1 Introduction

For implementing a fruitful strategy for climate change mitigation, in-depth knowledge of the global carbon budget and regional CO2 sources and sinks is indispensable. Countries signatory to the Paris Agreement (including India) are required to commit and report a nationally determined contribution (NDC) to reduce greenhouse gas emissions. CO2 sources and sinks can be estimated by the so-called top-down approach (inverse modeling) using measurements of atmospheric CO2 mixing ratios and combining them with an atmospheric chemistry forward transport model at a regional or local scale. One of the main challenges for the transport models used in the inversions is to properly reproduce CO2 vertical gradients between the boundary layer and the free troposphere, as these gradients impact the partitioning of the calculated fluxes between the different regions (e.g., Patra et al., 2011; Stephens et al., 2007). For the quantification of forward model transport uncertainty, validation of the simulated atmospheric CO2 vertical profile with a proper understanding of the variation of upper air CO2 and atmospheric transport processes is necessary (Esteki et al., 2017). The CO2 mixing ratio near the Earth’s surface is affected mainly by physical chemistry and biological processes, including photosynthesis, respiration, biomass burning, oxidation of organic matter, fossil fuel burning, and air-sea exchange (Siegenthaler, 1990; Schlesinger et al., 2000; Pearson and Palme, 2000; IPCC, 2001; Friedlingstein et al., 2019; Hauck et al., 2020; Tagesson et al., 2020). And CO2 source and sink are mainly present near the surface; however, its distribution throughout the atmosphere occurs due to meteorological factors. The process of turbulent mixing of air pollutants in the planetary boundary layer (PBL) is a major area of concern for determining their vertical distribution.

Though a substantial study of forward transport model validation has been performed (Patra et al., 2008; Corbin et al., 2010a; Ballav et al., 2012; Ballav et al., 2016; Palmi’eri et al., 2015 and references therein), three-dimensional validation of model simulations with time are very less (Allahudheen et al., 2023; Kunchala et al., 2022). There are few studies of global model and CarbonTracker model validations with vertical CO2 mixing ratio measurements taken from aircraft (Niwa et al., 2011; Patra et al., 2011; Wang et al., 2021), but regional model performances of simulating vertical profiles using aircraft data over the Asian region are rare. A study of regional features of upper-air CO2 over Europe (Crevoisier et al., 2010; Sarrat et al., 2007; Xueref-Remy et al., 2011) suggested that most of the transport models were biased to ventilate too much of the CO2 uptake signal from the PBL to the free troposphere (FT) during boreal summer (Stephens et al., 2007). For minimizing the transport model bias in terms of minimizing mixing height (MH) error, Kretschmer et al. (2012) performed a synthetic experiment and they found ∼25–30% uncertainties in simulated MH during daytime over land. Gerbig et al. (2008) showed that uncertainty in MH produces a 3 ppm error on the forward transport model which generates 30% uncertainty in the estimated CO2 flux. Using optimized MH in CO2 transport simulation, the model bias reduces 5–45% in day time and 60–90% in night time (Kretschmer et al., 2014).

Any CO2 measurement shows large changes in mixing ratio along the vertical profile due to strong signals from net uptake (dominated by photosynthesis) during the summer days, net release (dominated by respiration) during the night and anthropogenic emission which are mixed and propagated by the processes of advection, convection, and eddy mixing into the PBL (e.g., Bakwin et al., 1995; Haszpra et al., 2012; Shia et al., 2006). On the other hand, photosynthesis, respiration, and the mixing height of trace gases are functions of solar radiation and are correlated to each other (Seibert et al., 1998). As CO2 is chemically inert in the troposphere, it takes several months to transport from surface to the free atmosphere, and subsequently to the upper troposphere and stratosphere (B¨onisch et al., 2008; Bisht et al., 2021; Vogel et al., 2023).

