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.

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.

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 1xt+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.

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.

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).

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 2py|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 3L(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: 4L∗=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: 7LNBE=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.

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 10xa+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 11x′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 12Ma=M′+δMa.

With Eqs. (10) and (11), we can define the change in the state x in year a, δxa, as 13δxa=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 14δxaLAG=x′a+1-xa, the concurrent effect on ecosystem states in year a as 15δxaCON=xa+1-x′a+1, and the sum of concurrent and lagged effects in Eqs. (14) and (15) as 16δxa=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).

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).

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 17NBEa=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 18NBEa=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, 21ΔFa=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 22ΔNBEaLAG=∑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.

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.

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).

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).

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.

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.

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.

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.

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).