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.

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.

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 .

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.

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.

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 1.4×105 kgm-2d-1 (based on ) and 4.3×105 kgm-2d-1 (based on ) (Group 1 in Table ).

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.