In this work, we use the recently developed coupled ecohydrological-soil biogeochemical model, T&C-BG-2D , to evaluate the effect of different initialization schemes on the spatial distribution of soil carbon and nutrient pools. The original T&C model simulates coupled water, energy, and carbon cycles at the land surface. It includes modules for soil moisture dynamics and vegetation processes such as plant phenology, carbon allocation, and tissue turnover . The hydrological component simulates precipitation interception, transpiration, evaporation, infiltration, and snow/ice hydrology. Soil water movement is represented using a quasi-3D Richards equation, while surface water flow uses a kinematic wave approach . A soil biogeochemistry component, T&C-BG , was integrated into the T&C model to simulate soil carbon and nutrient dynamics, including nitrogen (N), phosphorus (P), and potassium (K). Vegetation growth is regulated by the availability of these nutrients, as plant tissue formation depends on flexible target stoichiometric constraints between carbon and nutrients, and nutrient limitation can constrain biomass production. The biogeochemistry module partitions plant litter into pools based on decomposability, and represents soil organic carbon (SOC) in three functional forms (mineral-associated, particulate, and dissolved). Soil organic nitrogen (SON) dynamics are tightly coupled to carbon through stoichiometric C : N ratios. The model simulates the temporal dynamics of SON, dissolved organic nitrogen (DON), and nitrogen stored in microbial and macrofauna biomass. It also explicitly tracks inorganic nitrogen pools – ammonium (NH4+) and nitrate (NO3-) – whose dynamics are regulated by mineralization, immobilization, biological uptake, leaching, volatilization, nitrification, and denitrification. A comprehensive description of T&C-BG is available in and . Recently, extended T&C-BG to a distributed framework (T&C-BG-2D) by explicitly accounting for the lateral transport of seven mobile carbon and nutrient pools, including DOC, NH4+, NO3-, dissolved inorganic phosphorus (DIP), dissolved potassium ions (K⁺), DON, and dissolved organic phosphorus (DOP), considered as passive tracers transported following the water flow. Tracers are assumed to be well-mixed in each storage compartment after vertical/lateral transport. At each hourly time step, the model updates soil carbon and nutrient pools in each grid cell by accounting for laterally transported solutes, which in turn regulate local vegetation dynamics. This enables the simulation of coupled ecohydrological-soil biogeochemical dynamics with the explicit consideration of the role of topographic features and lateral transport in shaping spatio-temporal carbon and nutrient patterns across a landscape. For clarity, Table  summarizes the different models referred to in this study. The proposed hybrid initialization technique is implemented in the coupled ecohydrological–biogeochemical T&C-BG-2D model.

The domain used to test and showcase the spin-up procedure in this study is the Erlenbach catchment (Fig. a), a 0.76 km² basin in the central Swiss Pre-Alps where T&C-BG-2D has already been applied . We considered a spatial square grid resolution of 20 m. Based on a previous application of T&C-BG-2D in this catchment , we used meteorological data to force the model covering a 9-year period (1 October 2011 to 30 September 2020). During this time, the catchment received an average annual precipitation of 2200 mm, with a mean air temperature of 6.5 °C . The spatial distribution of soil texture (here mostly loam and clay loam) was retrieved from , and vegetation cover was obtained from . As only one meteorological station (Erlenhöhe) is available in Erlenbach, constant lapse rate values typical of the region were assumed. For example, we considered a constant thermal lapse rate equal to -0.0045 °C m⁻¹ . The Erlenbach catchment is a suitable study area to showcase the spin-up and initialization procedure proposed here since model parameters have already been calibrated and the area is relatively small (thus reducing the computational costs) but still with a highly pronounced topography. Specific model settings and parameters for the simulations here can be found in .

The core strategy for the initialization framework proposed here involves two main steps: (1) performing a plot-scale spin-up in a limited number of selected cells while explicitly accounting for lateral fluxes of water, carbon, and nutrients, and (2) using a RF model to extrapolate the resulting steady-state pools across the entire model domain. While the RF is not used here to predict an independent external reference state, it enables spatial generalization from the sampled tracked cells to the remaining ones across the catchment. A primitive version of this procedure was successfully applied in . However, no formal workflow was developed, and neither large-scale benchmarking nor a systematic sensitivity assessment of the method was conducted. In this study, we formalize the framework, evaluate its performance across multiple scenarios, and test its generality to enable seamless application in other models and study areas.

