For the model calibration, we used the LUCAS points from a field campaign conducted in 2009 as reported in Cotrufo et al. (2019) and Lugato et al. (2021). This dataset comprises; (1) the main physico-chemical characteristic of topsoil (0–20 cm), including total SOC content for about 20 000 samples distributed across different land covers in the EU and UK; (2) a size-fraction of the bulk SOC into mineral-associated (MAOM) and particulate organic matter carbon (POM) in a representative sub-set of 350 samples. The latter were randomly drawn from the all the measurements with the only constraint being that both datasets were similarly distributed across ecosystems with approximately 73 % being grass- or croplands with the rest being various forest types. Figure 1 shows the LUCAS data points across Europe and the calculated SOC stock at each measurement site. The representativeness of the chosen 350 measurements points is elaborated upon in Lugato et al. (2021).

For the calibration, the 348 LUCAS measurements from the 2009 campaign containing POM/MAOM fractions are used. The remaining 19 476 total SOC measurements were set aside for validation. In both allocations, measurements which were not classified as agricultural, grassland or forest were removed as well as all the sampling points where the driver data was not available. As a result, 322 datapoints are used for calibration and 17 430 for validation.

While the benefit of the LUCAS dataset is its large spatial representation and inclusion of measurements from multiple different ecosystems, the execution of such a vast measurement campaign introduces different source of errors from sampling, labelling, analysis etc. Thus, it is almost more apt to be considered as a combination of several independent campaigns done with the same protocols, instead of a single consistently controlled campaign. Additionally, although locations of the measurement are known, we have the make the assumptions that the available driver data are representative for the actual conditions at the measurement plot.

The Microbial Efficiency-Matrix Stabilization V1 (referred to simply as MEMS for simplicity; Robertson et al., 2019) model is a novel soil organic carbon (SOC) model framework, which is built around the scientific understanding that the soil microbial pool modulates the SOC stocks. The model structure is presented in Fig. S1 in the Supplement. In the model, both surface vegetation and SOC decomposition are represented by multiple pools defined by their physical properties. There are several paths for carbon fluxes to transfer from one pool to another or lost as CO₂, with the rate of change calculated on a daily timestep. The model dynamics represents the depth of the soil measurements used to calibrate it. As we are using the LUCAS data here which is from the top 20 cm of the soil, the resulting MEMS model will thus simulate the SOC dynamics of top 20 cm layer as well.

Since the parameterization focuses on the SOC stock, only the model equations affecting MEMS pools C5 (Heavy particulate organic matter), C8 (Dissolved organic matter), C9 (Mineral associated organic matter (MAOM)) and C10 (Light particulate organic matter) were calibrated here. The vegetation decomposition pools C1 (hot-water soluble), C2 (acid soluble) and C3 (acid insoluble) as well as the surface microbial pool (C4) and the dissolved organic matter (C6) do determine the litter input entering to soil C pools. These mechanics were not included in the calibration as the type of data required to constrain them was not available. Therefore, we used the default parameters values established in Robertson et al. (2019) for the surface processes since they had been chosen to be representative of the LUCAS network environment. Meanwhile the released CO₂ (C7) and the leached dissolved material to the soil (C11) are cumulative removal pools and do not have any parameters to be calibrated.

The equations that govern the change in the relevant pools in MEMS are: 1dC5dt=C5,in2+C5,in3+C5,in4-Tmodk5C52dC8dt=C8,in5+C8,in6+C8,in10-sorp-DOClchC8-Tmodk8C83dC9dt=sorp-Tmodk9C94dC10dt=C10,in2+C10,in3-Tmodk10C10 Where Ci is the amount of carbon stored in pool i, Ci,inj is the carbon input to pool i from pool j as a result of the decomposition process and ki is the decomposition rate for pool i. The leaching coefficient DOClch represents the dissolution of SOC to deeper soil layers and the temperature coefficient Tmod reflects how soil temperature affects the decomposition rate. In this work, Tmod is the same for all pools and follows the STANDCARB 2.0 model (Harmon et al., 2009) which is an expanded version of the traditional Q10 temperature model where the limiting impact of the high temperatures is accounted for.