In this study, we extensively analyzed model simulated vertical profiles of CO2 mixing ratio over Delhi, India. In this context, this is to highlight that the atmospheric CO2 mixing ratio and flux measurements are initiated in India in the last few decades. The CO2 flux measurements from India are reported from different parts of the country like Himalayan ecosystem (Lohani et al., 2023; Mukherjee et al., 2018; Watham et al., 2014), and Mangroves of Sundarban and Pichavaram (Rodda et al., 2022). Similarly, clean air ground-based (Bhattacharya et al., 2009; Lin et al., 2015; Chandra et al., 2016; Chakraborty et al., 2020; Nomura et al., 2021) and aircraft-borne (Baker et al., 2011; Umezawa et al., 2016) CO2 measurements are carried out over different geographical location of India. Investigation of carbon cycle using long-term observed data and global model simulations were also carried out over India (Sreenivas et al., 2022; Tiwari et al., 2011) but regional scale simulations are rare (Allahudheen et al., 2023; Ballav et al., 2020). For the purpose of simulating CO2 vertical profile over India, we have setup and run a regional scale forward model, weather research forecast-chemistry for CO2 (hereafter WRF-CO2). The model is simulated for populous Asia and model simulated vertical profile of CO2 is validated with the observed vertical profile of CO2, obtained from an aircraft measurement dataset of the Comprehensive Observation Network for Trace gases by AIr-Liner (CONTRAIL) (Machida et al., 2008; Matsueda et al., 2008). Variations of the vertical CO2 mixing ratio for 2010–2012 are analyzed for different months and seasonal cycles at different altitudinal bins. The role of meteorology in the spatio-temporal variation of CO2 mixing ratio at different altitudes is also verified. Statistical analyses like the correlation coefficients and normalized standard deviations are estimated to quantify the model’s performance. Assessments are also made of the various fluxes’ contributions to the actual variability of the CO2 mixing ratio. The WRF-CO2 model results are also compared with the global model ACTM (Patra et al., 2009) simulations. This is to be noted that ACTM outputs are used as initial condition and boundary condition (IC/BC) for the WRF-CO2 simulation. Moreover, we test the influence of the model scale (global to regional scale) on the reproducibility of the observed vertical variability.

The manuscript is organized as follows: Sect. 2 describes the forward models used for the study (WRF-CO2 and ACTM), the observational data collection by aircraft measurement, and data processing. In Sect. 3, models and observation results are presented, followed by conclusions in final section.

2 Methodology

2.1 Forward models

2.1.1 WRF-CO2

A fully coupled online state-of-the-art, regional air quality model, WRF-Chemv3.01 (Weather Research Forecast Chemistry; Grell et al., 2005), is setup and run for CO2 tracer transport (WRF-CO2), in which meteorological fields are fully calculated and nudged towards the analyzed fields using Newtonian relaxation methods. Three-dimensional tracer distributions are largely influenced by sub-grid scale parameterized vertical transport of turbulent mixing and cumulus convection (Ballav et al., 2012, 2016 and 2020). Cumulus convections are parameterized by the Grell-Devenyi ensemble scheme (Grell & Devenyi, 2002). For vertical turbulent mixing, the Mellor-Yamada-Janjic scheme is used (Janjic, 2001; Mellor & Yamada, 1982). Model simulation is performed using 27 km horizontal grid and 31 vertical eta (η) levels up to 100 hPa pressure level. The model is run on a single domain, with Mercator projection, having horizontal extension from 68° to 124°E and 2°S to 45.2°N. Total grid-points within the model domain are 200 × 190 in latitudinal and longitudinal direction. The model is centered at 24° N and 96° E to encompass the entire south and south-east Asia including populous megacity Delhi, India. Global land use and terrain data are used from the 10 m USGS (US Geological Survey) data. Initial and lateral boundary conditions for the meteorological fields are used from FNL (final analysis) data of the NCEP (National Centers for Environmental Prediction) at 6 hourly interval with 1° × 1° grid resolution. The initial and boundary conditions for CO2 tracers are obtained from Atmospheric Chemistry Transport Model (ACTM: Patra et al., 2009). The model outputs are stored in 1 h interval. First 5 days of model simulations are considered as a spin up period and discarded from time series. Here, we provided brief description of the WRF-CO2 model; further information of the model is available in Ballav et al., (2012, 2016 and 2020).

2.1.2 ACTM

The online chemical transport model ACTM is developed based on the Center for Climate System Research/National Institute for Environmental Studies/Frontier Research Center for Global Change (CCSR/NIES/FRCGC) AGCM (Patra et al., 2009). ACTM is nudged with reanalysis meteorology data using Newtonian relaxation method for running the chemical tracer transport. Cumulus convections are parameterized by the scheme of Arakawa and Schubert (1974). For vertical turbulent mixing, the level 2 scheme of Mellor and Yamada (1974) is used. In ACTM simulations, the horizontal resolution of T42 spectral truncations (approximately 2.8° × 2.8°) and 32 vertical sigma-pressure (σ) levels up to ~ 50 km are used. The ACTM uses six hourly zontal and meridional velocities (U, V) and temperatures (T) from the National Center for Environmental Prediction-Department of Energy (NCEP-DOE) Atmospheric Model Intercomparison Project-II (AMIP-II) Reanalysis for nudging. The ACTM is simulated with the same input fluxes as used in the WRF-CO2 model simulation; i.e., both models have taken biospheric flux from the Carnegie-Ames-Stanford-Approach (CASA global model; Olsen & Randerson, 2004), fossil flux from EDGAR4.2 (2011), and ocean flux from Takahashi et al. (2009). The model output is stored in 1 h interval. More detailed information of the ACTM is available in Patra et al. (2009). Configurations options of different atmospheric processes and fluxes that are selected for present simulation of WRF-CO2 and ACTM model are presented in Table 1.