The scheme follows several steps, as shown in Fig. . First, a plot-scale simulation using the T&C model is run for each soil–vegetation combination to obtain climatologically-driven, nutrient-unstressed water and vegetation fluxes (dashed box in Fig. a). Ideally, one should perform this step for each major vegetation and soil type combination. For the application here, given the limited variability in soil texture across the catchment, an averaged soil texture was considered. Then, we run the T&C-BG biogeochemistry module to reach steady state (Fig. a) using the long-term average meteorological inputs and averaged water and vegetation fluxes (from T&C). The resulting steady-state carbon and nutrient pools are then uniformly assigned to all cells with the same land cover type, resulting in spatially homogeneous initial conditions for each soil–vegetation combination (see Fig. b for an example in the Erlenbach catchment). Next, a 2D simulation is performed using the initial conditions obtained from step (b) (Fig. c). In this simulation, lateral biogeochemical fluxes are tracked (i.e., lateral fluxes of DOC, NH4+, NO3-, DIP, K⁺, DON, and DOP) across all grid cells in the domain. Note that, in this step, available spatially variable information on soil texture is used. The soil biogeochemistry module is then run using dynamic meteorological forcing (here repeating the 9 years of data available), incorporating the tracked lateral exchanges, until a dynamic steady state is reached (Fig. d). The flux-tracking step (c) captures the influence of topography, although we should note that soil carbon and nutrient pools respond slowly to spatial gradients and are unlikely to fully equilibrate within a short simulation period. In the 2D simulation in Fig. c, the entire available forcing period should be used to capture representative vegetation dynamics and to track biogeochemical fluxes as accurately as possible. In this case, the 9-year data were used, but a longer simulation would provide a more robust basis for the subsequent spin-up of the biogeochemical pools. A sensitivity analysis comparing the dynamic steady state of the biogeochemical pools using different lengths of the fluxes tracking period is presented in Fig. S1 in the Supplement. Using only 1 year for the 2D simulation in step (c) introduced a bias of 3 % in the steady-state SOC in grassland areas in step (d) compared to using all 9 available years.

The case in which lateral fluxes are tracked in n=100 % of the cells is considered here as a benchmark. In this case, the dynamic steady-state conditions from all grid cells are used to initialize the subsequent 9-year simulation (from Fig. d–f). This approach provides the highest accuracy, as each cell undergoes its own spin-up process while accounting for lateral fluxes and topographic variability. However, such a comprehensive spin-up is computationally demanding and should not be repeated for every new case study, as it would undermine the purpose of an efficient initialization protocol. Our objective is therefore to identify the minimum fraction of tracked cells n needed to approximate this benchmark with acceptable accuracy. For this purpose, a RF model is trained using a subset of tracked cells n (equal to 10 %, 20 %, 40 %, 60 %, or 80 %) to predict the spatial distribution of soil carbon and nutrient pools across the domain (Fig. e). The covariates used as predictors include topographic features (elevation, slope, drainage area, and profile curvature), soil properties (sand content; clay content is additionally included in the random soil texture scenario described in the following section), and vegetation type (forest or grassland). In most RF models here, vegetation type was represented by integer class labels and used directly as a predictor. For vegetation-specific pools, such as above-ground woody carbon, separate RF models were trained for grassland and forest cells. A stratified random sampling approach based on vegetation classes was used for pixel selection, meaning that grid cells were first grouped according to vegetation type (in this case grassland and forest) and, within each group, pixels were randomly sampled without replacement according to a prescribed sampling fraction (10 %, 20 %, 40 %, 60 %, and 80 %). The steady-state pools predicted by the RF (from Fig. e to f) are then used to initialize the final simulation over the period of interest (here 9 years, Fig. g). Because the focus of this study is on robustness across different sampling fractions rather than on optimal sampling design, we adopted a stratified random sampling approach based on vegetation types. Given that the distributions of topographic, soil, and vegetation characteristics across the full domain are known in advance and do not exhibit pronounced extreme tails, this approach leads to training subsets that largely preserve these distributions and thus ensure representativeness (Fig. S2). In cases where predictors exhibit strong spatial heterogeneity or patchiness, more structured hierarchical sampling across multiple predictor bins could be implemented to ensure a balanced representation of environmental gradients.

