predictions.Ash cloud predictions make use of point source atmospheric dispersion models, for the simulation of continuous, horizontal and neutrally buoyant volcanic plumes. There exist a number of atmospheric dispersion models [15], specially constructed for handling eruption problems both analytically and numerically. In [16] the VAAC Name Model is presented; it is based on the horizontal advection-diffusion equation. The abstract states that they “provide advice on extent of ash” unfortunately the extent was sometimes 40 times too great as shown later in [3]. In this model and most others, vertical diffusion is assumed zero as is discussed in [17, 18]. This is a grave simplification, turbulence is always three-dimensional, but it may be a good approximation, if there is a strong density discontinuity both on the upper side and the underside of the plume. Negative density jumps in the upwards vertical direction make the interface very stable and curb the mixing process, but they also give reason to investigate possible gravitational flattening of the plume. The small vertical mixing approximation seems to be used by the majority of researchers. Suzuki uses it in his much cited publication, [19], and there seems to be a general agreement among researchers that the problem of neutrally buoyant volcanic plumes can be treated as horizontal diffusion and many atmospheric dispersion models that use this approach are now available on the internet [15]. In recent times 3D models are coming into use and they also use the classical diffusion-advection theory.The most commonly applied method to determine the point source strength in volcanic ash plume simulations is to calculate the eruption output from the plume height. Then an equation originally due to Wilson et al. [20] and Settle [21] is used. It is very simple and most researchers seem to be of the meaning that it can be inaccurate in a variety of situations. Several modifications do exist; one is mentioned in Appendix C on diffusion theory and the Eyjafjallajökull eruption in 2010.The fluid dynamics in volcanic plumes have been studied by many researchers [22–27], but the search for a more accurate method for a plume height-mass output relation than Wilsons is still on. Numerical studies of buoyant plumes by [16, 18, 28] show that simple forms of the diffusion-advection equation can give acceptable results.In general this paper is about that airborne measurements of volcanic ash concentrations in a plume can be used as a tool in both disaster prevention and volcanology research. It is clear from the Sakurajima results that the fluid dynamics of stratified flows are important as an analysis tool; so two appendices on gravitational effects on dispersion of volcanic plumes are included. AppendixA is on gravitational flattening of plumes, a process that can easily be mistaken for diffusion, Appendix B is on streak fallout, a fallout process many times more effective than fallout by way of terminal velocity of individual grains. These results can be very different from what the classical diffusion-advection theory, summarized in Appendix C, predicts.


## 2. Airborne Measurement of the Sakurajima Plume in January 2013

### 2.1. The Measurement Campaign

In 2013 Kyoto University undertook three airborne measurement campaigns in cooperation with the University of Iceland and University of Applied Sciences, Düsseldorf, Germany. The instruments used where two DustMate industrial OPCs, two OPCs from GRIMM for scientific measurements, and a DOAS (differential optical absorption spectrometry) system for detection of sulfur dioxide. The planning, organization, quality assurance, and overview of results from the first campaign on January 15, 16, and 18 are discussed in presentations in the IAVCEI 2013 conference in Kagoshima (IAVCEI, 2013). In this paper we will discuss the observation results measured 15 January 2013 and 27 November 2013.