The sorption coefficient sorp controls the flow of carbon between the microbial pool and the mineral associated carbon pool as determined by the equation 5sorp=C8KlmQmaxC81+KlmC8-C9Qmax6Qmax=d⋅ρsoil⋅1-prock⋅scConc7scconc=scslope⋅1-psand+scint In which Klm is the langmuir isotherm term that depends on the soil pH, Qmax is the maximum absorption capacity of the soil, ρsoil is the soil bulk density, prock is the rock percentage of the soil and psand is the sand percentage of the soil. The maximum concentration of fine fraction, scconc, is governed by the two coefficients scint and scslope. Consequently, those two parameters effectively control the saturation ratio for the MAOM pool.

The decomposition rate parameters k5, k8, k9 and k10 were the central parameters chosen for calibration as well as scint and scslope. As the primary focus of this work is to compare the calibration methods, these parameters were simply chosen as a straight-forward test case. The boundary values are presented in Table 1. As will explained in Sect. 2.5, we do need an expected value for these parameters in order to create a prior uncertainty distribution. We chose this value by randomly drawing a parameter value from near the middle of the set of the boundary conditions after testing that the model runs remained stable with these parameter values.

To determine how we divide the litter input to MEMS model pools, the site ecosystem type was assigned by the Corine Land Cover (Buttner, 2014). Following that, NPP is split into the MEMS model pools according to the following framework established in Robertson et al. (2019): 8C1,inputt=1-fdocecofsolecorecoNPPt9C2,inputt=1-fsoleco-fligecorecoNPPt10C3,inputt=fligecorecoNPPt11C6,inputt=fsolecofdocecorecoNPPt Where Ci,inputt is the carbon input to pool i from NPP at a given time t and eco refers to the ecosystem for the LUCAS point. Then, fsol is the hot water extractable fraction of the litter input, fdoc is the cold-water extractable fraction of the water extractable fraction and flig is the acid-insoluble fraction of the of the litter input. It is important to note that these fractions are not the totality of the litter input and, while equations from 8 to 11 do sum up to the total NPP, the fractions presented here do not sum up to 1. Finally, the reco represents the fraction of NPP that is assumed to have been removed from the system due to economic activies (harvest, grazing, etc.)

The coefficient values based on Campbell et al. (2016) are presented in Table 2. It is important to make two notes regarding these values. First, we are using a single fraction here and do not account for the uncertainty range provided in the work referenced. Second, only fsol and flig fraction ranges are presented in Campbell et al. (2016). For fdoc we used a constant value across land covers in line with the work Robertson et al. (2019).

Markov Chain Monte Carlo (MCMC; Geyer, 1992) is a widely used Bayesian model parameterization method. The basis of this approach is straightforward: First values for the parameters chosen for calibration are drawn by randomly perturbing accepted parameter values and the model is run for given locations with these parameters. Assuming that the uncertainties are normally distributed, the total likelihood F of these projections, given observations that correspond to model predictions, is calculated with 12F=∏l=1Nobs2πσl212e-12∑l=1Nobsxl-yl2σl⋅∏k=1Npar2πσθ,k212e-12∑l=1Nparθk-θk,prior2σθ,k Where l is the observation index, Nobs is the number of observations, σ is the associated uncertainty, xl is the model projection with parameter set θ and yl is the observation for index l. Furthermore, k is the parameter index, Npar is the number of parameters being estimated and Θprior is the prior estimate of parameters.

Once the likelihood is determined, it is compared to the likelihood of the previously accepted parameter set. If the new likelihood is higher, then that parameter set is automatically accepted and used as the parameters for the next iteration. However, if the new likelihood is lower than the previous one, there is still a probability that the new parameter set will still be accepted depending on how close the new likelihood is to the previous accepted likelihood.

By allowing the lower likelihoods to be possibly accepted, MCMC also provides an acceptable parameter range, which can be used to represent the parameter uncertainties. This iterative process is repeated until a given convergence goal is satisfied (Roy, 2020).

