An empirically based approach for estimating uncertainty associated with modelling carbon sequestration in soils
Introduction
Considerable research has supported the premise that agricultural land use and management can mitigate greenhouse gas emissions through soil C sequestration (Paustian et al., 1997, Lal et al., 1998, Bruce et al., 1999). Quantifying the amount of C sequestered in soils is needed to determine the net impact of past and current practices on greenhouse gas mitigation, informing both policy and management decisions (e.g., Ogle et al., 2003, VandenBygaart et al., 2004). When direct measurements are not feasible, models can be used to estimate the change in soil C stocks, and several approaches are available for this purpose (IPCC, 2004, Ogle and Paustian, 2005). These range from simple accounting procedures using default stock change rates for various practices, to more sophisticated simulation modelling. The latter is intended to introduce less bias into soil C estimates because simulation models typically represent more of the mechanisms affecting soil organic matter dynamics.
The Century model was developed for simulating ecosystem processes, with a focus on soil organic matter dynamics (Parton et al., 1987, Parton et al., 1994). Century has been applied and tested in a variety of agricultural and other land use systems, and has been shown to be reasonably consistent with measured C stocks (e.g., Paustian et al., 1992, Parton et al., 1993, Smith et al., 1997). However, even a well-tested model such as Century does not perfectly capture reality. Simulation models are conceptualizations of reality developed from experimental findings as well as theoretical concepts, and both can lead to imprecision and bias in model results. Together, imprecision and bias constitute model uncertainty.
Comparing model results to measurements is a common practice for evaluating model performance. Assuming there is a relationship between model results and measurements, and it is not perfect, the comparisons could demonstrate that model results are biased, imprecise, or both biased and imprecise. Bias in this context is the difference between the deterministic model results and the “true value” of the SOC stock, while imprecision refers to the variance of the modeled quantity (i.e., variance = 1/precision).
Some studies have taken model evaluation a step further, formalizing the comparisons as part of an uncertainty analysis using empirically based methods (Monte et al., 1996, Falloon and Smith, 2003, Knightes and Cyterski, 2005). Measurements are used as a proxy for reality in these analyses, and thus the degree of consistency between the modeled results and measurements is assumed to provide a robust estimate of uncertainty (Fig. 1A). Specifically, a confidence interval for a model estimate is approximated based on a statistical function developed from a comparison of model results with measurements.
Empirically based uncertainty analyses contrast with error propagation methods (e.g., Monte Carlo Analyses, see Ogle et al., 2003) that seek to quantify uncertainty by deriving probability distribution functions for uncertain quantities used in the modelling application. Multiple results are simulated based on repeated random draws from the distributions to obtain an approximate confidence interval for a model estimate (Fig. 1B). Typically, this approach does not address uncertainty in the model formulation although it is possible if alternative models or algorithms are selected during the Monte Carlo Analysis. Century has 100s of parameters, similar to many complex simulation models, and a Monte Carlo Analysis would be difficult due to the high dimensionality associated with its structural complexity. Essentially, a joint probability distribution function would be required for the parameter set, or at least a subset of the most sensitive parameters in the model.
Given the importance of determining uncertainty in modeled results used for reporting soil C sequestration or losses (IPCC, 2004), our objective was to develop an empirically based approach for quantifying bias and variance in Century model results. Specifically, we developed a statistical model based on the relationship between modeled values and measurements from agricultural experiments. The resulting statistical model formed the basis for an uncertainty estimator that can be applied in future Century-based assessments of soil C stock changes from site to regional scales.
Section snippets
Century simulations for agricultural experiments
The Century model simulates soil organic matter dynamics (Parton et al., 1987), and has been used to estimate agricultural management impacts on soil C storage in the US (e.g., Paustian et al., 2002, US-EPA, 2006). Century has been so successful in a variety of applications that its conceptual design for modelling soil C dynamics has been incorporated into several other models (e.g., Potter et al., 1993, Liu et al., 2003, Izaurralde et al., 2006).
