TECHNICAL ARTICLE
Inverse Modeling of CO2 Evolved During Laboratory Soil Incubation to Link Modeled Pools in CENTURY With Measured Soil Properties Hoyoung Kwon1 and Sabine Grunwald2 Abstract: Challenges associated with initialization of CENTURY soil organic matter (SOM) model might be addressed through a useful constraint between its conceptually defined pools and measurable soil properties. To develop such constraint, we linked soil properties directly measured in Florida sandy soils with initial CENTURY SOM pool sizes inversely modeled from CO2 evolved during 87-day laboratory incubation in the same soils. We conducted this inverse modeling by using a surrogate model for CENTURY's soil organic C (SOC) dynamics submodel. The model entails the mass balance and decomposition kinetics equations for residue and SOM pools identical to those of CENTURY that are coded in the programming language of the SAS statistical software to use various statistical functions embedded within a nonlinear regression procedure of SAS. We used the surrogate CENTURY to objectively estimate site-specific masses of SOC in three (active, slow, and passive) pools from the soils. From 28 of the total 100 soils modeled, we were able to estimate initial masses of SOC in active and slow pools, which were statistically significant (P < 0.05), by fitting the surrogate CENTURY to CO2 evolution data. In the 28 soils, we found that active and slow pool sizes were correlated with hot water–soluble C and clay percentage (R2 = 0.74 and 0.77, respectively). Applying the constraints to initialize CENTURY modeling of an independent validation set of an additional 39 soils showed a significant correlation between modeled and observed CO2 (R2 = 0.49), suggesting the potential for other practical applications to properly initialize CENTURY simulations. Findings further suggest that inverse modeling has promise to inform CENTURY initialization and other process-based models that adapt CENTURY's SOM structure. Key Words: CENTURY model initialization, CO2 evolution, inverse modeling, directly measured soil properties, surrogate CENTURY soil organic carbon model (Soil Sci 2015;180: 28–32)
S
imulation models, developed to better understand and quantify the dynamics of soil organic matter (SOM), are being increasingly used to analyze historical trends and to test hypothetical scenarios of soil C and nutrient changes for the purpose of environmental management and research. Although SOM models use a variety of conceptual and mathematical frameworks, they commonly conceptualize SOM in terms of multiple “pools” differing in their de-
grees of physical and/or chemical stabilization and, consequently, each SOM pool is decomposed by microbes at a different average rate and exhibits a different mean residence time. Among important models of this type, CENTURY (Parton et al., 1987) has been applied across a wide range of land uses (Paustian et al., 1992; Parton et al., 1993; Kirschbaum and Paul, 2002) and across timescales from years to centuries (Smith et al., 1997). Generally, it has shown a high level of acceptance in adequately simulating observed SOM dynamics with three primary “pools” (i.e., active, slow, and passive). Its performance can be substantially enhanced after model calibration wherein initial SOM status is adjusted for a site against short- or long-term time series of observations (e.g., total soil C (TC)). Without such observations for model calibration, CENTURY initialization for any particular plot, field, or site often involves indirectly reconstructing the antecedent conditions at a site via a model “equilibration” step (Ogle et al., 2007; Paustian et al., 1992). However, this approach can be inaccurate if equilibration from disturbance by fire, erosion, land use, or land use change is not easily reached because of very slow accumulation of SOM into slow and passive SOM pools (Wutzler and Reichstein, 2007). To overcome this limitation, researchers have been seeking to initialize models for particular sites by linking measured soil “fractions” with modeled “pools” (Christensen, 1996; Elliott et al., 1996; Motavalli et al., 1994; Shirato and Yokozawa, 2006). However, the challenge to parameterize the pools is profound because they are purely operationally defined and conceptualized (i.e., not measured) and it is not clear which chemical compounds contribute to which pool. This is further intensified by the heterogeneity of soils, vegetation, topography, hydrology, parent material, and climate (temperature and precipitation) across landscapes, which is extremely high and complex (Bosatta and Agren, 1996). In this article, we demonstrate the procedures to effectively address this challenge using a newly developed nonlinear regression tool for inversely modeling of CENTURY and the data of CO2 evolved during 87-day laboratory incubations in Florida sandy soils. We (i) estimated initial masses of soil organic C (SOC) in CENTURY pools that best describe CO2 evolution data, (ii) developed constraints between measured soil properties and modeled pool sizes, and (iii) used them to initialize modeling of additional CO2 evolution data.
