Influence of physiological phenology on the seasonal pattern of ecosystem respiration in deciduous forests

The dataset

In this analysis, data from version 2 of the LaThuile FLUXNET dataset (http://www.fluxdata.org) were used. The LaThuile dataset contains 253 research sites belonging to the FLUXNET eddy covariance flux measurements network (Baldocchi, 2008). The analysis focused on 19 deciduous broadleaved forest sites (Table 1) that have at least 1 year of good quality CO₂ fluxes and meteorological data (i.e., only days with <15% of gap-filled half-hours were retained), and maximum leaf area index (LAI) (Migliavacca et al., 2011).

These sites are located in the Northern Hemisphere in a latitudinal range that spans from 63.92°N at the Bonanza Creek site (US-Bn2) to 38.74°N at the Missouri Ozark site (US-MOz). The climatic regions analyzed include Humid Mesothermal Climates to Humid Microthermal Climates (classes C and D), according to the Köppen classification (Peel et al., 2007).

The following daily data products of the FLUXNET dataset were used: R_ECO, GPP, midday net ecosystem exchange (NEE) (11:00–13:00 hours), nighttime NEE [average of half-hourly NEE selected according to a global radiation threshold of 20 Wm⁻² as defined by Reichstein et al. (2005)], daily mean air temperature (T_A), soil temperature (T_S), and 30-day backward precipitation running average (P). At each site, flux data were storage-corrected and spike-filtered as described in Papale et al. (2006), and subsequently gap-filled and partitioned as described by Reichstein et al. (2005).

For each site, we used estimates of fAPAR, retrieved from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) following methods of Gobron et al. (2000). The validation of the Joint Research Centre (JRC) fAPAR products (hereafter referred as JRC fAPAR) is described by Gobron et al. (2006). The fAPAR used in this study covers the period from September 1997 to June 2006 with a nominal spatial resolution of 1.5 km (http://fAPAR.jrc.ec.europa.eu/) (Gobron et al., 2006). The fAPAR values correspond to the 10-day time composite products spatially averaged over 3 × 3 pixels around the tower location. For the analysis of the spatial heterogeneity of the canopy fAPAR standard spatial deviations were classified into low, medium, and high variability according to the terciles of the distributions of the spatial standard deviation of the fAPAR.

Ecosystem respiration model

Description of TPLinGPP model

The semiempirical ecosystem respiration model, TPLinGPP [Eqn 1], was based on the TP Model, a climate-driven model proposed by Raich et al. (2002), and further modified by Reichstein et al. (2003) and cross-validated by using R_ECO estimates from the FLUXNET network (Migliavacca et al., 2011). The TPLinGPP concept was developed to simulate R_ECO as a function of daily ambient temperature T (which, if not declared otherwise is usually, T_A), P, and some base respiration rate as:

(1)

where R_ref (gCm⁻² day⁻¹) is the base ecosystem respiration (i.e., R_ECO) at the reference temperature (T_ref, K) without water limitations and is expressed as follows:

(2)

where R₀ is the theoretical ecosystem respiration at T_ref when no other limiting factor interferes. R₀ can be considered to be a functional indicator of site ecosystem respiration, closely related to structural site characteristics (e.g., LAI) and history (e.g., management and disturbance, Migliavacca et al., 2011). The term h(GPP) represents the dependency of reference respiration on productivity:

(3)

where k₂ represents the influence of supply via GPP on R_ref. The temperature dependence of R_ECO is modeled by using an Arrhenius-type equation:

(4)

E₀ (K) is the activation energy parameter and represents the sensitivity of ecosystem respiration to temperature, T_ref is fixed here at 288.15 K (15 °C) and T₀ is fixed at 227.13 K (−46.02 °C) (Lloyd & Taylor, 1994).

The response of R_ECO to precipitation was formulated as a function of P, the 30-day backward running average of precipitation:

(5)

where k (mm) is the half saturation constant of the hyperbolic relationship and α is the response of R_ECO to zero P. Soil water content is widely recognized as a viable descriptor of soil water availability, and the use of precipitation can be limiting for the simulation of R_ECO in forest sites where precipitation and soil water content are not tightly coupled. However, we preferred to use precipitation since the model was developed with an emphasis toward upscaling to larger areas and soil water maps have greater uncertainty than precipitation distributions (Peters-Lidard et al., 2008), and are often difficult to obtain. On the other hand, satellite remote sensing data only capture the very first centimeters of the soil and are, therefore, only partly representative for the available water for plants.

