Atmospheric dispersion modelling in West Africa is crucial to understand, predict, and mitigate the impacts of air pollution on public health, ecosystems, and regional climate in a context of rapid urbanization and industrialization. This study develops a three-dimensional analytical model for carbon monoxide (CO) dispersion, governed by the turbulent scalar flux transport equation within a second-order Eulerian framework. A theoretical analysis of the model establishes the existence and uniqueness of the solution, and derives the associated optimality system using control theory and monotone operator techniques. From this formulation, an analytical solution is obtained that explicitly incorporates diffusion coefficients, turbulence intensities dependent on atmospheric stability (cloud cover and radiation), and three-dimensional wind components
derived from ERA5 reanalysis. The analytical model is then calibrated through four-dimensional variational data assimilation (4D-Var) using satellite-based CO observations from the Copernicus EAC4 reanalysis, to produce fields consistent with observations. An application over the Gulf of Guinea during the dry season demonstrates that the coupled Model-4D-Var system generates CO dispersion maps with finer spatial resolution (0.25? × 0.25?) than the input satellite products (0.75? × 0.75?), while maintaining good agreement with observations, as indicated by low RMSE, small negative fractional bias, and FAC2 values between 0.5 and 2 at most pressure levels. These high-resolution maps enable the quantification, identification, and tracking of CO plumes in space and time, including persistent plumes over southern and northern Nigeria, Ghana, and the Central African Republic, linked to gas flaring, biomass burning, and urban/industrial emissions. The results highlight the potential of combining an analytical dispersion model with 4D-Var to improve CO monitoring in data-sparse regions, such as the Gulf of Guinea.
References
[1]
Philip, J.L., Richard, F. and Nereus, J.R. (2007) The Lancet Commission on Pollution and Health. The Lancet, 391, 462-512.
[2]
Leguijt, G., Maasakkers, J.D., Denier van der Gon, H.A.C., Segers, A.J., Borsdorff, T. and Aben, I. (2023) Quantification of Carbon Monoxide Emissions from African Cities Using Tropomi. AtmosphericChemistryandPhysics, 23, 8899-8919. https://doi.org/10.5194/acp-23-8899-2023
[3]
Mayowa, B.L. and Moboladji S.S. (2024) An Assessment of Carbon Monoxide Emission in Nigeria and Recommendations for Suustainable Mitigation Strategies on Climate impact. FUTA Journal of Logistics and Innovation Technology, 3, Article 16.
[4]
Onojeghuo, A., Fleming, Z.L., Panagi, M., Balzter, H. and Monks, P.S. (2025) Investigating the Dispersion and Transport of Carbon Monoxide in West Africa with a Focus on Biomass Burning and Gas Flaring Sources. DiscoverAtmosphere, 3, Article No. 14. https://doi.org/10.1007/s44292-025-00038-6
[5]
Koppmann, R.K., Czaplewski, V. and Reld, J.S. (2005) A Review of Biomass Burning Emissions, Part I: Gaseous Emissions of Carbon Monoxide, Methane, Volatile Organic Compounds, and Nitrogen Containing Compounds. Atmospheric Chemistry and Physics Discussion, 5, 10455-10516.
[6]
Logan, J.A., Jones, D.B.A., Livesey, N.J., Megretskaia, I., Carouge, C. and Nedelec, P. (2010) Analysis of CO in the Tropical Troposphere Using Aura Satellite Data and the GEOS-Chem Model: Insights into Transport Characteristics of the GEOS Meteorological Products. Atmospheric Chemistry and Physics, 10, 12207-12232. https://doi.org/10.5194/acp-10-12207-2010
[7]
Orina, F., Amukoye, E., Bowyer, C., Chakaya, J., Das, D., Devereux, G., et al. (2024) Household Carbon Monoxide (CO) Concentrations in a Large African City: An Unquantified Public Health Burden? Environmental Pollution, 351, Article 124054. https://doi.org/10.1016/j.envpol.2024.124054
[8]
Menut, L., Flamant, C., Turquety, S., Deroubaix, A., Chazette, P. and Meynadier, R. (2018) Impact of Biomass Burning on Pollutant Surface Concentrations in Megacities of the Gulf of Guinea. Atmospheric Chemistry and Physics, 18, 2687-2707. https://doi.org/10.5194/acp-18-2687-2018
[9]
Isichei, A.O., Muoghalu, J.I., Akeredolu, F.A. and Afolabi, O.A. (1995) Fuel Characteristics and Emissions from Biomass Burning and Land-Use Change in Nigeria. Environmental Monitoring and Assessment, 38, 279-289. https://doi.org/10.1007/bf00546769
[10]
Ichoku, C., Ellison, L.T., Willmot, K.E., Matsui, T., Dezfuli, A.K., Gatebe, C.K., et al. (2016) Biomass Burning, Land-Cover Change, and the Hydrological Cycle in Northern Sub-Saharan Africa. EnvironmentalResearchLetters, 11, Article 095005. https://doi.org/10.1088/1748-9326/11/9/095005
[11]
Abdelhak, B. (2016) Le Golfe de Guinée, zone de contrastes: Richesses et vulnérabilités. OCP Policy Center.
