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Reported SARS-CoV-2 case counts, mortality and testing in SSA as of December 2020
Variables and data sources for reporting data
The numbers of reported cases, deaths and tests for the 48 SSA countries studied (Supplementary Table 1) were sourced from the Africa CDC dashboard on 20 December 2020 (and previously on 23 September and 30 June 2020). The Africa CDC obtains data from the official Africa CDC Regional Collaborating Centre and member state reports. Differences in the timing of reporting by member states results in some variation in the recency of data within the centralized Africa CDC repository, but data should broadly reflect the relative scale of testing and reporting efforts across countries. For Mauritius (https://covid19.mu/) and Rwanda (https://covid19.who.int/region/afro/country/rw), reporting to the Africa CDC was confirmed by comparison to country-specific dashboards.
The countries or member states within SSA in this study follow the United Nations and Africa CDC-listed regions of Southern, Western, Central and Eastern Africa (excluding Sudan). From the Northern Africa region, Mauritania is included in SSA.
For comparison to non-SSA countries, the number of reported cases in other geographical regions were obtained from the Johns Hopkins University Coronavirus Resource Center on 23 September 2020 (https://coronavirus.jhu.edu/map.html).
Case fatality ratios (CFRs) were calculated by dividing the number of reported deaths by the number of reported cases and expressed as a percentage. Positivity was calculated by dividing the number of reported cases by the number of reported tests. Testing and case rates were calculated per 100,000 population using population size estimates for 2020 from the United Nations Population Division (https://population.un.org/wpp/Download/Standard/Population/). Since reported confirmed cases are likely to be an underestimate of the true number of infections, CFRs may be a poor proxy for the IFR, defined as the proportion of infections that result in mortality4.
Variation in testing and mortality rates
Testing rates among SSA countries varied by multiple orders of magnitude as of 30 June and remain highly variable as of 23 September and 20 December 2020. The number of tests completed per 100,000 population ranged from 19.84 in Burundi to 13,508.13 in Mauritius in June 2020; from 65.98 in the Democratic Republic of the Congo to 18,321.83 in Mauritius in September 2020; and from 100.9 in the Democratic Republic of the Congo to 23695.0 in Mauritius in December 2020 (Extended Data Fig. 1a). Tanzania (6.50 tests per 100,000 population) has not reported new tests, cases or deaths to the Africa CDC since April 2020. The number of reported infections (that is, positive tests) was strongly correlated with the number of tests completed in June 2020 (Pearson’s correlation coefficient, r = 0.9667, P 50% coincident with population >50,000) within administrative 2 units61. For some countries, estimates at administrative 2 units were unavailable (Comoros, Cape Verde, Lesotho, Mauritius, Mayotte and Seychelles); estimates at the administrative-1 unit level were used for these cases (these were all island nations, with the exception of Lesotho).
Metapopulation model methods
Once SARS-CoV-2 has been introduced into a country, the degree of spread of the infection within the country is governed by subnational mobility: the pathogen is more likely to be introduced into a location where individuals arrive more frequently than one where incoming travelers are less frequent. Large-scale consistent measures of mobility are rare. However, recently, estimates of accessibility have been produced at a global scale26. Although this is unlikely to perfectly reflect mobility within countries, especially since interventions and travel restrictions are put in place, it provides a starting point for evaluating the role of human mobility in shaping the outbreak pace across SSA. We used the inverse of a measure of the cost of travel between the centroids of administrative level 2 spatial units to describe mobility between locations (estimated by applying the costDistance function in the gdistance package v1.3-6 in R to the friction surfaces supplied in Weiss et al.26). With this, we developed a metapopulation model for each country to develop an overview of the possible range of trajectories of unchecked spread of SARS-CoV-2.
We assumed that the pathogen first arrives in each country in the administrative 2 level unit with the largest population (for example, the largest city) and the population in each administrative 2 level (of size Nj) is entirely susceptible at the time of arrival. We then tracked the spread within and between each of the administrative 2 level units of each country. Within each administrative 2 level unit, dynamics are governed by a discrete time susceptible (S), infected (I) and recovered (R) model with a time step of approximately one week, which is broadly consistent with the serial interval of SARS-CoV-2. Within the spatial unit indexed j, with total size Nj, the number of infected individuals in the next time step is defined by:

