Complex Validation of Weather Research and Forecasting—Chemistry Modelling of Atmospheric CO₂ in the Coastal Cities of the Gulf of Finland

Abstract

The increase of the CO₂ content in the atmosphere caused by anthropogenic emissions from the territories of large cities (~70%) is the critical factor in determining the accuracy of emission estimations. Advanced experiment-based methods of anthropogenic CO₂ emission estimation are based on the solution of an inverse problem, using accurate measurements of CO₂ content and numerical models of atmospheric transport and chemistry. The accuracy of such models decreases the errors of the emission estimations. The aim of the current study is to adapt numerical weather prediction and atmospheric chemistry model WRF-Chem and validate its capability to simulate atmospheric CO₂ for the territories of the two large coastal cities of the Gulf of Finland—St. Petersburg (Russia) and Helsinki (Finland). The research has demonstrated that the WRF-Chem model is able to simulate annual variation, as well as the mean seasonal and diurnal variations of the near-surface CO₂ mixing ratio, in Helsinki, at a high spatial resolution (2 km). Correlation between the modelled and measured CO₂ mixing ratio is relatively high, at ~0.73, with a mean difference and its standard deviation of 0.15 ± 0.04 and 1.7%, respectively. The differences between the WRF-Chem data and the measurements might be caused by errors in the modelling of atmospheric transport and in a priori CO₂ emissions and biogenic fluxes. The WRF-Chem model simulates well the column-averaged CO₂ mixing ratio (XCO₂) in St. Petersburg (January 2019–March 2020), with a correlation of ~0.95 relative to ground-based spectroscopic measurements by the IR–Fourier spectrometer Bruker EM27/SUN. The error of the XCO₂ modelling constitutes ~0.3%, and most likely is related to inaccuracies in chemical boundary conditions and a priori anthropogenic CO₂ emissions. The XCO₂ time series in St. Petersburg by the WRF-Chem model fits well with global CAMS reanalysis and CarbonTracker-modelled data (the differences are less than ~1%). However, due to much higher spatial resolution (2 vs. over 100 km), the WRF-Chem data are in the best agreement with the ground-based remote measurements of XCO₂. According to the study, the modelling errors of XCO₂ in St. Petersburg during the whole simulated period are sufficiently minimal to fit the requirement of “Error ≤ 0.2%” in 60% of cases. This requirement should be satisfied to evaluate properly the anthropogenic CO₂ emissions of St. Petersburg on a city-scale.

1. Introduction

Anthropogenic CO₂ emissions from the territories of large cities contribute significantly to CO₂ content increases in the Earth’s atmosphere [1]. Nowadays, accurate estimation of anthropogenic CO₂ emissions from the territories of large cities is an important objective. It can be useful for the evaluation of the total and regional contribution of a country to the increase of CO₂ content in the atmosphere, and as a result, to the changes in CO₂ radiative forcing.

Nowadays, an inventory approach is actively used to estimate emissions of greenhouse gases (GHGs) [2]. However, it was shown that on a city scale its error level can reach 100% and above [3]. In the last decade, observation-based methods have been developed and used to validate GHG inventories and provide independent estimations of the emissions of GHGs on a city-wide scale [4].

The principle of the observation-based method is based on finding a correlation between the measured increment of a gas content and its potential sources by simulating the atmospheric transport of this gas from a priori sources. The gas increment can be, for instance, measured by a differential spectroscopic approach [5,6]. In the framework of this approach, parallel measurements of the total content of the gas are carried out in upwind and downwind locations of a city using inter-calibrated spectrometers. Estimating anthropogenic emissions of CO₂ using the described observation-based method is an ill-posed (in sense of Hadamard) inverse problem [5,6,7]. Examples of using this method for CO₂ emission estimation (also known as inverse modelling of atmospheric transport) for specific city areas are presented in many modern studies [5,6,7,8,9,10,11,12,13].

Errors of inverse modelling significantly depend on a priori information and a direct operator. Usually, the direct operators in inverse modelling of atmospheric transport are numerical models of different complexity that model atmospheric composition. The influences of different direct operators on the solutions of inverse modelling were investigated; some of the results can be found in [14,15]. It was demonstrated that differences in numerical models of atmospheric transport cause large deviations (~50% and more) between the estimates of anthropogenic and biogenic emissions of CO₂.

Box and particle dispersion models, together with spectroscopic differential observations of CO₂ total columns (TC), were used in studies [5,6,12,13] to estimate the anthropogenic emissions of St. Petersburg. St. Petersburg’s megapolis is one of the largest Russian industrial cities, with a population and area of ~5 mln people and ~1400 km², respectively [16]. There are ~10 combined heat and power plants, many industries and a large number of personal vehicles on the territory of St. Petersburg. Therefore, St. Petersburg is a large anthropogenic source of CO₂. The differences between the anthropogenic CO₂ emissions estimates obtained in studies [5,6,12,13] reach up to 30% and are ~1.5–2 times higher than the city’s emissions according to the inventory of anthropogenic CO₂ emissions, ODIAC (Open-source Data Inventory for Anthropogenic CO₂) [12,13]. Hence, it is important to set up and validate a model of atmospheric composition appropriate to the territory of interest before using it to estimate anthropogenic CO₂ emissions.

WRF-Chem (Weather Research and Forecasting—Chemistry) is a numerical model for weather forecasting and the composition of the troposphere and lower stratosphere at a high spatial resolution [17]. The errors of the WRF-Chem modelling of CO₂ transport have been investigated by scientists from different institutes. For instance, the mean mixing ratio of CO₂ in the troposphere according to both WRF-Chem and spectroscopic measurements (IR Fourier-spectrometer Bruker 125HR, Bruker Optics GmbH & Co., Ettlingen, Germany) near Saint-Denis (France, Réunion Island, Indian Ocean) for approximately a one-year period differ by only 0.09%, with a standard deviation of 0.2% and high correlation coefficient of 0.9 [18]. Somewhat higher levels of error (0.2–0.5%) were found in a study [19] of Berlin (Germany), but only for a one-month period. In contrast to the previous study, the authors used several mobile spectrometers (Bruker EM27/SUN, Bruker Optics GmbH & Co., Ettlingen, Germany) to validate the model.

In the study described in [20], authors used in situ measurements of the near-surface CO₂ mixing ratio made by a greenhouse gas analyser (GGA) [21] to validate WRF-Chem modelling of CO₂ atmospheric transport in St. Petersburg. The main disadvantage of such validation is that in situ observations characterise changes of CO₂ content in a relatively small air volume. Therefore, the near-surface CO₂ mixing ratio is sensitive to anthropogenic emissions only during particular weather conditions. In turn, the observed CO₂ total column is sensitive to all sources in the atmosphere (e.g., anthropogenic emissions, biogenic fluxes and advection), regardless of the atmospheric state. It is shown in study [22] that the mean difference between the values for column-averaged CO₂ mixing ratio (XCO₂) determined by the WRF-Chem model and by spectroscopic ground-based measurements for a period of more than a year in St. Petersburg is 0.6–1%, with a standard deviation of 0.5%.

Due to the possible influence of plant activity on CO₂ content during the vegetation season, it is important to adapt a model to the conditions of the region of interest. For example, the territory of St. Petersburg mainly borders large areas of mixed forests and fields located in the Leningrad region and Finland [23]. According to the Annual International Geosphere–Biosphere Programme (IGBP) classification, the “mixed forest” can be characterised as a mix of four forest types—“Evergreen needleleaf forests”, “Evergreen broadleaf forests”, “Deciduous needleleaf forests” and “Deciduous broadleaf Forests”. Each of these vegetation types covers less than 60% of the landscape [24].