Century simulates site-level hydrology, plant
Results and discussion
A significant relationship was found between modeled and measured soil organic C stock estimates (, p-value < 0.01, Table 2). If the relationship had not been significant, then Century would not be adequate for estimating C sequestration in agricultural systems. Rather, this analysis was consistent with the findings from past studies (e.g., Parton et al., 1987, Smith et al., 1997), demonstrating that the conceptual design of Century is able to estimate soil C stocks that are consistent
Conclusions
An empirically based approach has been developed to quantify uncertainties according to the relationship between modeled and measured data. A significant relationship was found between Century model results and measurements, demonstrating that the model is adequate for estimating soil organic C stocks in agricultural systems, consistent with past evaluations. However, there was not a perfect relationship between model results and measurements, and so a statistical function (i.e., linear
Acknowledgements
We thank Amy Swan and Kendrick Killian who provided assistance in addition to the investigators from the long-term experiments who provided unpublished data needed to parameterize Century. This research was funded by NRCS (Agreement No. 68-7482-2-44Y), USDA/CSREES (Agreement No. 2001-38700-11092) through funding for the Consortium for Agricultural Soils Mitigation of Greenhouse Gases (CASMGS), and USDA/CSREES Carbon Cycle Science Program (Agreement No. 2005-35615-15223).
References (90)
- et al.
Productivity parameters and soil health dynamics under long-term 2-year potato rotations in Atlantic Canada
Soil Till. Res.
(2003) - et al.
Soil carbon pools and fluxes in long-term corn belt agroecosystems
Soil Biol. Biochem.
(2000) - et al.
Soil microbial activity, nitrogen cycling, and long-term changes in organic carbon pools as related to fallow tillage management
Soil Till. Res.
(1998) - et al.
Bacterial and fungal abundance and biomass in conventional and no-tillage agroecosystems along two climatic gradients
Soil Biol. Biochem.
(1999) - et al.
Simulating soil C dynamics with EPIC: model description and testing against long-term data
Ecol. Model.
(2006) - et al.
Tillage system effects on 15-year carbon-based and simulated N budgets in a tile-drained Iowa field
Soil Till. Res.
(1998) - et al.
Crop residue effects on soil quality following 10-years of no-till corn
Soil Till. Res.
(1994) - et al.
Long-term tillage effects on soil quality
Soil Till. Res.
(1994) - et al.
Evaluating predictive errors of a complex environmental model using a general linear model and least squares means
Ecol. Model.
(2005) - et al.
Uncertainty analysis and validation of environmental models: the empirically based uncertainty analysis
Ecol. Model.
(1996)
Soil C and N changes on conservation reserve program lands in the Central Great Plains
Soil Till. Res.
A comparison of the performance of nine soil organic matter models using datasets from seven long-term experiments
Geoderma
Information theory and an extension of the maximum likelihood principle
Changes in soil microbial community structure in a tallgrass prairie chronosequence
Soil Sci. Soc. Am. J.
A conservation tillage-cropping systems study in the Northern Great Plains of the United States
Carbon sequestration in soils
J. Soil Water Conserv.
Carbon budgets for a prairie and agroecosystems: effects of landuse and interannual variability
Ecol. Appl.
Texture, climate, and cultivation effects on soil organic matter content in U.S. grassland soils
Soil Sci. Soc. Am. J.
Model Selection and Multi-Model Inference: A Practical Information-Theoretic Approach
Adopting zero tillage management: impact on soil C and N under long-term crop rotations in a thin Black Chernozem
Can. J. Soil Sci.
Evaluation of a simple model to describe carbon accumulation in a Brown Chernozem under varying Fallow Frequency
Can. J. Soil Sci.