Development of the TPdGPP model

TPLinGPP was modified in the present study to reduce the spring bias observed over deciduous forests. A key insight from previous studies is that R_ref can be assumed to vary during the growing season, but is dependent of specific site characteristics (Reichstein et al., 2003; Migliavacca et al., 2011), productivity (GPP, Mahecha et al., 2010a; Migliavacca et al., 2011), and physiological phenology.

The first derivative of a canopy development indicator in spring was introduced to reduce the spring bias in modeled R_ECO. Specifically, either GPP or fAPAR was used for this purpose, and the daily values of the first derivative of their smoothed time series (i.e., dGPP/dt and dfAPAR/dt, respectively) were computed. For this purpose the time series of daily GPP and 10-daily fAPAR were smoothed and gap-filled using a cubic spline with degrees of freedom adjusted to the length of the time series (30 for GPP and 20 for fAPAR). The first derivatives were numerically computed from the smoothed time series. Because our focus is on the spring period, we set the negative values of the first derivative that occurred in autumn to 0, retaining only values of dGPP/dt>0 (Fig. 1b).

The TPLinGPP was then modified by introducing the sensitivity to reference respiration to dGPP/dt (or dfAPAR/dt) as follows:

(6)

The final TPdGPP equation is:

(7)

where k₂₀ is the parameter describing the linear dependency of the reference respiration to physiological phenology (dGPP/dt or dfAPAR/dt).

Statistical analysis

Estimation of model parameters and evaluation of model performance

Model parameters were estimated using the Levenberg–Marquardt method, implemented using the optim routine in R (version 2.14.0). Model parameter standard errors were estimated based on 500 bootstrap samples. As described by Efron & Tibshirani (1993), the obtained distribution of parameter estimates approximates the distribution of the ‘true’ model parameters.

Model performance was evaluated using a range of metrics (root mean square error, RMSE; coefficient of determination, R²; and mean absolute error, MAE; Janssen & Heuberger, 1995) to examine whether the inclusion of physiological phenology improved the description of the temporal variability of R_ECO. Modeling efficiency (EF), a measure of the coincidence between observed and modeled data, was also computed. EF ranges between -∞ to 1. A value of 1 corresponds to a perfect match between model and observation, while EF <0 indicate that the mean of the observations is a better predictor than the model. EF is sensitive to systematic deviation between model and observation (Janssen & Heuberger, 1995). Model statistics and residuals (observation-modeled value) were computed for the whole year and for each season (MAM, March–April–May; JJA, June–July–August; SON, September–October–November; and DJF, December–January–February) in order to evaluate the improvement in the description of the seasonal cycle of R_ECO.

The Akaike's Information Criterion (AIC) was used to select amongst the two alternative model formulations considering both model explanatory power and the model complexity (i.e., number of parameters). The following formulation was used (Anderson et al., 2000; Richardson et al., 2006):

(8)

where n is the number of observations (i.e., days in the time series), equals the estimated within-sample residual sum of squares divided by n, and p is the number of parameters in the model. The model with the lowest AIC was considered the best model. The differences between the AIC (ΔAIC) computed for the TPdGPP (AIC_TPdGPP) model and the TPLinGPP (AIC_TPLinGPP) were computed. Negative differences indicated that the TPdGPP model, despite the higher complexity, was the best model formulation for the target dataset.

Evaluation of models performance

Across sites, the mean EF obtained for the two models, using the driver-observations GPP-dGPP-R_ECO, was 0.72 [interquartile distance 0.64–0.82] for the TPLinGPP model, and 0.76 [0.68–0.83] for the TPdGPP model (Table 3). For the driver-observations NEEm-dfAPAR-NEEn, the mean EF decreased to 0.66 (0.70) for the TPLinGPP (TPdGPP) (Table 4). By using the explicit description of physiological phenology, a decrease in RMSE of ~8% was achieved for GPP-dGPP-R_ECO and ~3% for NEEm-dfAPAR-NEEn. The largest improvement of model performance was observed at DE-Hai, FR-Fon, US-Bn2, IT-LMa, IT-Ro2, and US-MOz. Almost no improvement in model performance was observed at CA-Oas, FR-Hes, US-UMB, and US-LPH. The mean ΔAIC of −91.11 (−31.14) obtained for the driver-observations GPP-dGPP-R_ECO (NEEm-dfAPAR-NEEn) indicated that, even accounting for the higher models complexity (i.e., 1 parameter more), the TPdGPP model outperforms the TPLinGPP (Tables 3 and 4).

