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Title
The Millennial model: in search of measurable pools and transformations for modeling soil
carbon in the new century
Permalink
https://escholarship.org/uc/item/3ch0g6k8
Journal
Biogeochemistry, 137(1-2)
ISSN
0168-2563
Authors
Abramoff, Rose
Xu, Xiaofeng
Hartman, Melannie
et al.
Publication Date
2018
DOI
10.1007/s10533-017-0409-7
Peer reviewed
Powered by the California Digital Library
University of California
The Millennial model: in search of measurable pools and
transformations for modeling soil carbon in the new century
Rose Abramoff, Xiaofeng Xu, Melannie Hartman, Sarah O’Brien, Wenting
Feng, Eric Davidson, Adrien Finzi, Daryl Moorhead, Josh Schimel, Margaret
Torn, Melanie A. Mayes
R. Abramoff, M. Torn -- Climate and Ecosystem Sciences Division, Lawrence
Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA e-
mail: rzabramoff@lbl.gov; M. Torn e-mail: mstorn@lbl.gov
X. Xu -- Biology Department, San Diego State University, San Diego, CA
92182, USA e-mail: xxu@mail.sdsu.edu
M. Hartman -- Natural Resource Ecology Laboratory, Colorado State
University, Fort Collins, CO 80523-1499, USA e-mail:
melannie.hartman@colostate.edu
S. O’Brien -- Biosciences Division, Argonne National Laboratory, 9700 C Cass
Ave., Argonne, IL 60439, USA e-mail: slobrien1@gmail.com
Abstract
Soil organic carbon (SOC) can be defined by measurable chemical and
physical pools, such as mineral-associated carbon, carbon physically
entrapped in aggregates, dissolved carbon, and fragments of plant detritus.
Yet, most soil models use conceptual rather than measurable SOC pools.
What would the traditional pool-based soil model look like if it were built
today, reflecting the latest understanding of biological, chemical, and
physical transformations in soils? We propose a conceptual model—the
Millennial model—that defines pools as measurable entities. First, we discuss
relevant pool definitions conceptually and in terms of the measurements that
can be used to quantify pool size, formation, and destabilization. Then, we
develop a numerical model following the Millennial model conceptual
framework to evaluate against the Century model, a widely-used standard
for estimating SOC stocks across space and through time. The Millennial
model predicts qualitatively similar changes in total SOC in response to
single factor perturbations when compared to Century, but different
responses to multiple factor perturbations. We review important conceptual
and behavioral differences between the Millennial and Century modeling
approaches, and the field and lab measurements needed to constrain
parameter values. We propose the Millennial model as a simple but
comprehensive framework to model SOC pools and guide measurements for
further model development.
Keywords: Modeling, Soil carbon, Organic matter, Microbial activity,
Decomposition, Global change
Introduction
Changes to inputs or outputs of soil organic carbon (SOC) can affect land
carbon (C) storage, and can alter the function of terrestrial ecosystems and
their ability to serve as a source or sink of C (Schimel 1995). Researchers use
mathematical representations to estimate current distributions and future
changes in SOC, incorporating knowledge and assumptions about soil
biogeochemical processes. Current earth system models apply soil models
that assume first-order kinetic exchanges among conceptual pools defined
by empirical turnover times (Todd-Brown et al. 2011, 2013). These models
reflected the cutting edge of C cycle science in the 1970s and 1980s (e.g.,
based on Century and RothC; see review by Manzoni and Porporato 2009).
Such models are still of great utility as they capture many essential
dynamics, are mathematically simple, and run efficiently over large spatial
and temporal scales. However, first-order and empirical representations lack
the mechanisms to predict SOC response to global change perturbations
such as centennial-scale warming, drought, priming, and CO
2
or N
fertilization (Sierra et al. 2012; Grant 2013; Sulman et al. 2014; Todd-Brown
et al. 2014; Zaehle et al. 2014). Further, these models predict divergent SOC
stocks under global change scenarios, and do not reproduce current global
SOC patterns (Todd-Brown et al. 2013; Wieder et al. 2013). Most earth
system models (ESMs) use a soil model consisting of one to three SOC pools
(Jenkinson and Coleman 2008; Koven et al. 2013; Luo et al. 2015). Pools in
these models are operationally defined based on their presumed chemical
composition and turnover times (Parton et al. 1987). Advances in
spectroscopy, microscopy, and isotopic labeling, however, have provided a
better understanding of the chemical and physical characteristics of SOC
(Feng et al. 2016; Chenu and Plante 2006). These new approaches have
provided additional evidence that diverse SOC compounds can have similar
turnover times (Kleber et al. 2011). As a result, chemical composition is
recognized as only one of several factors contributing to the turnover times
of SOC pools (Schmidt et al. 2011). Other factors protecting SOC from
decomposition include the physical structure of soil and chemical
associations with soil minerals (von Lützow et al. 2007; Cotrufo et al. 2013;
Lehmann and Kleber 2015). Recent studies have called for a new generation
of soil biogeochemical models that better represent the chemical and
physical mechanisms controlling SOC turnover (Schmidt et al. 2011; Todd-
Brown et al. 2013; Luo et al. 2015; Wieder et al. 2015a, b).