Table 1 Details of the WRF-CO2 and ACTM model configurations
Full size table

2.2 Atmospheric observations by CONTRAIL

The CONTRAIL CO2 measurements between Narita (NRT), Japan, and Delhi (DEL), India, using the continuous CO2 measuring equipment (CME) on board of a Japan Airlines (JAL) passenger aircraft at about 11 km altitude level are used in this study for the period of 2010–2012 (details in Machida et al., 2008; Matsueda et al., 2008; Umezawa et al., 2016). During the years 2010–2012, the CONTRAIL measurement flights were conducted over Delhi 34, 67, and 37 numbers of times for each consecutive year, respectively (details in Table 2). The arrival time of the flight at Delhi airport was between 12 and 16 UTC and departure time from Delhi was between 15 and 16 UTC for the study period. Figure 1 shows the flight track (to and from) of CONTRAIL measurements. Air sampling started when aircraft reach around 1 km in altitude. The measurement data were averaged over a period of one minute, which is equivalent to about 10–15 km horizontal distance at cruising altitude. The measurement lag time was used to adjust the measurement locations beforehand (further details in Niwa et al., 2011). The CONTRAIL data were reported by the National Institute for Environmental Studies, Japan, on (NIES)-95 scale (Machida et al., 2009). The differences between the World Meteorological Organisation (WMO) calibration scale (Masarie et al., 2001) and the NIES-95 scale CO2 were less than 0.12 ppm. The CONTRAIL project measured atmospheric CO2 mixing ratios covered altitudes between the earth’s surfaces to the upper-troposphere/lower-stratosphere (UT/LS). The Delhi region covered around 26.5°–29.9° N and 75.6°–78.1° E area. Within this horizontal range, aircraft was lifted by around 8 km in height. However, for the study region, we have selected data between 27.4°–28.6° N and 77°–96° E. Therefore, rest of data were collected mainly over the Indo-Gangetic plain at upper atmosphere around 8–11 km height (as shown in Fig. 1).

Table 2 Total number of days of CONTRAIL flights measurement of vertical CO2 at the Delhi region (measured to and from New Delhi International Airport (DEL 28.20° N, 77.95° E)) for different months of the years 2010, 2011, and 2012, respectively
Full size table
Fig. 1
figure 1

Subplot (a) shows the WRF-CO2 model domain with terrain height (m). Subplot (b) highlights that the observation flight (JAL) tracks are shown towards (red) Delhi and from (yellow) Delhi. Spatial variation shows the vegetation fraction over the domain. The inner box represents the Delhi region. Around 10 km in vertical height, aircraft travel around 250 km in horizontal distance from New Delhi International Airport

Full size image

2.3 Data processing for CO2

The simulated atmospheric CO2 data from the WRF-CO2 and the ACTM for the years 2010–2012 are sampled at the same time and locations as those of the CONTRAIL measurements. A simple method is adopted for comparison of model and CONTRAIL data. Linear interpolations are made in the model data by selecting two nearest neighboring grid points of model output which are closed to the exact location of CONTRAIL data. The exercises are carried out for space and time both (Niwa et al., 2011; Patra et al., 2011). In CONTRAIL measurements, altitude data are available with us as height in meter. The model data are interpolated vertically using geo-potential height basic state and perturbation data. This is to be noted for the year 2012 that the observed data were inadequate and did not encompass all months of the entire year (Table 2). Hence, a comprehensive comparison between observed and model simulated data could not be made.

3 Results and discussions

3.1 Spatio-temporal distribution of vertical CO2

The atmospheric CO2 mixing ratio shows strong temporal and spatial variation between the earth’s surface and the troposphere. During the daytime and summer seasons, the CO2 signal from the photosynthesis process near the surface is diluted due to mixing through convective activity and CO2 signal is transported from the surface to the top of planetary boundary layer (PBL). However, during the night and winter seasons, PBL height (PBLH) reduces due to atmospheric cooling, and therefore, the CO2 signal from plant respiration and anthropogenic emissions are trapped almost near the surface layer of the earth. In spite of convective activity, the atmospheric transports also play an important role in the mixing of CO2 and transporting surface CO2 flux to PBLH. As a result, the overall feature of a horizontal and vertical gradient of CO2 with a higher CO2 mixing ratio at the surface of the earth and a lower CO2 mixing ratio above the surface is noticed (Denning et al., 1995).

In order to assess such variation, Fig. 2a–h is prepared which shows the spatio-temporal variation of CO2 mixing ratio along with wind vectors from the WRF-CO2 model at two different vertical levels (one is within mixing layer (850 hPa) and another is above mixing layer (200 hPa)) for four seasons, i.e., winter (DJF December, January, and February), spring (MAM March, April, and May), summer (JJA June, July, and August), and autumn (SON September, October, and November). Seasonal variations of PBLH (Fig. 2i–l) and outgoing long wave radiation (OLR) (Fig. 2m–p) are also presented.