The aim of the current study is a complex evaluation of the WRF-Chem model designed to simulate the spatio-temporal variation of CO₂ content in the atmosphere on a city-wide scale. The study is based on a comparison of the WRF-Chem-modelled data with in situ and remote ground-based observations of atmospheric CO₂ content and meteorological parameters for the territories of two large cities located on the Gulf of Finland—St. Petersburg (Russia) and Helsinki (Finland). In addition, the WRF-Chem-modelled data are compared to independent modelled data provided by Copernicus Atmosphere Monitoring Service (CAMS) and NOAA’s Global Monitoring Laboratory. The data and methods are described in Section 2. The results of the WRF-Chem model validation are provided in Section 3. The conclusion of the study is given in Section 4.

2. Data and Methods

2.1. Measurements of Meteorological Parameters and CO₂ Content in the Atmosphere

Remote ground-based measurements of CO₂ total column (TC) were carried out in St. Petersburg in January 2019–March 2020. A measurement site is located at the Faculty of Physics of St. Petersburg State University (SPbU, 59.88°N, 29.83°E) in Peterhof. Peterhof is a part of St. Petersburg (Petrodvorcovii district) which is located ~25 km from St. Petersburg’s centre. Peterhof is set almost in the background conditions, and surrounded mainly by mixed forests and fields. In contrast to St. Petersburg’s centre, there are no large stationary sources of CO₂ or intense automobile traffic on the territory of the Peterhof and Petrodvorcovii districts.

Scientists from the Finnish Meteorological Institute (FMI, Helsinki, Finland) and the University of Helsinki (UHEL) (60.20°N, 24.96°E) carry out regular observations of the CO₂ mixing ratio and many other atmospheric parameters in the surface layer of the atmosphere from the roof of FMI [25]. The measurement site is located in a semi-urbanised part of Helsinki surrounded by automobile roads, parks and forests, and the built environment is mainly defined by administrative buildings. The predominant vegetation type near the station is mixed forest. Due to the relatively small distance between Helsinki and St. Petersburg (~330 km) and the quite similar mean weather conditions in these cities, the observed near-surface CO₂ mixing ratio data in Helsinki are used in this study for an additional validation of the WRF-Chem model.

In addition, observations of CO₂ fluxes by plants recorded at a background Finnish measurement station are used in this study. The station is positioned in Southern Finland ~180 km from Helsinki’s anthropogenic influence, and is surrounded predominantly by coniferous forest [26].

Moreover, observations of several meteorological parameters (air temperature, wind speed and direction) are used to validate the WRF-Chem model’s ability to simulate the transport of CO₂ in the troposphere. Meteorological observations are carried out in St. Petersburg (Peterhof, SPbU), Voeikovo (Voeikov Main Geophysical Observatory, ~20 km from St. Petersburg’s centre and ~50 km from Peterhof) and Helsinki (FMI and UHEL). The main characteristics of the measurement systems and observation data used in this study, together with the WRF-Chem numerical experiment settings, are provided below.

2.1.1. Meteorological Parameters

Near-Surface Wind Speed and Direction

Regular observations of near-surface meteorological parameters (including wind speed and direction) have been performed at a 10 s frequency since 2018 in Peterhof (St. Petersburg) on the premises of the Faculty of Physics in SPbU. For this, a WXT536 weather station, which is located on the roof of the building (~18–20 m above ground level or agl), is used [27].

In Helsinki, observations of near-surface wind speed and direction are performed at the station SMEAR (Station for Measuring Ecosystem–Atmosphere Relations) III Kumpula [28], which is located on the roof of the Faculty of Physics of UHEL. The observations are performed at ~30 m agl [29]. A Vaisala WAA14 cup anemometer is used to observe wind parameters. The data are available with a frequency of 1 min and can be downloaded from https://smear.avaa.csc.fi (accessed on 21 January 2022).

Vertical Profiles of Wind and Air Temperature

In the Voeikov Main Geophysical Observatory (Voeikovo, Leningrad region), aerological observations of meteorological parameters (wind, air temperature, relative humidity, etc.) relative to vertical distribution are measured at 0 and 12 UTC by a radiosonde attached to a weather balloon. The observations are provided from the ground up to ~30 km and are freely available on a website [30]. The measurement site is located on the opposite side of the St. Petersburg city centre, relative to Peterhof. Therefore, the validation of the WRF-Chem model using aerological observations from Voeikovo can be helpful in analysing cases of air mass transport toward Peterhof from the most-CO₂-polluted regions of St. Petersburg.

To compare the modelled and measured data, the modelled profiles of meteorological parameters were linearly interpolated to the vertical levels of the measurements (up to 50 hPa, which is WRF-Chem’s approximate upper limit). Note that it is recommended to estimate whether energy and mass are conserved after an interpolation. However, we supposed that the contribution of the vertical interpolation to the mass and energy balance deviation would be small. This is because the heights of the vertical levels of the observation data are quite similar to the heights of the levels of the original modelled data (i.e., before the interpolation). Figure 1 shows examples of air temperature and wind direction and speed in vertical profiles, derived by the observations in Voeikovo and WRF-Chem modelling, (before and after the interpolation) for 19 December 2019 12 UTC. It can be seen that the interpolated modelled profiles do not differ significantly from the original modelled profiles.

2.1.2. Near-Surface CO₂ Mixing Ratio

In situ measurements of near-surface CO₂ mixing ratio have been carried out on the roof of FMI, Helsinki (60.20°N, 24.95°E, ~36 m agl) since 2010 [25]. A G1301 gas analyser manufactured by Picarro, Santa Clara, California, USA [31] is used; the technique is based on cavity ring-down spectroscopy. The instrument is calibrated 2–3 times per year according to WMO/GAW standards (https://community.wmo.int/activity-areas/gaw (accessed on 30 July 2021)). The mean difference (systematic error) between this instrument and a given standard is 0.01–0.04 ppm, with a standard deviation of the mean difference (random error) of 0.02–0.07 ppm. The data are available with a 1 h frequency.

2.1.3. Column-Averaged CO₂ Mixing Ratio (XCO₂)

Retrieved values of the column-averaged CO₂ mixing ratio (or XCO₂, in ppm) are used in the study. XCO₂ is calculated as the following:

$${XCO}_2={(TCCO}_2)/({TC}_{air}-{TC}_{water}),$$

(1)

where $TCCO$ is a CO₂ total column (TC), i.e., the number of CO₂ molecules in an atmospheric column of a particular area (which usually is given in mol. cm⁻²); ${TC}_{air}$ is the number of all air molecules in the atmospheric column; ${TC}_{water}$ is the number of water molecules in the atmospheric column.

XCO₂ characterises the content of CO₂, on average, in the total column of dry atmosphere. By “dry” we mean that the effect of water vapour variation is mitigated by the subtraction of water vapour content from the TC of air (1). TCCO₂ values are retrieved from measured spectra of incoming infrared (IR) solar radiation by a calibrated IR–Fourier spectrometer Bruker EM27/SUN [32]. This instrument measures spectra in the IR range of wavelengths (4000–12,000 cm⁻¹) with 0.5 cm⁻¹ spectral resolution. To interpret spectra and retrieve CO₂, total columns and other parameters, the algorithm described in [32] was used. TCCO₂ values are calculated as integrals of the retrieved CO₂ vertical profiles. After that, Equation (1) is used to calculate XCO₂. The systematic and random error levels of the retrieved XCO₂ values observed by the Bruker EM27/SUN measurements and the algorithm [32] are ~0.5% and 0.025–0.075%, respectively [32,33,34].

The measurements were carried out from January 2019 to March 2020 within the framework of the international campaign EMME (Emission Monitoring Mobile Experiment) [5], with the following objectives: measurements and emission estimations of greenhouse gases for the territory of St. Petersburg [6,35]. The measurements were performed only during cloudless conditions, and therefore the dataset contains gaps during certain days and months. In total, the dataset includes 83 days of measurements for the abovementioned period. The data are available with ~1 min frequency, but for only ~3–4 h per day, with long gaps within days and months.

