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For the nonlinear Kirchhoff-type wave system with logarithmic nonlinearities and weak dissipation the global well-posedness of initial boundary value problem is analyzed. Focusing on the interplay between Kirchhoff terms and logarithmic sources, we investigate the Kirchhoff system controlled by logarithmic forces thus amplifying the difficulties in blow up analysis which is the primary scenario of interest. By employing potential well method and concavity method, we obtain several results related to the sufficient conditions posed on subcritical initial energy and critical initial energy, which is used to classify initial data for global existence and finite time blow up. Finally, via careful analysis involving the unstable invariant set under supercritical initial energy, we are able to show an affirmative result that the solution blows up in finite time when initial data satisfy some suitable assumptions.

The leaf litter collection method is often used as a baseline for assessing leaf area index (LAI) measurements in forests by optical methods, but different protocols for measuring specific leaf area (SLA) may introduce biases in stand-level LAI estimates, which have not been quantified yet. To develop a standardized protocol for measuring SLA of leaf litter for estimating LAI via litterfall collection, we quantified the relative errors (RE) in the SLA measurements introduced by six protocols commonly-used in the literature with 46 deciduous woody species in a temperate forest, and assessed the stand-level LAI estimates derived from the SLA with eight permanent plots in the forest. The mean leaf area shrinkage from the litter collection across the species varied from 7.31 – 25.41% among the protocols, while the mean leaf mass loss varied from 2.07 – 24.68%. Compared with the reference, the mean RE of SLA introduced by the rest five protocols varied from −25.59 – 7.18%, and the subsequent RE of the stand-level LAI varied from −32.43 – 8.97%. We recommended a practical and reliable protocol for measuring SLA from leaf litter, i.e., weighing the dry mass first, then measuring the leaf area after rehydration with wet-filter-papers, and finally correcting for the leaf area shrinkage relative to the green leaf. We also provided general models for correcting for the SLA biases due to area shrinkage and mass loss of senesced leaves in temperate forests. Our findings will extend the direct measurements of LAI and improve the estimation of carbon and nutrient budgets in forest ecosystems.

We establish a new finite time blowup theorem for the solution to the initial boundary value problem of a class of semilinear pseudo-parabolic equations at high initial energy level. And we also estimate the upper bound of the blowup time.

Carbon dioxide (CO 2 ) fluxes between terrestrial ecosystems and the atmosphere are primarily measured with eddy covariance (EC), biometric, and chamber methods However, it is unclear why the estimates of the CO 2 -fluxes, when measured using different methods, converge at some sites but diverge at others. We synthesized a novel global dataset of forest CO 2 -fluxes to evaluate the consistency between EC and biometric or chamber methods for quantifying the CO 2 budget in forest ecosystems. The EC approach, compared with the other two methods, overestimated net ecosystem production (NEP) by 25% (0.52 Mg C ha −1 yr −1 ), and underestimated ecosystem respiration (Re) by 10% (1.39 Mg C ha −1 yr −1 ) and gross primary production by 3% (0.48 Mg C ha −1 yr −1 ). The differences between EC and the other methods were greater at the sites with complex topography and dense canopy than at the sites with flat topography and open canopy. Forest age also influenced the differences mainly through changes in leaf area index. Open-path EC system induced large positive bias in the NEP estimated by EC, presumably due to its surface-heating effect. These results suggest that EC method likely produce biased estimates of NEP and Re in forest ecosystems. A global extrapolation suggests that the differences in the forest CO 2 -fluxes measured with different methods be consistent with the global overestimation of NEP and underestimation of Re by EC method. Accounting for these differences would substantially improve our estimates of the forest carbon budget. The uncertainties involved in each method were also discussed. To reduce uncertainty in quantifying both local and global carbon budgets, we recommend cross-validation of forest CO 2 -fluxes measured by different methods with more accurate measurements and careful data processing strategies.

