Parameter identifiability, constraint, and equifinality in data assimilation with ecosystem models

Convergence in simulating global soil organic carbon by structurally different models after data assimilation

Current biogeochemical models produce carbon-climate feedback projections with large uncertainties, often attributed to their structural differences when simulating soil organic carbon (SOC) dynamics worldwide. However, choices of model parameter values that quantify the strength and represent properties of different soil carbon cycle processes could also contribute to model simulation uncertainties. Here, we demonstrate the critical role of using common observational data in reducing model uncertainty in estimates of global SOC storage. Two structurally different models featuring distinctive carbon pools, decomposition kinetics, and carbon transfer pathways simulate opposite global SOC distributions with their customary parameter values yet converge to similar results after being informed by the same global SOC database using a data assimilation approach. The converged spatial SOC simulations result from similar simulations in key model components such as carbon transfer efficiency, baseline decomposition rate, and environmental effects on carbon fluxes by these two models after data assimilation. Moreover, data assimilation results suggest equally effective simulations of SOC using models following either first-order or Michaelis-Menten kinetics at the global scale. Nevertheless, a wider range of data with high-quality control and assurance are needed to further constrain SOC dynamics simulations and reduce unconstrained parameters. New sets of data, such as microbial genomics-function relationships, may also suggest novel structures to account for in future model development. Overall, our results highlight the importance of observational data in informing model development and constraining model predictions.

Assessing Ecosystem State Space Models: Identifiability and Estimation

Hierarchical probability models are being used more often than non-hierarchical deterministic process models in environmental prediction and forecasting, and Bayesian approaches to fitting such models are becoming increasingly popular. In particular, models describing ecosystem dynamics with multiple states that are autoregressive at each step in time can be treated as statistical state space models (SSMs). In this paper, we examine this subset of ecosystem models, embed a process-based ecosystem model into an SSM, and give closed form Gibbs sampling updates for latent states and process precision parameters when process and observation errors are normally distributed. Here, we use simulated data from an example model (DALECev) and study the effects changing the temporal resolution of observations on the states (observation data gaps), the temporal resolution of the state process (model time step), and the level of aggregation of observations on fluxes (measurements of transfer rates on the state process). We show that parameter estimates become unreliable as temporal gaps between observed state data increase. To improve parameter estimates, we introduce a method of tuning the time resolution of the latent states while still using higher-frequency driver information and show that this helps to improve estimates. Further, we show that data cloning is a suitable method for assessing parameter identifiability in this class of models. Overall, our study helps inform the application of state space models to ecological forecasting applications where (1) data are not available for all states and transfers at the operational time step for the ecosystem model and (2) process uncertainty estimation is desired.

Inferring pesticide toxicity to honey bees from a field-based feeding study using a colony model and Bayesian inference

Honey bees are crucial pollinators for agricultural crops but are threatened by a multitude of stressors including exposure to pesticides. Linking our understanding of how pesticides affect individual bees to colony-level responses is challenging because colonies show emergent properties based on complex internal processes and interactions among individual bees. Agent-based models that simulate honey bee colony dynamics may be a tool for scaling between individual and colony effects of a pesticide. The U.S. Environmental Protection Agency (USEPA) and U.S. Department of Agriculture (USDA) are developing the VarroaPop + Pesticide model, which simulates the dynamics of honey bee colonies and how they respond to multiple stressors, including weather, Varroa mites, and pesticides. To evaluate this model, we used Approximate Bayesian Computation to fit field data from an empirical study where honey bee colonies were fed the insecticide clothianidin. This allowed us to reproduce colony feeding study data by simulating colony demography and mortality from ingestion of contaminated food. We found that VarroaPop + Pesticide was able to fit general trends in colony population size and structure and reproduce colony declines from increasing clothianidin exposure. The model underestimated adverse effects at low exposure (36 µg/kg), however, and overestimated recovery at the highest exposure level (140 µg/kg), for the adult and pupa endpoints, suggesting that mechanisms besides oral toxicity-induced mortality may have played a role in colony declines. The VarroaPop + Pesticide model estimates an adult oral LD₅₀ of 18.9 ng/bee (95% CI 10.1-32.6) based on the simulated feeding study data, which falls just above the 95% confidence intervals of values observed in laboratory toxicology studies on individual bees. Overall, our results demonstrate a novel method for analyzing colony-level data on pesticide effects on bees and making inferences on pesticide toxicity to individual bees.