### 2.2. Data for the Eruption in Sakurajima 15 January 2013

The Sakurajima Volcanological Observatory (SVO) has provided minute-to-minute data of Sakurajima explosions during the campaign. In Figure1 the emission data from SVO is shown. Counting consecutive explosions as one event, Figure 1 contains 5 big events, the first 9:01. The puffs shown in Figure 1 can be identified; identification data for the 9:50 event (puff number 1) is shown in Table 1.Table 1
Identification data for puff number 1.
Data for puff number 1
Total mass, SVO
1697
Tons
Creation time
15.01.2013 09:50  9:53
Cent obs. time
15.01.2013 10:25:06
Distance from crater
23045
m
Wind (JMA*)
N   12
m/sec
Downwind time
1920
sec
*Japan Meteorological Agency.Figure 1
Sakurajima volcano, SVO ash emission data 15 January 2013 9:00–11:00.By downwind tracking, using wind data from Japan Meteorological Agency (JMA), three puffs occurring 15 January 2013 09:50–9:53 are found to be the source of the tops in Figure2.Measured puffs on 15 January 2013. (a) GPS tracks, starting in point number 221 (blue) and ending in 354 (violet), 25 points in each track, and black arrow is the radius vector from the crater. Black circles, centers of puff 1 and 2. (b) Measured TSP concentrations values in each point, filtered with the F-16 filter.
(a)
(b)The track numbers shown in the left side of Figure2 refer to the numbered tops in the right side of the picture. The OPC results are filtered with 16 convolutions of a (1/4, 1/2, 1/4) filter kernel to remove turbulent fluctuations in the raw data (Figure 4) here called the F-16 filter. The filter kernel is Gaussian; so the filtered values have concentrations gradients that fit the advection-diffusion model.Figure3 shows the big explosion puff at 9:53 o’clock. It is an almost a round ball of ash followed by a tail of gas. The ball is about 1100 meters in diameter.Figure 3
Picture of the 9:53 explosion puff byhttp://373news.com/, Kagoshima, Japan (their clock).Figure 4
F-16X-filtered results. Measured concentrations of the puffs in Figure2, X-filtered with 16 convolutions of a (1/4, 1/2, 1/4) filter kernel, X-filtering keeps ambient air and ash puffs separated.


## 2.1. The Measurement Campaign

In 2013 Kyoto University undertook three airborne measurement campaigns in cooperation with the University of Iceland and University of Applied Sciences, Düsseldorf, Germany. The instruments used where two DustMate industrial OPCs, two OPCs from GRIMM for scientific measurements, and a DOAS (differential optical absorption spectrometry) system for detection of sulfur dioxide. The planning, organization, quality assurance, and overview of results from the first campaign on January 15, 16, and 18 are discussed in presentations in the IAVCEI 2013 conference in Kagoshima (IAVCEI, 2013). In this paper we will discuss the observation results measured 15 January 2013 and 27 November 2013.


## 2.2. Data for the Eruption in Sakurajima 15 January 2013

The Sakurajima Volcanological Observatory (SVO) has provided minute-to-minute data of Sakurajima explosions during the campaign. In Figure1 the emission data from SVO is shown. Counting consecutive explosions as one event, Figure 1 contains 5 big events, the first 9:01. The puffs shown in Figure 1 can be identified; identification data for the 9:50 event (puff number 1) is shown in Table 1.Table 1
Identification data for puff number 1.
Data for puff number 1
Total mass, SVO
1697
Tons
Creation time
15.01.2013 09:50  9:53
Cent obs. time
15.01.2013 10:25:06
Distance from crater
23045
m
Wind (JMA*)
N   12
m/sec
Downwind time
1920
sec
*Japan Meteorological Agency.Figure 1
Sakurajima volcano, SVO ash emission data 15 January 2013 9:00–11:00.By downwind tracking, using wind data from Japan Meteorological Agency (JMA), three puffs occurring 15 January 2013 09:50–9:53 are found to be the source of the tops in Figure2.Measured puffs on 15 January 2013. (a) GPS tracks, starting in point number 221 (blue) and ending in 354 (violet), 25 points in each track, and black arrow is the radius vector from the crater. Black circles, centers of puff 1 and 2. (b) Measured TSP concentrations values in each point, filtered with the F-16 filter.
(a)
(b)The track numbers shown in the left side of Figure2 refer to the numbered tops in the right side of the picture. The OPC results are filtered with 16 convolutions of a (1/4, 1/2, 1/4) filter kernel to remove turbulent fluctuations in the raw data (Figure 4) here called the F-16 filter. The filter kernel is Gaussian; so the filtered values have concentrations gradients that fit the advection-diffusion model.Figure3 shows the big explosion puff at 9:53 o’clock. It is an almost a round ball of ash followed by a tail of gas. The ball is about 1100 meters in diameter.Figure 3
Picture of the 9:53 explosion puff byhttp://373news.com/, Kagoshima, Japan (their clock).Figure 4
F-16X-filtered results. Measured concentrations of the puffs in Figure2, X-filtered with 16 convolutions of a (1/4, 1/2, 1/4) filter kernel, X-filtering keeps ambient air and ash puffs separated.