For the study here, we used the MCMC framework established in Viskari et al. (2022), which utilizes the BayesianTools R-library (Hartig et al., 2019). The chosen MCMC algorithm is the Differential evolution Markov Chain with snooker updater (DEzs; ter Braak and Vrugt, 2008), where multiple calibration chains progress concurrently from different starting point with information shared between the chains at given intervals. This should lead to a more efficient and faster convergence of the calibration, especially as this approach makes it possible to parallelize the different chains.

Six chains were used for the calibration with the initial values for each chain randomly drawn from the prior parameter range. The MCMC was run for 100 000 accepted iterations with the convergence test and statistical values calculated from the last 10 000 iterations.

Instead of iteratively exploring the variable space like MCMC does, 4-Dimensional Ensemble Variational data assimilation (4DEnVar) uses an ensemble of model runs with different variable sets and that are independent of each other. The ensemble of model runs is used to approximate information required by other calibration techniques, such as the gradient of the cost function and a mapping from variable space to observation space. Because there is no need for a large amount of model run repetitions such as in MCMC, this method is a computationally much faster. However, this approach is built on certain assumptions – in particular that the observations can be predicted by a linear combination of the different ensemble members – which make it important to test before-hand how well it is able to find the correct values in different systems.

The foundational theory for the 4DEnVar method is explained in Liu et al. (2008). The formulation established in Pinnington et al. (2020) was used as the basis for this work. In this section, we will provide a simplified description of the method as it applies to our purposes.

In traditional baseline 4-Dimensional Variational data assimilation (4DVar; Le Dimet and Talagrand, 1986), similarly to MCMC, the most likely state, i.e. the model parameter set, is solved by determining the minimum of the cost function J 13J=12(θ-θpriorTB-1θ-θprior+∑t=1KM0→t(θ,x0)-ykTRt-1M0→t(θ,x0)-yk) In which θ and θprior are, respectively, the suggested and prior parameter value vectors, B is the prior parameter error covariance matrix and Rt is the observation error covariance matrix at the measurement time t. The model operator M0→t calculates from the given parameters and the initial state x0 the output comparable to the observation vector yk. The measurement times in the chosen time window is represented by K.

Two brief notes on this formulation. First, it is essentially the same as exponent component in Eq. (12), except that is written it in vector form. Second, in an effort to simplify the equations, we did not include an observation operator component in the equations. All our observations are point measurements that can be directly compared with the model output, hence a separate observation operator was unnecessary for our purposes.

4DVar, like MCMC, is also an iterative approach that calculates the cost function with different state vectors to test if the cost function value decreases. However, with 4DVar, the iterations suggested after the first attempt are not randomly drawn, but rather determined by the gradient function 14∇J=B-1θ-θprior+∑t=1KM0→tTRt-1M0→t(θ,x0)-yk Where M0→tT is the adjoint of the tangent-linear version M0→t of the model operator M.

The benefit of the gradient use is that it results in a value of zero for the state vector that produces the cost function minimum. Thus, gradient descent techniques (Ruder, 2016) are able to use the information from the gradient to efficiently locate the cost function minimum and the optimal state vector.

Naturally, there are challenges in applying this method. The core hurdle is the adjoint operator in equation Eq. (14), which is the transpose of the tangent-linear version of process model. Creating these model versions, though, is not a simple task and imposes a linearity assumption on the driving processes. Furthermore, since background error covariance matrix B can have non-diagonal terms representing error covariances, the inverse matrix can become computationally implausible to be calculated for larger systems.

In 4DEnVar, these issues are approached by expanding on the square root transform framework established in Tippett et al. (2003). Let us have an ensemble of model runs where, in our case, every ensemble has a different parameter set randomly drawn from the same baseline prior distribution. In the 4DEnVar formulation, this prior distribution is assumed normally distributed. For each ensemble member, we can then determine how its output differs from the prior parameter set output. These perturbations from the mean across the ensemble can be written in matrix format Θb′ as follows 15Θb′=(θb,1-θ‾b,θb,2-θ‾b,θb,3-θ‾b,…,θb,L-θ‾b)L-1 Where L is the ensemble size, θb,i is the ith vector of the perturbation matrix, and θ‾b is the average over the perturbations. In our case, the average over the perturbations is the same as the prior parameter vector θprior.

