ISAM has a dynamic growth module to simulate various crops (Song et al., 2013). Gahlot et al. (2020) used the dynamic crop module to represent Indian spring wheat by calibrating the allocation and growth parameters (supplement of Gahlot et al., 2020). The allocation and the growth parameters were calibrated using data from the experimental site at IARI, New Delhi, which was operational for three growing seasons: 2013–2014, 2014–2015, and 2015–2016. Carbon fluxes were measured during the 2013–2014 growing season, and phenology data were measured during the latter two seasons. ISAM was calibrated and validated using phenology observations from the 2014–2015 and 2015–2016 growing seasons (Gahlot et al., 2020). Taking this work forward, we used the same configuration of the model to estimate the carbon fluxes in the spring wheat croplands of India. The modeling approach used in the study is as follows. First, ISAM was run in site-scale mode to simulate the carbon fluxes at the IARI site driven by prescribed management data. The simulations were evaluated against field measurements from the IARI site for the 2013–2014 growing season. Next, ISAM was run at a country scale to simulate carbon fluxes over wheat-growing regions of India from 1901–2016. Finally, we conducted numerical experiments to simulate the impacts of environmental drivers and agricultural management practices on carbon fluxes.

This study used ISAM in the same configuration as Gahlot et al. (2020). For brevity, here we briefly describe the model and its configuration. More details are available in Gahlot et al. (2020) and Gahlot (2020). We used two versions of ISAM crop modules to validate the improvements made by Gahlot et al. (2020), ISAMC3_crop and ISAMdyn_wheat. The two versions were run for the same period and used the same input data, and the simulated carbon fluxes were compared. The ISAMC3_crop module has static phenology and prescribed leaf area index (LAI) using observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard the Terra and Aqua satellites. The ISAMC3_crop module used a static root parameterization with fixed rooting depth and fixed root fraction in each soil layer. Energy and water fluxes as well as carbon assimilation are calculated through coupled canopy photosynthesis, energy, and hydrological processes. Assimilated carbon is allocated to vegetation pools in fixed fractions. Gahlot et al. (2020) used the dynamic equations in ISAM developed by Song et al. (2013) for soybeans and updated a few parameters from the literature and a few through calibration to simulate spring wheat (ISAMdyn_wheat) (supplement of Gahlot et al., 2020). ISAMdyn_wheat differs from the static version in three schemes: dynamic phenology, carbon allotment, and vegetation structure growth. For example, allocating net assimilated carbon to leaves, roots, stems, and grain pools at each model time step is a dynamic process based on the crop's light, temperature, water, and nitrogen availability. This allocation scheme aims to minimize the adverse effects of limited light, water, and nutrient stress on the crop (Gahlot, 2020). For more details on the dynamic modules in ISAMdyn_wheat, please refer to Gahlot (2020).

ISAMdyn_wheat is equipped with dynamic planting date criteria and heat stress modules to simulate the effects of environmental factors on the spring wheat growing season and phenology (Gahlot et al., 2020). The dynamic planting date is calculated in ISAM, as shown in Table S2 of Gahlot et al. (2020). The wheat-growing regions are divided based on the 1901–1950 climatological minimum temperature. A specific criterion is assumed for each region depending on the region's characteristics (Table S2: Gahlot et al., 2020).

Yield is a proxy for the carbon uptake by the crops. The initial reproductive stage in ISAM marks the onset of the storage organs. The allocation of assimilated carbon to the storage organ begins, and the vegetative development of the plant stops. The next stage, the post-reproductive stage, marks the solidification of grains and increased nutrient allocation to the grains while ensuring that capable roots support the plant. After the crop reaches maturity, the total grain allocation from the initial reproductive stage to maturity is converted to yield. Various factors like light availability, temperature stress, and nitrogen availability act as limiting factors to crop growth, and nutrient allocation is promoted in the crop so that the impact of these factors is minimized (supplement of Gahlot et al., 2020). Since yield is a major part of the carbon taken up by the crop, its validation against observations is necessary and is shown in Sect. 3.2.

