A total of 70 eucalyptus trees from five planting geometries (16 from three planting geometries and 11 from two boundary plantations) were destructively harvested at the age of 8 years of planting, separated, sorted, sub-sampled, dried to constant weight at 63°C (Beets and Garrett, 2018), and weighted for biomass components [leaf, branch, bole, stump root (stump, coarse root, and fine root)] to extrapolate total component-wise dry biomass and fitting of models. The heights of selected trees were measured with the help of a measuring tape after being measured in meters (m) with an error of ±0.1 mm. The diameter at breast height (DBH) was also recorded with the help of an aluminum caliper in centimeters (m). The biomass of harvested trees was divided into two categories, i.e., aboveground biomass (stem, branch, and leaf) and belowground biomass (stump and fine–coarse roots) by using standard methodologies given by Snowdon et al. (2002) and Newaj et al. (2014). In case of fine and coarse root biomass, monoliths (50 cm × 50 cm × 50 cm) were randomly laid out at 1 m and 2 m away from the tree base in five planting geometries with five replications. The monolith sampling was done in the month of March 2017. After complete washing, the roots were filtered with 0.5-mm sieve and sorted into fine and coarse roots. All live and dead roots were sorted out and placed on soaking paper for a few minutes to minimize the water content. The root samples were dried at 63°C to a constant weight and then weighed. Furthermore, based on the monolith volume (50 cm³), total fine coarse roots (FCR) biomass was determined and extrapolated to hectare (Mg ha⁻¹) and single trees (kg tree⁻¹).

To construct accurate tree growth models, a combination of theoretical principles and practical observations relies on two distinct datasets—one for model estimation and another for validation. In the absence of an independent dataset for validation, the original datasets (derived from destructively harvested trees) were randomly split into two exclusive sets, comprising 80% for model estimation and 20% for validation, ensuring a pseudo-independent approach (Ajit et al., 2011).

The crop biomass was determined by the quadrat method in replicated quadrates of 1 m² each from the center of the tree rows of various spacing geometries. In case of boundary plantation (east–west and north–south directions), quadrate basis (1 m²) crops were harvested at the distances of 0–3, 3–6, 6–9, 9–12, 12–15, and 15–18 m from the tree lines on four aspects (northern and southern in east–west and eastern and western in north–south boundary plantation) in three replicates and averaged to get crop biomass per hectare basis.

The harvested green fodder yield was weighed in kg plot⁻¹ and converted to Mg ha⁻¹. The random multiple samples of 500 g were taken from fresh biomass, air-dried, and further kept in an oven at a temperature of 60°C for 72 h. Based on the dry matter content of these samples, the green fodder biomass was converted into dry fodder biomass (Mg ha⁻¹). D r y m a t t e r c o n t e n t ( % ) = W e i g h t o f o v e n d r y s a m p l e W e i g h t o f f r e s h s a m p l e × 100 D r y f o d d e r b i o m a s s = F r e s h f o d d e r y i e l d × d r y m a t t e r c o n t e n t 100 whereas in case of barley, a quadrate basis crop was harvested and threshed with the help of a mini-plot-thresher; the clean grain obtained was weighed to record grain yield (kg per net plot), which was then converted using appropriate conversion factor and reported as grain yield (Mg ha⁻¹). The remaining straw after threshing was weighed as a straw yield per net plot and then converted to hectare basis (Mg ha⁻¹).

The study calculated carbon stock by multiplying dry biomass and the number of trees per hectare with their corresponding carbon values. Carbon content in all tree components was determined from oven-dried and ground samples, which were analyzed using a CHNS-O analyzer after passing through a 1.0 mm sieve. For each treatment, five trees (stem, root, leaves, and branch) were considered for carbon content estimation. Crop carbon was calculated using a reference value of 40% based on Stewart (1993).

Soil samples were collected at depths ranging up to 90 cm (0–15, 15–30, 30–45, 45–60, 60–75, and 75–90 cm) to determine soil chemical properties. However, the mean value of six soil depths was considered. The soil pH and EC were measured using a pH meter and a conductivity meter in 1:2 soil-to-water ratio (Jackson, 2005). The soil available nitrogen (N), phosphorus (P), and potassium (K) were determined by the alkaline potassium permanganate distillation (Subbiah and Asija, 1956), Bray’s method (Bray and Kurtz, 1945), and ammonium acetate extractant method (Jackson, 2005), respectively.

