Inter-annual variations in the tropical land carbon (C) balance are a
dominant component of the global atmospheric CO2 growth rate.
Currently, the lack of quantitative knowledge on processes controlling net
tropical ecosystem C balance on inter-annual timescales inhibits accurate understanding and projections of land–atmosphere C exchanges. In particular, uncertainty on the relative contribution of ecosystem C fluxes attributable
to concurrent forcing anomalies (concurrent effects) and those attributable
to the continuing influence of past phenomena (lagged effects) stifles
efforts to explicitly understand the integrated sensitivity of a tropical ecosystem to climatic variability. Here we present a conceptual
framework – applicable in principle to any land biosphere model – to
explicitly quantify net biospheric exchange (NBE) as the sum of anomaly-induced
concurrent changes and climatology-induced lagged changes to terrestrial
ecosystem C states (NBE = NBECON+NBELAG). We apply this framework to an
observation-constrained analysis of the 2001–2015 tropical C balance: we use
a data–model integration approach (CARbon DAta-MOdel fraMework – CARDAMOM) to merge satellite-retrieved land-surface C observations (leaf area, biomass, solar-induced fluorescence), soil C inventory data and satellite-based atmospheric
inversion estimates of CO2 and CO fluxes to produce a data-constrained
analysis of the 2001–2015 tropical C cycle. We find that the inter-annual
variability of both concurrent and lagged effects substantially contributes to the 2001–2015 NBE inter-annual variability throughout 2001–2015 across
the tropics (NBECON IAV = 80 % of total NBE IAV, r= 0.76;
NBELAG IAV = 64 % of NBE IAV, r= 0.61), and the prominence of NBELAG IAV persists across both wet and dry tropical ecosystems. The
magnitude of lagged effect variations on NBE across the tropics is largely
attributable to lagged effects on net primary productivity (NPP; NPPLAG IAV
113 % of NBELAG IAV, r=-0.93, p value < 0.05), which emerge due to the dependence of NPP on inter-annual variations in foliar C and
plant-available H2O states. We conclude that concurrent and lagged
effects need to be explicitly and jointly resolved to retrieve an accurate
understanding of the processes regulating the present-day and future trajectory of the terrestrial land C sink.
Introduction
Immediate ecosystem responses to external forcings are invariably followed
by time-lagged ecosystem responses, attributable to a continuum of lagged
biotic and physical processes. For example, contemporaneous ecosystem state
changes attributable to disturbances, climatic variability and increasing
atmospheric CO2 levels all induce a temporal spectrum of lagged
processes, such as diurnal to seasonal dynamics in canopy and groundwater
storage and multi-annual changes in mortality rates, and induce ecosystem dynamics relating to species distributions, nutrient availability and soil
properties on timescales spanning from decades to millennia (Schimel et al.
1997; Smith et al., 2009; Reichstein et al., 2013). Conversely, for a given
time span, the sum of these “lagged effects” on ecosystem states ultimately represents the ecosystem dynamics attributable to a unique integrated legacy of past phenomena, spanning from diurnal to geologic timescales, making
lagged effects a ubiquitous dynamical property of any terrestrial ecosystem.
As a consequence, ecosystem function at any given time (such as
photosynthetic uptake, respiration and evapotranspiration rates) is an
emergent consequence of an ecosystem's initial physical and biotic states
and the contemporaneous impact of meteorological and disturbance forcings on
these states.
Disentangling the cumulative lagged consequences of past phenomena from
contemporaneous impacts of external forcings is a critical priority for
understanding and quantifying the contemporary terrestrial carbon (C) cycle
responses to climatic variability. Global-scale efforts to resolve the state
of the C cycle (Le Quéré et al., 2015) identify the tropical C cycle as a dominant contributor to the inter-annual variability (IAV) of the
terrestrial C sink. Recent efforts to characterize the tropical C sink IAV
have been largely focused on quantifying the role of concurrent responses to
climatic variability, including the contribution of semi-arid ecosystems
(Poulter et al., 2014; Ahlström et al., 2015), ecosystem responses to
drought (Gatti et al., 2014), and more generally continental-scale
sensitivities of photosynthesis, respiration and fire fluxes to concurrent
temperature and precipitation anomalies (Cox et al., 2013; Andela and van
der Werf, 2014; Alden et al., 2016; Jung et al., 2017; Liu et al., 2017; Piao
et al., 2019). However, on comparable timescales, time-lagged manifestations
of climatic variability on the state of the terrestrial biosphere have been
extensively theorized and observed (Thompson et al., 1996; Schimel et al., 1996, 2005; Richardson et al., 2007; Arnone et al., 2008; Sherry et al.,
2008; Saatchi et al., 2013; Frank et al., 2015; Doughty et al., 2015;
Baldocchi et al., 2017; Schwalm et al., 2017; amongst many others).
Specifically, lagged relationships between climate variability and the
terrestrial C fluxes – namely mediated through lagged impacts on
photosynthetic uptake and respiration fluxes, groundwater storage, mortality
and subsequent shifts of ecosystem function – indicate that lagged effects
may be a fundamental component in the inter-annual evolution of the
terrestrial C balance. Observational constraints on terrestrial ecosystem
responses to climatic variability further suggest that time-lagged phenomena
are a non-negligible component of terrestrial ecosystem C dynamics on
continental-to-global scales (Braswell et al., 1997; Saatchi et al., 2013;
Anderegg et al., 2015; Detmers et al., 2015; Fang et al. 2017; Yang et al.,
2018; Yin et al., 2020). Therefore, while recent efforts to diagnose
inter-annual variations of the tropical C balance overwhelmingly emphasize
the roles of concurrent forcings, observed ecosystem responses to climatic variability on multi-annual timescales indicate that the tropical C balance
may be substantially affected – if not governed – by lagged responses to
inter-annual variations in meteorological and disturbance forcings across
tropical ecosystems.
Accurate knowledge of both instantaneous sensitivities and time-lagged
processes of terrestrial C cycling to climate is critical for constraining
model representations of the terrestrial C cycle. Uncertainty in the
long-term terrestrial C flux imbalance and the associated carbon-climate
feedbacks is a prevailing source of uncertainty in Earth system projections (Friedlingstein et al., 2014; Friend et al., 2014), and these are likely
underestimated due to a range of under-represented and/or poorly constrained
C cycle responses to a changing climate (Luo, 2007; Lovenduski and Bonan,
2017). Furthermore, assessments of Earth system projections based on present-day constraints (Cox et al., 2013; Mystakidis et al., 2016) provide
little insight into the integrated roles of largely uncertain process controls, including C flux responses to drought (Powell et al., 2013), under-determined C pool dynamics (Bloom et al., 2016), nutrient dynamics and limitations (Wieder et al., 2015), and higher-order dead organic C
dynamics (Schimel et al., 1994; Hopkins et al., 2014). In tropical
ecosystems, rapid turnover rates of live and dead organic matter pools relative to extra-tropical ecosystems (Carvalhais et al., 2014; Bloom et
al., 2016) imply interactions between uptake, respiration, and fires
(Randerson et al., 2005; Chen et al., 2013; Bloom et al., 2015) on comparable timescales: specifically, given that (a) the mean C residence time in tropical biomass and soil organic matter pools typically spans
∼ 5–50 years and (b) multi-year observational constraints reveal rapid ecosystem vegetation/C responses to climatic extremes (Saatchi
et al., 2013; Alden et al., 2016), sub-decadal timescales are likely
critical for disentangling concurrent and lagged effect impacts on the
evolution of tropical C balance. However, despite numerous studies on the
roles of productivity (Doughty et al., 2015), water stress (Kurc and Small,
2007; Williams and Albertson, 2004), respiration (Trumbore, 2006; Exbrayat
et al., 2013a, b; Guenet et al., 2018) and mortality (Saatchi et al., 2013; Anderegg et al., 2015; Rowland et al., 2015), there is currently a major gap
between knowledge of individual processes controlling the tropical C balance
on inter-annual timescales and the integrated impact process interactions leading to complex net C exchanges represented in terrestrial biosphere
models (Huntzinger et al., 2013, 2017). As a result, while models provide
critical mechanistic insight into complex process interactions, model
representations of the net effect of competing and interacting C flux
responses to climate variability and disturbance remain highly uncertain on
regional and pan-tropical scales. Ultimately, given that tropical ecosystems account for 850 Pg of C and the majority of the Earth's photosynthetic
uptake, plant respiration and fire C emissions (Saatchi et al., 2011;
Hiederer and Köchy, 2011; Beer et al., 2010; van der Werf et al.,
2010), quantitatively understanding the concurrent and long-lived impacts of
climatic variability, drought and anthropogenic disturbance is critical for
predicting their function in Earth system projections.
Recent inverse estimates of tropical C fluxes from satellite CO2
measurements provide much-needed spatial and temporal constraints on
continental-scale net biospheric exchange (NBE; e.g. Takagi et al., 2014, Liu et al., 2014, 2017; Feng et al., 2017, Detmers et al., 2015; amongst
others). Satellite-based NBE estimates – combined with land-surface
observations of solar-induced fluorescence (SIF, Frankenberg et al. 2011),
leaf-to-soil constraints on total C stocks (Saatchi et al., 2011) and
disturbance (Giglio et al., 2013) – provide a unique opportunity for
quantitatively informing terrestrial biosphere model representations of the
tropical C balance; recent continental- to global-scale model–data fusion efforts have demonstrated the synergistic potential of the present-day “carbon-observing system” to resolve the dynamics of the terrestrial C
balance (Liu et al., 2017; Bloom et al., 2016; MacBean et al., 2018; Exbrayat
et al., 2018; Quetin et al., 2020; Yin et al., 2020). Ultimately, model–data fusion representations of terrestrial ecosystem C cycling allow for an
explicitly mechanistic representation of the terrestrial C balance with
in-built states and process parameterizations optimized to represent the observed C cycle variability in the observations; contingent on their
mechanistic accuracy of the C cycle to external forcings, these terrestrial
C balance models can be used to quantitatively diagnose the concurrent and
lagged sensitivities of terrestrial ecosystems to external forcings.