The use of the TPdGPP model led to a reduction of the model-observation mismatch, particularly in spring (Figs 2, 3, Table 5). The reduction of annual model residuals was not as relevant as that at seasonal time scale, likely because the seasonal bias in spring was partly compensated by negative biases in summer.

Spectral analysis of model residuals

The boxplots of the model residual variance computed at each site for the monthly and annual time scales indicated a tendency toward lower variance on the monthly time scale for the TPdGPP model compared to the TPLinGPP model, for both driver-observation combinations (Fig. 4). On the annual time scale, a reduction in residual variance was also observed, however, differences were less pronounced than at the monthly time scale. For the driver-observations NEEm-dfAPAR-NEEn, the reduction of the residual variance at the monthly time scale was lower at sites with high spatial heterogeneity (Fig. 5). The latter was derived using the spatial standard deviation of JRC fAPAR computed in spring (Fig. 5a) and during the whole year (Fig. 5b).

Sources of uncertainty for the TPdGPP model

Comparing R² values for the TPdGPP model driven by T_S and T_A indicates that the model driven by T_A outperformed the model driven by T_S in winter and early spring, while the R² are similar in August and September (Fig. 6). The relative differences in RMSE between the TPLinGPP and TPdGPP model driven by T_S and T_A were generally low, except in a few sites (CA-Oas, IT-PT1, US-LPH, US-MMS, US-UMB; Table 6). At these sites we observed a small improvement of the performance using the TPdGPP model driven by T_A, whereas, when using T_S, the reduction of RMSE was larger, indicating that T_S is likely the most important driver over these sites. The analysis conducted with a lagged response between dGPP/dt and R_ECO did not show a clear relationship between improvement in model performance and the time lag. Only the two sites with the largest improvement in model performances (i.e., DE-Hai and FR-Fon) were characterized by no or short lags between the physiological phenology and R_ECO, whereas at sites with a larger lag time, the improvement in model performance from introducing TPdGPP was less important (Fig. 7).

Physiological phenology controls on ecosystem respiration

In a previous study, (Migliavacca et al., 2011) we showed that taking into consideration the dependency of R_ECO on some measure of short-term productivity (e.g., via coupling the base respiration to GPP) improved the skill of empirical R_ECO models significantly. Here, we show that, for a sample of deciduous broadleaved forests, R_ECO is controlled by climate (temperature and precipitation pulses) and canopy photosynthesis, and also by springtime physiological phenology. The latter can be approximated by the first derivative of daily smoothed GPP or fAPAR. The results obtained with the combination GPP-dGPP-R_ECO were more robust than those obtained with NEEm-dfAPAR-NEEn. This might be due to the higher noise in NEE time series, to scale mismatch between the eddy covariance flux tower and satellite footprint (Jung et al., 2008), and to the fact that nighttime NEEn reflects primarily the dynamics of soil respiration and, to a lesser extent, the dynamics of the aboveground respiration that are an important cause for the bias observed during the springtime period. Fig. 5 highlights that the largest reduction of the model-observation bias was observed in spatially homogeneous sites, suggesting that the proposed approach is sensitive to landscape heterogeneity. GPP is a more direct descriptor of the canopy photosynthetic capacity than fAPAR, which tracks the development of leaf area index. Interestingly, regardless of the driver-observations used (i.e., NEEm-dfAPAR-NEEn and GPP-dGPP-R_ECO), we identified a clear effect of physiological phenology on R_ECO. This finding leads to the proposed data-oriented semiempirical model that takes these linkages into account to improve the description of the seasonal cycle of R_ECO.

The analysis of the ratio of the R² between TPdGPP models driven by T_S and T_A confirms the importance of air temperature during springtime (Fig. 6), suggesting that aboveground respiration plays an important role in spring. This supports the need to include physiological phenology as an additional driver in modeling R_ECO (Irvine et al., 2008). The seasonal dynamics observed in Fig. 6 are consistent with Davidson et al. (2006) and Giasson et al. (2013), who reported a spring pulse of aboveground respiration, leading to a minimum in the ratio between soil respiration and R_ECO in March and early April.

