Soil carbon (C) models are important tools for understanding soil C balance and projecting C stocks in terrestrial ecosystems, particularly under global change. The initialization and/or parameterization of soil C models can vary among studies even when the same model and data set are used, causing potential uncertainties in projections. Although a few studies have assessed such uncertainties, it is yet unclear what these uncertainties are correlated with and how they change across varying environmental and management conditions. Here, applying a process-based biogeochemical model to 90 individual field experiments (ranging from 5 to 82 years of experimental duration) across the Australian cereal-growing regions, we demonstrated that well-designed optimization procedures enabled the model to accurately simulate changes in measured C stocks, but did not guarantee convergent forward projections (100 years). Major causes of the projection uncertainty were due to insufficient understanding of how microbial processes and soil C pool change to modulate C turnover. For a given site, the uncertainty significantly increased with the magnitude of future C input and years of the projection. Across sites, the uncertainty correlated positively with temperature but negatively with rainfall. On average, a 331 % uncertainty in projected C sequestration ability can be inferred in Australian agricultural soils. This uncertainty would increase further if projections were made for future warming and drying conditions. Future improvement in soil C modelling should focus on how the microbial community and its C use efficiency change in response to environmental changes, and better conceptualization of heterogeneous soil C pools and the C transformation among those pools.
Soil is the largest carbon (C) reservoir in the terrestrial biosphere, and
CO
Uncertainty in simulation results derived from dynamic models can arise from inaccuracies in input data, deficiencies in model structure and inappropriate optimization of model parameters. For SOM models, initialization of the SOM pools can also be a major cause of divergent model projections. Most SOM models divide SOM into several conceptual pools (e.g. fast, slow and recalcitrant pools) and simulate the decomposition of each pool as a first-order decay process (Smith et al., 1997; Davidson and Janssens, 2006; Schmidt et al., 2011). In many cases, measurements are only available for total SOC, and there is no agreed-on procedure for initialization of these model pools using total SOC (Basso et al., 2011). As a result, model optimization was often conducted based on limited SOC measurements (usually at temporal scales less than decades) together with empirical initialization. The optimized model was then used to project SOC change at wider spatiotemporal scales (Friedlingstein et al., 2006; Thornton et al., 2007). Such projection is subject to unknown uncertainty (Friedlingstein et al., 2006; Tang et al., 2008; Luo et al., 2013), because it does not properly address the inaccuracies in both model initialization and model parameters, with the latter potentially caused by imperfect knowledge and model structure (Schmidt et al., 2011).
To illustrate the uncertainty propagation in SOC projections caused by initialization and parameterization and to understand what correlates with the change in the patterns of projection uncertainty, we used the Agriculture Production System sIMulator (APSIM) (Keating et al., 2003; Wang et al., 2002; Holzworth et al., 2014) together with data from 90 agricultural experiments at 26 sites across the Australian cereal-growing regions. The data include measurements of total SOC stock (0–30 cm), C input (i.e. amount of residue retention), crop yield, and records of management practices. The APSIM model uses a very similar SOM pool structure and first-order decay approach to simulate SOM dynamics to other common Earth system models (Smith et al., 1997; Friedlingstein et al., 2006; Thornton et al., 2007). We firstly conducted sensitivity analysis to identify the model parameters whose change impacted most on simulated SOC dynamics. We then used Bayesian optimization approach to derive the posterior joint distribution of the identified parameters that enabled best match between measured and observed SOC. These ensembles of parameters were used to run APSIM for each of the 90 experiments, and simulations were continued for a further 100 years after the end of the experiment to produce SOC projections for uncertainty analysis. We quantified the uncertainty in SOC projections induced by both initialization of SOC pools and parameterization of algorithms for simulation of process dynamics. While the uncertainty obviously increases with years of projections, we further hypothesized that it is also influenced by site-specific climate, soil and management conditions, in addition to the impact of model initialization and parameterization. We further investigated how the projection uncertainty can be quantified by using these drivers, so that future SOC projections can become more useful with attached and well-quantified uncertainties.