Random soil samples were collected in three replicates from the surface soil (0–15 cm) before planting trees and after 8 years of planting (0–90 cm) from five different geometries to determine bulk density and soil organic carbon (SOC). The bulk density of the soil was determined using metal core samplers of known volume. The soil samples were oven-dried at 105 ± 10°C for 48 h, and the bulk density of soil in g cm⁻³ was calculated by dividing the oven dry weight of the sample by the volume of the core sampler (Cresswell and Hamilton, 2002; Halli et al., 2022). The Walkley–Black method (Walkley and Black, 1934) was used to determine the SOC content. Samples were also collected from a control field for comparison.

Soil organic carbon stock (Mg ha⁻¹) = soil organic carbon (%) × depth (cm) × bulk density (g/cm³).

The total system carbon sequestration potential (Mg C ha⁻¹) was computed as per the crop rotation in eucalyptus-based agroforestry systems. The formula is followed as:

The economic analysis was carried out by comparing various agroforestry systems with sole annual crops that cover one cycle of eucalyptus harvest. The costs associated with establishing the plantation were categorized into establishment cost (A), covering expenses incurred during the initial year of planting (including planting material, transportation, land preparation, transplanting, and plant protection). Operational cost (B) encompassed subsequent years’ expenses for crop and tree maintenance, irrigation, fertilizer application, crop seeds, hoeing, weeding, and inter-row cultivation to prevent unwanted vegetation during non-crop periods. The interest rate on working capital (A + B) was set at 9%. Other factors, such as management cost (10%) and risk cost (10%), along with year-wise existing rental value of land, were included for the estimation of financial analysis. The cost–benefit parameters used for comparing the systems were net returns, net present value (NPV) at a 12% discounting rate, internal rate of return (IRR), and benefit–cost ratio (BCR). The calculation of LEV has been done using the Faustmann model that combines annual revenue flow from intercropping production and final timber harvest of eucalyptus trees (Klemperer, 2003; Guo et al., 2006). The value (price) of trees was determined by referencing the Haryana Forest Development Corporation’s purchase list for eucalyptus, which is fixed on girth basis. Concurrently, the price of crops was computed based on the market rates prevailing in the respective years. The costs and income from intercropping and trees were also calculated. The economic viability of different planting geometries for eucalyptus-based food systems was assessed using standard methodology, aligning with previous research methodologies outlined by Chavan and Dhillon, 2019 and Chavan et al. (2022b).

Net present value: NPV was estimated as under: N e t P r e s e n t v a l u e ( R s / h a ) = ∑ t = 1 n B i − C i 1 + r t 2 where B represents benefits in the year t, C the costs in year t, r the selected discount rate, and n the number of years.

Benefit–cost ratio (BCR): Discounted benefits were divided by the discounted costs to obtain the BC ratio. BCR can be expressed as follows: B C R = ∑ t = 1 n ( B i ( 1 + r ) t 2 ) / ( C i ( 1 + r ) 2 ) where B represents the benefits in the year t, C the costs in year t, r the selected discount rate, and n the number of years.

Internal rate of return (IRR): Internal rate of return is defined as that rate of discount that equates the present value of a stream of net benefits with the initial investment outlay, or IRR, which is that rate at which the PNV of cash flow is zero.

Tree height (20.03 m), DBH (20.87 cm), and total biomass (274.46 kg tree⁻¹) under five planting geometries differed significantly. Variation was found to be high for the biomass components and ranged from 33.17 (aboveground biomass) to 46.06% (roots; Table 2). Ajit Rai et al. (2006), Rojo Alboreca et al. (2015), and Ajit et al. (2016) also reported variation in biomass components in eucalyptus. There was a moderate correlation between height (0.68) and total biomass; however, a strong positive correlation was observed between DBH (0.93) and total biomass. Kuyah et al. (2013) also reported that DBH was strongly and significantly correlated with above- and belowground biomass. The other parameters of statistics, such as skewness, kurtosis, and S-W normality test, proved that the datasets were derived from a normally distributed population. The negative skewed (−0.35) and kurtosis values (−0.74) were found for height and DBH in eucalyptus. This negative value indicated that distribution slightly flatter than a normal curve with the same mean and standard deviation. Kuyah et al. (2013) also reported negative skewness for height and DBH in biomass studies in eucalyptus.