2.2. The WRF-Chem Model—Adaptation to St. Petersburg and Helsinki

The WRF-Chem model (Weather Research and Forecasting—Chemistry) [17] is a numerical regional model for weather prediction and the composition of the troposphere and lower stratosphere at a high spatial resolution. The modelling of CO₂ transport in the atmosphere was performed for the period of January 2019–March 2020 on the territory of the Gulf of Finland and its surroundings, with a focus on St. Petersburg (Russia) and Helsinki (Finland). Complex observations of atmospheric CO₂ (near-surface and total column) and meteorological parameters are available for this period of time.

2.2.1. Description of the WRF-Chem Numerical Experiment

The modelling of CO₂ transport was performed on four modelling domains, three of which are nested to the largest parent domain. This step allowed us to set boundary conditions on the inner domains with higher spatial resolution more correctly (Figure 2). The outer parent domain (d01) covers an area of 800 × 800 km² with a space resolution (Δx) of 8 km. The area contains parts of northwest Russia, southern Finland, Estonia and Latvia. The second modelling domain (d02) is nested to d01, covering 320 × 320 km², and Δx = 4 km. Two of the smallest domains—d03 and d04—have the same areas (110 × 110 km²) and, for both, Δx = 2 km. Moreover, d03 is nested to d02, covering St. Petersburg, while d04 is nested to d01, covering Helsinki. We nested the d04 domain only to d01 due to the following reason. Only near-surface CO₂ mixing ratio is analysed in d04, which is more dependent on local CO₂ emissions than on advection from the domain`s boundaries. In contrast, CO₂ total content is analysed in d03, a measurement which is more sensitive to processes in the whole troposphere (e.g., advection from remote territories) than those in a surface layer. In addition, for the nesting of d04 to d02, the domains d01 and d02 have to be expanded westward to provide some space (several hundred kilometres) between the west boundaries of the d01 and d02 domains. According to our analysis, this action would significantly increase the WRF-Chem computation time. That is why the d03 domain is nested to d02 and the d04 domain is nested directly to d01.

The vertical distribution of the modelling was set to 25 hybrid levels, with the top at 50 hPa, which corresponds to ~18–20 km. This number of layers should be roughly enough to simulate the spatio-temporal distribution of CO₂ in the atmosphere above St. Petersburg and Helsinki. For example, in a prior study [19], 26 vertical layers were used to simulate CO₂ total columns in Berlin, Germany. A time step (Δt) constituted 40 s for d01, 20 s for d02, and 10 s for d03 and d04. To use the available observations of CO₂ content in the atmosphere more effectively, the WRF-Chem-modelled data were output for every 10 min.

Table 1. The main parameters of WRF-Chem simulation. GHG—greenhouse gases; hor. res.—horizontal resolution.

Parameter		Description
Horizontal extent and resolution		d01 (800 × 800 km2)—8 km, d02 (320 × 320 km2)—4 km, d03 (110 × 110 km2, St. Petersburg) and d04 (110 × 110 km2, Helsinki)—2 km
Vertical resolution		25 hybrid levels, from the surface up to 50 hPa
Initial and boundary conditions	Meteorology	ERA5 reanalysis, hor.res. 0.25°, up to ~80 km on 137 hybrid levels
	Atmospheric CO2 content	CT-NRT.v2022-1, hor.res. 2 × 3°, up to ~200 km on 35 hybrid levels
CO2 sources and sinks	Anthropogenic emissions	ODIAC 2019, hor.res. ~0.43 km2
	Biogenic fluxes	VPRM (online, every model time step); Partially optimised by flux observations in Hyytiälä, Finland (see Appendix B); Hor.res.—as in d01-d04, Temporal resolution—8 days
Simulation period		January 2019–March 2020, 10 min output
Chemistry option		GHG option: CO2 is treated as a fully inert tracer

summarises the main parameters of the WRF-Chem numerical experiment. The current setup of the WRF-Chem model is based on several independent studies [19,36] and on our own experience [20,22].

In the current study, CO₂ in the atmosphere is considered to be a fully inert gas, i.e., no CO₂ chemical reactions are used in the simulation. Four main factors determining the variation of CO₂ content in the atmosphere are considered. These are (1) atmospheric transport, (2) chemical boundary conditions (BCs), (3) anthropogenic emissions of CO₂, and (4) CO₂ biogenic fluxes due to the activity of plants (vegetation). Details of the three last factors are given in the next sections.

Initially the WRF-Chem model simulates the change of CO₂ content in the atmosphere characterised by three main factors—chemical BCs, anthropogenic emissions, and biogenic fluxes. Therefore, the model output provides CO₂ content as three separate variables—CO₂ BCs, CO₂ Ant (anthropogenic) and CO₂ Bio (biogenic). The sum of the three components gives the CO₂ content, which is analysed in next sections. Such an approach allows us to estimate how the total content of CO₂ in the atmosphere depends on each of the three components.

XCO₂ according to the WRF-Chem-modelled data is calculated by Equation (1). Above the model’s top, CO₂ content was determined from the modelling data of the Copernicus Atmosphere Monitoring Service (CAMS) [37]. This step is described in Appendix A.

Table 2. Atmospheric processes and their parameterization schemes considered in the WRF-Chem model on a sub-grid scale.

Process	Scheme Name	Source
Transfer of long-wave EM radiationin the atmosphere	RRTM Longwave Scheme	[39]
Transfer of short-wave EM radiationin the atmosphere	Dudhia Shortwave Scheme	[40]
Earth’s boundary layer model	Mellor–Yamada–Janjic	[41]
Earth’s surface layer model	Eta Similarity Scheme	[42,43]
Model of land-surface layers’ interaction	Unified Noah land-surface scheme for non-urban landcover surface energy fluxes	[44]
Vertical transport and convective clouds	The Grell 3D ensemble cumulus convection scheme	[45]
Microphysics of clouds	WRF single-moment six-class schemes	[46]
Urban effect	Building Effect Parameterization (BEP)	[47]

shows the atmospheric processes which are parametrized on a sub-grid scale in the WRF-Chem model. Note that all processes from Table 2, except for vertical transport, were modelled by these parametrizations on each of the four modelling domains. In case of vertical transport modelling, the corresponding scheme was only used for the d01 and d02 domains (Δx 8 and 4 km, respectively). To simulate vertical transport on the two smallest domains, d03 and d04, a hydro-dynamical equation system in an approximate form was used. According to [38], such an approach is supposed to be the most correct choice when Δx < 5 km.

2.2.2. Initial and Boundary Conditions

To set initial (IC) and boundary (BC) meteorological conditions, the data of meteorological global reanalysis ERA5 [48] are used in this study. The ERA5 reanalysis data are based on numerical modelling and 4DVar assimilation of the measurements. The data have 0.25° (~25 km) spatial resolution and are spread vertically on 137 hybrid levels, covering a layer from the Earth’s surface to ~80 km [48,49]. The ERA5 data include such parameters as atmospheric pressure, wind speed and direction, air temperature, specific humidity, geopotential, etc. The meteorological BCs were set for the whole period of modelling, with a 6 h frequency.

CarbonTracker data from Near-Real Time v.2022-1 (CT-NRT.v2022-1) version [50] are used to set chemical BCs. The data consist of the CO₂ mixing ratio on a global scale with a 2 × 3° (~200 × 300 km²) horizontal resolution, spreading vertically on 35 hybrid levels up to ~200 km. The CT-NRT.v2022-1 data were created by a global numerical model of atmospheric transport T5 and assimilation of observations (ground-based in situ, ship, aircraft and measurements from masts) (https://gml.noaa.gov/ccgg/carbontracker/CT2019B/ (accessed on 15 June 2021)). In the current study, the chemical BCs are set every 6 h. The CarbonTracker data were developed by scientists from NOAA ESRL, Boulder, CO, USA (http://carbontracker.noaa.gov (accessed on 15 June 2021)).