Probabilistic early warning signals

Ecological communities and other complex systems can undergo abrupt and long-lasting reorganization, a regime shift, when deterministic or stochastic factors bring them to the vicinity of a tipping point between alternative states. Such changes can be large and often arise unexpectedly. However, theoretical and experimental analyses have shown that changes in correlation structure, variance, and other standard indicators of biomass, abundance, or other descriptive variables are often observed prior to a state shift, providing early warnings of an anticipated transition. Natural systems manifest unknown mixtures of ecological and environmental processes, hampered by noise and limited observations. As data quality often cannot be improved, it is important to choose the best modeling tools available for the analysis.We investigate three autoregressive models and analyze their theoretical differences and practical performance. We formulate a novel probabilistic method for early warning signal detection and demonstrate performance improvements compared to nonprobabilistic alternatives based on simulation and publicly available experimental time series.The probabilistic formulation provides a novel approach to early warning signal detection and analysis, with enhanced robustness and treatment of uncertainties. In real experimental time series, the new probabilistic method produces results that are consistent with previously reported findings.Robustness to uncertainties is instrumental in the common scenario where mechanistic understanding of the complex system dynamics is not available. The probabilistic approach provides a new family of robust methods for early warning signal detection that can be naturally extended to incorporate variable modeling assumptions and prior knowledge.

Parameter Optimization of the 3PG Model Based on Sensitivity Analysis and a Bayesian Method

Sensitivity analysis and parameter optimization of stand models can improve their efficiency and accuracy, and increase their applicability. In this study, the sensitivity analysis, screening, and optimization of 63 model parameters of the Physiological Principles in Predicting Growth (3PG) model were performed by combining a sensitivity analysis method and the Markov chain Monte Carlo (MCMC) method of Bayesian posterior estimation theory. Additionally, a nine-year observational dataset of Chinese fir trees felled in the Shunchang Forest Farm, Nanping, was used to analyze, screen, and optimize the 63 model parameters of the 3PG model. The results showed the following: (1) The parameters that are most sensitive to stand stocking and diameter at breast height (DBH) are nWs(power in stem mass vs. diameter relationship), aWs(constant in stem mass vs. diameter relationship), alphaCx(maximum canopy quantum efficiency), k(extinction coefficient for PAR absorption by canopy), pRx(maximum fraction of NPP to roots), pRn(minimum fraction of NPP to roots), and CoeffCond(defines stomatal response to VPD); (2) MCMC can be used to optimize the parameters of the 3PG model, in which the posterior probability distributions of nWs, aWs, alphaCx, pRx, pRn, and CoeffCond conform to approximately normal or skewed distributions, and the peak value is prominent; and (3) compared with the accuracy before sensitivity analysis and a Bayesian method, the biomass simulation accuracy of the stand model was increased by 13.92%, and all indicators show that the accuracy of the improved model is superior. This method can be used to calibrate the parameters and analyze the uncertainty of multi-parameter complex stand growth models, which are important for the improvement of parameter estimation and simulation accuracy.

Warming-induced global soil carbon loss attenuated by downward carbon movement

The fate of soil organic carbon (SOC) under warming is poorly understood, particularly across large extents and in the whole-soil profile. Using a data-model integration approach applied across the globe, we find that downward movement of SOC along the soil profile reduces SOC loss under warming. We predict that global SOC stocks (down to 2 m) will decline by 4% (~80 Pg) on average when SOC reaches the steady state under 2°C warming, assuming no changes in net primary productivity (NPP). To compensate such decline (i.e. maintain current SOC stocks), a 3% increase of NPP is required. Without the downward SOC movement, global SOC declines by 15%, while a 20% increase in NPP is needed to compensate that loss. This vital role of downward SOC movement in controlling whole-soil profile SOC dynamics in response to warming is due to the protection afforded to downward-moving SOC by depth, indicated by much longer residence times of SOC in deeper layers. Additionally, we find that this protection could not be counteracted by promoted decomposition due to the priming of downward-moving new SOC from upper layers on native old SOC in deeper layers. This study provides the first estimation of whole-soil SOC changes under warming and additional NPP required to compensate such changes across the globe, and reveals the vital role of downward movement of SOC in reducing SOC loss under global warming.