The performance of different initialization schemes (i.e., without RF (n=0 %) and with n<100 %) is assessed by comparing the spatial distributions of SOC, DOC, and SON with the benchmark case (n=100 %). First, simulations without RF or dynamic lateral fluxes (the direct output of step (c) in Fig. ) are compared with the benchmark to address hypothesis H1, testing the need for spatially-informed spin-up to capture carbon and nutrient spatial variability. Second, RF-initialized simulations are compared with the benchmark to address H2, thus evaluating whether extrapolation from a subset of representative cells can reasonably approximate the benchmark.

Random forest models consisting of 100 regression trees were trained to predict each carbon and nitrogen pool. This was implemented using the TreeBagger function in MATLAB R2024b (Statistics and Machine Learning Toolbox). Default settings were used for tree growth and, at each split, a random subset of predictors (one-third of the total predictors) was considered. The robustness of the RF model was validated using k-fold (k=10) cross-validation , and by evaluating the mean absolute percentage error (MAPE) and the normalized root mean squared error (NRMSE). NRMSE was calculated by normalizing RMSE by the range (maximum minus minimum) of the observed values, and both metrics were averaged across the 10 folds (see Table S2).

A sensitivity analysis was also performed to assess the relative importance of individual predictors in the RF algorithm. The six predictors considered were elevation, slope, flow accumulation area, profile curvature, percentage of sand, and vegetation type. Each predictor was individually removed from the RF training process using n=40 % tracked cells under the original simulation scenario (see other simulation scenarios in Sect. ). For each reduced predictor set, a new RF model was trained, and its ability to reconstruct the spatial patterns of carbon and nutrient pools was compared against the full model (with all six covariates). This analysis provides insight into the relative influence of individual predictors and helps assess how predictor choice may affect the sampling requirements (hypothesis H3). The primary purpose of this analysis was pragmatic: to identify which predictors are essential for reproducing spatial variability, and which could be omitted when reliable spatial data are unavailable. Besides, for the original scenario and random soil scenario (see simulation scenarios in Sect. 2.3) with n=40 % tracked cells, we further implemented a SHAP-based interpretability analysis (Shapley values) to quantify the importance of each predictor in the RF model.

In addition to the original simulation scenario (hereafter Original), a set of modified simulation setups was designed to evaluate the generality of the proposed initialization method, assess its performance, and evaluate variations in the required number of tracked cells and predictors under different levels of landscape complexity. Each simulation scenario introduces a targeted modification to one aspect of the catchment configuration, while keeping all other properties unchanged:

Vegetation cover (Fig. b): the existing vegetation is replaced either with a randomized spatial distribution while maintaining the original forest-to-grassland ratio (Random Veg), or with a uniform grassland cover across the entire domain (Homog. Veg).

In all cases, only one factor is varied per simulation scenario (i.e., vegetation, soil, or topography), while the remaining inputs are kept consistent with the Original simulation setup. For each scenario, the full initialization sequence described in Fig.  (steps a–g) is applied, with different RF initialization settings based on the percentage of tracked cells n (steps e–g). For clarity, simulations are denoted as n %, where n indicates the percentage of tracked cells used in the RF initialization (n=0, 10, 20, 40, 60, 80, or 100). n=0 % corresponds to simulations applying initial conditions from the 1D spin-up without RF or dynamic lateral fluxes (the direct output of step (c) in Fig. ), while n=100 % represents benchmark simulations in which lateral fluxes in all cells are tracked.

