G. A. Grell, S. Peckham, R. Schmitz, S. Mckeen, G. Frost, W. Skamarock, and B. Eder, “Fully coupled chemistry within the WRF model,” Atmos. Environ. 39 (37), 6957–6975 (2005).https://doi.org/10.1016/j.atmosenv.2005.04.027

Article  ADS  Google Scholar 

W. C. Skamarock, J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, M. G. Duda, X.-Y. Huang, W. Wang, and J. G. Powers, A Description of the Advanced Research WRF Version 4. NCAR Technical Note (NCAR, Boulder, Colorado, 2019).https://doi.org/10.6084/m9.figshare.7369994.v4

Book  Google Scholar 

C. Knote, D. Brunner, H. Vogel, J. Allan, A. Asmi, M. Aijala, S. Carbone, H. Gon, J. Jimenez, A. Kiendler-Scharr, C. Mohr, L. Poulain, A. Prevot, E. Swietlicki, and B. Vogel, “Towards an online-coupled chemistry-climate model: Evaluation of trace gases and aerosols in COSMO-ART,” Geosci. Model Develop. 4 (4), 1077–1102 (2011).https://doi.org/10.5194/gmd-4-1077-2011

Article  ADS  Google Scholar 

A. Baklanov, U. Korsholm, A. Mahura, C. Petersen, and A. Grosset, “ENVIRO-HIRLAM: On-line coupled modelling of urban meteorology and air pollution,” Adv. Sci. Res. 2 (1), 41–46 (2008).

Article  MATH  Google Scholar 

M. Bocquet, H. Elbern, H. Eskes, M. Hirtl, R. Zabkar, G. R. Carmichael, J. Flemming, A. Inness, M. Pagowski, J. L. Prez Camano, P. E. Saide, R. San Jose, M. Sofiev, J. Vira, A. Baklanov, C. Carnevale, G. Grell, and C. Seigneur, “Data assimilation in atmospheric chemistry models: Current status and future prospects for coupled chemistry meteorology models,” Atmos. Chem. Phys. Discuss. 14 (23), 32 233–32 323 (2014).https://doi.org/10.5194/acpd-14-32233-2014

Article  Google Scholar 

A. Carrassi, M. Bocquet, L. Bertino, and G. Evensen, “Data assimilation in the geosciences: An overview of methods, issues, and perspectives,” WIREs 9 (5). e535 (2018).https://doi.org/10.1002/wcc.535

Article  MATH  Google Scholar 

V. V. Penenko and N. N. Obraztsov, “A variational initialization method for the fields of the meteorological elements,” Sov. Meteorol. Hydrol. 11, 3–16 (1976).

MATH  Google Scholar 

F.-X. L. Dimet and O. Talagrand, “Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects,” Tellus 38A, 97–110 (1986).https://doi.org/10.3402/tellusa.v38i2.11706

Article  ADS  MATH  Google Scholar 

H. Elbern, A. Strunk, H. Schmidt, and O. Talagrand, “Emission rate and chemical state estimation by 4-dimensional variational inversion,” Atmos. Chem. Phys. Discuss. 7 (1), 1725–1783 (2007).https://doi.org/10.5194/acpd-7-1725-2007

Article  ADS  MATH  Google Scholar 

G. R. Carmichael, A. Sandu, T. Chai, D. N. Daescu, E. M. Constantinescu, and Y. Tang, “Predicting air quality: Improvements through advanced methods to integrate models and measurements,” J. Comput. Phys. 227 (7), 3540–3571 (2008).https://doi.org/10.1016/j.jcp.2007.02.024

Article  ADS  MathSciNet  MATH  Google Scholar 

G. I. Marchuk, Mathematical Modeling and Environmental Problems (Nauka, Moscow, 1982) [in Russian].

MATH  Google Scholar 

R. M. Errico, “What is an adjoint model?,” Bull. Am. Meteorol. Soc. 78 (11), 2577–2591 (1997).https://doi.org/10.1175/1520-0477(1997)078<2577:WIAAM>2.0.CO;2

Article  ADS  MATH  Google Scholar 

A. Hakami, D. K. Henze, J. H. Seinfeld, K. Singh, A. Sandu, S. Kim, D. Byun, and Q. Li, “The adjoint of CMAQ,” Environ. Sci. Technol. 41 (22), 7807–7817 (2007).https://doi.org/10.1021/es070944p

Article  ADS  MATH  Google Scholar 

V. V. Penenko, A. V. Penenko, E. A. Tsvetova, and A. V. Gochakov, “Methods for studying the sensitivity of air quality models and inverse problems of geophysical hydrothermodynamics,” J. Appl. Mech. Tech. Phys. 60 (2), 392–399 (2019).https://doi.org/10.1134/S0021894419020202

Article  ADS  MathSciNet  MATH  Google Scholar 

A. Penenko, “Convergence analysis of the adjoint ensemble method in inverse source problems for advection-diffusion-reaction models with image-type measurements,” Inverse Probl. Imaging 14 (5), 757–782 (2020).https://doi.org/10.13140/RG.2.2.26550.14409