1
Environment and Production Technology Division, International Food Policy Research Institute, Washington, DC, USA. 2 Soil and Water Science Department, University of Florida, Gainesville, Florida, USA. Address for correspondence: Dr. Hoyoung Kwon, Environment and Production Technology Division, International Food Policy Research Institute, 2033 K St, NW, Washington, DC 20006, USA. E-mail:
[email protected] Received May 19, 2014. Accepted for publication January 2, 2015. Funding was provided through the grant “Geotemporal Estimation and Visualization of Nitrogen and Other Soil Properties in the Mixed-Use Santa Fe River Watershed,” U.S. Department of Agriculture (USDA)–Nutrient Science for Improved Watershed Management Program. Copyright © 2015 Wolters Kluwer Health, Inc. All rights reserved. ISSN: 0038-075X DOI: 10.1097/SS.0000000000000101
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MATERIALS AND METHODS A Nonlinear Regression Tool for Inversely Modeling of CENTURY Recent efforts to quantify the uncertainty in initial pool estimates of SOM models have focused on Bayesian calibration (Yeluripati et al., 2009; Scharnagl et al., 2010). But there is still need for a rapid approach of inverse modeling to reduce uncertainties and parameterize models. Here, model parameters that are difficult to measure are estimated by optimizing model fits to environmental data. In response to this need, Kwon and Hudson Soil Science • Volume 180, Number 1, January 2015
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Soil Science • Volume 180, Number 1, January 2015
Inverse Modeling of CO2 Evolution Data
(2010) developed a nonlinear regression tool that is especially designed for the parameter estimation of CENTURY (version 4.0)’s SOC dynamics submodel, surrogate CENTURY. In the surrogate CENTURY, the mass balance and decomposition kinetics equations for residue and SOM pools of CENTURY are coded in the programming language of SAS statistical software (SAS Institute, 2012a) and embedded within a nonlinear regression procedure of SAS version 9.2 (MODEL procedure). Because of the capability of the MODEL procedure to estimate and solve ordinary differential equations, conduct parameter estimation, and run Monte Carlo simulation of nonlinear simultaneous equation models, the surrogate CENTURY has important features to (i) efficiently run CENTURY under various assumptions made during model simulation, (ii) objectively estimate parameters and their standard errors by using iterative parameter estimation algorithms, (iii) statistically conduct significance tests on parameters, and (iv) rapidly quantify uncertainties in simulations (Fig. 1). Other features of the model are the capability of using daily, monthly, or annual time steps and the decoupling from models of plant growth, nutrient cycling, and hydrologic processes. The latter feature provides the advantage of transparency and relative simplicity while allowing users to easily modify time-dependent CENTURY inputs, including crop/plant C input rates to soil and the site-specific decay rates of pools. More details of surrogate CENTURY variables and equations can be obtained in the article and online supplemental document of Kwon and Hudson (2010).
collected in the Santa Fe River watershed (a 3,585-km2 watershed in north-central Florida). The samples encompass nine land use/ land cover types, including pine plantations, crops, improved pasture, and upland forest, and their main soil orders are Ultisols, Spodosols, Entisols, and Alfisols (Ahn et al., 2009). Importantly, all soil samples have high sand contents (Table 1) representative of soils in Florida and other areas of the southern coastal plain. After 5 days of preincubation, 87-day laboratory soil incubation was conducted at 35°C in the dark, and the cumulative concentrations of CO2 evolved (cumCO2) during incubation were measured at 8, 15, 22, 29, 36, and 87 days (Ahn et al., 2009). The soil samples were also used to measure various soil properties. Total soil C was determined by high-temperature combustion on a Flash EA 1112 Elemental Analyzer (Thermo Electron Corp., Waltham, MA) after the soil samples had been oven-dried at 70° C for 72 h and ground in a ball mill. Note that TC is mostly composed of organic C because inorganic C content is less than 2% of TC in these soil samples of the Santa Fe River Watershed. Recalcitrant C (RC) was measured by high-temperature combustion after samples were refluxed with 6 mol L−1 HCl for 16 h (Paul et al., 2001; McLauchlan and Hobbie, 2004). Hydrolyzable C (HC) was calculated by the difference between TC and RC. Hot water– soluble C (SC) was measured on a Shimadzu TOC 5050 Analyzer (Shimadzu Scientific Instruments Inc., Columbia, MD) after extraction using hot water (Sparling et al., 1998; Gregorich et al., 2003) and filtration through a 0.2-μm membrane. Soil textures were measured by the pipette method (Day, 1965).