Fig. 2
figure 2

Longitude-latitude distributions of CO2 mixing ratio (ppm) along with wind vector (m/s) at vertical level 8 (around 850 hPa) and level 20 (around 200 hPa) of the WRF-CO2 model for different seasons (winter, spring, summer, and autumn) of 2010. The lower two panels represent seasonal variations of planetary boundary layer height (in kilometers) and outgoing long wave radiation (W/m2). Wind vectors legends of Fig. 2 a–d are same and Fig. 2 e–h are same

Full size image

Wind field analysis could determine which source locations are responsible for the transport of CO2 to a particular region. The CO2 mixing ratio is higher (> 8 ppm) during winter-spring and autumn in east China than in west China and the Indian region (Fig. 2e, f and h). Strong eastward moving air is blowing from the west part of the domain and converging over the east China region. This is one of the favorable conditions for elevating the concentration of pollutants in addition to high-level local emissions emerging from the energy consumption during cold months in eastern Chinese metropolises. Moreover, it is likely to be too slow vertical ventilation of CO2 over the eastern region to effectively erase the east and west CO2 gradients. Therefore, in these three seasons, the WRF-CO2 model simulates CO2 with a large horizontal gradient between west and east China and a large vertical gradient over east China. However, the gradient in vertical CO2 is very low during the summer/monsoon months all over the domain. A strong cyclonic vortex associated with the monsoon circulation is noticed over the Indian subcontinent and Chinese periphery. The associated convection with the cyclonic vortex is supposed to transport air mass from lower level to the free troposphere (Fig. 2g). Furthermore, this is also to note that due to the strong westerly prevailing jet wind in the upper atmosphere during summer (Fig. 2c), the horizontal gradient of CO2 in that region is less around northward latitudinal belt.

Air masses are trapped within PBL and convection plays a big role in mixing the air masses under favorable terrain and meteorological conditions within PBL (Mukherjee et al., 2020). Therefore, with increasing PBLH, CO2 is well mixed in the atmosphere under favorable terrain and meteorological conditions. Wintertime PBLH is low over India and eastern China (range 600–1000 m, Fig. 2i); however, PBLH is high (range 1000–1800 m, Fig. 2k) during monsoon season over the continent, which indicates the presence of high concentrations of CO2 in the winter and low concentrations of CO2 in the growing season at lower atmospheres. During winter (Fig. 2i), PBLH is typically lower than 1000 m in northern latitudes of India. Simulation of average PBLH height is in good agreement with the study results of the PBLH over the Delhi region obtained by in situ measurement, satellite observation, and model simulation obtained by Nakoudi et al. (2019) during the EUCAARI (European Integrated Project on Aerosol Cloud Climate and Air Quality Interactions) project. They found that the maximum daily PBLH spread between 600 and 1800 m in the pre-monsoon and monsoon periods and 600–900 m in the winter period. Furthermore, our study shows that the PBLH does not change significantly between inter seasons over the ocean, as because there is almost no seasonal variation in the sea-surface temperature. Therefore, inter-seasonal changes in CO2 are less noticeable over the ocean. Monsoon circulation and associated rainfall add complexities to the boundary layer features over the Indian subcontinent (e.g., Patil et al., 2013 and references therein), henceforth adding complexities to the vertical mixing of CO2. Study by Patil et al. regarding seasonal climatology revealed increased or reduced PBLH during excess or deficit monsoon years and higher PBLH during pre-monsoon and monsoon seasons as compared to post monsoon and winter seasons. Our results corroborate well with the observation of Patil et al. (2013) that PBLH is higher during pre-monsoon season whereas PBLH is lower during post monsoon and winter seasons.

Low OLR indicates that a region is covered with clouds in the presence of a low pressure system. Under cloudy conditions, net primary production is reduced and respiratory release exceeds net primary production; however, during high OLR situations, this is reversed as clear sky condition prevails. Therefore, the OLR and atmospheric CO2 mixing ratio is expected to have good agreements. Over eastern China, low OLR is noticed during the winter and spring seasons (range 220–260 W/m2) compared to the summer (range 270–300 W/m2) (Fig. 2m and n). This could be attributed to the higher concentration of CO2 over the region or enhancement in the cloud formation due to convective activities. Over the Indian subcontinent, OLR is very strong during the spring (above 310 W/m2) and moderate in the winter (above 290 W/m2). However, OLR over Indian subcontinent is very low during the summer months (around 250 W/m2). Here, the variation of CO2 with OLR shows a complex feature as CO2 source and sink are not determined only by a single parameter; these are the combined and complex effects of many synoptic and micro-scale parameters.

