NHESSNatural Hazards and Earth System SciencesNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus PublicationsGöttingen, Germany10.5194/nhess-17-861-2017High-resolution modelling of atmospheric dispersion of dense gas using TWODEE-2.1: application to the 1986 Lake Nyos limnic eruptionFolchArnauafolch@bsc.eshttps://orcid.org/0000-0002-0677-6366BarconsJordihttps://orcid.org/0000-0001-5550-1986KozonoTomofumiCostaAntoniohttps://orcid.org/0000-0002-4987-6471CASE Department, Barcelona Supercomputing Center (BSC), Barcelona, SpainDepartment of Geophysics, Graduate School of Science, Tohoku University, Sendai, JapanIstituto Nazionale di Geofisica e Vulcanologia (INGV), Sezione Bologna, ItalyArnau Folch (afolch@bsc.es)13June201717686187924October201621December20163May2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://nhess.copernicus.org/articles/17/861/2017/nhess-17-861-2017.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/17/861/2017/nhess-17-861-2017.pdf
Atmospheric dispersal of a gas denser than
air can threat the environment and surrounding communities if the terrain and
meteorological conditions favour its accumulation in topographic depressions,
thereby reaching toxic concentration levels. Numerical modelling of
atmospheric gas dispersion constitutes a useful tool for gas hazard
assessment studies, essential for planning risk mitigation actions. In
complex terrains, microscale winds and local orographic features can have a
strong influence on the gas cloud behaviour, potentially leading to
inaccurate results if not captured by coarser-scale modelling. We introduce a
methodology for microscale wind field characterisation based on transfer
functions that couple a mesoscale numerical weather prediction model with a
microscale computational fluid dynamics (CFD) model for the atmospheric
boundary layer. The resulting time-dependent high-resolution microscale wind
field is used as input for a shallow-layer gas dispersal model (TWODEE-2.1)
to simulate the time evolution of CO2 gas concentration at different
heights above the terrain. The strategy is applied to review simulations of
the 1986 Lake Nyos event in Cameroon, where a huge CO2 cloud released by a
limnic eruption spread downslopes from the lake, suffocating thousands of
people and animals across the Nyos and adjacent secondary valleys. Besides
several new features introduced in the new version of the gas dispersal code
(TWODEE-2.1), we have also implemented a novel impact criterion based on the
percentage of human fatalities depending on CO2 concentration and exposure
time. New model results are quantitatively validated using the reported
percentage of fatalities at several locations. The comparison with previous
simulations that assumed coarser-scale steady winds and topography
illustrates the importance of high-resolution modelling in complex terrains.
Introduction
The atmospheric dispersion of gases (of natural, accidental or intentional
origins) can be very hazardous to life and the environment. In industry,
historic examples of tragic accidents include the dioxin release in Seveso
(Italy, 1976), the methyl isocyanate in Bophal (India, 1984), or the
petroleum gas explosions in Mexico City (Mexico, 1984), among several others
e.g.. From the point of view of natural hazards, cold
CO2 gas released from natural Earth degassing can be of concern because,
being denser than air at standard temperature and pressure, CO2 gas
clouds hug the ground and spread downslopes governed by local topography and
near-surface winds. Under particular conditions (e.g. atmospheric stability),
gas can accumulate in topographic depressions reaching concentration levels
toxic for humans and animals. For example, many gas manifestations in Central
and Southern Italy, characterised by persistent CO2 emissions, have
caused several periodic accidents . Another case of
natural origin, much rarer than diffuse emissions but potentially much more
hazardous, are limnic eruptions triggered during overturning of CO2-rich
volcanic lakes e.g., such as the eruptions that occurred
at lakes Monoun and Nyos (Cameroon) in 1984 and 1986, respectively.
The most tragic event occurred on 21 August 1986 at Lake Nyos, when a
CO2 gas cloud spread across the surrounding valleys, suffocating
inhabitants and animals. On the 30th anniversary of this disaster, the
Commission on Volcanic Lakes of the International Association of Volcanology
and Chemistry of the Earth's Interior (IAVCEI) organised the workshop
“CVL9-Cameroon” (Yaounde, 14–20 March 2016) to gather scientific experts
from several disciplines with the objective of reviewing the groundbreaking
research advances in that field and discuss future road maps for research and
risk assessment and mitigation . One of the outcomes from
this workshop was that, despite the successful mitigation measures taken at
these two lakes (e.g. installation of degassing pipes, relocation of local
communities to safer settlements) reducing the level of hazard notably, there
is not yet a quantitative hazard assessment from volcanic lakes in Cameroon
or elsewhere in Africa (e.g. Lake Kivu in Democratic Republic of Congo and
Rwanda). In this regard, dense gas dispersal simulations and characterisation
of eruption/gas emission scenarios constitute the backbone of a probabilistic
quantitative hazard assessment.
Few studies have been conducted to simulate atmospheric dispersion of dense
CO2 clouds from natural Earth degassing
e.g..
In particular, have recently used the TWODEE-2.0 model
to simulate the CO2 cloud from the 21 August
1986 Lake Nyos limnic eruption by considering various scenarios for cloud volume
and eruption duration estimated from previous studies . For their simulations, considered a
digital terrain elevation model with a resolution of 90 m. Results
evidenced the strong effect of the topography and local wind field, leading
to different gas flow patterns across the different valleys of the complex
topography of the area. Despite some scenarios could reproduce lethal CO2
concentrations in many of the sites where fatalities did actually occur,
these simulations were unable to capture the full dispersal pattern given
some model limitations including, but not limited to, steady winds and gas
emission rates or insufficient accuracy of near-surface winds. This later
aspect is particularly critical on very complex terrains, where local-scale
(tens of metres) wind patterns and the resolution of the digital elevation
model (DEM) can have a strong influence on model results.