For the soil texture and topography scenarios, results for n equal to 60 % and 80 % are omitted, as a satisfactory performance (i.e., more than 90 % of SOC and SON spatial variability captured) was already achieved with n=40 % of tracked cells. Note that, for the analysis related to soil texture, in step (a) of the procedure (see Fig. ) the average soil texture is used, while spatial variability in soil textural properties is only taken into account from step (c) onward. The implications of this assumption were investigated with additional dedicated numerical tests and are discussed in Sect. 4. Overall, the design of these scenarios allows us to evaluate how vegetation, soil, and topographic heterogeneity may affect the number of representative locations required for RF initialization (hypothesis H3).

In steps (a) and (d) of the initialization workflow (Fig. ), vegetation fluxes are held constant and only the biogeochemistry module is used for spin-up. This decoupling strategy further reduces computational costs, as instead of solving the full system of coupled ordinary differential equations, the model reduces to a single biogeochemical system that can be solved at minimal computational cost. Such an approach is commonly used to approximate near-equilibrium states in terrestrial biosphere models . To evaluate the effect of neglecting vegetation dynamics during spin-up, we selected five cells for each vegetation type (forest and grassland) across a range of topographic conditions. For each selected cell, we compared the resulting steady state from the decoupled spin-up (using only the biogeochemistry module) to the steady state obtained from the fully coupled T&C-BG model, simulating the long-term vegetation-soil biogeochemistry dynamics (Fig. h). Details on the selected cells are provided in Fig. S2 and Table S3. For the fully coupled T&C-BG model, the repeated 9-year meteorological data were used to force the model, and the simulations were initialized using the soil carbon and nutrient pools from step (b) in Fig. . For every 9-year simulation, the long-term trend of all simulated soil carbon and nutrient pools was evaluated, using singular spectrum analysis to exclude interannual seasonalities. The steady state was considered reached when the long-term trends in all soil carbon and nutrient pools satisfied at least one of three predefined criteria over the final 9-year simulation period: (i) an absolute linear trend (slope) smaller than 0.1 [gC m⁻² d⁻¹ or gN m⁻² d⁻¹], (ii) an absolute difference between the first and last values of the fitted linear trend smaller than 0.1 [gC m⁻² or gN m⁻²], or (iii) a relative change between the first and last values of the fitted linear trend smaller than 1 %. Note that the slope threshold of 0.1 [gC m⁻² d⁻¹ or gN m⁻² d⁻¹] differs in units from those used in some previous studies e.g., 1 gC m⁻² yr⁻¹ in, reflecting the daily temporal resolution of our model outputs. However, when converted to annual units, the simulated slopes are of comparable magnitude and generally remain within the range of this stricter criterion (see Fig. S3 for an example). Then, the average of the final 3-year simulation period was adopted and compared to results from the uncoupled dynamics using the biogeochemistry module with constant vegetation fluxes. This numerical experiment was specifically designed to address hypothesis H4, testing whether uncoupled spin-up simulations provide adequate steady-state conditions compared to the fully coupled case.

Figure  shows the spatial distribution and associated probability density functions (PDFs) of 9-year averaged SOC, DOC, and SON (step (g) in Fig. ) under the Original setup. Results are shown for the benchmark simulation (n=100 %), the 2D simulation applying initial conditions from 1D spin-up without RF or dynamic lateral fluxes (n=0 %, direct output of step (c) in Fig. ), and RF-based initializations using different percentages of tracked cells n (see also Fig. S4 for additional results). Compared to the n=0 % simulation, which neglects long-term topographic effects on the initial soil biogeochemical conditions, the benchmark case exhibits greater spatial variability in SOC and SON, highlighting the role of topography in shaping soil carbon and nutrient distributions. In contrast, the spatial distribution of DOC (a small fraction of SOC) remains nearly identical between the benchmark and all initialization settings, regardless of the percentage of tracked cells considered. This is likely because DOC is rapidly transported by water and its spatial variability is largely captured during the 9-year simulation, even without dynamic spin-up or RF-based initialization. Since the spatial performance of DOC is satisfactory even without RF, subsequent analyses and results presented here will focus on SOC and SON only. The PDFs of SOC and SON (Fig. ) further indicate that the n=0 % simulation underestimates both the spatial variability and median values. This bias arises because the n=0 % simulation uses steady-state conditions from a single location (the meteorological station), which would require much longer simulation time to reflect the effects of heterogeneous environmental conditions and lateral exchanges (see more details in Sect. ). Note that the bimodality of the PDFs arises from the two different types of vegetation cover in the catchment.