The accuracy of a biomass equation depends on the selection of appropriate independent variables to develop best-fit equations. In this study, various combinations of independent (effect) variables [viz., DBH, Height, DBH²H, DBH² × WD × H, DBH², and ln (DBH)] were tried and plotted against the total biomass of eucalyptus to testify the accuracy and efficiencies in the prediction of biomass. On the basis of model adequacy criteria, DBH²H was found to be a better-fit independent variate than DBH alone. It was further confirmed that D²H, i.e., inclusion of height as an additional interpreter variable to DBH, increases the R² for eucalyptus (Zewdie et al., 2009; Luna et al., 2014; Tewari, 2016) and other mixed tree species equations (Chave et al., 2001; Bastien-Henri et al., 2010).

The destructive biomass sampling method is a prerequisite for precise and accurate modeling of tree biomass. Therefore, the sufficient number of field measurements is the precondition for developing biomass estimation models and for evaluating the biomass estimation results (Deo, 2008). In our study, 70 trees were randomly selected and harvested with a DBH range of 15.45–27.50 cm and measured component-wise to develop biomass equations. To obtain a good regression equation, at least 25 trees should be selected randomly from a wide range of DBH (de Gier, 2003).

Total biomass and DBH²H relationship for eucalyptus trees were investigated by fitting six regression functions such as allometric, logistic, Chapman, Gompertz, linear, and exponential (Table 3). Among the six fitted models, allometric model, i.e., biomass = 300.96 × DBH²H^0.93 (adjusted R² of 0.96) was the best-fit over the others. Global model characteristics like adjusted R², F ratio, and AIC cannot guarantee model adequacy. Graphical examination of residuals (primarily studentized residuals) was used to evaluate the best-fit regression models in Figure 4 for independence, homogeneity, constant variance, and normality. There was also a detailed residual diagnosis for allometric function. Scatter plot of studentized residuals vs. predicted total biomass was clearly portrayed the homogeneity of variance over the entire range of predicted total biomass. Autocorrelation plots showed no relationships among allometric function residuals. Autocorrelation plot residuals were randomly distributed at zero slope and scattered within the confidence limit. The residuals’ independence was further shown. The quintile–quintile and probability plots showed that residuals were regularly distributed. Error term variance was constant too. Based on these statistical criteria, allometric model was best of six regression functions fitted. The results of biomass models in eucalyptus are consistent with the prior findings (Tandon et al., 1988; Dhanda and Singh, 1990; Tewari, 2016). However, these researchers did not do residual diagnosis and validation, which raises the question of reliability. The research conducted by earlier researchers (Ajit Rai et al., 2006; Kuyah et al., 2013; Ajit et al., 2016; Ounban et al., 2016) has demonstrated the superiority of allometric models in estimating biomass using residual diagnostic and validation criteria.

Data pertaining to dhaincha–barley crop rotation under different planting geometries are presented in Tables 4, 5. During the Kharif season, dhaincha was planted in the initial 2 years of the study. The presence of moderate to dense shade, arising from various plant geometries of eucalyptus, led to a significant decrease in the green biomass of dhaincha. A notable 24.75% reduction in yield was observed in the 3 × 3 m spacing, whereas the least reduction was noted in the boundary plantation (2%–6%). A similar result was obtained by Prasad et al. (2010) in eucalyptus in that they reported 48%–53% loss in the post-rainy season.