3.2 Monthly mean variations of vertical CO2

Figure 3 presents monthly varying vertical profiles of CONTRAIL measurement and the model simulated (WRF-CO2 and ACTM) CO2 mixing ratio over the Delhi region for the year 2010 (measurement taken from (/to) New Delhi International Airport), and Fig. 4 represents the same during 2011. Table 3 shows the correlation coefficients (CC) between the observed and model (WRF-CO2 and ACTM) simulated vertical CO2 data for different months and seasons. CC and NSD are calculated using > 100 data points for each month and season for both the years (2010 and 2011). Generally, CC value above 0.90 is considered very highly correlated, 0.7 high correlated, and 0.5 moderately correlated (Taylor, 1990). Our results show that all the CC values above 0.5 are statistically significant at 99% confidence interval in the Student’s T test. Therefore, we define good model performance when CC is > 0.5. Similarly, normalized standard deviations (NSDs) of WRF-CO2 and ACTM data of CO2 mixing ratio is produced with the ratio of model standard deviation and observed standard deviation. NSD value 1 means the circumstances when model and observed fluctuations are similar. When an aircraft flew around 5 km and 10 km height, it traveled around 100–250 km of horizontal distance from New Delhi International Airport. The figures show unique features of the vertical CO2 mixing ratio for individual months and individual years. Interestingly, despite the fact that each monthly CO2 vertical profile is distinct, the simulated CO2 vertical profiles capture several observed patterns. For example, performance of the WRF-CO2 model is good in February, April, June, and November and same is true for the ACTM in January, April, May, June, and November for both years 2010 and 2011 respectively (Table 3). Generally, the ACTM shows much more smooth vertical variation of the CO2 mixing ratio, implying steady mixing process, but the WRF-CO2 model reveals more trough and ridge patterns which are many times closer to reality, indicating that mixing in the model rely on other environmental conditions also. For example, the WRF-CO2 shows better NSD (0.96 and 0.75) than the ACTM (0.61 and 0.49) in April and May, 2010, respectively, despite having comparable CC. Key features from the statistical analysis are that NSD, for most of the months, is higher and deviation is closed to observation for the WRF-CO2 model than the ACTM for the year 2010 (Table 3). There are exceptions as well, when the WRF-CO2 shows better CC (0.71 and 0.48) than the ACTM (0.29 and − 0.76) in February and September, 2011, respectively, despite having underestimated or comparable NSD. Seasonal CC between WRF-CO2 model and observation are almost equal or better (~ 0.6– ~ 0.9) than the ACTM (~ 0.3– ~ 0.9) for both the years (2010 and 2011), except in winter (2010). The WRF-CO2 model has an absolute bias < 5 ppm for estimating the CO2 mixing ratio vertical gradient for each month between surface and top altitude level, except for the month of August, 2011. Absolute bias is estimated with this following formula: |Bias| =||{(observed CO2 mixing ratio at lowest level—observed CO2 mixing ratio at top level)|—|(model CO2 mixing ratio at lowest level—model CO2 mixing ratio at top level)}||

Fig. 3
figure 3

Monthly mean vertical profiles of CO2 over Delhi region (1–8 km) and Indo-Gangetic plane region (8–11 km) using CONTRAIL observation (taken from (to) Delhi airport), WRF-CO2, and ACTM data for the year 2010. In the month of July, no observation data are available from CONTRAIL. The model results are adjusted to 389 ppm at 2 km altitude for the month of January and the variable x-axis range is fixed for all months but set in such a way that reveal maximum information content in each monthly set of profiles

Full size image
Fig. 4
figure 4

Monthly mean vertical profiles of CO2 over Delhi region (1–8 km) and Indo-Gangetic plane region (8–11 km) using CONTRAIL observation (taken from (to) Delhi airport), WRF-CO2, and ACTM data for the year 2011

Full size image
Table 3 Statistical analysis (correlation coefficients (CC) and normalized standard deviations (NSD)) of observed and models (WRF-CO2 and ACTM) simulated vertical CO2 data for different months and seasons
Full size table

In general, the CO2 mixing ratio displays a lower value at the highest altitudinal level than the surface to near-surface region; however, there are many exceptions (Niwa et al., 2011; Vogel et al., 2023; Wang et al., 2021). The exceptions are likely to be the covariance of emission sources, meteorological parameters, geographical location, and canopy representation. Figure 3 shows that during monsoons (e.g., August and September), the atmospheric CO2 mixing ratio is lower at the ground level (~ 1 km) compared to the top most altitude level (~ 11 km) (the maximum vertical gradient is around ~ 15 ppm in August) and a sharp increase in the CO2 mixing ratio with height up to PBL, reflecting strong uptake during the growing season due to photosynthesis by the vegetation growth at near surface. These results are consistent with the study of Vogel et al. (2023) for Asian summer monsoon region. Analysis reveals that within ~ 2.5 km height, the positive gradient of the CO2 mixing ratio observed in August (~ 13.4 ppm) and September (~ 8.4 ppm) in 2010. Both models do not show such steep slope of CO2 mixing ratio up to ~ 2.5 km height during August and September (capture up to 5% vertical gradient); it is likely to be due to insufficient sinks in input flux (Lokupitiya et al., 2009), or overestimation of convective parameters by the models (Varga & Breuer, 2022; Yang et al., 2012). Both models are also unable to produce the same for August and September in the year 2011.