Article  MathSciNet  MATH  Google Scholar 

A. Penenko, V. Penenko, E. Tsvetova, A. Gochakov, E. Pyanova, and V. Konopleva, “Sensitivity operator framework for analyzing heterogeneous air quality monitoring systems,” Atmosphere 12 (12), 16971 (2021).https://doi.org/10.3390/atmos12121697

Article  MATH  Google Scholar 

A. Penenko and E. Rusin, “Parallel implementation of a sensitivity operator-based source identification algorithm for distributed memory computers,” Mathematics 10 (23), 45221 (2022).https://doi.org/10.3390/math10234522

Article  MATH  Google Scholar 

G. I. Marchuk, “Anout statement of certain inverse problems,” Dokl. Akad. Nauk SSSR, No. 3, 503–506 (1964).

MATH  Google Scholar 

A. Penenko, M. Emelyanov, E. Rusin, E. Tsybenova, and V. Shablyko, “Hybrid deep learning and sensitivity operator-based algorithm for identification of localized emission sources,” Mathematics 12 (1), 781 (2023).https://doi.org/10.1109/OPCS59592.2023.10275758

Article  Google Scholar 

A. V. Penenko, “Algorithms for the inverse modelling of transport and transformation of atmospheric pollutants,” IOP Conf. Ser.: Earth Environ. Sci. 211, 012052–1 (2018).https://doi.org/10.1088/1755-1315/211/1/012052

A. V. Penenko, E. V. Rusin, and V. V. Penenko, “Emission sources identification scenario for a three-dimensional atmospheric transport and transformation model,” Proc. SPIE 1278068 (2023).https://doi.org/10.1117/12.2690844

K. Markakis, M. Valari, O. Perrussel, O. Sanchez, and C. Honore, “Climate-forced air-quality modeling at the urban scale: Sensitivity to model resolution, emissions and meteorology,” Atmos. Chem. Phys. 15 (13), 7703–7723 (2015).https://doi.org/10.5194/acp-15-7703-2015

Article  ADS  Google Scholar 

P. Holnicki and Z. Nahorski, “Emission data uncertainty in urban air quality modeling—case study,” Environ. Model. Assess. 20 (6), 583–597 (2015).https://doi.org/10.1007/s10666-015-9445-7

Article  MATH  Google Scholar 

S.-Y. Hong, J. Dudhia, and S.-H. Chen, “A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation,” Mon. Weather Rev. Am. Meteorol. Soc. 132 (1), 103–120 (2004).https://doi.org/10.1175/1520-0493(2004)132<0103:ARATIM>2.0.CO;2

Article  ADS  MATH  Google Scholar 

E. J. Mlawer, S. J. Taubman, P. Brown, M. Iacono, and S. Clough, “Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave,” J. Geophys. Res.: Atmos. 102 (D14), 16 663–16 682 (1997).https://doi.org/10.1029/97JD00237

Article  ADS  Google Scholar 

J. Dudhia, “Numerical study of convection observed during the winter monsoon experiment using a mesoscale two-dimensional model,” J. Atmos. Sci. Am. Meteorol. Soc. 46 (20), 3077–3107 (1989).https://doi.org/10.1175/1520-0469(1989)046<3077:NSOCOD>2.0.CO;2

Article  ADS  MATH  Google Scholar 

S.-Y. Hong, Y. Noh, and J. Dudhia, “A new vertical diffusion package with an explicit treatment of entrainment processes,” Mon. Weather Rev. Am. Meteorol. Soc. 134 (9), 2318–2341 (2006).https://doi.org/10.1175/MWR3199.1

Article  ADS  MATH  Google Scholar 

A. C. M. Beljaars, “The parametrization of surface fluxes in large-scale models under free convection,” Q. J. R. Meteorol. Soc. 121 (522), 255–270 (1995).

ADS  MATH  Google Scholar 

F. Chen and J. Dudhia, “Coupling an advanced land surface—hydrology model with the Penn state—NCAR MM5 modeling system. Part I: Model implementation and sensitivity,” Mon. Weather Rev. Am. Meteorol. Soc. 129 (4), 569–585 (2001).https://doi.org/10.1175/1520-0493(2001)129<0569:CAALSH>2.0.CO;2

Article  ADS  Google Scholar 

P. N. Antokhin, A. V. Gochakov, A. B. Kolker, and A. V. Penenko, “Comparison of WRF-Chem chemical transport model calculations with aircraft measurements in Norilsk,” Atmos. Ocean. Opt. 31 (4), 372–380 (2018).

Article  MATH  Google Scholar 

National Centers for Environmental Prediction/National Weather Service/NOAA/U.S. Department of Commerce. 2000, updated daily. NCEP FNL Operational Model Global Tropospheric Analyses, continuing from July 1999. Research Data Archive at the National Center for Atmospheric Research, Computational and Information Systems Laboratory.https://doi.org/10.5065/D6M043C6