$$I_{j,t + 1} = beta I_{j,t}^alpha S_{j,t}/N_j + iota _{j,t}$$

where β captures the magnitude of transmission over the course of one discrete time step; since the discrete time step chosen is set to approximate the serial interval of the virus, this will reflect the R0 of SARS-CoV-2, and is thus set to 2.5; the exponent α = 0.97 is used to capture the effects of discretization62 and Ij,t captures the introduction of new infections into site j at time t. Susceptible and recovered individuals are updated according to:

$$begin{array}{l}S_{j,t + 1} = S_{j,t} + wR_{j,t} – I_{j,t + 1} + b\ R_{j,t + 1} = (1 – w)R_{j,t} + I_{j,t}end{array}$$

where b reflects the introduction of new susceptible individuals resulting from the birth rate, set to reflect the most recent estimates for that country from the World Bank Data (https://data.worldbank.org/indicator/SP.DYN.CBRT.IN), and w reflects the rate of waning of immunity. The population is initiated with Sj,1 = NjRj,1 = 0, and Ij,1 = 0 except for the spatial unit corresponding to the largest population size Nj for each country since this is assumed to be the location of introduction; for this spatial unit, we set Ij,1 = 1.
We made the simplifying assumption that mobility linking locations i and j, denoted as ci,j, scales with the inverse of the cost of travel between sites i and j evaluated according to the friction surface provided in Weiss et al.26. The introduction of an infected individual into location j is then defined by a draw from a Bernouilli distribution following:

$$iota _{j,t} approx {mathrm{Bernouilli}}left( {1 – {mathrm{exp}}left( { – mathop {sum }limits_1^L {c_{i,j}}{I_{i,t}}/{N_i}} right)} right)$$

where L is the total number of administrative 2 units in that country and the rate of introduction is the product of connectivity between the focal location and each other location multiplied by the proportion of population in each other location that is infected.
Some countries show rapid spread between administrative units within the country (for example, a country with parameters that broadly reflect those available for Malawi; Extended Data Fig. 7), while in others (for example, reflecting Madagascar), connectivity may be so low that the outbreak may be over in the administrative unit of the largest size (where it was introduced) before introductions successfully reach other poorly connected administrative units. Where duration of immunity is sufficiently long, the result may be a hump-shaped relationship between the proportion of the population that is infected after five years and the time to the first local extinction of the pathogen (Extended Data Fig. 7, top right). In countries with lower connectivity (for example, resembling Madagascar), local outbreaks can go extinct rapidly before traveling very far; in other countries (for example, resembling Gabon), the pathogen goes extinct rapidly because it travels rapidly and rapidly depletes susceptible individuals everywhere. The U-shaped pattern diminishes as the rate of waning of immunity increases and is replaced by a monotonic negative relationship. With sufficiently rapid waning of immunity, local extinction ceases to occur in the absence of control efforts.
The impact of the pattern of travel between centroids is echoed by the pattern of travel within administrative districts: countries where the pathogen does not reach a large fraction of the administrative 2 units within the country in five years are also those where within-administrative-unit travel is low (Extended Data Fig. 7, right).
These simulations provide a window into qualitative patterns expected for subnational spread of the pandemic virus but there is no clear way of calibrating the absolute rate of travel between regions of relevance for SARS-CoV-2; this is further complicated by the remaining uncertainties around rates of waning of immunity. Thus, the time scales of these simulations should be considered in relative, rather than absolute terms. Variation in lockdown effectiveness, or other changes in mobility for a given country, may also compromise relative comparisons as might large volumes of land border crossings in some settings, which we have not accounted for in this study. Variability in testing and case reporting complicates clarifying this (Extended Data Fig. 7, bottom left and bottom right, respectively) but we have highlighted countries with less connectivity (that is, less synchronous outbreaks expected) relative to the median among SSA countries and with older populations (that is, a greater proportion in higher-risk age groups) (Extended Data Fig. 8).
The University of Oxford’s Blavatnik School of Government generated composite scores of government response, interventions for containment and economic support provided, with each scored from 0 to 100 (Coronavirus Government Response Tracker; https://www.bsg.ox.ac.uk/research/research-projects/coronavirus-government-response-tracker). These data were compared with the day on which ten cases were exceeded in a country according to the Johns Hopkins dashboard data (Johns Hopkins Coronavirus Resource Center; https://coronavirus.jhu.edu/map.html).
While faster waning of immunity will act to increase the rate of spread of the infection, resulting in a higher proportion infected after one year, control efforts will generally act to slow the rate of spread of the infection (Extended Data Fig. 9). Since different countries are likely to have differently effective control efforts (Extended Data Fig. 9), this precludes making country-specific predictions as to the relative impact of control efforts on delay.
Modeling epidemic trajectories in scenarios where transmission rate depends on climate
Climate data sourcing: variation in humidity in SSA
Specific humidity data for selected urban centers comes from the ERA5 using an average climatology (1981–2017)53; we did not consider year-to-year climate variations. Selected cities (n = 56) were chosen to represent the major urban areas in SSA. The largest city in each SSA country was included as well as any additional cities that were among the 25 largest cities or busiest airports in SSA.
Methods for climate-driven modeling of SARS-CoV-2
We used a climate-driven susceptible-infected-recovered-susceptible model to estimate epidemic trajectories (that is, the time of peak incidence) in different cities in 2020, assuming no control measures were in place or a 10 or 20% reduction in R0 beginning 2 weeks after the total reported cases for a country exceeded 10 cases25,63. The model is given by:

