PUFF: A Lagrangian Trajectory Volcanic Ash Tracking Model
This is a condensed version of a paper originally published as:
Searcy, C., Dean, K., Stringer, W., 1998, PUFF: A Lagrangian Trajectory Volcanic Ash Tracking Model, Journal of Volcanology and Geothermal Research (80) 1-16
Abstract
PUFF is a volcanic ash tracking model developed to simulate the
movement of airborne ash in near real-time following an eruption. The
model tracks particles through a Lagrangian formulation of advection,
fallout and turbulent diffusion using a random-walk technique.
Introduction
Volcanic eruptions and associated ash clouds are a natural hazard of
concern throughout the world. In the North Pacific region, eruptions
are a serious problem because of the many active volcanos located near
major population centers and heavily used air traffic routes. The high
frequency of eruptions here (about one per month) with durations
ranging from hours to a year constantly threaten the region. The area
is vast and remote making it difficult to monitor volcanos, detect
eruptions and issue warnings of potential ash hazards. This region is
shown here along with the Anchorage North Pacific (NORPAC) air traffic
region and several recently active volcanos.
The Alaska Volcano
Observatory (AVO) and the Anchorage Volcanic Ash
Advisory Center (AAWU VAAC) monitor and assess volcanos and
eruptions in this region. As an aid to monitoring techniques, the PUFF
ash tracking model has been developed for predicting ash
movement. These forecasts provide information on the location and
extent of the ash cloud when observations are not available. Results
are also used to alert concerned parties in near-real time of
potential ash cloud location usually, in less than an hour after an
eruption.
The PUFF model is mainly concerned with the tracking of "young"
eruption clouds. Young clouds are defined here as less than 48-60
hours old. These are especially dangerous to aircraft since
concentrations are highest during this period. The North Pacific
region includes some of the heaviest air traffic in the world, mostly
in the form of cargo flights. Young eruption clouds offer great
potential for loss of life, equipment, productivity and commerce
during an eruption.
The PUFF Model
PUFF is a dynamic pollutant tracer model developed to simulate the
behavior of young ash clouds. For emergency-response applications, it
requires near real-time forecast wind data to predict the movement of
the ash cloud.
The model is based on the three-dimensional Lagrangian formulation of
pollutant dispersion. PUFF initializes a collection of discrete ash
particles representing a sample of the eruption cloud and calculates
transport, turbulent dispersion and fallout for each particle. In
Lagrangian form, given a time step Dt, the position vector for
each particle is updated from time t to time t +
Dt by the
equation:
Ri(t + Dt) = Ri(t) + W(t)Dt + Z(t)Dt + Si(t)Dt
(1)
where Ri is the position vector of the
ith ash particle at time t,
W is the local wind velocity, Z is a
vector representing turbulent dispersion and
Si is the terminal gravitational fallout
vector, dependent on the ith particle's
size. The particles are driven by subsampling wind from a
four-dimensional mesoscale model at a particle's position and
calculating its next position according to the above formulation.
Lagrangian random walk formulations have been used successfully in a
variety of numerical applications. Other numerical techniques used to
model ash transport such as the VAFTAD model (Heffter and Stunder,
1993) employ a gridded Eulerian formulation. These techniques
calculate mass concentrations for a three-dimensional grid cell at
each time step. Grid cells are defined by the driving wind data, which
typically are on 6 hour time increments. While this method has proven
accurate and reliable, it suffers from the low time and spatial
resolution of gridded wind data, prohibiting tracking an ash cloud
over a short time or region such as the scale of Cook
Inlet. Subsampling wind data in a Lagrangian formulation as in the
PUFF model allows a higher resolution for tracking ash clouds during
the first critical few hours. The Lagrangian method also requires no
estimate of the mass distribution of the cloud which would not be
available in real-time during an eruption.