[12]
Mir Alvarez, C., Hourcade, R., Lefebvre, B. and Pilot, E. (2020) A Scoping Review on Air Quality Monitoring, Policy and Health in West African Cities. International Journal of Environmental Research and Public Health, 17, Article 9151. https://doi.org/10.3390/ijerph17239151
[13]
Haslett, S.L., Taylor, J.W., Evans, M., Morris, E., Vogel, B., Dajuma, A., et al. (2019) Remote Biomass Burning Dominates Southern West African Air Pollution during the Monsoon. Atmospheric Chemistry and Physics, 19, 15217-15234. https://doi.org/10.5194/acp-19-15217-2019
[14]
Real, E., Orlandi, E., Law, K.S., Fierli, F., Josset, D., Cairo, F., et al. (2010) Cross-hemispheric Transport of Central African Biomass Burning Pollutants: Implications for Downwind Ozone Production. Atmospheric Chemistry and Physics, 10, 3027-3046. https://doi.org/10.5194/acp-10-3027-2010
[15]
Nicolas, M., Pierre, C. And Laurence, R. (2015) Paronama de la modélisation de la dispersion atmosphérique Atmospheric dispersion Models: An Overview. Pollution Atmosphérique.
[16]
DeWitt, H.L., Gasore, J., Rupakheti, M., Potter, K.E., Prinn, R.G., Ndikubwimana, J.D.D., et al. (2019) Seasonal and Diurnal Variability in O3, Black Carbon, and CO Measured at the Rwanda Climate Observatory. AtmosphericChemistryandPhysics, 19, 2063-2078. https://doi.org/10.5194/acp-19-2063-2019
[17]
Frédéric, D. (2012) Modélisation statistique des écoulements turbulents en convection forcée, mixte et naturelle. Thèse Mécanique des fluides. Université de Poitiers.
[18]
Hersbach, H., Comyn-Platt, E., Bell, B., Berrisford, P., et al. (2023) ERA5 Post-Processed Daily-Statistics on Pressure Levels from 1940 to Present. Copernicus Climate Change Service (C3S) Climate Data Store (CDS).
[19]
Inness, A., Ades, M., Agustí-Panareda, A., Barré, J., Benedictow, A., Blechschmidt, A., et al. (2019) The CAMS Reanalysis of Atmospheric Composition. AtmosphericChemistryandPhysics, 19, 3515-3556. https://doi.org/10.5194/acp-19-3515-2019
[20]
Brezis, H. (2011) Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer.
[21]
Troltzsch, F. (2010) Optimal Control of Partial Differential Equations Theory, Methods and Application. American Mathematical society Providence.
[22]
Schulze, B.W. and Wong, M.W. (2008) Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations. Birkäuser Verlag.