$$frac{{mathrm{d}}S}{{mathrm{d}}t} = frac{{N – S – L}}{L} – frac{{beta (t)IS}}{N}$$

$$frac{{mathrm{d}}I}{{mathrm{d}}t} = frac{{beta (t)IS}}{N} – frac{I}{D}$$

where S is the susceptible population, I is the infected population and N is the total population. D is the mean infectious period, set at 5 d following ref. 25.
To investigate the effects on epidemic trajectories of a climate dependency of SARS-CoV-2 on cities with the climate patterns of the selected cities in SSA, we used parameters from the most climate-dependent scenario in ref. 25, based on the endemic betacoronavirus HKU1 in the United States. In this scenario L, the duration of immunity, was 66.25 weeks (that is, >1 year and such that waning immunity did not affect the timing of the epidemic peak). We initially selected a range where R0 declined from R0max = 2.5 to R0min = 1.5 (that is, transmission declined 40% at high humidity) since this exceeds the range observed for influenza and other coronaviruses for which data are available (from the United States). R0max = 2.5 was chosen because 2.5 is often cited as the approximate R0 for SARS-CoV-2. Thus, we initially assumed that the climate dependence of SARS-CoV-2 in SSA would not greatly exceed that of other known coronaviruses from the US context. Then, we explored the effects of different degrees of climate dependency (that is, wider ranges between R0max = 2.5 to R0min = 1.5 and scenarios where R0min approached 1) (Extended Data Fig. 10).
Transmission is governed by β(t), which is related to the basic reproduction number R0 by R0(t) = β(t)D. The basic reproduction number varies based on climate and is related to specific humidity according to the equation:

$$R_0 = {mathrm{exp}}{[a times q(t) + {mathrm{log}}(R_{0{mathrm{max}}} – R_{0{mathrm{min}}})]} + R_{0{mathrm{min}}}$$