ISAM simulates the processes through which external drivers can affect crop growth. For example, temperature influences maximum carboxylation rates, which regulates carbon assimilation (Song et al., 2013). ISAM can simulate nitrogen dynamics and the interactive effects of carbon–nitrogen cycles caused by climate change or increasing [CO2] (Yang et al., 2009). Nitrogen fertilization through deposition onto the soil serves as a nitrogen input to the ISAM nitrogen cycle (Jain et al., 2009). When water and mineral N are scarce, the carbon cycle and assimilation suffer because of reduced carbon allocation to leaves and stems (Song et al., 2013). Added water through irrigation reduces the water stress on crops in water-limited situations, thereby increasing carbohydrate production.

To evaluate the ISAMdyn_wheat crop phenology and yield, we digitized the spring wheat crop dataset from 2000–2021. The dataset was extracted from the theses of MSc and PhD students at various agricultural institutions across India. Until recently, these theses were not available in the public domain, but through the efforts of KRISHIKOSH, a thesis repository, it now holds a large number of theses. The dataset we compiled comprises nine spring wheat sites and 26 growing seasons (Table S1). Comparing the spring wheat phenology and yield simulated by ISAM across 26 growing seasons adds to the much-needed validation of ISAM.

Field observations of carbon fluxes are limited in India, and none are available in the public domain. We obtained field observations of carbon fluxes for the 2013–2014 spring wheat-growing season from the IARI (New Delhi) experimental spring wheat farm (Kumar et al., 2021). The farm, covering 650 m2, is located at 28∘40′ N, 77∘12′ E. The site has an eddy covariance (EC) flux tower that gave gross primary production (GPP), total ecosystem respiration (TER), and net ecosystem production (NEP). The tower had enough area to ensure an upwind stretch of homogeneous vegetation, essential for measuring fluxes using the EC technique (Schmid, 1994). The spring wheat crop was planted on 16 December 2013 at the site. Nitrogen fertilizer at 120 kg N ha-1 was applied in three installments of 60, 30, and 30 kg N ha-1 on the planting day and the 25th and 67th days after sowing. The field was irrigated five times throughout the growing season to avert water stress.

To extend our validation of carbon fluxes simulated by ISAM, we conducted a literature review to find papers that reported carbon fluxes from spring wheat. We found two such studies: Patel et al. (2011) and Patel et al. (2021). Data were not available as a supplement in these papers. Therefore, we extracted the data from the figures. We extracted the monthly mean NEP data from Fig. 2 of Patel et al. (2011) and Fig. 2b of Patel et al. (2021). Although we extracted the flux data, we do not have the field activities to simulate site-scale simulations. Therefore, we compared our regional-scale simulations against these carbon flux data.

All ISAM simulations need data for both environmental and anthropogenic drivers. We used annual atmospheric [CO2] data from Le Quéré et al. (2018) and climate data from Viovy (2018) for both site-scale and country-scale simulations. The temporal resolution of the climate data is 6 h, and we interpolated the climate data to hourly values. The planting date, nitrogen, and irrigation data used for the site-scale runs are described in Sect. 2.3.

For the country-scale runs, we used nitrogen fertilizer data developed by Gahlot et al. (2020) by combining data from Ren et al. (2018) and Mueller et al. (2012). Data on the harvested wheat area in a gridded format are needed (1980–2016) for calculating fluxes at a country scale in units of teragrams of carbon per year (TgC yr-1). We used spring wheat harvested area data developed by Gahlot et al. (2020), combining harvested area from Monfreda et al. (2008) and MAFW (2017).

Site-scale ISAMdyn_wheat simulations are validated against observations for the 2013–2014 growing season. Our results show that the spring wheat module ISAMdyn_wheat simulates the magnitude and seasonality of carbon fluxes in spring wheat croplands better than ISAMC3_crop. Figure 1 and Table 2 compare ISAMdyn_wheat and ISAMC3_crop against site observations for monthly average fluxes for the 2013–2014 growing season. Figure 1 shows that the observed carbon fluxes increased from leaf emergence in mid-December 2013. The fluxes increased until they reached their peaks in March, after which they declined until the harvest in April.

The simulated fluxes follow the observed pattern. ISAMdyn_wheat was in better agreement with site observations than the ISAMC3_crop model. ISAMdyn_wheat captured the seasonality and accumulated GPP, TER, and NEP for the growing season better than the ISAMC3_crop model (Table 2). The ISAMdyn_wheat peak coincided with the observations, whereas the fluxes simulated by the ISAMC3_crop model peaked about a month earlier. The ISAMdyn_wheat model in ISAM compares better with site measurements for plant biomass at harvest and maximum LAI than the ISAMC3_crop model (Table 2).

