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DOE OSTI2019

Understanding Monsoonal Water Cycle Changes in a Warmer Climate in E3SMv1 Using a Normalized Gross Moist Stability Framework

Abstract One of the grand challenges of climate science is understanding the changes of the tropical rain belts and monsoon systems owing to CO 2 ‐induced warming. A promising path forward links the fluxes of energy and moisture to tropical circulation features. To this end, we make use of the Energy Exascale Earth System Model version 1, where the divergence of moist static energy and moisture have been calculated online, and employ a normalized gross moist stability (NGMS) diagnostic framework to understand the linkages between changes in the flow of energy and moisture within the monsoons. We focus on the Asian Summer Monsoon system and utilize a series of atmosphere‐land and atmosphere‐land‐ocean simulations to understand the connection between fluxes and monsoons. Uncoupled simulations with prescribed sea surface temperatures indicate that decreases in NGMS over land are important in explaining precipitation increases in response to both sea surface temperature and CO 2 increases. In fully coupled experiments, NGMS decreases remain an important contributor to the increase in P‐E, but the coupled simulations highlight the importance of consistent ocean and land responses in interpreting the monsoon changes. This study indicates that transient eddy fluxes play an important role in NGMS decreases and that a time‐mean view of the monsoon circulations is insufficient to quantify the link between future changes in the fluxes of energy and moisture. Compensation between dynamic and thermodynamic components of vertical moist static energy advection occurs, with the thermodynamic contribution dominating. The compensation is shown to be sensitive to relative humidity, with higher relative humidity leading to a stronger thermodynamic component.

Harrop, Bryce E.↗

DOE OSTI2023

BUZZ : an essential gene for postinitiation root hair growth and a mediator of root architecture in Brachypodium distachyon

Here, we discover a player in root development. Recovered from a forward-genetic screen in Brachypodium distachyon, the buzz mutant initiates root hairs but they fail to elongate. In addition, buzz roots grow twice as fast as wild-type roots. Also, lateral roots show increased sensitivity to nitrate, whereas primary roots are less sensitive to nitrate. Using whole-genome resequencing, we identified the causal single nucleotide polymorphism as occurring in a conserved but previously uncharacterized cyclin-dependent kinase (CDK)-like gene. The buzz mutant phenotypes are rescued by the wild-type B. distachyon BUZZ coding sequence and by an apparent homolog in Arabidopsis thaliana. Moreover, T-DNA mutants in A. thaliana BUZZ have shorter root hairs. BUZZ mRNA localizes to epidermal cells and develops root hairs and, in the latter, partially colocalizes with the NRT1.1A nitrate transporter. Based on qPCR and RNA-Seq, buzz overexpresses ROOT HAIRLESS LIKE SIX-1 and -2 and misregulates genes related to hormone signaling, RNA processing, cytoskeletal, and cell wall organization, and to the assimilation of nitrate. Overall, these data demonstrate that BUZZ is required for tip growth after root hair initiation and root architectural responses to nitrate.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2017

X-Ray Spectro-Polarimetry with Photoelectric Polarimeters

We derive a generalization of forward fitting for X-ray spectroscopy to include linear polarization of X-ray sources, appropriate for the anticipated next generation of space-based photoelectric polarimeters. We show that the inclusion of polarization sensitivity requires joint fitting to three observed spectra, one for each of the Stokes parameters, I(E), U(E), and Q(E). The equations for StokesI (E) (the total intensity spectrum) are identical to the familiar case with no polarization sensitivity, and for which the model-predicted spectrum is obtained by a convolution of the source spectrum, F (E), with the familiar energy response function,(E) R(E,E), where (E) and R(E,E) are the effective area and energy redistribution matrix, respectively. In addition to the energy spectrum, the two new relations for U(E) and Q(E) include the source polarization fraction and position angle versus energy, a(E), and 0(E), respectively, and the model-predicted spectra for these relations are obtained by a convolution with the modulated energy response function, (E)(E) R(E,E), where(E) is the energy-dependent modulation fraction that quantifies a polarimeters angular response to 100 polarized radiation. We present results of simulations with response parameters appropriate for the proposed PRAXyS Small Explorer observatory to illustrate the procedures and methods, and we discuss some aspects of photoelectric polarimeters with relevance to understanding their calibration and operation.