where q(t) is specific humidity53 and a is set at −227.5 based on estimated HKU1 parameters25. We assumed the time of introduction for cities to be the date at which the total reported cases for a country exceeded 10 cases.
Sensitivity analysis
Selecting an R0min value of 1, such that epidemic growth stops at high humidities, is likely implausible since simulations indicated no outbreaks would occur in cities such as Antananarivo (countered by the observation that SARS-CoV-2 outbreaks did in fact occur) (Extended Data Fig. 10b; see Supplementary Table 1 for the reported case counts at the country level). Expanding the range between R0min and R0max by increasing R0max resulted in epidemic peaks being reached earlier after outbreak onset but did not increase the difference in timing between cities with different climates (Extended Data Fig. 10c; for example, the difference in timing between peaks in Windhoek and Lomé is similar in 10a and 10c). Finally, we explored scenarios where the R0min was between 1.0 and 1.5. When R0min  > 1.1, epidemic peaks were seen in each SSA city with the difference in timing of the peak growing larger when smaller values of R0min were selected (Extended Data Fig. 10d). However, the difference in timing, even when small values of R0min were selected, was a maximum of 25 weeks and rapidly reduced to only a few weeks when R0min approached 1.5.
Reporting Summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article. More

We selected 10 permanent plots with long-term observations from CERN to include typical forest types of various ages in the East China monsoon forest region, including tropical rainforests, subtropical evergreen coniferous and broad-leaved mixed forests, warm temperate deciduous broad-leaved forests and temperate coniferous and broad-leaved forests, with evident precipitation and temperature gradients from south to north (Fig. 1). The spatial representativeness of the selected 10 sites across the Chinese forest region was evaluated by calculating the Euclidean distance based on various environmental factors. The 10 sites performed well and represented more than 80% of the Chinese forest region (Fig. S1). Of these forests, the Xishuangbanna tropical seasonal rainforest (BNF), Dinghu Mountain subtropical evergreen coniferous and broad-leaved mixed forest (DHF), Ailao Mountain subtropical evergreen broad-leaved forest (ALF), and Changbai Mountain temperate deciduous coniferous and broad-leaved mixed forest (CBF) are mature natural forests; the Shennongjia subtropical evergreen deciduous broad-leaved mixed forest (SNF) and Huitong subtropical evergreen broad-leaved forest (HTF) are natural secondary forests; and the other sites, i.e., the Beijing warm temperate deciduous broad-leaved mixed forest (BJF), Maoxian warm temperate deciduous coniferous mixed forest (MXF), Qianyanzhou subtropical evergreen artificial coniferous mixed forest (QYF), and Heshan subtropical evergreen broad-leaved forest (HSF), are plantations or middle- and young-age forests. All 10 sites are well protected and subject to minimal human activities, thus reflecting the C cycle dynamics under global environmental change, e.g., climate change, increasing CO2 and nitrogen deposition. The detailed characteristics of each plot can be found in their profiles in the CFCCD database.
There are three main steps to create the observation-based basic dataset and assimilated dataset of typical Chinese forests C cycle dynamics:
1.
Observation-based basic data acquisition. An ensemble of daily atmospheric and water data at ten CERN sites were used as forcing datasets for MDF and future scientific analysis; biological and soil data were also collected from CERN and processed by quality control and statistical calculation as benchmark to constrain the model.

2.
Implementation of a multiple data-model fusion framework. The Markov Chain Monte Carlo (MCMC) that integrated the Data Assimilation Linked Ecosystem Carbon (DALEC) model with multiple and dynamic observational data was used to retrieve C-cycle process parameters in a realistic disequilibrium state.

3.
Key process parameters and C function data assimilation. The key parameters of the process-based C cycle model (DALEC) were determined via the model-data fusion method; then the ecosystem C sequestration datasets were simulated by forward running the DALEC model with optimized parameters and then validated based on observational data and other previous studies.