Limitations and future perspectives

Model performance statistics (Tables 3 and 4) show that the use of the explicit description of physiological phenology for some sites does not reduce the springtime bias in R_ECO. While all investigated sites are classified as deciduous broadleaved forests, some are composed of multiple tree species. Different species could have different and asynchronous phenological patterns that might confound the influence of physiological phenology on R_ECO at the ecosystem level. Moreover, considering that the R_ECO is observed at the ecosystem level with a variable footprint, the spatial heterogeneity of the canopy (Cescatti et al., 2012) might contribute to the poor model performances at some sites. For sites characterized by no or short lags between the physiological phenology and R_ECO, TPdGPP showed the largest improvement, whereas for sites characterized by larger lags the improvement of model performance by introducing TPdGPP was less (Fig. 7). For some sites, the springtime peak of R_ECO might precede the peak of dGPP/dt because production of new leaves requires an increase in metabolic activity (e.g., translocation of carbon stored in woody tissues) that would precede the onset of photosynthetic activity. This lag between foliage expansion and the development of photosynthetic capacity has been reported in the literature (e.g., Morecroft et al., 2003) and might be one of the causes of the limited improvement in model performance for some sites.

Future work is necessary to reduce the autumn bias of R_ECO, though less pronounced than the bias in spring, observed with the empirical model proposed by Migliavacca et al. (2011). The autumn bias might be related to the rapid decomposition of fresh litter inputs (DeForest et al., 2009), which is not accounted for by the empirical model. Decomposition in autumn may also be higher because of a large pulse of fine root turnover in addition to leaf litter fall. The inclusion of leaf or fine root litter pools would effectively turn our simple, empirical model into a more complex process-based model. Autumn bias might also be related to the difference between soil and air temperature, as soil temperature is higher than air temperature in the autumn. Thus, the TPLinGPP model driven by T_A may lead to an underestimation of autumn respiration. In Fig. 8, the mean residuals during autumn at each site are correlated (r = 0.42 P < 0.1) with the mean difference between daily mean autumn T_S and T_A. In general, sites with higher model residuals in autumn are the ones with a more positive soil–air temperature difference (i.e., soil warmer than air).

Implication for data-oriented modeling

DeForest et al. (2006) showed that phenophase-specific models of soil respiration improve estimates of annual respiration. In fact, incorporating phenology into soil respiration models indirectly accounts for changes in environmental and/or biological factors that were not explicitly defined in the proposed model. The authors suggested that, ideally, the component fluxes of respiration should be modeled independently, or at least grouped according to time windows and environmental conditions during which common regulatory mechanisms (e.g., phenology) can be assumed. In this study, we proposed an empirical model for R_ECO that includes the first derivative of GPP (or fAPAR) to explicitly account for the physiological phenology-related pulse of R_ECO during spring (from bud-break to leaf unfolding), before reaching the maximum LAI.

Our results suggest that the proposed model structure reduces the spring-summer bias in R_ECO estimates. Annual estimates of R_ECO are also less biased even though to a lesser extent than at seasonal time scale. This is probably due to the compensation of the model bias in spring (positive) and summer (negative) without the explicit dependency of R_ECO on physiological phenology. The spring bias is particularly relevant to global carbon cycle studies for several reasons. First, spring is considered the most critical period determining the interannual variability of the net ecosystem CO₂ uptake (Le Maire et al., 2010) in ecosystems that are not characterized by summer drought and, therefore, an accurate modeling of respiration will likely improve estimates of the net CO₂ uptake in this crucial period. Second, the mean springtime and annual bias introduced by using the two different modeling approaches at global scale results in a difference in the net carbon uptake of about 1.4 PgC yr⁻¹ at the annual time scale, while a difference of 0.6 PgC and 0.8 PgC are expected in spring and summer, respectively. These results were obtained by multiplying the average residuals by the global coverage of deciduous forests in m² [1752105 km² according to Hansen et al. (2000)]. The springtime bias in R_ECO might significantly affect the estimates of land–atmosphere CO₂ fluxes obtained from atmospheric inversion models when these data are used as priors. This is particularly relevant for regional-scale inversions because the distribution of temperate deciduous forests is divided mainly between Northern Eurasia and Northeastern America.

In conclusion, our study suggests that it is necessary to account for the dependence of ecosystem respiration on short-term productivity (e.g., daily GPP) and on the physiological phenology to guarantee reliable simulations of R_ECO of deciduous broadleaved forests. By explicitly including the effects of physiological phenology on R_ECO, we found that spring and summertime biases observed in previous studies are significantly reduced. This implies that for global or regional-scale application of data-oriented empirical models, some measure of rate of development of physiological phenology needs to be included to improve the simulation of seasonal and interannual variability of R_ECO. This improvement is necessary to strengthen the analysis and interpretation of the seasonal cycle of the global CO₂ growth rate and annual carbon balance. Although the present study using the FLUXNET database clearly reveals a tight linkage between physiological phenology and ecosystem respiration in deciduous forests, future experimental efforts should focus on refining the mechanistic understanding of this linkage. From a modeling perspective, future work is also needed to improve the simulation of the respiration pulse in autumn.