## 3. Diffusion Case

### 3.1. Puff Identification and Diffusion Parameter Estimation

The tracks 1, 2, and 3 in Figure2 penetrate the big puff in Figure 3 and track 4 penetrates a smaller puff or the tail. The Gaussian distribution Appendix C can be used to find the diffusion coefficient K.Table2 shows the properties estimated for puff number 1 from the concentrations and point locations in Figure 2. The Gaussian length scale (the constant a in Table 2) and the centerline concentration are estimated by maximizing the correlation coefficient (98%) of the theoretical curve (equations (C.1) and (C.13)) and the measurements of the puff number 1 in Figure 2 and minimizing the standard error.Table 2
Diffusion properties and scaling of puff number 1.
Diffusion parameters
Puff size and grain size
Scaled puff
a (a
2 = 4 Kt)
1630
Meters
Puff mass
363*
Tons
Puff mass
17805
Tons
K
346
m2/s
SVO est.
1697*
Tons
ScaledK
2424
m2/s
Correl.
98%
e-(r/a)2
Total rad
3357*
m
Total rad
8886
m
St error
984
μgr/m3
Visible rad
1660*
m
Visibler
4395
m
CenterC
15081
μgr/m3
Eff. rad
1791*
m
Eff. Rad
4740
m
Aerosol
21
%
d
90  μm
d
50  μm
d
10  μm
d
90  μm
d
50  μm
d
10  μm
10,1
4,7
1,4
13,2
6,2
1,8
*Three explosions, 831 + 722 + 144 = 1697 tons 15.1.2013 09:50–9:52.The total radius is estimated from the nearest background concentration value, visible radius is out to the 2000μgr/m3 value, and effective radius evenly distributed total mass of 363 tons with the center concentration throughout. Here it must be noted that the radius of the original puff in Figure 3 is only 600 m so the center concentration there is 26 times Table 2 value, according to the advection-diffusion model.The measurements give PM1, PM2.5, PM10, and TSP, and these are used to estimate the grain size distribution given. Variations in grain size distribution inside the puffs are very small so average values only are given. Almost 90% of the dust is aerosol size, that is, grain size below PM10. This is the dust dangerous to jet airliners because it is carried over very large distances due to its low settling velocity. Comparing the total puff mass 363 tons to the SVO estimate we see that aerosol size grains make up 21% of the total erupted mass (1697 tons); this is far higher than in stronger eruptions. If the measured results are scaled up, according to the scaling in AppendixC, to a 4500 m high plume in a 12 m/s wind the results may be seen in Table 4. The scaled puff mass is about 18000 tons erupted in eight minutes. This may be compared to the Eyjafjallajökull 2010 eruption where eruption output was generally 6000–60000 tons/min [29].ResultingK value is shown in Table 2. It is quite lower than in stronger eruptions. When the K value is scaled up to the altitude of the Eyjafjallajökull plume discussed earlier, we get a value of K
=
2424 m2/sec. This is about 2/3 of the Eyjafjallajökull value (Table 6 and Appendix C).The calculated size of the puff is very big. The visible and total radius values show that it reaches all the way to the ground. The distance across the puff from visible concentration to visible concentration in Figure2 is 3 km.


### 3.2. The Plume as a Series of Puffs

A volcanic plume may be treated as a series of individual puffs, where each puff is an ash cloud that results from one single explosion. This is the approximation that is used when the differential equation of the advection-diffusion process is derived (AppendixC (C.1)). As the concentration of the volcanic ash does not affect the wind velocity or the mixing properties, the concentration in a given place at any given time, C
(
x
,
y
,
z
;
t
) is equal to the sum of the concentrations from all the individual puffs. This method will not be discussed further in this paper.