Each step is explained in more detail below.
Observation-based basic data acquisition
Atmospheric and water data
In situ observations of daily air temperature (Ta), photosynthetically active radiation (PAR), relative humidity (RH), precipitation (Precip), and soil moisture (Sw) at the 10 sites from 2005 to 2015 were obtained from the CERN scientific and technological resources service system (http://www.cnern.org.cn/). These atmospheric and water data were mostly observed by an automatic meteorological station at each site. Among them, the PAR was estimated by a LI-COR LI-190SZ Quantum Sensor; Ta and RH were measured by a QMT110 sensor; Sw was estimated by a soil moisture neutron probe or the Time-Domain Reflectometry (TDR) soil moisture probe; the associated saturated soil water capacity (Sc) was measured by the cutting ring method to sample soil in each field campaign and the oven-drying method to measure saturated moisture content after the soil was soaked in water for 48 h; and Precip was artificially observed by CERN staff using an SM1-1 rain gauge. These monitoring data were collected in keeping with CERN’s protocols of observation and quality control29,30.
There were occasional missing data in time-continuous meteorological observations; therefore, the data were processed by standardized gap filling31. Specifically, for Ta, PAR, and RH, which were applied as model driver, we used a linear interpolation method to interpolate continuous missing data with less than three observations; otherwise, we established a regression model using the CERN observations and other observations from adjacent stations of the China Meteorology Administration (756 meteorological stations; http://data.cma.cn/en) to interpolate continuous missing data with more than three observations.
Biological data
Biomass.
At each site, the diameters at breast height (DBHs) and tree heights were measured for each tree in a regular inventory performed at least once every five years. The allometric equations of the DBH and/or tree heights with the biomasses of different plant tissues (i.e., leaves, branches, stems and roots) were developed at each site for various species based on the felled standard trees in the destructive plot. Then, we calculated the biomasses for the ten ecosystems using these allometric equations (FA02 table downloaded from http://www.cnern.org.cn/), which all passed the significance test (0.01 level) and have the R2 most above 0.9 when its estimation compare to observations from standard trees. For some unfelled species under protection, the allometric equations were obtained from Luo et al.32, which were developed based on national inventories and meta analyses from the published literature.
Litterfall.
The aboveground litterfall biomass was measured monthly by ten replicates with 1 m × 1 m baskets during the growing season or once during the nongrowing season. All collected litter was dried at 70 °C for 24 h in the laboratory and then weighed. To avoid the effects of wind on the measurement of litterfall biomass within an individual month, annual litterfall biomass data were finally adopted for each site.
LAI.
The leaf area index (LAI) at each site was measured optically with an LAI-2000 plant canopy analyzer (LI-COR, Lincoln, NE, USA) at least quarterly every year.
Soil data
Soil organic matter (SOM) was measured by the potassium dichromate oxidation titrimetric method. Soil bulk density (SBD) was measured by the cutting ring method in each field campaign at 10 forest sites. Soil particle size (i.e., soil mechanical composition) was measure by the laser particle analyzer. At least three samples were collected from each of the five soil layers (0–10, 10–20, 20–40, 40–60, and 60–100 cm) once every five years.
SOC.
The soil organic C (SOC) content was calculated from SOM, SBD, and volume percentage of gravel with particle size >2 mm at 10 forest sites as follows33:

$$SOC={sum }_{i=1}^{n}0.58times {H}_{i}times {B}_{i}times {O}_{i}times (1-{rm{theta }})times 100$$
(1)

where SOC is the soil organic C density (g C/m2) of all n layers, Hi is the soil thickness (cm), Bi is the soil bulk density (g/cm3), Oi is the SOM content of the ith layer (%), and θ is the volume percentage (%) of gravel with particle size >2 mm. In the absence of soil bulk density or soil organic matter content measurements in some layers, the missing soil measurements corresponding to specific soil depths of theses forest ecosystems were supplemented according to the empirical formulas of the relationships between SOM/soil bulk density and soil depth in different layers, which were developed based on the long-term and across-site CERN soil observations34.
All these raw atmospheric, biological, and soil data mentioned above can be directly download from CERN scientific and technological resources service system (http://www.cnern.org.cn/data/initDRsearch) or obtained after online application via protocol sharing.
Auxiliary flux data
Net ecosystem exchange (NEE).
These data were obtained from ChinaFLUX (http://www.chinaflux.org/), covering CBF, QYF, and BNF. The data were aggregated to the daily time step from half-hourly CO2 flux data measured by the eddy covariance technique and processed with quality control and gap filling procedures35.
Implementation of MDF method
The assimilated data were retrieved from a multiple data-model fusion method (Fig. 2). Specifically, the long-term and dynamic observations of biomass, litterfall, LAI and SOC were used as the model constraint data; Ta, PAR, and RH were used as the meteorological driving data; and the metropolis simulated annealing algorithm, a variation in the MCMC technique36,37, was applied to retrieve the C cycle parameters (e.g., C allocation and C turnover times) against the observations and prior knowledge. Then, we forward-simulated the model to produce the dynamic and time-continuous changes in ecosystem C sequestration function.
Fig. 2

Flowchart of the generation of assimilated datasets in a multiple- and long-term data assimilation framework.