[23]
Chang, J.C. and Hanna, S.R. (2004) Air Quality Model Performance Evaluation. Meteorology and Atmospheric Physics, 87, 167-196. https://doi.org/10.1007/s00703-003-0070-7
[24]
Nino Ruiz, E.D. and Sandu, A. (2016) A Derivative-Free Trust Region Framework for Variational Data Assimilation. Journal of Computational and Applied Mathematics, 293, 164-179. https://doi.org/10.1016/j.cam.2015.02.033
[25]
Guedje, F.K., Houeto, A.V.V., Houngninou, E.B., Fink, A.H. and Knippertz, P. (2019) Climatology of Coastal Wind Regimes in Benin. MeteorologischeZeitschrift, 28, 23-39. https://doi.org/10.1127/metz/2019/0930
[26]
Lewellen, W.S., Teske, M. and Donaldson, C.D. (1973) Application of Turbulence Model Equations to Axisymmetric Wakes. AIAAJournal, 12, 620-625. https://doi.org/10.2514/3.49308
[27]
Hanna, T.R., Gary, A.B. and Rayford, P.H. (1981) Handbook on Atmospheric Diffusion, Atmospheric Turbulence and Diffusion Laboratory, National Oceanic and Atmosphere Admnistration. Technical Information Center U.S. Departement of Energy.
[28]
Foulet, A. and Aissani, L. (2020) Caractérisation et évaluation de l’impact des odeurs en gestion de déchets. Jalon 22-1-Choix du modèle de dispersion. Centre pour la Communication Scientifique Directe.
[29]
Batchelor, G. (1949) Diffusion in a Field of Homogeneous Turbulence. I. Eulerian Analysis. Australian Journal of Scientific Research Series A: Physical Sciences, 2, 437-450. https://doi.org/10.1071/ch9490437
[30]
Cirillo, M.C. and Poli, A.A. (1992) An Intercomparison of Semiempirical Diffusion Models under Low Wind Speed, Stable Conditions. Atmospheric Environment, 26, 765-774. https://doi.org/10.1016/0960-1686(92)90236-e
[31]
Pasquill, F. (1974) Atmospheric Diffusion: The Dispersion of Windbome Material from Industrial and Other Sources. Van Nostrand.
[32]
Sharan, M. and Yadav, A.k. (1998) Simulation of Diffusion Experiments under Light Wind, Stable Conditions by a Variable K-Theory Model. Atmospheric Environment, 32, 3481-3492. https://doi.org/10.1016/s1352-2310(98)00048-x
[33]
Yeh, G.T. and Huang, C.H. (1975) Three-Dimensional Air Pollutant Modeling in the Lower Atmosphere. Boundary-Layer Meteorology, 9, 381-390. https://doi.org/10.1007/bf00223389
[34]
Park, S.K. and Liang, X. (2013) Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications. Springer.
[35]
Lenfle, S. (2018) De l’interpolation optimale au 4D-Var: L’émergence d’un nouveau dominant design en assimilation de données météorologiques. LaMétéorologie, 100, 37-46. https://doi.org/10.4267/2042/65141
[36]
Evensen, G., Vossepoel, F.C. and Van Leeuwen, P.J (2022) Data Assimilation Fundamentals: A Unified Formulation of State and Parameter Estimation Problem. Springer.
[37]
Philip, D., Vishwas, R. and Mihai, A. (2025) Weakly-Constrained 4D-Var for Downscalling with Uncertainty Using Data-Driven Surrogate Models. https://arxiv.org/abs/2503.02665
[38]
Klinker, E., Mahfouf, J. and Rabier, F. (2000) Une nouvelle technique d’assimilation des données d’observation au CEPMMT: L’assimilation variationnelle quadridimensionnelle. LaMétéorologie, 8, 87-101. https://doi.org/10.4267/2042/36125
[39]
Lions, J.L. (1968) Contrôle optimal des systèmes gouvernés par des équations aux dérivés partielles. Dunod/Gauthier-Villars (Paris).
[40]
Le Dimet, F.X. and Talagrand, O. (1986) Variational Algorithms for Analysis and Assimilation of Meteorological Observations. Dynamic Meteorology and Oceanography, 38, 97-110. https://doi.org/10.3402/tellusa.v38i2.11706
[41]
Lewis, J.M. and Derber, J.C. (1985) The Use of Adjoint Equations to Solve a Variational Adjustment Problem with Advective Constraints. Tellus A: Dynamic Meteorology and Oceanography, 37, 309-322. https://doi.org/10.3402/tellusa.v37i4.11675
Courtier, P. and Talagrand, O. (1990) Variational Assimilation of Meteorological Observations with the Direct and Adjoint Shallow-Water Equations. Tellus A: Dynamic Meteorology and Oceanography, 42, 531-554. https://doi.org/10.3402/tellusa.v42i5.11896
[44]
Tikhonov, A. and Arsenin, V. (1977) Solutions of III Posed Problems. Washington.
