Introduction

Forest growth is a fundamental process driving the carbon balance of terrestrial ecosystems. Developing and maintaining forest carbon sinks is an important strategy for climate change mitigation and adaptation (Millar et al. 2007; Thuiller et al. 2008; Moss et al. 2010), and many studies have been conducted to identify forest carbon sinks using terrestrial ecosystem models (e.g., Sitch et al. 2008; Schaefer et al. 2012; Piao et al. 2013; Brunet-Navarro et al. 2016; Sonntag et al. 2016). These models have focused mainly on the source side (i.e., photosynthetic production) of the equation, with the sink side (forest growth) considered simply with empirical allocation schemes due to the complexity of abiotic and biotic factors (Brüggemann et al. 2011). Thus, the mechanisms connecting forest photosynthetic production and forest growth remain unclear (Fatichi et al. 2014). Current ecosystem models tend to use single allocation parameters throughout the season (Litton et al. 2007; Gim et al. 2017), which does not reflect the natural growth phenology of various plant structures (Badeck et al. 2004; Menzel et al. 2006; Cleland et al. 2007). This deficiency of source-sink allocation schemes causes uncertainty in forest carbon stock estimates (Fatichi et al. 2014), possibly causing problems with projections used for climate change mitigation strategies. Source-sink allocation schemes (e.g., those estimating the amount of photosynthetic product allocated to the stem in each season) can be informed by direct observation using stable or radioactive carbon isotopes (Brüggemann et al. 2011; Epron et al. 2012), but these methods are costly. Therefore, more feasible methods of observing the spatiotemporal patterns of source-sink allocation are needed to improve on the allocation schemes used in current ecosystem models.

Among structures that store carbon, the stem is the main one. Tree-ring (TR) analysis, a method of observing the stem radial growth increment (Wimmer and Vetter 1999), has informed studies of long-term forest growth dynamics and their underlying ecophysiological mechanisms (Ehleringer and Dawson 1992; Briffa et al. 1998; Salzer et al. 2009). Recently, researchers have begun to compare TR observations with forest photosynthetic production. Babst et al. (2014b) compared TR-based aboveground woody biomass estimates with eddy covariance-based carbon flux observations in Europe using precise allometric functions and TR measurements from all trees within circular plots (i.e., considering stand density) located in the vicinity of a flux tower. They found that the seasonal sum of net ecosystem productivity from January to June or July correlated with TR-based aboveground woody biomass. In addition to carbon flux observations, TR data have also been compared with terrestrial process-based models. Babst et al. (2013) reported differing responses of TR and model-estimated net primary production (NPP) to climatic parameters (i.e., temperature and precipitation) in Europe. They also suggested the necessity of improving NPP estimates from dynamic global vegetation models through consideration of carry-over effects from the previous growing season, especially under harsh climatic conditions (e.g., cold or drought). Rammig et al. (2015) demonstrated coincident reductions in the tree-ring width index (TRWI) and model-estimated NPP during a year of extreme climatic conditions in Europe. Ueyama et al. (2011) directly compared flux-based gross primary production (GPP), the TRWI, and model-estimated NPP in Japanese conifer plantations and found a consistent interannual pattern. Because many models use simplified algorithms to predict the carbon sink (growth) side compared to those used for the source (photosynthesis) side (Fatichi et al. 2014; Zhang et al. 2018), these reports suggest high potential for a comparison between model NPP and tree-ring width (TRW) to improve our understanding of how photosynthetic products are allocated to growth processes.

Previous analyses of the relationship between TR and model-estimated NPP have four limitations. First, most of these TR–NPP reports have used data from North America and Europe (Babst et al. 2013, 2014b; Belmecheri et al. 2014). Data from a broader range of climatic and biogeographic zones are crucial to reveal interregional differences in TR–NPP patterns and their underlying mechanisms. Second, the seasonality of NPP and TR growth needs to be further investigated. Previous analyses of the relationship between NPP and TR parameters (Babst et al. 2014b) have focused on the seasonal sum of NPP, which shows a strong correlation with TR patterns. Considering that both TR formation and NPP exhibit seasonal cycles (Babst et al. 2014a), correlations between TR parameters and monthly NPP should differ, even among months within a highly-correlated growing season (e.g., Babst et al. 2014b). The TR–NPP correlation should be stronger when photosynthate produced in the target month are allocated to TRs. A monthly approach may increase the temporal resolution of allocation schemes used in ecosystem models. The third limitation is a lack of research into the effects of environmental changes on TR–NPP relationships. Given temporal changes in forest productivity (Nemani et al. 2003; Sitch et al. 2008) and phenology (Menzel et al. 2006; Cleland et al. 2007) due to past environmental changes, the TR growth season may have changed as well (Rossi et al. 2011; Lugo et al. 2012). Spatially, TR growth seasons have been shown to be longer in warmer regions (Rossi et al. 2008; Moser et al. 2010; Rossi et al. 2011). This extended growing season is predicted to co-occur with an extended allocation season. However, few studies have assessed such temporal changes using the correlation between seasonal or monthly NPP and TR data. Finally, simultaneous comparisons of TR–climate and NPP–climate relationships are lacking. Although many studies have investigated the TR–climate relationship (Briffa et al. 2002; Dittmar et al. 2003; Pederson et al. 2004) or the NPP–climate relationship (Schimel et al. 1996; Lobell et al. 2002; Piao et al. 2013), these analyses are rarely reported together, hindering development of a complete understanding of causal mechanisms based on external climatic variables.