A similar pattern is obtained in February, month of winter season (strong positive gradient of CO2 mixing ratio is ~ 4.5 ppm with height up to ~ 2.5 km), which corresponds to the impact of newly growing vegetation uptake (such as “Rabi” crop), which exceeds vegetation respiration and fossil fuel emissions due to stubble burning, transport, etc. (Umezawa et al., 2016). Impact of crop uptake is also found in the study of Corbin et al. (2010b) over United State mid-continent region. Both models, WRF-CO2 and ACTM, capture the variation of vertical CO2 mixing ratio quite well in February. Positive gradients of CO2 up to ~ 2.5 km height are noticed (~ 1.7 ppm) then quite well-mixed layer up to 9.5 km altitude followed by strong decrease of CO2 (~ 2 ppm) up to 11 km corroborated with observation, likely to be the results of horizontal transport of CO2 from other areas with upper level jet streams. In general, the situation is reversed in the autumn, spring, and winter seasons, with observations revealing the maximum CO2 mixing ratio at the surface level, which is attributed to the dominance of carbon release by heterotrophic respiration and fossil fuel emissions (Patra et al., 2011; Zhang et al., 2023). In addition, extensive post-harvest stubble burning in the northwest Indian states of Panjab and Haryana, especially in the months of October, November, March, and April, results in severe air pollution that is trapped beneath the planetary boundary layer of the surrounding area and a strong vertical gradient of CO2 is observed over the Delhi region (Abdurrahman et al., 2021; Porichha, et al., 2021). Similar consistent vertical profiles of observed CO2 for winter were found in the study of Umezawa et al. (2016) over Delhi region for different year.

During the pre-monsoon season, which corresponds to the end of the dry season, the air temperature remains quite high. A strong anticyclone circulation persists over the Indian subcontinent, preventing surface flux from mixing with surrounding air masses and transferring to the upper troposphere. Analysis reveals that within ~ 2.5 km height, the maximum gradient (negative) of the observed CO2 mixing ratio observed in October (~ − 9.3 ppm) followed by November (~ − 7.6 ppm) in 2010. Both models (WRF-CO2 and ACTM) capture the variation to some extent in October (~ − 3.3 and ~  − 2.7 ppm) and November (~ − 3.8 and ~  − 4.3 ppm), respectively. The vertical gradient of CO2 is very low from ~ 2.5 km height to top altitude level in the months of June, July, and August (Fig. 4), indicating strong cyclonic circulation during the Indian summer monsoon that allows for rapid ventilation of surface flux signals to the upper troposphere. Overall, above ~ 2.5 km elevation, models quite well simulate the vertical profiles irrespective of months, where the WRF-CO2 model simulations are better in general than the ACTM (e.g., February, April, and May, 2010), implying that the WRF-CO2 model significantly ventilates surface flux up to upper troposphere.

December and January months depict quite well-mixed CO2 vertical profile for the years 2010–2011 (vertical gradients of CO2 from surface to upper troposphere are about 2–3 ppm), indicating no additional source and sink at the earth surface during that time. CO2 is quite well mix in the atmosphere at that time and upper air CO2 is higher compare to other months, implying that excess CO2 source from stubble burning during autumn season has begun to mix and transport to upper air (CO2 mixing ratio is about 2 ppm higher during December and January than the post-harvest period of autumn). Both models demonstrate a similar pattern (CO2 gradient from surface to upper troposphere is around 2–3 ppm), however have tendency to produce negative gradient of CO2 up to ~ 2.5 km altitude, implying model unable to ventilate surface flux to upper layer. The mismatch between observation and model simulation of vertical CO2 mixing ratio profiles are attributed from uncertainty of surface CO2 flux data, boundary layer schemes, cumulous convection schemes, and meteorology such as wind vectors, which are treated differently in offline and online models. Consequently, the ACTM has weaker vertical mixing between 850 and 500 hPa for boreal winter and a stronger one for boreal summer (Patra et al., 2011).