Table 3 shows the Willmott index and RMSE for the two ISAM runs against the site observations. The Willmott index is a more sophisticated tool for evaluating land surface models' efficiency than the usual statistical data comparison indices (Song et al., 2013; Willmott et al., 2012). The Willmott index (Eq. 1) ranges from -1 to 1, where -1 indicates no agreement, while +1 indicates perfect agreement. The Willmott index values for GPP, TER, and NEP for the ISAMdyn_wheat model are 0.85, 0.73, and 0.83, respectively. The corresponding values for the ISAMC3_crop model are much lower at 0.47, 0.46, and 0.47, respectively. The higher index value for the dynamic crop suggested better agreement of ISAMdyn_wheat over ISAMC3_crop with the site-scale observations. 1Willmotindex=1-∑i=1nModeli-Obsic⋅∑i=1nObsi-Obs‾,if∑i=1nModeli-Obsi≤c⋅∑i=1nObsi-Obs‾c⋅∑i=1nObsi-Obs‾∑i=1nModeli-Obsi-1,if∑i=1nModeli-Obsi>c⋅∑i=1nObsi-Obs‾2RMSE=∑i=1nModeli-Obsi2n Here, c=2, n is the number of observations, Modeli represents the ISAM-simulated carbon fluxes, and Obsi represents the site-scale observations.

Therefore, the ISAMdyn_wheat module appropriately represents spring wheat crop dynamics in ISAM. The dynamic phenology, dynamic carbon allotment, and dynamic vegetation structure growth improve crop simulation in a land surface model. However, one should use caution in calibrating and validating the model with sufficient data.

A major limitation of Gahlot et al. (2020) was validating ISAM against just one experimental site. To increase the confidence in model simulations, we compared the sowing date (Fig. S1), LAI (Fig. S2), and yield (Fig. 2) simulated by ISAMdyn_wheat against the crop dataset we compiled.

The yield simulated by ISAM is compared against the gridded EarthStat dataset (Monfreda et al., 2008) and site-scale observations (Fig. 2). The EarthStat data are reported as a 5-year mean yield for 1995, 2000, and 2005. The ISAM simulations over a similar period are compared in Fig. 2. The comparison confirms that the ISAM simulation agrees with the EarthStat gridded data in most wheat-growing regions except for small parts of the eastern and northwestern regions. This bias is explained by the difference in the sowing date simulated by ISAM and the GGCMI dataset (Fig. S1). However, analyzing the LAI site-scale comparison (Fig. S2), the growing season simulated by ISAM in the northwestern region (Jobner site) has good agreement with the observations in three growing seasons (2013, 2014, and 2015). This gives us the confidence that the dynamic planting date module in ISAM performs reasonably well. Additionally, even in the site-scale data we have at the IARI site, the spring wheat is sown on 16 December, which aligns with our ISAM simulations for this region. The northeastern and eastern parts of the wheat-growing areas of India are mostly irrigated, have very fertile soil, and have high yields; one of the largest wheat producers in India is in this region. Therefore, we are confident about the yields simulated by ISAM in this region and believe that the EarthStat data used for this yield generation might be biased. This assumption is supported by the site-scale yield comparison in Fig. 2c, which shows that ISAM-simulated yield has good agreement with the observations (Pearson's r=0.57). The yields are high in the western parts of EarthStat data, a semi-arid region with less rain and no irrigation. These regions often have lower yields, and we believe that the EarthStat data are biased in this region.