Data from a total of 90 experimental plots located within 26 different sites (Fig. S1 in the Supplement) and compiled and described by Skjemstad and Spouncer (2003) were used in this study. The experimental duration of these trials ranged from 5 to 82 years; the experiments cover diverse climate, soil and agricultural management conditions and are representative of Australian cereal-growing regions (Table S1 in the Supplement). The data set included detailed records on crop sequence, crop yield, crop residue production (estimated according to harvest index) and agricultural management practices such as residue management (removal or retention) and fertilizer application over each year. SOC stock was determined for representative 0–30 cm soil samples at least at the beginning and end of the each experiment, with some experiments having as many as six temporal measurements. Other soil properties at the start of the experiment were also measured, including total nitrogen content, bulk density, clay content and pH, and were used to initialize the APSIM model.
APSIM was developed to simulate biophysical process in agricultural systems, and has been comprehensively verified and used to study productivity, nutrient cycling and environmental impacts of farming systems as influenced by climate variability and management practice (Keating et al., 2003; Wang et al., 2002; Holzworth et al., 2014). APSIM simulates crop growth and soil processes on a daily time step in response to climate (i.e. temperature, rainfall, and radiation) and soil conditions (water availability, nutrient status, etc.). The model allows flexible specification of management options like crop and rotation type, tillage, residue management, fertilization and irrigation. The ability of APSIM to simulate SOC dynamics under different cropping and management practices has been verified (Probert et al., 1998; Luo Z. et al., 2011).
APSIM simulates the dynamics of both soil C and N stocks in each soil layer.
Similar to other SOM models like RothC and Century, SOM in APSIM is divided
into six conceptual pools (i.e. microbial biomass, humic organic matter and
inert organic matter, together with three fresh organic matter pools;
Fig. S2). Inert organic matter is considered to be non-susceptible to
decomposition, i.e. indecomposable, due to physicochemical and/or biological
protections. The amount of inert organic C is initialized at the start of the
simulation and dos not change during the simulation. The decomposition of
other pools is treated as a first-order decay process modified by soil
temperature, moisture and nitrogen availability (for fresh organic matter
pool only), leading to the release of CO
The model requires values for initial SOC content, total soil N content,
bulk density, and soil hydraulic parameters for each soil layer simulated.
In the Skjemstad and Spouncer (2003) data set, measured values for SOC
content, bulk density and total soil nitrogen content were provided for the
0–30 cm layer. For the deeper soil layers and hydraulic parameters in the
whole soil profile, values from a measured soil profile nearest to the site
were selected from the Agricultural Production Systems Research Unit (APSRU)
reference sites soil database (
The APSIM model was first set up for each experiment. Agricultural
management including crops, residue management and fertilizer application
was set according to available historical records. Crops were sown depending
on rainfall (> 20 mm in five successive days) and soil water
content (90 % of saturation water content in the top 20 cm soil). Crop
cultivars were assigned according to sowing date, i.e. the earlier the
sowing date, the later the maturity type of the crop cultivar. For
simplification, three cultivars for each crop representing early, middle and
later maturity cultivars were selected from the default cultivars in the
files released with the APSIM model. For pasture, however, there was no
record on the species and cultivar. Here, perennial lucerne (
In the experiments included in this study, C from assimilation of crop growth was the only source of C input to the soil. In the APSIM model, crop growth is simulated using light interception and radiation use efficiency, modified by water and nitrogen supply. In order to achieve credible simulation of crop growth, plant available water capacity (PAWC) of the soil was adjusted. This adjusted PAWC at each site was used throughout the simulations. Despite the reliability of the APSIM model to simulate crop growth (both belowground and aboveground), we did not use the simulated aboveground C input during the simulation. Alternatively, the recorded aboveground C input (as crop residue) was manually incorporated into the model at the time of crop harvesting, whilst the simulated crop residue was removed. This manipulation eliminated the effect of imperfect match of modelled with observed crop residue on SOC dynamics.
A total of eight parameters (Table S2) that directly link
to the SOC dynamics in the model were selected for sensitivity analysis in
order to identify the most important ones regulating SOC dynamics. One model
input for model initialization, i.e. the fraction of inert organic carbon
in the total SOC at the start of the simulation (finert), was also included in the
sensitivity analysis, due to a lack of observed data of finert and its great effect
on simulated soil C changes. To inspect the response of simulated SOC to
variations of those parameters (finert was also called as a parameter for
convenience hereafter), a univariate local sensitivity analysis was
conducted by looking at the impact of one parameter at a time and fixing all
other parameters. As the purpose was to identify the most influential
parameter(s), a continuous wheat system with 100 % residue retention (the
dominant crop in the studied experiments; see Table S1) and
a nitrogen application of 200 kg N ha
The differential evolution (DE) algorithm (which belongs to the class of genetic algorithms) was used to optimize the most influential parameters identified. The optimization was performed in R 3.0.3 using the DEoptim function in the “DEoptim” package (Mullen et al., 2011). DE is a global optimization algorithm for continuous numerical minimization problems, which use biology-inspired operations of crossover, mutation, and selection on population in order to minimize an objective function over the course of successive generations.