Wind transport
Wind transport, or advection, is calculated for each particle by
interpolating four-dimensional wind data to the particle's position
and time and transporting it to a new position at the next time step
through W(t) in equation 1. Four-dimensional wind
fields are derived from forecast meteorological data generated by the
National Centers for Environmental
Prediction (NCEP) twice-daily forecast runs. This data is
available in a variety of formats and from differing forecast
models. In the Alaska Aviation
Weather Unit (AAWU) office, PUFF is available with the AVN, NGM
and ETA models. PUFF is also run using the Unidata grid model 77,
available through University
Corporation for Atmospheric Research (UCAR).
All of these models are gridded lat/lon data sets with forecast times
at specified intervals (usually 6 hours) The vertical coordinate is
typically in millibars and uses the standard levels from 1000mb
(surface) to 100mb (approx. 16km). PUFF converts the vertical
dimension to meters by interpolating onto the geopotential height
gridded data set. In general, any data set at various grid resolutions
which can be mapped and suitably packed into a 4D (longitude,
latitude, height, time) grid is acceptable as input for PUFF.
The advection term W(t) in equation 1 accounts for the
bulk of each particle's motion, and as such, PUFF essentially computes
simple trajectories for each ash particle. In a simulation, each
particle independently subsamples the 4D wind field at its position
and time and integrates its motion as the simulation proceeds.
Turbulent dispersion
In a real atmosphere where turbulent flow is present, particles tend
to disperse with time due to small-scale fluctuations in the
field. Since gridded mean wind data cannot resolve these smaller scale
turbulent eddies, a numerical technique must be employed to simulate
particle dispersion. PUFF uses an approximation of pollutant turbulent
mixing described by a stochastic process. In a Lagrangian framework,
this is realized by superimposing a random walk for each particle on
the wind transport term. This motion is described by Z,
the second term in equation 1. This is a vector containing
three-component gaussian random numbers with zero mean and a standard
deviation which is related to the "speed", or rate, of diffusion.
In a Lagrangian framework, random walks, or "Brownian" motion provides
an approximate solution to the diffusion term in an Eulerian
frame. Thus, particles moving along a trajectory with some Brownian
motion superimposed on their path will, as a collective group, appear
to disperse. The amount of dispersion is given by a single, modifiable
parameter in the PUFF model.
Fallout
Ash fallout is included in the model through the last term,
Si in equation 1. The terminal speed is
approximated by Stoke's law and is a function of particle size. Each
particle in the PUFF model is initialized with a size based on a
gaussian distribution.
Model Description
PUFF was developed to provide a fast, near real-time model predicting
ash cloud location and spatial dimension for some period following an
eruption. PUFF basically 4D trajectories, integrating the motion of a
collection of ash particles over the simulation period. It goes beyond
standard trajectory models, however, by including fallout and
turbulent dispersion in the ash particle motion. Given a sufficient
number of representative particles to provide meaningful statistical
measurements, PUFF provides a reliable forecast tool to predict ash
cloud migration and dispersion.
Since PUFF is designed for emergency response, it makes simple
assumptions for the default values of many of its parameters,
releasing the burden to provide input, some of which is most likely
not available during the early stages of an eruption. PUFF requires
the location of the volcano and the eruption time. Other commonly set
options include simulation run-time, desired output interval, number
of ash particles, eruption duration and plume height. There are still
other, more esoteric options included in the model intended for more
detailed studies of an eruption and not usually needed in an
emergency-response setting.
To begin a simulation, PUFF initializes a collection of ash particles,
each of which have three basic properties: location (longitude,
latitude, height), size and age. The particles are given the location
of the volcano in the lat/lon dimension and assigned a height value
randomly distributed from the surface to the plume top. During a
simulation, particles are independently released over a length of time
represented by the eruption duration. The method is to randomly
release particles linearly distributed over the duration of the
eruption. Particles are tracked until the requested simulation time is
reached or until a particle settles to the surface. Output for
requested time intervals is a binary netcdf file that records the
location, height, and age of each particle.