Canopy litterfall is an important component of net primary productivity (NPP) in forests, but the climatic and biotic controls on its interannual fluctuation remain poorly understood. In this study, we quantified the interannual variation in and the influencing factors of the canopy litterfall with 45 litter traps in nine plots for 12 years (2008 − 2019) in a temperate deciduous broad-leaved forest in Northeast China. The coefficients of interannual variation in the total (7.3%) and leaf (5.6%) litterfall were substantially lower than those in the basal area (BA) increment (21.0%) and gross primary productivity (10.2%). Climatic (i.e., air temperature, thermal time, precipitation, and radiation) and biotic (i.e., BA and species richness) factors jointly controlled the annual production of litterfall for individual plots and species. Significant climate legacy effects were detected in all components of the litterfall, with the strongest in woody tissue component that contributed to 58.9% of the total litterfall variability. The most important factor driving the variability of the total litterfall and its non-leaf components was climate legacy effect (67.2% to 86.6%), while those for the leaf litterfall were BA (40.4%) and species richness (38.3%). We conclude that high species richness of the deciduous forest increases the temporal stability of canopy productivity, and leaf productivity is much more stable than wood productivity as indicated by BA increament. These findings provide insight into spatiotemporal dynamics in the litterfall and canopy NPP in temperate deciduous forests.

Litterfall collection is a non-destructive direct method to estimate forest leaf area index (LAI) and validate indirect LAI products. However, the potential errors associated with the variation in specific leaf area (SLA) are rarely explored. Here, we measured the SLA of leaf litter for each tree species in a temperate deciduous forest using the litterfall collection method from 2012 to 2018, and assessed the spatial and temporal variation in SLA and its consequence on LAI estimates. The results showed that the spatial and temporal variation in SLA for the 10 major species across the seven years ranged from 0.8% to 24.3%, with the variation across the nine permanent plots (20 m × 30 m) being higher than that within plot (five 1-m2 traps), and interannual higher than seasonal. Across the 63 plot-years, the 10 simplified SLA sampling protocols introduced the errors in LAI by −12.4% to 22.2% relative to the reference protocol (sampling leaves from each trap at each collection date for the major species). Applying the SLA obtained from one trap in each plot, one plot, at the leaf fall peak for each year, or for a single year induced the errors in LAI by –3.7% to 2.9%, −6.4% to 14.7%, −9.2% to 4.7%, and −8.1% to 8.6%, respectively. Considering the trade-off between inter-plot and interannual variation, we recommend sampling from one-trap for each plot at the leaf-fall peak for measuring SLA and quantifying the spatial pattern of LAI, and sampling each species in the typical plot for measuring SLA and monitoring the temporal fluctuation in LAI. The tight relationship between the MODIS and ground reference LAI across the seven years (R2 = 0.77) validated the use of MODIS LAI to study the long-term change in forest LAI. These findings help to establish a standardized protocol for long-term accurately measuring forest LAI with the litterfall collection.

The interannual variability (IAV) of CO2 fluxes of temperate forests in continental East Asia was rarely explored via direct measurements. To explore the IAV of net ecosystem exchange of CO2 (NEE) and its driving factors, we continuously measured the CO2 fluxes of a temperate deciduous broadleaved forest at the Maoershan site, northeast China with a continental monsoon climate, by eddy covariance over 11 years (2008 – 2018). The means of NEE, gross primary production (GPP), and ecosystem respiration (Re) were −157 ± 64 (mean ± standard deviation), 1356 ± 148, and 1200 ± 138 g C m−2 yr−1, respectively. For annual fluxes, the IAV of NEE was jointly controlled by the length of net CO2 uptake period and the summer peak of net CO2 uptake, whereas those of GPP and Re were predominated by the summer peaks (GPPmax and Remax). Meanwhile, the dominant role of GPPmax on the IAV of GPP was attributed to the leaf-level photosynthetic capacity rather than the maximum leaf area index. However, the environmental factors showed weak impacts on NEE, largely because of the offset between the positive responses of GPP and Re to the spring and autumn soil water content, respectively. For particular seasons, phenology was the dominant biotic driver of the spring and autumn NEE, whereas spring precipitation and autumn photosynthetically active radiation were the main environmental drivers of the spring and autumn NEE, respectively. Overall, this work filled the gap of the relatively long-term CO2 fluxes measured in the temperate forests of continental East Asia. Taking the influences of ecosystem- and leaf-level physiology, canopy structure, and phenology, together with their environmental interactions, on the CO2 fluxes into account will improve the understanding and prediction of the forest carbon dynanics.