[45]
Nocedal, J. (1980) Updating Quasi-Newton Matrices with Limited Storage. MathematicsofComputation, 35, 773-782. https://doi.org/10.1090/s0025-5718-1980-0572855-7
[46]
Liu, D.C. and Nocedal, J. (1989) On the Limited Memory BFGS Method for Large Scale Optimization. Mathematical Programming, 45, 503-528. https://doi.org/10.1007/bf01589116
[47]
Akinyemi, M. (2012) Diminishing Atmospheric Carbon Monoxide Fluxes as a Forecast of the New Planting Season in West Africa. American Journal of Scientific and Industrial Research, 3, 198-202. https://doi.org/10.5251/ajsir.2012.3.4.198.202
[48]
Si, G.X., Fu, S.L. and Yao, W. (2024) Unlocking the Potential: Multi-Task Deep Learning for Spaceborne Quantitative Monitoring of Fugitive Methane Plumes.
[49]
Groshenry, A., Giron, C., Lauvaux, T., d’Aspremont, A. and Ehret, T. (2022) Detecting Methane Plumes using PRISMA: Deep Learning Model and Data Augmentation. https://arxiv.org/abs/2211.15429v1
[50]
Bertrand, R.L., Kerdreux, T., Tuel, A. and Claudia H. (2023) Autonomous Detection of Methane Emissions in Multispectral Satellite Data Using Deep Learning. https://arxiv.org/abs/2308.11003v1
[51]
Wang, H.Z., Fan, X.T., Jian, H.D. and Yan, F. (2024) Exploiting the Matched Filter to Improve the Detection of Methane Plumes with Sentinel-2 Data. Remote Sensing, 16, Article 1023. https://doi.org/10.3390/rs16061023
[52]
Bruno, J.H., Jervis, D., Varon, D.J. and Jacob, D.J. (2024) U-Plume: Automated Algorithm for Plume Detection and Source Quantification by Satellite Point-Source Imagers. Atmospheric Measurement Techniques, 17, 2625-2636. https://doi.org/10.5194/amt-17-2625-2024
[53]
Monin, A. and Obukhov, A. (1954) Basic Laws of Turbulent Mixing in the Surface Layer of the Atmosphere. Contributions of the Geophysical Institute. Academy of Sciences of the USSR, 151, 163-187.
[54]
World Health Organisation (2021) WHO Global Air Quality Guidelines. Particulate Matter (PM2.5 and PM10), Ozone, Nitrogen Dioxide, Sulfur Dioxide and Carbon Monoxide. World Health Organisation.
[55]
Bell, M.L., Peng, R.D., Dominici, F. and Samet, J.M. (2009) Emergency Hospital Admissions for Cardiovascular Diseases and Ambient Levels of Carbon Monoxide. Circulation, 120, 949-955. https://doi.org/10.1161/circulationaha.109.851113
[56]
Chen, R., Pan, G., Zhang, Y., Xu, Q., Zeng, G., Xu, X., et al. (2011) Ambient Carbon Monoxide and Daily Mortality in Three Chinese Cities: The China Air Pollution and Health Effects Study (CAPES). Science of the Total Environment, 409, 4923-4928. https://doi.org/10.1016/j.scitotenv.2011.08.029
[57]
Chen, K., Breitner, S., Wolf, K., Stafoggia, M., Sera, F., Vicedo-Cabrera, A.M., et al. (2021) Ambient Carbon Monoxide and Daily Mortality: A Global Time-Series Study in 337 Cities. The Lancet Planetary Health, 5, e191-e199. https://doi.org/10.1016/s2542-5196(21)00026-7
[58]
Samoli, E., Touloumi, G., Schwartz, J., Anderson, H.R., Schindler, C., Forsberg, B., etal. (2007) Short-term Effects of Carbon Monoxide on Mortality: An Analysis within the APHEA Project. Environmental Health Perspectives, 115, 1578-1583. https://doi.org/10.1289/ehp.10375