In this study we present a framework for expressing the ecosystem state
changes in a given year as the sum of (a) “concurrent effects”,
attributable to concurrent forcing anomalies, and (b) “lagged effects”,
attributable to the cumulative impacts of past forcings. We apply this
framework on a data-constrained ecosystem C balance modelling framework to
quantitatively diagnose the role of concurrent and lagged effects on the
2001–2015 inter-annual tropical C balance. Our analysis is motivated by some
key unanswered questions on the large-scale tropical C cycle variability:
for instance, are lagged effects significant contributors to inter-annual
flux variability on pan-tropical scales? Which C fluxes (e.g. photosynthetic
or respiratory) explain the majority of NBE variability attributable to
lagged phenomena? Are lagged effects a ubiquitous property across both dry
and wet tropical biomes? Here we hypothesize that on a pan-tropical scale,
the integrated impact of lagged effects is a critical component of tropical
NBE IAV. To test this hypothesis, we reconcile large-scale C cycle processes
and satellite-based estimates of land-to-atmosphere CO2 fluxes using
the CARbon DAta-MOdel fraMework (CARDAMOM) diagnostic ecosystem C balance model–data fusion approach. We outline our method in Sect. 2, where we present an analytical methodology for attributing inter-annual ecosystem state variability to concurrent and
lagged effects; we present and discuss a quantification of the relative role
of concurrent and lagged effects on continental-scale NBE and the attribution of lagged effects to inter-annual variations in C stock and
plant-available water states in Sect. 3; we conclude our paper in Sect. 4.
Methods
To quantitatively diagnose concurrent and lagged effects on the inter-annual
variability of the tropical C balance, we (i) present a conceptual framework
for attributing annual ecosystem state changes to concurrent and lagged
components, (ii) implement the CARDAMOM model–data fusion framework at a 4∘×5∘ monthly resolution to observationally constrain 2001–2015 C cycle states, fluxes and process controls, and (iii) attribute ecosystem state changes to concurrent and lagged effects based on
the CARDAMOM 2001–2015 representation of the tropical C balance. In summary,
the CARDAMOM model–data fusion framework (Bloom et al., 2016) employs a Bayesian inference approach to constrain model parameters and initial states
within the prognostic Data Assimilation Linked Ecosystem Carbon model
(DALEC, Williams et al., 2005), based on observation constraints – where and
when these are available. Since DALEC parameters are independently estimated
at each location, the 4∘×5∘ resolution was
chosen to accommodate recent estimates of land-surface CO2 and CO
fluxes produced at the GEOS-Chem atmospheric chemistry and transport model
4∘×5∘ grid (Bowman et al., 2017; Liu et al.,
2017; Jiang et al., 2017). We implement the CARDAMOM analysis across
tropical and near-tropical latitudes (30∘ S–30∘ N) and evaluate the tropical C balance across six sub-continental regions as well as the dry tropics and the wet tropics (Fig. A1 in the Appendix); we chose to focus
the evaluation of our results at sub-continental and pan-tropical scales to
conform with the fundamental spatial resolution limitations of
satellite-based surface CO2 flux estimates (Liu et al., 2014; Bowman et al., 2017). The following subsections describe a conceptual framework for
concurrent and lagged effect attribution (Sect. 2.1), the DALEC ecosystem carbon
balance model (Sect. 2.2), satellite and inventory-based observations (Sect. 2.3), the
estimation of DALEC parameters and states within the CARDAMOM model–data fusion framework (Sect. 2.4), and the attribution of the observation-informed
DALEC C cycle dynamics to their concurrent and lagged effect components
(Sect. 2.5).
Concurrent and lagged effects
Ecosystem function – such as photosynthesis, respiration and
evapotranspiration rates – at all stages of ecological succession is both a
consequence of an ecosystem's initial physical and biotic states and the
contemporaneous impact of meteorological and disturbance forcings on these
states. For example, ecosystem water and nutrient availability along with
species demography and species composition – effectively amounting to the
time-integrated ecosystem legacy – will govern an ecosystem's function under
a nominal forcing. The cumulative impact of both episodic or prolonged
variability in external forcings will be “remembered” in ecosystem states,
thus shaping ecosystem function as an emergent property of external forcing
history. Ecosystem states under a constant and perpetual environmental
forcing will follow a trajectory towards an equilibrium state (as has been
largely hypothesized as the typical outcome for ecosystem C stocks; Luo and
Weng, 2011; Luo et al., 2015) or more generally a transient trajectory about a
domain of attraction (Holling, 1973), with stable equilibria, stable limit
cycles, stable nodes and/or neutrally stable orbits as potential
trajectories. Here, we define lagged effects as the sum of ecosystem state changes induced
by a reference climatological mean forcing (Fig. 1); these include the
functional responses of ecosystems under climatological conditions (e.g. joint photosynthesis, respiration and evapotranspiration responses to
non-equilibrium plant-available water, leaf area, biomass and dead organic C
states) as well as functional shifts (e.g. succession-induced changes in demography and species composition and consequently changes in
ecosystem-scale photosynthetic capacity). In addition to an attraction
towards a fixed equilibrium or domain, ecosystem states are perpetually
disturbed by exogenous forces, such as meteorological and disturbance
forcing anomalies relative to a climatological mean forcing. Here we define
these concurrent effects as all anomaly-concurrent changes to ecosystem states unaccounted for
by climatology-induced state changes (i.e. lagged effects); these include functional
responses to anomalous forcings (e.g. drought impact on photosynthetic
uptake and respiration in responses to meteorological phenomena) as well as functional shifts on demographics and species composition induced by
concurrent mortality and disturbance events. The combined state changes
resulting from both concurrent and lagged effects throughout a 1-year time period will in turn propagate into future ecosystem states. In this manner,
forcing anomalies are perpetually propagated into ecosystem states, and
lagged effects in subsequent years represent an aggregate legacy of all
prior phenomena. The choices of (a) “concurrent effects” to describe
effects contemporaneous to a meteorological event and (b) “lagged effects”
to describe all time-lagged processes are consistent with Frank et al. (2015) definitions associated with effects occurring during or after a climatic anomaly. We note a distinction between (i) single-event lagged
effects, which represent ecosystem state changes attributable to a single
past forcing event, and (ii) aggregate lagged effects, which represent the sum and interactions between past single-event lagged effects. For example,
single-event lagged effects might include the ecosystem state changes
attributable to a single drought or disturbance event, while aggregate
lagged effects can include the effects of cumulative drought impacts, the interactions in between dry and wet year events, and the longer-term
succession processes (as described in Fig. 1); we henceforth use “lagged
effects” to refer to aggregate lagged effects throughout the paper. Finally, while in this study we confine our analysis to the estimation of
concurrent and lagged effects on annual timescales, we note that the
conceptual framework presented in Fig. 1 can be adapted to diagnose
concurrent and lagged ecosystem state changes on any timescale of relevance.
Conceptual figure denoting annual ecosystem state changes attributable to concurrent and lagged effects. Throughout a 1-year cycle
(circular arrows), lagged effects amount to the sum of ecosystem state
changes induced by a reference climatological mean forcing, and concurrent
effects amount to ecosystem state changes solely attributable to a contemporaneous forcing anomaly. The total state changes resulting from both
concurrent and lagged effects will in turn determine the next year's initial
ecosystem states.
Model and drivers
We use the DALEC model (Williams et al., 2005) to represent the principal terms and major pathways of the terrestrial C cycle. The DALEC model family has been extensively used to
diagnose terrestrial C cycle dynamics across a range of site-level and spatially resolved approaches (Fox et al., 2009; Rowland et al., 2014; Bloom
et al., 2016; Smallman et al., 2017; Exbrayat et al., 2018; amongst several
others). Here we use DALEC version 2a (henceforth DALEC2a): a summary of the
DALEC2a states and processes is depicted in Fig. 2. For the sake of
brevity, we solely report changes in reference to DALEC2 (previously
described by Bloom et al., 2016) and refer the reader to the Supplement (and references therein) for a complete description of the model.
Schematic of the CARbon DAta-MOdel fraMework (CARDAMOM) Bayesian
model–data fusion approach: the DALEC2a model (described in Sect. 2.2) represents the ecosystem C and plant-available H2O balance; the dashed
blue boxes denote the observational constraints used in this study (see
Table 1 for abbreviations and details). The solid lines denote C and H2O fluxes between pools and/or external gains and losses. CARDAMOM is
implemented at a 4∘×5∘ resolution across the
tropics (30∘ S–30∘ N). Within each 4∘×5∘ grid cell, DALEC2a model parameters and initial
ecosystem states are optimized using an adaptive Metropolis–Hastings Markov chain Monte Carlo algorithm.
We extended the DALEC2 structure to include the first-order plant-available water (H2O) pool, where the hydrological balance is defined as the sum
of precipitation inputs (P) and evapotranspiration (ET) and runoff (R)
outputs. In turn, the plant-available H2O limits gross primary
productivity through conservation of the inherent water-use efficiency (Beer et al., 2009), where ET is calculated as a function of gross primary
production (GPP) and atmospheric vapour pressure deficit (Appendix B1). Effectively, the interaction between plant-available H2O, GPP and ET
constitutes a first-order plant–soil carbon–water feedback. We further appended the DALEC2 structure by including a parameterization of soil
moisture limitation on heterotrophic respiration (Appendix B2), given that
heterotrophic respiration dependence on soil moisture remains highly
uncertain (Moyano et al., 2013; Sierra et al., 2015) as well as a dominant source of uncertainty amongst terrestrial C models (Falloon et al., 2011;
Exbrayat et al., 2013a, b).
Given a range of in situ and continental-scale studies highlighting the uncertainties of fire combustion factors across a range of ecosystems (Ward
et al., 1996; Bloom et al., 2015), the errors involved in representing
fine-scale fire-type variability (Giglio et al., 2013), and spatial variability of fuel loads, we optimize fire C pool combustion factors (in
contrast, combustion factors were prescribed as constants in Bloom et al.,
2016): specifically, we optimize the combustion factors of foliar biomass
(πfoliar), non-foliar biomass pools (πnfb), soil C
(πSOM) and the fire resilience factor (we approximate the litter C
combustion factor as the arithmetic mean of πfoliar and πSOM, given that the DALEC2a litter pool represents both above-ground
and below-ground C reservoirs). Prior ranges for all π and the
fire resilience are conservatively defined as spanning 0.01 to 1. We
implement the ecological and dynamic constraints (Bloom and Williams, 2015)
to ensure that foliar C combustion factors are greater than both non-foliar
biomass and soil C combustion factors (πfoliar > πnfb and πfoliar > πSOM), which are comprehensively consistent with detailed measurements of C pool combustion
factors across a range of ecosystem fire types (Shea et al., 1996;
Araújo et al., 1999; van Leeuwen et al., 2014; amongst others). Finally, we also represent the uncertainty in the longevity of plant labile C; specifically, we now optimize – rather than prescribe – the labile C
lifespan used during leaf flushing in DALEC2a (previously all labile C was
used during leaf flush; see Bloom and Williams, 2015). The updated model structure is depicted in Fig. 2. We henceforth summarize the dynamical
description of DALEC2a as
xt+1=DALEC2a(xt,Mt,p),
where xt represents the ecosystem state vector at time t,
Mt represents the corresponding meteorological and disturbance forcings
(namely monthly temperature, precipitation, global radiation, vapour pressure deficit, burned area and atmospheric CO2), p represents a vector of
time-invariant process parameters and DALEC2a represents the DALEC2a
operation on states xt throughout time t→t+1. In summary, DALEC2a
optimizable quantities consist of 26 process parameters, p, and seven initial
ecosystem states (C and H2O pools; Fig. 2) at time step t=0, x0. For the sake of brevity, we include a complete description of
DALEC2a state variables, process parameters and diagnostic C fluxes in the
Supplement, except where an explicit mention is necessary in the paper.