The CO 2 storage ( F s ) measurement can contribute significantly to the estimation of the net ecosystem exchange of CO 2 (NEE) especially in tall-canopy forest ecosystems. The F s is often measured with a profile of CO 2 concentration or with an eddy covariance system at the tower top, but few studies investigated potential errors in the F s measurements. We assessed the errors in F s relevant to the vertical distribution of sampling levels and window sizes of averaging time of CO 2 mixing ratio and their effects on NEE in a temperate deciduous forest site in Northeast China using the standardized major axis method. The CO 2 storage per unit height typically decreased with the height increasing, suggesting that the below-canopy layer need a higher spatial resolution. CO 2 storage could be underestimated by up to one third based only on the tower-top measurement. The uncertainty (standard deviation) of the F s decreased with the length of the averaging time window increasing. However, taking time averaging of CO 2 mixing ratio caused significant underestimate of F s , and consequently led to significant underestimates of CO 2 uptake and release at a 30-min time scale. Our results highlight that appropriately combining spatial resolution and temporal resolution (response time for a whole sampling of all levels) is essential to improving the F s estimates with the existing CO 2 profile systems in forest ecosystems. Since the systematic bias and random error in F s estimate with a single profile system are irreconcilable, there is an urgent need to develop a fast response planar-averaging profile or measure the instantaneous vertical-mean concentration to improve the accuracy of F s measurement.

Despite the economic and ecological importance of key carbon (C) traits (concentration, sequestration, and allocation to different tree components), there are few studies on their variation among populations of a tree species and the possible adaptive significance of these traits. We investigated differences in the C traits among 16 white birch populations grown in two provenance trials in northeastern China. Effects of provenance were significant for most combinations of C trait, tree portion, and trial site. Substantial differences among provenances were found in (1) C concentration in the bole wood and in bark, in fine roots, and at the whole tree scale; (2) C amount sequestered in each studied tree component and in the whole tree; and (3) ratios of C partitioning to bole wood, bole bark, leaves, and existing fine roots. Mostly, significant variations in C concentration and partitioning ratios were independent of provenance volume growth, while those in C amount were strongly positively correlated with volume growth. Summer climate at the provenance origin was the best predictor, of C concentration and allocation but clinal patterns in these traits were found for only some tree components. The C sequestration showed a clinal pattern following the mean annual temperature at the provenance origin. While this suggests an adaptive nature of C traits in white birch, site conditions and/or tree density act strongly on expression of these traits. Implications of this study to C budgeting, trading C credits, and to genetic selection are discussed. Our results may interest ecologists studying dynamics of ecosystems in times of climate change.

Leaf nutrient resorption helps plants minimize nutrient loss via litterfall. The commonly-used parameter to express the resorption, nutrient resorption efficiency (NuRE, the percentage of the leaf nutrient pool withdrawn before abscission), can be compromised by leaf mass loss (LML) and leaf area shrinkage (LAS) when they are not correctly accounted. However, the variations in LML and LAS and their consequences on real NuRE are still poorly understood. To explore the drivers of LML and LAS and their impact on NuRE, we conducted a comprehensive measurement on LML and LAS concomitant with NuRE for 46 deciduous woody species in a temperate forest. The LML and LAS ranged from –3.13% to 32.21% and 0.65% to 18.07%, respectively. On average, ignoring LML (LAS) underestimated the nitrogen and phosphorus resorption efficiencies by 6.93% and 7.39% (4.66% and 4.57%), respectively. The differences in LML and LAS among species and regions should be considered in NuRE studies. The LAS was significantly influenced by plant functional groups and leaf structural traits, while the LML was only weakly related to leaf-fall date. Green leaf area and thickness shrinkages could be used to model LAS. We finally provided suggestions for recovering the historical data and improving future measurements of NuRE.