Full size image

Since the dynamic C cycle observations provided an effective solution to constrain the C cycle states without the steady state assumption (SSA), the novelty of our MDF framework involves estimating these C cycle dynamics in better agreement with the actual dynamic disequilibrium state38. Therefore, the uncertainty in allocation and turnover parameters and in C pool states have largely been reduced based on the time-series observations under the non-SSA (NSSA)21,39,40, thereby significantly enhancing the model’s ability to predict the C sequestration function19,41,42.
Carbon cycle process model description
DALEC is a box model of C pools connected via fluxes running at a daily time step and has been applied extensively to the MDF research21,43. Its main structure (i.e., C cycle, C allocation, and turnover process) is generally consistent with state-of-the-art process-based models (Fig. S2; Table S1), with five pools (i.e., foliage (Cf), fine root (Cr), woody (Cw, including branches, stems, and coarse roots), litter (Clit) and SOM (Csom)) for evergreen forests and an additional labile pool (Clab) of stored C that supports leaf flushing for deciduous forests. The C cycle was initiated with the canopy C influx: gross primary productivity (GPP), which was predicted by the Aggregated Canopy Model (ACM)44 (Appendix S1). After GPP is consumed by autotrophic respiration (Ra), the remaining photosynthate (NPP) is allocated to plant tissue pools (Cf, Cr, or Cw). The C exiting from all C reservoirs was based on a first order differential equation with various turnover rates, with temperature and moisture dependency on the turnover from the litter and soil pools. In contrast to the original DALEC model only with temperature scalar fTa, here we added a new function fSw to express soil moisture pressure on litter and soil decomposition processes (Appendix S1). In general, the C pools and fluxes in DALEC were iteratively calculated at a daily time step and determined as a function of the key turnover and allocation parameters. A detailed model description can be found in Williams et al.45 and Fox et al.46.
Multiple data-model fusion at the nonsteady state
In a realistic disequilibrium state, C pools are time-variant, i.e., the C efflux is not equal to the C influx (left(frac{dC}{dt}ne 0right)); thus, the MDF was run via the dynamic and long-term CERN observations to constrain the DALEC model at the non-steady state (Eq. 2). Here, to avoid the uncertainty arising from the spin-up process under SSA, we determined the initial state of the C pools by the initial observations of C stocks or by optimization (i.e., Clab, which cannot be directly observed). Then, the turnover and allocation parameters were retrieved under the disequilibrium state with dynamic environmental forcing. This method avoids the considerable uncertainties when invoking the SSA to estimate the initial state of C pools and the C cycle parameters(e.g., allocation coefficients and turnover rates)39,40,47, which could lead to obvious biases in C sequestration19.

$$left{begin{array}{l}Delta {C}_{i}ne 0\ {C}_{i}left({rm{t}}+1right)={C}_{i}left({rm{t}}right)+{I}_{i}left({rm{t}}right)-{k}_{i}{C}_{i}left({rm{t}}right),{rm{i}}=1,2ldots n\ {C}_{i}left({rm{t}}=0right)={C}_{i}0end{array}right.$$
(2)

where Ci, Ii, and ki represent the size, input and turnover rate of the ith C reservoir, respectively; Ci0 represents the initial state of the ith C reservoir; t represents the specific model-running time step (daily step); and ΔCi represents the ith C pool change between t day and t +1 day when applicable into actual calculation. According to the Bayesian theory, the posterior distributions of the parameters are calculated by maximizing the likelihood function (Eq. 3).