2.2.3. Sources and Sinks of CO₂ Emissions

Anthropogenic Emissions

The ODIAC (Open-source Data Inventory for Anthropogenic CO₂) global inventory of anthropogenic CO₂ emissions, with a high spatial resolution (0.43 km² for the modelling domain), is used in this study to set sources of anthropogenic CO₂ emissions for the WRF-Chem domains [51]. The ODIAC inventory is based on official reports on the amount of fossil fuel burned by countries. Spatial discretization of the total emissions inside a particular country with a high spatial resolution is achieved by satellite observations of urban lights at night and by information on stationary sources’ locations (for example, combined heat and power plants or CHP). The ODIAC inventory for 2019 is available as total monthly anthropogenic CO₂ emission per area.

Figure 3 depicts anthropogenic CO₂ emissions on the territories of St. Petersburg (a) and Helsinki (b), in March 2019, in tCO₂ per month according to the ODIAC inventory. The white circles in Figure 3 point to measurement stations (Peterhof and Kumpula). According to the ODIAC inventory, the spatial distribution of anthropogenic CO₂ emissions in the territory of St. Petersburg is quite inhomogeneous, with a maximum in the city centre and minimum at its periphery. In contrast, anthropogenic emissions of CO₂ from the territory of Helsinki are significantly lower and more spatially homogeneous. In this example, the specific anthropogenic emission of CO₂ from the territory of Helsinki is ~2.3 times lower than that from St. Petersburg.

The CO₂ emissions from the ODIAC inventory which, according to https://openinframap.org (accessed on 14 March 2021), corresponded to the positions of CHP in St. Petersburg and Helsinki, were placed on four lowest vertical levels of the model (heights in a range 50–200 m agl).

Biogenic Fluxes

The territories of St. Petersburg and Helsinki are surrounded by different types of vegetation—from coniferous forests to grasslands. Therefore, the biogenic factor, which is constituted by the consumption and emission of CO₂ by plants, can significantly influence CO₂ content in the atmosphere from the second part of spring to the beginning of autumn [52]. The Vegetation Photosynthesis and Respiration Model (VPRM) is used in the WRF-Chem simulation to consider the consumption and release of carbon dioxide by plants [53]. The VPRM is a part of the WRF-Chem model. Both models run simultaneously.

The VPRM allows us to estimate the CO₂ consumption by plants due to photosynthesis (Gross Ecosystem Exchange or GEE) during daytime and CO₂ release in the night-time (Respiration or Resp) for seven types of vegetation. The sum of GEE and Resp (Net Ecosystem Exchange or NEE) determines whether plants act as a source of CO₂ or a sink. A more detailed description of the model can be found in [53]. In the framework of the VPRM, the parameters GEE and Resp are functions of near-surface air temperature, reflected shortwave solar radiation in particular ranges of wavelengths, and the amount of photosynthetically active radiation consumed by plants. The reflected shortwave solar radiation data are measured by the Moderate Resolution Imaging Spectroradiometer (MODIS), which is onboard the Aqua and Terra satellites (product MCD12Q1 v006, https://lpdaac.usgs.gov/products/mcd12q1v006/ (accessed on 12 December 2022)). The satellite data are available with an 8 day-frequency.

In the current study, the VPRM was partially optimised by the correction of the Resp parameter using the corresponding measurements from the background Finnish observation station “SMEAR II Hyytiälä Forest”. The correction was provided only for one of seven vegetation types—needleleaf forest. The trees of this type are predominant in the area of the station. The characteristics of the CO₂ biogenic fluxes according to the measurements at the SMEAR station are described in Appendix B.

The parameter Resp in the VPRM is calculated by linear regression from near-surface air temperature (Tair). The parameters of linear regression (a and b) are fitted for a particular vegetation type based on the measurements of Tair and Resp.

Table A1. VPRM parameters “a” and “b” for a vegetation type “mixed forest” before and after optimization.

Parameters	Before Correction	After Correction
a	0.1797	1.4650
b	0.8800	1.4650

in Appendix B contains the original values of the regression parameters, and those corrected to the conditions of Hyytiälä.

Figure A1 in Appendix C demonstrates the time series of GEE and Resp by the VPRM modelling in the framework of the WRF-Chem run, as well as the measurements at the Hyytiälä station, for March 2019–January 2020. The correlation coefficient is ~0.9. On average, the model underestimates and overestimates GEE and Resp by 11.7 and 6.9%, respectively. The maximum differences were found in summer, i.e., during the peak of the vegetation season.

Other Sources and Sinks of CO₂

Another possible factor influencing CO₂ content is absorption and emission of the gas by a water surface. St. Petersburg and Helsinki are located on the shore of a large water body—the Gulf of Finland. To estimate the possible influence of the water surface of the Gulf of Finland on CO₂ content in St. Petersburg, a prior study [54] was carried out. In this study, the CO₂ fluxes from the Gulf of Finland were investigated using methods from independent studies and ship-based observation data.

The study has demonstrated that the possible contribution of the gulf’s water surface to the atmospheric CO₂ content is very small in relation to anthropogenic emissions (1.7–3%). Therefore, in the current study the contribution of the water body to the atmospheric CO₂ content was neglected.

The contribution of biomass burning to the CO₂ content is set implicitly via chemical BCs on the largest modelling domain (d01).

2.2.4. Correction of the Chemical Boundary Conditions

According to analysis, the CarbonTracker data (ICs and BCs in the WRF-Chem model run) overestimate XCO₂ by ground-based remote measurements in Peterhof during January 2019–March 2020 by 3.3 ppm, with a standard deviation of 1.3 ppm (Figure 4). This can be related to errors in a priori anthropogenic emissions of CO₂, crude spatial resolution of the modelling, etc. Therefore, the CarbonTracker data should be corrected before using them as chemical ICs and BCs in the WRF-Chem simulation for the territory of the current study.

However, it is impossible to directly compare the CarbonTracker data with the measured CO₂ total column (TC) on the boundaries of the parent modelling domain since there are no corresponding observations in these regions. Let’s assume that CO₂ content in an air mass which is advected to St. Petersburg is influenced only by advection from a remote territory (for example, from the domain’s boundaries). Such conditions can be achieved if there are few large anthropogenic sources of CO₂ and weak fluxes by vegetation on the path of the air mass moving toward St. Petersburg. Therefore, to use the available CO₂ observations in St. Petersburg, the pairings of XCO₂ in the city from CarbonTracker and the measurements were filtered according to those two conditions.

In a previous study [55], it was shown that with particular directions of the near-surface wind, ground-based remote observations of CO₂ TC in Peterhof registered the anthropogenic contribution of the centre of St. Petersburg to the CO₂ content in the atmosphere. Hence, to filter the data by the first condition, ground-based measurements of XCO₂ and near-surface wind direction in Peterhof were analysed. The measurements of TC CO₂ when the near-surface wind direction corresponded to atmospheric transport from the territory of St. Petersburg (20–150°) were excluded from the further correction of the CarbonTracker data. To consider the second filtering condition, the data were filtered by the period when the biogenic influence on CO₂ content would be at its maximum. According to the VPRM, this is the period from the beginning of spring to the middle of autumn.

The filtration reduced the dataset from 128 to 14 pairs of XCO₂ values by the CarbonTracker and measurement data in St. Petersburg for January 2019–March 2020. At this point, it can be said that the filtered values of XCO₂ characterise the TC CO₂ in St. Petersburg, which, in general, was influenced by air mass transport from the boundaries of the WRF-Chem modelling domain. The mean difference (MD) between the filtered pairs constitutes −1.8 ppm (~−0.4%), which means that the CarbonTracker data overestimate observed XCO₂ values. Therefore, chemical BCs (the CarbonTracker data) were reduced by 0.4%.