Sakhalin spruce (Picea glehnii) is an evergreen conifer and a major climax species in the conifer–hardwood mixed forests of Hokkaido, the northernmost island of Japan. This species plays an important role in carbon stocks due to its high xylem density relative to other conifer species (i.e., Picea jezoensis and Abies sachalinensis) in Hokkaido (Greenhouse Gas Inventory Office of Japan 2017). TR data for P. glehnii have been compared with climatic variables, showing a climate-sensitive response of TR chronologies, especially with monthly temperature during the warm season (Yasue et al. 1997; Davi et al. 2002). The recent warming trend on Hokkaido (Sugimoto et al. 2015) may alter the TR–climate relationship in this species, which could affect overall productivity in conifer–hardwood mixed forests in which P. glehnii is dominant. Hokkaido contains large carbon stocks in natural forests (Fang et al. 2005), and the effect of warming on their carbon storage function should be investigated, considering the relatively high sensitivity of the growth response to environmental change in Hokkaido plantations (Fang et al. 2014).

This study aimed to assess spatiotemporal variations in the relationship between observed TR growth and model-estimated photosynthetic production on annual and monthly bases to reveal source-sink allocation patterns. If a specific month’s photosynthetic production (source) is allocated to the stem structure (sink) and plays a major role in stem building, a correlation should occur; therefore, the TR–NPP correlation was analyzed. We used TR data from P. glehnii on Hokkaido and a process-based ecosystem model to estimate NPP. Because the TR data used for analysis lacked size information, we focused on high-frequency variables (i.e., year-to-year variations), rather than on the total mass of stem growth. By analyzing correlations between annual TRW and model-estimated NPP values in northern Japan, we addressed the limitations discussed above with three questions: (1) Does the TR–NPP correlation show a seasonal pattern? (2) Have relationships between TR growth and NPP changed over the twentieth century? (3) How do temperature and precipitation affect TR growth and NPP?

Methods

Tree-ring data

TR data collected at seven sites on Hokkaido Island were obtained from the International Tree-Ring Data Bank (Grissino-Mayer and Fritts 1997) (Fig. 1, Table 1). Data quality was controlled by removing 50-year segments exhibiting low correlations (R < 0.3281) with the mean series of the corresponding site using the COFECHA program (Holmes 1983). This quality control procedure removes highly noisy samples that dominate sites with mild climate (i.e., weak climatic signal) to enable construction of reliable mean site series. We used TRW data from 1900 to 2010 to match the period of available climate data. Among the seven sites, TRW data had similar first-order autoregressive coefficients (0.60–0.70) at all sites except for ONB (0.44; Table 1). The average correlation among trees (R-bar; 0.32–0.42) and the expressed population signal (0.93–0.97) showed similar values. Annual mean temperature ranged from − 0.7 to 5.7 °C and annual precipitation ranged from 807 to 1485 mm year−1 at the seven sites (Table 1), according to 1-km mesh climate data averaged over 1981–2010 (Japan Meteorological Agency 2012).