To use DE, each parameter was first assumed to exhibit a uniform distribution bounded within a range (i.e. the prior distribution; see Table S2) that was biologically and physically possible based on previous knowledge about the process, thereby eliminating solutions in conflict with prior knowledge. The optimization performed a quasi-random walk through the multi-dimensional parameter space to find the parameter set that caused the model to generate the best match between predicted and observed SOC. The “best match” was defined as the model output that minimized the criteria selected for model evaluation (Table S3). Seven criteria that are commonly used in the literature were selected to assess the possible effects of criterion selection on modelling results. Using each criterion, the optimization was conducted 100 times (i.e. 100 ensembles of initial parameter values through quasi-random walk), which generated 100 ensembles of parameters (i.e. the joint posterior distribution of the most influential parameters), giving simulation results with approximately equally good matches to the observed data. Consequently, 700 ensembles of parameters (from using seven criteria) for each experiment were produced. The optimizing procedure and related simulations were operated on Bragg and Dell CPUs of CSIRO clusters.
However, the required computing time (
For all the experiments, a Bayesian sampling approach was substituted for the DE optimization in order to complete the work within a reasonable time but without much sacrificing of model performance. The APSIM model was run for each experiment for 100 000 times using 100 000 ensembles of parameters that were randomly sampled from their prior distributions. The best 100 ensembles of parameters were selected as their posterior distributions through using each criterion listed in Table S3. At Brigalow and Tarlee, the distributions of parameters “optimized” through this Bayesian sampling approach were compared with those optimized through DE optimization. The identified parameter ensembles by Bayesian sampling approach were referred to as “optimized parameters” in the following text and used to assess the uncertainty in projected SOC.
After obtaining the 700 ensembles of optimized parameters (i.e. after
“optimization period”), the APSIM model was run continuously from the
start to the end of each experiment and then for an additional 100 years
after the end of each experiment using each parameter set (i.e. 700
simulations for each experiment). For the last 100-year simulations (i.e.
projection period), a continuous wheat system was assumed together with
100 % residue retention, which is the same as that used in sensitivity
analysis. Carbon input through crop residue retention was expected to be an
important factor regulating SOC dynamics in the projection period. As
residue (or biomass) production is dominantly controlled by fertilizer
application rates under natural rainfall condition at each site, scenarios
with nitrogen application rates ranging from 0 to 300 kg N ha
Climate data from the start year of each experiment through to 2013 were used for the corresponding simulation period. For all years from 2014 onwards, the corresponding years of the latest historical climate data were used. For example, for the possible simulations from 2014 to 2104 (91 years), the historic climate data of 91 years from 1923 to 2013 were used. As we focused on the potential uncertainty induced by model parameterization and initialization, we did not consider the uncertainty related to climate change.
SOC content in the 0–30 cm soil layer was output at the start of projection
(excluding the optimization period) and at the end of each year of projection
(C
After estimating
To assess the variation in individual-level coefficients (
Three parameters were identified as most influential on simulated SOC (Fig. S3). Microbial carbon use efficiency (CUE) had the biggest
impact. This highlights the key role of microbial process to control SOM
decomposition, and the need for better capturing the dynamics and impact of
microbial process in SOM models (Allison et al., 2010; Singh et al., 2010;
Sinsabaugh et al., 2013; Xu et al., 2014). As CUE was treated as a constant in
most SOM models, a framework is needed to incorporate microbial data (e.g.
community, activity, and their responses and feedbacks to biotic and abiotic
factors) into SOM models to provide robust estimations and predictions.