The country-scale SCON run described in Sect. 2.5.2 was designed to provide a quantitative understanding of the spatiotemporal variability of carbon fluxes across the wheat-growing regions of India. Before evaluating the regional-scale ISAM runs, we compared the simulated NEP from the SCON run with the carbon flux data from Patel et al. (2011, 2021). The monthly averaged carbon flux data were digitized from the figures. Patel et al. (2011) measured the carbon fluxes from January–April 2009 over spring wheat farmland in Meerut in northern India. The measurements provided diurnal variation of net ecosystem exchange (NEE) during four growing stages: tillering, anthesis, post-anthesis, and at maturity. The diurnal data at a growing stage were averaged, and a value representing a monthly NEE was calculated and converted to NEP. Patel et al. (2021) provided daily NEE values for spring wheat farmland in Saharanpur in northern India. The Patel et al. (2021) data were used to generate the monthly average fluxes for the growing season of 2014–2015. The simulated NEP at the grid cells where Meerut and Saharanpur are located is extracted from the SCON output. Figure 3 represents the comparison of simulated monthly average NEP (NEPISAM) and NEPOBS measured at Meerut (2009) (Patel et al., 2011) and Saharanpur (2014–2015) (Patel et al., 2021). The sowing dates simulated by ISAM are in the second week of December, while the spring wheat is sown in the last week of November in the observation data. Therefore, Fig. 3 shows the season-to-season comparison of the sites and ISAM simulations. The seasonality at Saharanpur is captured very well, although with a small bias. The R2 value for the sites is high and significant at p<0.1, showing that the ISAM-simulated NEP captures the variation in observed NEP. The mean absolute bias between observed and simulated NEP at Saharanpur and Meerut is 30.96 and 43.69 gC m-2 month-1, respectively. The bias may be because we compare site-scale observations with simulated values averaged over the 0.5∘×0.5∘ (∼ 2500 km2) grid cell area. Nonetheless, the high correlations with site observations point to the ISAM simulations' robustness.

Figure 4 shows the spatial maps of GPP, TER, and NEP for the growing season (December–March). The fluxes for each month of the growing season were averaged over 16 years (2000–2016) for that specific month. Because the climatic conditions across wheat-growing regions of India are diverse, the wheat crops are sown on different dates, which was reflected in ISAM using the dynamic planting day criteria. Spring wheat is planted in late October in central India and in early November in eastern India. The northern and northwestern planting dates are late November to early December (Fig. S1). Consequently, there are regional variations in the seasonal flux dynamics. The wheat-growing regions' central and eastern parts show the maximum flux value in January and February, respectively, while the northern and western parts show the maxima in March. The spatial plots show very low values of GPP and NEP during December because the crops are still in early growth. The croplands show very low values of NEP during March in the central and eastern parts of wheat-growing regions. Even though the croplands are not active, heterotrophic respiration leads to moderate values of TER in March for the eastern and central parts of India.

Figure 5 depicts the temporal pattern of annual and decadal fluxes. From 1980–2016, the GPP, NEP, NPP, Ra, and Rh over the spring wheat croplands increased at 1.272, 0.945, 0.579, 0.328, and 0.366 TgC yr-2, respectively. The trends represent the slope of the linear trend line, and the trends are significant at p<0.01, calculated using a two-tailed test. Figure 5b shows the box–whisker plots. The box represents the 25–75th percentile of the data, and the whisker shows 3 times the interquartile range (3IQR). The data outside this 3IQR whisker are extreme outliers. The median of all the fluxes showed a more significant increase from the 1980s to the 1990s compared to the 1990s to the 2000s. The rise was again steep from the 2000s to the 2010s.

The spatial trends of the fluxes over 36 years were examined. Figure 6 depicts the difference in the linear trend of total carbon uptake by spring wheat between the 2010s and 1980s. The linear trend was calculated at each grid point using singular spectrum analysis (Golyandina et al., 2013). The difference between the calculated trend line at each grid between the 2010s and 1980s gives us the total change in carbon fluxes over the period. The stippling in the figure shows the grids with significant trend signals from 1980–2016, calculated at a significance level of 95 %. The results show that the Indo-Gangetic Plain (IGP) region of India saw a significant increase in GPP than all other regions over the 37-year period. We can also observe a slight decrease in GPP in the western region. A similar trend in TER is observed, but the magnitude is less than that of GPP. The total carbon taken up by the spring wheat during the growing season is given by NEP, and the figure shows no significant increase in carbon uptake in the southern and northwestern parts. However, the IGP, along with Punjab and Haryana, has a significant increase in carbon uptake. Figures 5 and 6 highlight how the carbon uptake by spring wheat has changed over 3 decades and the spatial variation in this trend. The impact of climatic and management practices causing the above-observed trends is analyzed in the next section.

