We compiled publications reporting seasonal wood productivity of tropical forests. Seasonal tree growth measurements in 68 pantropical forest sites, representing 14 481 individuals, were obtained from published sources or directly from the authors (Table , Fig. ). The data set consists of repeated seasonal measurements of tree diameter, mostly with dendrometer bands (94.1 %), electronic point surveys (4.4 %) or graduated tapes (1.5 %). The names of all recorded species were checked using the Taxonomic Name Resolution Service and corrected as necessary . Botanical identifications were made at the species level for 11 967 trees, at the genus level for 1613 trees, family level for 171 trees and unidentified for 730 trees. Wood density values were taken from the Global Wood Density Database or from the authors, when measured on the sample (Table ). Direct determination was available for 455 trees and species mean was assumed for an additional 8671 trees. For the remaining 5355 trees, we assumed genus mean (4639), family mean (136) or site mean (580) of wood density values as computed from the global database . Palms, lianas and species from mangrove environments were excluded from the analysis. Diameter changes were converted to biomass estimates using a tropical forest biomass allometric equation – which uses tree height (estimated in the allometric equation if not available), tree diameter and wood density – and then the mean monthly increment of the sample was computed for each sample. Recently, showed that stem woody biomass production lags behind stem-girth increase by over 1 month in temperate coniferous forests, but here we assume that stem-girth increase represents woody biomass production as no such information is yet available for tropical forest trees. To detect the errors of overestimated or underestimated growth, the increment histogram of each site was plotted. For each suspected error, the increment trajectory of trees was then visually assessed to confirm the error. If the error was clearly identifiable, such as an abnormal increase (or decrease) in diameter values followed by a large decrease (or increase) of the same amplitude resulting from typographic errors, for example 28 whereas 2.8 was expected, the typographic error was corrected. When the typographic error was not clearly identifiable, the value was corrected with linear approximation with the mean increment of t+1 and t-1. In some cases there was an identifiable increase of diameter values (or decrease), but not followed by a decrease (or an increase) of the same amplitude. This pattern was associated to the repositioning of the dendrometer bands (reported in the source data set). In this case, the increment was deleted and set to zero and the new time series of cumulative diameter values were computed. As the diameter values are needed to compute biomass, this strategy was used to benefit of the full time series of diameter increment even after solving the error.

Seasonal litterfall productivity measurements from a previously published meta-analysis were used for South America description in Table 1 of. In this data set, we used only monthly measurement data from old-growth forests, as some sites have plots of both secondary and old-growth forests; flooded forests were excluded. In addition to these 23 sites, we compiled the seasonal leaf/litterfall data of 12 sites where we already had tree-growth measurements (Fig.  and Table ). For these 35 sites, 26 had monthly leaf fall and 9 had monthly litterfall data (leaf fall, twigs usually less than 2 cm in diameter, flowers and fruits). The Pearson correlation coefficient between leaf fall and litterfall for the 20 sites where both data are available is 0.945 (Pearson test, t=42.7597, df=218, p value < 0.001). Consequently, we assumed that the seasonal pattern of litterfall is not different from the seasonal pattern of leaf fall.