Research challenges and opportunities for using big data in global change biology

Global change biology has been entering a big data era due to the vast increase in availability of both environmental and biological data. Big data refers to large data volume, complex data sets, and multiple data sources. The recent use of such big data is improving our understanding of interactions between biological systems and global environmental changes. In this review, we first explore how big data has been analyzed to identify the general patterns of biological responses to global changes at scales from gene to ecosystem. After that, we investigate how observational networks and space-based big data have facilitated the discovery of emergent mechanisms and phenomena on the regional and global scales. Then, we evaluate the predictions of terrestrial biosphere under global changes by big modeling data. Finally, we introduce some methods to extract knowledge from big data, such as meta-analysis, machine learning, traceability analysis, and data assimilation. The big data has opened new research opportunities, especially for developing new data-driven theories for improving biological predictions in Earth system models, tracing global change impacts across different organismic levels, and constructing cyberinfrastructure tools to accelerate the pace of model-data integrations. These efforts will uncork the bottleneck of using big data to understand biological responses and adaptations to future global changes.

Ensuring identifiability in hierarchical mixed effects Bayesian models

Ecologists are increasingly familiar with Bayesian statistical modeling and its associated Markov chain Monte Carlo (MCMC) methodology to infer about or to discover interesting effects in data. The complexity of ecological data often suggests implementation of (statistical) models with a commensurately rich structure of effects, including crossed or nested (i.e., hierarchical or multi-level) structures of fixed and/or random effects. Yet, our experience suggests that most ecologists are not familiar with subtle but important problems that often arise with such models and with their implementation in popular software. Of foremost consideration for us is the notion of effect identifiability, which generally concerns how well data, models, or implementation approaches inform about, i.e., identify, quantities of interest. In this paper, we focus on implementation pitfalls that potentially misinform subsequent inference, despite otherwise informative data and models. We illustrate the aforementioned issues using random effects regressions on synthetic data. We show how to diagnose identifiability issues and how to remediate these issues with model reparameterization and computational and/or coding practices in popular software, with a focus on JAGS, OpenBUGS, and Stan. We also show how these solutions can be extended to more complex models involving multiple groups of nested, crossed, additive, or multiplicative effects, for models involving random and/or fixed effects. Finally, we provide example code (JAGS/OpenBUGS and Stan) that practitioners can modify and use for their own applications.

Ecological Dynamics: Integrating Empirical, Statistical, and Analytical Methods

Understanding ecological processes and predicting long-term dynamics are ongoing challenges in ecology. To address these challenges, we suggest an approach combining mathematical analyses and Bayesian hierarchical statistical modeling with diverse data sources. Novel mathematical analysis of ecological dynamics permits a process-based understanding of conditions under which systems approach equilibrium, experience large oscillations, or persist in transient states. This understanding is improved by combining ecological models with empirical observations from a variety of sources. Bayesian hierarchical models explicitly couple process-based models and data, yielding probabilistic quantification of model parameters, system characteristics, and associated uncertainties. We outline relevant tools from dynamical analysis and hierarchical modeling and argue for their integration, demonstrating the value of this synthetic approach through a simple predator-prey example.

A river runs through it: The causes, consequences, and management of intraspecific diversity in river networks

Rivers are fascinating ecosystems in which the eco-evolutionary dynamics of organisms are constrained by particular features, and biologists have developed a wealth of knowledge about freshwater biodiversity patterns. Over the last 10 years, our group used a holistic approach to contribute to this knowledge by focusing on the causes and consequences of intraspecific diversity in rivers. We conducted empirical works on temperate permanent rivers from southern France, and we broadened the scope of our findings using experiments, meta-analyses, and simulations. We demonstrated that intraspecific (genetic) diversity follows a spatial pattern (downstream increase in diversity) that is repeatable across taxa (from plants to vertebrates) and river systems. This pattern can result from interactive processes that we teased apart using appropriate simulation approaches. We further experimentally showed that intraspecific diversity matters for the functioning of river ecosystems. It indeed affects not only community dynamics, but also key ecosystem functions such as litter degradation. This means that losing intraspecific diversity in rivers can yield major ecological effects. Our work on the impact of multiple human stressors on intraspecific diversity revealed that-in the studied river systems-stocking of domestic (fish) strains strongly and consistently alters natural spatial patterns of diversity. It also highlighted the need for specific analytical tools to tease apart spurious from actual relationships in the wild. Finally, we developed original conservation strategies at the basin scale based on the systematic conservation planning framework that appeared pertinent for preserving intraspecific diversity in rivers. We identified several important research avenues that should further facilitate our understanding of patterns of local adaptation in rivers, the identification of processes sustaining intraspecific biodiversity-ecosystem function relationships, and the setting of reliable conservation plans.