This paper is devoted to the blowup phenomena for a class of fourth-order wave equation with nonlinear strain term. First, for the model equation with strain structure, we prove the finite time blowup of solution for the critical initial energy, i.e., E ( 0 ) = d . Then, the finite time blowup and the upper bound of the blowup time are established for the sup-critical initial energy, i.e., E ( 0 ) > 0 .

A sufficient condition on initial profile ensuring high initial energy finite time blowup along with the upper bound of the corresponding blowup time for the classical semilinear parabolic equations involving initial boundary value problem is established in this paper.

Autumn (i.e., leaf-fall) phenology plays an important role in regulating the canopy duration and is often monitored using near-surface and satellite remote sensing techniques, but the measurements have rarely been validated by the ground observation. The objectives of this study were to: (1) evaluate the performance of radiometer-based broadband vegetation index (VIB) and Moderate Resolution Imaging Spectroradiometer (MODIS) vegetation index (VIM) in monitoring the autumn phenology of a Chinese temperate deciduous forest with decadal (2008 – 2018) leaf-litterfall measurements, and (2) explore the feasibility of using VIB to validate the VIM products for monitoring the autumn phenology. We found that the seasonal and interannual trends of both VIB and VIM agreed well with those of the leaf-litterfall (correlation coefficients r > 0.93). The broadband normalized difference vegetation index (NDVIB) best tracked the interannual variation in the end-of-season (EOS) among the six metrics of the VIB investigated, while the MODIS enhanced vegetation index (EVIM) did so among the six metrics of the VIM, with the corresponding determination coefficient (R2) of 0.66 and 0.44 with the EOS estimated by the leaf-litterfall. The EOS estimated by VIB and VIM was 0 – 11 d earlier than that by the leaf-litterfall. Comparing the six metrics of VIM with the corresponding ones of VIB, the EOS derived from the NDVI had the closest correlation with each other (R2 = 0.67). Conclusively, our study validated the remote-sensed leaf-fall phenology with decadal ground measurements, and suggested that radiometer and MODIS could effectively track the autumn phenology in temperate deciduous forests and the leaf-litterfall collection could be used as a complementary approach.

Accurate estimation of seasonal leaf area index (LAI) variations is essential for predicting forest growth, but rapid and reliable methods for obtaining such estimates have rarely been reported. In this study, direct measurements of LAI seasonal variations in deciduous broadleaf forests in China were made through leaf seasonality observations in the leaf-out season and litter collection in the leaf-fall season. Meanwhile, indirect LAI measurements were made using a digital hemispherical photography (DHP) method. Our objectives were to explore the relationship between direct and indirect LAI measurements and to recommend a rapid and reliable method to determine the seasonal variation of LAI in forests. To achieve these objectives, we first evaluated seasonal variations of the biases due to key factors (woody materials, clumping effects and incorrect automatic exposure) known to influence the estimation of LAI by DHP. The results showed that the biases due to these factors exhibited different seasonal variation patterns, and the total contribution of these factors could explain 72% of the difference between direct LAI and DHP LAI throughout the entire growing season. Second, linear regression models between direct and DHP LAI were first constructed for each 10-day period as well as the entire growing season. Significance tests were made to the differences among the models for different dates, and models for estimating LAI based on DHP in each date were aggregated to 4 periods with R 2 and RMSE values of 0.91 and 0.22, 0.79 and 0.29, 0.81 and 0.14, 0.97 and 0.14, respectively. There was no significant difference between direct LAI and estimated LAI using the four models in each aggregated period ( p