polarization↗

NASA NTRS2017

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗

DOE OSTI2024

CCUS 2024, Interpreting the strain tensor Larry Murdoch Interpreting strain tensor data to characterize and monitor reservoirs for CO2 storage and other applications

Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and this has opened the door to new opportunities for characterization and monitoring during CCUS. We have demonstrated this method by deploying strainmeters at shallow depths (30 to 40m) and then conducting injection well tests in an underlying reservoir at 530m depth. The resulting data indicated that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. We have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS. Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and our objective was to evaluate opportunities for strain monitoring during characterization and monitoring for CCUS. Our approach was to deploy strainmeters at shallow depths (30 to 40m) and then conduct injection well tests in an underlying reservoir at 530m depth. The results indicate that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. In conclusion, we have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS.

Murdoch, Larry↗

DOE OSTI2020

Validation of SAS4A/SASSYS-1 for Steady-State Single-Phase Natural Circulation

The development of numerical software for engineering applications requires the validation of the code against experimental benchmark datasets. To support the validation of SAS4A/SASSYS-1 in simulating the single-phase natural circulation within nuclear reactor systems, high-precision steady-state experiments are performed to capture single-phase natural circulation phenomena on an existing scaled facility with comprehensive instrumentation. Forced convection tests are designed precisely capturing the facility’s critical thermal-hydraulic parameters required for one-dimensional modeling, and a comprehensive single-phase natural circulation dataset is obtained with well-documented experimental uncertainty and facility description. Analysis and discussion based on the finalized dataset confirm the dataset’s ability in capturing dominant phenomena and address important physical interpretation of parameters. The dataset reported in this project provides a valuable benchmark resource for the validation of system analysis codes under single-phase natural circulation inside nuclear reactors. Validation of SAS4A/SASSYS-1 is then performed against the obtained benchmark dataset to confirm the capability of its physics model in simulating the steady-state single-phase natural circulation. The experimental facility is modeled in the candidate code. Solution verification is performed using Richardson-extrapolation-based estimators to quantify and restrict numerical errors from discretization. Numerical uncertainty originating from finite maximum pseudo-transient time is also quantified and restricted. Input uncertainty provided by the benchmark dataset is forward propagated through the candidate code, directly quantifying the simulation output in a Monte Carlo approach. The composition of the output uncertainty is further determined by the estimators of Sobol’ indices through a variance-based sensitivity analysis. With uncertainty quantified for each individual condition, detailed comparison between the simulation results and experimental data is performed covering the whole dataset, which shows consistent agreement for all important quantities. The validation activity reported in this project demonstrates that SAS4A/SASSYS-1 can predict the primary parameters with satisfactorily accuracy under steady-state single-phase natural circulation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Hypercomplex Automatic Differentiation in the Eulerian Hydrocode PAGOSA

Enabling the computation of partial derivatives or sensitivities in production hydrocodes is beneficial for design, optimization, sensitivity analysis, and uncertainty quantification. Traditional finite difference approximations of these sensitivities are inefficient since convergence studies of the step size is required for each parameter of interest. For these reasons, HYPercomplex Automatic Differentiation (HYPAD) was implemented in the Eulerian hydrocode PAGOSA. HYPAD is analogous to forward-mode automatic differentiation except hypercomplex numbers (numbers with multiple imaginary parts) are used instead of dual numbers. Accurate partial derivatives can be computed of all state variables with respect to multiple input variables in a single run. The method was implemented using operator overloading to handle hypercomplex algebra. HYPAD was demonstrated and verified on Sod’s shock tube problem to compute derivatives of the state variables with respect to a material parameter, initial conditions, and geometry.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Studies of e+e- Pair Photo-Production on Proton Target at 8 GeV in the GlueX Experiment