Interestingly, RF initialization using just n=10 % of the cells can reproduce approximately 75 % of the spatial variability in SOC (Fig. ). Model performance improves with increasing percentages of tracked cells, and using n=80 % yields results that are nearly indistinguishable from the benchmark simulation. A notable performance jump occurs between n=20 % and 40 %. For example, in the Original simulation scenario, the overlap area (A value, quantifying the overlap between the PDFs of each simulation and the benchmark, with a value of A close to 1 indicating high similarity between distributions) increases from 0.82 to 0.91 for SOC and from 0.86 to 0.92 for SON (Table ). Considering A≥0.9 as a threshold for satisfactory performance yields n=40 % of tracked cells being sufficient to accurately capture most of the spatial variability in SOC and SON (see Table ) for the Original Erlenbach simulation scenario. Values of the Jensen–Shannon divergence, used to further compare similarities between PDFs, are reported in Table S4. Note, however, that the optimal percentage of tracked cells may vary depending on catchment characteristics such as vegetation composition, soil texture, topographic complexity, and background climate (see Sect. ).

Black lines in Fig.  show the temporal evolution of the coefficient of variation (CV, defined as the ratio of standard deviation to the mean) for spatial SOC under different RF initialization settings in forested and grassland areas (corresponding results for SON are provided in Fig. S5). In the n=0 % case, CV increases steadily over the 9-year simulation, indicating that spatial variability has not reached a steady state. In contrast, simulations initialized using the RF scheme maintain relatively stable CV values throughout the simulation period, with variability reflecting responses to dynamic environmental drivers rather than spin-up imbalance. CV values gradually increase across RF initialization settings with higher tracking percentages (n), approaching those of the benchmark. Notably, CV trajectories for RF settings using n=40 % and 100 % of tracked cells are nearly identical, confirming that n=40 % is sufficient to reproduce the full temporal dynamics of SOC spatial variability in the catchment here. Table S2 summarizes the robustness of the random forest models trained using 40 % of the tracked cells in the Original scenario. For most carbon and nitrogen pools, MAPE values are below 10 % and NRMSE values are below 0.1, indicating that the RF models exhibit satisfactory performance. These results provide direct support for H1, demonstrating that spatially explicit initialization is required to capture spatial variations of SOC and SON, as well as for H2, showing that spin-up at a subset of representative locations combined with RF extrapolation can satisfactorily reproduce benchmark dynamics.

Table  and Fig.  also report the performance of using different n values in the RF model across different catchment configurations. Across all simulation scenarios, n=40 % can capture over 90 % of the spatial variability in both SOC and SON. An exception is observed in the Homog. Veg simulation scenario, where even n=20 % of tracked cells yields satisfactory performance.

A comparison among Original, Random Veg, and Homog. Veg simulations suggests that the number of tracked cells required for satisfactory RF performance is more sensitive to the proportion of vegetation types than to their spatial arrangement. As expected, when vegetation cover is spatially homogeneous, fewer cells are needed to achieve accurate predictions.

In contrast, results from the Original, Random Soil, and Homog. Soil simulations indicate that reducing the spatial heterogeneity of soil texture lowers the absolute spatial variability of SOC but does not necessarily reduce the number of tracked cells required for RF initialization. This is likely because soil texture is already included as a predictor in the RF model, and because in the Original scenario soil texture is relatively uniform (i.e., sand content: mean = 41 %, standard deviation = 2 % based on ). As a result, the model can capture soil-related variability effectively without the need for additional soil information. However, in the Random Soil scenario, where soil texture is highly heterogeneous, adding supplementary predictors such as the percentage of clay significantly improves the model’s ability to reproduce benchmark SOC spatial patterns (Table ). This highlights the importance of including sufficient soil information when simulating spatial variability under heterogeneous soil conditions. Notably, the spatial CV is also higher in this scenario relative to the others, reflecting higher spatial variability of SOC. This is due to the expanded soil texture parameter space, especially variations in silt and clay contents, as this fine-particle-associated carbon contributes substantially to SOC (see also Table S5). These findings are consistent with previous studies showing that soil properties are among the most influential predictors in digital mapping of SOC e.g.,.