a b s t r a c t Changes in characteristics of snowfall and spring freeze-thaw-cycle (FTC) events under the warming cli- mate make it critical to understand biophysical controls on soil CO2 efflux (RS) in seasonally snow-covered ecosystems. We conducted a snow removal experiment and took year-round continuous automated mea- surements of RS, soil temperature (T5) and soil volumetric water content at the 5 cm depth (W5) with a half-hour interval in a Chinese temperate forest in 2010-2011. Our objectives were to: (1) develop statistical models to describe the seasonality of RS in this forest; (2) quantify the contribution of seasonal RS to the annual budget; (3) examine biophysical effects of snowpack on RS; and (4) test the hypothesis that an FTC-induced enhancement of RS is jointly driven by biological and physical processes. Empirical RS-T5-W5 models explained 65.3-94.1% of the variability in the RS data, but the number of the regression terms and their coefficients varied with season. This indicates that the model should be fitted to the seasonal data sets separately to explicitly describe the seasonality of RS. The RS during the winter, spring FTC period, and growing season contributed 5.7%, 3.5%, and 91.1%, respectively, to the total annual RS. The relative enhancement of RS due to snowpack and FTCs averaged 3.4 and 2.5, respectively. The snowpack- induced enhancement of RS exponentially increased with T5 (R 2 = 0.83) and snow depth (R 2 = 0.16), while the FTC-induced enhancement of RS exponentially decreased with T5 (R2 = 0.45) and W5 (R2 = 0.67). These results suggest that the snowpack-induced enhancement mainly results from the snow-depth-dependent insulation of soil from low air temperatures, while the FTC-induced enhancement is dominantly driven by biological processes. Accumulatively, the snowpack and spring FTCs made a minor net contribution (2.3% and 1.2%, respectively) to the annual RS budget.

A mass-based carbon (C) concentration ([C]) of 50% in dry wood is widely accepted as a constant factor for conversion of biomass to C stock. However, the [C] varies with tree species, and few data on [C] are available for the Chinese temperate tree species. In this study, we examined inter- and intra-specific variations of [C] in biomass tissues for 10 co-occurring temperate tree species in northeastern China. The species were Korean pine ( Pinus koraiensis Sieb. et Zucc.), Dahurian larch ( Larix gmelinii Rupr.), Mongolian oak ( Quercus mongolica Fisch.), white birch ( Betula platyphylla Suk.), Amur cork-tree ( Phellodendron amurense Rupr.), Manchurian walnut ( Juglans mandshurica Maxim.), Manchurian ash ( Fraxinus mandshurica Rupr.), aspen ( Populous davidiana Dode), Mono maple ( Acer mono Maxim.), and Amur linden ( Tilia amurensis Rupr.). The mean tissue [C] across the species varied from 47.1% in fine root to 51.4% in foliage. The mean stem [C] of the 10 species was 49.9 ± 1.3% (mean ± SE). The weighted mean C concentration (WMCC) for the species ranked as: Amur cork-tree (55.1%) > Amur linden (53.9%) > Korean pine (53.2%) > Manchurian ash (52.9%) > Manchurian walnut (52.4%) > Mongolian oak (47.6%) > Dahurian larch (46.9%) > Mono maple (46.4%) > white birch (46.1%) > aspen (43.7%). The WMCC of the dominant trees was negatively correlated to mean annual increment of biomass (MAI), suggesting that planting fast-growing tree species for C sequestration in afforestation and reforestation practices sacrifice some C gain from increasing MAI due to decreasing [C]. Failing to account for the inter- and intra-specific variations in [C] will introduce a relative error of −6.7% to +7.2% in estimates of biomass C stock from inventory data, of which >93% is attributed to ignoring the inter-specific variation in [C].