Based on all these previous considerations, the objective of this paper is to
address high-resolution (tens of metres) numerical modelling of CO2
atmospheric dispersal in complex terrains. To this purpose, we introduce a
methodology for local wind field characterisation based on transfer functions
that couple mesoscale numerical weather prediction (NWP) models with a
microscale Reynolds-averaged Navier–Stokes (RANS) computational fluid
dynamics (CFD) model for the atmospheric boundary layer. The resulting
high-resolution time-dependent wind field is given as input to the TWODEE
shallow-layer gas dispersal model to simulate the evolution of gas
concentration with time at different heights above the terrain. In addition
to coupling with mesoscale/microscale 4-D meteorological models,
the TWODEE-2.0 code has been improved (updated to version 2.1) in order to
overcome a few limitations, including the option to easily describe
time-dependent gas sources, heterogeneous terrain roughness, and assessment
of the impact through a novel probabilistic approach that estimates the
percentage of fatalities depending on gas concentration and exposure time
(dose) at near-ground levels. The new version of the code is applied to
reconstruct gas dispersion from the 1986 Lake Nyos event compared with
previous simulations , and results are used to illustrate
the model gain on the time evolution of the gas source.
In this paper, Sect. overviews the main
characteristics of the TWODEE model and the modifications introduced to
account for heterogeneous high-resolution 4-D wind fields, time-dependent
source term, and terrain variable roughness. The new probabilistic impact
criterion for TWODEE model validation is also presented. Section summarises the events occurred at Lake Nyos and surroundings
during 21 and 22 August 1986 and the results (and limitations) from previous
simulation studies . A novel strategy for high-resolution
local wind field characterisation on very complex terrains is presented on
Sect. . The methodology uses the concept of transfer
functions to couple the mesoscale Weather Research and Forecasting (WRF)
model with the CFD code Alya
adapted to atmospheric boundary layer flows . Section shows the TWODEE-2.1 model results for the 1986 Lake Nyos
case of study and discusses how and why the model new features increase the
accuracy of simulations. In addition, we also perform a model parametric
study varying the source term to constrain its intensity, evolution, and
duration. Finally, Sect. summarises and discusses the
main results and future developments.
The TWODEE dense gas dispersal model
TWODEE-2 is a FORTRAN90 code for the
atmospheric dispersal of dense gases based on the shallow-layer approach.
Under the assumption that h/L≪1 (h being the gas cloud depth and L a
characteristic length), the 2-D shallow-layer approach allows a compromise
between more realistic but computationally demanding 3-D CFD models and
simpler 1-D integral models. The TWODEE family models build on the depth-averaged equations for a gas cloud resulting from mixing a gas of density
ρg with an ambient fluid (air) of density ρa (ρg>ρa).
The integration of volume, mass, and momentum balance equations over the
mixed cloud depth from the ground to the top of the cloud yields to
e.g.∂h∂t+∇⋅(hu‾)=ue+us,∂h(ρ‾-ρa)∂t+∇⋅(hρ‾-ρa)u‾=ρaue+ρgus,∂hρ‾u‾∂t+∇⋅hρ‾u‾⊗u‾+12S1∇g(ρ‾-ρa)h2+S1g(ρ‾-ρa)h∇e+12ρ‾CD|u‾|u‾+F+κρa∂∂t+va∂∂x+wa∂∂y⋅h(u‾-ua)=ρaueua,
where h is the cloud depth (defined as the height below which 95 % of
the buoyancy is located), ρ‾ is the depth-averaged cloud
density, u‾=(u‾x,u‾y) is the
depth-averaged cloud velocity, ua)=(va,wa) is the
ambient fluid (air) velocity vector, ue is the ambient fluid
entrainment velocity modulus, us is the gas inflow velocity
modulus (source term), e=e(x,y) is the terrain elevation, CD
is a drag coefficient, F is the turbulent shear stress force (per
unit area), and S1≈0.5 and κ are semi-empirical parameters.
The terms in the momentum equation (Eq. ) include the local time
derivative, the convective term, the pressure gradient (assumed hydrostatic
although the density profile can be non-uniform), the effect of terrain
slope, the surface shear stress (depending on the terrain roughness and
characterised by the drag coefficient), the force per unit area exerted by
turbulent shear stress, and, finally, the leading edge terms that account for
interaction among dense and ambient fluids. Given closure equations for the
drag coefficient CD, shear stress force F and
entrainment velocity ue, the set of
equations above can be resolved numerically to obtain cloud height and
vertically averaged density and velocity depending on terrain, source term
(definition of us), and ambient fluid velocity (wind field).
Although TWODEE is a shallow water model, it can also estimate the vertical
density profile from the depth-averaged density ρ‾ assuming an
empirical exponential decay :
ρ(z)=ρa+2S1(ρ‾-ρa)exp-2S1zh0≤z≤h,
from which the vertical concentration profile c(z) (expressed in
ppm) and the dosage Do(t,z) during a time interval (0,t)
can be computed as
c(z)=cb+(106-cb)ρ(z)-ρaρg-ρa,Do(t,z)=∫0tc(z)ndt,
where cb is the background concentration (in
ppm) and n is the so-called toxicity exponent.