A growing number of soil models consider an explicit microbial biomass pool
that affects the decomposition rate of SOC (Schimel and Weintraub 2003;
Allison et al. 2010; German et al. 2012). These models often require greater
numbers of parameters and equations, but may have an improved ability to
predict responses to novel environmental conditions, e.g., global change
scenarios (Wieder et al. 2013; Hararuk et al. 2013). Questions remain about
the feasibility of applying microbial models to global SOC predictions
(Bradford et al. 2016). Nevertheless, it is timely to rethink how we model key
soil processes in light of new emphasis on the nature of SOC and
decomposition pathways.
If we were to start over and develop a mathematical model for SOC based on
current understanding of soil C pools, it would reflect the biological,
chemical, and physical knowledge of soils gained in the last decades. The
model would classify organic C into categories defined by measurable
chemical and physical properties, such as mineral-associated C, C physically
entrapped in aggregates, dissolved C, and fragments of plant detritus. A
model based on measurable pools would represent explicit processes
regulating the transfers of C between pools, in contrast to models based on
imposed turnover times. For example, if SOC is occluded within aggregates,
the processes that determine whether C is decomposed to CO
2
, preserved, or
transformed include those that regulate aggregate turnover such as slaking,
freeze–thaw, and tillage. In this approach, the factors that cause aggregate
formation and destruction would be simulated to the extent possible, rather
than simply assigning the C within aggregates as part of a pool defined by a
conceptually- or empirically-derived first-order decay constant. Thus, starting
with measurable pools and transformations of SOC would allow us to define
the rate-limiting processes for each pool and to build a model that
incorporates an expanded suite of the most important driving processes in
soil—biological, chemical,
and
physical.
The Millennial model
Herein we describe a conceptual model that retains the tractability of
Century but is more directly testable because it is based on measureable soil
pools. We then develop a numerical model (Appendix) following the
Millennial conceptual model, and evaluate this model against the Century
model to illustrate potential differences between the two model structures.
Last, we discuss what measurements are needed to constrain the Millennial
model and the empirical challenges related to those measurements.
Definitions of SOC pools for the Millennial model
The Millennial model has five measurable soil C pools: particulate organic
matter (i.e., free fragments of plant detritus; POM), low molecular weight C
(i.e., root exudates and the by-products of exoenzyme activity; LMWC),
aggregate C, mineral-associated organic matter (MAOM), and microbial
biomass carbon (Fig. 1). In the following section, we define each pool
conceptually and in terms of the measurements that can be used to quantify
pool size, formation, and destabilization.
Particulate organic matter
POM is material that retains identifiable characteristics of its source material.
POM is derived primarily from plant material, but also from dead insects,
fungi, and detritus generated through fragmentation and decomposition of
litter, and from breakup of pre-existing soil aggregates (Segoli et al. 2013;
Cotrufo et al. 2015). POM can be measured using an operationally-defined
size and/or density separation (Six et al. 2006; Six and Paustian 2014). POM
may become associated with soil aggregates, but is broadly defined by
limited association with soil minerals. POM can be chemically altered by
microbial activity, leaching, and UV exposure (Baker and Allison 2015).
Low molecular weight carbon
LMWC refers to generally mono- or oligomeric, soluble products of microbial
decomposition and plant inputs such as root exudates and leaf leachate.
LMWC concentrations measured by an elemental analyzer are typically
higher in surface soil horizons, but preferential flow from biological activity
(e.g., rooting and invertebrate activity), physical forces (e.g., erosion, cracks,
and fractures formed by freeze–thaw), leaching (advection), or management
practices (e.g., plowing) may enable vertical transport (Gerke 2006; Boddy et
al. 2007). LMWC can be removed from solution during transport by becoming
adsorbed to soil minerals or consumed by microbes (Kaiser and Kalbitz 2012;
Jardine et al. 2006). The pore structure of soils, however, may limit microbial
and enzyme access to LMWC (Young and Crawford 2004; Zhuang et al. 2008;
Smith et al. 2017). Sorption of LMWC can vary according to its functional
groups (Jagadamma et al. 2012).
Aggregate C
We define soil aggregates as three-dimensional arrangements of organic
matter and minerals where the forces holding them together are stronger
than the forces attracting them to other aggregates (Martin et al. 1955).
Aggregate structures form when microbial residues and organic binding
agents attract soil particles, often in the presence of structural support and
chemical residues provided by plant roots and fungal hyphae (Jastrow et al.
1998; Young and Crawford 2004). Aggregates range in size from silt-sized
objects < 20 μm to microaggregates (53–2000 μm) to large
macroaggregates (2000–8000 μm) (Plante et al. 2006; Virto et al. 2008).
These operationally-defined size classes can exist in a hierarchical network
(e.g., microaggregates within macroaggregates) in the soil, and tend to be
more stable as size decreases and layers of protection increase (Tisdall and
Oades 1982; Dexter 1988). SOC in aggregates can be protected from
decomposition when the pore network limits diffusion of gases or nutrients
(Sexstone et al. 1985; Horn et al. 1994; Ranjard and Richaume 2001; Young
et al. 2008), isolates substrates from extracellular enzymes (Mayer 1994;
Ekschmitt et al. 2005; Allison 2006; Allison and Jastrow 2006), or limits
access of grazing organisms (Mayer 1994; Ranjard and Richaume 2001).
Aggregate formation and disruption occurs as a natural part of soil formation
and carbon cycling, whereby physical or chemical processes (e.g., drying,
wetting, freeze–thaw, tillage, electrostatic interactions) interact with
biological mechanisms (e.g., microbial exudation, root and hyphal
entanglement) to build and destabilize aggregates over time (Six et al. 2000;
Denef et al. 2002; Pronk et al. 2012).