## 3.1. Puff Identification and Diffusion Parameter Estimation

The tracks 1, 2, and 3 in Figure2 penetrate the big puff in Figure 3 and track 4 penetrates a smaller puff or the tail. The Gaussian distribution Appendix C can be used to find the diffusion coefficient K.Table2 shows the properties estimated for puff number 1 from the concentrations and point locations in Figure 2. The Gaussian length scale (the constant a in Table 2) and the centerline concentration are estimated by maximizing the correlation coefficient (98%) of the theoretical curve (equations (C.1) and (C.13)) and the measurements of the puff number 1 in Figure 2 and minimizing the standard error.Table 2
Diffusion properties and scaling of puff number 1.
Diffusion parameters
Puff size and grain size
Scaled puff
a (a
2 = 4 Kt)
1630
Meters
Puff mass
363*
Tons
Puff mass
17805
Tons
K
346
m2/s
SVO est.
1697*
Tons
ScaledK
2424
m2/s
Correl.
98%
e-(r/a)2
Total rad
3357*
m
Total rad
8886
m
St error
984
μgr/m3
Visible rad
1660*
m
Visibler
4395
m
CenterC
15081
μgr/m3
Eff. rad
1791*
m
Eff. Rad
4740
m
Aerosol
21
%
d
90  μm
d
50  μm
d
10  μm
d
90  μm
d
50  μm
d
10  μm
10,1
4,7
1,4
13,2
6,2
1,8
*Three explosions, 831 + 722 + 144 = 1697 tons 15.1.2013 09:50–9:52.The total radius is estimated from the nearest background concentration value, visible radius is out to the 2000μgr/m3 value, and effective radius evenly distributed total mass of 363 tons with the center concentration throughout. Here it must be noted that the radius of the original puff in Figure 3 is only 600 m so the center concentration there is 26 times Table 2 value, according to the advection-diffusion model.The measurements give PM1, PM2.5, PM10, and TSP, and these are used to estimate the grain size distribution given. Variations in grain size distribution inside the puffs are very small so average values only are given. Almost 90% of the dust is aerosol size, that is, grain size below PM10. This is the dust dangerous to jet airliners because it is carried over very large distances due to its low settling velocity. Comparing the total puff mass 363 tons to the SVO estimate we see that aerosol size grains make up 21% of the total erupted mass (1697 tons); this is far higher than in stronger eruptions. If the measured results are scaled up, according to the scaling in AppendixC, to a 4500 m high plume in a 12 m/s wind the results may be seen in Table 4. The scaled puff mass is about 18000 tons erupted in eight minutes. This may be compared to the Eyjafjallajökull 2010 eruption where eruption output was generally 6000–60000 tons/min [29].ResultingK value is shown in Table 2. It is quite lower than in stronger eruptions. When the K value is scaled up to the altitude of the Eyjafjallajökull plume discussed earlier, we get a value of K
=
2424 m2/sec. This is about 2/3 of the Eyjafjallajökull value (Table 6 and Appendix C).The calculated size of the puff is very big. The visible and total radius values show that it reaches all the way to the ground. The distance across the puff from visible concentration to visible concentration in Figure2 is 3 km.


## 3.2. The Plume as a Series of Puffs

A volcanic plume may be treated as a series of individual puffs, where each puff is an ash cloud that results from one single explosion. This is the approximation that is used when the differential equation of the advection-diffusion process is derived (AppendixC (C.1)). As the concentration of the volcanic ash does not affect the wind velocity or the mixing properties, the concentration in a given place at any given time, C
(
x
,
y
,
z
;
t
) is equal to the sum of the concentrations from all the individual puffs. This method will not be discussed further in this paper.