Enhanced vegetation index (EVI) was used as a proxy for canopy photosynthetic capacity in tropical forest regions . EVI for the 89 experimental sites (Fig. ) was obtained from the Moderate Resolution Imaging Spectroradiometer (MODIS) MCD43 product collection 5 provided every 16 days at 500 m spatial resolution (from 4 May 2002 to 30 September 2014). Before computing the mean monthly EVI per site, we did a pixel selection in five steps. (i) Selection of all the pixels in a square of side 40 km, centred on the pixel containing each site (6561 pixels per site). This surface was selected to maximize the quantity of valid pixels to estimate monthly site's EVI, as, due to persistent cloud cover in tropical forest regions, valid observations of EVI are limited, producing incomplete time series of EVI values for a given pixel. (ii) In this area, the pixels containing the same or at least 90 % of the site land cover pixel were selected, based on MCD12Q1 for 2001–2012 at 500 m resolution . (iii) Thereafter, only the pixels forested in 2000 and without loss of forest and with tree cover above or equal to the site tree cover were retained using global forest cover loss 2000–2012 and Data mask based on Landsat data . (iv) Only pixels with a range of ±200 m the site altitude were retained, using NASA Shuttle Radar Topographic Mission (SRTM) data, which were reprocessed to fill in the original no-data holes . (v) For corrected reflectance computation we used quality index from 0 (good quality) to 3 (all magnitude inversions or 50 % or less fill-values) extracted from MCD43A2. When required, data sets used to make the selection were aggregated to the spatial resolution of MCD43 product (500 m) and reprojected in the MODIS sinusoidal projection. The reflectance factors of red (0.620–0.670 µm, MODIS band 1), NIR (0.841–0.876 µm, MODIS band 2) and blue bands (0.459–0.479 µm, MODIS band 3) of the retained pixels were modelled with the RossThick-LiSparse-Reciprocal model parameters contained in the MCD43A1 product with view angle θv fixed at 0∘, sun zenith angle θs at 30∘ and relative azimuth angle Φ at 0∘ and EVI was computed as shown in Eq. (): EVI=2.5×NIR-redNIR+6×red-7.5×blue+1. To filter the time series, EVI above or below the 95 % confidence interval of the site's EVI values were excluded. Then, the 16-day time series were interpolated to a monthly time step. Finally, the interannual monthly mean of EVI for each site was computed. Further, the ΔEVIwet-dry index was computed for each site, that is, the differences of wet- and dry-season EVI normalized by the mean EVI, whereas dry season is defined as months with potential evapotranspiration above precipitation . For the sites where evapotranspiration is never above precipitation, dry season was defined as months with normalized potential evapotranspiration above normalized precipitation. In this study ΔEVIwet-dry computed from MODIS MCD43A1 is correlated with MOD13C1 (Amazonian sites: ρSpearman=0.90; pan-tropical sites: ρSpearman=0.86) and MAIAC (Amazonian sites: ρSpearman=0.89) products (Supplement Fig. S4).

To extract the monthly climate time series for the 89 experimental sites (Fig. ), we used climate data sets from three sources: the Climate Research Unit (CRU) at the University of East Anglia , the Consortium for Spatial Information website (CGIAR-CSI, http://www.cgiar-csi.org) and from NASA . From the CRU, we used variables from the CRU-TS3.21 monthly climate global data set available at 0.5∘ resolution from 1901 to 2012: cloud cover (cld, unit: %); precipitation (pre, mm); daily mean, minimal and maximal temperatures (respectively tmp, tmn and tmx, ∘C); temperature amplitude (dtr, ∘C); vapour pressure (vap, hPa); and potential evapotranspiration (pet, mm). The maximum climatological water deficit (CWD) is computed with CRU data by summing the difference between monthly precipitation and monthly evapotranspiration only when this difference is negative (water deficit) . From the CGIAR-CSI, we used the Global High-Resolution Soil-Water Balance dataset, soil water content (swc, %) . Additionally, we used monthly incoming radiation at the top of the atmosphere (rad, W m-2) covering the period from 2000 to 2015 at 1∘ spatial resolution from the CERES instruments on the NASA Terra and Aqua satellites and monthly incoming radiation at the surface (radsurf, W m-2) from CERES SYN1deg product computed for all-sky conditions, provided at 1∘ spatial resolution from 2000 to 2015. Monthly incoming radiation at the surface (shortwave radiation) refers to radiant energy with wavelengths in the visible, near-ultraviolet, and near-infrared spectra and is produced using MODIS data and geostationary satellite cloud properties . In addition to the temporal series of climate variables, we extracted the global ecological zones (GEZs) of the sites. These GEZs are defined by the Food and Agriculture Organization of the United Nations (FAO) and relies on a combination of climate and (potential) vegetation .