TWODEE-2.1
The TWODEE code version 2.0 has been improved so that the
upgraded version 2.1 can deal with the following:
It can handle time-dependent heterogeneous wind fields furnished by mesoscale or microscale wind models. The previous code version admitted only a steady homogenous
wind profile or heterogeneous wind fields furnished by a meteorological
processor (included in the code distribution package) based on a diagnostic
wind model DWM. The DWM generates a gridded wind field
from input data (observations) at a point of the domain by adjusting the
domain-scale mean wind for terrain effects and performing a divergence
minimisation to ensure mass conservation. This implies an obvious limitation
if winds vary (e.g. during long-lasting emissions) or in very complex
terrains or large domains, where the winds adjusted by DWM can be notably
different depending on the location of the points where observations are
available. In contrast, the updated TWODEE code version can read outputs from
either the WRF mesoscale model (see
Sect. ) or from CFD microscale model simulations. In the case of
WRF, a meteorological pre-processor reads the WRF model outputs for a
user-defined time interval (nt WRF output time steps) and performs an
interpolation from the WRF native grid (Arakawa staggered C grid in the
horizontal, pressure levels for the vertical) to a series of user-defined z
cuts on a terrain-following regular grid. In the case of microscale
simulations, the meteorological pre-processor reads outputs from the
ALYA-CFDWind model (see Sect. ) and, for each WRF time slice,
performs the mesoscale-to-microscale downscaling using
transfer functions as explained in Sect. . This results in nt
downscaled wind fields on the same set of terrain-following z cuts. Whichever
the approach considered for the wind field (i.e. mesoscale WRF or WRF
downscaled with ALYA-CFDWind), TWODEE-2.1 reads winds
at the gridded z cuts and then interpolates to its computational mesh at a
user-defined reference height.
TWODEE-2.1 can easily handle multiple point sources or time-dependent source terms by
using piece-wise constant pulses of arbitrary duration (the previous version had to use the “restart” option).
It can deal with multiple input file formats for DEMs and terrain roughness. In addition, the model output has also
been generalized including netCDF and kml output file formats.
It can assess the impact of dense CO2 gas dispersal. According to the Occupational Safety and Health Administration (OSHA),
the long-term exposure limit (LTEL) of CO2 is set at air concentrations of 0.5 % (5000 ppm) for exposures up to 8 h per day,
whereas the short-term exposure limit (STEL) is set at air concentrations of 3 % (30 000 ppm) for exposures up to 15 min.
However, at higher concentrations/dosage, CO2 causes several adverse health effects when inhaled. Experience shows that CO2 air
concentrations of around 5 % (50 000 ppm) produce heavy breathing, sweating, quicker pulse, weak narcotic effects, and headaches.
Under these concentrations, the exposure time to avoid the development of adverse health symptoms is only a few minutes. For example,
a 30 min exposure to 5 % concentration (50 000 ppm) produces intoxication manifested as headaches, dizziness, restlessness,
breathlessness, increased heart rate and blood pressure, and visual distortion. At around 10 % concentration (100 000 ppm)
humans are affected by respiratory distress, impaired hearing, nausea, vomiting, and loss of consciousness in only 10 min.
Finally,
CO2 air concentrations > 15 % (150 000 ppm) are considered lethal causing coma, convulsions, and rapid death. The UK
Health and Safety Executive (HSE; http://www.hse.gov.uk) developed an assessment of dangerous toxic substances, including CO2, defining
the specified level of toxicity (SLOT) and the significant likelihood of death (SLOD) depending on concentration and duration of
exposure . Considering these values , we assume a cumulative normal distribution for the
percentage of human fatalities:P(c,d)=121+erfc-μ2σ,μ=a0+b01+dc0,σ=a1+b11+dc1,where P is the probability of death, c is the CO2 concentration
(expressed in %), d is the exposure duration (expressed in minutes), and
ai and bi are empirical constants. After calibration of
Eq. () with the HSE tabulated values (assuming SLOT at 3 %), we
obtained the following values for the constants: a0=5.056, b0=17.885,
c0=0.357, a1=0.662, b1=2.421, and c1=0.354. Results are shown in
Fig. , plotting the percentage of fatalities (probability
of death in %) as a function of CO2 concentration for different exposure
durations. An impact criterion based on these empirical curves was added in
TWODEE-2.1 to compute, at each point of the computational domain, the
predicted percentage of fatalities at user-defined heights.
Percentage of fatalities (probability of death in %) depending on
exposure duration (in min) according to Eq. (). Values are shown
for different values of CO2 concentration ranging from 7 to 14 %
vol.
The 1986 Lake Nyos event and previous modelling results
Lake Nyos (Fig. ) is one of the ∼ 40 volcanic
lakes scattered along the 1600 km long Cameroon Volcanic Line
e.g.. This lake became famous worldwide on Thursday
21 August 1986 after the occurrence of the most tragic limnic eruption ever
registered. During few (< 5) hours, a huge (0.1–1 km3) CO2
gas cloud released during the Lake
Nyos overturning spread downslopes from the lake (1100 ma.s.l.),
filling up the underlying Nyos valley and suffocating around 1700 people and
3000 cattle e.g.. Evidence from eyewitness reports
indicated that the cloud was directed primarily W-NW at around 21:00 LT
(20:00 UTC) affecting the bottom valleys of Cha and Fang (see
Fig. ), but without causing reported deaths at the latter
location . Following this initial dispersal phase, the gas
cloud direction shifted towards NE, probably as a consequence of a sudden
wind veer, filling up the Nyos valley down to the Subum village
(∼ 10 km line of sight from the lake), where the largest number
of casualties occurred. Deaths in humans and animals (including birds)
occurred at a distance of up to 20 km across the main and adjacent
secondary valleys .
Map of Cameroon showing the Lake Nyos area (red square).
Topographic map of the area around Lake Nyos showing elevation
contours (in m a.s.l.). The locations listed in
Table are shown by halved circles coloured according the
percentage of fatalities (in %) reported by .