Fig. 1
figure 1

Map of study site locations. Climate 61 and 06 represent the Automated Meteorological Data Acquisition System (AMeDAS) climate data stations, which provided data for the 1961–2010 and 2006–2010 periods, respectively. See Table 1 for site name abbreviations. Color figure available online

Full size image
Table 1 Tree-ring width and climate data from the seven tree-ring sampling sites (see Fig. 1 for locations)
Full size table

Climate data

To determine climate conditions in the long-term past, we used meteorological reanalysis data for the twentieth century produced by the European Centre for Medium-Range Weather Forecasts (ERA-20C; Compo et al. 2011; http://www.ecmwf.int/en/research/climate-reanalysis/era-20c). The resolution of the ERA-20C data grid is 0.5° × 0.5°. Eight climatic variables (total cloud cover [tcc], surface thermal radiation downward [strd]; surface solar radiation downward [ssrd], total precipitation [tp], surface pressure [sp], temperature at 2-m height [t2], specific humidity at 2-m height [q], and wind speed at 10-m height [w10]) were utilized to estimate NPP using an ecosystem model, which is described in the next section. Because these eight climatic variables were not measured at every TR site and the nearest meteorological stations tended to lack data from the early twentieth century, we constructed statistical models to estimate these climatic variables at each TR site using Automated Meteorological Data Acquisition System (AMeDAS) data for Hokkaido. Based on differences in measurement periods among AMeDAS sites, two data periods (1961–2010 and 2006–2010) were analyzed for each AMeDAS site (Fig. 1). The total number of AMeDAS sites used in this study was 212. The statistical model estimated AMeDAS observations using several predictor variables: the eight ERA-20C climatic variables, differences in elevation between AMeDAS observation site and ERA-20C grid elevation, latitude, and longitude. Three climatic variables (tcc, strd, and ssrd) were not modeled because AMeDAS observations were limited or absent. Because AMeDAS data included relative humidity measurements, specific humidity was derived as follows:

$$ Q = 0.622 \times \left( {RH \times SWVP} \right)/\left( {P - RH \times SWVP} \right), $$
(1)

where Q is specific humidity (kg kg−1), RH is relative humidity (%), P is atmospheric pressure (hPa), and SWVP is saturated water vapor pressure (hPa) derived from air temperature (°C) using the Goff–Gratch formula.

A random forest model (Ibarra-Berastegi et al. 2011; Shi et al. 2015) and a linear model were chosen as candidate statistical models. Spatiotemporal estimation capabilities were compared between these two candidate models by randomly assigning 70% of the dataset to training data and 30% to test data. Following this preliminary analysis, the random forest model was used to estimate four parameters (tp, q, t2, and w10) and a linear model was used for one parameter (sp). The mean squared coefficients of correlation between observed and estimated values over 12 months were 0.51, 0.86, 0.71, 0.87, and 0.84 for tp, sp, w10, t2, and q, respectively.

Using these statistical models, climatic variables at the seven TR sites were derived from ERA-20C data. For three parameters (t2, tp, and sp), the mean values from 1981 to 2010 of model-derived climatic variables were compared with mesh climate data (Japan Meteorological Agency 2012) at each TR site. The differences between the mesh climate data (averaged over 1981–2010) and model-estimated values were used to correct for biases in model-derived climatic parameters.

VISIT model application

NPP was estimated at the seven conifer–hardwood mixed forest sites using the Vegetation Integrative SImulator for Trace gases (VISIT) model (Ito 2010). The VISIT model was initially based on a simple carbon cycle model (Ito and Oikawa 2002) and subsequently improved to include trace gas exchange processes (Ito et al. 2005). It simulates the carbon, water, and nutrient cycles of terrestrial ecosystems and evaluates fluxes of greenhouse gases (CO2, CH4, and N2O) between the atmosphere and terrestrial ecosystems. This model can estimate net ecosystem productivity, GPP, ecosystem respiration, and NPP of terrestrial ecosystems, including vegetation and soil components, by simulating biogeochemical and hydrological processes. The VISIT model can account for differences among plant functional types, and the conifer–hardwood mixed forest type was used in this study. Hirata et al. (2014) provided details of the VISIT model structure and parameters used in this study, and confirmed that the model captures carbon fluxes well in northern conifer–hardwood mixed forests using data from the Teshio flux tower site in 2002. GPP is simulated using the canopy schemes of Monsi and Saeki (1953) or de Pury and Farquhar (1997). After removing maintenance respiration as a vital cost, specific fractions of assimilated carbon are allocated to the foliage, stem, and root structures. Foliage allocation is preferred until the leaf area index reaches an optimal value. A constant fraction of GPP is allocated to storage (i.e., non-structural carbohydrates) until storage reaches its maximum amount (or capacity), and is divided into set fractions for stem and root mass. This storage helps developing organs, especially in spring of the following year (carry-over). Thus, this model statistically describes carbon source (photosynthesis) and sink (growth) dynamics (Fatichi et al. 2014).