Because at some sites wood productivity or litterfall measurements are older than the EVI measurements (before 2002), and, for recent site measurements, climate data are not yet available (after 2012), all the data sets were averaged monthly by site. Then, in order to remove the site effect on the mean and the variance of the variables and to analyse only seasonality, all the variables were centred on zero and scaled to a variance of 1 by site. That is, for a given variable of a site, monthly values were subtracted by their annual mean and divided by their annual standard deviation. The obtained normalized variable had a mean of 0 and a variance of 1, but the time variation in the variable time-series, that is in our case the seasonality, remained completely unchanged.

The 89 sites represent a large sample of tropical forests under different tropical and subtropical climates corresponding to six global ecological tropical zones : tropical rain forest (TAr, 41 sites), tropical moist deciduous forest (TAwa, 23 sites), tropical dry forest (TAwb, 14 sites), tropical mountain systems (TM, 7 sites), tropical shrubland (TBSh, 1 site) and subtropical humid forest (SCf, 3 sites).

Changes in tree circumference measured with dendrometers are commonly used to characterise seasonal wood productivity. However, accelerated changes in circumference increments during the onset of the wet season can be caused by bark swelling as stems become hydrated . Similarly, bark shrinking during dry periods can mask any secondary growth and even lead to negative growth increments . Stem shrinkage during dry periods may be an important limitation of this work , as negative monthly growth values exist at almost all the study sites. Since the measurements are stem radius or circumference changes rather than wood formation, it is difficult to distinguish between true wood formation and hydrological swelling and shrinking. Direct measurements of cambial growth, such as pinning and micro-coring, currently represent the most reliable techniques for monitoring seasonal wood formation; however, all these methods are highly time-consuming, which severely restricts their applicability for collecting large data sets . Nevertheless, some observations already exist to compare growth from dendrometers and cambial growth at a seasonal scale for the same trees. In a tropical forest in Ethiopia experiencing a strong seasonality, high-resolution electronic dendrometers have been combined with wood anatomy investigation to describe cambial growth dynamics . These authors concluded that water scarcity during the long dry season induced cambial dormancy . Furthermore, after the onset of the rainy season, (i) bark swelling started synchronously among trees, (ii) bark swelling was maximum after few rainy days, and (iii) evergreen trees were able to quickly initiate wood formation. In a laboratory experiment of trunk section desiccation, have shown a decrease in the diameter of the trunk sections ranging from 0.08 to 1.73 % of the initial diameter. This decrease was significantly correlated with the difference in water content in the bark, but not with the difference in water content in sapwood. The variation in the diameter of the trunk sections were observed when manipulating the chamber relative air humidity from 90 to 40 %. However, these values are not representative of the in situ French Guiana climatic conditions, which is where the trunk sections have been collected and where relative humidity never falls below 70 %. Negative increments were reported for one-quarter of their sample with dendrometers measurements in the field. Recently, at the same site, some authors showed that biomass increments were highly correlated between the first and last quantiles of trunk bark thickness and between the first and the last quantile of trunk bark density, thereby suggesting that secondary growth is driven by cambial activity and not by water content in bark. At Paracou, a recent study showed a decrease or stop in the cambial growth for some species during the dry season, based on analysis of tree rings .