In the rabi season, barley was sown (every year) up to the harvesting of trees. In block spacing, the average higher grain yield of barley was obtained in paired row spacing (2.41 Mg ha⁻¹), followed by 6 m × 1.5 m (2.12 Mg ha⁻¹) and 3 × 3 m (1.75 Mg ha⁻¹) spacing over a period of 8 years. Barley experienced an average yield loss of 8.92–39.0% under 1–4 years of plantation, and it further increased from 44.21 to 64.48% (fifth–eighth year of plantation) under block plantation of eucalyptus over control (sole cropping). The highest yield loss of 70.29% was recorded in 3 × 3 m at 8 years of planting. However, 20.21% higher yield in barley yield was observed when row spacing increased from 3 × 3 m to 6 m × 1.5 m spacing, and it further increased up to 36.71% in 17 × 1 × 1 m spacing at 8 years of rotation. This may be due to the fact that low light intensity intercepts decrease the rate of photosynthesis, affect directly the relative growth rate, reproductive, and ripening phases of crops, and ultimately lead to a loss of yield (Luna et al., 2009).

In boundary plantation, the maximum grain yield (2.59 Mg ha⁻¹) was observed in the north–south in comparison to the east–west boundary plantation (2.42 Mg ha⁻¹) but was less than control (3.24 Mg ha⁻¹). The observation on barley crops under 8 years of plantation revealed that crop growth was severely affected near tree line (up to 6 m away), but growth increased and further improved with proceeding away from tree line in all four aspects of boundary plantation (data are not presented). Studies by Dhillon et al. (1979, 1982) revealed a maximum reduction in yield of wheat (64%), rice (58.4%), and potato (42.6%) near the tree baseline of the boundary plantation of eucalypt near the base line. In the present study, crops performed better in north–south planting of eucalyptus over other planting geometries. Similar trend was also observed in the straw yield of barley under various spacings of eucalyptus. Distance from tree line also played a noteworthy role in the yield of annual crops. Furthermore, the yield of crops increased with the increase in distance from the boundary tree lines. The results demonstrated in boundary plantation match with other studies by Singh and Kohli (1992), Kidanu et al. (2005), and Yadava (2010). Biomass and yield of dhaincha and barley crops were significantly affected due to various spacing geometries of trees. The magnitude of crop yield loss in the eucalyptus-based cropping system increased with the age of the trees due to increased competition for resources (light, moisture, and space) and subsequently hampered the growth and yield of agricultural crops. Increased competition with age is due to the increased size of the trees and their ability to mop up greater resources at the expense of crops (Dhyani and Tripathi, 1998; Prasad et al., 2010). The yield reduction was found to be higher in Kharif season as compared to the Rabi season. Tree density or spacing geometry of eucalyptus affects annual crop yield severely (Ahmed, 2004; Prasad et al., 2010, 2012).

Manipulation of planting geometry under agroforestry provides opportunity to choose appropriate crop combinations for higher yield and profitability. Therefore, modified planting geometry may help to reduce the yield reduction losses under tree-based agroforestry systems. Crop performance under eucalyptus was testified with various crop combinations by the number of authors throughout the country as well as the globe (Prasad et al., 2010; Kumar et al., 2013; Gill et al., 2016; Dhillon et al., 2018; Nyaga et al., 2019).

Biomass plays a crucial role in the global carbon cycle and has emerged as an imperative solution for reducing climate change. Such region-specific periodic measurement studies on biomass accumulation can be used further to establish the value of agroforestry practice (Eamus et al., 2000). In this study, planting geometry had strong influence on total biomass production and partitioning among components under eucalyptus (Table 6).