The model was initialized with a spin-up run of 1200 years to reach the equilibrium forest ecosystem by randomly applying annual data from the corrected ERA-20C dataset from 1900 to 2010 for each site. Past atmospheric CO2 concentrations (1900–2010) were derived from the historical part of the Special Report on Emissions Scenarios (IPCC 2000) derived from ice core data up to 1958, and observations from Scripps and the National Oceanic and Atmospheric Administration thereafter. NPP at each of the seven TR sites was estimated using the VISIT model and bias-corrected ERA-20C climatic variables. Estimates of NPP were summarized for annual or monthly intervals and then compared with TRW data and climatic variables. For validation of model-estimated NPP, we further compared VISIT-estimated annual NPP with the MODerate resolution Imaging Spectroradiometer (MODIS) NPP land product (MOD17A3), and moderate coincidence was observed (Fig. S1), suggesting that this model sufficiently predicted NPP at our sites. This validation was mainly for the carbon source (photosynthesis) side of NPP, as MODIS NPP mainly captures light reflected from foliage. In the VISIT model, NPP estimation is based primarily on physiological processes on the carbon source side (i.e., photosynthesis and respiration). TRs represent the sink side of production (growth); thus, the source-sink distinction remained in our NPP and TRWI dataset. This dataset fits with our focus on examining correlations between sources and sinks to determine how seasonal photosynthetic production affects stem growth.

TR, NPP, and climatic data preparation

Non-climatic effects on TRW, such as the biological age–size trend characteristic, were removed using a spline detrending technique (Fritts 1976; Esper et al. 2002) with a 50% frequency response cutoff at 20 years. The detrended series were averaged using a biweight robust mean method to create a mean TRWI chronology for each site. Autocorrelations of TRWI were nearly zero (AR[1]: − 0.18 to 0.19). To focus on correlations among high-frequency variables, first differencing (i.e., calculation of differences from the previous year) was performed on TRWI and annual or monthly values of NPP, temperature, and precipitation. The first differencing method is known to amplify high-frequency variables (Zhu et al. 2011; He et al. 2014). Because the previous year’s production and climatic conditions tend to affect TRW and NPP, first difference values for the previous year (Vt−1,m − Vt−2,m) were calculated for explanatory variables separately from the current year’s values (Vt,m − Vt–1,m), where V, t, and m represent the variable (NPP, temperature, or precipitation), calendar year, and month, respectively. First differencing obscures differences from high to moderate and from moderate to low values of TRWI or NPP. This difference may be important because the TRWI–NPP correlation can differ between high-productive years and less-productive years (e.g., stem growth is not a priority for trees under stress). Therefore, we also preliminarily compared a simple linear model (diff.TRWI ∼ diff.NPP) with an interaction model (diff.TRWI ∼ diff.NPP + previous.NPP + diff.NPP × previous.NPP), where diff refers to the first difference value. Based on Akaike’s information criterion (AIC), the simple linear model performed better at all seven sites (delta AIC = 0.72–3.72), suggesting that high to moderate and moderate to low changes were not apparent and that usage of first differencing with our dataset is not problematic. Hereafter, all descriptions of TRWI, NPP, temperature, and precipitation variables represent this difference in value from the previous year.

Although TRWI chronologies represent only a portion of stand-level production derived from the VISIT model, which includes branches, leaves, and roots, as well as other tree species, we assumed that these mean TRWI chronologies would covary with annual or monthly stand-level production, at least when describing the general increasing or decreasing trends of high-frequency variables (i.e., interannual variation). This assumption is based on previous reports showing correspondence between stand-level production and the TRWI (Ueyama et al. 2011; Belmecheri et al. 2014; Rammig et al. 2015). Although target species growth is not the same as stand-level production, TR data tend to be collected from large individuals, which are responsible for much of the variability in stand-level production. This popular TR sampling method has limitations for the estimation of long-term growth trends (e.g., basal area increment) and forest productivity (e.g., aboveground biomass) due to lack of consideration of stand density and size-age growth differences between dominant and suppressed individuals (Babst et al. 2013; Nehrbass-Ahles et al. 2014). On the other hand, high-frequency variables estimated from the TRWI showed no bias with this popular sampling methodology and are comparable with other productivity adjusted TR sampling methodologies (Nehrbass-Ahles et al. 2014). Because our focus is on high-frequency variables, we used TRWI chronologies for the dominant species.

Analysis of correlations of TR with NPP and climate

The correlations between mean TRWI chronologies and NPP, temperature, and precipitation were analyzed by (1) calculating Pearson’s coefficients of correlation between the TRWI and annual or monthly NPP at each site, (2) construction of a linear model that predicts the TRWI based on annual and monthly NPP and an interaction parameter between NPP and calendar year, and (3) calculating Pearson’s correlation between the TRWI or annual NPP and annual or monthly temperature or precipitation at each site.