2.3. Independent XCO₂ Modelling Data in St. Petersburg

The global reanalysis of atmospheric CO₂ by the Copernicus Atmosphere Monitoring Service (CAMS), version v21r2 [37], was used in the study as independent modelled data. The data have horizontal resolution of 1.86 × 3.75° (~200 × 400 km²), spreading vertically on 39 hybrid levels up to ~70 km agl. The data are available for the whole period of investigation with a 3 h frequency. The CAMS reanalysis was made using a numerical model of global atmospheric transport with assimilated ground-based measurements of near-surface CO₂ content [56].

3. Results and Discussion

3.1. Comparison between Modelling and Measurement Data

3.1.1. Near-Surface Wind Speed and Direction

The WRF-Chem model simulates near-surface (10 m) wind speed and direction in St. Petersburg and Helsinki with rather different errors. The mean differences (MDs) are −1.7 m/s and 38.2° for St. Petersburg and −0.8 m/s and 21.6° for Helsinki. The standard deviation of the difference (SDD) of wind speed is almost the same in both cities, at 1.5–1.6 m/s. However, the SDD of wind direction is higher in Helsinki (48.2°) than in St. Petersburg (29.3°). Probable reasons for the WRF-Chem model to overestimate near-surface wind speed include higher uncertainties in the simulations of windless conditions (e.g., during winter) [57,58]. In addition, the overestimation of near-surface wind speed by the WRF-Chem model relative to observations can be caused by local small-scale tropospheric circulations due to the proximity of St. Petersburg and Helsinki to the Gulf of Finland [59] and Ladoga Lake (on the west). Correlation coefficients (CC) between the modelled and measured near-surface wind speed and direction are, respectively, 0.76 and 0.8 in St. Petersburg and 0.67 and 0.78 in Helsinki. Similar estimates are provided in [18,60].

Figure 5 demonstrates histograms of the distribution of near-surface wind direction and speed in St. Petersburg (January 2019–March 2020) and Helsinki (2019) according to the WRF-Chem modelling and observations. First, note how different the wind direction distribution is in the two cities. Wind directions 140–180° (SSE-S) and 220–260° (WSW) (Figure 5a) with a wind speed of 1–4 m/s (Figure 5c) are predominant in St. Petersburg. The distribution of near-surface wind direction in Helsinki (Figure 5b) is more complicated and doesn’t have prevailing ranges. Nevertheless, the following ranges of wind direction were registered more frequently—100–120°, 200–240° and 280–320° (respectively, ESE, SSW-WSW and WNW-NNW). Only one of these ranges was also registered in St. Petersburg—200–240°. It is probable that such differences in the distribution of near-surface wind direction between two cities are caused by local factors of an urban scale, even though the cities are only ~330 km apart from each other. Analysing the seasonal change of wind direction (not shown in this study’s figures), it can be said that the left hump of the distribution for Helsinki is related, in general, to wind directions during spring and summer.

The WRF-Chem model simulates the predominant near-surface wind directions in both cities. However, its results fit the observations in Helsinki worse than those in St. Petersburg. This is also shown by the SDD values given above.

The distribution of near-surface wind speed is quite similar in both cities. It constitutes 1–3 m/s for St. Petersburg (Figure 5c) and 2–4 m/s for Helsinki (Figure 5d). The model simulates some features of the wind speed distribution for both cities, but in general overestimates this meteorological parameter. The better agreement between the modelled and measured near-surface wind speed is found for Helsinki. The representations of the distributions of both wind speed and direction in St. Petersburg for 2019 (as in Helsinki) demonstrate that they are almost the same as for the period January 2019–March 2020.

Figure 6 presents the mean diurnal variations of 10 m wind speed in St. Petersburg and Helsinki by the WRF-Chem model and measurements. The analysis is provided for 2019 only, and the time is given in local hours with the purpose of comparing the diurnal variation of 10 m wind speed in the two cities.

According to the observations (black dashed line), in St. Petersburg the wind speed increases from 8 to 12–14 h with a subsequent decrease (Figure 6a), while in Helsinki the maximum is reached at ~16 h (Figure 6b). The model simulates the temporal variation of the 10 m wind speed in both cities relatively well. However, according to the modelled data, the maximum in Helsinki is reached slightly earlier, relative to the observations (12–14 h). The WRF-Chem model significantly overestimates the wind speed in both cities (by ~2 times). This was also found in the previous analysis (Figure 5). More complex urban features and their influence on air-mass flow in St. Petersburg can be one reason for the worse fit between the measured and modelled 10 m wind speed relative to Helsinki. The analysis has demonstrated that the model simulates 10 m wind speed during night- and daytime in St. Petersburg with almost the same differences relative to measurements. However, for Helsinki, the difference between the modelled and observed wind speed during night- and daytime hours constitutes ~50%.

The seasonal variation of 10 m wind speed in both cities (Figure 7) is not so pronounced as the diurnal variation. On average, in both cities, the wind speed increases in winter, with the maximum in February, and decreases in spring and summer, with the minimum in April and August. According to the observations, the 10 m wind speed in St. Petersburg (Figure 7a) is slightly lower than the wind speed in Helsinki (Figure 7b by 0.5–1 m/s). A lookalike pattern of a near-surface wind speed seasonal variation, although above a water surface, was found near Hong Kong in a prior study [61].

The WRF-Chem model simulates well the times of maximum and minimum monthly mean wind speed in both cities. Nevertheless, the model overestimates the observed wind speed values, with the maximum differences in February (2–2.5 m/s) and minimum differences in July (St. Petersburg, ~0.5 m/s) and August (Helsinki, 0.1–0.2 m/s).

It should be noted that the modelling domain d04, which covers Helsinki, is nested to the domain with a spatial resolution of 8 km (d01). In contrast, the modelling domain covering St. Petersburg (d03) is nested to a domain a with finer resolution (4 km, d02). This also can influence the consistency between the modelled data and the measured data. Near-surface wind speeds and directions at the St. Petersburg measurement station from domains d01, d02 and d03 were compared. It was found that the differences between the wind direction and speed from d01 and d03 amount to ~58° and 1.2 m/s, respectively (graphics are not shown). In addition, the wind direction and speed from d02 and d03 differ by ~50° and 0.7 m/s. Nevertheless, it was revealed that the background near-surface CO₂ mixing ratios (i.e., advected from the boundaries, CO2_BCK) in St. Petersburg as determined by the modelling from three domains do not significantly differ with each other. The differences are below 0.1%. Therefore, in this case, it can be assumed that the choice of CO₂ boundary conditions does not significantly influence the near-surface CO₂ mixing ratio in the centre of the domains.

3.1.2. Vertical Distribution of Meteorological Parameters near St. Petersburg

The WRF-Chem model simulates the vertical profiles of three meteorological parameters—wind speed, direction and air temperature—in the troposphere and lower stratosphere above Voeikovo for January 2019–March 2020 relatively well. The distributions of these profiles by the modelling and measurements are presented in Figure A2 (Appendix C). In general, the shapes of three meteorological-parameter distributions determined by the modelling and radiosonde observations are quite similar. It can be seen that in the troposphere and lower stratosphere near St. Petersburg, eastward atmospheric transport (Figure A2a) with 4–10 m/s wind speed (Figure A2b) and 50–60 °C and 0–10 °C air temperature ranges (Figure A2c) are predominant.

The best fit between the modelling and measurement data is for air temperature, with MD = 0.4 °C, SDD = 2.5 °C and CC = 0.99. MD and SDD for wind speed are 0.5 and 4.1 m/s and 12.1 and 28.3° for wind direction, respectively. In the upper troposphere, the wind speed arrived at by the measurements and modelling can reach 40–50 m/s. This explains the large SDD of the parameter. The CC for the wind speed and direction are 0.93 and 0.86, respectively.

According to the analysis, the WRF-Chem model can probably be used to simulate horizontal and vertical distribution of the CO₂ in the atmosphere. This will be the subject of our investigations in the next sections.

3.1.3. Near-Surface CO₂ Mixing Ratio in Helsinki

Figure 8 depicts a time series of hourly averaged near-surface CO₂ mixing ratios in Helsinki for 2019 according to the WRF-Chem simulation and the measurements.

