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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Stochastic multiscale flux basis for Stokes-Darcy flows

Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic variable, with its log represented as a sum of local Karhunen-Loève (KL) expansions. The problem is approximated by stochastic collocation on either tensor-product or sparse grids, coupled with a multiscale mortar mixed finite element method for the spatial discretization. A non-overlapping domain decomposition algorithm reduces the global problem to a coarse scale mortar interface problem, which is solved by an iterative solver, for each stochastic realization. In the traditional domain decomposition implementation, each subdomain solves a local Dirichlet or Neumann problem in every interface iteration. To reduce this cost, two additional algorithms based on deterministic or stochastic multiscale flux basis are introduced. The basis consists of the local flux (or velocity trace) responses from each mortar degree of freedom. It is computed for each subdomain independently before the interface iteration begins. The use of the multiscale flux basis avoids the need for subdomain solves on each iteration. The deterministic basis is computed at each stochastic collocation and used only at this realization. The stochastic basis is formed by further looping over all local realizations of a subdomain's KL region before the stochastic collocation begins. It is used over multiple realizations. Numerical tests are presented to illustrate the performance of the three algorithms, with the stochastic multiscale flux basis showing significant savings in computational cost compared to the other two algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Robust verification of stochastic simulation codes

We introduce a robust verification tool for computational codes, which we call Stochastic Robust Extrapolation based Error Quantification (StREEQ). Unlike the prevalent Grid Convergence Index (GCI) [1] method, our approach is suitable for both stochastic and deterministic computational codes and is generalizable to any number of discretization variables. Building on ideas introduced in the Robust Verification [2] approach, we estimate the converged solution and orders of convergence with uncertainty using multiple fits of a discretization error model. In contrast to Robust Verification, we perform these fits to many bootstrap samples yielding a larger set of predictions with smoother statistics. Here, bootstrap resampling is performed on the lack-of-fit errors for deterministic code responses, and directly on the noisy data set for stochastic responses. This approach lends a degree of robustness to the overall results, capable of yielding precise verification results for sufficiently resolved data sets, and appropriately expanding the uncertainty when the data set does not support a precise result. For stochastic responses, a credibility assessment is also performed to give the analyst an indication of the trustworthiness of the results. Furthermore, this approach is suitable for both code and solution verification, and is particularly useful for solution verification of high-consequence simulations..

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An optimization method for chaotic turbulent flow

Evidence indicates that quantities-of-interest in some turbulent flows can be controlled despite the overall chaotic dynamics. It is typically thought that this is via relatively deterministic, larger-scale components of the turbulence. However, finding such controls, if they exist, is challenging because chaos causes sensitivity gradients to explode and the search space to become intractably non-convex. This challenge is analyzed, and a penalty method is introduced to cope with it. In the new approach, the time domain is broken into segments approximately matching the chaos time scales, so that the solution within each segment is both physical and relatively deterministic. The initial condition of each segment is included in an adjoint-based gradient optimization, which temporarily introduces artificial Δq discontinuities in the overall solution. The optimization then proceeds in stages with increasing penalization of Δq. The method is developed and illustrated for a logistic map, the Lorenz Equation, and an advection augmented Kuramoto–Sivashinsky Equation. These examples show how the Δq temporarily increases the search scale prior to the strong Δq → 0 penalization that recovers a physical solution. It is then applied to turbulent Kolmogorov flow, for which it also far outperforms a standard adjoint-based gradient search. Finally, the utility of such an optimized chaotic solution is discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Identifying stochastic dynamics via finite expression methods

Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a combination of deterministic and stochastic terms. However, these models usually lack interpretability and have difficulty in generalizing beyond their training domain. Here, this paper introduces the Finite Expression Method (FEX), a symbolic learning approach designed to derive interpretable mathematical representations of the deterministic component of SDEs. For the stochastic component, we integrate FEX with advanced generative modeling techniques to provide a comprehensive representation of SDEs. The numerical experiments on linear, nonlinear, and multidimensional SDEs demonstrate that FEX generalizes well beyond the training domain and delivers more accurate long-term predictions compared to neural network-based methods. The symbolic expressions identified by FEX not only improve prediction accuracy but also offer valuable scientific insights into the underlying dynamics of the systems.