Observations
The observations assimilated into CARDAMOM are summarized in Table 1.
Following Bloom et al. (2016) we assimilate Moderate Imaging
Spectroradiometer (MODIS) leaf area index (LAI) soil organic matter (SOM) from the Harmonized World Soil Database (HWSD; Hiederer and Köchy,
2011) and above- and below-ground biomass (ABGB, Saatchi et al., 2011).
Solar-induced fluorescence (SIF) – retrieved from the Greenhouse Gases
Observing Satellite (GOSAT) – is a robust proxy for photosynthetic activity:
while non-linear inter-relationships at plant level and flux-tower level
have been observed under certain conditions (Verma et al., 2017; Magney et
al., 2017), GPP is observed to be linearly inter-related to SIF at ecosystem and regional scales (Frankenberg et al., 2011; Sun et al., 2017).
Given that SIF : GPP linear relationships are known to vary substantially
across individual species and entire ecosystems, here we solely assume that
monthly SIF provides a constraint on the relative temporal variability of
GPP (following MacBean et al., 2018). The monthly averaged 2010–2015
4∘×5∘ SIF values were derived with the
polarizations and selection criteria described by Parazoo et al. (2014).
The assimilation of relative SIF variability is described in Sect. 2.4.
Observational constraints assimilated into the 4∘×5∘ CARDAMOM simulation.
Observation (abbreviation)Dataset descriptionUncertainty1Number ofobservationalConstraints6Leaf area index (LAI)MODIS LAI retrievals2.±log(1.2)1Soil organic matter (SOM)Soil C inventory (Hiederer and Köchy, 2011)±log(1.5)1Above- and below-ground biomass (ABGB)3GLAS-informed biomass map (Saatchi et al., 2011)≥±log(1.5)41Solar-induced fluorescence (SIF)Monthly averaged 2010–2015 GOSAT retrievals of fluorescence (Frankenberg et al., 2011)5±log(2)≤72Fire C emissions (BB)Mean 2001–2015 4∘×5∘ inverse estimates of fire C emissions (Worden etal., 2017; Bowman et al., 2017)± 20 %1Net biospheric exchange (NBE)Monthly 2010–2013 GOSAT CO2 derived 4∘×5∘ inverse estimates ofterrestrial NBE (Liu et al., 2018)Seasonal =± 2 gC/m2 d-1 Annual =± 0.02 gC/m2 d-148
1 Uncertainties denoted as ±log() indicate log-transformed model
and observed quantities (i.e. m and o in Eq. 4).
2 Only mean 2001–2015 LAI is assimilated into CARDAMOM, in order to
mitigate the influence of seasonal LAI
retrieval biases (Bi et al., 2015).
3 The ABGB estimate is applied as a constraint on the sum of all
CARDAMOM live biomass pools (Fig. 1).
4 See Bloom et al. (2016) for details on biomass uncertainties.
5 Time-resolved SIF is assimilated as a relative constraint on the temporal variability of GPP (see Sect. 2.4).
6 See Fig. S1 for observational constraint spatial coverage.
We assimilate the GOSAT-derived 2010–2013 net biospheric C exchange (NBE)
dataset (NBE > 0 for a net biosphere-to-atmosphere flux)
estimated using the Carbon Monitoring System Flux atmospheric CO2
inversion framework (CMS-Flux; Liu et al., 2014, 2018). In summary, total
monthly 4∘×5∘ surface CO2 fluxes were
scaled using a Bayesian 4D variational (4D-Var) inversion approach in order
to minimize differences between GOSAT 2010–2013 observations and CMS-Flux
representations of total column CO2 (we refer the reader to Liu et al.,
2018, for additional details on the derivation of surface CO2 fluxes). Following Liu et al. (2017) and Bowman et al. (2017), we subtract prior
estimates of anthropogenic CO2 emissions from total CMS-Flux total
CO2 flux estimates, and we assume that prior anthropogenic CO2
emissions errors are minimal compared to the biospheric CO2 fluxes,
given that these are typically much smaller than natural CO2 fluxes at
a 4∘×5∘ resolution across the tropics. We
withhold 2015 CMS-Flux NBE estimates – constrained by Orbiting Carbon
Observatory (OCO-2) total column CO2 observations (Liu et al.,
2017) – to validate CARDAMOM 2015 regional NBE estimates and their
associated uncertainties in the absence of CO2 constraints (OCO-2 NBE
estimates are therefore withheld from the CARDAMOM NBE assimilation step
described in Sect. 2.4); in effect, we employ the validation of CARDAMOM
NBE predictions against the withheld data effect as a means of evaluating the mechanistic representations of CARDAMOM's time-varying C cycle processes.
Finally, we assimilate mean 2001–2015 fire C emission estimates derived from
monthly 4∘×5∘ satellite-based estimates of
fire CO emissions (Jiang et al., 2017; Worden et al., 2017; Bloom et al.,
2019): the estimates of biomass burning CO emissions were derived based on an ensemble of atmospheric CO inversions of column CO measurements from the Measurements of Pollution in the Troposphere (MOPITT) instrument onboard the
NASA EOS/TERRA satellite (Deeter et al., 2014). We refer the reader to Jiang
et al. (2017) for the details of the atmospheric CO inversion using the
GEOS-Chem adjoint model and to Worden et al. (2017) for the attribution of
optimized CO fluxes to biomass burning. Biomass burning CO emission
estimates by Worden et al. (2017) were then used to derive total biomass
burning C emissions based on monthly estimates of CO2 : CO; the approach
is detailed in Bowman et al. (2017). We note that NBE estimates exhibit
substantial spatial error covariance structures across individual
4∘×5∘ grid cells, and the effective information content of the NBE inversions is larger than the 4∘×5∘ resolution. To mitigate the spatial error
correlation features identified in the NBE dataset (Bowman et al., 2017; Liu
et al., 2017), we employed a 3×3 grid-cell smoothing window for monthly NBE estimates, following the approach by Liu et al. (2018).
Model–data fusion
Within each 4∘×5∘ grid cell, the C cycle
dynamics in DALEC are a function of meteorological and disturbance drivers
M, model parameters p and initial conditions x0 (as summarized in Eq. 1). We
use a Bayesian inference formulation to independently retrieve the optimal
distribution of x0 and p given observations O for each 4∘×5∘ grid cell, where
py|O∝pyp(O|y).y is the control vector {x0,p}, p(y) is the
prior probability distribution of y, and p(O|y) is proportional to the
likelihood of y given O, L(y|O). At any given grid cell, the observation
vector O consists of LAI, SOM, ABGB, SIF, NBE and CO-derived fire CO2
emissions (henceforth OLAI, OSOM, OABGB, OSIF, ONBE, and OCO, respectively), and – assuming errors are uncorrelated – the overall likelihood of y given
O can be expressed as
L(y|O)=LLAILSOMLABGBLSIFLNBELCO.
For LAI, SOM, ABGB and CO, we derive the corresponding likelihood function L∗ (i.e. LLAI, LSOM, LABGB and LCO, respectively) as follows:
L∗=e-12∑imi(y)-oiσi2,
where oi and mi(y) correspond to the ith observation and corresponding
modelled quantity derived from control vector y, respectively; σi represents the combined errors of model and data, namely the combined
effects of DALEC model structural error, model driver errors and observation
errors. In contrast to Bloom et al. (2016), given that MODIS LAI retrievals have exhibited systematic seasonal biases across the wet tropics (Bi et al.,
2015), we solely use mean LAI as a constraint on the mean DALEC2a LAI values
(therefore, for the derivation of LLAI, m and o in Eq. (3) correspond to
the 2001–2015 mean modelled and observed LAI).
To constrain the relative variability of GPP based on SIF without imposing
constraints on the absolute GPP magnitude, we derive LSIF – based on
Eq. (4) – by formulating m and o as follows:
5mi(y)=GPPiGPP‾,6oi=SIFiSIF‾,
where SIFi and GPPi are SIF and corresponding DALEC2a GPP values
at time index i and SIF‾ and GPP‾ are the corresponding means
during the 2010–2015 time period.
We constrain CARDAMOM NBE using 4∘×5∘ monthly
CMS-Flux NBE estimates, derived from GOSAT atmospheric total column CO2
retrievals (Liu et al., 2018) spanning 2010–2013. At each 4∘×5∘ location, we define the LNBE as the product of
mean annual NBE and seasonal NBE anomalies using the following equation:
LNBE=e-12∑ama′(y)-oa′σ′2e-12∑i,ami,a′′(y)-oi,a′′σ′′2,
where ma′ denotes the annual mean DALEC2a NBE value for year a and mi,a′′ denotes DALEC2a NBE seasonal deviations from their annual
means; specifically, for a given month i with corresponding year a,
8ma′(y)=112∑i=112NBEi,a,9mi,a′′(y)=NBEi,a-ma′,
where NBEi,a is the DALEC2a NBE; observations oa′ and
oi,a′′ were derived identically to ma′ and mi,a′′.
Similarly to Desai (2010), we implement the likelihood function outlined in
Eq. (7) in order to capture both the seasonal and inter-annual modes of NBE
variability; we found that solely minimizing the monthly NBE residuals
following the formulation based on Eq. (4) led to disparate inter-annual
variations between the model and observation-constrained NBE. Effectively
the formulation in Eq. (7) – in comparison to Eq. (4) – increases the relative
weight of mean annual CMS-Flux NBE constraints on DALEC2a NBE.