The ash size distribution is initialized using a gaussian shape on a
logarithmic scale. The model uses two parameters which the user may
modify to describe this: the base 10 logarithm of the mean size in
meters and the logarithmic standard deviation, or spread, also in
meters. The size of each particle determines the fall speed of that
particle and PUFF only tracks particles for positive height
values. Large particles typically settle to the surface within the
first few time steps and the size distribution remaining aloft rapidly
shifts toward smaller particles.
The model currently does not consider topography when tracking ash
particles since the current wind field data sets used generally ignore
boundary-layer physics. This is not considered a limitation since the
intended use of the model is for tracking upper-level airborne ash
well away from boundary effects. Thus the surface is defined in the
model at 0 meters (1000 mb) and particles are only tracked until their
height becomes 0 or negative.
Case Study: 1992 Mount Spurr/Crater Peak Eruptions
On 27 June, 1992, the Crater Peak vent on the south side of Mount
Spurr began a period of eruptive activity after 39 years of
dormancy. This activity followed a 10 month period of elevated seismic
activity. Eruptions continued on and off for the next few months, with
significant ash produced in August and September eruption events. For
more details of these events, see Alaska Volcano Observatory (1992)
and Schneider, et al. (1995).
At 2348 on August 18 UTC, a pilot reported an ash-rich plume. The main
eruption followed an hour later at 0042 August 19 when strong tremor
was recorded on all Spurr seismic stations. By 0058 a subplinian ash
column projected ash up to 11 km altitude. Ultimately, the
radar-determined plume top reached about 14 km - pilot reports were
higher. Upper-level winds took the plume east-southeast directly over
Anchorage, where sand-sized ash fell as thick as 3 mm. Beyond
Anchorage, the axis of the plume crossed the Chugach Mountains and
followed the coast toward Yakutat Bay. At Yakutat, 550 km downwind,
ashfall was significant; at Juneau, 1000 km downwind, the plume was
sufficiently opaque to disrupt air traffic. Ashfall forced the closing
of Anchorage International Airport for 20 hours. Air-quality alerts
were issued during the ashfall and on the following day, as vehicular
traffic resuspended the ash.
The August eruption event was recorded on several NOAA 11 and 12
Advanced Very High Resolution Radiometer (AVHRR) satellite passes
Schneider, et al. (1995). The AVHRR instruments can record the Cook
Inlet region over ten times per 24 hour period. The data have a
spatial resolution of 1.1 km and a swath width of approximately 2400
km and the images are recorded in five wavelengths. For this event, 6
scenes over a 20 hour period following the eruption provide clear
images of the ash cloud as it traversed Cook Inlet and moved
east-southeast along the coast. This data set provides an excellent
source for comparison and validation of PUFF model performance.
Figure 1 depicts two AVHRR
thermal (band 4) image scenes recorded by the NOAA-12 satellite. The
first scene (left) has an image date of 1992 August 19 0331 UTC
(Julian day J232) and shows the plume 2:49 hours following the
eruption. The ash cloud is clearly distinguishable from
meteorological clouds as it traverses Cook Inlet to the east-southeast
of Mount Spurr. In these scenes, the -10° C contour is shown on the
images to delineate the ash cloud. The second scene (right) at
J232.1338 follows the eruption by 12:56 hours where the ash cloud has
moved further down the coastline in a south-eastward direction and
significantly dispersed spatially, spreading along a north-south axis.
Temperature conditions at the time of the eruption are displayed in figure 2 while wind vectors for three
vertical levels are shown in figure
3. Both figures generated data from an interpolation of the
Unidata files used in the simulation. These data are used to analyze
the movement of the ash cloud and aid in comparisons to PUFF model
output.