Complex dynamical systems↗
DOE OSTI2024

Comparison of source-location algorithms for atmospheric samplers

Numerous algorithms have been developed to determine the source characteristics for an atmospheric release, e.g., (Bieringer et al., 2017). This study compares three models that have been applied to the data collected by the International Monitoring System operated by the Comprehensive Nuclear-Test-Ban Treaty Preparatory Commission to estimate source event parameters. Each model uses a different approach to estimate the parameters. A deterministic model uses a possible source region (PSR) approach (Ringbom et al., 2014) that is based on the correlation between predicted and measured sample values. An unnamed model developed at Pacific Northwest National Laboratory (herein called BAYEST) uses a Bayesian formulation (Eslinger et al., 2019; Eslinger et al., 2020; Eslinger and Schrom, 2016). The FREAR model uses a different Bayesian formulation (De Meutter and Hoffman, 2020; De Meutter et al., 2021; Pieter De Meutter, 2021). The performance of the three source-location models is evaluated with 100 synthetic release cases for the single xenon isotope, 133 Xe. The release cases resulted in detections in a fictitious network with 120 noble gas samplers. All three source-location models use the same sampling data. The two Bayesian models yield more accurate location estimates than the deterministic PSR model, with FREAR having slightly better location performance than BAYEST. Samplers with collection periods of 3, 6, 8, 12, and 24-h were used. Results from BAYEST show that location accuracy improves with each reduction in sample collection length. The BAYEST model is slightly better for estimating the start time of the release. The PSR model has about the same spread in start times as the FREAR model, but the PSR results have a better average start time. The Bayesian source-location algorithms give more accurate results than the PSR approach, and provide release magnitude estimates, while the base PSR model does not estimate the release magnitude. This investigation demonstrates that a reasonably dense sampling grid will sometimes yield poor location and time estimates regardless of the model. The poor estimates generally coincide with cases where there is a much larger distance between the release point and the first detecting sampler than the average sampler spacing.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2025

A statistical approach to screening isotopic signatures in monitoring for underground nuclear explosions

The ability to differentiate between atmospheric radionuclide signatures from underground nuclear explosions (UNEs) and signals from other sources, such as medical isotope-production facilities and nuclear reactors, can be critical to the detection and monitoring of unannounced, low-yield nuclear events. Signatures having anomalously high amplitudes, compared to background levels, remain the best indicator in screening for a UNE. However, isotopic composition can further validate a suspected UNE signature, but separation from any atmospheric background composition is first necessary. To date, evaluating the challenges of performing this separation has typically involved comparing an observed background with a highly idealized deterministic model of radioxenon signature production by a UNE that does not consider the influence of post-detonation chemical/physical processes in the detonation cavity or the subsequent gas transport mechanisms that can also affect the isotopic composition of the detected gas signature. In addition, purely deterministic models, as previously employed, overlook the uncertainty inherent in estimating critical parameters characterizing the UNE and its detonation environment. In this paper, we create detailed, multi-parameter models of radionuclide evolution using the widely accepted England and Rider post-detonation radionuclide decay-chain network coupled to detailed models simulating physical production and transport processes affecting the gas signature. Because these models are governed by uncertain parameters including barometric fluctuations, realistic ranges of variation for each of the parameters influencing isotopic composition are then defined. A Latin-Hypercube sampling approach is used to obtain a random distribution of isotopic production and gas transport results associated with a given value of each parameter. We apply these results to background histories of two stations, one providing 4-isotope background measurements and the other providing two-isotope measurements associated with the 2013 DPRK announced UNE.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2022

Accelerated radiation transport modeling techniques for pencil beam computed tomography using gamma rays