Since this matrix essentially represents the uncertainty related to the parameter values, the prior error covariance matrix B can be approximated as 16B≈Θb′Θb′,T We admit that in this formulation we ignore model structural error and assume the dominant error is from the parameter uncertainty.

Furthermore, we can define a vector w with the length of L that satisfies the equation 17w=Θb′,-1θ-θprior With these formulations and assumptions, the cost and gradient functions can be written as 18Jw=12wwT+12∑t=1KM0→tΘb′w+M0→t(θ,x0)-ykT⋅Rt-1M0→tΘb′w+M0→t(θ,x0)-yk19∇Jw=w+∑t=1KΘb′,TM0→tT⋅Rt-1M0→tΘb′w+M0→t(θ,x0)-yk With this new formulation, we can further approximate 20∇Jw=w+∑t=1KM0→tΘb′T⋅Rt-1M0→tΘb′w+M0→t(θ,x0)-yk This formulation removes the need for the adjoint version of the model. An additional benefit of the 4DEnVar method is that the gradient function value can be calculated for each ensemble member, since we are already running an ensemble to approximate the prior error covariance matrix. This information, then, makes straightforward determining the state estimate.

Compared to filter-based data assimilation methods (for example the Ensemble Kalman Filter; Evensen, 2003), the variational methods do not estimate the posterior uncertainty directly. However, we used the method established in Pinnington et al. (2021) to calculate the posterior distributions.

For the study here, we used the 4DEnVar algorithm provided in Quaife (2023). The gradient approach method used there is BFGS2 (Saito and Nakano, 1997) from the GNU Scientific Library (GSL).

The 4DEnVar methodology holds crucial benefits for our model calibration even beyond the reduction in computational cost compared to MCMC. Even though all the measurements used for calibration in this work are from the same year, the model outputs are steady state products that take hundreds of simulated years to produce. Hence, a 3-dimensional variational data assimilation (3DVar; Lorenc et al., 2000) cannot be applied and the adjoint of the model would be required, as the gradient function needs to be calculated at the start of the simulation. To complicate things further, the validity of the tangent-linear assumption would be questionable due to the length of the simulation in this situation.

After having set up the algorithmic framework for both calibration methods for the selected LUCAS data points, the first task was to complete twin experiments. In those, we randomly drew a value for each the parameter chosen for calibration from the uncertainty distributions assigned for them in Table 1. Synthetic observations were generated with the model using the new parameter set. Then, we performed the calibration with both tested methods using these synthetic observations with their associated uncertainties set to be 1 % of those synthetic observations and still using the same prior distribution established in Table 1. This allows us to check if both methods were able to find the correct parameter sets in a situation where the true answer was known. For the 4DEnVar, the additional importance of these tests is to assess the ensemble size dimension required to consistently estimate the correct parameter set. This was accomplished by repeating the twin experiment multiple times with different ensemble sizes and choosing the ensemble size where the calibration always found the correct parameter set. The repetitions were necessary because the 4DEnVar ensemble members are randomly drawn, therefore there are potential situations where a given ensemble size can retrieve the correct parameter set several times in a row, but then fails on the next time.

After the twin experiments have been conducted, the calibration itself is performed with the calibration dataset, before the validation runs are done for the validation dataset locations. In both situations the SOC is assumed to reflect a steady state. It should be noted that with agricultural soils and commercial forests are expected to have a large variability in litter input over a given time window, which does raise challenges for the steady state approach. We are still including those data points in the analysis here as this is intended as a general calibration across European ecosystems and there is no additional data to constrain those specific ecosystems, but this is expected to be an additional uncertainty source. As a part of the testing here, we also wished to experiment how varying assumptions regarding model drivers affected the potential differences between the calibration results. For our test case study on the impact of the NPP assumptions on the parameterization, we repeated the calibrations with a small adjustment. We changed the fdoc value of grass- and croplands from 0.15 to 0.35. This increases the amount of the litter that is directly deposited to the soil and consequently adsorbed by the mineral matrix instead of being lost during the transition between the surface and soil carbon pools. In our expert opinion, there is a higher proportion of exudates and root litter (i.e. low molecule weight compounds that can directly sorbed by the soil minerals) entering the topsoil in grasslands and herbaceous compared to forests. Thus, this change is suitable for a plausible change to the NPP assumptions and makes an ideal test study to see how it affects the parameterization results and if the system depicted by the parameterizations still remains consistent after the potential change.