Lepton pair production has played an important role in both nuclear and particle physics, being among the earliest calculations utilizing QED, and seen most famously in the discovery of the J= at BNL. A technique is presented for measuring the linear polarization of GeV scale photon beams through the detection of e+e? pairs photo-produced in the target. This technique is applied to the analysis of GlueX data on proton target. Simulation predicts the analyzing power for pair production to be :5725 ? 0:0025 for the GlueX data, and the analysis of experimental data gives a linear polarization of approximately 35%, in good agreement with other measurements of beam polarization. The pair production technique is complementary to other electromagnetic and hadronic measurements of beam polarization, and is generally applicable in experiments that allow for forward angle electron and positron identi?fication and tracking. To facilitate this study, a neural net was trained for e=? separation to eliminate the pion background. Further, it is demonstrated that these e+e? pairs are sensitive to the proton charge form factor, which opens up the possibility for a new method to measure the proton RMS charge radius.

Schick, Andrew↗

NASA NTRS2022

Understanding Sampling Hardware Cleanliness from Perseverance Lessons Learned, and Forward Approach to Biosignature Missions

The search for biosignatures on other solar system bodies drives the scientific objectives of many ongoing and proposed exploration missions, including the Europa Lander mission concept.[1] The detection of trace and unfamiliar biosignatures in extreme environments necessitates state-of-the-art scientific instrumentation with extraordinary sensitivity – and often, extraordinary susceptibility to terrestrial and spacecraft self-induced contamination vectors.[2] While instruments can be carefully designed to operate remotely at high performance, in situ scientific measurements can only analyze the samples they’re given: samples or sample handling hardware that have been inadvertently tainted by outgassed organic molecules, thruster plume effluents, or other common sources of spacecraft contamination may yield ambiguous or false results. Maintaining and verifying the purity of collected samples and the cleanliness of sample handling hardware throughout the lifecycle of biosignature detection missions like Europa Lander is a primary responsibility of the Contamination Control group at JPL.

Alred, John↗

NASA NTRS2012

Accuracy Assessments of Cloud Droplet Size Retrievals from Polarized Reflectance Measurements by the Research Scanning Polarimeter

We present an algorithm for the retrieval of cloud droplet size distribution parameters (effective radius and variance) from the Research Scanning Polarimeter (RSP) measurements. The RSP is an airborne prototype for the Aerosol Polarimetery Sensor (APS), which was on-board of the NASA Glory satellite. This instrument measures both polarized and total reflectance in 9 spectral channels with central wavelengths ranging from 410 to 2260 nm. The cloud droplet size retrievals use the polarized reflectance in the scattering angle range between 135deg and 165deg, where they exhibit the sharply defined structure known as the rain- or cloud-bow. The shape of the rainbow is determined mainly by the single scattering properties of cloud particles. This significantly simplifies both forward modeling and inversions, while also substantially reducing uncertainties caused by the aerosol loading and possible presence of undetected clouds nearby. In this study we present the accuracy evaluation of our algorithm based on the results of sensitivity tests performed using realistic simulated cloud radiation fields.

Rainbow↗

DOE OSTI2024

Ultra-high Q cavity-based search for the Dark Photon: new exclusion limit from Dark SRF phase 1 and step forward for phase 2

We present here the first results of Dark SRF, a light-shining-through-wall (LSW) experiment that leverages ultra-high quality factor superconducting radio frequency (SRF) cavities to search for dark photons. The use of Nb SRF cavities combined with a strict calibration and measurement protocol increased sensitivity to dark photons by several orders of magnitude compared to other LSW experiments, as demonstrated by our new limit that excluded a broad range of previously unstudied dark photon mass and mixing angle.In addition to the results of the search conducted in liquid helium using 1.3GHz SRF cavities, we also present the first steps of the second phase of the experiment, which will take place in a dilution refrigerator using 2.6GHz SRF cavities. These experiments are part of a wider effort of the Superconducting Quantum Materials and Systems (SQMS) Center to employ ultra-high Q SRF cavities to search for Beyond the SM particles and wavelike dark matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Demonstration of Machine Learning-Based Model-Independent Stabilization of Source Properties in Synchrotron Light Sources