Monte Carlo radiation transport modeling studies were performed for a compact, and high-resolution gamma-ray computed tomography system designed for imaging irradiated nuclear fuel. The system comprises a 60 Co source – chosen for its highly penetrating 1173 keV and 1332 keV gamma rays – a pair of high-aspect-ratio pencil beam collimators, and an inorganic scintillator detector. Here two acceleration methods are proposed to rapidly model a transmission type gamma-ray tomography system. The first, a variance reduction technique, is based on performing Monte Carlo simulations with a monodirectionally-biased source, sampled from a characteristic sub-volume of the full source volume. The second acceleration method is based on the deterministic calculations using the Beer–Lambert law and detector response characteristics. Comparison of simulations using acceleration approaches with analog simulations of the fully isotropic, full-volume equivalent, show that the Monte Carlo variance reduction technique gives quantitatively accurate predictions for large collimator aspect ratios while the deterministic calculations are semi-quantitative but converge close to the correct result as the collimator aspect ratio increases. As such, these techniques can be used to reduce the computational cost in generating simulated radiographs and tomographs by several orders of magnitude. Experimental validation efforts are currently underway and will be demonstrated in future work.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2015

Analyzing simulation-based PRA data through traditional and topological clustering: A BWR station blackout case study

Here, dynamic probabilistic risk assessment (DPRA) methodologies couple system simulator codes (e.g., RELAP and MELCOR) with simulation controller codes (e.g., RAVEN and ADAPT). Whereas system simulator codes model system dynamics deterministically, simulation controller codes introduce both deterministic (e.g., system control logic and operating procedures) and stochastic (e.g., component failures and parameter uncertainties) elements into the simulation. Typically, a DPRA is performed by sampling values of a set of parameters and simulating the system behavior for that specific set of parameter values. For complex systems, a major challenge in using DPRA methodologies is to analyze the large number of scenarios generated, where clustering techniques are typically employed to better organize and interpret the data. In this paper, we focus on the analysis of two nuclear simulation datasets that are part of the risk-informed safety margin characterization (RISMC) boiling water reactor (BWR) station blackout (SBO) case study. We provide the domain experts a software tool that encodes traditional and topological clustering techniques within an interactive analysis and visualization environment, for understanding the structures of such high-dimensional nuclear simulation datasets. We demonstrate through our case study that both types of clustering techniques complement each other for enhanced structural understanding of the data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Internal cycle modeling and environmental assessment of multiple cycle consumer products

Highlights: Black-Right-Pointing-Pointer Dynamic flow models are presented for remanufactured, reused or recycled products. Black-Right-Pointing-Pointer Early loss and stochastic return are included for fast and slow cycling products. Black-Right-Pointing-Pointer The reuse-to-input flow ratio (Internal Cycle Factor, ICF) is determined. Black-Right-Pointing-Pointer The cycle rate, which is increasing with the ICF, monitors eco-performance. Black-Right-Pointing-Pointer Early internal cycle losses diminish the ICF, the cycle rate and performance. - Abstract: Dynamic annual flow models incorporating consumer discard and usage loss and featuring deterministic and stochastic end-of-cycle (EOC) return by the consumer are developed for reused or remanufactured products (multiple cycle products, MCPs), including fast and slow cycling, short and long-lived products. It is shown that internal flows (reuse and overall consumption) increase proportionally to the dimensionless internal cycle factor (ICF) which is related to environmental impact reduction factors. The combined reuse/recycle (or cycle) rate is shown capable for shortcut, albeit effective, monitoring of environmental performance in terms of waste production, virgin material extraction and manufacturing impacts of all MCPs, a task, which physical variables (lifetime, cycling frequency, mean or total number of return trips) and conventional rates, via which environmental policy has been officially implemented (e.g. recycling rate) cannot accomplish. The cycle rate is shown to be an increasing (hyperbolic) function of ICF. The impact of the stochastic EOC return characteristics on total reuse and consumption flows, as well as on eco-performance, is assessed: symmetric EOC return has a small, positive effect on performance compared to deterministic, while early shifted EOC return is more beneficial. In order to be efficient, environmental policy should set higher minimum reuse targets for higher trippage MCPs. The results may serve for monitoring, flow accounting and comparative eco-assessment of MCPs. They may be useful in identifying reachable and efficient reuse/recycle targets for consumer products and in planning return via appropriate labelling and digital coding for enhancing environmental performance, while satisfying consumer demand.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2015

