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NASA NTRS2023

Impact of Design Factors for ESA CCI Satellite Soil Moisture Data Assimilation over Europe

In this study, soil moisture retrievals of the combined active–passive ESA Climate Change Initiative (CCI) soil moisture product are assimilated into the Noah-MP land surface model over Europe using a one-dimensional ensemble Kalman filter and an 18-yr study period. The performance of the data assimilation (DA) system is evaluated by comparing it with a model-only experiment (at in situ sites) and by assessing statistics of innovations and increments as DA diagnostics (over the entire domain). For both assessments, we explore the impact of three design choices, resulting in the following insights. 1) The magnitude of the assumed observation errors strongly affects the skill improvements evaluated against in situ stations and internal diagnostics. 2) Choosing between climatological or monthly cumulative distribution function matching as the observation bias correction method only has a marginal effect on the in situ skill of the DA system. However, the internal diagnostics suggest a more robust system parameterization if the observations are rescaled monthly. 3) The choice of atmospheric reanalysis dataset to force the land surface model affects the model-only skill and the DA skill improvements. The model-only skill is higher with input from the MERRA-2 than with input from the ERA5 reanalysis, resulting in larger DA skill improvements for the latter. Additionally, we show that the added value of the DA strongly depends on the quality of the satellite retrievals and land cover, with the most substantial soil moisture skill improvements occurring over croplands and skill degradation occurring over densely forested areas.

Soil moisture↗

DOE OSTI2017

Assimilation of repeated woody biomass observations constrains decadal ecosystem carbon cycle uncertainty in aggrading forests

Forest carbon sink strengths are governed by plant growth, mineralization of dead organic matter, and disturbance. Across landscapes, remote sensing can provide information about aboveground states of forests and this information can be linked to models to estimate carbon cycling in forests close to steady state. For aggrading forests this approach is more challenging and has not been demonstrated. Here in this paper we apply a Bayesian approach, linking a simple model to a range of data, to evaluate their information content, for two aggrading forests. We compare high information content analyses using local observations with retrievals using progressively sparser remotely sensed information (repeated, single, and no woody biomass observations). The net biome productivity of both forests is constrained to be a net sink with <2 Mg C ha -1 yr -1 variation across the range of inputs. However, the sequestration of particular carbon pool(s) varies with assimilated biomass information. Assimilation of repeated biomass observations reduces uncertainty and/or bias in all ecosystem C pools not just wood, compared to analyses using single or no stock information. As verification, our repeated biomass analysis explains 78–86% of variation in litter dynamics at one forest, while at the second forest total dead organic matter estimates are within observational uncertainty. The uncertainty of retrieved ecosystem traits in the repeated biomass analysis is reduced by up to 50% compared to analyses with less biomass information. This study quantifies the importance of repeated woody observations in constraining the dynamics of both wood and dead organic matter, highlighting the benefit of proposed remote sensing missions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Robustness of the Ensemble Score Filter to the Type of Assimilated Observation Networks

Recent advances in data assimilation (DA) have focused on developing more flexible approaches that can better accommodate nonlinearities in models and observations. However, it remains unclear how the performance of these advanced methods depends on the observation network characteristics. In this study, we present initial experiments with the surface quasi‐geostrophic model, in which we compare a recently developed ensemble filter using score‐based diffusion models with the standard Local Ensemble Transform Kalman Filter (LETKF). Our results show that the analysis solutions respond differently to the number, spatial distribution, and nonlinear fraction of assimilated observations. We also find notable changes in the multiscale characteristics of the analysis errors. Given that standard DA techniques will eventually be replaced by more advanced methods, we hope this study sets the ground for future efforts to reassess the value of Earth observing systems in the context of newly emerging algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Osh6p, a homologue of the oxysterol-binding protein, is involved in production of functional cytochrome P450 belonging to CYP52 family in n-alkane-assimilating yeast Yarrowia lipolytica