3.3 Seasonal cycle of CO2 at different heights of the atmosphere

Figure 5 presents monthly mean variations of observed and simulated CO2 (WRF-CO2 model and ACTM) mixing ratio at different altitude bins (< 2 km, 2–4 km, 4–6 km, and 6–8 km) over the study region for the year 2010. Generally, several months are required for surface air to transport the upper troposphere or lower stratosphere and biospheric uptake is stronger near the surface; therefore, the CO2 mixing ratio and the seasonal cycle amplitude are lower in the upper atmosphere as compared to the surface layer (Diallo et al., 2017). As a consequence, more pronounced CO2 seasonal cycle amplitudes (~ 21 ppm) are noticed at the lowest bin (0–2 km), followed by the 2–4 km bin (~ 7 ppm) and ~ 6 ppm both at the 4–6 km and 6–8 km bins (Fig. 5). Observation shows the lowest CO2 mixing ratio in the month of August (~ 376 ppm at the lowest bin and ~ 385 ppm at the top bin) and the maximum CO2 mixing ratio in the month of May at the lowest bin (~ 397 ppm) and in June at the top bin (~ 393 ppm).

Fig. 5
figure 5

Monthly mean variation of CO2 from CONTRAIL measurements and model simulations (WRF-CO2 and ACTM) at different altitudinal bins for the year 2010. No data is available for the month of July. The values of model biospheric CO2 and fossil CO2 are adjusted in the month of January with the value of total CO2 simulated by the WRF-CO2 model

Full size image

The models reasonably reproduced seasonal variations at different levels of the atmosphere. The WRF-CO2 model underestimated seasonal amplitude at the lowest altitude bin (~ 30%), but overestimated it (~ 66%) at higher altitude bins. Generally, the ACTM-simulated amplitude is lower than the WRF-CO2 model simulation. Both models produce timing of minimum CO2 later (September and October) than observed (August). Figure 6 presents the same for the year 2011, where the seasonal cycle pattern is almost similar to that of 2010. The minimum CO2 mixing ratio is obtained in the month of September (~ 385 ppm at lowest layer and ~ 388 ppm at the top altitude layer). The maximum CO2 mixing ratio is obtained in the month of April (~ 403 ppm in the lowest bin and ~ 393 ppm in the top bin). Though the phase is not quite good for the WRF-CO2 model with observation, amplitude is quite close to reality compared to the ACTM. The WRF-CO2 model underestimated seasonal amplitude at the lowest altitude bin (~ 64%), but overestimated it (~ 20%) at higher altitude bins.

Fig. 6
figure 6

Monthly mean variation of CO2 from CONTRAIL measurements and model simulations (WRF-CO2 and ACTM) at different altitudinal bins for the year 2011. The values of model biospheric CO2 and fossil CO2 are adjusted in the month of January with the value of total CO2 simulated by the WRF-CO2 model

Full size image

The correlation coefficients (CC) and normalized standard deviations (NSDs) are calculated using 34 and 138 data points for the years 2010 and 2010–2012 for quantitative verification of the WRF-CO2 model performance compared to observation and the ACTM with different altitudinal bins at the Delhi region (Table 4). All the CC values for the WRF-CO2 model are statistically significant at 99% confidence interval in the Student’s T test. NSDs, which are calculated by normalizing the model standard deviation (SD) by the observed SD of the same time series, are used to compare the seasonal cycle amplitudes. At the lowest level (0–2 km), CC is 0.6 but it is above 0.7 for higher altitudinal bins for the WRF-CO2 model for 2010–2012 analysis. NSD is close to observation (1.35) at lowest altitudinal bin and almost double in all the height altitudinal bins (about 1.92–2.37). Model-observation mismatches are much larger than model-model mismatches. For the year 2010, all CC of different altitudinal bins are better for the WRF-CO2 model (CC ranges 0.65–0.77) compared to the ACTM (CC ranges 0.45–0.75). Amplitude is very close to observation for the WRF-CO2 model (NSD = 0.95) near ground (0–2 km); however, for the rest of the altitudinal bins, the WRF-CO2 model overestimates the amplitude (NSD = 1.45–1.88); however, ACTM always underestimates (NSDs < 0.66). The possible reason of model-model mismatches may be due to the Mellor and Yamada (1974) PBL scheme employed in the ACTM (wherein the depth of the mixed layer has been found to be underestimated (Sun & Ogura, 1980)), horizontal and vertical resolution difference between the models (Agusti-Panareda et al., 2019; Youssef et al., 2021), and use of different cloud parameterization scheme (Ballav et al., 2016). However, model-observation mismatch are likely to be the input flux data resolution, lack of three dimensional emission input, and improved parameterisation schemes (PBL and convective boundary layer) (Patra et al., 2011). However, by modifying the empirical constants in MYJ scheme (Janjic, 2001), some progress has been reported on the growth of the convective boundary layer (Xu et al., 2015). The difference in results between single year analysis and 3 years analysis may be due to the reason of sparseness of the data.