Effectiveness of the food recovery at the retailing stage under shelf life uncertainty: An application to Italian food chains

Highlights: • The food recovery is seen as suitable way to manage food near to its expiry date. • The variability of the products shelf life must be taken into account. • The paper addresses the mathematic modeling of the profit related to food recovery. • The optimal time to withdraw the products is determinant for food recovery. - Abstract: Food losses represent a significant issue affecting food supply chains. The possibility of recovering such products can be seen as an effective way to reduce such a phenomenon, improve supply chain performances and ameliorate the conditions of undernourished people. The topic has been already investigated by a previous paper enforcing the hypothesis of deterministic and constant Shelf Life (SL) of products. However, such a model cannot be properly extended to products affected by uncertainties of the SL as it does not take into account the deterioration costs and loss of profits due to the overcoming of the SL within the cycle time. Thus the present paper presents an extension of the previous one under stochastic conditions of the food quality. Differently from the previous publication, this work represents a general model applicable to all supply chains, especially to those managing fresh products characterized by uncertain SL such as fruits and vegetables. The deterioration costs and loss of profits are included in the model and the optimal time at which to withdraw the products from the shelves as well as the quantities to be shipped at each alternative destination have been determined. A comparison of the proposed model with that reported in the previous publication has been carried out in order to underline the impact of the SL variability on the optimality conditions. The results show that the food recovery strategy in the presence of uncertainty of the food quality is rewarding, even if the optimal profit is lower than that of the deterministic case.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

Inertial impedance of coalescence during collision of liquid drops

The fluid dynamics of the collision and coalescence of liquid drops has intrigued scientists and engineers for more than a century owing to its ubiquitousness in nature, e.g. raindrop coalescence, and industrial applications, e.g. breaking of emulsions in the oil and gas industry. The complexity of the underlying dynamics, which includes occurrence of hydrodynamic singularities, has required study of the problem at different scales – macroscopic, mesoscopic and molecular – using stochastic and deterministic methods. In this work, a multi-scale, deterministic method is adopted to simulate the approach, collision, and eventual coalescence of two drops where the drops as well as the ambient fluid are incompressible, Newtonian fluids. The free boundary problem governing the dynamics consists of the Navier–Stokes system and associated initial and boundary conditions that have been augmented to account for the effects of disjoining pressure as the separation between the drops becomes of the order of a few hundred nanometres. This free boundary problem is solved by a Galerkin finite element-based algorithm. The interplay of inertial, viscous, capillary and van der Waals forces on the coalescence dynamics is investigated. It is shown that, in certain situations, because of inertia two drops that are driven together can first bounce before ultimately coalescing. This bounce delays coalescence and can result in the computed value of the film drainage time departing significantly from that predicted from existing scaling theories.

Mechanics↗
DOE OSTI2019

Derivative-free optimization methods

In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen–Cooper–Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. Here, the method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree–Fock based electronic structure methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Laser-Assisted Synthesis of Monolayer 2D MoSe 2 Crystals with Tunable Vacancy Concentrations: Implications for Gas and Biosensing