To analyze the TRWI, we conducted weighted correlation or regression analyses using the number of series sampled in each year as weighting variables to account for differences in the number of samples within each period of the mean TRWI chronologies. For the second analysis, two models were constructed and AIC values were compared. The structures of the two models were as follows: model 1 included annual or monthly NPP only,

$$ {\text{TRWI}} = {\text{a}} \times {\text{NPP}} + {\text{b}}, $$
(2)

and model 2 included the interaction between NPP and calendar year,

$$ {\text{TRWI}} = {\text{a}} \times {\text{NPP}} + {\text{b}} \times \left( {{\text{NPP}} \times {\text{year}}} \right) + {\text{c}}, $$
(3)

where a, b, and c are parameters. All predictor variables in these models were centered and scaled prior to model construction. The selection of model 2 as the best model would mean that the corresponding annual or monthly NPP exhibits temporal changes in its relationship with the TRWI (i.e., TRWI ∼ NPP × [year + 1]). The selection of model 1 would mean that the TRWI–NPP relationship has not changed during the twentieth century. Because the interaction parameter was also the slope of temporal change in the NPP parameter, indicating how much the NPP regression coefficient changed over time, we calculated this parameter by constructing model 2 for each site and comparing the interaction parameters between sites and months. All analyses were conducted using the “randomForest,” “reshape2,” “snow,” “weights,” and “dplR” packages in R software (R Core Team 2016).

Results

Correlation between the TRWI and NPP

Monthly TRWI–NPP correlation coefficients showed a clear seasonal pattern (Fig. 2), suggesting seasonal source-sink allocation phenology. In most cases, the TRWI increased with increasing monthly NPP during April to June (i.e., positive TRWI–NPP correlations); therefore, photosynthetic production in these months was estimated to be allocated to the stem. June NPP values had higher correlation coefficients (R = 0.08–0.39, mean = 0.26) than did those of other months; the correlations were significant (P < 0.05) at five of the seven sites sampled (ASH, MtONB, TOK, STK, and ONB). Significant relationships were also found with other monthly NPP values, but their correlations were inconsistent among sites (i.e., significant at only one or two of the seven sites) and the absolute values of their correlation coefficients were lower than that of June NPP. Most monthly NPP values from the current year were correlated positively with the TRWI, whereas monthly NPP from the previous year was correlated negatively with the TRWI. No spatial trend or difference was observed in monthly TRWI–NPP correlations (Fig. 2).

Fig. 2
figure 2

Pearson’s coefficients of correlation between the tree-ring width index (TRWI) and annual or monthly net primary production (NPP) during the a current and b previous years (see Table 1 for site name abbreviations). Correlations were calculated using the first differenced values of the TRWI and NPP to amplify high-frequency variables. Note that correlation coefficients between TRWIt − TRWIt−1 and NPPt,m − NPPt−1,m are given for the current year, and those between TRWIt − TRWIt−1 and NPPt−1,m − NPPt−2,m are given for the previous year, where t represents the calendar year and m represents annual or monthly sums. Data gathered during 1900–2010 were used. Color figure available online

Full size image

Annual NPP of the current year correlated significantly with the TRWI at the TOK and ONB sites, but this correlation was inconsistent among sites (Fig. 2). The absolute values of the correlation coefficients between TRWI and annual NPP were lower than those for June TRWI–NPP.

Temporal change of the TRWI–NPP correlation

Between the two candidate models, model 2 (i.e., TRWI ∼ NPP + [NPP × year]) was selected for February, March, April, July, September, and annual NPP of the current year and for March, June, July, October, and annual NPP of the previous year (Table 2). Model 1 was selected for all other monthly NPPs. The interaction parameter between NPP and year showed the temporal trend of the relationship between NPP (source) and the TRWI (sink; Table 2), as this interaction term is also the slope of temporal change (i.e., TRWI ∼ NPP × [year + 1]). Increasing trends were detected for February, March, April, July, and annual NPP of the current year and for October NPP of the previous year, showing that the effect of photosynthetic production on TRW during these months increased with time. A decreasing trend was detected for September NPP of the current year and for March, June, July, and annual NPP of the previous year, indicating that the effect of photosynthetic production on TRW in these periods decreased over time. Each site exhibited differing trends in NPP × year (Fig. 3). Despite this difference, the overall trend of the pooled data was moderately consistent with each site’s trend, showing the same general direction (positive or negative) as the combined data, except at one or two sites (Fig. 3).