The atmospheric temperature profile records temperature values of
-50° C to -60° C for a range of heights between 10 and 14
km. These temperatures were observed on the first images recorded
within 3 hours of the eruption. This is consistent with the initial
pilot reports of an ash cloud spotted at 11 km and a later radar
measurement at 14 km. Temperatures on later scenes (figure 1, right) record coldest plume
temperatures at around -40° C, corresponding to profile
temperatures at 8 km.
Wind speed and direction can also provide clues to plume levels and
dispersal. Surface winds for this event are generally in a north to
northeast direction while winds turn more to the south and increase in
speed up to levels around 10 km where they are in a strong
south-eastward direction. Above this level, winds turn slightly back
to a more eastern direction and lessen in speed. The plume dispersal
pattern seen by comparing the two image scenes (figure 1) suggest plume heights at all
levels up to about 15 km. The second image shows a strong elongation
in the ash cloud in a north-south direction where upper level winds
have advected the plume to the southeast. The plume also maintains a
significant amount of ash in the eastern direction suggesting a lower
level component following winds below 5 to 10 km.
As stated earlier, PUFF is essentially a trajectory model with fallout
and turbulent dispersion included in the motion. The turbulent
diffusivity is a parameter that can be adjusted by the user. Setting
this parameter to zero ``turns off'' the turbulent motion and the
model traces out a wind trajectory for each particle. Also, setting
the mean ash size to a very small value effectively turns off the
fallout motion of each particle. PUFF was used in this manner to
depict trajectories at three altitudes (figure 4). These trajectories
demonstrate what was expected from analyzing the wind field - that the
vertical variations in wind direction create a north-south elongation
to the ash cloud.
The PUFF simulation for this event with turbulent dispersion and
fallout included is shown in figure
5. The time of each model run corresponds to the image scenes in
figure 1. Each simulation
initialized an ash column of 10000 particles linearly distributed in
height from the surface to a maximum of 16 km. The turbulent
diffusivity was 2 X 104
m2s-1 in the horizontal direction and 10
m2s-1 in the vertical direction. Ash particles
are displayed as a scatter plot color-coded according to each
particle's altitude. For reference, the -10° C contour from the
image scenes is over-lain on each figure. In the simulation,
upper-level particles are seen mostly in the southern portion of the
ash cloud where they have followed the southeast trajectory expected
from the wind profiles. Likewise, the northern portion of the ash
cloud mainly consists of lower-level ash particles following a more
eastern trajectory.
As a final example of this event, figure 6 displays six AVHRR thermal
images of the August 19 Spurr eruption with the corresponding PUFF
simulation. Since PUFF is a Lagrangian tracking model, output can be
tailored to any interval of time following an eruption. The input
parameters are the same as those in the previous examples, however,
separate ash levels are not distinguished in this figure.
Case Study: Klyuchevskoy Volcano, October 1994
Klyuchevskoy Volcano, located on the Kamchatka peninsula about 135 km
north of Petropavlovsk, Russia is one of the largest on-land active
volcanos in the world and reaches an altitude of 4,739 m above mean
sea level. It lies near the north end of a belt of 30 active
Kamchatkan volcanos that average 3 to 5 eruptions a year. Because
prevailing winds are from the west and northwest, airborne ash from
these eruptions tends to move into the heavily used North Pacific
(NORPAC) air routes that both cross and parallel the shoreline of the
Kamchatka Peninsula. These routes are used by up to 70 flights a day
carrying about 10,000 passengers and large tonnages of cargo.
The 1994 eruption of Klyuchevskoy began September 8 with minor
explosive activity. Reported ash clouds were below 9 km (30,000 feet)
- the minimum altitude for most air traffic in the region and thus was
not of immediate concern.
This activity was followed later that month by a major eruption on
September 30 (Julian day 273) at approximately 0500 UTC (Global
Volcanism Network 1994). This eruption disrupted air traffic across
the North Pacific for the next 60 hours. An eruption column of ash and
gas rose to 11 km, moving southeast into the NORPAC traffic system.