List of affected points with coordinates and percentage of observed
fatalities. (x,y) coordinates are in UTM zone 32N (datum WGS84). Points
starting with an L have been digitalised from ; points
starting with an N were obtained by the authors after interviewing survivors
in situ. Comments as reported by in their Table 1.
collected multiple testimonies of survivors that allowed
the authors to reconstruct the timeline of the event, locating where
casualties occurred, and constructing a map of the areas impacted by the
disaster (see Table and Fig. 1 in ). It
should be stressed that the percentages of fatalities reported by
resulted from posterior interviews by anthropologists and
are subject to large uncertainties related to translation and interpretation,
approximate location of sites, and actual number of casualties.
Notwithstanding these limitations, data inferred from eye witnesses
constitute the only source of information available for indirect model
validation given the lack of any wind or gas concentration measurement at
Nyos on that time. At present, the level of risk at lakes Nyos and Monoun has
decreased notably after the successful deployment of degassing pipes in March
2001 and February 2003, respectively. The progressive gas removal resulted in
considerable deepening of the level of gas-rich water in a short period of
time . However, there is still the recognised
need to perform a quantitative CO2 hazard assessment for several
reasons, including the possibility of future gas build-up or a breakthrough
of the dam built at the northern shore of the lake. Thus, for example,
estimated that dam break could cause a sudden drop in lake
level by 40 m, followed by decompression and inevitably a new gas
burst.
Previous modelling results from scenario II
(4 h of gas emission assuming a constant mass flux of 1.4×105kgm-2d-1 from a diffuse source of 235×235m2). Left: maximum CO2 concentration (%vol.) achieved
at 1 m height. Right: percentage of fatalities (in %) predicted by
the model applying Eq. () at 1 m height. Halved circles
show the actual reported percentages at locations using the same colour
scale.
have recently used the TWODEE-2.0 model to simulate four
different scenarios (released gas mass ranging from 0.29 to 1.95 Tg,
wrongly reported in their table as Gg) using a 90 m resolution
DEM. Surface wind data resulted from applying the DWM mass-consistent
pre-processor to a constant wind profile extracted from the closest point of
the NCEP/NCAR Reanalysis 1 . As a result of this
limitation, none of their simulations was able to capture properly the cloud
dispersion pattern, strongly influenced by a sudden wind veering.
Figure shows, for illustrative purposes, results for
their scenario II, the one that better reproduced the observations (see
Fig. 5 in , for other scenario results). In the following
sections, these previous simulations are revisited considering a higher DEM
accuracy (30 m instead of 90 m; from ASTER G-DEM, a product
of METI and NASA) and high-resolution transient microscale surface winds
derived from downscaling the Advanced
Research WRF (WRF-ARW) mesoscale winds with the ALYA-CFDWind
model.
WRF-ARW model configuration and physical parameterisations used for
the 1986 Lake Nyos simulations.
WRF-ARW configuration Model version3.4.1Initial and lateral BCsNCEP/DOE Reanalysis 2DomainsOne parent and four nestsHorizontal resolutions81 km (parent) and 27, 9, 3, and 1 km (nests)Horizontal grid sizes110 × 110 (parent) and 136 × 127, 121 × 133, 181 × 166, and 151 × 151 (nests)Vertical levels60 levels, with top at 70 hPaSimulation length48 h (spin-up of 24 h)Time step180 s (parent), ratios of 1 : 3 for nestsParameterisationSchemeMicrophysicsWRF single-moment six-class (WSM6) CumulusModified Kain–Fritsch (disabled for 1 km nest) Surface layerMM5 Monin–ObukhovLand surfaceUnified Noah land surface model (LSM) Planet boundary layerMellor–Yamada–Janjic (MYJ) Long-wave radiationRapid radiative transfer model (RRTM) Short-wave radiationDudhia Wind field characterisationMesoscale wind modelling using WRF-ARW
The WRF is a fully compressible, nonhydrostatic mesoscale NWP model and
atmospheric simulation system designed to serve both operational forecasting
and atmospheric research needs . The model uses finite
differences schemes on a staggered horizontal Arakawa C grid and a
terrain-following vertical coordinate system to solve the atmospheric flow.
Here, the version 3.4.1 of the dynamical solver WRF-ARW was configured with
the physical parameterisations and schemes summarised in Table .
For the Nyos application, the WRF-ARW simulation starts on Thursday 21 August
1986 at 00:00 UTC lasting 48 h (around 18 h are allowed for
model spin-up). Initial and daily (four times) boundary conditions driving WRF
come from the NCEP/DOE Reanalysis 2. Figure shows the
five domains used, consisting of one parent grid at 81 km horizontal
resolution, covering the African continent, and four nested domains at 27, 9, 3,
and 1 km horizontal resolutions, all centred around Lake Nyos. The
regional synoptic situation on Thursday, 21 August 1986 is illustrated in
Fig. , showing WRF-ARW results for the first nest domain
(27 km resolution) at different times. It can be observed how a low-pressure (< 800 hPa at 2000 m) region and its cyclonic
circulation located NE of Cameroon coexists with strong winds from both south and
north and a region of weak winds over NW Cameroon at around 16:00 UTC
(Fig. a). The simulations indicate that this situation
lasted for about 6 h until 22:00 UTC, when winds over Nyos became
stronger and pointed SE. In contrast, near-surface winds followed a very
different pattern (Fig. ) reflecting the topography-induced
forcing at lower atmospheric levels. However, given the orographic
complexity, the WRF-ARW results at 1 km resolution (inner nest) are
still insufficient for driving high-resolution gas transport simulations,
indicating the need for an ulterior downscaling.