Table 4 Statistical analysis (correlation coefficients (CC) and normalized standard deviations (NSD)) of observed and models (WRF-CO2 and ACTM) simulated data at different altitudinal bins
Full size table

CO2 is primarily produced and consumed on the ground; its concentration at high altitudes is affected by the variation of ground-level sources and sinks as well as the processes of atmospheric dispersion and transportation. Recent studies (Umezawa et al., 2016) highlight the relatively overlooked role of agriculture in the global carbon cycle, even though an increased CO2 exchange by the northern terrestrial biosphere has likely made a significant contribution to the observed increasing trends in the seasonal amplitude of CO2. Therefore, we also study the biospheric CO2 contribution compared to the fossil contribution over the Delhi region. The study shows that the WRF-CO2 model–simulated biospheric CO2 mixing ratio (obtained from CASA flux) is in phase with observed atmospheric CO2 mixing ratio compared to fossil CO2. The biospheric contribution is highest (~ 80%) at the near ground, decreases with height due to the mixing processes, and finally reaches ~ 60% at the top most level. However, a more detailed study about source area identification of CO2 fluxes could be carried out using footprint analysis (Mukherjee et al., 2015). For an in-depth study regarding the vertical distribution of CO2, more vertical observation data are required, such as balloon borne in situ observation from different locations. A major limitation of CONTRAIL aircraft data is that only 1 or 2 vertical profiles could be obtained for a domain of interest as the data is taken from flights near airports. However, this data could be useful to study the upper-level horizontal gradient of CO2.

4 Conclusions

Realistic simulation of CO2 by the forward transport model will lead to a reduction in the uncertainty of the carbon budget. In this regard, assessment of vertical profile of CO2 using the high-resolution WRF-CO2 model simulation in conjunction with observation from aircraft measurement of CONTRAIL and existing global model (ACTM) are performed over Delhi region. The experiments are carried out for the years 2010–2012. Variations of the vertical CO2 mixing ratio are analyzed for different months of the year and seasonal cycles at different altitudinal bins. Statistical analyses like the correlation coefficients and normalized standard deviations are used to quantify the model performance. The role of meteorology in the spatio-temporal variation of CO2 mixing ratio at different altitudes is also identified. In addition, contribution of different fluxes in the vertical variation of CO2 mixing ratio is assessed.

It is found that during monsoon months (August and September), vertical CO2 profile significantly decreases towards the ground, and CO2 gradient between lowest level and ~ 2.5 km height is around 13.4 ppm, due to strong CO2 uptake by newly growing vegetation. Similar pattern is noticed in winter month (February), where CO2 gradient between lowest level and ~ 2.5 km height is around 4 ppm, suggesting not only the existence of continuous local to regional scale ground CO2 sources throughout the winter but also the appearance of relatively strong CO2 sinks due to photosynthesis by newly growing winter crops. It is further noted that generally, CO2 is quite well mixed within 3 to 8 km height. The WRF-CO2 model is also found unable to produce strong ground level uptake during growing season (capture up to 5% vertical gradient), however is able to capture moderate uptake during winter month (February, ~ 1.7 ppm). Analysis reveals that in 2010, October (− 9.3 ppm) and November (− 7.6 ppm) have shown the largest gradient within 2.5 km of height induced by stubble burning. Both models (WRF-CO2 and ACTM) partially reflect the instability in November (− 3.8 and − 4.3 ppm), as well as in October (− 3.3 and − 2.7 ppm). Besides, above 2.5 km height, model simulation is found to be good. Generally, the ACTM shows much more smooth vertical variation of CO2, but the WRF-CO2 model shows more trough and ridge pattern which are more realistic. Study of monthly mean seasonal variation with changing atmospheric levels indicates that seasonal amplitudes decrease with increasing height (amplitude is ~ 21 ppm at lowest bin and ~ 6 ppm at top bin), as several days are required to transport surface air to the upper troposphere and less biospheric activity in high altitude. The WRF-CO2 model underestimates seasonal amplitude at lowest altitude bin (~ 30%), however over estimate (~ 66%) at higher altitude bins in the year 2010. Correlation coefficients (CC) between the WRF-CO2 model and observation are noted to be greater than 0.59 at the 99% confidence level for all the altitude bins. In general, NSD is greater for the WRF-CO2 model than the ACTM. The study demonstrates that terrestrial biospheric CO2 mixing ratio (obtained from CASA flux) is in phase with observed atmospheric CO2 in contrast to fossil CO2. The contribution from the terrestrial biosphere is strongest (~ 80%) at the lowest level, then declines with height due to the mixing processes and eventually reaches ~ 60% at the top most altitude layer (6–8 km). Analysis of meteorological field (wind speed, PBLH, and OLR) suggested that meteorology plays significant role of horizontal (upper air horizontal transport through jet stream) and vertical gradient of CO2 (vertical mixing with variation of PBLH).

Overall, it is inferred that the WRF-CO2 model is able to capture fine scale structure of vertical profile of CO2 compared to the global model (ACTM); however, there are scopes for improvement in the WRF-CO2 model’s performances with sensitivity studies using different high-resolution flux data, three dimensional emission input, and with more improved parameterisation schemes (PBL and convective boundary layer) that could infer strong CO2 dynamics.