## 4. Application of Gravitational Dispersion

Puff identification data is the same as in Figure2 in chapter 2. However, the filtering needs to be done separately for the ambient air and the ash contaminated air in the puff, as the F-16 filter is a Gaussian filter and smoothens non-Gaussian distributions. We shall apply a F-16X filter that supposes no, or very low, mixing across the concentration discontinuities in Figure 2 by introducing a fixed concentration in a point between the two air masses. The result is shown in Figure 4.The different filter does not change the overall picture except for the boundary gradients. The center concentration is unchanged. Initial radius is measured from Figure3, final size from Figure 4 and (A.8) is used for the deformation together with the data in Table 1.The result is dramatically different, especially the ash mass in the puff. The two last lines in Table3 show diffusion velocity and puff radius growth according to the measured concentration gradients.Table 3
Gravitational dispersion of puff number 1.
Gravitational deformation and size
Puff mass
14
Tons
Initial rad
600
m
Measured rad
1250
m
T
p
885
sec
B
Δ
0,00008
Δ estimated, B = 0,1
0,0008
Inversion temp diff.
0,2
°C
Final puff height
272
m
Gradient:Δ
C
/
Δ
Y
26,7
µgr/m
Diff. front velocity:K
*
/
Δ
Y
0,77
m/sec
Downwind radius increase**
1476
m
*
K from Table 2, Δ
Y thickness for mixing layer in Figure 4.
*
*Migration in downwind time in Table 1.Table 4
Eyjafjallajökull plumes in [30].
Date
April 17
May 4
May 7
May 8
May 10
Wind m/s
10
12
15
15
12
R
0 km1
2,5
2,8
2,5
2,7
2,3
2
L (90)2
10,8
10,8
7,2
7,7
7,5
Correlation
0,99
0,99
0,97
0,96
0,98
Rms km
0,61
0,68
0,52
0,60
0,50
T
p
1 secs
703
702
911
907
908
Δ
o
/
o
o
0,506
0,566
0,302
0,326
0,275
Temp°C3
2
2
4
5
2
Vel. Corr.
0,275
0,291
0,151
0,140
0,203
1Optimized, 2full width 90 km downwind, 3inversion temp. diff, Keflavik airport.


## 5. Discussion

The scaling of the Eyjafjallajökull plume in Table2 looks to be quite successful. Using the model laws for continuous plumes gives satisfactory results, when a big 3-minute plume from Sakurajima (as model) is scaled up to Eyjafjallajökull 2010 (as prototype). In disaster prevention research, scaling can be used to scale plumes, measured or simulated, up to scenarios for hazardous events that can be a help for civil protection authorities in hazard assessment.As a by-product, the self-similarity relations for ash fallout may prove a useful tool. Figure13 looks promising for a situation with stable weather when no scaling is necessary. When scaling is necessary, as in Figure 14, unscaled values cannot be supposed to show any similarity at all. In the self-similarity relations lies a possibility to improve total estimates for ash output.However, the advection-diffusion equation (C.1) has to be valid. The diffusion results in Section 3.1 give credible results; the main discrepancy is that the visible puff grows very big and it is not possible to explain the value of the resulting diffusion coefficient K.The gravitational flattening in chapter 4 gives different results. Puff mass is only a fraction of the diffusion estimate. When the boundary is no longer adapted to diffusion theory, the observed sharp boundary and the initial center concentration value are maintained; so this model produces a much smaller puff mass. In the diffusion case; the center concentration is diluted about 26 times during the almost half an hour and 23 kilometers long downwind migration. This difference between the two methods will always exist. To use diffusion models to simulate an observed plume, it simply demands more ash than is the case for gravitational flattening models.The temperature difference in an inversion big enough to facilitate the gravitational dispersion is low, indeed hardly measureable. The time constantT
p of the Sakurajima plume spreading in Table 3 compares to the Eyjafjallajökull values in Table 4; so dispersion of the puff in Figure 2 is on the same time scale as the Eyjafjallajökull plume. But assuming diffusion only, the puff also scales to the Eyjafjallajökull plume according to the diffusion-advection scaling rules in Appendix C. Working with horizontal dispersion only, gravitational flattening can therefore easily be mistaken for horizontal diffusion and vice versa.All this points to that it is necessary to merge the two models; that is, the dispersion is not either diffusion or gravitational but both. To assume zero vertical diffusion together with full horizontal diffusion does not work properly. Assuming zero vertical diffusion, Table2 mass estimate would go down to 120 tons, but that is still too high.The boundary data in Table3 is very interesting. The puff boundary gradients in Figure 4 compare much better to the actual measured gradients (the raw data) than the gradients in Figure 2, as a Gaussian filtering across boundaries flattens the concentrations gradients out in order to produce an optimal fit to the diffusion theory. X-filtering, on the other hand, supposes the measured gradients to represent the average gradient across the boundary. The three last lines in Table 3 show the speed of the diffusion process, if the K value was as in Table 2 and the gradients as in Figure 4. This shows the outward speed of the high concentrations for this value of K in Table 3 second line from bottom and that the boundary would move 1476 m in all directions in the downwind time and the puff become almost 4 km in diameter. K values thus have to be very low, only 10% or so of the diffusion vale, if gravitational dispersion is active.Some of the difference in puff size estimations in Tables2 and 3 can possibly be due to fallout. Streak fallout especially like the one observed in July 27, 2013, can explain some of the differences but not all. It cannot be assumed that a puff is sending out streak fallouts until it is under 10% of original size only 20 kilometers from the source. Such process would have been detected and described by the volcanologists. But the diffusion theory gives that the concentration has been 26 times higher than Table 2 value in the newly formed puff Figure 3. This would mean a many times higher density than in the streak fallout in Appendix B and would certainly start large streak fallouts, but not 90% of the plume disappear in unobserved streaks.If both dispersion methods are active, the plumes core undergoes gravitational deformation, and the concentrations gradients at the boundary produce a diffusion envelope around it. The fluid mechanics of this process demand much more complicated flow model than the simple Bernoulli approximation in AppendixA and will not be attempted in this paper. Besides, the inversion temperature difference in Table 3 is estimated; we would need an observed value in a combined model. But to measure such a small temperature difference is very difficult.