The uncertainty for each observational constraint (i.e. σ values in
Eqs. 4 and 7) implicitly represents the combined impacts of observational random errors, systematic errors, and model structural error. In the absence
of knowledge on the relative roles of observation errors in the monthly
4∘×5∘ observation uncertainties and explicit
knowledge of model structural error, we prescribed σ values through
trial and error in order to (a) ensure that model states and diagnostic variables capture the predominant variability of the observational
constraints O while (b) ensuring that σ values are comparable to the observational uncertainty. For all land surface variables (namely LAI,
ABGB, SOM and SIF), m and o were log-transformed (following Bloom et al.,
2016). For the mean 2001–2015 LAI constraint, we assumed log-normal
uncertainty of σ=± log(1.2); we prescribed a σ=± log(2) log-normal uncertainty structure for each SIF observation. We approximated the uncertainty of the CO-derived mean 2001–2015 fire C values
as σ=±20 %, which is broadly consistent with the
monthly 4∘×5∘ CO uncertainty estimates and
the corresponding CO2 : CO uncertainty estimates reported by Bowman et
al. (2017) and Worden et al. (2017). For NBE we prescribed σ′=0.02 and σ′′=2 gC/m2 d-1; we found that these were suitable for capturing the first-order 2010–2013 seasonal and inter-annual components of continental-scale NBE variability. The uncertainties assumed
for each observational constraint are summarized in Table 1; we note that
these implicitly include the combined assumption about observational random errors, systematic errors, and model structural error. We discuss the
potential impacts of observation uncertainty assumptions and make
recommendations for future efforts in Sect. 3.3.
To retrieve the distribution of p(y|O), we employed an adaptive
Metropolis–Hastings Markov chain Monte Carlo (MHMCMC) approach following Bloom et al. (2016) to sample the objective function, namely the product of
p(y) and p(O|y); for reference, we list the individual components of
the objective function in the paper's Supplement (Sect. S3). We generally found that the computational costs required to meet the MHMCMC convergence criterion reported by Bloom and Williams (2015) for each
4∘×5∘ grid cell were prohibitively expensive. We updated the adaptive MHMCMC to the Haario et al. (2001) MHMCMC approach,
where the MHMCMC proposal distribution is adapted as a function of
previously accepted samples (see Haario et al., 2001, for algorithm details). We ran four adaptive MHMCMC chains for 108 iterations in each 4∘×5∘ grid cell. We found that the latter half of the chains converged within a Gelman–Rubin convergence criterion value of
< 1.2 in 75 % of the grid cells. For the subsequent analysis, we
use a subset of 500 samples of y from the latter half of each MHMCMC chain, totalling 4×500 samples of y per 4∘×5∘ grid cell.
Dynamical formulation of concurrent and lagged effects
Here we present a dynamical formulation for the derivation of concurrent and
lagged effects on the inter-annual ecosystem state changes. To explicitly
quantify the concurrent effects and lagged effects, we define the trajectory
of the modelled dynamic state variables x at year a+1 as
xa+1=D(xa,Ma,p),
where the state vector xa+1 – which is comprised of DALEC2a states at
the beginning of year a+1 – is computed from the DALEC2a model operator
D(), which is a function of the previous state xa at the beginning of year a, the meteorological and disturbance forcing history of the previous year
Ma, and time-invariant ecosystem parameters p. We note that Eq. (10) is
resolved on an annual time step; however, the DALEC2a operator time step is monthly, hence the operator in Eq. (10) is a composite of monthly operators as
denoted in Eq. (1). To isolate the role of concurrent meteorological and
disturbance anomalies in Ma, we define the C trajectory under a
reference climatological mean forcing M′ as
x′a+1=D(xa,M′,p).
Here we define M′ as the monthly climatological mean of the
2001–2015 meteorological and disturbance drivers and δMa as the corresponding anomaly in year a, where
Ma=M′+δMa.
With Eqs. (10) and (11), we can define the change in the state x in year a, δxa, as
δxa=xa+1-xa=xa+1-xa+1′+xa+1′-xa.
This formulation allows us to define the lagged effect on ecosystem states
in year a as
δxaLAG=x′a+1-xa,
the concurrent effect on ecosystem states in year a as
δxaCON=xa+1-x′a+1,
and the sum of concurrent and lagged effects in Eqs. (14) and (15) as
δxa=δxaLAG+δxaCON.
We conceptually illustrate the derivation of annual concurrent and lagged
effects on a given ecosystem state x in Fig. 3. Under a climatological mean
forcing (blue line), the ecosystem state trajectory – solely induced by
lagged processes – would diverge from an externally forced ecosystem state trajectory (black line) and would eventually converge to an equilibrium
state or oscillate about a domain of attraction (Fig. 3a). For a 1-year time span, the change in ecosystem state x throughout year a, δxa, can be decomposed into a climatology-induced lagged effect change δxaLAG and an anomaly-induced concurrent
effect change δxaCON (Fig. 3a, inset).
(a) Schematic of meteorology-forced trajectory of ecosystem state
x (solid black line) and trajectory of x under a climatological mean forcing (light blue solid line). Inset: state trajectory xa→xa+1
(δxa), decomposed as the sum of climatology-induced
lagged effect vector xa→x′a+1 (δxaLAG)
and anomaly-induced concurrent effect vector x′a+1→xa+1
(δxaCON). (b) Hypothetical scenario depicting
approximately time-invariant annual lagged effects δxLAG (blue dashed arrows), in reference to changes in transient states x0, x1, x2, etc.; the temporal changes in x for each
time interval, δx, δxLAG and δxCON, are shown in the
underlying bar chart. In this scenario, δxLAG
is relatively constant and its variability (denoted as “var()” in the schematic equation) is negligible relative to δxCON. (c) Hypothetical scenario depicting time-varying annual
lagged effects δxLAG, in reference to
transient states x0, x1,
x2, etc.; in this scenario, the variability of
δxCON is comparable to the variability of
δxLAG.
From a mechanistic standpoint, the variability of δxaLAG is independent of meteorological forcing anomalies and
is therefore solely dependent of all ecosystem states xa. For example, in a hypothetical scenario where a climatological mean forcing induces no
net ecosystem state changes, δxaLAG=xa-xa+1′=0
and δx=δxCON. In a more general
scenario, δxaLAG=xa-xa+1′∼constant for all
a: in this instance xaLAG is non-zero but largely
insensitive to variations in xa within a typical range of
ecosystem states x; therefore, (i) the year-to-year variability of δx is largely dependent on the variability of δxCON and (ii) δxLAG amounts to an approximately constant offset term (Fig. 3b). Alternatively, if δxLAG is sufficiently sensitive to the variability of
x, the variability of δx will be a function of
both δxLAG and δxCON: in this
instance, year-to-year variations in x are influencing both the
sign and magnitude of lagged effects (Fig. 3c).
Here we investigate the possible contributions of the annual variability of
δxCON and δxLAG to δx for the 2001–2015 time period across tropical ecosystems.
Specifically, we test the following two hypotheses.
Hypothesis 1: varδxLAG≪varδxCON. In this instance, the impact of M′ on
x is largely independent of the variability of x; consequently the year-to-year variability of the lagged effect force
δxLAG is relatively small, and the year-to-year changes
in ecosystem states, δx, are dominated by δxCON (Fig. 3b).
Hypothesis 2: varδxLAG∼var(δxCON). In this instance, the impact of M′ on x is
dependent on the variability of x; consequently, the year-to-year
variability of the lagged effects δxLAG is substantial,
and the year-to-year changes in ecosystem states, δx, are
substantially attributable to both δxCON and δxLAG (Fig. 3c).
The mechanistic nature of the DALEC2a model within CARDAMOM (namely the
representation of allocation fractions, residence times, meteorological
sensitivities and explicit representation of dynamical states) allows for a
data-constrained probabilistic assessment of the relative role of lagged and concurrent effects on net ecosystem state changes. The disaggregation of δxa into δxaCON and δxaLAG (and the associated hypotheses 1 and 2) can be
projected onto any subset of net ecosystem fluxes or additive combination of
gross fluxes. For example, the NBE in year a (NBEa) corresponds to the
net C loss between xa and
xa+1; in turn, NBEa can be decomposed
into its lagged effect component (NBEaLAG) and the concurrent effect
component (NBEaCON), where
NBEa=NBEaCON+NBEaLAG.
NBEa and NBEaLAG can be directly calculated from
D(xa,Ma,p) and
D(xa,M′,p), respectively, and NBEaCON is calculated as NBEa–NBEaLAG. By definition
in the DALEC2a model, NBE is the sum of primary productivity (NPP),
heterotrophic respiration (RHE) and fire (FIR) fluxes, where
NBEa=RHEa+FIRa-NPPa.
In turn, disaggregation of RHE, FIR and NPP into their respective concurrent and lagged components gives
19NBEaCON=RHEaCON+FIRaCON-NPPaCON,20NBEaLAG=RHEaLAG+FIRaLAG-NPPaLAG.
To diagnose relative inter-annual variations of a given flux F (namely the
2001–2015 time series of NBE, RHE, FIR and NPP), we derive annual anomalies ΔF relative to the mean 2001–2015 flux F‾,
where, for a given year a,
ΔFa=Fa-F‾.
The Δ operation in Eq. (21) can be implemented in each term in Eqs. (18)–(20) without loss of equivalence between the left-hand and right-hand
sides (for example, ΔNBEaLAG=ΔRHEaLAG+ΔFIRaLAG-ΔNPPaLAG).
Finally, we diagnose the 2001–2015 ΔNBEaLAG
variability as a function of the inter-annual anomalies in individual
ecosystem states, Δxa(∗)={Δxa1,Δxa2,…,ΔxaN}, relative to the
mean ecosystem state x‾. For DALEC2, these consist of annual anomalies in initial C and H2O states (see Fig. 2). For a given year, the total
NBE lagged effect anomaly, ΔNBEaLAG, can be decomposed into
ΔNBEaLAG=∑n=1NΔNBEanLAG+ΔIa.
ΔNBEanLAG represents the NBE lagged
effect component solely attributable to an anomaly in ecosystem state n (Δxan), and ΔIa collectively accounts
for the contribution of higher-order interactions between individual
ecosystem states. In other words, given that ΔNBEaLAG is solely attributable to variability of annual initial
conditions xa, the decomposition of ΔNBEaLAG to
individual pool contributions provides a first-order attribution of lagged
effect IAV to underlying C and H2O pool dynamics. The derivation of Eq. (22) is explicitly described in Appendix C.
To derive uncertainty estimates for each annual flux Fa or corresponding anomaly ΔFa, we calculate each term based
on the 2000 samples of y at each grid cell (see Sect. 2.4), and we calculate the corresponding median and inter-quartile range (25th–75th
percentiles) for each term. Inter-annual variations in 2001–2015
F and ΔF time series are reported as standard deviations of median values. We conservatively assume that
F and ΔF errors are fully correlated
when propagating these uncertainties across each region.