When calculating the steady state, the MEMS model is simulated over the period of 700 years from an initial state vector (Table S1 in the Supplement). Here, during calibration each LUCAS point is simulated for 700 years with the last output values compared to the measurements. At some sites, the MEMS model did not reach full steady state during this time, but the difference was within fractions of a percentage of the final steady state. As the change was so marginal already at this point, the shorter time period was chosen for computational efficiency.

As driver data at the European level, the model uses daily air temperature extracted from the E-OBS grid (Cornes et al., 2018). For each day of the year, an average temperature is calculated from a time series that spans from 2009–2018, with the temperature cycle then repeated for each year when calculating the steady state. Furthermore, the clay, sand and rock content of the soil as well as the soil bulk density and pH from LUCAS are used to determine soil properties driving SOC processes.

For Net Primary Production (NPP), first the average annual NPP over the decade 2000–2010 is extracted from the MODIS product MOD17A3 (Running et al., 2004) grid cell overlaying each LUCAS point. Then, a standard sine function is used to distribute the NPP across the year in order to produce the daily litter input. This approach was used instead of an averaged MODIS NPP annual time series as the NPP reflects the time when the atmospheric carbon is allocated into vegetation, not when the vegetation becomes litter input. Hence, we simplified the time series here and, since the total annual NPP remains the same, it is not expected to affect the modelling results to a notable degree.

The total SOC measurement uncertainties from the LUCAS dataset are used as the uncertainties in this application. Since LUCAS protocol requires to take a composite soil sample (out of 5 samples), the uncertainty was estimated propagating the error associated to all variables for calculating SOC stock (i.e. SOC content, depth, rock fragment). We run a Monte Carlo simulation with 5000 draws, using a standard deviation derived from the coefficient of variation reported in Goidts et al. (2009) for the microsite scale, with a similar sampling scheme of LUCAS. It is important to note, though, that these values are calculated from mixed samples. Thus, it may be an underestimation of the real uncertainty for several reasons as, for example, how LUCAS samples are overall representative of the field conditions. However, we do not have more information concerning the SOC measurement uncertainties available.

Regarding the MAOM fraction, there is no established uncertainty estimate to utilize. Because of that, we assigned an uncertainty where the standard deviation was 5 % of the measured MAOM value. This choice was driven by both a discussion with the data collection team about the reliability of the data and to ensure an appropriate weight during the calibration process. When the initial cost function is calculated using the baseline MEMS parameter set with this uncertainty, the total SOC values account for approximately two thirds of the cost function value, with the MAOM fraction being responsible for the remainder.

The prior uncertainty assigned to the parameters introduced challenges in this work. With MCMC, because we only use the prior parameter value range for the initial sampling, we were able to apply a uniform uncertainty distribution that was used to approximate the baseline parameter set from Robertson et al. (2019). For those parameters where the uncertainty was not provided, we approximated a wide enough uniform distribution around the assigned parameter value. The 4DEnVar method, though, requires a Gaussian uncertainty distribution as explained in Sect. 2.4. As there is no prior information available, we used the baseline parameter values as the expected values, with the uncertainty represented by a standard deviation of 10 % of the parameter value. This uncertainty range, deliberately imposing a larger uncertainty, resulted in 4DEnVar calibration producing negative parameter values, which are naturally unrealistic. We will discuss the reasons and implications of this behaviour later.