Synchrotron light sources, arguably among the most powerful tools of modern scientific discovery, are presently undergoing a major transformation to provide orders of magnitude higher brightness and transverse coherence enabling the most demanding experiments. In these experiments, overall source stability will soon be limited by achievable levels of electron beam size stability, presently on the order of several microns, which is still 1–2 orders of magnitude larger than already demonstrated stability of source position and current. Until now source size stabilization has been achieved through corrections based on a combination of static predetermined physics models and lengthy calibration measurements, periodically repeated to counteract drift in the accelerator and instrumentation. In this paper, we now demonstrate for the first time how the application of machine learning allows for a physics- and model-independent stabilization of source size relying only on previously existing instrumentation. Such feed-forward correction based on a neural network that can be continuously online retrained achieves source size stability as low as 0.2 μm (0.4%) rms, which results in overall source stability approaching the subpercent noise floor of the most sensitive experiments.

43 PARTICLE ACCELERATORS↗

NASA NTRS2013

Per-Pixel, Dual-Counter Scheme for Optical Communications

Free space optical communications links from deep space are projected to fulfill future NASA communication requirements for 2020 and beyond. Accurate laser-beam pointing is required to achieve high data rates at low power levels.This innovation is a per-pixel processing scheme using a pair of three-state digital counters to implement acquisition and tracking of a dim laser beacon transmitted from Earth for pointing control of an interplanetary optical communications system using a focal plane array of single sensitive detectors. It shows how to implement dim beacon acquisition and tracking for an interplanetary optical transceiver with a method that is suitable for both achieving theoretical performance, as well as supporting additional functions of high data rate forward links and precision spacecraft ranging.

Farr, William H.↗

NASA NTRS2016

Evaluating A Priori Ozone Profile Information Used in TEMPO Tropospheric Ozone Retrievals

Ozone (O3) is a greenhouse gas and toxic pollutant which plays a major role in air quality. Typically, monitoring of surface air quality and O3 mixing ratios is primarily conducted using in situ measurement networks. This is partially due to high-quality information related to air quality being limited from space-borne platforms due to coarse spatial resolution, limited temporal frequency, and minimal sensitivity to lower tropospheric and surface-level O3. The Tropospheric Emissions: Monitoring of Pollution (TEMPO) satellite is designed to address these limitations of current space-based platforms and to improve our ability to monitor North American air quality. TEMPO will provide hourly data of total column and vertical profiles of O3 with high spatial resolution to be used as a near-real-time air quality product. TEMPO O3 retrievals will apply the Smithsonian Astrophysical Observatory profile algorithm developed based on work from GOME, GOME-2, and OMI. This algorithm uses a priori O3 profile information from a climatological data-base developed from long-term ozone-sonde measurements (tropopause-based (TB) O3 climatology). It has been shown that satellite O3 retrievals are sensitive to a priori O3 profiles and covariance matrices. During this work we investigate the climatological data to be used in TEMPO algorithms (TB O3) and simulated data from the NASA GMAO Goddard Earth Observing System (GEOS-5) Forward Processing (FP) near-real-time (NRT) model products. These two data products will be evaluated with ground-based lidar data from the Tropospheric Ozone Lidar Network (TOLNet) at various locations of the US. This study evaluates the TB climatology, GEOS-5 climatology, and 3-hourly GEOS-5 data compared to lower tropospheric observations to demonstrate the accuracy of a priori information to potentially be used in TEMPO O3 algorithms. Here we present our initial analysis and the theoretical impact on TEMPO retrievals in the lower troposphere.

ozone↗

NASA NTRS2016

Evaluating a Priori Ozone Profile Information Used in TEMPO Tropospheric Ozone Retrievals