Results and discussionEvaluation of observation-constrained tropical C balance
Ultimately inferences about the concurrent and lagged effects on NBE can
only be drawn if the CARDAMOM analysis is able to both (i) accurately
represent observed NBE and (ii) accurately represent underlying states and processes controlling IAV. To assess the CARDAMOM 2001–2015 re-analysis,
here we present an evaluation of CARDAMOM against (a) the assimilated
2010–2013 GOSAT-derived NBE dataset, (b) the withheld OCO-2-derived 2015 NBE dataset, and (c) assimilated and independent datasets of tropical
terrestrial ecosystem states and fluxes.
CARDAMOM NBE evaluation against assimilated and predicted NBE.
a RMSE units are PgC yr-1. b Prediction RMSE values are equivalent to absolute errors, since only one error value is considered.
* Correlation p value < 0.05.
Optimized CARDAMOM NBE (a function of the optimized DALEC2a parameters and
initial 2001 ecosystem states) broadly represents the monthly variability of
the 2010–2013 regional-scale assimilated GOSAT-retrieved NBE (Fig. 4;
Table 2). In individual regions, monthly CARDAMOM versus CMS-Flux NBE r≥0.69, with the exception of the South-East Asia and Indonesia region (r= 0.57), where the CARDAMOM and GOSAT-retrieved NBE exhibits a relatively small seasonality compared to other regions. Evaluation of CARDAMOM NBE against
withheld NBE estimates from OCO-2 exhibits a degradation in the correlation and RMSE values but agrees favourably on the amplitude and timing of the NBE variability (Table 2). We find that the CARDAMOM analysis is able to
robustly capture the 2010–2013 GOSAT-derived annual NBE estimates at
regional scales (see Fig. 5 and Table 2; regional CARDAMOM versus CMS-Flux
NBE r≥0.9). On an annual basis, all regional OCO-2 NBE estimates for 2015 except Northern Hemisphere South America are within the 90 % CARDAMOM prediction confidence intervals (Fig. 5); furthermore, all OCO-2 annual
NBE estimates are within CARDAMOM 2015 prediction confidence intervals for
the wet tropics, dry tropics and the entire tropical study region. We
found generally lower seasonal correlations between CARDAMOM NBE and
GOSAT retrieved across 4∘×5∘ grid cells (Fig. S2; 25th–75th percentile = 0.19–0.63) and corresponding annual mean correlations (25th–75th percentile = 0.31–0.89) relative to the sub-continental and pan-tropical regions (Table 2); the lower correlative agreement is likely due to the limited
4∘×5∘ information content of satellite-based
NBE flux estimates (Liu et al., 2014; Bowman et al., 2017).
CARDAMOM monthly analyses of 2001–2015 median NBE (red line) and
associated uncertainty intervals (25th–75th percentiles in dark
pink and 5th–95th percentiles in light pink). The analyses were constrained by CMS-Flux GOSAT-derived top-down fluxes (Liu et al., 2018) for the 2010–2013 period; CMS-Flux OCO-2-derived 2015 NBE fluxes were withheld for validation. The geographical definitions for each region are
shown in Fig. A1 in the Appendix.
We also evaluate the 2001–2015 CARDAMOM NBE against the inter-annual
variability of the NOAA ESRL surface-based global atmospheric CO2
growth rate observations (https://www.esrl.noaa.gov/gmd/ccgg/trends/, last access: 5 May 2020;
see Supplement for dataset details). We assume that the
atmospheric CO2 growth rate variability – once detrended to remove
decadal trends in fossil fuel emissions and biogenic CO2 uptake – predominantly exhibits inter-annual variations of the tropical C balance (Baker et al., 2006; Cox et al., 2013; Sellers et
al., 2018). We find that 2001–2015 detrended CARDAMOM NBE (Fig. 5,
bottom-right panel) exhibits broad consistency with the atmospheric CO2 growth rate; the detrended datasets exhibit comparable levels of
inter-annual variability (atmospheric CO2 growth rate IAV =±0.62 PgC yr-1, CARDAMOM tropical NBE IAV =±0.80 PgC yr-1) as well as a significant correlation between annual NBE growth rate anomalies (r= 0.62, pval = 0.01).
CARDAMOM yearly analyses of 2001–2015 NBE (red line) and
associated uncertainty intervals (25th–75th percentiles in dark
pink and 5th–95th percentiles in light pink). The analyses were constrained by CMS-Flux GOSAT-derived top-down fluxes (Liu et al., 2018) for the 2010–2013 period. CMS-Flux OCO-2-derived 2015 NBEs (blue squares) are withheld for regional and pan-tropical NBE validation. CARDAMOM NBE and NOAA ESRL atmospheric CO2 growth rates were detrended for
inter-comparison (bottom-right panel). The geographical definitions for each
region are shown in Fig. A1.
The spatial variability of CARDAMOM state variables and fluxes constrained
by static datasets, namely LAI, biomass, soil C and mean fire C emissions
(Table 1), is broadly correlated with the observational constraints by the CARDAMOM analysis (r= 0.7–0.98; p<0.05; Fig. S2); for the
above-mentioned quantities total median errors amounted to <10 %,
with the exception of soil C (median error CARDAMOM soil C = 25 %). The
correlation between CARDAMOM GPP and GOSAT SIF is positive and significant
(p value < 0.05) in 67 % of 4∘×5∘ pixels, with higher correlations in the dry tropics (25th–75th
percentile = 0.41–0.78) relative to the wet tropics (25th–75th percentile = 0.13–0.63); the lower correlations in the wet
tropics are generally expected, given that wet tropical ecosystems
fundamentally exhibit a weaker GPP seasonal cycle.
We also evaluate the mean and inter-annual variability of CARDAMOM GPP, ET
and LAI outputs against (i) two independent measurement-based GPP estimates
for 2007–2015 (FLUXCOM GPP, Jung et al., 2020; and FLUXSAT GPP, Joiner et
al., 2018), (ii) two independent measurement-based ET estimates (FLUXCOM ET,
Jung et al., 2019; MODIS ET, Mu et al., 2011) for 2001–2013, and (iii) 2001–2015 MODIS LAI (we note that only mean 2001–2015 MODIS LAI was
assimilated into CARDAMOM; see Sect. 2.3). Dataset details and regional evaluations are included Sect. S2 and Tables S2–S3 in the Supplement. In summary, we find that mean CARDAMOM pan-tropical GPP is within
20 % of both independent estimates and that regional estimates are within 40 % of both independent estimates; regional GPP IAV in CARDAMOM (0.8 %–7.4 %) is broadly consistent with FLUXSAT GPP (1.3 %–10.7 %) and FLUXCOM
GPP (0.3 %–4.2 %). Pan-tropical GPP correlations are positive and
significant (p value < 0.05) among all three estimates (r= 0.69–0.74); regional correlations are by and large positive but not significant. CARDAMOM mean ET values are lower but within 25 % of
independent ET estimates, and differences in regional mean ET are within
50 % of independent estimates; regional ET IAV in CARDAMOM (2.3 %–5.5 %) is broadly consistent with FLUXCOM ET (0.3 %–5.9 %) and MODIS ET
(1.3 %–13.4 %). Correlations between three datasets span positive and
negative values but are mostly not significant; regional CARDAMOM ET
correlations against MODIS and FLUXCOM (r=-0.64–0.41) are generally
lower than inter-agreement between the two datasets (r=-0.27–0.94).
Mean CARDAMOM LAI is within 15 % of MODIS LAI across all regions. Regional
CARDAMOM LAI values (1.6 %–4.8 %) are broadly consistent with the range of
MODIS LAI values (0.7 %–5.2 %); none of the regional correlation values
were significant. The notable lack of correlative agreement between CARDAMOM
and independent LAI and ET estimates is potentially due to (a) the lack of
direct observational constraints on the temporal variability of ET and LAI
in CARDAMOM, (b) systematic errors or limitations of independent LAI and ET estimation approaches on inter-annual timescales (Bi et al., 2015;
Pan et al., 2020), and/or (c) fundamental limitations of CARDAMOM ET and LAI
estimates (further discussed in Sect. 3.3).
Overall, we argue that (i) CARDAMOM NBE and associated uncertainties compare
favourably against withheld and independent data on seasonal and inter-annual timescales, and (ii) the spatial variability and the IAV magnitude of
CARDAMOM ancillary states and fluxes are in general agreement with a range
of assimilated and independently estimated quantities. We discuss noteworthy
caveats and limitations of retrieved CARDAMOM ecosystem dynamics – and the
implications of inferred variability of concurrent and lagged effects – in Sect. 3.3. We anticipate that the ever-growing satellite CO2 record,
along with increasing volume and quality of terrestrial ecosystem
observations, will ultimately lead to improved seasonal and inter-annual
process representations in future model–data fusion analyses of the terrestrial C balance.
Regional and pan-tropical median annual ΔNBE (blue bars) and
its attribution to concurrent effects (ΔNBECON, green bars) and
lagged effect (ΔNBELAG, orange bars) components. The geographical
definitions for each region are shown in Fig. A1. Error bars denote the
25th–75th percentile uncertainty estimates for each flux
anomaly.
2001–2015 regional ΔNBE IAV and corresponding contributions of
concurrent effects (ΔNBECON) and lagged effects (ΔNBELAG); IAV values are represented here as standard deviations of annual
2001–2015 NBE values; bracketed values represent Pearson's correlation coefficients between total NBE and concurrent and lagged effect IAV. The
regional masks are depicted in Fig. A1.