In some studies, for example, uncertainty has also been a parameter estimated with MCMC (Cailleret et al., 2020). Considering the meaningful unknowns regarding the uncertainty approximations, this would be a valid approach to be applied here. We did not estimate uncertainties for the initial MCMC/4DEnVar comparison, as varying the uncertainties might cause issues with the gradient approach methods and, consequently, would make it difficult to interpret the differences between the two. After the comparison, though, we did perform a MCMC calibration of MEMS, where we also estimated a scaling parameter for both total SOC and MAOM fraction uncertainties. However, these results are not shown here, as the calibration did not result in a successful convergence.

As seen in the results, the 4DEnVar approach is a straightforward tool for calibrating the MEMS v1 model with LUCAS data, as valid as the MCMC approach. Both had issues with the first parameterization attempt when it came to the validation dataset, but performed similarly when the direct litter fraction to soil was increased. Hence, the central problem with the first calibration attempt was not due to the calibration method itself. This supports 4DEnVar as a meaningful approach for initial calibration of soil carbon models, especially considering the massive difference in the required computational costs. For MCMC, the 100 000 iterations used here took over a month to compute on our HPC server while, simulating the 250 ensemble members without using parallelization, took approximately four hours. It should be noted that the MCMC calibration did begin to converge to the final values already after 40 000 iterations, but there is a risk in accepting the local cost function minima after such a relatively short calibration cycle. The computational cost for calibration from having to spin-up to steady state is a known issue with land system models in general (Raoult et al., 2025).

What is striking, though, is how much the parameter sets produced by the two calibration methods in both litter distribution scenarios differ from each, even with the higher fdoc, they perform approximately equally well with regard to the total SOC measurements in the validation dataset. As mentioned in the Introduction, equifinality, a situation where there exists multiple parameter sets that produce similar model outputs, is a known issue in ecosystem modelling and is evidently represented by the results here. The notable element here is that the calibration method itself determines the resulting parameter set as even when repeated, the MCMC calibration approach does not suggest the solution is in the same part of the parameter space as the 4DEnVar results indicate. Generally, twin experiments are efficient first pass to test for equifinality and the challenge can be addressed by reducing the amount of parameters being calibrated, but here there are questions how much those efforts can be relied on in assessing equifinality.

While we are not certain of what is driving these systematic differences between calibration sets, we hypothesize that one crucial component is that the total SOC and MAOM fraction measurements appear to incentivize contradicting model behaviours. Our twin experiment results support this theory as, with synthetic datasets, we were able to retrieve the same parameter set of both total SOC and MAOM that internally coherent with the model dynamics. This tension is especially evident when the fdoc is lower and there is less litter to distribute between the SOC pools. In that situation, MCMC is still able to find a solution by forcing a reduction in the decomposition rate for the MAOM pool and increasing the decomposition rate for the POM pool. This leads to a high MAOM fraction but at the cost of lower POM pool values and, consequently, a tendency to project lower SOC values. Meanwhile, this conflict between the two measurement types does seem to cause issues with the gradient approach method applied by 4DEnVar to determine the ideal parameter set. This could be because the disagreement between the data sources will create such a degree of noise in the likelihood space that determining a correct gradient descent from a collection of ensembles will become much more challenging. Simultaneously, though, this vulnerability in the 4DEnVar could be exploited in future work to quickly test if different measurement types and drivers are compatible within the model framework.

These results further highlight the fundamental impact of the priors on the calibration results, especially with the 4DEnVar approach, that has been recognized as a larger challenge in ecosystem modelling (Dietze, 2017). While experimenting with the initial setup, we found that the 4dEnVar calibration produced unrealistic parameter values with negative decomposition rates, if prior was set to be too loose. This remained true even when increasing the fdoc value, although then the uncertainty could be loosened slightly more. Our hypothesis is that, while the MCMC iterative approach allows setting boundaries for the region where the values are sampled, such hard constraints are not present with the 4DEnVar. Additionally, the 4DEnVar does rely on the first order Taylor expansion, making it vulnerable to non-linear behaviours. Thus, incongruities resulting from missing model processes such as soil moisture, for example, can drive the parameterization beyond acceptable values if there is not a sufficient prior constrain implemented. This could be a partial explanation for the Iberian Peninsula error biases visible in Fig. 5 as the soil moisture dynamics are much more complicated in arid climates vulnerable to drought (Almendra-Martin et al., 2021). A further limitation is that the 4DEnVar algorithm used here draws the ensemble members by sampling the prior distribution. While this is a logical approach when those distributions are reliably approximated, here we do not know what the prior distributions are and must use a tight uncertainty range in order to avoid unrealistic estimations. Consequently, our application of 4DEnVar samples the parameter space in a more limited manner than would be preferable.