Crop production and soil organic matter in long-term crop rotations in the semi-arid Northern Great Plains of Canada
Crop production and soil organic matter in long-term crop rotations in the sub-humid Northern Great Plains of Canada
Soil organic matter in sugar beet and dry bean cropping systems in Michigan
A statistical-topographic model for mapping climatological precipitation over mountainous terrain
J. Appl. Meteorol.
Soil organic carbon changes through time at the University of Illinois Morrow Plots
Continuous application of no-tillage to Ohio soils: changes in crop yields and organic matter-related soil properties
Accounting for changes in soil carbon under the Kyoto Protocol: need for improved long-term data sets to reduce uncertainty in model projections
Soil Use Manage.
Carbon sequestration under the Conservation Reserve Program in the historic grassland soils of the United States of America
Tillage-induced seasonal changes in soil physical properties affecting soil CO2 evolution under intensive cropping
Soil Till. Res.
Tillage and crop effects on seasonal dynamics of soil CO2 evolution, water content, temperature, and bulk density
Appl. Soil Ecol.
Soil organic matter under long-term no-tillage and conventional tillage corn production in Kentucky
Long-term changes in soil carbon under different fertilizer, manure, and rotation: testing the mathematical model ecosys with data from the Breton plots
Soil Sci. Soc. Am. J.
Long-term tillage and rotation effects on corn growth and yield on high and low organic matter, poorly drained soils
Agron. J.
Corn yields, root volumes, and soil changes on the Morrow Plots
J. Soil Water Conserv.
Long-term tillage and crop residue management study at Akron, Colorado
Nitrogen fertilization effects on soil carbon and nitrogen in a dryland cropping system
Soil Sci. Soc. Am. J.
Tillage, nitrogen, and cropping system effects on soil carbon sequestration
Soil Sci. Soc. Am. J.
Management effects on soil organic carbon and nitrogen in the East-Central Great Plains of Kansas
Long-term patterns of plant production and soil carbon dynamics in a Georgia piedmont agroecosystem
Long-term N management effects on corn yield and soil C of an aquic haplustoll in Minnesota
Long-term tillage effects on soil chemical properties and organic matter fractions
Soil Sci. Soc. Am. J.
Soil quality indicator properties in the mid-Atlantic region as influenced by conservation management
J. Soil Water Conserv.
Carbon balance of the Breton Classical Plots over half a century
Soil Sci. Soc. Am. J.
Cited by (62)
DayCent-CUTE: A global sensitivity, auto-calibration, and uncertainty analysis tool for DayCent
2023, Environmental Modelling and SoftwareAssessing the provision of carbon-related ecosystem services across a range of temperate grassland systems in western Canada
2019, Science of the Total EnvironmentCitation Excerpt :Varying ecological conditions across the province can explain the variation in optimized PUR across different regions. Alberta's grasslands are characterized by distinct ecological regions with diverse vegetation (Fig. 1, Table 1; Downing and Pettapiece, 2006), resulting in high spatial variability in the production of carbon-related ES (Ogle et al., 2007; Hewins et al., 2018). Climatic (e.g., precipitation, temperature), edaphic (e.g., soil texture, structure, nutrient availability) and biotic factors (e.g., plant and microbial diversity, grazing) predominantly control the provision of carbon-related ES in grasslands (Parton et al., 1987; Schimel et al., 1994; Álvaro-Fuentes et al., 2012; Abdalla et al., 2018; Wiesmeier et al., 2019).
Simulating the effects of management practices on cropland soil organic carbon changes in the Temperate Prairies Ecoregion of the United States from 1980 to 2012
2017, Ecological ModellingCitation Excerpt :In our study, we used 10 years as the initialization time, which is a common pre-run time in the regional studies (Potter et al., 2009; Zhang et al., 2015). Some studies used long initial time from 2000 to 7000 years and assumed the long-term land use as grassland (Ogle et al., 2007; Ogle et al., 2009; Hartman et al., 2011). The second was the decrease-increase pattern under the other scenarios.