ΔNBE IAV ΔNBECON IAVΔNBELAG IAV(PgC yr-1)(as % of ΔNBE IAV)(as % of ΔNBE IAV)(Pearson's r)(Pearson's r)SH South America0.21107 % (0.81*)63 % (0.18)NH South America0.0861 % (0.16)105 % (0.83*)Southern Africa0.1483 % (0.10)122 % (0.76*)Northern sub-Saharan Africa0.1974 % (0.70*)71 % (0.68*)Australia0.1263 % (0.56*)84 % (0.78*)SE Asia and Indonesia0.1584 % (0.91*)41 % (0.54*)Wet tropics0.4279 % (0.89*)45 % (0.63*)Dry tropics0.2899 % (0.65*)83 % (0.43)Tropics0.6280 % (0.76*)64 % (0.61*)Concurrent and lagged effects on the tropical C balance
The attribution of annual ΔNBE into its concurrent and lagged
components (ΔNBECON and ΔNBELAG) reveals that both are prominent contributors to regional and pan-tropical ΔNBE (Fig. 6). On
a regional scale, ΔNBECON IAV and ΔNBELAG IAV during
2001–2015 amount to 61 %–107 % and 41 %–122 %, respectively, relative to
ΔNBE IAV (Table 3). Notable ΔNBECON anomalies include (i) the
positive ΔNBECON values in both South American regions during drier conditions in 2005, 2007 and 2010, in contrast with negative ΔNBECON responses during wetter conditions in 2009 and 2011, and (ii) negative ΔNBECON values during the relatively wet 2010–2011
conditions in Australia; both continental-scale responses corroborate the
generally hypothesized responses of tropical ecosystems to wet and dry
extreme events (Lewis et al., 2011; Bastos et al., 2013). For the most part,
both ΔNBECON and ΔNBELAG contribute substantially to the
year-to-year ΔNBE anomaly changes on a regional scale. Across
the wet tropics, the signs of the largest ΔNBE anomalies are predominantly explained by ΔNBECON; in contrast, dry tropics
ΔNBELAG IAV and ΔNBECON IAV both
substantially contribute to annual ΔNBE anomalies. Instances
where ΔNBELAG or ΔNBECON IAV values amount to
> 100 % of ΔNBE IAV are attributable to regional and
pan-tropical anti-correlations between ΔNBELAG and ΔNBECON: specifically, ΔNBELAG and ΔNBECON are
anticorrelated across the tropics (r=-0.05) and all regions except SE Asia and Indonesia (r=-0.56–0.14); the consistent anticorrelation
across five out of six regions suggests that lagged effects may
significantly and systematically dampen the impact of ΔNBECON. On a pan-tropical scale, we found that ΔNBECON IAV and
ΔNBELAG IAV are both substantial contributors to NBE IAV (80 %
and 64 %); the relative importance of ΔNBELAG IAV relative to
ΔNBECON is largest in the dry tropics (83 % and 99 %,
respectively) and remains substantial albeit smaller in the wet tropics (79 % and 45 %, respectively). Uncertainties in ΔNBE, ΔNBECON and
ΔNBELAG (Fig. 6) are generally linked to confounding NBE trend
uncertainties throughout 2001–2015 (Fig. 4), particularly on a pan-tropical scale, where NBE uncertainties are considerably larger than median NBE IAV. To directly assess the uncertainty of ΔNBELAG IAV contributions to
NBE IAV irrespective of annual NBE uncertainties, we (a) rank all
4∘×5∘ grid-cell CARDAMOM samples by their
corresponding 2001–2015 ΔNBELAG IAV and (b) combine CARDAMOM samples by ranking to generate a corresponding ensemble of regional and
pan-tropical ΔNBELAG IAV estimates (summarized in Table S5). We
find that the regional 95 % confidence ranges are all within 50 % of the
median ΔNBELAG IAV values reported in Table 3. Notably, the
ensemble of pan-tropical ΔNBELAG IAV estimates spans 42 %–97 % of NBEIAV (2.5th–97.5th percentile range), indicating that – even under overwhelmingly conservative assumptions about grid-cell ΔNBELAG IAV – lagged effects are invariably a prominent
component of tropical NBE IAV.
Variations in ΔNBELAG throughout 2001–2015 include a range of lagged processes spanning between (a) ΔNBELAG changes induced by
recent forcing events and (b) the gradual changes in ΔNBELAG attributable to an ecosystem's approach or oscillation around a domain of
attraction (see Sect. 2.1). Notably, even in the absence of a recent
forcing event, ΔNBELAG will potentially continue to change in
magnitude from year to year as ecosystem states approach or oscillate around
a domain of attraction. We conducted a sensitivity test for the Southern Hemisphere South America region (top-left panel of Fig. 6) to disentangle the range of contributions to 2001–2015 ΔNBELAG values:
specifically, we (a) resolve ΔNBELAG in the absence of 2001–2015
forcing anomalies and (b) sequentially add 2001–2015 forcing anomalies to resolve ΔNBELAG attributable to annual forcing events (Fig. S6).
In the absence of 2001–2015 forcing anomalies, lagged effects account for a
±0.11 PgC yr-1 variability in total NBE, explained by an approximately linear +0.02 PgC yr-1 increase throughout the 2001–2015 time period. The sequential addition of 2001–2015 forcing anomalies indicates the sign and
magnitude of lagged effects are substantially influenced by annual forcing
events; while the inter-annual variability modestly increased to ± 0.13 PgC yr-1, year-to-year changes exceed 0.3 PgC yr-1 (Fig. 6). Furthermore, while most years induced relatively short-lived (1–2-year) contributions to subsequent ΔNBELAG values, 2007 and 2010 – both notably dry
years – induced more long-lasting impacts on 2010–2015 ΔNBELAG (Fig. S6). Given the combined importance of short- and long-lived impacts of forcing anomalies on lagged effects, we highlight the need to
further investigate the relative contributions and potential interactions
between single-event lagged effects (e.g. lagged effects attributable to a
single forcing anomaly), their longevity, and their net contribution to
ΔNBELAG and ΔNBE IAV.
The decomposition of ΔNBECON into constituent fluxes – namely net
primary productivity (ΔNPPCON), heterotrophic respiration (ΔRHECON) and fires (ΔFIRCON) – reveals that ΔNPPCON is the largest contributor to ΔNBECON IAV (Fig. 7;
Table 4), while ΔFIRCON and ΔNPPCON are comparable
contributors to ΔNBECON in Australia. In Northern Hemisphere South America and South-East Asia and Indonesia, ΔRHECON variability is a smaller but substantial contributor to ΔNBECON, indicating that
the integrated impacts of meteorological and disturbance forcing IAV on
respiration are comparable to those on photosynthetic uptake. In Australia,
the concurrent impact of fires on ΔNBECON is comparable to ΔNPPCON (Table 4). Similarly, the decomposition of ΔNBELAG into
constituent fluxes (ΔNPPLAG, ΔRHELAG and ΔFIRLAG) reveals that ΔNBELAG is ubiquitously dominated by ΔNPPLAG variability, followed by modest contributions from
ΔRHELAG variability and minimal contributions by ΔFIRLAG variability (see Table 4). The prominence of ΔNPPLAG is attributable to faster continental-scale response of C uptake
following year-to-year variations in initial C and H2O states (relative
to ΔRHELAG), indicating that live biomass dynamics (rather than
dead organic C states) dominate initial ecosystem responses to external
forcing anomalies. The relatively small contribution of ΔFIRLAG values to ΔNBELAG indicates that the magnitude of fires is, to first order, dominated by variability in the forcing rather than
variability in fuel load within fire-prone ecosystems.
Concurrent and lagged effect NBE attributed to constituent fluxes (net
primary production, heterotrophic respiration and fires, abbreviated as
NPP, RHE and FIR, respectively): IAV values are represented here as the ratio of constituent flux standard deviation to NBE standard deviations of annual
2001–2015 NBE values; bracketed values correspond to Pearson's correlation coefficients between constituent flux and NBE (“*” denotes p values < 0.05). The underlined values denote the largest % IAV
contribution to ΔNBECON and ΔNBELAG.
Regional and pan-tropical median annual net primary productivity
(left column), heterotrophic respiration (centre column) and fire (right column) anomalies (ΔNPP, ΔRHE and ΔFIR, respectively). Blue bars represent total anomalies and green and orange bars represent the corresponding annual concurrent and lagged effects. ΔNPP anomaly signs were reversed such that all anomalies are represented as
positive for net land-to-atmosphere C flux. The sum of annual ΔNPP,
ΔRHE and ΔFIR is equivalent to annual ΔNBE values presented in Fig. 6. Error bars denote the 25th–75th
percentile uncertainty estimates for each flux anomaly.
We find that variability in foliar C, plant-available H2O and soil C
contributes to the majority of regional and pan-tropical ΔNBELAG variability (Fig. 8). For example, both the enhanced foliar C
and plant-available H2O in 2011 over the Australian continent (relative
to 2010) – attributable to a combination of reduced fires and increased
productivity due to anomalously wet 2010 conditions over the Australian
continent (Fig. S3) – each contributed to a 0.1 PgC yr-1 net uptake increase (i.e. NBE reduction) relative to 2010. Similarly, we found that reduced
foliar C in Southern Hemisphere South America following dry conditions in 2005, 2007 and 2010 induced a 0.1 PgC yr-1 NBE response in 2006, 2008 and 2011,
respectively. We find that the sum of all the pool-specific ΔNBELAG anomalies approximately adds up to ΔNBELAG (Fig. S3), indicating that – insofar as these are represented in DALEC2a – ΔNBELAG is (a) to first order equivalent to the sum of NBELAG sensitivities to individual initial states and that (b) cross-pool interactions (“I” in Eq. 22) are a secondary component of ΔNBELAG. In
aggregate, we find that foliar C variability contributes 41 %–120 % of ΔNBELAG variability across all regions and 58 % of the
pan-tropical ΔNBELAG. Northern Hemisphere sub-Saharan Africa and South-East Asia and Indonesia are the only regions where inter-annual
variations in soil C and plant-available H2O (respectively) contribute
more variability than foliar C (Table 5). Notably, our results indicate that under a climatological mean forcing, (a) year-to-year changes in foliar
C and plant-available H2O initial conditions are sufficient to induce
substantial year-to-year changes in C uptake and (b) year-to-year changes in soil C are sufficient to substantially influence total heterotrophic
respiration rates; we find that the remaining states (labile C, wood C, fine
root C and litter C) explain < 0.2 PgC yr-1 variability of ΔNBELAG across all regions. We also find that the sum of regional foliar C and plant-available H2O impacts on ΔNBELAG (Fig. 8) are
approximately equivalent to ΔNPPLAG (Fig. 7); in turn, the
considerable contributions of both ΔNPPLAG and ΔNPPCON across tropical ecosystems indicate that both climatic variability and initial ecosystem states are substantial contributors to
tropical ΔNPP IAV. Inter-annual variations of foliar C, soil C and
plant-available H2O states exhibit substantial correlations with their corresponding ΔNBELAG components (Fig. S5): regional
correlations are negative for foliar C (r=-0.6 to -1.0) and
plant-available H2O (r=-0.7 to -0.2) and positive for soil C (r=0.6–1.0). We note that the general agreement between regional
2001–2015 foliar C IAV (1.1 %–4.0 %), CARDAMOM LAI IAV (1.6 %–4.8 %)
and MODIS LAI IAV(0.7 %–5.2 %) corroborates the estimated impact of
CARDAMOM C foliar dynamics on ΔNBELAG. In contrast to foliar C and
plant-available H2O, soil C impacts on ΔNBELAG are
predominantly induced by long-term soil C trends rather than year-to-year variability. Soil C regional trend signs (Fig. 7) are generally opposite
to mean 2001–2015 NBE signs within each region (Fig. 5), indicating that
the observed regional C imbalances are substantially mediated by 2001–2015
soil C trends.