WRF-ARW domains for the Nyos run. The model configuration consists
of one parent domain (d01) at 81 km horizontal resolution and four nests
(d02 to d05) at 27, 9, 3, and 1 km resolution centred at the Lake Nyos
(red triangle, not on scale). Colour contours indicate the WRF-ARW model
topography at each resolution.
Synoptic meteorological situation according to the WRF-ARW
simulation showing pressure contours (hPa) and wind vectors
(ms-1) for domain d02 (first nest, 27 km resolution
domain) at 2000 m height above sea level. Results for 21 August 1986
at 16:00 (left), 20:00 (centre), and 24:00 (right) UTC. The red triangle shows
the location of the Nyos Lake. For clarity, only a few model wind vectors are
shown.
Local meteorological situation according to the WRF-ARW simulation
showing terrain height contours (m a.s.l.) and wind vectors
(ms-1) for domain d05 (last nest, 1 km resolution domain)
at 10 m above the surface. Results for 21 August 1986 at 16:00
(left), 20:00 (centre), and 24:00 (right) UTC. The red triangle shows the
location of the Nyos Lake. For clarity, only few model wind vectors are
shown.
Microscale wind modelling using ALYA-CFDWind
ALYA e.g. is a high performance computing
(HPC) multi-physics parallel solver based on a finite element method
able to run with thousands of processors with an optimal scalability. Within
this multi-physics general framework, implemented a solver
for the atmospheric boundary layer based on the RANS equations and a κ-ϵ turbulence model
adapted to atmospheric flows in complex terrains. This model, called
ALYA-CFDWind, can handle thermal coupling assuming the Boussinesq
approximation although here we constrain to neutral atmospheric stability for
simplicity. The ALYA-CFDWind module, originally developed in the context of
wind energy, includes Coriolis effects, a consistent limitation of the mixing
length, a wall law for atmospheric boundary layers (logarithmic profile
depending on terrain roughness and wind friction velocity), automatic
meshing,
and generation of boundary conditions for atmospheric boundary layer wind
profiles over a flat terrain. In order to have consistent inflow boundary
conditions (i.e. flat terrain inflow profile) and also to prevent flow
recirculation at the outflow boundary, the ALYA-CFDWind computational domain
is made of an external flat buffer designed to accommodate the flow, an
adjacent transition zone, and an inner higher-resolution zone with the real
topography and where the flow is actually computed.
For the Nyos case, the ALYA-CFDWind computational domain consists of an inner
zone of 20×20km2 at 50 m horizontal resolution, a
transition zone of 15 km, and a flat buffer zone of 10 km to
accommodate the flow. Along the vertical direction, the structured hexahedral
grid extends up to 5 km above the terrain with 64 vertical layers
growing geometrically in size from 0.5 m at surface to 250 m at
the top of the computational domain. The resulting computational mesh (see
Fig. ) has a total number of grid points of about 30 million.
The Coriolis force was set to that of a latitude of 6∘ N and the
maximum mixing length was calculated depending on the wind at top as in
. As boundary conditions, we prescribed the wind at top
(geostrophic wind) to a reference value of 10 ms-1 considering
different geostrophic wind directions (sectors) at 15∘ intervals. One
ALYA-CFDWind simulation was performed for each reference direction of the
geostrophic wind (i.e. 24 different runs are necessary to scan all
possible geostrophic wind directions). Assuming self-similarity, these
reference runs can be scaled to actual velocity and interpolated in direction
during the meso-to-micro downscaling strategy (see Sect. )
depending on the mesoscale (WRF) time-dependent geostrophic wind direction
and intensity.
Meso-to-micro downscaling strategy
Mesoscale NWP models like WRF-ARW can be used to forecast winds at horizontal
resolutions down to around 1 km. This grid resolution may be
insufficient to drive subsequent gas dispersion simulations over complex
terrains, where sub-grid-scale topographic features can alter near-surface
winds and therefore the resulting gas dispersal pattern. For this reason, a
meso-to-micro downscaling strategy may be necessary in order to capture
wind-forcing effects caused by the local sub-grid topography.
Detail of the ALYA-CFDWind computational mesh (50 m
horizontal resolution) around the Nyos Lake. The bottom-left inset shows the
extent of the computational domain composed of three differentiated zones, flat
buffer (red), transition (pale blue), and inner domain (green) at
50 m resolution containing the detailed terrain information. The
arrows indicate the approximate gas flow path according to observations.
At present, model downscaling is the subject of active research within the
atmospheric and wind engineering communities, with two well-differentiated
strategies dominating the scene. On the one hand, statistical downscaling
methodologies e.g. build on
finding correlations between global/regional model simulations and
observations during long periods of time in order to identify patterns used
to forecast in time and space by extrapolation. This has proven to be
effective for some applications (e.g. wind farm power production forecast)
but requires long series of wind observations that, for the application
considered here, do not exist. On the other hand, dynamical or physical
downscaling (e.g. ) couples different nested models so
that the outer mesoscale model furnishes boundary conditions to the inner
microscale solver at each model time integration step. The inner microscale
model can range in complexity from simpler mass-consistent diagnostic models
to a CFD solver. This option is clearly more attractive but, apart from the
higher computational cost, still presents some challenges related to not
well-resolved inconsistencies in the physics of models across scales. On top
of this, a pure dynamical downscaling approach becomes computationally
prohibitive for hazard assessment purposes, where climatically representative
wind series have to be considered (note that this implies thousands of
coupled simulations in order to statistically cover all meteorological
situations with its associated probability). Given these constrains, we adopt
an intermediate physical–statistical strategy based on transfer functions, a
concept inspired on methodologies used for microscale wind resource
assessment over regional scales e.g..