Mineral-associated organic matter
MAOM is protected from microbial decomposition (and transport) through a
variety of sorption mechanisms, such as surface complexation, cation
bridging, and hydrophobic interactions (Sollins et al. 1996; Kaiser et al. 1996;
Kleber et al. 2007; Torn et al. 2009). MAOM typically refers to the heavy
mineral soil fraction isolated by density fractionations or the fine soil
particles measured by size fractionation. Across a wide variety of soil types
and geographical locations, MAOM accounts for a large proportion (50–85%)
of the total SOC stock in bulk soil (Sollins et al. 2009; Marin-Spiotta et al.
2009; Heckman et al. 2014; Cai et al. 2016), and in most soils SOC in MAOM
has a longer mean turnover time than other measurable soil fractions such
as aggregates and POM (Feng et al. 2016; Marin-Spiotta et al. 2009;
Jagadamma et al. 2013; Torn et al. 1997).
The formation of MAOM is regulated by adsorption of compounds such as
LMWC and microbially-derived products to mineral surfaces (Kalbitz and
Kaiser 2008; Lehmann and Kleber 2015). Microbially-derived products may
be preferentially adsorbed onto soil minerals compared to other compounds
(Sollins et al. 2009; Rumpel et al. 2010; Cotrufo et al. 2015). Layering of
organic compounds on soil minerals may also impart protection (Wershaw
1986; Kleber et al. 2007). Factors that influence the formation and stability
of MAOM include OM chemistry, soil texture, structure, the physico-chemical
properties and abundance of soil minerals, pH, the ionic strength of soil
water, temperature, and moisture (Jardine and McCarthy 1989; Kothawala et
al. 2009; Mayes et al. 2012; Feng et al. 2015).
Microbial biomass
Microbial biomass herein is defined as the mass of C contained within soil
microbial cells. Microbial biomass can be estimated using a variety of
methods, such as substrate-induced respiration, chloroform fumigation,
phospholipid fatty acid analysis, and quantitative PCR (Anderson and
Domsch 1978; Vance et al. 1987; Båth and Anderson 2003; Junicke et al.
2014). Microbial biomass controls the flow of C in soils through uptake of C
and nutrients for microbial growth, the release of waste products, and
microbial turnover. Specifically, microbes produce extracellular enzymes to
decompose SOC, and they release CO
2
through maintenance and growth
respiration (Schmidt et al. 2011). Necromass can be transferred to LMWC,
aggregate C, and MAOM pools (Cotrufo et al. 2013; Kallenbach et al. 2016).
Given the significantly different turnover rates of these carbon pools, the
relative fraction of these allocations could determine how long necromass C
will remain in the soil.
Microbial biomass is not a large pool, typically < 5% of SOC (Fahey et al.
2005; Fontaine et al. 2007; Abramoff and Finzi 2016), but microbial activity
has a disproportionate effect on C cycling. As such, microbial activity largely
controls the SOC response to global change. Global change is proposed to
affect microbial functions in a number of ways. Particularly, soil warming
may (1) increase the activity of microbial predators, (2) alter the proportion
of C taken up that is allocated to growth [carbon use efficiency (CUE)], (3)
shift microbial community composition, (4) accelerate protein turnover, and
(5) increase microbial metabolic activity (Steinweg et al. 2008; Frey et al.
2013; DeAngelis et al. 2015). Beyond soil temperature, other factors that
may affect growth rates and turnover times include the size of microbial
biomass, soil moisture, soil texture, microbial biomass C:N:P ratio, soil pH,
and supply of substrates such as litter, root turnover, root exudates, and SOC
(Grant 2001; Manzoni et al. 2014; Sinsabaugh et al. 2014b; Tang and Riley
2015).
Major differences between the Millennial and Century models
The Century model has been a standard for estimating soil C stocks across
space and through time for three decades (Parton et al. 1987, 1995; Paustian
et al. 1992; Bonan et al. 2013). For this reason, we compare the conceptual
organization of the Millennial model to that of the Century model. The
Century and Millennial models both transfer C between several solid-phase C
pools and a LMWC pool, modifying rates of transfer based on edaphic and
climatic factors. The ‘active’ pool in Century represents material with short
turnover times (6 months–1 year) and is often conceptualized as live
microbial biomass and microbial products, the ‘slow’ pool is defined by
having an intermediate turnover time (10–50 years) and is thought to be
chemically-resistant or physically-protected, and the ‘passive’ pool, with the
longest turnover time (100–1000 years), is considered chemically or
physically-stabilized (e.g., charcoal or bound to clay particles). The transfer
of C between pools is controlled by constant maximum specific decay rates
that can be set to site-specific values. Turnover rates are then empirically
modified by environmental factors (e.g., temperature, moisture, pH,
aeration) and soil physical properties (e.g., sand, silt, and clay content).
Implicitly, Century considers SOC to be stabilized by physico-chemical
interactions such as humification and adsorption to clay particles. The result
is a direct transfer of C from the active or slow pools to the passive pool. The
proportion of C allocated to the passive pool from the active pool compared
to the slow pool has increased over time, reflecting accumulating evidence
(e.g., Cotrufo et al. 2013, 2015) of the role of microbes and labile C in
forming protected C. Dissolved organic C (DOC) in Century is formed as a
linear function of sand content and the amount of water flowing through the
organic horizon, but it cannot be stabilized and eventually leaches out of the
system.