Simulation results from the flatter topography scenarios (0.5 hmax and 0.2 hmax) indicate that a gentler topography does not necessarily lower the number of tracked cells needed for accurate RF initialization. In general, RF models require more samples when predictor distributions are not evenly distributed within their overall range of variation (e.g., when extreme values are underrepresented), in order to adequately represent the edges and tails of the input space . In our sampling design, the distributions of predictor variables were known in advance, and the selected cells were chosen to represent the full range of topographic and land cover features across the domain (Fig. S2). This targeted selection likely contributed to consistent RF performance across topographic conditions. It is also important to note that, in these simulations, the use of flatter topographies only results in reduced elevation differences, slopes, and curvatures, without altering the overall catchment shape, size, and contributing area, as the underlying catchment skeleton remains identical across scenarios. Additionally, the topographies were modified by tilting the surface around the lowest elevation point. While this can affect the average temperature values in the domain (and resulting absolute values of SOC and SON), it has no impact on the number of cells required within the same simulation configuration. Overall, these results highlight that the number of representative locations needed for satisfactory RF initialization is shaped by catchment-specific heterogeneity and predictor distributions, thereby supporting H3.

Figure  presents the relationship between relative SOC bias (ΔSOC=(SOCsimulation-SOCbenchmark)/SOCbenchmark×100) and the topographic wetness index (TWI) from the Original simulation scenario with n=0 %, 10 %, 20 %, 40 %, together with the PDFs of ΔSOC. Additional results covering all simulation scenarios are provided in Figs. S6 and S7.

Figure a shows that the n=0 % initialization configuration results in a systematic underestimation of SOC in many cells, with deviations reaching up to 20 %–30 % in some cases. This is because the initial pools (Fig. b) are derived from the 1D spin-up at the Erlenhöhe meteorological station, located at a relatively low elevation (1210 m a.s.l.) within the catchment. Since SOC generally increases with elevation due to temperature reductions – an effect captured by T&C-BG-2D – SOC in high-elevation areas gradually accumulates over time. However, the 9-year n=0 % simulation is insufficient for these areas to equilibrate, leading to a consistent underestimation (compared to the benchmark simulation, which instead captures the increasing trend of SOC with elevation) due to the lack of spatial information in the model initialization.

Interestingly, a positive relationship between ΔSOC and TWI is observed in the range TWI < 11, where the majority of grid cells are located (Fig. a). This trend can be explained primarily by the influence of water availability on soil respiration and, consequently, on SOC stocks. We note, however, that TWI is weakly but significantly correlated with elevation, and thus with air temperature (r=-0.14, p<0.05). This suggests that temperature may also contribute to the observed relationship, although its influence is relatively minor compared to that of water availability. When the n=0 % initialization is applied, SOC exhibits almost no trend with TWI (Fig. a and b). However, the benchmark simulation shows a decreasing SOC trend with increasing TWI for TWI < 11, reflecting a long-term steady-state pattern shaped by soil respiration processes during spin-up. Simulations with n=10 % and n=40 % successfully capture the SOC–TWI relationship, with results from n=40 % being closer to the benchmark simulation. This relationship is consistent with previous findings showing an increase in soil respiration with water availability due to enhanced microbial activity , as shown in Fig. c and d. However, under excessively wet conditions (such as TWI > 11), this relationship reverses due to oxygen limitation . Figure c and d further shows that while the n=0 % case reproduces the correct qualitative relationship between fast carbon fluxes (e.g., soil respiration) and TWI, correct flux magnitudes are only captured when n=10 % of the cells are tracked, and the performance is further improved for n=40 %. Because the SOC distribution in the benchmark simulation shows much higher spatial variability than in the n=0 % case, the decreasing SOC–TWI trend from the benchmark dominates the ΔSOC–TWI relationship, leading to an apparent positive correlation in Fig. a. The PDFs in Fig. e further confirm that the RF initialization scheme substantially reduces this topography-related bias. Using only n=10 % of the cells for RF training already eliminates most of the systematic bias (Fig. b), while n=20 % (Fig. c) and n=40 % (Fig. d) eliminate it almost entirely. The analysis here clearly highlights that the bias between plot-scale initialization and spatially-informed ones is strongly linked to grid-cell interactions via topography-controlled lateral transport.