We investigated the impact of two climate drivers, changing temperature and [CO2], as well as two agricultural practices, nitrogen fertilizer and water availability due to irrigation, on carbon fluxes from spring wheat croplands. Figure S4 depicts the variation of these variables. Figure S4a shows the temperature anomaly between SCON and STemp. The temperatures are always warmer in SCON compared to STemp. During the study period, the temperature anomaly increased at 0.038 ∘C yr-1 (Fig. S4a). [CO2] has also shown a consistent rise and increased at 1.743 ppm yr-1 (Fig. S4b). The nitrogen fertilizer added to the C3 crops increased at 1.86 kg ha-1 yr-1 over 36 years from 1980–2016 (Fig. S4c) (Hurtt et al., 2011). Figure S4d displays the anomaly in water in the root zone during the growing season, estimated as the difference between SCON and SWater. Irrigation increases the water available to crops during the growing season in the SCON run. The SCON run provides ∼ 120 mm per season more water to the crop than the SWater run, which is ∼ 50 % of the wheat crop water requirement during the growing season.

The effects of these factors are estimated by analyzing the difference in simulated carbon fluxes between the control and experimental simulation (Fig. 7 and Table 4). Results show that the increase in temperature has a negative effect on all the fluxes. The temperature anomaly rose at 0.038 ∘C yr-1, and yearly GPP decreased at 0.597 TgC yr-12 during the study period. The mean temperature anomaly during the growing season in each decade is 0.25, 0.67, 1.43, and 0.9 ∘C. The temperature varied less between the 1980s and 1990s. Therefore, a slight difference in median GPP between these two decades is observed (Fig. 7a). However, a higher spread in the box–whisker plot of GPP is observed in the 1990s, which reflects a few growing seasons with considerable high-temperature variation. The higher temperatures during the 2000s and 2010s caused a significant decrease in GPP. Since the temperatures varied considerably during the 2000s and 2010s, a large spread in simulated GPP can be observed. Similar trends in NPP and NEP can be observed with a decrease of 21.9 and 13.9 TgC yr-1 ∘C-1 rise in temperature. Due to a temperature rise, the growing period and the crop phenology shorten (Koehler et al., 2013; Sonkar et al., 2019), which is also simulated by ISAM (Figs. S5a and S6a). Hence a decrease in fluxes is observed. As the crop growth decreases, the TER and NEP also decrease.

We analyzed the spatial variation in the impact of temperature on the GPP, TER, and NEP (Fig. 8). The figure shows the impact of temperature (SCON-STemp) averaged from 1980–2016. The stippling in the figure shows the grids with significant trend signals from 1980–2016, calculated at a significance level of 95 %. The temperatures in STemp are the de-trended climatological values from 1900–1930. Figure S4 shows the anomaly in growing season temperatures between the SCON and STemp simulations. We observe that the higher temperatures in the SCON run caused a decrease in carbon taken up by the spring wheat compared to the lower temperatures in the STemp run. However, the carbon uptake decrease is inconsistent across the wheat-growing regions. The IGP, Punjab, Haryana, and a few parts of central India are primarily affected by the higher temperatures, while the impact is less in other regions. Interestingly, only some trend signals are significant at 95 %, especially in the eastern IGP, Punjab, and Haryana. The trend in the impact of the temperature of TER is consistent over most wheat-growing regions, although the magnitude is less. The impact on NEP due to higher temperatures is consistently negative across the wheat-growing regions but insignificant in the IGP, Punjab, and Haryana. This behavior in these regions might be because these areas are highly irrigated.

Results showed that the increase in [CO2] alone has led to a rise in annual GPP, NEP, Ra, and Rh of 0.805, 0.422, 0.201, and 0.175 TgC yr-12, respectively (Table 4). During the study period, [CO2] rose at 1.743 ppm yr-1, causing an increase in GPP by 462 GgC yr-1 for a unit parts per million (ppm) rise in [CO2]. The GPP had a consistent rise each decade (Fig. 7). A large spread in GPP was observed in the 1980s. The [CO2] has consistently increased (Fig. S4b), but the temperature anomaly in the 1980s was below zero for a few growing seasons (Fig. S4a). Therefore, significant variation in GPP and other fluxes was observed (Fig. 5a) in this decade. Similarly, due to higher CO2 availability for the wheat crops, NPP, NEP, and TER increased by 202, 100, and 173 GgC yr-1 per part per million rise in [CO2]. As the [CO2] level increases in the environment, more carbon is available for crop uptake by photosynthesis (Saha et al., 2020). Analyzing the spatial variation in the impact of [CO2] (Fig. 8), we observe that the higher [CO2] in SCON led to higher carbon uptake across all the wheat-growing regions, with a higher impact observed in the IGP, Punjab, and Haryana. The impact of [CO2] is significant in all the wheat-growing regions. Similar trends in TER and NEP are observed, although with a lower magnitude.