Highlights: • Yarrowia lipolytica has four OSBP homolog genes, OSH1, OSH3, OSH4, and OSH6. • OSH3 and OSH6 are required for growth on n-alkanes. • OSH6 is involved in the production of functional P450 of CYP52 family. • Osh6p might provide an ideal ER membrane environment for CYP52 P450 in Y. lipolytica. In this study, we investigated the role of OSH6, which encodes a homolog of the oxysterol-binding protein, in the assimilation of n-alkanes in the yeast Yarrowia lipolytica. The deletion mutant of OSH6 showed growth defects on n-alkanes of 10–16 carbons. In the deletion mutant, production of the functional cytochrome P450 was not observed. However, transcription of ALK1, encoding a major P450 belonging to the CYP52 family that plays a critical role in n-alkane hydroxylation, and further translation of its transcript were noted in the deletion mutant as well as in the wild-type strain. The phospholipid composition was altered and, the ratio of phosphatidylserine (PS) was reduced by the deletion of OSH6. Residues involved in the transport of PS and phosphatidylinositol-4-phosphate in Osh6 of Saccharomyces cerevisiae are conserved in Y. lipolytica Osh6p and substitutions of these residues resulted in a defect in the n-alkane assimilation by Y. lipolytica. From these results, we propose a hypothesis that Osh6p provides an ideal endoplasmic reticulum membrane environment for Alk proteins to have a functional conformation via lipid transport activity in Y. lipolytica.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

Expression of heterologous non-oxidative pentose phosphate pathway from Bacillus methanolicus and phosphoglucose isomerase deletion improves methanol assimilation and metabolite production by a synthetic Escherichia coli methylotroph

Synthetic methylotrophy aims to develop non-native methylotrophic microorganisms to utilize methane or methanol to produce chemicals and biofuels. We report two complimentary strategies to further engineer a previously engineered methylotrophic E. coli strain for improved methanol utilization. First, we demonstrate improved methanol assimilation in the presence of small amounts of yeast extract by expressing the non-oxidative pentose phosphate pathway (PPP) from Bacillus methanolicus . Second, we demonstrate improved co-utilization of methanol and glucose by deleting the phosphoglucose isomerase gene ( pgi ), which rerouted glucose carbon flux through the oxidative PPP. Both strategies led to significant improvements in methanol assimilation as determined by 13 C-labeling in intracellular metabolites. As a result, introduction of an acetone-formation pathway in the pgi -deficient methylotrophic E. coli strain led to improved methanol utilization and acetone titers during glucose fed-batch fermentation.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Global Temperature Responses to Large Tropical Volcanic Eruptions in Paleo Data Assimilation Products and Climate Model Simulations Over the Last Millennium

Abstract Large volcanic eruptions are one of the dominant perturbations to global and regional atmospheric temperatures on timescales of years to decades. Discrepancies remain, however, in the estimated magnitude and persistence of the surface temperature cooling caused by volcanic eruptions, as characterized by paleoclimatic proxies and climate models. We investigate these discrepancies in the context of large tropical eruptions over the Last Millennium using two state‐of‐the‐art data assimilation products, the Paleo Hydrodynamics Data Assimilation product (PHYDA) and the Last Millennium Reanalysis (LMR), and simulations from the National Center for Atmospheric Research Community Earth System Model‐Last Millennium Ensemble (NCAR CESM‐LME). We find that PHYDA and LMR estimate mean global and hemispheric cooling that is similar in magnitude and persistence once effects from eruptions occurring in short succession are removed. The estimates also compare well to Northern‐Hemisphere reconstructions based solely or partially on tree‐ring density, which have been proposed as the most accurate proxy estimates of surface cooling due to volcanism. All proxy‐based estimates also agree well with the magnitude of the mean cooling simulated by the CESM‐LME. Differences remain, however, in the spatial patterns of the temperature responses in the PHYDA, LMR, and the CESM‐LME. The duration of cooling anomalies also persists for several years longer in the PHYDA and LMR relative to the CESM‐LME. Our results demonstrate progress in resolving discrepancies between proxy‐ and model‐based estimates of temperature responses to volcanism, but also indicate these estimates must be further reconciled to better characterize the risks of future volcanic eruptions.