The biomass production was recorded higher under 3 × 3 m (344.60 Mg ha⁻¹) and 17 × 1 × 1 m (323.12 Mg ha⁻¹) planting geometry, whereas the lowest (56.17 Mg ha⁻¹) was found in north–south boundary plantation. However, the tree biomass was statistically at par between 3 × 3 m and 17 × 1 × 1 m spacing at 8 years of rotation. The annual biomass accumulation was maximum (43.04 Mg ha⁻¹ year⁻¹) in 3 × 3 m, followed by 17 × 1 × 1 m (40.39 Mg ha⁻¹ year⁻¹) and 6 m × 1.5 m (28.11 Mg ha⁻¹ year⁻¹) in block plantation. The aboveground biomass ranged from 42.73 to 279.17 Mg ha⁻¹, whereas belowground biomass ranged from 13.43 to 65.43 Mg ha⁻¹. George (1982) and Tandon et al. (1988) reported 301.50 Mg ha⁻¹ and 302.1 Mg ha⁻¹ at 8- to 9-year eucalyptus plantation, respectively. In addition to this, the growth of eucalyptus under block plantation was not as like in widely spaced trees, but biomass production was huge due to the high number of trees. This is a general rule that the number of trees per unit area gives a higher yield, and it is in accordance with earlier studies (Prasad et al., 2010; Forrester et al., 2013; Ajit et al., 2016). In agroforestry, tree biomass is enhanced due to management practices as compared to forest and sole plantation. However, the contribution of different tree components in total tree biomass was: 62.50%–74.09% of stem; 6.59%–9.14% of branch; 3.18%–5.73% of leaves; 12.20%–20.44% of roots; and 1.71%–3.48% of fine–coarse roots (Figure 5). The biomass portioning in the study is in similar line with earlier literature (Pande et al., 1987; Tandon et al., 1988; Prasad et al., 2010), where they reported approximately 70% biomass accumulated in eucalyptus stem/bole. Kuyah et al. (2012) reported that the contribution of different components to the total AGB was 73.7%, 22.3%, and 4.0% in stem, branch, and leaves, respectively. In case of eucalyptus, higher tree density helps to initiate self-pruning; ultimately, the percentage contribution of branches and leaves will be lower in compact spacing than in boundary plantation. Eucalyptus grows better under competition in stands (blocks), whereas tree tends to become heavily branched if planted wide apart, especially on boundaries.

Carbon accumulation in trees is in prime focus due to climate change mitigation measures. The percentage carbon concentration in different components of eucalyptus trees differed from 43% to 49% (Figure 6). The mean carbon content of the stem, branch, leaves, and roots in the present study was 49.00%, 47.00%, 43.00%, and 49.00%, respectively. Matthews (1993) compiled the carbon content of eucalyptus tree, which was 47.2%–49.5% in various parts. Ribeiro et al. (2015) also reported that the average carbon content in the stem, branch, leaf, and root compartments was 44.6%, 43.0%, 46.1%, and 37.8%, respectively. The highest amount of aboveground, belowground, and total carbon was estimated to be 134.29, 32.00, and 166.29 Mg ha⁻¹ in 3 × 3 m, followed by 133.82, 21.98, and 155.80 Mg ha⁻¹ in 17 × 1 × 1 m (paired row), respectively, while the lowest were 20.47, 6.57, and 27.03 Mg ha⁻¹ in north–south boundary planting at 8 years of rotation (Table 7). An average carbon sequestration rate was 12.79 Mg C ha⁻¹ year⁻¹ in five spacing geometries (Figure 7). In boundary plantation, carbon sequestration rate was 6.78 and 3.38 Mg C ha⁻¹ year⁻¹ in east–west and north–south plantation, respectively, at 8 years of rotation, which was lower than block plantation. Therefore, block plantation of eucalyptus sequestrated four times more carbon than boundary plantation of eucalyptus after 8 years of rotation.

Recent studies suggest that agroforestry systems (AFSs) have a higher carbon sequestration potential (Pandey, 2002; Nair et al., 2010; Ajit et al., 2016; Dhyani et al., 2016; Zhou et al., 2017; Chavan et al., 2022a,b). Zhou et al. (2017) observed an average sequestration rate of eucalyptus was 19.53 Mg C ha⁻¹ year⁻¹ in China. Ajit et al. (2016) also reported carbon sequestration rates for various tree species under agroforestry ranging from 0.39 to 15.91 Mg C ha⁻¹ year⁻¹. Specifically, carbon stock in AFSs can vary widely, with estimates ranging from 0.29 to 15.21 Mg ha⁻¹ year⁻¹ aboveground and 30–300 Mg C ha⁻¹ up to a depth of 1 meter in the soil (Nair et al., 2010). In India, agroforestry systems have been estimated to sequester between 0.25 and 19.14 Mg C ha⁻¹ year⁻¹ for tree components and between 0.01 and 0.60 Mg C ha⁻¹ year⁻¹ for crop components (Pandey, 2002; Dhyani et al., 2016). There are several studies reporting either the lower or higher side of carbon sequestration rate. Hence, several factors, such as type, structure, and function of agroforestry, climate, planting geometry, soil type, socio-economic factors, management techniques, end-use, etc., significantly affect the carbon sequestration potential (Albrecht and Kandji, 2003; Tian et al., 2005) at different plantation. Among several factors, choice of planting density is a primary silvicultural decision in agroforestry, which reflects the trade-off between individual tree size and total biomass production, affecting the type, quantity, and quality of products throughout the rotation (Forrester et al., 2013).