Table 2 Model comparison based on Akaike’s information criterion (AIC) and parameters of the best model for each monthly or annual net primary production (NPP)
Full size table
Fig. 3
figure 3

Seasonal changes in the interaction parameter between calendar year and annual or monthly net primary production (NPP) of the a current and b previous years, obtained with model 2 (see Table 1 for site name abbreviations). Model 2 (tree-ring width index [TRWI] ∼ NPP + [NPP × year]) was applied to each site’s annual or monthly NPP; the interaction parameter (NPP × year) is shown on this graph. “All sites” represents results of the model using data from all sites, shown in Table 2. Larger circles represent sites where the Akaike’s information criterion for model 2 was less than that for model 1 (TRWI ∼ NPP), suggesting that the interaction term is significant. Note that the TRWI was defined as the difference in value from the previous year (i.e., TRWIt − TRWIt−1), and current and previous NPP was given as NPPt,m − NPPt−1,m and NPPt−1,m − NPPt−2,m, respectively. The value t represents the calendar year and m represents annual or monthly sums. Note that a positive or negative value of the interaction parameter represents a temporal increase or decrease, respectively, in the corresponding NPP linear regression coefficient. Data gathered during 1900–2010 were used. Color figure available online

Full size image

In June of the current year, which showed the highest TRWI–NPP correlation (Fig. 2), model 1 was selected as the best model (Table 2). Thus, the effect of June photosynthetic production on TRW did not change with year, and this relationship maintained a relatively strong positive correlation (Fig. 2) throughout the twentieth century. Model 1 in June of the current year had the lowest AIC (AIC = − 553.8), followed by model 2 in June of the current year (AIC = − 552.4), model 2 in June of the previous year (AIC = − 552.1), and model 1 in June of the previous year (AIC = − 546.2; Table 2). These results suggest a relatively strong effect of June photosynthetic production, whereas those from other months did not notably affect TRW, even when temporal changes were considered.

Climatic effects on the TRWI and NPP

The TRWI had a positive relationship with June–September temperatures of the current year, with the strongest effect in July, correlating significantly at all sites (R = 0.25–0.59, mean = 0.39; Fig. S2a). Monthly temperature in the previous year correlated negatively during this period (Fig. S2b). Precipitation showed a weak correlation with the TRWI compared with temperature, and significant correlations between monthly precipitation and the TRWI were sporadic and site dependent (Fig. S2c, d).

On the other hand, annual model-estimated NPP was clearly correlated with both temperature and precipitation. Temperature in May through September of the current year was correlated positively with annual NPP, especially in May (R = 0.30–0.42, mean = 0.37), with significant correlations obtained for each site (Fig. S3a). Temperature in the previous May was correlated negatively with annual NPP (R = − 0.48 to − 0.36, mean = − 0.39) at each site (Fig. S3b). Current year precipitation in March through October was correlated negatively with annual NPP, especially in August (R = − 0.41 to −0.26, mean = − 0.32; Fig. S3c). Precipitation in May through August of the previous year was correlated positively with annual NPP, especially in July (R = 0.24–0.39, mean = 0.29) and August (R = 0.22–0.39, mean = 0.31; Fig. S3d).

Discussion

Strong TR growth–NPP correlation in TR growth months

Regarding whether the TR growth–NPP correlation shows a seasonal pattern, we found that NPP in April–June of the current year was correlated positively with TR growth (Fig. 2), suggesting that photosynthetic production in this season would be allocated to stem growth. This season is reported to be the period of early wood cell formation in P. glehnii in our research area. Yasue et al. (1994) reported that the number of early wood cells of P. glehnii on Hokkaido Island starts to increase in April, and that the cell division rate peaks in June. Consistent with the timing of early wood cell formation, June NPP was correlated significantly with the TRWI at five of the seven study sites, suggesting a strong effect of photosynthetic production (carbon source) on stem growth (carbon sink) during the early wood-growing season of P. glehnii on Hokkaido. Our results are consistent with those of previous research on carbon allocation in Picea abies (Kuptz et al. 2011). Using carbon stable isotope labeling, these researchers revealed that the fractional contribution of immediate photosynthesis (i.e., within several days to weeks) on stem CO2 efflux showed no seasonal trend, but that CO2 efflux was greatest in the early summer; therefore, more carbon acquired in the early summer was allocated to stem than in other seasons. The strong correlation between June NPP and TRW may be caused by day length changes, as days in late June are the longest of the year and their subsequent shortening can trigger the cessation of xylem cell enlargement (Cuny et al. 2015; Delpierre et al. 2016). As June is more productive than earlier months in the current year, June NPP had a strong correlation with the TRWI. Cell enlargement duration has been reported to affect cell radial diameter (Cuny et al. 2014), but our results further suggest that the amount of photosynthetic production during cell enlargement is also important for TR growth. The early wood zone occupies most of the TRW, such that early wood formation is a key driver of TRW, although late wood formation and its allocation phenology must be included when considering the total carbon stock in the stem (Cuny et al. 2015). Our results further suggest that stem volume and growth rate should be explanatory for NPP, with positive correlations in the early wood-growing season.