## 6. Conclusions

Airborne measurements in the plume from the volcano Sakurajima in Japan show very good results that can be used to find the properties of volcanic puffs. To model the dispersion, two methods have to be considered, advection-diffusion method and gravitational dispersion. The fallout can be streak fallout due to vertical gravity currents.Gravitational Dispersion. This is a new method, only the in Appendix A approximate theory exists. Modeling and dispersion prediction according to this method need very accurate temperature data from the plume center, normally not available. This method explains why there is little or no vertical dispersion but plumes and puffs flatten out horizontally due to density currents instead. It also explains how plume boundaries with large concentration gradients can spread horizontally without any diffusion. Gravitational dispersion is a nonlinear process and scaling is not possible. The approximate theory assumes that plume (or puff) center concentrations are preserved which leads to much smaller estimates for the erupted mass than diffusion models. However, diffusion cannot be totally absent. Over large distances these two models have to be combined.Streak Fallout. This is a new fallout model; the theory for it is in Appendix B. Streak fallouts carry large quantities of ash to the ground by vertical gravity currents containing all grain size fractions. These currents may be considered as chunks of the ash cloud that fall to the ground with higher velocity than the terminal fallout velocity of the grains in still air. The vertical gravity currents have similarities to microburst and downburst winds but do not reach as high wind velocities as they do. Streak fallouts can deplete the mass in the plume much faster than ordinary fallout can.Advection-Diffusion Method. Sakurajima eruptions scale to larger eruptions in a convincing manner when this method is used. The scaling also produces self-similarity rules for ordinary fallout that may prove useful in fallout studies (Appendix C). However, the diffusion coefficients that have to be used in the modeling to explain observed dispersion of the plumes are too big. This leads to an overestimation of the erupted mass, especially PM10 and smaller. The commonly used approximation of zero vertical diffusion keeps the overestimation down, but it is still there.Satellite pictures can also be used to estimate diffusion coefficients by tracking the visible boundary of the plume, as demonstrated by using the data for the Eyjafjallajökull eruption in 2010 in AppendixC. Such estimates of the K value are presumably to high as the same data fits very well to the gravitational theory as shown in Appendix A. Center concentrations in the plume will be unaffected by horizontal diffusion for a long time, but fallout, especially streak fallout, will deplete the total mass in the plume.The dispersion of volcanic plumes is advection-diffusion combined with gravitational flattening. The gravitational flattening is in the plumes core, the diffusion in an outside envelope. Considerable research may be needed in order to establish the new dispersion theory. New data like temperature may be needed, and one second sampling frequency in the OPC measurements is certainly a help.When diffusion models are used and gravitational flattening is entirely left out, theK values have to be very high. Taking the visible limit as 2000 μgr/m3 the ash outside these limits will become a larger and larger part of the total flux as the concentration gradients grow smaller in the downwind direction. This makes the simulated plumes an order of magnitude too wide. The gravitational effects need to be included in ash cloud predictions.



---

*Source: 372135-2014-10-19.xml*