The lack of knowledge on prior distributions for the parameters is an obstacle that is further hindered by the lack of reliable measurement uncertainty estimates. An important aspect of Bayesian statistics is that the weight of an individual information source depends on how accurate it is in comparison to the other available information sources. Hence, the width of the prior uncertainty that we can assign to constrain the parameter estimate to remain in a reasonable range is dependent on the measurement uncertainty. In this work, those uncertainties were so low that we had to use a relatively narrow prior parameter range for the 4DEnVar approach. Furthermore, as detailed in the Methods section, we do not have reliable approximations of the measured MAOC : SOC fraction uncertainties. Their uncertainty here is, thus, defined by how much weight we wished to give them in relation to the total SOC measurements. When we tested a larger measurement error, which in turn allowed us to increase the prior parameter distribution for the 4DEnVar without producing unrealistic estimates, the 4DEnVar ensembles also changed with the new values moving farther away from the baseline values. The implication is that the 4DEnVar is much more sensitive to the measurement uncertainty representation than MCMC, due to how the prior constraint is applied.

Naturally this underlines the overall importance of providing reliable measurement uncertainties along with measurements themselves, but that is not something a model user can simply produce by themselves. When implementing the calibration, based on the results here we would recommend of initially looking through the calibration data and confirming that all the values there are sensible for the model/system being calibrated. As a more practical solution, it is possible to repeat the 4DEnVar calibration multiple times by using the previous posterior distributions as the priors to the next cycle. This way it is possible to ensure that the resulting parameter set is not simply because the prior had been set too far from the correct value and thus partially reduce the impact of the assigned prior distribution. However, the downside of repeating the calibration cycle in this manner is that not only does it reduce the impact of the prior, but each iteration reduces the resulting uncertainty distribution. Thus, the final parameter distributions would be artificially too confident. While the repeated calibration is a worthwhile tool in certain circumstances, it always needs to be implemented with great care and consideration.

Our results clearly underline how the fundamental assumptions regarding the NPP, as a litter proxy, impact the model calibration results. The lower fdoc resulted in a noticeable bias on total SOC predictions, especially with regard to the MCMC calibration. Another encouraging aspect of the work is that the differences between the two calibration methods results remain consistent even when changing the litter input assumption. This supports the capability of using the quicker 4DEnVar calibration to explore the impact of the NPP assumptions on the parameterization as any signal noted there should be reflected also in MCMC results.

What complicates future work is that coefficients associated with litter input are challenging to calibrate simultaneously with parameters associated with SOC decomposition, as their influence on the SOC overlap too much. It is important to note that while the focus in this experimentation has been the fdoc value, what it actually represents is the assumption of dividing NPP between upper- and below ground biomass as it reflects the amount of litter deposited directly into the soil. This is a central assumption that has to be included in some manner in SOC modelling and is represented by the plant species traits assigned to the surface vegetation. This highlights why better understanding of the vegetation qualities of the ecosystem being modelled is important for calibrating even simple SOC models.

As for even attempting to calibrate the NPP/litter coefficients simultaneously would first necessitate determining which exact coefficients would be calibrated. For example, in our case, there is first the question how well the MODIS NPP product represents reality for different systems. Then, part of that NPP is removed to represent economic activity before it is distributed to the four MEMS initial pools based on the three coefficients. Any of these three parts can be altered to change the final NPP input to the soil in different ways, but there is really no certainty at the moment what is the correct manner to better regulate the NPP based litter input. This complicated relationship in the surface vegetation driving litterfall and the SOC state has been shown in prior work such as in Raczka et al. (2021). There when they used remote sensing data to constrain their model state, while this improved their modelled aboveground biomass and carbon exchange accuracy, it also caused their modelled SOC accuracy to decrease because they were only using the aboveground data for both systems.