Table 3. Statistical characteristics of the differences between near-surface CO₂ mixing ratios determined by the measurements and by WRF-Chem modelling for 2019; values in % are given relative to the mean measured value. STD—standard deviation from mean, MD—mean difference, SDD—STD of MD, CC—correlation coefficient, GGA—greenhouse gas analyser; a confidence interval at a 95% confidence level is given for means.

Data	Dataset Size	Mean and STD, ppm	MD and SDD, ppm (%)	CC
GGA—WRF-Chem	8565	418.0 ± 0.2 and 9.7/ 417.4 ± 0.2 and 9.5	0.6 ± 0.15 and 7.0 (0.15 ± 0.04 and 1.7)	0.73

presents the main characteristics of the discrepancies between the data. According to [62], a confidence interval of 95% confidence level is given for means

$$\overline{{\mathit{V}\mathit{M}\mathit{R}}_{{\mathit{C}\mathit{O}}_2}}\pm \mathit{z}\frac{\mathit{S}\mathit{T}\mathit{D}}{\sqrt{\mathit{N}}}[\mathit{p}\mathit{p}\mathit{m}],$$

(2)

where $\overline{{VMR}_{{CO}_2}}$—mean near-surface CO₂ mixing ratio (VMR—volume mixing ratio); z—quantile of normal distribution or Student coefficient for 95% confidence level; $STD$—standard deviation from mean; $N$—size of a dataset.

The WRF-Chem model simulates well the temporal variation of the near-surface CO₂ mixing ratio in Helsinki. The correlation is 0.73. MD and SDD are 0.15 and 1.68%, respectively. In general, the model underestimates the CO₂ mixing ratio relative to the measurements.

From approximately April to October 2019, there was a clear influence from the vegetation season, which caused increases in the biogenic fluxes of CO₂; this was registered by the measurements and modelling data and can be seen in Figure 8. Nevertheless, the WRF-Chem model underestimates the CO₂ mixing ratio during vegetation season by ~3 ppm.

Excluding the biogenic influence causes an increase in MD from 0.15 to 0.45%, but a slight decrease in SDD, from 1.68 to 1.56%. In addition, this leads to an increase in MD by ~0.2% from April to August. It is probable that the small change in MD, while excluding the biogenic factor, is related to the influence of biogenic activity via chemical BCs which also influence diurnal variation of the near-surface CO₂ mixing ratio during vegetation season. If the analysis excludes anthropogenic CO₂ emissions and biogenic fluxes inside the modelling domain d04, MD increases from 0.15 to 1.44%, and CC decreases from 0.73 to 0.69.

A total of ~59.6% (from 8500) of all MDs are less than 4.2 ppm (1%), 32.6% of MDs are higher than 4.2–12.5 ppm (~1–3%) and only 8% of all MDs are higher than 12.5 ppm (3%). There are only a few (9, or 0.1% of all MDs) large differences which constitute ~40–60 ppm (10–15%). It is probable that they can be called anomalies.

The analysis of the relation between the near-surface CO₂ mixing ratio modelling error and errors in the modelling of near-surface wind speed in Helsinki has demonstrated that there is no explicit relation (CC = ~−0.1). However, using only CO₂ mixing ratio modelling errors larger than 3% (~12.5 ppm), weak negative correlation with the wind speed modelling error was found (CC = −0.4, with a dataset size of 732 vs. 8500). If one uses CO₂ mixing ratio modelling errors which are higher than 17 ppm, CC also increases to −0.48, but for a significantly reduced dataset (282 vs. 8500). It was found that change in the sign of the CO₂ mixing ratio modelling error leads to the opposite sign of the wind speed modelling error. It is logical, since if the model overestimates the wind speed, it should underestimate near-surface CO₂ mixing ratio. Therefore, it can be said that the largest modelling errors of the near-surface CO₂ mixing ratio in Helsinki are related to the near-surface wind speed modelling errors.

Modelling of Diurnal and Seasonal Variation of the Near-Surface CO₂ Mixing Ratio

Figure 9 presents the mean diurnal variation of the near-surface CO₂ mixing ratio at the measurement station in Helsinki for 2019, as determined by the WRF-Chem modelling and the measurements. The time is given in UTC. The shaded area shows confidence intervals.

In general, the WRF-Chem model simulates well the mean diurnal variation of the near-surface CO₂ mixing ratio in Helsinki. The model underestimates the CO₂ mixing ratio during night and day hours relative to the measurements by 1.5 ppm and less than 1 ppm, respectively. An analysis of the diurnal variation of near-surface wind speed together with CO₂ mixing ratio was carried out. It demonstrated that the diurnal variation of the CO₂ mixing ratio is probably influenced by biogenic CO₂ fluxes during the vegetation season and clear diurnal variation of wind speed in spring and summer. It was found that the WRF-Chem model simulates low wind-speed conditions less accurately than high-speed conditions. This might be a reason for the lower CO₂ mixing ratio during night hours determined by the WRF-Chem model [58,59]. In winter the diurnal variation of the CO₂ mixing ratio in Helsinki is quite smooth, with an increase by 5 ppm to 12 UTC (according to the measurements). By contrast, in summer the diurnal variation of the mixing ratio is more pronounced, with a CO₂ content variation of 10 ppm during the day. It is probable that the winter’s increase in atmospheric CO₂ content is caused by the more frequent windless conditions and the larger number of air-temperature inversions. The worst fit between the modelled and measured mean diurnal variation of the CO₂ mixing ratio is found for the winter season, and the best—for the spring. This could be caused by the larger errors in the modelling for near-surface wind speed during windless conditions. The confidence intervals for the observed and modelled data are quite similar, at ~±1 ppm, with an increase to 11–12 UTC.

An analysis of the variations of the near-surface CO₂ mixing ratio during the week shows that both the WRF-Chem model and the measurements give a decrease in the mixing ratio by 1–1.5 ppm during weekends (Saturday and Sunday). This probably is related to the reduction of automobile traffic during the weekends and, as a result, to the decrease of anthropogenic CO₂ emissions. However, the weekly variation of anthropogenic CO₂ emissions was not set explicitly in the WRF-Chem model run. It is probable that the weekly variation of anthropogenic CO₂ emissions was indirectly set via chemical BCs (CT-NRT.v2022-1) which were refreshed with a 6 h frequency. According to [63], in the framework of the CarbonTracker program, scaling factors are applied to fossil-fuel emissions. These factors characterise weekly and diurnal temporal variation of the emissions [64]. Hence, the weekly, and even diurnal, variation of CO₂ atmospheric content due to anthropogenic activity was set in the WRF-Chem simulation via the boundaries of the d01 domain (Figure 2).

It can be seen from Figure 10 that the WRF-Chem model is able to simulate mean seasonal variation of the near-surface CO₂ mixing ratio. Both the modelled data and the measurements show clear decreases of the CO₂ mixing ratio from April to July, along with a subsequent increase. The amplitude of the change is 24 ppm (~5–6% from the mean measured value). The pronounced seasonal variation of the near-surface CO₂ mixing ratio in Helsinki might be the consequence of plant activity during the vegetation season (~from the end of April to the end of September). During this period, plants start acting as the relatively large CO₂ source during night hours and as a sink during daytime hours (see, for example, [36]). The largest differences between the main seasonal CO₂ mixing ratios determined by the model and measurements in Helsinki are found in January–February (3–4 ppm). These can be caused by overestimation of near-surface wind speed in Helsinki by the WRF-Chem model, which is more significant during the winter season. On average, the confidence interval is ~0.5 ppm for both datasets.

Figure A3 of Appendix C demonstrates the spatial distribution of seasonally averaged near-surface CO₂ mixing ratios (Figure A3a) and 10 m wind speed and direction (Figure A3b) as determined by the WRF-Chem modelling with an 8 km spatial resolution (domain d01) and by the ERA5 meteorological reanalysis (Figure A3c) for 2019. Note that the ERA5 reanalysis data are used in the WRF-Chem simulation as meteorological BCs.