Deep Learning Optimizes Data-Driven Representation of Soil Organic Carbon in Earth System Model Over the Conterminous United States

Soil organic carbon (SOC) is a key component of the global carbon cycle, yet it is not well-represented in Earth system models to accurately predict global carbon dynamics in response to climate change. This novel study integrated deep learning, data assimilation, 25,444 vertical soil profiles, and the Community Land Model version 5 (CLM5) to optimize the model representation of SOC over the conterminous United States. We firstly constrained parameters in CLM5 using observations of vertical profiles of SOC in both a batch mode (using all individual soil layers in one batch) and at individual sites (site-by-site). The estimated parameter values from the site-by-site data assimilation were then either randomly sampled (random-sampling) to generate continentally homogeneous (constant) parameter values or maximally preserved for their spatially heterogeneous distributions (varying parameter values to match the spatial patterns from the site-by-site data assimilation) so as to optimize spatial representation of SOC in CLM5 through a deep learning technique (neural networking) over the conterminous United States. Comparing modeled spatial distributions of SOC by CLM5 to observations yielded increasing predictive accuracy from default CLM5 settings (R ² = 0.32) to randomly sampled (0.36), one-batch estimated (0.43), and deep learning optimized (0.62) parameter values. While CLM5 with parameter values derived from random-sampling and one-batch methods substantially corrected the overestimated SOC storage by that with default model parameters, there were still considerable geographical biases. CLM5 with the spatially heterogeneous parameter values optimized from the neural networking method had the least estimation error and less geographical biases across the conterminous United States. Our study indicated that deep learning in combination with data assimilation can significantly improve the representation of SOC by complex land biogeochemical models.

Improving plant allometry by fusing forest models and remote sensing

Allometry determines how tree shape and function scale with each other, related through size. Allometric relationships help scale processes from the individual to the global scale and constitute a core component of vegetation models. Allometric relationships have been expected to emerge from optimisation theory, yet this does not suitably predict empirical data. Here we argue that the fusion of high-resolution data, such as those derived from airborne laser scanning, with individual-based forest modelling offers insight into how plant size contributes to large-scale biogeochemical processes. We review the challenges in allometric scaling, how they can be tackled by advances in data-model fusion, and how individual-based models can serve as data integrators for dynamic global vegetation models.

A hierarchical Bayesian approach for handling missing classification data

Ecologists use classifications of individuals in categories to understand composition of populations and communities. These categories might be defined by demographics, functional traits, or species. Assignment of categories is often imperfect, but frequently treated as observations without error. When individuals are observed but not classified, these "partial" observations must be modified to include the missing data mechanism to avoid spurious inference.We developed two hierarchical Bayesian models to overcome the assumption of perfect assignment to mutually exclusive categories in the multinomial distribution of categorical counts, when classifications are missing. These models incorporate auxiliary information to adjust the posterior distributions of the proportions of membership in categories. In one model, we use an empirical Bayes approach, where a subset of data from one year serves as a prior for the missing data the next. In the other approach, we use a small random sample of data within a year to inform the distribution of the missing data.We performed a simulation to show the bias that occurs when partial observations were ignored and demonstrated the altered inference for the estimation of demographic ratios. We applied our models to demographic classifications of elk (Cervus elaphus nelsoni) to demonstrate improved inference for the proportions of sex and stage classes.We developed multiple modeling approaches using a generalizable nested multinomial structure to account for partially observed data that were missing not at random for classification counts. Accounting for classification uncertainty is important to accurately understand the composition of populations and communities in ecological studies.

Loci That Control Nonlinear, Interdependent Responses to Combinations of Drought and Nitrogen Limitation

Crop improvement must accelerate to feed an increasing human population in the face of environmental changes. Including anticipated climatic changes with genetic architecture in breeding programs could better optimize improvement strategies. Combinations of drought and nitrogen limitation already occur world-wide. We therefore analyzed the genetic architecture underlying the response of Zea mays to combinations of water and nitrogen stresses. Recombinant inbreds were subjected to nine combinations of the two stresses using an optimized response surface design, and their growth was measured. Three-dimensional response surfaces were fit globally and to each polymorphic allele to determine which genetic markers were associated with different response surfaces. Three quantitative trait loci that produced nonlinear surfaces were mapped. To better understand the physiology of the response, we developed a model that reproduced the shapes of the surfaces, their most characteristic feature. The model contains two components that each combine the nitrogen and water inputs. The relative weighting of the two components and the inputs is governed by five parameters, and each QTL affects all five parameters.