In a temperate forest, simultaneously using dendrometer pinning and micro-coring on Norway spruce and Scots pine, see Figs. 3 and 5 in showed that a lag of 2 weeks exists between the growth measured by dendrometers, but the general pattern of growth is highly correlated. In La Selva (Costa Rica), where there is no month with precipitation below 100 mm, a seasonal variation is reported, thereby suggesting a seasonality only driven by cambial growth. In conclusion, swelling and shrinking exist and could result from different biotic and abiotic causes, cell size, diameter, bark thickness and relative air humidity . To test how swelling and shrinking affect our results, we made first a linear model of wood productivity with precipitation as a single predictor with all the data, and then a similar linear model discarding the first month of the wet season (first month with precipitation >100 mm) and the first month of the dry season (precipitation <100 mm). Here, we assume that swelling occurs in the first month of the wet season and shrinking occurs in the first month of the dry season, as already observed. The removal of the first month of dry and wet seasons (defined, respectively, as the first month with precipitation >100 mm and the first month with precipitation <100 mm) did not affect the results of the linear model of wood productivity as a function of precipitation, that is, intercepts and slopes are not significantly different in both models (overlaps of the 95 % confidence interval of coefficients and parameters, Table ).

To address the first question “Are seasonal aboveground wood productivity, litterfall productivity and photosynthetic capacity dependent on climate?”, we analysed with linear models the relationship between our variable of interest (wood productivity, litterfall productivity and photosynthetic capacity) and each climate variable at each site and at t, t-1 month and t+1 month. These lags were chosen to account for variations between years in the climate seasonality, as we used in our analysis the average climate per site. For example, if the tree diameter increments were measured during a year with a wet-season initiation delayed by 1 month in relation to the average year, a lag of 1 month could exist in the relation of the tree diameter increments and the monthly averages of precipitation used in linear models. The results were classified for each variable as a count of sites with significantly positive, negative or non-significant results. To enable between-sites comparison, when the overall link was negative, the linear model was then run with the climate variable multiplied by -1. For a given climate variable, a site with a significant association at only one of the time lags (-1, 0 or 1) was classified as significant. This strategy enables us to highlight the potential drivers of our variable of interest, which are the climate variables with a constant relation with the variable of interest in all the sites. Climate variable with no effect, or effect due to a particular correlation with a potential driver at some sites, will show changes in the sign of the relation with the variable of interest. Then, a McNemar test was run to compare the proportion of our classification (negative, positive or no relationship) between all paired combinations of climate variables accounting for dependence in the data, that is, to compare not only the proportion of positive, negative and no significant effect between two climate variables and the variable of interest but also to detect if the sites in each of the classes (positive, negative and no significant effect) were similar. In order to summarise all the relations between the climate variables, a table (similar to a correlation table) containing all paired combination p values of the McNemar test was built. In this table a p value < 0.05 indicate that a different association between the two climate variables and the variables of interest cannot be rejected. To determine which climate variables explain the same part of variance and to enable interpretation, a cluster analysis was performed on the table of p values of the McNemar test using Ward distance. Climate variables in the same cluster indicate that they share a similar relation with the variable of interest.

When the climate variable with direct effect was identified, we built a linear model to predict wood and litter productivity seasonality with climate in all sites. For EVI, two climate variables were identified and their influence was dependent on the site values of ΔEVIwet-dry. To find the ΔEVIwet-dry threshold of main influence of each variable, the R2 of the linear relationship EVI as a function of the climate variable for different values of ΔEVIwet-dry threshold were computed. R2 was computed for the sample above or below ΔEVIwet-dry depending on the relationship of each variable to the threshold. The optimal threshold of ΔEVIwet-dry for climate variable influence on normalized EVI was defined by a break in the decrease of R2 values. Optimal thresholds were then used to define the range of ΔEVIwet-dry where EVI is influenced by one of the climate variables, the other and by both. To find the best linear combination of variables that contains the maximum information to predict EVI, we ran an exhaustive screening of the candidate models with the identified climate variables and their interactions with the ΔEVIwet-dry classes using a stepwise procedure based on the Bayesian information criterion, BIC .

To address the second question “Does a coherent pan-tropical rhythm exist among these three key components of the forest carbon fluxes?”, we analysed the linear relationship between wood, litter productivity and canopy photosynthetic capacity. The non-parametric Mann-Whitney test was used to determine the association between wood/litter productivity and photosynthesis rhythmicity depending on site limitations.