The idea behind transfer functions is simple. Given a mesoscale wind field
(in our case WRF-ARW at 1 or 3 km grid resolution, see Sect. ) and a set of microscale wind fields, each characterised by a
reference wind direction ϕ and intensity (in our case 24 ALYA-CFDWind
runs at 50 m grid resolution and 15∘ geostrophic wind binning,
see Sect. ), the transfer functions determine a new
(downscaled) wind field as
udown=f×uWRF→CFD=uCFDθ<uCFDθ>R×uWRF→CFD,
where udown(x,y,z,t) is the resulting downscaled wind velocity,
f=f(θ,t) is the point-dependent transfer function at time t,
uWRF→CFD is the WRF wind velocity interpolated to the (finer)
microscale mesh, uCFDθ is the ALYA-CFDWind velocity for a
reference wind direction θ, and <uCFDθ>R is the
CFDWind velocity for the same direction θ averaged over a radius of
influence R (of size similar to that of the WRF cells). Note that, by
construction, at each point, the CFD field uCFDθ averaged over
its circumference of influence R equals the WRF velocity interpolated at
that point. In other words, the resulting downscaled wind field coincides on
average (over a WRF cell) with that of the mesoscale model but, at the same
time, it has all the local wind fluctuations around this mean (caused by the
microscale topographic forcing) which cannot be captured by the (coarser)
mesoscale grid. Moreover, the methodology is thought to preserve flow
characteristics due to the thermal stratification present in the WRF model.
A central point in this hybrid downscaling methodology is how to determine
the reference wind direction θ and then how to link it consistently
with the mesoscale flow. For this, we adopt the following strategy to obtain
downscaled 2-D fields at given heights zt above the terrain:
The first step consists of extracting from the microscale computational domain (ALYA-CFDWind) a series of 2-D plains
Ω2-D at user-defined heights above the terrain (e.g. zt=2, 10, and 50 m). Each of these Ω2-D
planes is then decomposed in a series of structured patches or segments Sij, allowing for some overlap at the borders of
the sub-domains (i.e. ∪Sij=Ω2-D; ∩Sij≠∅). In particular, we consider here one squared
patch around each WRF mass point with sizes 2dxWRF×2dyWRF, dxWRF×dyWRF being the WRF cell area (see Fig. ).
For each sub-domain Sij, the reference wind direction θ at time t is computed as the averaged WRF velocity
over the segment. Note that, for small computational domains or flat terrains, few variations in θ are expected across
different segments Sij. However, over large areas or in very complex terrains, synoptic-scale effects may result on variations of θ at different segments.
For each sub-domain Sij and time t, the microscale (ALYA-CFDWind) reference solution uCFDθ
is determined by performing a linear interpolation between the two reference runs ϕ1 and ϕ2 that limit the bin direction containing
θ (i.e. θ∈(ϕ1,ϕ2)). For example, if for a given segment and time one has θ=5∘, then
the bin-bounding solutions uCFD0 and uCFD15 (i.e. precomputed solutions for θ=0∘ and
θ=15∘, respectively) are combined to obtain uCFD5.
A smoothing operation in the overlap regions between neighbouring sub-domains Sij is performed. This is necessary because
different values of θ in adjacent segments can result on discontinuous values of uCFDθ across segments. In
particular, we consider a simple weighted interpolation in the regions with overlap.
Finally, the transfer functions is applied using Eq. () to scale the microscale wind modulus and obtain udown.
Segmentation strategy adopted for downscaling on a 2-D plane
Ω2-D. A patch or segment Sij is defined for each WRF-ARW
grid mass point (black squares) containing many ALYA-CFDWind grid points (red
small squares). The last plot shows the overlapped region.
Wind vectors at 10 m above terrain as given by WRF-ARW at
3 km resolution (left column) and the downscaling (right column) for
21 August 1986 at 18:00 (top), 19:00 (middle), and 21:00 (bottom) UTC. For
visualisation and point-to-point comparison purposes, WRF results have been
interpolated to the CFD mesh and, when necessary, extrapolated below its
lower level. The red triangle shows the location of the Lake Nyos.
Figure compares the 3 km
resolution WRF results at 10 m above the terrain with the downscaled
field at the area of interest around the Lake Nyos. This figure highlights
the local information added by the microscale model over mountainous areas
and valleys, where WRF shows a smoother behaviour. Unfortunately, no surface
wind data existed at that time to validate these results. However, some
consistency with reports exists. For example, a strong microscale wind
rotation from NE to SW (wind origin direction) is clearly visible along the
Nyos valley from 18:00 to 21:00 UTC, in agreement with cloud dispersal
reports indicating two differentiated dispersal phases. In order to
illustrate this phenomenon, Fig. plots time series of
10 m wind velocity and direction from 16:00 to 24:00 UTC at two locations
of special interest, the lake itself and a point at the bottom of the Nyos
valley (see Fig. ). Note how near-surface wind direction
changes sharply at both locations between 17:30 (wind from NE) and 19:30
(wind from SW) UTC. A systematic WRF model error phase of about 3 h seems to
exist because dispersal reports suggest such a strong wind veering occurring
after 22:00 LT (21:00 UTC). In any case, these wind field variations
strongly indicate the need for including time-dependent heterogeneous winds
for the gas dispersal simulations. Finally, it is worth looking at the
atmospheric stability during the time of the event since this parameter also
favours the accumulation of dense gas at depressions.
Figure plots the static stability versus time, clearly
reflecting a unstable to stable transition related to the diurnal cycle
occurring at around 16:00 UTC.