In the Millennial model, the soil pools—POM, LMWC, aggregate C, MAOM, and
microbial biomass—are based on measurable components of SOC, and
transfers between pools are conceptualized as transfers that would occur in
nature. For example, C transfers between pools do not result in CO
2
loss
unless they are mediated by microbial activity. POM can become associated
with aggregate C, or transformed into LMWC by microbial biomass. LMWC
can be taken up by microbial biomass and transformed to CO
2
, sorbed to
minerals or leached away. LMWC and microbial necromass are the main
sources of C in MAOM. Rather than a linear transfer from POM to aggregate C
to MAOM, both POM and MAOM can reversibly bind to aggregate C. Because
microbes mediate or transfer mass between all of the C pools, we would
expect this model to have several significant differences in dynamics, and
the potential to generate a wider range of feedbacks in responses to climate
perturbations, when compared to a first-order model.
Several recent models have explicitly represented the microbial
decomposition of soil organic matter. These models all have different
approaches to microbial decomposition and soil C protection. For example, a
model by Wang et al. (2013) used the Michaelis–Menten equation, with
enzymes produced by an explicit pool of microorganisms, to estimate
production of DOC from both POM and MAOM, while allowing the latter to
dynamically sorb to soil minerals. Ahrens et al. (2015) also used a saturating
sorption isotherm, but used microbial biomass instead of enzyme
concentration to simulate decomposition and predict the vertical age profile
of SOM. A third model by Tang and Riley (2015) used equilibrium
approximation kinetics to represent both enzymatic decomposition and
sorption to minerals, while Dwivedi et al. (2017) used a surface complexation
model to estimate sorption. Other models do not use sorption to minerals but
represent soil C cycling in new ways. For example, Wieder et al. (2015a, b)
introduced microbial functional groups to constrain the decomposition rates
of two litter and soil pools, while Sistla et al. (2014) included multiple
substrate and enzyme functional groups. Sulman et al. (2014) tracked three
substrate pools (simple, chemically resistant, and dead microbes) allocated
between protected and unprotected fractions. In this model, decay rate was
a saturating function of the microbe:substrate ratio, and protected SOM was
a composite of aggregate C and MAOM.
None of the models above explicitly simulated soil aggregates or aggregate
C. In contrast, Segoli et al. (2013) explicitly simulated soil aggregate
dynamics, hierarchically nesting four size classes. Aggregation was driven by
litter decomposition and microbial production, albeit with first-order kinetics
and omitting other soil organic matter pools. To our knowledge, no existing
model matches our conceptualization of the pools both necessary and
minimally sufficient to meet the emerging consensus on biological, chemical,
and physical controls on SOC, though the key pools and fluxes are well
represented across recent models when considered together. The Millennial
model expands on these recently developed models not by including all of
their features, but by focusing on the processes that control our five C pools,
such as microbial decomposition, mineral sorption, and aggregation.
Model comparison
We developed a numerical model following the Millennial model conceptual
framework to illustrate potential behaviors of such a model structure. We
describe the five C pools of the Millennial model and the rate of transfer
between them in a series of ordinary differential equations defined in the
Appendix. To illustrate key conceptual and structural differences between
the Millennial model and the Century model, we compared predicted SOC
stocks using both models across a gradient of clay content and in response
to global change scenarios. We used the same parameter values for both
models when possible (Table 3), and adjusted a subset of parameters (Table
3, “Calibrated”) in the Millennial model to better match the steady-state SOC
stocks predicted by the Century model. The purpose of this fitting was to
perturb both models from a similar initial condition in order to focus on the
different perturbation responses between the two models. We ran the
Millennial model and Century for 2000 years after an initial spin-up of 4000
years, using identical soil temperature, moisture, and plant inputs (Table 1).
The soil temperature and moisture forcing was a global average derived from
the Community ESM (Oleson et al. 2013). The carbon input is representative
of mid-high latitudes. All input files are available at https://github.com/email-
clm/Millennial, along with the model code. One year of input forcing was
repeated for the number of years of the model simulation. The initial soil C in
each of the five soil C pools was set to 1 g m
−2
prior to spin-up. In the first set
of scenarios, we compared steady-state C pools in soils with different clay
content (10, 20, 30, 40, 50, 60, 70, 80%), reflecting a gradient in the sorption
capacity of soil. Second, we compared the equilibrium size of soil C pools
after 2000 years following temperature, moisture, and substrate
perturbations. The initial values for the soil C pools in the perturbation
scenarios were derived from the end of the 4000-year spin-up scenario at
40% clay. We chose the following perturbations to represent common global
change scenarios (Melillo et al. 2011; Suseela et al. 2012; Lajtha et al.
2014a) used for model sensitivity analysis (Sierra et al. 2015; Wang et al.
2016), 5 °C warming (W), double C input (I), 50% of the original soil moisture
content (D), 5 °C warming and double C input (WI), and 5 °C warming and
50% soil moisture (WD).