Under various planting geometries of eucalyptus, the total biomass varied from 137.37 to 407.13 Mg ha^− 1 in dhaincha–barley crop rotation (Table 7). Over the 8-year period, spacing geometry of 3 × 3 m performed better in terms of total biomass production (407.13 Mg ha^− 1), contributed by tree biomass (344.60 Mg ha^− 1) and crop biomass (62.53 Mg ha^− 1). Irrespective of spacing geometry, mean total biomass of eucalyptus was 285.79 Mg ha⁻¹, whereas in control (treeless system), biomass production was only 101.87 Mg ha⁻¹. It is interesting to point out that 80.61 and 49.93% biomass was contributed by tree components under block and boundary plantations, respectively over 8 years of rotation. Furthermore, eucalyptus-based cropping system exhibited 27.70% reduction in crop biomass over control (sole cropping). Toky et al. (1989) reported that 68% biomass was contributed by the trees in agri-hortisilvicultural system; these findings support the present investigation.

In the present study, carbon stock (Mg C ha⁻¹) among various carbon pools indicates that vegetation stock (aboveground biomass followed by belowground biomass) and soil carbon contributed toward aggregate carbon pools (i.e., system total carbon) under various planting geometries at 8 years of study (Table 8).

The total carbon stocks of eucalyptus-based cropping systems (including trees, crops, and soil) exhibited significant variation across different planting geometries and sole crop rotations (dhaincha–barley). The findings clearly indicate that integrating tree components into sole cropping can enhance carbon stock by two to three times. Notably, the highest carbon stock (237.27 Mg ha⁻¹) was observed in the 3 × 3 m spacing, with the breakdown showing 166.29 Mg ha⁻¹ in trees, 25.01 Mg ha⁻¹ in crops, and 45.97 Mg ha⁻¹ in soil (Figure 8). Moreover, the total carbon stock in the system was notably influenced by tree density and planting geometry. In close-planted systems (block) and boundary plantation systems, trees contributed an average of 66.94 and 35.92%, crops contributed 13.32 and 29.57%, and soil contributed 19.73 and 34.51% of the total carbon stock, respectively. In contrast, in the control (sole crop), crops accounted for 54.34% and soil for 45.66%, respectively.

Du et al. (2015) reported similar findings in a eucalyptus-based cropping system in China. They found a total carbon content of 156 Mg C ha⁻¹, with aboveground and belowground components (understory, root, and soil carbon) contributing 43.1 and 59.9%, respectively, in trees aged 6–7 years. The understory (shrub and herbaceous material), litter, and fine roots individually comprised <2% of the total carbon, while the soil contained between 53 and 94% of the total carbon. Zhou et al. (2017) highlighted the significant carbon sequestration potential of eucalyptus, noting that the total ecosystem carbon pool varied between 167.66 and 234.04 Mg C ha⁻¹ in eucalyptus stands aged 7–10 years. Additionally, Luna et al. (2016) reported aboveground carbon stocks ranging from 14.38 to 408.97 Mg C ha⁻¹ in eucalyptus plantations with a 3 × 3 m spacing in Hoshiarpur, Punjab. Consequently, the reported carbon stock values, encompassing contributions from trees, crops, and soil, ranging from 95.20 to 237.27 Mg C ha⁻¹, align closely with findings from other studies conducted in India and abroad.

Therefore, the integration of eucalyptus in annual crops increased the carbon stock of sole cropping by 2.8 times in block planting (3 × 3 m, 6 m × 1.5 m, and 17 × 1 × 1 m) and 1.5 times in boundary plantation after 8 years of age. These results further indicate that, owing to the fast growth and adaptability of eucalyptus, it can produce adequate quantity of biomass carbon rapidly. Moreover, eucalyptus is a fast-growing tree species with high potential of biomass carbon sequestration than poplar.