IAV of 2001–2015 regional and pan-tropical NBE lagged effects
attributable to annual anomalies in column-denoted ecosystem states (Eq. 22) as % of total NBE lagged effects (ΔNBELAG) IAV; bracketed values correspond to Pearson's correlation coefficients between single-state
NBE lagged effects and total ΔNBELAG; “*” denotes
p values < 0.05. The underlined values denote the maximum contribution in each region.
Attribution of 2001–2015 annual regional and pan-tropical NBE
lagged effect estimates (ΔNBELAG) to individual ecosystem state
anomalies (i.e. the lagged effect in year a solely attributable to anomaly in
ecosystem state n, ΔNBEa(n)LAG; see Eq. 22). In addition to foliar C (green circles), soil C (dark pink triangles), and plant-available H2O (blue squares), the grey areas (labelled as
“Other” in the figure legend) denote the collective range of ΔNBELAG anomalies attributable to labile, wood, root and litter C.
Percentage values indicate the inter-annual variability (reported as
standard deviation) of median foliar C, soil C and plant-available H2O
states throughout the 2001–2015 period, relative to mean 2001–2015 values
within each region. The sum of annual state-specific ΔNBELAG
values is approximately equal to the ΔNBELAG (see Fig. S4).
Error bars denote the 25th–75th percentile uncertainty
estimates for each flux anomaly.
Overall, our results indicate that (i) ΔNBELAG IAV is a
prominent component of NBE IAV across tropical ecosystems; (ii) ΔNBELAG IAV is largely mediated by changes in ecosystem NPP
capacity (ΔNPPLAG IAV); and (iii) ΔNPPLAG variability is
regulated by inter-annual variations in ecosystem canopy and plant-available
H2O states. In other words, our results highlight that inter-annual
changes in ΔNBE – regardless of external forcing anomalies – are
substantially determined by inter-annual anomalies in ecosystem H2O and
canopy states. Lagged heterotrophic respiration responses (ΔRHELAG) are mediated by soil C states changes and are secondary component
of NBE IAV; the dampened role of ΔRHELAG (relative to ΔNPPLAG) is likely due to the inherent lags between biomass growth and
subsequent mortality inputs to soil C states, combined with ∼ 5–50-year mean dead organic C residence times across tropical ecosystems (Bloom et al., 2016). The relative importance of NPP-mediated lagged effects
in responses to climatic anomalies has also been inferred on from in situ and continental-scale measurements (Sherry et al., 2008; Detmers et al.,
2015; Wolf et al., 2016). Our findings also suggest that tracking the
long-term evolution of tropical ecosystem canopy cover (Saatchi et al.,
2013; Shi et al., 2017) and reducing the process-level uncertainties
associated with foliar C dynamics relationships to meteorological and
disturbance forcings (discussed in Sect. 3.3) are potentially critical for
advancing process-level understanding of tropical NBE IAV. We anticipate
that continued monitoring of NBE (e.g. following the 2015–2016 ENSO event) and subsequent attribution to concurrent and lagged effects will also be
critical to better quantify the longevity NPP recovery (e.g. Schwalm et al.,
2017) and to improve confidence in characterizing concurrent and lagged NPP
impacts on the tropical C balance. Finally, while our analysis is focused on
the ΔNBELAG sensitivity to year-to-year ecosystem state changes, we note that the magnitude of ΔNBECON is also in principle
dependent on time-varying ecosystem states (Fig. 1); we recognize that
further investigation on whether ΔNBECON IAV is (a) predominantly
sensitive to forcing anomalies, or (b) sensitive to year-to-year ecosystem
state changes, could amount to a critical step towards accurately
characterizing the climate sensitivity of ΔNBE.
Observation and model uncertainty caveats
The prescribed observation uncertainty characteristics (Table 1) are
potentially a critical source of error in the data-informed representation
of terrestrial C cycle dynamics and its subsequent partitioning into
concurrent and lagged effects. For example, relative differences in the mean
NBE values retrieved from aircraft and satellite CO2 measurements over
the Amazon Basin (Alden et al., 2016; Bowman et al., 2017) highlight the need
to determine the sensitivity of our results to top-down estimates of NBE.
While the uncertainty structures of top-down CO2 inversion estimates are beyond the scope of our paper, we recognize the need to robustly assess and
characterize uncertainties in seasonal and inter-annual variations in NBE.
Potential limitations in the linear SIF : GPP assumption include (i) systematic underestimations of afternoon GPP stress, given that the GOSAT
overpass time is ∼ 1 pm, and (ii) uncharacterized biases
emerging from non-linear SIF : GPP under extreme conditions (Verma et al.,
2017). We highlight that recent efforts to merge multiple SIF datasets
(Zhang et al., 2018) and process-based representations of SIF : GPP (Bacour et al., 2019) can together be used to improve the accuracy of SIF : GPP
representation in CARDAMOM. We also note that the CARDAMOM likelihood
function (Eq. 3) fundamentally assumes all errors are independent; however,
commonalities in the derived datasets – such as systematic representation
errors across all datasets and transport errors in the GEOS-Chem-derived CO2 and CO emissions – may lead to unrepresented error correlations in
the likelihood functions.
We generally acknowledge that more elaborate approaches and a more
comprehensive treatment of model and data error characteristics are
necessary to understand the contribution of individual data stream error (Keenan et al., 2011; Heald et al., 2004; MacBean et al., 2016, 2018).
Specifically, the explicit and accurate representation of model structural
error is critical for both accurate retrievals of physical parameters and
accurate model predictions (Brynjarsdottir and O'Hagan, 2014) and solving
for error model parameters (Schoups and Vrugt, 2010; Xu et al., 2017) is
potentially advantageous for physical parameter retrievals and prediction
purposes. For example, we note that without an error model structure we
cannot explicitly account for cross-correlations in the errors between observations or the impacts of heteroscedasticity (Schoups and Vrugt,
2010). While the identification and optimization of an appropriate
structural error model are beyond the scope of this paper, we highlight that this as an important priority for future CARDAMOM analyses.
Unrepresented processes DALEC2a model structure – particularly processes
that are potentially substantial contributors to ΔNBECON and
ΔNBELAG – amount to an additional source of uncertainty in our
analysis. Potentially critical processes include time-varying autotrophic
respiration (Rowland et al., 2014), plant C allocation and plant mortality,
as well as explicit representation of coarse woody debris (Smallman et al.,
2017). In particular, given that our results suggest that foliar C is a
major contributor to ΔNBE, unrepresented processes relating to tropical
leaf phenology may substantially impact the accuracy of lagged effect
attribution, including phenological processes regulating leaf onset, leaf
lifespan and litterfall seasonality (Chave et al., 2010; Caldararu et al.,
2012; Xu et al., 2016), as well as the time-varying allocation regimes
(Doughty et al., 2015). Furthermore, while the DALEC2a phenology assumes a
time-invariant ratio between LAI and foliar C (i.e. a time-invariant
ecosystem-level leaf carbon mass per area), the joint roles of leaf
demographics and species distribution on the temporal variability of leaf
carbon mass per area could potentially amount to a significant impact on
photosynthetic capacity, and subsequently on the variability of ΔNBECON and ΔNBELAG. We also highlight year-to-year changes in
species composition (such as C3 : C4 plants) and the temporal
dynamics of vegetation and soil nutrients as potential contributors to
ΔNBELAG (Sherry et al., 2008; Schimel et al., 1997) are
potentially unrepresented but critical processes, particularly in fire-prone
regions (Pellegrini et al., 2018) and nutrient-limited tropical forest
ecosystems (Wieder et al., 2015). A potential limitation in CARDAMOM ET
estimates is the assumed inherent water-use efficiency relationship between
GPP, ET and VPD (Eq. B4); recent efforts (Zhou et al., 2015; Boese et al.,
2017) advocate for improved parameterizations for semi-empirical GPP : ET
relationships, which could ultimately impact the sign and magnitude of
inter-annual CARDAMOM ET variations – and the associated plant-available
H2O balance – across tropical ecosystems. Finally, we highlight the
need to investigate the sensitivity of our results to the 2001–2015
climatological mean forcing: while to first order the diagnosis of lagged
effect anomalies from the mean (rather than absolute values) are insensitive
to the reference forcing, further efforts are required to determine whether
non-linear impacts of an alternative reference forcing (e.g. a
climatological mean forcing based on a 30-year climate normal) may amplify
or dampen ΔNBELAG IAV estimates.
Our continental-scale results indicate that DALEC2a model complexity is
adequate to both represent NBE variability and accurately predict NBE
outside the training window on a pan-tropical scale (2015), which provides a
first-order assessment of the adequacy of the DALEC2a model structure. A
notable exception is the substantial underestimation of CARDAMOM 2015 NBE
within the Northern Hemisphere South America region (Fig. 5); given the considerable impact of the 2015 ENSO event within the region (Liu et al.,
2017), the biased CARDAMOM NBE prediction suggests that either (a) the
DALEC2a model structure cannot adequately represent NBE responses to
climatic extremes or (b) the 2010–2013 NBE observational constrains are insufficient to accurately inform the regional DALEC2a states and process
parameters. To determine the relative impact of model error, we anticipate
that additional insights could be obtained by retrieving ΔNBECON and ΔNBELAG based on alternative DALEC model structures
(Fox et al., 2009; Smallman et al., 2017). The implementation of DALEC2a
assimilation and prediction evaluation across long-term records eddy
covariance CO2 and H2O fluxes would amount to a useful evaluation
of the model structure constrained by multiple data streams (e.g. following
Richardson et al., 2010; Keenan et al., 2013; Smallman et al., 2017), and
the potential sensitivities of ΔNBECON and ΔNBELAG to underlying model structures. While there are currently few tropical
ecosystem sites where multi-year NBE constraints are available, we highlight
that the analysis of ΔNBECON and ΔNBELAG at eddy
covariance sites would also benefit from the relative wealth of ancillary
site-level repeat measurements of C and H2O states and fluxes, and
would ultimately allow more in-depth evaluation and hypothesis tests on
lagged effect processes and their role on ΔNBE dynamics. Finally, to
diagnose the potential role of higher-order process interactions on lagged
and concurrent effects – such as nutrient limitations, ecosystem demography
and explicit representations of carbon–water–energy interactions – we highlight that the ΔNBECON and ΔNBELAG attribution
methodology introduced here can in principle be applied using higher
complexity terrestrial biosphere models (e.g. Huntzinger et al., 2013, 2017;
Macbean et al., 2018; Longo et al., 2019).