Adding to the challenges discussed above is that the various assumptions are not expected to be spatially homogeneous even in the same ecosystem type. For instance, the Nordic countries, especially Sweden and Finland, are dominated by economic forests where the NPP-to-litter pathway is heavily impacted by the growth stage as newly growing forest will have a large NPP, but not a corresponding amount of litter due to mortality. This could be connected to bias seen in the northern Europe in Fig. 5. Another example would be agricultural ecosystems as climate conditions affect which crops will be dominant in a given region. The type of crops naturally affects its traits as, for instance, the root depth distribution, which in turn is expected to impact the soil carbon stocks (Fan et al., 2016). These various components could be a reason why when analysing global soil databases, there is a weak statistical relationship between NPP and SOC despite that dynamic being well understood (Luo et al., 2021). Naturally this is not to questioning the use of NPP as a litter input for soil carbon models. Rather it is another reminder on how important it is to be aware of the various assumptions related to the NPP and remain consistent with them while running the calibrated model in various systems. Additionally, when doing future SOC projections, the uncertainties related to the various NPP/litter assumptions should be considered during analysis.

The error distributions for both calibration methods when applying the higher litter input is in itself worthy of analysis. The MEMSv1 model used is lacking several dynamics that are known to impact soil carbon stock, such as soil moisture (Falloon et al., 2011), various nutrient cycles (Gardenas et al., 2011; Feng et al., 2023) and mycorrhiza abundance (Hawkins et al., 2023). However, when considering the multitude of simplifications made to calculate the steady state approximations using parameters calibrated with data from 322 sites, the error distribution for the 17 000+ validation sites is much narrower than we initially expected. Which raises question how much of a further performance issue could be expected with addition of new processes? And, consequently, how can this limited data be used to evaluate which processes are most important for future projections?

Notably, while the spatial presentation of the model error under the higher fdoc shows only few regions where the differences between the two model errors are consistently larger than 10 t of carbon per hectare, such as the Nordic countries, the MAOM fraction projections by the two model calibrations differ systematically to a meaningful degree. For instance, 4DEnVar calibration resulted in a higher turnover rate of the MAOM pool, which in turn causes lower MAOM stocks. Both calibration methods are adjusting the parameters to produce lower total SOC, as the baseline parameters tend to overestimate the SOC stocks, but they solve the issue with very different representations of the internal SOC state that would have a major impact on future projections. With the current available information, it is not possible to evaluate which of the two states is more realistic; while the MCMC modelled MAOM fractions are on average high for all ecosystems (Georgiou et al., 2022), the LUCAS dataset leans towards arable soils where the MAOM fraction is expected to be larger in the top layer than for forests (Schrumpf et al., 2013; Sokol et al., 2022).

These outcomes emphasise the importance of carefully considering how model performance improvements are assessed with large-scale datasets such as the LUCAS measurement data, since the total SOC seems not sufficient which is in line with previous studies (Braakhekke et al., 2014; Guo et al., 2022). This is especially relevant as the model validation should be a crucial aspect of model choice regarding different SOC sequestration projects (Garsia et al., 2023). New measurement analysis methods allow for more efficient POM/MAOM fractioning of SOC samples (Leuthold et al., 2023), thus providing more detailed measurements to use during validation. However, as our results show, the SOC fractions might not be compatible with the total SOC measurements within the model context and indicate that there are missing processes within our model framework. Consequently, their value might be rather to evaluate what missing processes are needed within the model than validate existing parameterizations. Another approach for evaluation could be to examine the model performance within sub-regions or individual ecosystems instead of weighing it against the total dataset at once. A more nuanced approach to do this would be to use a hierarchical Bayesian approach (Gelman and Hill, 2007), but that requires more research on the applicability of that approach in solving the challenges highlighted by our results.