At first, a pronounced CO₂ seasonal variation can be seen in Figure A3a. The CO₂ mixing ratio significantly decreases from spring to summer (on average, by 15–20 ppm). Then, from summer to autumn, the amount of CO₂ starts to increase and does not significantly change from autumn to winter. Two main sources of CO₂ which determine the local maximums of the CO₂ mixing ratio are clearly seen, associated with the values higher than 450 ppm. These are anthropogenic emissions from the territories of the cities of St. Petersburg and Kirishi (Leningrad region). The source of CO₂ in Kirishi might be a state regional power plant which is one of the largest power plants in the northwest part of Russia [65].

The mean wind speed and direction on average vary significantly from season to season. According to the modelling data, the largest near-surface wind speed values are found in winter (up to 4–4.5 m/s), and the lowest—in spring (less than 1 m/s). The mean maximum and minimum values of wind speed in general occupy the southern part of the domain (see Figure A3b, spring and winter). In addition, it was found that there was a pronounced tendency of wind speed to increase from spring to winter. It is probable that the highest values of near-surface wind speed during colder seasons are related to the higher contrasts of air temperature above water and earth surfaces. Comparing Figure A3b,c and Figure 1, it can be seen that a small local area of relatively high wind speed values (to the northeast of St. Petersburg) spatially correlates with the area of lowest terrain height (<50 m above sea level).

Comparing the spatial distribution of the mean wind-speed determined by the WRF-Chem model and by ERA5 reanalysis (Figure A3b,c), a relatively good spatial correlation was found. However, in general, the WRF-Chem model over- and underestimates wind speed values relative to the ERA5 data. On average, both modelled datasets represent quite similar 10 m wind directions within the domain. In particular, this can be seen in autumn and winter, when, according to both datasets, there are 10 m winds, predominantly in the north and north-east directions.

3.1.4. XCO₂ in St. Petersburg

The time series of XCO₂ determined by the WRF-Chem modelling and the measurements by the Bruker EM27/SUN in Helsinki are quite close to each other, with CC = 0.95 (Figure 11 and

Table 4. Statistical characteristics of the differences between XCO₂ as determined by the Bruker EM27/SUN measurements and by WRF-Chem modelling, for January 2019–March 2020; values in % are given relative to the mean measured value; STD—standard deviation from mean, MD—mean difference, SDD—STD of MD, CC—correlation coefficient; a confidence interval of 95% confidence level is given for means.

Data	Mean and STD, ppm	MD and SDD, ppm (%)	CC
Bruker EM27/SUN—WRF-Chem	408.4 ± 0.2 and 3.4/ 409.7 ± 0.2 and 3.9	−1.3 ± 0.07 and 1.2 (−0.3 ± 0.02 and 0.3)	0.95

). The model simulates a decrease in XCO₂ due to plant activity (approximately from May to October 2019), together with the subsequent increase, relatively well. In general, the modelled seasonal variation of XCO₂ is influenced by transport from the boundaries of the modelling domain. In turn, the VPRM simulates local features of biogenic fluxes of CO₂. MD and SDD between the modelled and measured data are −1.3 and 1.2 ppm, respectively (~0.3%). The MD can be caused by the errors in chemical BCs even though the BC correction was carried out. Note that the correction was based on the small dataset (14 pairs), which predominantly covers the winter season and does not reflect how the CarbonTracker data differ from the measurements obtained in other seasons of 2019. If chemical BCs are decreased by 0.3%, the MD also decreases to ~0%. However, such a correction cannot be provided without a solid argument (for instance, additional accurate measurements of XCO₂).

In our previous study [22] a series of the WRF-Chem model runs with different settings were carried out to simulate CO₂ transport in St. Petersburg for January 2019–March 2020. In particular, chemical BCs were set with more inaccuracies in the upper troposphere. Also, to calculate XCO₂ using Equation (1), total water content measurements by a ground-based Bruker 125 HR in St. Petersburg were used. According to the results of [22], MD between the modelled and measured XCO₂ constitutes 0.6%, which is about two times larger than the MD from the current study (Table 4). First, a worse fit between the modelled and measured XCO₂ in St. Petersburg might be due to errors in the chemical BCs in the upper troposphere and lower stratosphere. Secondly, it can be caused by the use of a quite limited dataset of water vapour content in the atmosphere. For example, the dataset of water vapour content, as measured by the Bruker 125HR spectrometer, contains only 77 days of measurements in January 2019–March 2020. The current study has demonstrated that, by correctly setting chemical BCs and using modelled data of water vapour content in the atmosphere, it is possible to achieve better correspondence between the modelled and measured values of XCO₂ in St. Petersburg.

In our estimation, three main factors determine the modelled XCO₂—(1) atmospheric transport from the boundaries of the modelling domain, (2) anthropogenic CO₂ emissions and (3) biogenic fluxes of CO₂.

Table 5. Scenarios of variation of XCO₂ components modelled by WRF-Chem. bio—biogenic influence; ant—anthropogenic influence; BCs—boundary conditions.

N	Name	Description
1	Control	Control WRF-Chem modelling XCO2 = XCO2 BC + XCO2 Ant + XCO2 Bio
2	No bio	XCO2 = XCO2 BC + XCO2 Ant
3	No ant	XCO2 = XCO2 BC + XCO2 Bio
4	No bio and ant	XCO2 = XCO2 BC
5	BCs reduced by 0.1%	XCO2 = XCO2 BC × 0.999 + XCO2 Ant + XCO2 Bio
6	BCs reduced by 0.3%	XCO2 = XCO2 BC × 0.997 + XCO2 Ant + XCO2 Bio
7	BCs reduced by 0.5%	XCO2 = XCO2 BC × 0.995 + XCO2 Ant + XCO2 Bio
8	BCs reduced by 0.7%	XCO2 = XCO2 BC × 0.993 + XCO2 Ant + XCO2 Bio
9	BCs reduced by 1.0%	XCO2 = XCO2 BC × 0.990 + XCO2 Ant + XCO2 Bio

presents a description of nine scenarios of the variations of modelled XCO₂ components. Figure 12 depicts MDs (a) and SDDs (b) between XCO₂ values in St. Petersburg for January 2019–March 2020 by the measurements and by WRF-Chem modelling. In addition, the figures show confidence intervals for every value.

As can be seen from Figure 12b, SDDs vary within the range of 0.30–0.33% (~0.1 ppm). This variation is quite small, and it can be assumed that none of the scenarios changes the SDD. Turning off the biogenic factor (Scenario 2) leads to an increase of MD by ~0.1% relative to the Control run (Scenario 1). Conversely, turning off the anthropogenic CO₂ emissions causes an insignificant decrease of MD by 0.05%. It should be noted that MDs for the first five scenarios cover each other by confidence intervals. Therefore, they differ from each other insignificantly. The smallest MD is found for Scenario 6 (reduction of XCO₂ from the chemical BCs by 0.3%). In addition, its confidence interval does not cover other MDs. Further reduction of XCO₂ from the chemical BCs (Scenarios 7–9) leads to an almost linear increase of MDs.

Therefore, the MD between the modelled and measured XCO₂ in St. Petersburg can be reduced to ~0% by an additional decrease in chemical BCs by 0.3%. However, SDD does not change significantly and still constitutes ~0.3%. It can be assumed that SDD is influenced by errors in a priori anthropogenic CO₂ emissions and modelling of CO₂ biogenic fluxes. The fact that turning off both of these factors does not reduce SDD probably means that there are inaccuracies in the spatial distribution of anthropogenic emissions, and in their diurnal, weekly, monthly variations.