The spatial tendency of the TRW–NPP trends at seven sites was unclear (Fig. 2). Site-specific environmental differences likely had strong effects, hindering possible spatial trends during distinct cambial growth periods (Moser et al. 2010; Rossi et al. 2011). For example, differences among soils, substrates, nutrients, topography, competition, and/or disturbance history may have affected seasonal photosynthetic production and, in turn, seasonal source (photosynthetic production) to sink (TRW) allocation patterns.

Opposite correlations between the current and previous years arose for the TRWI, NPP, temperature, and precipitation (Figs. 2, 3, S2, S3) due to the nature of each temporally autocorrelated variable. These variables tended to show oscillating temporal patterns, such as a low-production year following a high-production year. When differences from the previous year are calculated for these oscillating variables, the first-order autocorrelation of the resulting temporal variables (e.g., the correlation between Vt − Vt−1 and Vt−1 − Vt−2) tends to be negative (e.g., a production increase [Vt − Vt−1] just after a high-production decrease [Vt−1 − Vt−2]). Our data (i.e., TRWI, NPP, temperature, and precipitation after first differencing) also exhibited negative first-order autocorrelations (AR1s of − 0.57 to − 0.29 for mean TRWI chronologies, − 0.61 to − 0.42 for annual NPP, − 0.47 to − 0.37 for annual mean temperature, and − 0.51 to − 0.43 for annual precipitation). This negative first-order autocorrelation affected our results, causing opposing correlations between the current and previous years (e.g., the correlation with TRWIt − TRWIt–1 was positive for NPPt − NPPt–1 and negative for NPPt–1 − NPPt–2; Figs. 2, 3).

Temporal changes in TRW–NPP relationships

Investigating whether the relationship between TRW and NPP changed temporally over the twentieth century, we found that the relationships between annual or monthly NPP and TR growth changed over time in some months (Table 2, Fig. 3), suggesting temporal changes in source-sink allocation. Given that June NPP maintained a high correlation with the TRWI, whereas the correlations with February, March, April, and July NPP strengthened over time, our results suggest that the effective photosynthetic production season in terms of TRW is lengthening, raising the possibility that the stem allocation period is lengthening as a result of environmental change (Fig. 4).

Fig. 4
figure 4

Conceptual diagram of changes in correlations between the tree-ring width index (TRWI) and net primary production (NPP) over the twentieth century. Note that the graph of early-wood radial growth speed is a summary of previous reports on cambial growth phenology (i.e., increased cells per month) of Picea glehnii on Hokkaido Island (Yasue et al. 1994). According to our results (Figs. 2, 3, Table 2), June NPP sustained a strong correlation and NPP in February, March, April, and July had increasing correlations with the TRWI over the twentieth century. These trends suggest that the number of months when NPP and TRWI are correlated has increased during the twentieth century, further supporting the possibility that the stem allocation period is lengthening. Color figure available online

Full size image

Warming should increase photosynthesis in February–April (Schaberg et al. 1995), possibly lengthening the effective photosynthetic production season through earlier onset of source-sink carbon allocation. An increase in the duration of the stem allocation period is consistent with field observations of the cambial growth period (Rossi et al. 2008; Moser et al. 2010; Lugo et al. 2012) and with lengthening of the leaf-growing season (Menzel and Fabian 1999; Linderholm 2006; Vitasse et al. 2009). However, caution is warranted because AIC values for model 2 in February, March, April, and July of the current year were higher than the value for model 1 in June of the current year (i.e., the best model among all annual or monthly NPP models; Table 2), suggesting a relatively weak trend of temporal change in the NPP correlations for these months. TRWI–NPP correlations were also weak in these months (Fig. 2). Wide inter-site differences in the interaction parameter (Fig. 3) also imply that this trend is weak. Site-specific factors, such as soil type, species competition, disturbance history, and topography, complicate and weaken the temporal trend.