Time series of 10 m wind speed and direction at two points located
at the Nyos Lake (a, c) and at the bottom of the Nyos
valley (b, d). Results from WRF simulations at 1 km
resolution (blue lines) and downscaling using ALYA-CFDWind at 50 m
(red lines). Wind direction criterion is that of the coming direction; i.e.
0∘ indicates wind coming from the N, 90∘ coming from the E. Note the sudden short-lived wind veering from NE to SW starting at
around 18:00 UTC.
Source term settings used in the different groups of simulations.
Table shows the considered ranges for eruption starting time, total CO2
emitted mass, CO2 mass flux, and constant of decay (or growth) for the
exponential phase.
RunSourceStarting timeTotal massMass fluxConstant of decay (growth)grouptype(UTC)(Tg)(given parameter)for the exponential(104kgm-2d-1)phase (10-4s-1)1Constant (180 min)17:300.78–1.5610–20–2Linear decrease (180 min)17:300.78–1.56from 19–28 to 1–2–3Linear increase (180 min)17:300.78–1.56from 1–2 to 19–28–4Exponential decrease (180 min)17:300.78–1.56–2–105Exponential increase (180 min)17:300.78–1.56–56Constant (60 min) +17:300.16–2.341–152–4exponential decrease (120 min)(for constant phase)7Constant (30 min) +16:30, 17:00,0.16–2.340.1–502–25exponential decrease (90 to 210 min)17:30(for constant phase)
Static stability (gradient of potential temperature in
∘ K km-1) versus time at the same two points than in
Fig. (lake in blue and valley in red) according to WRF
simulations at 1 km resolution. The potential temperature gradient
has been computed using WRF σ levels 1 and 6, at roughly 12 and
100 m above terrain, respectively. Positive values indicate stable
atmosphere. Note the transition from unstable to stable stratification
occurring after 16:00 UTC.
High-resolution dispersal modelling results
Once the high-resolution winds (i.e. WRF-ARW winds downscaled with
ALYA-CFDWind using transfer functions) have been obtained for the period and
area of interest, 10 m wind values every 20 min (i.e. three times
hourly) were given to the TWODEE-2.1 model together with the 30 m
resolution DEM and the definition of the source term to simulate the CO2
cloud dispersal. Our simulations assume the eruption started at 17:30 UTC
(18:30 LT), i.e. 2–3 h advanced with respect to eyewitness reports.
This source term shift in the dispersal simulations was necessary because of
the WRF model phase error discussed in Sect. . However,
given the large uncertainties in the source term concerning eruption
duration, intensity, and evolution of CO2 mass flow rate with time, we
performed a source term characterisation considering different sets of
simulations, each set with different source term characteristics (see
Table ):
Eruptions lasting 3 h with a constant CO2 emission but varying source intensity. This is similar to the scenarios considered by , who ranged
the source intensity between 1.4×105kgm-2d-1 (based on ) and
4.3×105kgm-2d-1 (based on ) (Group 1 in
Table ).
Eruptions lasting 3 h with a CO2 emission decreasing linearly and considering different time rates and source intensities
(Group 2).
Eruptions lasting 3 h with a CO2 emission increasing linearly and considering different time rates and source intensities
(Group 3).
Eruptions lasting 3 h with a CO2 emission decreasing exponentially considering different decay rates and source intensities
(Group 4).
Eruptions lasting 3 h with a CO2 emission increasing exponentially considering different growth rates and source intensities
(Group ).
Eruptions with an initial phase with low constant CO2 emission followed by a burst and exponential decay considering different durations for each phase, decay
rates and source intensities (groups 6 and 7). In addition, eruption durations for these groups were varied between 2 and 4 h as in .
Results for all these simulations (a total of 62 source term scenarios) were
validated on a point-by-point basis comparing the TWODEE-2.1 predicted
probability of fatalities with the actual percentage of fatalities reported
at 53 locations (Table ). When defining a metric for the
skill score of a simulation, it is important to consider whether observations are
distributed well across the possible range of values or not. In our case, for
example, 29 observations of 53 (i.e. 55 %) and 8 observations of 53
(i.e. 15 %) have 0 and 100 % of observed fatalities, respectively. It
means that around 70 % of the values are at the tails of the distribution
and, consequently, the evaluation of scores without binning would lead to
biassed skills, favouring those scenarios in which the source intensity
(emitted mass) is largely under- or overpredicted. In order to prevent this, we
adopt binning strategy and evaluate scores first for each discrete bins and
then globally by averaging over all bins. Ideally, the number of bins should
scale as n so that, in our case (n=53), around seven bins would be
recommendable. However, in order to avoid having bins with little or even no
observations, we considered the following five-class binning for the percentage
of fatalities: the first bin 0–5 % (no significant mortality), the second bin
5–35 %, the third 35–65 %, the fourth 65–95 %, and the fifth 95–100 % (total
mortality). This allows us to compute the Pearson cumulative test statistic
χ2 as
Source term characteristics of the best-fit simulation showing total
CO2 emitted mass, mass flux variation, χ2, and mean absolute error
(MAE) considering the five-class binning criterion.
DurationTotal massMass fluxχ2MAE(h)(Tg)(104kgm-2d-1)(%)30.864 for 30 min followed by a burst4.9834.7to 18 and 150 min exponential decay
χ2=∑i=1nb(Oi-Mi)2Mi,
where nb=5 is the number of bins, Oi is the number of observations
(localities) within the ith bin, and Mi is the number of model
localities laying in the same bin. However, we also compute the
total mean absolute error (MAE) as
MAE=1nb∑i=1nb(MAE)i,
with
(MAE)i=1m∑j=1m|POj-PMj|,
where (MAE)i is the bin absolute error, m the number of observations
(localities) in the jth bin, PO is the observed percentage of
fatalities, and PM is the modelled probability at the same locality.