Conclusions
The prominent role of ΔNBELAG across the tropics throughout
2001–2015 supports our second hypothesis (Sect. 2.5), namely that
concurrent and lagged effect variations are comparable on inter-annual
timescales. By constraining a diagnostic ecosystem C balance model with an
array of terrestrial C cycle observations (LAI, biomass, soil C, SIF,
CO-derived fire C emissions and CO2-derived NBE), we show that on annual
timescales both ΔNBECON and ΔNBELAG effects are
substantial contributors to the 2001–2015 tropical C balance. The IAV of
ΔNBECON is largely accounted for by NPP, with sizeable fire
contributions from Australia, South-East Asia, Indonesia and South America and heterotrophic respiration contributions from wet tropical ecosystems. ΔNBELAG variability is overwhelmingly dominated by the
impact of inter-annual variations in lagged NPP effects, followed by a
modest contribution from the state dependence of heterotrophic respiration. In aggregate, anomalies in foliar C, plant-available H2O, and soil C
were identified as the primary influences on ΔNBELAG variability.
Our findings therefore highlight a critical need to explicitly account for
lagged effects when investigating the process-level tropical NBE responses
to climatic variability on inter-annual timescales. Furthermore, our
findings highlight the need to accurately and continuously resolve NBE at
sub-continental scales in order to advance our mechanistic and process-level
understanding of terrestrial C cycling and its evolving sensitivity to
climate.
Regional definitions
Regional masks used in this study. The 1500 mm yr-1 precipitation thresholds were based on the ERA-Interim mean annual precipitation rates throughout the 2001–2015 study period.
Model description
The following sections provide a summary of the process parameterizations
introduced in the DALEC version implemented in the Bloom et al. (2016)
study. For completeness, a full description of DALEC2a is provided in the
paper's Supplement.
DALEC2a water balance and GPP water stress
The DALEC2a plant-available water balance at time step t+1 is derived as
Wt+1=Wt+Pt-Rt-ETtΔt,
where W denotes total plant-available H2O (in mm H2O storage equivalent) and P, R and ET precipitation, runoff and evapotranspiration fluxes
(mm d-1) over the time period Δt (d). We note that this equation represents a water balance in the dynamic plant-available H2O pool and does not include deep groundwater, confined aquifers or other
unconnected/static storages. Following a generalized non-linear reservoir
formulation, we parameterize monthly runoff losses as a second-order decay
function with respect to storage, Wt, as
Rt=αWt2,
where α is a second-order decay constant (mm-1 d-1). The dependence of runoff on W2 – instead of W – ensures that the
fractional rate of plant-available H2O loss is proportional to W;
relative to a first-order linear kinetics model, this provides a better
representation of faster relative plant-available H2O depletion
following high precipitation events, followed by slower losses during lower
precipitation time spans (e.g. Matteucci et al., 2015) and serves a functional approximation of both storage-excess and infiltration-excess runoff generation mechanisms in most cases. Following previous results from
land surface model development experiments (e.g. Liang et al., 1994;
Lawrence et al., 2011), we assume that net runoff inputs from adjacent
pixels are a negligible term in the lumped grid-scale H2O budget at
4∘×5∘ spatial resolution. By construction,
Rt values predicted at Wt>1aΔt are unphysically
high (Wt-RtΔt<0), while loss rates at
Wt>12aΔt produce implausibly low residual storage
(Wt-RtΔt) values. Therefore, in the eventuality of
Wt>12aΔt, we calculate runoff as
Rt=Wt-12aΔt, effectively representing a storage-excess overflow mechanism by introducing a transition between a state-dependent
regime to a direct runoff regime.
We apply a linear scaling on GPP with respect to the plant-available
H2O, where
GPPt=GPPmax(t)max1,Wtω,
where ω represents the plant-available H2O stress threshold;
Eq. (B3) effectively imposes a stress factor on GPP spanning between 0 and 1,
and offers a simplified representation of the integrated effects of
leaf–soil H2O potential differences and their impact on canopy conductance. Evapotranspiration at time t is derived as
ETt=GPPtVPDtυe,
where υe is the inherent water-use efficiency (Beer et al.,
2009) and VPD is the vapour pressure deficit derived from ERA-Interim monthly reanalysis datasets. Equations (B1)–(B4) amount to a plant–water feedback parameterization, and together represent a reduced complexity version of the
DALEC water module implemented by Spadavecchia et al. (2011). All
parameters involved in the above-mentioned parameterization – namely α, υe, ω and W0 – are optimized along with other
DALEC2a parameters in CARDAMOM; the prior ranges are described in Table S1.
Heterotrophic respiration
We parameterize the meteorological dependence of heterotrophic respiration ρ at time t as follows:
ρt=eΘ(Tt-T‾)PtP‾-1sp+1,
where T and P represent the monthly temperature and precipitation vectors. We
chose to use P as a driver for heterotrophic respiration sensitivity to
moisture, given that (a) the majority of heterotrophic respiration is
expected to occur in the near-surface soil layer, and (b) near-surface soil
moisture strongly covaries with P – rather than water storage – at monthly
timescales. Previous versions of DALEC solely parameterized ρt as a
function of temperature (e.g. Bloom et al., 2016 and references therein);
effectively, the formulation in Eq. (B5) induces a joint sensitivity to
relative changes in both temperature and near-surface moisture. The prior
ranges for the respiration temperature and precipitation sensitivity
parameters (Θ and sp) are reported in Table S1.
Sensitivity of lagged effects to individual ecosystem states
In the DALEC2a representation of the ecosystem C balance, the state vector
xa consists of the C and H2O pool values at the start of
year a. To diagnose the sensitivity of 2010–2015 lagged effects to the variability of ecosystem states, we conduct a sensitivity analysis to
explicitly quantify the impact of individual ecosystem state
anomalies – relative to their 2010–2015 mean values – on the variability of
δxLAG throughout 2010–2015. To do this, we define the
anomaly of the nth individual state in year a as the sum of finite differences
relative to the mean state:
xa=x‾+∑n=1N[xan-x‾],
where x‾ is an N-element vector of the mean 2010–2015 states; N is the
number of model state variables; xa(n) is an N-element vector
of ecosystem states, where for the ith element xani=xa(i) for i=n, and
xani=x‾(i) for i≠n. Based on Eqs. (11) and
(14), we can derive the state change under a climatological mean forcing of
each term in Eq. (C1), and therefore
δxaLAG=δx‾LAG+∑n=1NδxanLAG-δx‾LAG+Ia.Ia collectively accounts for the unaccounted contribution of higher-order
interactions between individual pool anomalies [xan-x‾] on δxaLAG. As outlined in Sect. 2.5, the “δx” terms in Eq. (C2) can be mapped
onto any DALEC2a flux variable; specifically, NBEaLAG can be defined as the sum of lagged effect NBE components attributable to δxanLAG and δx‾LAG as follows:
NBEaLAG=NBE‾LAG+∑n=1NNBEa(n)LAG-NBE‾LAG+Ia.NBE‾LAG and NBE‾a(n)LAG can be directly calculated from
D(x‾,M′,p) and D(xan,Ma,p), respectively. More succinctly, we
summarize Eq. (B3) as
NBEaLAG=NBE‾LAG+∑n=1NδNBEanLAG+Ia,
where δNBEa(n)LAG represents the lagged effect anomaly
attributable solely to the initial condition anomaly in ecosystem state n. By
applying the “Δ” operator (Eq. 21) on Eq. (C3), Eq. (C4) can
alternatively be expressed as
ΔNBEaLAG=∑n=1NΔNBEanLAG+ΔIa.
Effectively, the lagged effect partitioning formulation outlined in Eq. (C5)
allows us to quantitatively diagnose the NBE lagged effect dependence on the
inter-annual dynamics of individual C and H2O states depicted in Fig. 2.
Data availability
ECMWF re-analysis datasets were obtained from https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim (Berrinsford et al., 2011). Burned area was
obtained from https://globalfiredata.org/pages/data/ (Giglio et al., 2013). MODIS LAI data were obtained from
https://e4ftl01.cr.usgs.gov/MOLT/ (Myneni et al., 2015). CMS-Flux datasets are available at
cmsflux.jpl.nasa.gov. Biomass is available from Sassan Saatchi
(sasan.s.saatchi@jpl.nasa.gov) upon reasonable request. The HWSD soil
data was obtained from https://esdac.jrc.ec.europa.eu/content/global-soil-organic-carbon-estimates (Hiederer and Kochy, 2012). Gridded GOSAT fluorescence datasets
used in this analysis are available from Nicholas Parazoo
(nicholas.c.parazoo@jpl.nasa.gov) upon reasonable request. Biomass burning
CO fluxes data was obtained from https://dashrepo.ucar.edu/dataset/CO_Flux_Inversion_Attribution.html (Bloom et al., 2019). FLUXCOM datasets were obtained from https://www.bgc-jena.mpg.de/geodb/ (Jung 2018, Jung 2020). FLUXSAT data were obtained from https://avdc.gsfc.nasa.gov/pub/tmp/FluxSat_GPP/ (Joiner et al., 2018). MODIS ET data are available from http://files.ntsg.umt.edu/data/NTSG_Products/MOD16/ (Running, 2020). The NOAA ESRL dataset was obtained from https://www.esrl.noaa.gov/gmd/ccgg/trends/ (Dlugokencky and Tans, 2020). The CARDAMOM
results presented throughout the paper are available upon request.
The supplement related to this article is available online at: https://doi.org/10.5194/bg-17-6393-2020-supplement.
Author contributions
AAB, KWB, JL, AGK, and DSS designed the research, AAB conducted the analysis, and all the co-authors extensively contributed to evaluation of results and writing of
the manuscript.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Part of this work was carried out at the Jet Propulsion Laboratory,
California Institute of Technology, under a contract with the National
Aeronautics and Space Administration (NASA). Part of this study was funded as a
component of NERC's support of the National Centre for Earth Observation.
SSS and AGK were also supported by NASA through the Earth Science Program. We are thankful for feedback from Michael Keller, Paul Levine, Marcos Longo, Shuang Ma and Alexander Norton. The NCAR MOPITT project is supported by the National Aeronautics
and Space Administration (NASA) Earth Observing System (EOS) Program. The
MOPITT team is grateful for the contributions of COMDEV and ABB BOMEM with support from the Canadian Space Agency (CSA), the Natural Sciences and
Engineering Research Council (NSERC) and Environment Canada.
Financial support
This research was supported by a NASA Earth Sciences grant (no. NNH16ZDA001N-IDS).
Review statement
This paper was edited by Andreas Ibrom and reviewed by two anonymous referees.
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