Nitrogen fertilization increased NEP, Ra, and Rh at 0.468, 0.231, and 0.197 TgC yr-2, respectively. The impact of nitrogen fertilization on GPP at 0.897 TgC yr-2 was the highest among all the factors. Nitrogen fertilization caused an increase in GPP by ∼ 33 TgC on an annual basis. Similarly, NEP increased by ∼ 17 TgC yr-1, and Ra and Rh increased by by ∼ 8 and ∼ 7 TgC yr-1, respectively. Nitrogen fertilization is essential in India due to its tropical climate and multiple cropping systems (Gahlot et al., 2020). Studies have shown that nitrogen availability impacts carbon uptake through progressive nitrogen limitation (Jain et al., 2009). Though progressive nitrogen limitation is observed over longer timescales than the growing period of the crops, the decadal carbon flux simulations revealed some exciting results. Even under excess [CO2], if nitrogen is limited, crop growth does not show a significant difference, but a decrease in carbon uptake is observed (Jain et al., 2009; Luo et al., 2006). Under excess [CO2], if sufficient nitrogen is available, the ecosystem's carbon uptake increases; therefore, the maximum flux increase was observed in the nitrogen fertilization case (Table 4 and Fig. 8). The study by Lin et al. (2021) focusing on maize and soybean crops emphasized the importance of fertilization to improve crop growth, and our study proves that with adequate fertilization, even the spring wheat in the Indian region also grows well and the carbon uptake is higher. Nitrogen fertilization was consistent over the decades, leading to a constant rise in GPP. However, the variation in GPP in the 2000s was the least (Fig. 7) influenced by high temperatures during this decade (Fig. S4). A similar pattern of low variation was observed in NEP, Ra, Rh, and NEP during this period. The spatial variation across wheat-growing regions in the impact of nitrogen fertilization reveals the same pattern as seen in SCO2. However, the impact on carbon fluxes is more significant due to nitrogen fertilization than CO2. A higher impact was observed in the IGP and adjoining regions, which are highly cultivated and irrigated. The results show that using nitrogen fertilization improves the carbon uptake by spring wheat, in line with earlier studies (Jain et al., 2009; Luo et al., 2006).

The impact of water added to the crop led to an annual increase of ∼ 9 TgC in GPP, ∼ 6.5 TgC in NPP, ∼ 2 TgC in Ra, and ∼ 6 TgC in Rh. The reason for the small trend was the fluxes increasing through the 1980s, 1990s, and 2000s but declining in the 2010s. The decline in the 2010s was due to less water availability for the crops during this period, as shown in Fig. S4d, hence affecting the trends in the fluxes (Table 4). The higher GPP, NPP, and NEE in the 2000s compared to the 1990s, even though the temperatures were higher in the 2000s, suggests that the adverse effects of high temperatures can be overcome if the crops are provided with enough water. Studies like Hatfield and Prueger (2015) and Green et al. (2019) explored the impact of water availability in terrestrial ecosystems on carbon fluxes. They concluded that higher water availability improves the carbon uptake in terrestrial ecosystems. The spatial variation analysis (Fig. 8) shows that the higher water availability in the SCON run caused higher carbon uptake throughout the wheat-growing regions. The highest impact is observed in the northwestern regions of the country (Punjab and Haryana), which are highly irrigated, and most of the crop water requirements are met through irrigation. However, the stippling, which shows if a region has a significant trend over the 36 years, reveals that most wheat-growing regions do not have a significant increasing or decreasing trend. Nevertheless, the impact of adequate water causing higher carbon uptake by spring wheat is evident in Fig. 8.