We estimated the model’s parameter values for the experimental surfaces using a mesh of points that covered the surfaces’ most distinctive regions. Surfaces computed using these values reproduced the experimental surfaces well, as judged by three different criteria at the mesh points. The modeling and shape comparison techniques used here can be extended to other complex, high-dimensional, nonlinear phenotypes. We encourage the application of our findings and methods to experiments that mix crop protection measures, stresses, or both, on elite and landrace germplasm.

Estimating parametric phenotypes that determine anthesis date in Zea mays: Challenges in combining ecophysiological models with genetics

Ecophysiological crop models encode intra-species behaviors using parameters that are presumed to summarize genotypic properties of individual lines or cultivars. These genotype-specific parameters (GSP’s) can be interpreted as quantitative traits that can be mapped or otherwise analyzed, as are more conventional traits. The goal of this study was to investigate the estimation of parameters controlling maize anthesis date with the CERES-Maize model, based on 5,266 maize lines from 11 plantings at locations across the eastern United States. High performance computing was used to develop a database of 356 million simulated anthesis dates in response to four CERES-Maize model parameters. Although the resulting estimates showed high predictive value (R2 = 0.94), three issues presented serious challenges for use of GSP’s as traits. First (expressivity), the model was unable to express the observed data for 168 to 3,339 lines (depending on the combination of site-years), many of which ended up sharing the same parameter value irrespective of genetics. Second, for 2,254 lines, the model reproduced the data, but multiple parameter sets were equally effective (equifinality). Third, parameter values were highly dependent (p<10⁻⁶⁹¹⁹) on the sets of environments used to estimate them (instability), calling in to question the assumption that they represent fundamental genetic traits. The issues of expressivity, equifinality and instability must be addressed before the genetic mapping of GSP’s becomes a robust means to help solve the genotype-to-phenotype problem in crops.

Matrix approach to land carbon cycle modeling: A case study with the Community Land Model

The terrestrial carbon (C) cycle has been commonly represented by a series of C balance equations to track C influxes into and effluxes out of individual pools in earth system models (ESMs). This representation matches our understanding of C cycle processes well but makes it difficult to track model behaviors. It is also computationally expensive, limiting the ability to conduct comprehensive parametric sensitivity analyses. To overcome these challenges, we have developed a matrix approach, which reorganizes the C balance equations in the original ESM into one matrix equation without changing any modeled C cycle processes and mechanisms. We applied the matrix approach to the Community Land Model (CLM4.5) with vertically-resolved biogeochemistry. The matrix equation exactly reproduces litter and soil organic carbon (SOC) dynamics of the standard CLM4.5 across different spatial-temporal scales. The matrix approach enables effective diagnosis of system properties such as C residence time and attribution of global change impacts to relevant processes. We illustrated, for example, the impacts of CO₂ fertilization on litter and SOC dynamics can be easily decomposed into the relative contributions from C input, allocation of external C into different C pools, nitrogen regulation, altered soil environmental conditions, and vertical mixing along the soil profile. In addition, the matrix tool can accelerate model spin-up, permit thorough parametric sensitivity tests, enable pool-based data assimilation, and facilitate tracking and benchmarking of model behaviors. Overall, the matrix approach can make a broad range of future modeling activities more efficient and effective.

Uncertain future soil carbon dynamics under global change predicted by models constrained by total carbon measurements

Pool-based carbon (C) models are widely applied to predict soil C dynamics under global change and infer underlying mechanisms. However, it is unclear about the credibility of model-predicted C pool size, decay rate (k), and/or microbial C use efficiency (e) as only data on bulked total C is usually available for model constraining. Using observing system simulation experiments (OSSE), we constrained a two-pool model using simulated data sets of total soil C dynamics under topical hypotheses on responses of soil C dynamics to warming and elevated CO₂ (i.e., global change scenarios). The results indicated that the model predicted great uncertainties in C pool size, k, and e under all global change scenarios, resulting in the difficulty to correctly infer the presupposed "real" values of those parameters that are used to generate the simulated total soil C for constraining the model. Furthermore, the model using the constrained parameters generated divergent future soil C dynamics. Compared with the predictions using the presupposed real parameters (i.e., the real future C dynamics), the percentage uncertainty in 100-yr predictions using the constrained parameters was up to 45% depending on global change scenarios and data availability for model-constraining. Such great uncertainty was mainly due to the high collinearity among the model parameters. Using pool-based models, we argue that soil C pool size, k, and/or e and their responses to global change have to be estimated explicitly and empirically, rather than through model-fitting, in order to accurately predict C dynamics and infer underlying mechanisms. The OSSE approach provides a powerful way to identify data requirement for the new generation of model development and test model performance.