Ozone (O3) is a greenhouse gas and toxic pollutant which plays a major role in air quality. Typically, monitoring of surface air quality and O3 mixing ratios is primarily conducted using in situ measurement networks. This is partially due to high-quality information related to air quality being limited from space-borne platforms due to coarse spatial resolution, limited temporal frequency, and minimal sensitivity to lower tropospheric and surface-level O3. The Tropospheric Emissions: Monitoring of Pollution (TEMPO) satellite is designed to address these limitations of current space-based platforms and to improve our ability to monitor North American air quality. TEMPO will provide hourly data of total column and vertical profiles of O3 with high spatial resolution to be used as a near-real-time air quality product.TEMPO O3 retrievals will apply the Smithsonian Astrophysical Observatory profile algorithm developed based on work from GOME, GOME-2, and OMI. This algorithm uses a priori O3 profile information from a climatological data-base developed from long-term ozone-sonde measurements (tropopause-based (TB) O3 climatology). It has been shown that satellite O3 retrievals are sensitive to a priori O3 profiles and covariance matrices. During this work we investigate the climatological data to be used in TEMPO algorithms (TB O3) and simulated data from the NASA GMAO Goddard Earth Observing System (GEOS-5) Forward Processing (FP) near-real-time (NRT) model products. These two data products will be evaluated with ground-based lidar data from the Tropospheric Ozone Lidar Network (TOLNet) at various locations of the US. This study evaluates the TB climatology, GEOS-5 climatology, and 3-hourly GEOS-5 data compared to lower tropospheric observations to demonstrate the accuracy of a priori information to potentially be used in TEMPO O3 algorithms. Here we present our initial analysis and the theoretical impact on TEMPO retrievals in the lower troposphere.

TEMPO↗

NASA NTRSDate not supplied

Advanced Material Options for the Portable Life Support System

Meeting an aggressive mass requirement is a challenge for new space suit development efforts, including that of the Exploration Extravehicular Mobility Unit Portable Life Support System (PLSS) government reference design. To reduce overall system mass, titanium was selected as the primary metal for the PLSS backplate and thermal loop. However, galvanically compatible metals (Hastelloy, Inconel, Monel) have relatively high densities and require further design complexities such as coatings and more challenging manufacturing. Efforts to reduce the mass of the government reference design for an International Space Station (ISS) or lunar mission were halted due to the government’s transition to a commercial Extravehicular Activity (EVA) services approach, but research was conducted into methodologies for mass savings using advanced materials. With the advent of a lunar Artemis mission and potential for future Mars missions, mass becomes a more critical driver going forward. Therefore, alternative materials and processes must be considered to fully close the mass requirement. There are many new materials and processes that can be considered; however, considerations must be made to ensure galvanic compatibility, radiation concerns for sensitive electronics, vacuum compatibility, tight tolerances, fluid compatibility with oxygen and water, and thread insert options. Individual PLSS components may have different requirements and need to be considered separately for reducing overall mass. This report will touch on comparisons between advanced materials, focusing on composites, additive manufacturing, and plastics. It will also address the different processes that may need to be applied when using these materials in the harsh environment of space. Lastly, it will look at specific components and make recommendations for options to reduce the mass of each one.

Ryan Ogilvie↗

NASA NTRS2024

Advanced Material Options for the Portable Life Support System (PLSS)

Ryan Ogilvie↗

DOE OSTI2022

Matrix Approach to Land Carbon Cycle Modeling

Land ecosystems contribute to climate change mitigation by taking up approximately 30% of anthropogenically emitted carbon. However, estimates of the amount and distribution of carbon uptake across the world's ecosystems or biomes display great uncertainty. The latter hinders a full understanding of the mechanisms and drivers of land carbon uptake, and predictions of the future fate of the land carbon sink. The latter is needed as evidence to inform climate mitigation strategies such as afforestation schemes. To advance land carbon cycle modeling, we have developed a matrix approach. Land carbon cycle models use carbon balance equations to represent carbon exchanges among pools. Our approach organizes this set of equations into a single matrix equation without altering any processes of the original model. The matrix equation enables the development of a theoretical framework for understanding the general, transient behavior of the land carbon cycle. While carbon input and residence time are used to quantify carbon storage capacity at steady state, a third quantity, carbon storage potential, integrates fluxes with time to define dynamic disequilibrium of the carbon cycle under global change. The matrix approach can help address critical contemporary issues in modeling, including pinpointing sources of model uncertainty and accelerating spin-up of land carbon cycle models by tens of times. The accelerated spin-up liberates models from the computational burden that hinders comprehensive parameter sensitivity analysis and assimilation of observational data to improve model accuracy. Such computational efficiency offered by the matrix approach enables substantial improvement of model predictions using ever-increasing data availability. Overall, the matrix approach offers a step change forward for understanding and modeling the land carbon cycle.

54 ENVIRONMENTAL SCIENCES↗