We report tuning the structural and electronic properties of atomically thin two-dimensional (2D) materials via defect and vacancy engineering is the key to enabling their potential use in various applications, including electronics, energy, and sensing devices. Vacancies are, for instance, becoming highly promising for the enhanced interaction of gases and biomolecules with 2D materials in energy and sensing applications. However, the deterministic generation of desirable vacancies with tunable concentrations remains a challenge in 2D materials due to the limitations in the current growth methods, such as the complex reaction chemistries and gas flow dynamics. Therefore, engineering defects and vacancies in 2D materials have been mainly limited to destructive top-down processes such as heating, ion bombardments, and laser postprocessing. Here, we introduce a single-step bottom-up synthesis approach for the growth of monolayer MoSe 2 crystals with tunable vacancy concentrations. This method utilizes the spatiotemporal properties and adjustable power densities of the lasers to control the vaporization dynamics of the stoichiometric MoSe 2 powders. Such a mechanism in the vaporization allows us to grow tunable stoichiometry monolayer MoSe 2–x crystals on the substrates. The localized and time-controlled (250 ms to 2 s) vaporization of the MoSe 2 powder by a CO 2 laser enables the formation of monolayer crystals with controlled vacancy concentrations ranging from ~1 to 20%. The effects of laser power, laser irradiation time, and background pressure on the tuning range and subsequent properties of the crystals are investigated and quantified using Raman and photoluminescence spectroscopy, scanning transmission electron microscopy (STEM), and time-correlated single-photon counting (TCSPC). This bottom-up synthesis is a promising approach that allows the deterministic vacancy tuning for future electronics and, in particular, gas and biosensing applications without the need for further postprocessing and potential structural disruption of the crystals.

2D materials↗
DOE OSTI2021

Strain-Induced Growth of Twisted Bilayers during the Coalescence of Monolayer MoS 2 Crystals

Tailoring the grain boundaries (GBs) and twist angles between two-dimensional (2D) crystals are two crucial synthetic challenges to deterministically enable envisioned applications such as moiré excitons, emerging magnetism, or single-photon emission. Here, we reveal how twisted 2D bilayers can be synthesized from the collision and coalescence of two growing monolayer MoS 2 crystals during chemical vapor deposition. The twisted bilayer (TB) moiré angles are found to preserve the misorientation angle (θ) of the colliding crystals. The shapes of the TB regions are rationalized by a kink propagation model that predicts the GB formed by the coalescing crystals. Optical spectroscopy measurements reveal a θ-dependent long-range strain in crystals with stitched grain boundaries and a sharp (θ > 20°) threshold for the appearance of TBs, which relieves this strain. Reactive molecular dynamics simulations explain this strain from the continued growth of the crystals during coalescence due to the insertion of atoms at unsaturated defects along the GB, a process that self-terminates when the defects become saturated. The simulations also reproduce atomic-resolution electron microscopy observations of faceting along the GB, which is shown to arise from the growth-induced long-range strain. These facets align with the axes of the colliding crystals to provide favorable nucleation sites for second-layer growth of a TB with twist angles that preserve the misorientation angle θ. This interplay between strain generation and aligned nucleation provides a synthetic pathway for the growth of TBs with deterministic angles.

2D materials↗
DOE OSTI2011

Representative elementary volume estimation for porosity, moisture saturation, and air-water interfacial areas in unsaturated porous media: Data quality implications

Achieving a representative elementary volume (REV) has become a de facto criterion for demonstrating the quality of {mu}CT measurements in porous media systems. However, the data quality implications of an REV requirement have not been previously examined. In this work, deterministic REVs for porosity, moisture saturation (S{sub W}), and air-water interfacial area (A{sub I}) were estimated using a set of 49 {mu}CT images of eight unsaturated homogeneous porous media with heterogeneity in moisture distributions present in varying degrees. Estimated porosity REVs were <8 mm{sup 3} for all cases, smaller than typical CT image sizes ({approx}100 mm{sup 3}). Estimated S{sub W} and A{sub I} REVs were <55 mm{sup 3} for cases with homogeneous moisture distributions but could not be estimated for cases with heterogeneous moisture distributions, due to the absence of a distinct 'REV plateau' within the maximum imaged volume. Conventionally, S{sub W} and A{sub I} data from such non-REV cases would be excluded. The implications of excluding data on the basis of REV were examined by comparing A{sub I}-S{sub W} data measured on image windows of increasing size against the expected linear A{sub I}-S{sub W} relationship. At measurement scales exceeding porosity REV, random fluctuations in A{sub I}-S{sub W} data were excluded, even for cases containing heterogeneous moisture distributions. In contrast, requiring measurement scales to exceed S{sub W} and A{sub I} REV appeared overly restrictive and resulted in visible loss of reliable A{sub I}-S{sub W} data. We attribute these findings to overestimation of REVs due to inherently problematic estimation of deterministic REVs in real systems. Implications of these findings for ensuring CT data quality and the efficient use of CT data are discussed.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2011