On improving the communication between models and data

The potential for model-data synthesis is growing in importance as we enter an era of 'big data', greater connectivity and faster computation. Realizing this potential requires that the research community broaden its perspective about how and why they interact with models. Models can be viewed as scaffolds that allow data at different scales to inform each other through our understanding of underlying processes. Perceptions of relevance, accessibility and informatics are presented as the primary barriers to broader adoption of models by the community, while an inability to fully utilize the breadth of expertise and data from the community is a primary barrier to model improvement. Overall, we promote a community-based paradigm to model-data synthesis and highlight some of the tools and techniques that facilitate this approach. Scientific workflows address critical informatics issues in transparency, repeatability and automation, while intuitive, flexible web-based interfaces make running and visualizing models more accessible. Bayesian statistics provides powerful tools for assimilating a diversity of data types and for the analysis of uncertainty. Uncertainty analyses enable new measurements to target those processes most limiting our predictive ability. Moving forward, tools for information management and data assimilation need to be improved and made more accessible.

Model systems for a no-analog future: species associations and climates during the last deglaciation

As the earth system moves to a novel state, model systems (experimental, observational, paleoecological) are needed to assess and improve the predictive accuracy of ecological models under environments with no contemporary analog. In recent years, we have intensively studied the no-analog plant associations and climates in eastern North America during the last deglaciation to better constrain their spatiotemporal distribution, test hypotheses about climatic and megaherbivory controls, and assess the accuracy of species- and community-level models. The formation of no-analog plant associations was asynchronous, beginning first in the south-central United States; at sites in the north-central United States, it is linked to declining megafaunal abundances. Insolation and temperature were more seasonal than present, creating climates currently nonexistent in North America, and shifting species-climate relationships for some taxa. These shifts pose a common challenge to empirical paleoclimatic reconstructions, species distribution models (SDMs), and conservation-optimization models based on SDMs. Steps forward include combining recent and paleoecological data to more fully describe species' fundamental niches, employing community-level models to model shifts in species interactions under no-analog climates, and assimilating paleoecological data with mechanistic ecosystem models. Accurately modeling species interactions under novel environments remains a fundamental challenge for all forms of ecological models.

Traceable components of terrestrial carbon storage capacity in biogeochemical models

Biogeochemical models have been developed to account for more and more processes, making their complex structures difficult to be understood and evaluated. Here, we introduce a framework to decompose a complex land model into traceable components based on mutually independent properties of modeled biogeochemical processes. The framework traces modeled ecosystem carbon storage capacity (Xss ) to (i) a product of net primary productivity (NPP) and ecosystem residence time (τE ). The latter τE can be further traced to (ii) baseline carbon residence times (τ'E ), which are usually preset in a model according to vegetation characteristics and soil types, (iii) environmental scalars (ξ), including temperature and water scalars, and (iv) environmental forcings. We applied the framework to the Australian Community Atmosphere Biosphere Land Exchange (CABLE) model to help understand differences in modeled carbon processes among biomes and as influenced by nitrogen processes. With the climate forcings of 1990, modeled evergreen broadleaf forest had the highest NPP among the nine biomes and moderate residence times, leading to a relatively high carbon storage capacity (31.5 kg cm(-2) ). Deciduous needle leaf forest had the longest residence time (163.3 years) and low NPP, leading to moderate carbon storage (18.3 kg cm(-2) ). The longest τE in deciduous needle leaf forest was ascribed to its longest τ'E (43.6 years) and small ξ (0.14 on litter/soil carbon decay rates). Incorporation of nitrogen processes into the CABLE model decreased Xss in all biomes via reduced NPP (e.g., -12.1% in shrub land) or decreased τE or both. The decreases in τE resulted from nitrogen-induced changes in τ'E (e.g., -26.7% in C3 grassland) through carbon allocation among plant pools and transfers from plant to litter and soil pools. Our framework can be used to facilitate data model comparisons and model intercomparisons via tracking a few traceable components for all terrestrial carbon cycle models. Nevertheless, more research is needed to develop tools to decompose NPP and transient dynamics of the modeled carbon cycle into traceable components for structural analysis of land models.