Comparison of Millennial and Century model runs
Sensitivity to clay content
The Millennial and Century models had similar amounts of C in analogous
pools. The majority of C in the Millennial model at steady state was in the
MAOM pool, similar to Century’s passive pool (Fig. 2a, b). Aggregate C in the
Millennial model was 14–20% of total SOC, similar to Century’s slow pool. In
the Millennial model, LMWC, microbial biomass, and POM represented < 6%
of total C, similar to the active pool in Century. In the simulations, a greater
proportion of C inputs were stabilized as MAOM in the 80% clay compared to
the 20% clay soil, because of the larger sorption capacity of the 80% clay
soil.
There were, however, several differences between the Millennial and Century
model outputs. First, the Millennial model uses nonlinear functions based on
experiments to predict the relationship between the maximum sorption
capacity (Q
max
) and clay content, imposing maximum carbon storage
capacity in the MAOM pool (Mayes et al. 2012; Wang et al. 2013; Riley et al.
2014; Ahrens et al. 2015; Dwivedi et al. 2017), whereas in Century, the C
stored in each pool changes proportionally with forcings such as clay content
and plant inputs. As a result, SOC approaches a maximum value as soil clay
content increased in the Millennial model (Fig. 2a) whereas the size of these
pools increased proportionally with clay content in the Century model (Fig.
2b). Second, the Millennial model reached an equilibrium C stock more
quickly than did Century (Fig. 3a, b). This reflects the faster transfer of C
inputs to the dominant SOC pool (MAOM) in the Millennial model than to the
dominant pool (passive C) in Century.
Response to single factor climate and environmental forcings
The models made different SOC predictions in single factor climate and
environmental forcing simulations (Figs. 4a, b, 5a, b). Century accumulated
more C in response to doubled input than did the Millennial model. Georgiou
et al. (2017) demonstrated that soil C accumulation in a first-order model
was proportional to plant inputs, but a microbial model was insensitive to
plant inputs because of the concomitant increase in microbial growth and
respiration that removes some of the added plant inputs via respiration. This
feedback between plant inputs and biomass growth may explain why
increased C input has a smaller effect on SOC pools in the Millennial model
compared with the Century model. The Millennial results are consistent with
experiments which demonstrate that increased plant inputs and SOC
responses are not linearly related (Lajtha et al. 2014a, b). It is notable that
some of the added C remained in the POM pool rather than becoming
incorporated into a physically or chemically protected pool, making it
theoretically more vulnerable to remineralization.
Warming by 5 °C decreased SOC in both models (Fig. 4a, b). The
temperature sensitivity of decomposition in the Millennial model is greater
than in the Century model and thus it lost more SOC in response to the
warming perturbation (Fig. 4a). The Millennial model uses the same scalar
for temperature sensitivity as Century, but also uses a temperature-sensitive
microbial CUE (Table 3) that increases the respiratory loss of SOC with
warming.
Both models gained SOC with a 50% decrease in field moisture content (Fig.
4a, b). The Millennial model gained more SOC than the Century model
compared to the control treatment (Figs. 4, 5). The Millennial model may be
somewhat more sensitive to drought because the water scalar affects
multiple microbial processes such as decomposition and uptake, as well as
physical processes such as sorption and aggregate formation. Neither model
is coupled to a model of plant productivity; thus, feedback effects on SOC
simulated here only reflect soil processes. Given the sensitivity of SOC to
plant inputs in the Century model, it is likely that the negative effect of
drought on plant productivity would reduce SOC. In the Millennial model, this
effect may be dampened because plant inputs are less important to SOC
concentrations than are the internal biophysical processes (e.g., microbial
growth, enzyme production, sorption).
Response to dual-factor climate and environmental forcings
In contrast to the single-factor perturbations, the interaction of warming with
double-litter inputs or drought resulted in fundamentally different SOC
responses in the two models. When warming was coupled with double inputs
or decreases in soil moisture, the Millennial model lost SOC relative to the
control simulations, whereas the Century model gained SOC compared to the
control. In Century, doubled plant inputs and drought strongly increased
SOC, while warming moderately decreased SOC—thus, the strong effect of
plant inputs and soil moisture resulted in a net SOC increase (Figs. 4, 5). In
the Millennial model, warming had the strongest effect, ultimately
decreasing SOC to a greater extent than the positive effect on SOC of plant
inputs and drought. It is notable that the two models had the same sign of
change in SOC stock with regards to single-factor variation in clay content,
temperature, soil moisture, and double inputs. Yet, when simultaneous
perturbations were applied, the direction of the SOC trend diverged. The
unique features of the Millennial model—the use of a temperature-sensitive
CUE, and nonlinear responses to increases in plant inputs—are likely
responsible for the different responses compared to Century. We cannot say
which model simulation was most accurate, and in fact, the answer is likely
dependent on local edaphic conditions. Few large-scale field manipulations
have been able to test more than one forcing factor (Norby and Luo 2004;
Castro et al. 2010; Hanson et al. 2016). But the divergence observed here
clearly demonstrates the sensitivity of future predictions of the SOC sink to
different model formulations (e.g., Todd-Brown et al. 2013).
What are the costs of process-rich models?
Including measurable SOC pools in the Millennial model adds realism to C
fluxes and transformations, while increasing flexibility to respond to climate
and environmental forcing factors. However, this added realism has costs.
For example, replacing the empirical equations in Century with the more
mechanistic ones in the Millennial model increases the number of model
equations and parameters. The additional costs may be partly offset by
defining pools and fluxes that are potentially measurable, thus providing
empirical constraints to at least some of the additional parameters that can
be measured (but see section below on measurement challenges).