Potential decomposition rate constant of humic organic matter (
Our optimization procedure enabled accurate simulation of SOC change during
the optimization period (Fig. 1a) using distinct ensembles of model
parameters for each experiment (Fig. 1b). Pooling together all data of the
90 experiments, the modelled average SOC of the 700 simulations could explain
96 % (
Model performance in simulating soil organic carbon (SOC) dynamics
The accurate simulations of past SOC, however, do not guarantee convergent
projections beyond the model optimization period. In contrast, running the
model with the same parameter ensembles generated very divergent future
projections (Fig. 2a and b), indicating significant uncertainty propagation
with time of projection (Luo Y. et al., 2011; Tang and Zhuang, 2008). Furthermore,
the uncertainty is also related to management in terms of C input level and
site conditions. At Brigalow (Fig. 2b), for example, the 95 % confidence
interval of projected SOC under optimal N input (i.e. no N stress for
crops) ranged from 37 to 56 t ha
It is important to note that the posterior distributions of model
parameters were apparently different across experiments (Fig. 1b, c and d,
and S4), confirming that model parameters are
sensitive to the data constraining the model (Keenan et al., 2012; Hararuk
et al., 2014; Luo et al., 2015) Our results indicate that CUE was likely
higher for the site with a longer cultivation history (the Tarlee site) than
for the newly cleared site (the Brigalow site, Fig. 2c vs. 2d), implying the potential
importance of land use history for constraining model parameters such as
microbial carbon use efficiency because land use history has a direct effect
on the quantity and quality of carbon input as well as on soil properties.
However, such impact needs further confirmation with more data. The
distributions of the optimized model parameters were also influenced by the
choice of criteria to evaluate model performance (Figs. 2d, S5). The differences in parameter distributions subsequently impact
on the SOC projections as shown in Fig. 2b, albeit with near-identical model
performance in simulating historical SOC. In addition, finert and
Projected soil organic carbon dynamics at two case sites Tarlee
Projected SOC (
Coefficients (estimate
The effects of experiment-specific variance of model parameters and
climate on individual-level coefficients (i.e.
If a continuous wheat system was practiced for 100 years after the end of
each experiment at the 26 sites, optimal N management was predicted to
result in an average increase in SOC (Fig. 3a), whereas a SOC decline would occur under
zero N input (Fig. 3b). The amount of potential SOC change depends on not
only the management level (N input) and the climate and soil conditions that
determine the potential productivity of crops but also the initial SOC
level at the start of the projections. Across the 90 experiments, the
percentage uncertainty in the SOC projections ranged from 2 to 140 %
with an average of 53 % under optimal N management (Fig. 3c), and from
0.8 to 108 % with an average of 40 % under zero N input (Fig. 3d).
From applying this result to Australia's cereal-growing regions, the simulated
potential SOC stock of
The uncertainty propagation with time of prediction and across experiments
could be explained using a linear model by linking the percentage
uncertainty (
The variance in model parameters (GV) across experiments had a major effect
on the intercepts (positive at
Rainfall and temperature, together with their interaction, had a significant
impact on SOC projection uncertainty through their impact on the fitted model
intercepts across experiments (Table 1).
Our results demonstrate that great uncertainty exists in soil C projections from process-based SOM models, due to deficiency in model initialization and parameterization in capturing the process interactions, such as microbial C use efficiency and its drivers, as well as a lack of detailed information to initialize the model, e.g. the heterogeneous SOM with different decomposability. The prediction uncertainty propagates with extended years of projections and C input into soil. It is also influenced by site-specific climate (temperature and rainfall) and soil conditions together with management inputs, which determine both the C input (through primary productivity) and the SOM decomposition processes. The results also suggest that C projection into warming and drying future climate will be subject to even greater uncertainty. For agricultural land uses, uncertainty caused by management practices has to be carefully considered due to its impact on microbial activity and subsequent projected SOC. For any future predictions of SOC change, ensemble simulations conditioned on total observed data sets together with a Bayesian inference technique should be used in order to quantify the uncertainties in modelling results. Based on our results, future improvement in SOM modelling should focus on how the microbial community and its carbon use efficiency change in response to environmental changes, better quantification of heterogeneous SOM and the effects of its change on total soil C turnover.
Z. Luo collected data, ran simulations, and performed data analysis; Z. Luo, E. Wang, J. A. Baldock designed the study; H. Zheng and Q. Shao were involved in statistical analysis; Z. Luo, E. Wang and O. J. Sun wrote the paper. All authors discussed the results and commented on the manuscript.
This study was supported by funding from the Australian Government Department of Agriculture, Fisheries and Forestry (DAFF) and the Grains Research and Development Corporation (GRDC). Thanks to Yiqi Luo of the University of Oklahoma and Petra Kuhnert and Jonathan Sanderman of CSIRO for their helpful comments on an earlier version of the manuscript. Edited by: A. Ito