Later that day, the eruption intensified and the ash column reached 18
km by some reports. Wind speeds at the 10 to 15 km level were 40 to 50
m/sec (120 miles per hour) and generally east/southeast. The first
pilot reports came at 2005 and 1010 UTC on September 30 when a thin
layer of ash was reported at 163.5E, 51.5N. Many additional reports
were received for the next 49 hours in NORPAC flight routes R220,
R580, G583, A590 and A591.
By 1700 October 1 UTC (Julian day 274) the eruption began to subside
and was no longer considered a hazard to aviation by 1700 October
2. The major explosive phase of this eruption lasted about 36 hours
and was particularly intense for 10 hours between 1800 September 30
and 0400 October 1.
The NOAA 12 thermal band 4 satellite image (figure 7A) on Oct 1 0641 UTC shows a
distinct volcanic ash plume emanating from Klyuchevskoy and extending
east-southeast. Plume temperatures derived from this image range from
about -40° C to 0° C on the edges. Background temperatures
offshore from the volcano range from about 5° C to 20°
C. Atmospheric temperature profiles record -40° C temperatures at
around 8 km. Given uncertainties in measurements and field reports of
plume altitudes, this is an acceptable agreement with initial
estimates of 11 km. Winds in the region were generally to the
east-southeast and steady (figure 8).
The PUFF simulation for this event is shown in figure 7B. The model run began at
day 273 0500 UTC and ran for 25.67 hours to the image scene date at
day 274 0640 UTC. The simulation initialized an ash plume 12 km high
with a linear vertical distribution and continuously emitted the
particles for the duration of the simulation. Ash particles in the
figure are colored according to their altitude. It is evident from
comparing the simulation to the thermal image that the eruption has
placed ash at nearly all levels. Note particularly the dual plume in
the thermal infrared image, where the main trajectory is southeast of
the site while there is a smaller lobe that begins east and turns
southeast about 50 to 100 km offshore. This second lobe appears to be
following surface level winds where one can see from the PUFF
simulation a similar trajectory for low level particles. Higher
altitude trajectories follow a more direct southeast
direction. Eventually, nearly all levels curve east and north far
offshore at about 180E, 40N (beyond the AVHRR image region) as the
winds are changing in time and space over the model run. The
horizontal diffusivity was decreased in this simulation from the
default value of Kh = 2 X
104 m2s-1 to 8 X 103 m2s-1,
most likely a result of strong winds (greater than 50 m/sec) at the
higher altitudes.
Conclusions
This paper presented the technical background of a Lagrangian ash
tracking and prediction model. The model was designed for operational
use during an eruption to provide near real-time forecasts of ash
movement. Several examples of recent eruptions were used for
comparison to simulation results and to validate the model. These
examples show good agreement with plumes observed on satellite
images. Other sources of information such as vertical temperature and
wind profiles are useful for interpreting results. The model does not
include any source physics such as thermal buoyancy or initial
momentum and therefore could not resolve such behavior. However, in
most cases plumes cool to the ambient temperature and show wind driven
motion very soon after initial emplacement. In such conditions, this
model provides a reliable forecast tool during an eruption.
References
Alaska Volcano Observatory, 1992, Mt. Spurr's 1992 eruptions. EOS 74 (199), 217-222
Schneider, D.J., Rose, W.I., Kelly, L., 1995, Tracking of 1992
eruption clouds from Crater Peak Vent of Mt. Spurr Volcano, Alaska,
using AVHRR data. In: Keith, T. (Ed.), The 1992 eruptions of Crater
Peak Vent, Mount Spurr Volcano, Alaska. U.S. Geol. Surv. Bull. 2139,
27-36
Global Volcanism Network, 1994. Kliuchevskoi Bull. Global Volc. Net. 19 (9), 2.
Heffter, J.L., Stunder, B.J., 1993. Volcanic ash forecast and
dispersion (VAFTAD) model. Weath. Forecast. 8, 533-541
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craig.searcy@noaa.gov