To address the third question – is the rhythm among these three key components of the forest carbon controlled by exogenous (climate) or endogenous (ecosystem) processes? – we analysed the linear relationship between ΔEVIwet-dry and mean annual precipitation, as well as the relationship between ΔEVIwet-dry, Δwood productivitywet-dry and Δlitter productivitywet-dry and maximum climatological water deficit (CWD). ΔEVIwet-dry, Δwood productivitywet-dry and Δlitter productivitywet-dry indices are the differences of wet- and dry-season variable values normalized by the mean of the variable, where the dry season is defined as months with potential evapotranspiration above precipitation.

To avoid over-representation of sites with the “same climate” (that is, to account for spatial and temporal autocorrelation in the climate data) cross correlation (positive and negative) were computed within sites for the monthly climate variables rad, pre, pet, dtr, tmn and tmx. The site's annual values of the same climate variables were added in the table. After scaling and centring the table, the Euclidian distance between each site and the mean table of all other sites (barycentre) was computed. We defined the weight of each site as the distance to the other divided by the maximum distance to the other. This distance was used as a weight in the linear models.

All analysis were performed in R .

A direct and dominant signal of precipitation seasonality was found in seasonality of wood productivity for 59 out of the 68 sites (86.8 %) where wood productivity data were available (cluster of variables in Fig. 2a with temperature amplitude (dtr), cloud cover (cld), precipitation (pre) and soil water content (swc), Sect. 2.2 and Supplement Table S1). All the variables in this cluster are wet season indicators: low temperature amplitude, high precipitation, high soil water content and high cloud cover. Two other clusters of climate variables are apparently associated with wood productivity. However, the climate variables that better explained wood productivity in these two clusters, vapour pressure (vap) and mean temperature (tmp), respectively, are highly correlated with precipitation in the clusters (Fig. a and Tables S3–S4). In spite of this dominant signal, these are outliers in our data, that exhibit no relationship or a negative relationship with precipitation (Appendix ). Four of the five sites that have no dry season (months with precipitation below 100 mm) were amongst these outliers.

It is interesting to note that 48.0 % of the monthly wood productivity is explained by the single variable “precipitation” (model mWP in Table ). The linear model with monthly precipitation only (mWP) was able to reproduce the seasonality of the majority of the sites analysed (Fig. a). No monthly lag between predicted and observed seasonality was observed for 35 sites. For 63 sites, a lag between -2 and +2 months was observed (Fig. a).

Canopy photosynthetic capacity, as estimated by EVI, for the 89 experimental sites, displayed an intriguing pattern with monthly precipitation, apparently related to the difference of ΔEVIwet-dry (Fig. a), an indicator of the dry season evergreen state maintenance , computed as the difference between the mean EVI of the wet season (pre ≥ pet) and of the dry season (pre < pet) (Sect. ). This pattern can be explained by a change in the climate parameters that mainly control photosynthesis, from precipitation in water-limited sites (ΔEVIwet-dry>0.0378, Fig. b) to maximal temperature in light-limited site (ΔEVIwet-dry<-0.0014, Figs. c and S1). Sites with mixed influence of precipitation and temperature are found between the range of ΔEVIwet-dry [-0.0014; 0.0378] (Fig.  for the definition of the thresholds). In our sample, the shift in climate control depends on the annual water availability. That is, sites are not water-limited above 2000 mm yr-1 of mean annual precipitation (Fig. d), as previously observed . Rather, they are light-limited as shown by the relationship between photosynthetic capacity and maximal temperature (Fig. c). Light-limited sites are located in Amazonia, in the south of Brazil and in south-east Asia (Fig. ). For all the sites, maximal temperature is highly correlated with incoming solar radiation at the surface (rPearson=0.80, p < 0.0001), approximating solar energy available for the plants (Fig. ). With the model mBICEVI (Table ), precipitation, maximal temperatures and their thresholds explained 54.8 % of the seasonality of photosynthetic capacity (Fig. c). For 39 sites, no seasonal lag between predicted and observed seasonality of canopy photosynthetic capacity was observed using the model mBICEVI. However, a majority of the sites (82 sites) appeared to have a lag between -2 and +2 months (Fig. c). The model failed to reproduce the seasonality for seven sites (one water-limited, one light-limited and five mixed sites).