Predicting yields of short-rotation hybrid poplar (Populus spp.) for the United States through model-data synthesis

Hybrid poplar (Populus spp.) is an important biomass crop being evaluated for cellulosic ethanol production. Predictions of poplar growth, rotation period, and soil carbon sequestration under various growing conditions, soils, and climates are critical for farmers and managers planning to establish short-rotation forestry (SRF) plantations. In this study, we used an ecoinformatics workflow, the Predictive Ecosystem Analyzer (PEcAn), to integrate literature data and field measurements into the Ecosystem Demography 2 (ED2) model to estimate yield potential of poplar plantations. Within PEcAn 164 records of seven different traits from the literature were assimilated using a Bayesian meta-analysis. Next, variance decomposition identified seven variables for further constraint that contributed > 80% to the uncertainty in modeled yields: growth respiration, dark respiration, quantum efficiency, mortality coefficient, water conductance, fine-root allocation, and root turnover rate. Assimilation of observed yields further constrained uncertainty in model parameters (especially dark respiration and root turnover rate) and biomass estimates. Additional measurements of growth respiration, mortality, water conductance, and quantum efficiency would provide the most efficient path toward further constraint of modeled yields. Modeled validation demonstrated that ED2 successfully captured the interannual and spatial variability of poplar yield observed at nine independent sites. Site-level analyses were conducted to estimate the effect of land use change to SRF poplar on soil C sequestration compared to alternate land uses. These suggest that poplar plantations became a C sink within 18 years of conversion from corn production or existing forest. Finally, poplar yields were estimated for the contiguous United States at a half degree resolution in order to determine potential productivity, estimate the optimal rotation period, and compare poplar to perennial grass yields. This regional projection suggests that poplar yield varies considerably with differences in soil and climate, reaching as much as 18 Mg x ha(-1) x yr(-1) in eastern, southern, and northwest regions. In New England, the upper Midwest, and northern California, yields are predicted to exceed those of the highly productive C4 perennial grass, Miscanthus. In these poplar-productive regions, 4-11 year rotations give the highest potential yields. In conclusion, poplar plantations are predicted to have a high yield potential across a wide range of climates and soils and could be sustainable in soil C sequestration.

Nitrous oxide emissions from soils: how well do we understand the processes and their controls?

Although it is well established that soils are the dominating source for atmospheric nitrous oxide (N₂O), we are still struggling to fully understand the complexity of the underlying microbial production and consumption processes and the links to biotic (e.g. inter- and intraspecies competition, food webs, plant–microbe interaction) and abiotic (e.g. soil climate, physics and chemistry) factors. Recent work shows that a better understanding of the composition and diversity of the microbial community across a variety of soils in different climates and under different land use, as well as plant–microbe interactions in the rhizosphere, may provide a key to better understand the variability of N₂O fluxes at the soil–atmosphere interface. Moreover, recent insights into the regulation of the reduction of N₂O to dinitrogen (N₂) have increased our understanding of N₂O exchange. This improved process understanding, building on the increased use of isotope tracing techniques and metagenomics, needs to go along with improvements in measurement techniques for N₂O (and N₂) emission in order to obtain robust field and laboratory datasets for different ecosystem types. Advances in both fields are currently used to improve process descriptions in biogeochemical models, which may eventually be used not only to test our current process understanding from the microsite to the field level, but also used as tools for up-scaling emissions to landscapes and regions and to explore feedbacks of soil N₂O emissions to changes in environmental conditions, land management and land use.

Estimating demographic parameters using hidden process dynamic models

Structured population models are widely used in plant and animal demographic studies to assess population dynamics. In matrix population models, populations are described with discrete classes of individuals (age, life history stage or size). To calibrate these models, longitudinal data are collected at the individual level to estimate demographic parameters. However, several sources of uncertainty can complicate parameter estimation, such as imperfect detection of individuals inherent to monitoring in the wild and uncertainty in assigning a state to an individual. Here, we show how recent statistical models can help overcome these issues. We focus on hidden process models that run two time series in parallel, one capturing the dynamics of the true states and the other consisting of observations arising from these underlying possibly unknown states. In a first case study, we illustrate hidden Markov models with an example of how to accommodate state uncertainty using Frequentist theory and maximum likelihood estimation. In a second case study, we illustrate state-space models with an example of how to estimate lifetime reproductive success despite imperfect detection, using a Bayesian framework and Markov Chain Monte Carlo simulation. Hidden process models are a promising tool as they allow population biologists to cope with process variation while simultaneously accounting for observation error.