3.2. XCO₂ in St. Petersburg as determined by Independent Modelling

Due to the much cruder spatial resolution of the CAMS reanalysis relative to the WRF-Chem data, comparison was carried out for XCO₂ only. For instance, in a prior study [66], the near-surface CO₂ mixing ratio and XCO₂ by CAMS reanalysis of the v18r3 version were compared to in situ and remote measurements in St. Petersburg (Peterhof) for 2018. It was shown that the differences between the modelled and measured near-surface CO₂ mixing ratio significantly depended on the season, and vary by up to 3%. CC also depends on the month, varying from 0.26 to 0.81. However, that was expected, since near-surface CO₂ mixing ratio is influenced by small-scale local processes which cannot be fully taken into account with a spatial resolution of more than 100 km.

The XCO₂ time series in St. Petersburg for January 2019–March 2020 determined by CAMS and WRF-Chem fit with each other well (Figure A4 in Appendix C). MD and SDD are 0.15 and 0.3%, respectively, with a very high CC = 0.96. In general, the WRF-Chem data slightly underestimate XCO₂ values relative to the CAMS reanalysis (positive difference). The maximum differences (up to 5 ppm) are found during the vegetation season. This probably means that biogenic fluxes of CO₂ are treated differently in the models. In addition, XCO₂ variation by the CAMS reanalysis is more smooth than that by the WRF-Chem model. It is probable that this is related to the cruder spatial resolution of the CAMS data.

Figure 13 depicts differences between XCO₂ values determined by the Bruker EM27/SUN measurements and by the modelling (WRF-Chem, CAMS v21r2 and CarbonTracker v2022-1). The CAMS and CarbonTracker data are available with 3 and 6 h frequencies, respectively. Therefore, the minimum time step for the data comparison was 6 h. It can be summarised that the WRF-Chem-modelled data present XCO₂ in St. Petersburg during the period of interest better than do the two other modelled datasets. MDs between the measurements and modelled data constitute 1.3, 2.3 and 3.3 ppm (0.3, 0.5 and 0.8%) for WRF-Chem, CAMS and CarbonTracker data, respectively. The SDDs are quite similar, at 0.2–0.3%. It is likely that the better agreement between the measurements and WRF-Chem data is related to the higher spatial resolution.

3.3. Compliance of XCO₂ Modelling Errors with Modern Requirements

Today, there are many studies available which have assessed the ability of the WRF-Chem model to represent the near-surface concentration, vertical profile, and CO₂ total column, from daily intervals to multi-year time intervals [18,19,22]. It is possible to achieve 0.1% or 0.5 ppm XCO₂ modelling errors.

Prior studies [5,6] show that the anthropogenic contribution of St. Petersburg to the CO₂ total column, as measured using paired high-precision spectrometers, ranges from less than 0.5 to 5 ppm. This characteristic is directly related to anthropogenic CO₂ emissions from the city. The essence of paired measurements is the possibility of excluding all the main factors influencing the CO₂ content except for anthropogenic emissions from the territory of the city under study. With this approach, taking into account the fact that the model qualitatively represents atmospheric transport, by varying the a priori anthropogenic emissions of the city, it is possible to achieve the best agreement between the modelling results and the measurements of XCO₂.

However, if XCO₂ measurements are available from only one instrument, then it is important to correctly take into account other influencing factors in the model (i.e., CO₂ transfer from the boundaries of the modelling domain, contribution of plant activity, etc.). Therefore, with this approach, the permissible error of the modelling of CO₂ content in the atmosphere depends on the magnitude of the anthropogenic contribution of a city. For example, if the anthropogenic contribution of a city to the total CO₂ content according to measurements is 5 ppm, then, with a modelling error of 1 ppm, the systematic error of adjusted anthropogenic CO₂ emissions will be 20%. If the contribution of a city according to measurements is 1 ppm, then, with the same modelling error, the systematic error of estimated emissions will be 100%.

Based on the range of the anthropogenic contribution of St. Petersburg to CO₂ total atmospheric content from studies [5,6], it can be said that to assess the city’s anthropogenic emissions of CO₂ using only one measuring instrument, the modelling error should be smaller than 1 ppm (0.2%).

Figure 14 shows histograms of the distribution of XCO₂ modelling errors as determined by the WRF-Chem model for St. Petersburg for January 2019–March 2020. Figure 14a shows the differences between the measurements and original modelling data, and Figure 14b—the differences for the modelled data, with BCs reduced by 0.3% (scenario 6 from Table 5). The error ranges that can be considered as acceptable are highlighted in green (from −1 to 1 ppm).

The interval of acceptable differences in the case of the original WRF-Chem modelling (Figure 14a) covers ~35% (425) of all differences. The distribution of the differences seems to have a normal mode. The shift of the distribution to the left from a zero value indicates that the WRF-Chem overestimates the measured values of XCO₂ in St. Petersburg due to systematic errors. These can be, for example, errors in chemical BCs. A decrease of chemical BCs by 0.3% (Figure 14b) moves the error distribution to the right. In this case, the interval of acceptable differences between the modelled and measured values of XCO₂ covers ~60% of all differences.

It can be said that the use of the WRF-Chem model in estimating anthropogenic CO₂ emissions from St. Petersburg requires careful validation, an example of which is given in the current study. First, based on a validation, the model will be adapted to the conditions of the modelling domain. Secondly, a validation allows for the filtering out of cases with the largest modelling errors. The current study has demonstrated that the WRF-Chem model, in ~60% of cases, can be used, together with high-precision measurements of total CO₂ content, to estimate anthropogenic CO₂ emissions for St. Petersburg for the period January 2019–March 2020.

4. Conclusions

In the current study, a complex validation of the WRF-Chem modelling of CO₂ transport in the troposphere above the region of the Gulf of Finland, with focus on St. Petersburg and Helsinki, was carried out.

It is shown that by using the WRF-Chem model it is possible to simulate the annual variation of the near-surface CO₂ mixing ratio and CO₂ total columns (with additional data above 20 km). The model represents the mean seasonal and diurnal variation of atmospheric CO₂ related to plants’ activity, and wind speed. The modelled and measured near-surface CO₂ mixing ratio in Helsinki for 2019 correlates well (correlation coefficient is 0.73) with the mean difference and its standard deviation of 0.15 ± 0.04 and 1.7%, respectively.

The WRF-Chem model is able to simulate temporal variation of the column-averaged CO₂ mixing ratio (XCO₂) in St. Petersburg, characterising on average the total atmospheric column of CO₂. A correlation coefficient between the modelled and measured (by ground-based Fourier–spectrometer Bruker EM27/SUN) time series of XCO₂ is 0.95 with a mean difference and its standard deviation of ~−0.3 ± 0.02 and 0.3%, respectively. These estimates are in agreement with independent studies of other cities (e.g., Berlin, Saint-Denis). It is likely that the modelling errors are related to inaccuracies in chemical boundary conditions and, probably, the spatial distribution of a priori anthropogenic emissions of CO₂.

XCO₂ values in St. Petersburg, as derived by the WRF-Chem model, fit well with independent modelled data such as CAMS reanalysis and the CarbonTracker dataset. At the same time, the WRF-Chem data are in the best agreement with the measurements. It is probable that this is related to the much higher spatial resolution of the WRF-Chem modelling (2 vs. over 100 km), due to which local small-scale processes and high-resolution spatial distribution of a priori anthropogenic CO₂ emissions can be considered in a simulation. This highlights the significance of numerical weather prediction and atmospheric composition models of high spatial resolution in estimating anthropogenic CO₂ emissions on a city-wide scale.

The study has shown that by using the WRF-Chem model it is possible to simulate the dynamics of CO₂ atmospheric content with a high spatial resolution (2 km). Following the recommendations given in this study, the modelling errors of XCO₂ for St. Petersburg during January 2019–March 2020 are smaller than 0.2% in 60% of cases. We suppose that this is a requirement which should be fulfilled to estimate anthropogenic CO₂ emissions on a city-wide scale for such megapolises as St. Petersburg.