Any formulation of the Millennial model including the one we present above,
is more complex than Century, and requires more knowledge to develop
equations and define parameters. For example, the microbial pool is
explicitly used to estimate POM decay, LMWC assimilation, respiration, and
MAOM sorption, requiring kinetic parameters instead of the simpler rate
coefficients used in Century. Estimates of these parameters in our numerical
model (Table 3) were derived from studies completed since Century was
developed, or were calibrated to constrain model behaviors within reported
bounds. Including additional processes, or developing existing processes to
be more mechanistic, would similarly require more equations, parameters,
and constraints.
No model can capture every biological process, and the Millennial model
omits some important controls. For example, decomposition is constrained
by both energetic and stoichiometric relationships between microorganisms
and nutrients (Sinsabaugh and Shah 2012), but we have only considered C in
the Millennial model. Including only C can increase model sensitivity to
parameters affecting carbon flow that would realistically be constrained by
other nutrients. Moreover, many model parameters are not constants, but
variables that change in ways that could dampen model responses. A good
example is CUE. Including temperature-dependent CUE can result in large
differences in SOC predictions after warming compared to fixed-CUE models
(Wang et al. 2013; Wieder et al. 2013). Yet the relationship between
temperature and CUE used in this and other models is based on few studies
(Devêvre and Horwáth 2000; van Ginkel et al. 2000; Steinweg et al. 2008),
and relationships between CUE and other attributes of the environment,
resources, and microbial community are areas of active research (Geyer et
al. 2016; Sinsabaugh et al. 2017).
Although the Millennial model is necessarily more mechanistic than Century
in calculating flows between pools of soil C, it remains empirical with regard
to underlying biochemical and physiological processes. For example,
microbial biomass is a surrogate, in part, for the actions of extracellular
enzymes catalyzing substrate degradation (Burns et al. 2013). Adding
specific classes of extracellular enzymes to the Millennial model would
provide context to more mechanistically evaluate the influence of substrate
quality or nutrient availability on patterns of C flow (Moorhead et al. 2012;
Averill 2014). It would also add several equations describing dynamics of
additional pools, require many parameters, and the need to balance enzyme
production, turnover, and activity with comparable substrate and microbial
dynamics (Sinsabaugh et al. 2014a, b).
The desired temporal and spatial scale of model predictions and scale of
model formulation can guide the necessary level of mechanistic
representation. Adapting models for problems at different scales also
requires consideration of mathematical complexity, parameter choice, and
feedback control. Some processes such as microbial growth and enzymatic
depolymerization operate on sub-hourly-to-daily timescales. While these
short-term processes may be important for long-term trends, it may be
computationally intractable to represent these processes in models that run
over timescales of decades to centuries (Fig. 6). Further, it may not be
necessary to represent these processes if they can be seasonally averaged
or otherwise collapsed into relationships between responses and their
drivers, creating a simplified model of response variables related to empirical
observations (Todd-Brown et al. 2011). For example, Xu et al. (2014) derived
an index of cumulative microbial activity from readily available climate data
that was then used in conjunction with substrate C:N to estimate the ratio of
microbial biomass C to substrate C for locations where microbial biomass
observations were not available. Wieder et al. (2013) used Michaelis–Menten
kinetics to model decay rate as a function of microbial biomass, which could
be estimated according to Xu et al. (2014), to generate soil C pools closer to
observations than predictions from Century-based models (DAYCENT and
CLM4CN; Thornton et al. 2007). These examples demonstrate how fine-scale
microbial models can be used to generate scalable relationships between
easily observed variables (e.g., soil C:N) and key model parameters (e.g.,
microbial biomass) for use in ESMs. Thus one of the practical advantages of
developing new fine-scale microbial models is the transfer of knowledge from
a modern representation of decomposition to large spatial and temporal
scales via their application in an ESM. Of course, the transfer must retain
sufficient mechanistic representation such that the ESM makes reasonable
projections under novel environmental conditions.
Measurability of pools
The Millennial model represents a hypothesis about what biological,
chemical, and physical soil processes are important to C cycling. Exploring
this hypothesis through simulations can provide guidance for prioritizing
measurements of soil pools, transfer rates, and environmental factors.
Models currently use a wide variety of data for fitting and validation,
including microbial biomass measurements from laboratory incubations
(Wang et al. 2013), litter decomposition and soil C pool measurements
(Wieder et al. 2014, 2015a, b), total soil C and protected C (Sulman et al.
2014), laboratory measurements of aggregate C (Segoli et al. 2013), and
field measurements of heterotrophic respiration (Abramoff et al. 2017).
Estimates of soil C pools and factors affecting them such as litter
decomposition, heterotrophic respiration, and clay content can be measured
in the field either directly or by proxy (Bailey et al. 2017; Table 2). However,
the Millennial model also requires new parameters governing process
equations that are challenging to measure, especially regarding aggregate
dynamics and MAOM. These processes have only been considered in a
handful of models due to a lack of observational data (Albalasmeh and
Ghezzehei 2013; Segoli et al. 2013; Wang et al. 2013; Ahrens et al. 2015;
Tang and Riley 2015).
It is relatively straightforward to quantify the proportion of soil mass or soil C
in aggregates, but it is far more challenging to estimate the rate of
aggregate formation and decay (Table 2). Most studies measure the turnover
of the carbon in aggregates at the time of sampling rather than the turnover
of the physical structure of the aggregates themselves (e.g., Jastrow et al.