The model-data fusion pitfall: assuming certainty in an uncertain world

Model-data fusion is a powerful framework by which to combine models with various data streams (including observations at different spatial or temporal scales), and account for associated uncertainties. The approach can be used to constrain estimates of model states, rate constants, and driver sensitivities. The number of applications of model-data fusion in environmental biology and ecology has been rising steadily, offering insights into both model and data strengths and limitations. For reliable model-data fusion-based results, however, the approach taken must fully account for both model and data uncertainties in a statistically rigorous and transparent manner. Here we review and outline the cornerstones of a rigorous model-data fusion approach, highlighting the importance of properly accounting for uncertainty. We conclude by suggesting a code of best practices, which should serve to guide future efforts.

Assimilation of multiple data sets with the ensemble Kalman filter to improve forecasts of forest carbon dynamics

The ensemble Kalman filter (EnKF) has been used in weather forecasting to assimilate observations into weather models. In this study, we examine how effectively forecasts of a forest carbon cycle can be improved by assimilating observations with the EnKF. We used the EnKF to assimilate into the terrestrial ecosystem (TECO) model eight data sets collected at the Duke Forest between 1996 and 2004 (foliage biomass, fine root biomass, woody biomass, litterfall, microbial biomass, forest floor carbon, soil carbon, and soil respiration). We then used the trained model to forecast changes in carbon pools from 2004 to 2012. Our daily analysis of parameters indicated that all the exit rates were well constrained by the EnKF, with the exception of the exit rates controlling the loss of metabolic litter and passive soil organic matter. The poor constraint of these two parameters resulted from the low sensitivity of TECO predictions to their values and the poor correlation between these parameters and the observed variables. Using the estimated parameters, the model predictions and observations were in agreement. Model forecasts indicate 15 380-15 660 g C/ m2 stored in Duke Forest by 2012 (a 27% increase since 2004). Parameter uncertainties decreased as data were sequentially assimilated into the model using the EnKF. Uncertainties in forecast carbon sinks increased over time for the long-term carbon pools (woody biomass, structure litter, slow and passive SOM) but remained constant over time for the short-term carbon pools (foliage, fine root, metabolic litter, and microbial carbon). Overall, EnKF can effectively assimilate multiple data sets into an ecosystem model to constrain parameters, forecast dynamics of state variables, and evaluate uncertainty.

Seasonal fluctuations and temperature dependence in photosynthetic parameters and stomatal conductance at the leaf scale of Populus euphratica Oliv

A combined model to simulate CO₂ and H₂O gas exchange at the leaf scale was parameterized using data obtained from in situ leaf-scale observations of diurnal and seasonal changes in CO₂ and H₂O gas exchange. The Farquhar et al.-type model of photosynthesis was parameterized by using the Bayesian approach and the Ball et al.-type stomatal conductance model was optimized using the linear least-squares procedure. The results show that the seasonal physiological changes in photosynthetic parameters (e.g., V(cmax25), J(max25), R(d25) and g(m25)) in the biochemical model of photosynthesis and m in the stomatal conductance model should be counted in estimating long-term CO₂ and H₂O gas exchange. Overall, the coupled model successfully reproduced the observed response in net assimilation and transpiration rates.

Concurrent and lagged impacts of an anomalously warm year on autotrophic and heterotrophic components of soil respiration: a deconvolution analysis

*Partitioning soil respiration into autotrophic (R(A)) and heterotrophic (R(H)) components is critical for understanding their differential responses to climate warming. *Here, we used a deconvolution analysis to partition soil respiration in a pulse warming experiment. We first conducted a sensitivity analysis to determine which parameters can be identified by soil respiration data. A Markov chain Monte Carlo technique was then used to optimize those identifiable parameters in a terrestrial ecosystem model. Finally, the optimized parameters were employed to quantify R(A) and R(H) in a forward analysis. *Our results displayed that more than one-half of parameters were constrained by daily soil respiration data. The optimized model simulation showed that warming stimulated R(H) and had little effect on R(A) in the first 2 months, but decreased both R(H) and R(A) during the remainder of the treatment and post-treatment years. Clipping of above-ground biomass stimulated the warming effect on R(H) but not on R(A). Overall, warming decreased R(A) and R(H) significantly, by 28.9% and 24.9%, respectively, during the treatment year and by 27.3% and 33.3%, respectively, during the post-treatment year, largely as a result of decreased canopy greenness and biomass. *Lagged effects of climate anomalies on soil respiration and its components are important in assessing terrestrial carbon cycle feedbacks to climate warming.