Figure  compares SOC values obtained from different simulation stages and spin-up strategies. The first column represents the initial SOC values (here, values in Fig. b are used, but can be derived from the steady state in areas with similar land cover, soil, and climatic conditions, or from a reasonable initial guess). The next three columns show SOC values after 9, 18, and 27 years of simulation using the full T&C-BG model (i.e., with coupled soil biogeochemical and vegetation dynamics). These three columns are used to exemplify the gradual convergence of SOC toward steady-state conditions. The gray box in the middle shows the SOC state obtained using the biogeochemistry-only spin-up with 9-year average vegetation fluxes after 1000 years (i.e., no coupled vegetation dynamics – equivalent to step (a) in Fig. ). Starting from this uncoupled spin-up steady state, an additional 27 years of simulation (3×9 years) were performed using the full T&C-BG model, with results shown in the three subsequent central columns. Such trajectories should not be interpreted as generally indicative of the direction toward the final steady state, as SOC and SON may follow non-monotonic pathways in dynamic systems. In the present simulations, however, both SOC and SON evolve toward the long-term coupled reference steady state during the first 27 years. The red box on the far right indicates the reference steady state achieved through long-term simulation with the fully coupled T&C-BG model, which considers the coupled vegetation-soil biogeochemistry dynamics. Each boxplot includes five representative sites with different vegetation types (see Fig. h). Site-specific vegetation and soil information, along with SOC and SON pool sizes, are provided in Table S3. A corresponding analysis for SON is shown in Fig. S8.

As shown in Fig. , the initial SOC values are substantially underestimated in the case here and gradually increase over the course of the simulation. After a 27-year simulation period with the fully coupled T&C-BG model, the resulting SOC is still largely underestimated compared to the long-term steady state (red shading). Reaching steady state with the fully coupled model would require approximately 1000 years. A direct comparison of SOC between the uncoupled spin-up steady state (middle gray box in Fig. ) and the reference steady state from the fully coupled plot-scale spin-up (red shading) reveals an average underestimation of 19.2 % and 10.6 % for grassland and forested sites, respectively (see also Table S3). The underestimation is further reduced for the case of SON (see Fig. S8). This uncoupled spin-up steady state can be reached by first running the fully coupled model for only a short period (here 9 years) to obtain average vegetation fluxes, which are then used to drive the biogeochemistry-only spin-up. This provides a substantial gain in computational efficiency, as the computation time for decoupled spin-up is negligible (Table S6) despite the slight disagreement in steady states, thus supporting the choice of adopting an uncoupled spin-up approach as a first step (Fig. a) within the proposed initialization framework and confirming H4.

In summary, the domain used here contains 1859 cells in total. Tracking lateral fluxes in all cells increases computational cost significantly (e.g., by approximately 50 % compared to a simulation without tracking any fluxes when n=20 %), whereas tracking only n=10 % of the cells has a less than 10 % impact on the overall spin-up procedure (Table S6). In Erlenbach, SOC requires over 300 years of simulation to reach steady state (Fig. S9) even without coupled vegetation-soil biogeochemical dynamics. The proposed initialization framework reduces this demand by collapsing the full 300-year 2D spin-up into two 9-year simulations (corresponding to Fig. b and f), combined with a 1D plot-scale spin-up. Ideally, the hybrid spin-up procedure requires two 9-year 2D simulations instead of 300 years (i.e., 18 years in total, corresponding to approximately 6 % of the original simulation length). Wall-clock times of different components of the spin-up procedure are reported in Table S6. While these times are expected to change based on the specific computational platform used, for the case here the hybrid spin-up procedure resulted in a computational saving of approximately 90 % using the recommended n=40 % configuration.