1996; Six et al. 1998; Liao et al. 2006). Carbon dynamics can be decoupled
from the turnover rates of the physical structures (O’Brien and Jastrow 2013;
McCarthy et al. 2008) and there can be a large range of SOC ages within a
single aggregate or group of aggregates, leading to dramatic overestimation
of aggregate turnover times (Jastrow et al. 1996). Approaches for estimating
aggregate turnover that are independent of soil C such as labeling with rare
earth elements, controlled laboratory studies, or observation after
disturbance in the field tend to find shorter turnover times, but the results
also depend on the time interval of observation (De Gryze et al. 2006) or
experimental treatment (O’Brien and Jastrow 2013; Denef et al. 2002;
Crawford et al. 2012; Blankinship et al. 2016) making it difficult to
generalize. Therefore, aggregate C parameters are the most uncertain of the
Millennial model parameters, though the physically-based definition of
aggregates makes them potentially measurable.
MAOM is difficult to measure consistently because there is no standard
fractionation procedure, either in terms of pre-treatment of samples or
threshold values for solution density and soil particle size. Different methods
estimate widely diverging turnover times for MAOM, ranging from 24 ± 7
years using incubations, 166 ± 44 years using
13
C labeling, and 709 ± 121
years using
14
C labeling (Feng et al. 2016). Studies that define MAOM using a
density fraction tend to estimate longer turnover times (e.g., 30–4500 years;
Heckman et al. 2014; Hall et al. 2015) than studies that estimate MAOM
using a size fraction (e.g., 18–665 and 24–1280 years for the silt and clay
size fractions, respectively; O’Brien et al. 2013). Given the potential value of
the Millennial model and the importance of the turnover times of modeled
pools, we contend that research effort should be directed toward robust
assays and protocols that will provide consistent estimates of aggregate and
MAOM turnover time in the field.
Conclusion
We developed a soil modeling framework that reflects current understanding
about the biological, chemical, and physical mechanisms controlling the
formation and destabilization of soil carbon and is based on the principle of
measurable model pools. This framework emphasizes how limited access of
microbial decomposers to soil C imparts stability to SOC, in contrast to the
Century model which defines decomposition rates empirically as a function
of environmental factors. We created a numerical model based on this
framework and identified areas of consistency with the Century model,
including similar predictions of SOC as a function of clay content,
temperature, soil moisture, and plant inputs. Because the Century model is
the standard by which other models are judged, we are encouraged by the
observed consistency. However, the Millennial model exhibited distinct
nonlinear responses due to the choice of functions affecting SOC in the soil
pools, e.g., the Michaelis–Menten equation for depolymerization, and the
sorption equation for stabilization of LMWC on MAOM. More importantly, the
two models diverged regarding the direction of SOC stock change (sink vs.
source) when more than one environmental or climate forcing factor was
imposed at the same time. It is uncertain whether the Millennial or Century
formulation is more consistent with observations, but the variation in model
behavior points to the importance of understanding underlying pool
transformations.
While the accuracy of the Millennial model is untested, it is our intent that
the underlying modeling framework represents the current conceptual
understanding of soil C, and therefore has the potential to be developed into
a model that skillfully represents a variety of global change processes,
including climate and land use change. The mechanistic C transformations
enable predictions of SOC under novel environmental conditions, and
measurable pools make the model more testable in theory. In practice, the
model demonstrates the need for field and laboratory measurements of rates
of aggregate and mineral-associated C formation and decay. Nevertheless,
we propose that the Millennial model offers a new, independent path for
improving understanding and predictions of soil responses to anthropogenic,
environmental, and climatic forcing factors by representing measurable soil
C pools and transfer processes in a transparent and parsimonious model
structure.
Acknowledgements
The Millennial model code, model inputs, and the model output used in this
manuscript are archived at a GITHUB Repository (https://github.com/email-
clm/Millennial) that is publicly accessible. The authors would like to thank the
Carbon Cycle Interagency Working Group, via the US Carbon Cycle Science
Program under the auspices of the US Global Change Research Program, for
providing funding for the “Celebrating the 2015 International Decade of Soil –
Understanding Soil’s Resilience and Vulnerability,” workshop held at the
University Corporation for Atmospheric Research in Boulder, CO, USA on 14–
16 March 2016. We would also like to thank the University Corporation for
Atmospheric Research for providing meeting space, as well as the 36
workshop participants, William J. Riley, and three anonymous reviewers for
helpful comments and discussion. Lawrence Berkeley National Laboratory is
managed and operated by the Regents of the University of California under
Contract DE-AC02-05CH11231 with the US Department of Energy. Argonne
National Laboratory is managed by UChicago Argonne, LLC, under contract
DE-AC02-06CH11357 with the US Department of Energy. Oak Ridge National
Laboratory is managed by the University of Tennessee-Battelle, LLC, under
Contract DE-AC05-00OR22725 with the US Department of Energy.
Appendix: Model description
The equations we have chosen below reflect one possible mathematical
expression of the Millennial conceptual model, but there are many possible
numerical models for different applications. For example, decomposition of
POM is here represented by a double Monod relationship, limited by both
POM and microbial biomass, but for an application where competition
between chemical species is particularly important, for example, ECA
kinetics could be used instead (Tang 2015). Similarly, we chose temperature
and moisture scalars to minimize steady-state differences between Millennial
and Century for the purpose of model comparison, but for dynamic
predictions one could apply Arrhenius temperature sensitivity and one of
several semi-mechanistic moisture functions (Davidson et al. 2012; Manzoni
et al. 2014).