$$L={prod }_{j=1}^{m}{prod }_{i=1}^{{n}_{j}}frac{1}{sqrt{2pi }{sigma }_{j}}{e}^{-{left({x}_{j,i}-{mu }_{j,i}left({boldsymbol{P}}right)right)}^{2}/2{sigma }_{j}^{2}}$$
(3)

where L is the integrated likelihood function; m is the number of multiple data types; n is the number of data points categorized by the jth data type; xj,i is the measured value composed of dynamic C cycle observations; μj,i(P) represents the modeled fluxes and stocks based on parameters under the NSSA (P); and σj is the standard deviation of each data point classified by the jth data type. Moreover, we imposed a sequence of ecological and dynamic constraints on the model parameter inter-relationships and pool dynamics (Appendix S2), which can significantly reduce uncertainty in model parameters and simulations48. The more detailed disequilibrium method can be found in our latest study19.
Key C-cycle process parameters and C sequestration data assimilation
Key process parameter estimation
Here, we mainly focus on how the C input (i.e., the net primary productivity) partitioned into various plant pools (i.e., foliar, wood, and fine roots), i.e., allocation coefficients, which could be directly determined from the optimized parameters (Fig. S3) of the DALEC model after the step 2: MDF method. Another key process parameter, C turnover time, needs further simple statistical calculation based on the model simulations with optimized parameters. Turnover time is commonly estimated by the equation “τ = stock/flux”20,49. Since the C influx is not equal to the C efflux in the realistic dynamic disequilibrium state, the turnover time should be defined as the ratio between the mass of a C pool and its outgoing flux50. Note that with few natural and anthropogenic disturbances in these well-protected CERN sites12,18, the C efflux is approximately equivalent to the Rh from soil and litterfall (mortality) and Ra (growth) from vegetation. Hence, the turnover time for vegetation, soil, and whole ecosystem can be derived as follows:

$${tau }_{veg}=frac{{C}_{live}}{{I}_{live}-Delta {C}_{live}}=frac{{C}_{live}}{litterfall+{R}_{a}}$$
(4)

$${tau }_{soil}=frac{{C}_{dead}}{{I}_{dead}-Delta {C}_{dead}}=frac{{C}_{dead}}{{R}_{h}}$$
(5)

$${tau }_{eco}=frac{{C}_{eco}}{{I}_{eco}-Delta {C}_{eco}}=frac{{C}_{live+}{C}_{dead}}{{R}_{a}+{R}_{h}}$$
(6)

where τveɡ, τsoil, and τeco refer to the biomass, soil and whole-ecosystem turnover times, respectively; Clive, Cdead and Ceco refer to the live biomass C pool size (Cf, Cr, and Cw,), dead organic C pool size (Csoil and Clitter), and the whole-ecosystem C pool size, respectively; Ilive, Idead and Ieco refer to the C input into the live biomass C pool, dead organic C pool, and whole ecosystem C pool, respectively; ΔClive, ΔCdead and ΔCeco refer to the changes in the live biomass C pool, dead organic C pool size, and whole-ecosystem C pool size, respectively; and Ra, Rh and litterfall refer to the autotrophic and heterotrophic respiration, and turnover from all live C pools (i.e., foliage, fine root and woody pools),respectively, as calculated from the DALEC output driven with the estimated parameters during 2005–2015. Since the C reservoirs, fluxes, and turnover times are instantaneous values, we used the averages of the fluxes and reservoirs over multiple years to reflect the average turnover time during a specific period (i.e., 2005–2015).
Time-continuous C sequestration estimation
The optimized parameter values under the NSSA along with the initial observations of the corresponding C pool sizes were used in forward modeling driven by dynamic environmental variables from 2005 to 2015 to obtain the time-continuous soil and vegetation C storage51. The difference between the ecosystem C influx (GPP) and ecosystem respiration (Ra+Rh) is used to examine the ecosystem C sequestration, i.e., net ecosystem productivity (NEP). Similarly, the difference between the ecosystem C influx (GPP) and ecosystem autotrophic respiration (Ra) is used to examine the net primary ecosystem productivity (NPP). More

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