Positive interaction parameters for October of the previous year (Table 2, Fig. 3) also suggest lengthening of the productive season and the consequent increase of storage until the following year. Considering previous reports that cambium formation ends in September in P. glehnii (Yasue et al. 1994), the recent increase in the relationship between October NPP and the TRWI suggests that environmental change has increased storage of non-structural carbohydrates, which may positively affect the next year’s TRW. Because cambial growth cessation is often restricted by photoperiod (Jackson 2009; Delpierre et al. 2016), the timing of growth cessation is believed to be stable, even through environmental change. Hence, any production during this season must be carried over, rather than allocated to the current year’s TR growth. The negative interaction parameter in September of the current year (Table 2, Fig. 3) may be due to temporal strengthening of the negative correlation between September NPP and March or April NPP (six of the seven sites had significant correlations between September NPP and either March or April NPP, and these correlations strengthened through the twentieth century). Negative correlations between September and April in solar radiation (− 0.04 to − 0.21, not significant) and cloud cover (from − 0.22 to − 0.40, significant) may have led to this seasonal NPP pattern. An increase in September NPP was associated with a reduction in March or April production and a decrease in initial growth or division of early wood cells.

Climatic effect on TR growth and NPP

Regarding the effects of temperature and precipitation on TR growth and NPP, our results indicate that these parameters showed different responses to precipitation (Figs. S2c, S3c). The negative correlation between NPP and precipitation may have been affected by moist conditions at the study sites, inhibiting the desiccation stress that leads to a positive NPP–precipitation correlation. Precipitation increases cloud cover and consequently decreases sunlight during the Asian monsoon season (Wu et al. 2009; He et al. 2016). This reduction in sunlight leads to reduced production from photosynthesis. However, high precipitation did not affect TR growth, suggesting that water supply contributed to stem growth (Gruber et al. 2009; Oberhuber and Gruber 2010; Lempereur et al. 2015).

In previous TR studies, temperature and precipitation were the main factors used to explain temporal patterns in TR growth (Graumlich 1991; Makinen et al. 2002; Babst et al. 2013). However, climatic factors tend to correlate with each other and show complex interactions, as discussed above, making disentanglement of the overall process of TR formation difficult. This analysis of TR and model-estimated NPP should provide a useful tool for disentangling the complex process of stem growth.

Model-estimated NPP

In this study, NPP was measured as stand-level NPP in stands that included species other than P. glehnii, under the assumption that stand-level NPP covaries with photosynthetic production by P. glehnii. Therefore, caution is required when interpreting the results of correlations between stand-level NPP and the TRWI of this species. Various interspecific differences, such as leaf phenology (Badeck et al. 2004), pioneer–climax strategy (Gea-Izquierdo et al. 2014), and use of non-structural carbohydrates (Michelot et al. 2012), can cause differences in the NPP–TRW relationship, especially when the functional characteristic of the target species is far from the site’s community mean. However, the corresponding trends of some physiological parameters indicate that the dominant tree, P. glehnii, exhibits cambial growth trends that follow stand-level NPP. Conifer species on Hokkaido show a similar pattern of decreasing photosynthetic activity with leaf age (Kayama et al. 2007). Seasonal patterns in leaf chlorophyll content are also roughly consistent among tree species in boreal and temperate forests, with a summer peak around August (Middleton et al. 1997; Koike et al. 2001; Thomas et al. 2009). In addition, correspondence between stand-level NPP and TRW of a single dominant species has been reported previously (Belmecheri et al. 2014; Rammig et al. 2015). Although further research is needed, we propose that the difference in timing of the interannual increase or decrease in stand-level NPP and photosynthetic production of P. glehnii is not very large.

Conclusions

Carbon source-sink allocation schemes (e.g., those examining timing and amount) require further improvement, as several current schemes are becoming less effective in predicting biomass and its seasonal cycles in some ecosystem models. Such model projection uncertainty for forest biomass may cause problems for planning of timber production or climate change mitigation. To improve this weakness, field observation is crucial, but the monitoring of carbon allocation requires great sampling effort. Our methodology has strong potential to reduce reliance on these difficult field observations through the use of precise correlation analysis. Our findings contribute to understanding of the timing of source-sink allocation. We clarified the significant correlation between mean TRWI chronologies and model-estimated monthly NPP during the early wood-growing season, suggesting that photosynthate produced in this season is allocated to driving stem growth. Although this TRWI–NPP comparison still relies on correlation analysis, the results offer a starting point for mechanistic modeling of carbon source-to-sink allocation schemes. We also revealed the temporal trend of a lengthening stem allocation period based on past environmental changes. These findings offer a novel approach for carbon source-sink allocation to tree stems. Further application in a broader range of climatic zones would contribute to revealing the broad-scale allocation scheme and its dynamics in a changing global environment.