The system of equations below is modeled on the conceptual figure (Fig. 1),
tracking the size of and transfers between five C pools: POM, LMWC,
aggregate C, MAOM, and microbial biomass. The change in POM (
P
) stock
with time is governed by the balance between plant C input and aggregate C
breakdown, aggregate C formation, and decomposition,
where
F
i
is aboveground plant litter, root litter and root exudates,
p
i
is the
proportion of C input allocated to POM (1/3 of inputs to POM and 2/3 of
inputs to LMWC after Oleson et al. 2013),
p
a
is the proportion of C in
aggregate breakdown allocated to POM,
F
a
is aggregate C breakdown,
F
pa
is
aggregate carbon formation from POM, and
F
pl
is decomposition of POM into
LMWC. Decomposition of POM is governed by a double Michaelis–Menten
equation,
where
V
pl
is the maximum rate of POM decomposition,
K
pl
is the half-
saturation constant,
B
is the microbial biomass carbon, and
K
pe
is the half-
saturation constant of microbial control on POM mineralization. The terms
S
t
and
S
w
refer to the temperature and moisture scalar, respectively, and are
taken from DAYCENT, the daily time-step version of the Century model
(Parton et al. 1998), to minimize differences in temperature and moisture
effects between the Century and Millennial models due to choice of scalar,
where
T
is the current temperature,
T
ref
is the reference temperature,
t
1
is
the x-axis location of the inflection point (°C),
t
2
is the y-axis location of the
inflection point,
t
3
is the distance from the maximum point to the minimum
point, and
t
4
is the slope of the line at the inflection point. For the water
scalar,
RWC
is the relative water content calculated as the fraction of field
capacity, and
w
1
and
w
2
are empirical parameters. The temperature scalar
is an arctangent function that predicts a decline in temperature sensitivity
with increasing temperature and the water scalar depends on RWC, where
the maximum effect on biological activity occurs at field capacity (volumetric
water content = 0.35, RWC = 1.0) (Parton et al. 2010).
The formation of aggregate C (
A
) from POM follows Michaelis–Menten
dynamics,
where
V
pa
is the maximum rate of aggregate formation,
K
pa
is the half-
saturation constant of aggregate formation, and
A
max
is the maximum
capacity of C in soil aggregates. Soil aggregate C breakdown is partitioned to
POM and MAOM,
where
k
b
is the rate of breakdown.
The change in LMWC (
L
) depends on LMWC input, the leaching rate,
decomposition of POM, adsorption to minerals, and microbial uptake. In a
multilayer version of the Millennial model LMWC would also depend on
leaching input, but in this single layer version we assume that the leaching
input is included in the LMWC input,
and where
k
l
is the leaching rate,
F
lm
is the adsorption of LMWC to MAOM,
and
F
lb
is the uptake of LMWC by microbial biomass. Adsorption of LMWC to
minerals is controlled by a Langmuir saturation function,
where
K
lm
is the binding affinity that is adjustable based on the pH.
Q
max
is
the maximum sorption capacity (mg C kg
−1
dry soil) that is converted to C
density (g C m
−2
) by multiplying soil bulk density (
BD
= 1350 kg m
−3
),
assuming a 1 m soil profile. The parameters
c
1
and
c
2
are the coefficients
for computing
Q
max
from the clay content in percent, derived from Mayes et
al. (2012). The Langmuir function parameters were derived from
measurements of DOC sorption on over 200 soils in the eastern US. The
measurements demonstrate a nonlinear saturation with respect to DOC
concentrations in soils, and several recent models have used approaches
that also impose a mechanism for DOC saturation on mineral surfaces (Wang
et al. 2013; Riley et al. 2014; Ahrens et al. 2015; Dwivedi et al. 2017).
Microbial uptake of LMWC is a function of microbial biomass and LMWC
concentration, temperature, water, and temperature-dependent CUE,
where V
lm
is the potential uptake rate of LMWC.
F
gr
is microbial growth-
related respiration, K
lb
is the half-saturation constant for microbial activity,
CUE
ref
is the reference CUE, and CUE
T
is the CUE dependence on
temperature. T
ae-ref
and T are the reference and current temperature,
respectively. Both MAOM and POM can be incorporated into the aggregate C
pool,
where
F
ma
is the carbon flow from MAOM to aggregate C,
V
ma
is the
maximum rate of aggregate formation, and
K
ma
is the half-saturation
constant of aggregate formation. MAOM is formed by adsorption of LMWC
and microbial necromass, and is affected by transfer into and out of the
aggregate C pool,
where
F
bm
is the carbon flow from microbial biomass to MAOM, namely
adsorption of necromass, and
k
mm
is the adsorption rate of microbial
biomass. In this particular iteration of the Millennial model, we assume that
adsorbed microbial biomass is no longer alive, but by allowing adsorbed
microbial biomass to take up LMWC and perform growth and maintenance,
one could modify the model to accommodate the assumption that live
microbial biomass can sorb to minerals, or even to other microbes (i.e.,
biofilms). Microbial biomass changes as a result of uptake, adsorption to
minerals, and loss via maintenance,
where
F
mr
is the maintenance respiration of microbial biomass, and
k
m
is the
microbial turnover rate (Table 3).
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