For 27 out of the 35 sites (77.1 %) where litter data were available, litter productivity was associated with dry season indicators (lack of precipitation, high evaporation, low soil water content and high temperature amplitude, Fig. b). Surprisingly, we found that cloud cover (cld), an indirect variable, was the best single predictor of litterfall seasonality (Table ). Direct effects are observed only for potential evapotranspiration (pet) and temperature amplitude (dtr) (Fig. 2b and Table S5). A second cluster of climate variables is associated with litter productivity but a key variable in this subgroup, minimal temperature (tmn), is correlated with cloud cover (cld) (Table S7). Despite this dominant signal, outliers showing no relationship with cld exist in our data (Appendix ). The predictive model with cloud cover as a single variable (Table ) explains 31.7 % of the variability and performs well to reproduce the seasonality of litterfall productivity (Figs. b and b).

At a pan-tropical scale, 48 % of the variability of monthly aboveground wood productivity (Fig. a and Table ) and 31.7 % of the monthly litterfall seasonality can be linearly explained with a single climate variable (Fig. b). The relationship between photosynthetic capacity (EVI) and climate is more complex; however, 54.8 % of the monthly EVI variability can be linearly explained with only two climate variables, precipitation and maximal temperature (Fig. c).

In sites where both measurements were available, we observed a negative relationship between wood productivity and litterfall (Fig. , supported by linear analysis, Fig. S2). This relationship is consistent across the tropics and constant for all our sites (Fig. c), independently of the site water or light limitations (Mann-Whitney test, U=746, p =0.0839). Wood productivity and litterfall are mainly driven by only one climate driver in our results, precipitation and cloud cover respectively. The seasonality of these climate drivers are coupled for all the sites, where maximum precipitation occurs in the wet season while minimum cloud cover occurs in the dry season.

In water-limited forests, the seasonality EVI and aboveground wood production are synchronous for the majority of the sites (Fig. a), as a consequence of their relationship with precipitation. However, aboveground wood production is better explained by precipitation than EVI (R2 of 0.503 and 0.451 respectively).

Conversely, in light-limited sites and forests with mixed limitations (mixed forests), EVI is weakly coupled with the seasonality of wood productivity (respectively p =0.0633, R2=0.017 and p =0.0124, R2=0.055). Therefore, we conclude that the relationship between EVI and wood productivity depends on site limitations (Mann-Whitney test, U=874.5, p =0.0012).

The relationship between EVI and litter production is not constant (Fig. b), and also depends on site limitations (Mann-Whitney test, U=1016.5, p < 0.001). EVI is consistently negatively associated with litterfall production for water-limited forests (p<0.001, R2=0.510), reflecting forest “brown-down” when litterfall is maximal. Litter production is slightly better explained by cloud cover than EVI (R2 of 0.533 and 0.510 respectively), and they predict the same effect for the same site (McNemar test, p=0.999). No significant associations are found between EVI and litter in forests with mixed limitations (p=0.8531, R2 < 0.0001) and in light-limited forests (p=0.4309, R2 < 0.0001).

ΔEVIwet-dry and Δwood productivitywet-dry are dependent on annual water availability (Figs. a–b and d). Δwood productivitywet-dry is close to zero and could be negative for light-limited sites; the amplitude of the seasonality is driven by the annual water availability. The values for Δwood productivitywet-dry in south-east Asia are all negative. This is consistent with the negative or null associations of wood productivity and precipitation at these sites (Appendix ). Δlitter productivitywet-dry is poorly correlated with maximum climatological water deficit (CWD).