CO2 Evolution Data and Various Soil Measurements
Procedures
The CO2 evolved during laboratory soil incubations were measured from 141 surface soil samples (0–30 cm), which were
We first excluded two soils as outliers that lie beyond the upper bound (i.e., the third quartile plus three times interquartile range). As a result, further analysis only included soils having less
FIG. 1. Overview of a surrogate model for CENTURY's SOC dynamics. © 2015 Wolters Kluwer Health, Inc. All rights reserved.
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TABLE 1. Descriptive Statistics of Measured Soil Properties Calibration Set (100 Soils) Statistic
TC
RC
HC
SC
cumCO2 (87 days)
Clay
772.9 696.8 405.7 220.6 2,319.0 1.5
441.2 377.8 250.3 78.6 1,335.8 1.3
3.2 2.3 3.5 0.1 23.8 3.9
92.5 94.0 7.2 46.3 99.5 −3.9
SC
cumCO2 (87 days)
Clay
Sand
−1
Mean Median S.D. Minimum Maximum Skewness (unitless)
13,644.0 10,884.6 11,403.5 2,669.6 73,856.8 3.2
10,085.6 7,789.0 9,849.9 1,134.0 61,528.0 3.4
TC
RC
mg C kg soil 3,565.8 2,906.0 2,204.3 178.0 12,329.0 1.3
Sand %
Validation Set (39 Soils) Statistic
HC −1
Mean Median S.D. Minimum Maximum Skewness (unitless)
10,128.3 9,438.1 5,675.4 3,523.1 29,393.1 2.0
7,165.4 6,387.0 4,750.6 2,253.0 25,322.0 2.2
mg C kg soil 2,962.8 2,749.0 1,501.6 37.0 8,059.0 1.0
% 653.0 551.5 300.0 272.0 1,410.0 0.9
376.7 335.4 194.4 92.4 910.4 1.2
3.1 2.2 3.9 0.5 23.1 4.0
93.4 94.7 4.7 71.7 98.2 −3.0
TC: total soil C; RC: recalcitrant C; HC: hydrolyzable C; SC: hot water–soluble C; S.D.: standard deviation; cumCO2: cumulative mineralized CO2.
than 1,500 mg C kg−1 soil of cumCO2 after 87-day incubation. Then, the 139 soils were randomly split into a calibration set (100 soils) and a validation set (39 soils) (Table 1) (Vasques et al., 2010). For the soils of each set, we calculated individual TC values at 8, 15, 22, 29, 26, and 87 days by subtracting measured TC at 0 day from measured cumCO2 at each time step. Thus, the homogeneity of variances for TC at each time step did not negatively impact the fitting analysis. Then, we ran the surrogate CENTURY to estimate the initial SOC in active and slow pools (CA(0)) and CS(0) by fitting the modeled TC to measured TC at distinct 8, 15, 22, 29, 36, and 87-day time steps through a Levenberg-Marquardt algorithm. We determined the initial SOC in the passive pool (CP(0)) as the difference between TC and the sum of the two pools’ SOC estimates. Note that the C input rates to soils were set to zero, assuming that there is no C inputs to soils during incubation periods. Last, we evaluated key statistical metrics generated from running the surrogate CENTURY, which included parameter estimates and the standard errors, t values, and significance levels against the null hypothesis (i.e., a parameter is zero) of parameter estimates. To develop constraints between the initial SOC pool estimates and measured soil properties, we used the guided data analysis of SAS/LAB (SAS Institute, 2012b) where an integrated environment for performing standard data analyses such as multiple regression and various statistical tests (e.g., chi-square and Levene test for nonconstant variance and studentized residuals for outlier detection) is provided. This analysis was conducted after log-transforming soil properties to normalize them because of their high skewnesses (Table 1). Finally, we applied the constraints to initialize the surrogate CENTURY modeling of the soils for the validation set to evaluate whether the cumCO2 modeled is consistent with the cumCO2 measured.