Best-fit simulation results. Left: maximum CO2 concentration
(%vol.) achieved at 1 m height. Right: percentage of fatalities
(in %) predicted by the model applying Eq. () at 1 m
height. Halved circles show the actual reported percentages at locations
using the same colour scale.
Histogram showing the fit between observations (green bars) and
best-fit run (red bars) across the bins. Results from are
also shown for comparison (blue bars).
As a best-fit criterion we considered the lowest value of χ2 but trying
also to minimise MAE. We found that the higher-score simulations belong to
the same group of source term runs – a source with two phases: an initial
phase with a constant CO2 emission followed by a second phase with
exponential source strength decay (group 6). This is a consistent result.
Table and Fig. summarise the
characteristics of the source term for the highest ranked run. The total
CO2 emitted mass is 0.86 Tg, released over 3 h. This value
is in good agreement with previous independent estimations, ranging from
0.29 Tg to 1.95 Tg. In contrast, the values of χ2 and MAE are 4.98 and 34.7 %, respectively,
giving a very good fit across all bins (see Fig. ). For
comparison, the scenario II in (see
Fig. ) gives a χ2 of 7.61 and a MAE of 36.6 %,
substantially higher even if the characteristics of the source term are
similar to our best-fit runs both in terms of duration (4 h) and total
mass (1.33 Tg). These differences can be explained because of the
high-resolution time-dependent winds, which are able to capture the wind
veering leading to the differentiated cloud dispersal branches (see
Fig. ). This can also be observed by looking at the
evolution of concentration with time at different locations. As observed in
Fig. , the TWODEE-2.1 simulations can reproduce a first
W-NW branch affecting the bottom valleys of Cha and Fang (location L34)
followed by a gas cloud direction shift towards NE affecting Subum
village (location L36). According to simulations, this occurred around 2 h after the eruption onset (i.e. 20:30 LT). Considering the
2–3 h shift necessary to correct the meteorological (WRF) phase error,
this is in excellent agreement with eyewitness reports.
Evolution with time (in h) of CO2 concentration
(%vol.) at different locations for the best-fit simulation. Results at
1 m height. Location L05 is near the Lake, L24 at the Nyos valley,
L34 near Cha (W branch), and L36 near Subum (E branch). See
Fig. for details.
Summary and discussion
We have developed a high-resolution numerical model for CO2 atmospheric
dispersal in complex terrains by introducing a methodology for time-dependent
microscale wind characterisation based on transfer functions that couple a
mesoscale numerical weather prediction model with a microscale computational
fluid dynamics model for the atmospheric boundary layer. The model was
applied to reconstruct the source conditions and the catastrophic CO2
dispersal at Lake Nyos in 1986. Simulation results were compared with the
observed fatalities through a novel probabilistic approach. We found that the
new model with high-resolution time-dependent winds shows better agreement
with the observations compared with previous simulations, indicating that the
model is capable of performing gas dispersal hazard assessment on very
complex terrains in the future.
The optimal runs (higher scores for percentage of fatalities) shared same
source evolution pattern: an initial phase with a low constant CO2
emission and a second phase with a burst followed by exponential decay in
CO2 mass flux. This suggests additional information about physical processes
at Lake Nyos during the 1986 limnic eruption. The scenario is compatible with
a gas eruption that started locally in some region of the lake, continuously
emitting a relatively low amount of CO2 near the equilibrium state;
then a perturbation, likely due to the gas ascent itself or to other
mechanism(s), grew that destabilised the whole lake and triggered the
exponential phase by overturn of the different layers in the lake in a
supersaturation state. One simple model explaining the exponential decay
during the second phase is that the driving force for CO2 emission is an
overpressure in the lake, such as caused by CO2 supersaturation, and the
temporal change in the overpressure is controlled by the emitted CO2 flux,
like it occurs in a volatile supersaturated magma chamber. This model can be
simply formulated as e.g.Q=C1p,
and
dpdt=-C2Q,
where Q is the emitted CO2 flux, p is the overpressure, and C1 and
C2 are two constants. These equations lead to the solution of exponential
decay form for Q:
Q(t)=Q0exp(-C1C2t),
where Q0 is the initial value of Q. Although the precise mechanism in
the lake during the limnic eruption is still under discussion, we can infer
from the above model that the second phase is simply explained by a
relaxation process of supersaturation state in the lake. Although further
investigations for the dynamics of lake water are necessary for reproducing
the physical process of the limnic eruption in detail, the features of the
CO2 emission obtained in this study may provide strong constraints on
physical modelling in the lake.
We use no new data; all datasets have been taken from
previous publications of other authors.
Arnau Folch has implemented the improvements to the TWODEE code and
written the bulk of the manuscript with input from all authors. Jordi Barcons and Arnau Folch
have performed the wind field characterisation. Tomofumi Kozono has configured and
performed TWODEE simulations. Antonio Costa has characterised the scenarios, defined the
strategy for the impact criterion, and contributed to the text. All authors
reviewed the manuscript.
The authors declare that they have no conflict of
interest.
Acknowledgements
Jordi Barcons has been partially funded by the Industrial Doctorate Program of the
Catalan Government (eco/2497/2013). We also thank the two anonymous reviewers
for their comments and suggestions. Finally, our colleagues Greg Tanyileke,
Fantog Wilson, and Romaric Ntchantcho from the Institut de Recherches
Géologiques et Minières (IRGM) (Cameroon) are warmly thanked for
their field guidance and scientific discussions during the workshop “30 years
of Lake Nyos disaster” (Yaounde, 14–20 March 2016).
Edited by: G. Macedonio
Reviewed by: two anonymous referees
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