Hydrological parameter estimations from a conservative tracer test with variable-density effects at the Boise Hydrogeophysical Research Site

Reliable predictions of groundwater flow and solute transport require an estimation of the detailed distribution of the parameters (e.g., hydraulic conductivity, effective porosity) controlling these processes. However, such parameters are difficult to estimate because of the inaccessibility and complexity of the subsurface. In this regard, developments in parameter estimation techniques and investigations of field experiments are still challenging and necessary to improve our understanding and the prediction of hydrological processes. Here we analyze a conservative tracer test conducted at the Boise Hydrogeophysical Research Site in 2001 in a heterogeneous unconfined fluvial aquifer. Some relevant characteristics of this test include: variable-density (sinking) effects because of the injection concentration of the bromide tracer, the relatively small size of the experiment, and the availability of various sources of geophysical and hydrological information. The information contained in this experiment is evaluated through several parameter estimation approaches, including a grid-search-based strategy, stochastic simulation of hydrological property distributions, and deterministic inversion using regularization and pilot-point techniques. Doing this allows us to investigate hydraulic conductivity and effective porosity distributions and to compare the effects of assumptions from several methods and parameterizations. Our results provide new insights into the understanding of variabledensity transport processes and the hydrological relevance of incorporating various sources of information in parameter estimation approaches. Among others, the variable-density effect and the effective porosity distribution, as well as their coupling with the hydraulic conductivity structure, are seen to be significant in the transport process. The results also show that assumed prior information can strongly influence the estimated distributions of hydrological properties.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2012

Ecosystem carbon storage capacity as affected by disturbance regimes: A general theoretical model

Disturbances have been recognized as a key factor shaping terrestrial ecosystem states and dynamics. A general model that quantitatively describes the relationship between carbon storage and disturbance regime is critical for better understanding large scale terrestrial ecosystem carbon dynamics. We developed a model (REGIME) to quantify ecosystem carbon storage capacities (E[x]) under varying disturbance regimes with an analytical solution E[x] = U {center_dot} {tau}{sub E} {center_dot} {lambda}{lambda} + s {tau} 1, where U is ecosystem carbon influx, {tau}{sub E} is ecosystem carbon residence time, and {tau}{sub 1} is the residence time of the carbon pool affected by disturbances (biomass pool in this study). The disturbance regime is characterized by the mean disturbance interval ({lambda}) and the mean disturbance severity (s). It is a Michaelis-Menten-type equation illustrating the saturation of carbon content with mean disturbance interval. This model analytically integrates the deterministic ecosystem carbon processes with stochastic disturbance events to reveal a general pattern of terrestrial carbon dynamics at large scales. The model allows us to get a sense of the sensitivity of ecosystems to future environmental changes just by a few calculations. According to the REGIME model, for example, approximately 1.8 Pg C will be lost in the high-latitude regions of North America (>45{sup o} N) if fire disturbance intensity increases around 5.7 time the current intensity to the end of the twenty-first century, which will require around 12% increases in net primary productivity (NPP) to maintain stable carbon stocks. If the residence time decreased 10% at the same time additional 12.5% increases in NPP are required to keep current C stocks. The REGIME model also lays the foundation for analytically modeling the interactions between deterministic biogeochemical processes and stochastic disturbance events.

09 BIOMASS FUELS↗