RESULTS AND DISCUSSION Positive values of both CA(0) and CS(0) were estimated from 99 soils, but further examination on the standard statistics
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of the parameters showed that CA(0) estimates were significant in 85 soils, whereas CS(0) estimates were different in only 28 soils (P < 0.05). This was because the cumCO2 evolved from 87-day incubations in the soils were mostly derived from the decay of CA (0). Thus, the cumCO2 would not be sensitive to CS(0), which resulted in large uncertainties of CS(0) estimates. From the 28 soils where both parameter estimates were significant, we obtained an overall fit of R2 = 0.99 by relating the cumCO2 modeled to the cumCO2 observed, indicating that the inverse modeling of CO2 evolution data was successful. Furthermore, multiple regression analyses between modeled pools and measured soil properties showed the best fit (R2 = 0.74) when log-transformed CA(0) was related to log-transformed SC and clay content (in percent) (Eq.(1) and Fig. 2). Log10 CA ð0Þ¼−0:078þ0:905 log10 ðSCÞþ0:155 log10 ðclayÞ
ð1Þ
This relationship with SC is consistent with findings that SC partly originates from microbial biomass and soluble carbohydrates
FIG. 2. The linear models between modeled pools and measured soil properties in 28 soils where inverse modeling of CO2 evolved during laboratory soil incubations generated significant estimates at P < 0.05. Degrees of freedom in the models are 25. The SC and clay indicate water-soluble C (mg C kg−1 soil) and clay content (in percent), respectively. © 2015 Wolters Kluwer Health, Inc. All rights reserved.
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Soil Science • Volume 180, Number 1, January 2015
Inverse Modeling of CO2 Evolution Data
CONCLUSIONS We addressed the challenges associated with CENTURY initialization by using the SC SOC for inversely modeling CO2 evolved from laboratory soil incubations and measured soil properties in Florida sandy soils. By investigating the uncertainty of initial pool estimates generated from the surrogate CENTURY, we could identify statistically significant estimates and further use them to derive useful constraints with measured soil properties. Although practical uses of the constraints require further studies, the procedures demonstrated can help model users to carefully assess parameter uncertainties and identify constraints associated with the initialization of CENTURY.
FIG. 3. The comparison of observations with simulation results obtained from inverse modeling of the 39 soils of the validation set using the surrogate model for CENTURY's SOC dynamics.
REFERENCES
(Ghani et al., 2003; Sparling et al., 1998), and it has been used as a proxy for soil mineralizable C (Leinweber et al., 1995). Also, the positive correlation with clay content could be supported by less mineralization of SOC in fine-textured soils and the protection of SOC by silt and clay particles (Hassink, 1997). In fact, this relationship with soil texture has been parameterized in CENTURY, wherein the decay rate of an active pool is reduced with increasing clay content. Similar to CA(0), log-transformed CS(0) showed significant correlation with SC and clay content (R2 = 0.77) (Eq. (2) and Fig. 2) because of a high correlation between CA(0) and CS(0) (R2 = 0.87). Log10 CS ð0Þ¼1:031þ0:938 log10 ðSCÞþ0:125 log10 ðclayÞ
ð2Þ
Interestingly, CS(0) was not well correlated with HC, resulting in an R2 = 0.23, although HC has been regarded as a slow or intermediate SOC fraction. In fact, there has been recent and ongoing discussions that SOM stabilization and turnover rates have strong links to ecosystem properties and microbial processes (e.g., physical protection, microbial growth efficiency) (Schmidt et al., 2011). Cotrufo et al. (2013) proposed the Microbial Efficiency–Matrix Stabilization hypothesis, suggesting that microbial processes rather than chemical characteristics of SOM and litter inputs alone stabilize SOM. CP(0), which was calculated from the parameter estimates and TC, showed significant correlation with SC and clay (R2 = 0.52), but the best fit was obtained from RC (R2 = 0.84), followed by TC (R2 = 0.80). This is somewhat expected because passive or refractory SOC pools have been often estimated with nonhydrolyzable C (Collins et al., 2000). Last, when we applied the statistical constraints pertaining to CA(0) and CS(0) to initialize SOC in pools for simulation of the validation set, we observed a significant correlation between simulated and observed cumCO2 (P < 0.05, R2 = 0.49) (Fig. 3). Initial findings from this study on soils from the southeastern United States strongly suggest the potential for other practical applications to properly initialize CENTURY. Further studies to validate this potential should be conducted. First, additional CO2 evolution data obtained from wide ranges of soil textures should be incorporated in further refining the constraints between measured soil properties with initial pool estimates. Second, other measured soil properties that may impact differentiation of pools should be considered. An example would be the particulate organic matter fraction, which is commonly used as an index of the labile SOM fraction (Buyanonovsky et al., 1994; Wander and Bollero, 1999). Last, the use of longer incubation periods is desirable for finer-textured soils where CO2 evolved during extended periods unlike coarse soils used in this study.
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