Tejedor, E.↗

DOE OSTI2024

The ‘photosynthetic C 1 pathway’ links carbon assimilation and growth in California poplar

Although primarily studied in relation to photorespiration, serine metabolism in chloroplasts may play a key role in plant CO 2 fertilization responses by linking CO 2 assimilation with growth. Here, we show that the phosphorylated serine pathway is part of a 'photosynthetic C 1 pathway' and demonstrate its high activity in foliage of a C 3 tree where it rapidly integrates photosynthesis and C 1 metabolism contributing to new biomass via methyl transfer reactions, imparting a large natural 13 C-depleted signature. Using 13 CO 2 -labelling, we show that leaf serine, the S-methyl group of leaf methionine, pectin methyl esters, and the associated methanol released during cell wall expansion during growth, are directly produced from photosynthetically-linked C 1 metabolism, within minutes of light exposure. We speculate that the photosynthetic C 1 pathway is highly conserved across the photosynthetic tree of life, is responsible for synthesis of the greenhouse gas methane, and may have evolved with oxygenic photosynthesis by providing a mechanism of directly linking carbon and ammonia assimilation with growth. Although the rise in atmospheric CO 2 inhibits major metabolic pathways like photorespiration, our results suggest that the photosynthetic C 1 pathway may accelerate and represents a missing link between enhanced photosynthesis and plant growth rates during CO 2 fertilization under a changing climate.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2019

Study of argon assimilation into the post-disruption runaway electron plateau in DIII-D and comparison with a 1D diffusion model

The assimilation of argon injected into post-disruption runaway electron (RE) plateaus is studied and compared to the vertical loss rate for vertically unstable RE plateaus. A 1D diffusion model is developed to include neutral diffusion and ionization and is used to help in data interpretation. It is found that the radial mixing time scale of argon ions (~0.05 s) is comparable to the vertical loss timescale. Neutral argon becomes the dominant Ar species in the RE plateau for large Ar numbers (> 3 x 10 21 ); at the same time the neutral Ar diffusivity decreases due to plasma cooling, causing a saturation in the assimilation of injected Ar on the vertical loss time scale. Injection of Ar into vertically unstable RE plateaus in DIII-D does increase the vertical loss rate, as predicted by previous modeling of ITER. Furthermore, there is a decreasing trend in RE current at the wall strike as the Ar quantity is turned up or as the Ar is injected earlier, indicating a decrease in RE energy deposited to the wall.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Towards real-time monitoring: data assimilated time-lapse full waveform inversion for seismic velocity and uncertainty estimation

SUMMARY Rapid development of time-lapse seismic monitoring instrumentations has made it possible to collect dense time-lapse data for tomographically retrieving time-lapse (even continuous) images of subsurface changes. While traditional time-lapse full waveform inversion (TLFWI) algorithms are designed for sparse time-lapse surveys, they lack of effective temporal constraint on time-lapse data, and, more importantly, lack of the uncertainty estimation of the TLFWI results that is critical for further interpretation. Here, we propose a new data assimilation TLFWI method, using hierarchical matrix powered extended Kalman filter (HiEKF) to quantify the image uncertainty. Compared to existing Kalman filter algorithms, HiEKF allows to store and update a data-sparse representation of the cross-covariance matrices and propagate model errors without expensive operations involving covariance matrices. Hence, HiEKF is computationally efficient and applicable to 3-D TLFWI problems. Then, we reformulate TLFWI in the framework of HiEKF (termed hereafter as TLFWI-HiEKF) to predict time-lapse images of subsurface spatiotemporal velocity changes and simultaneously quantify the uncertainty of the inverted velocity changes over time. We demonstrate the validity and applicability of TLFWI–HiEKF with two realistic CO2 monitoring models derived from Frio-II and Cranfield CO2 injection sites, respectively. In both 2-D and 3-D examples, the inverted high-resolution time-lapse velocity results clearly reveal a continuous velocity reduction due to the injection of CO2. Moreover, the accuracy of the model is increasing over time by assimilating more time-lapse data while the standard deviation is decreasing over lapsed time. We expect TLFWI-HiEKF to be equipped with real-time seismic monitoring systems for continuously imaging the distribution of subsurface gas and fluids in the future large-scale CO2 sequestration experiments and reservoir management.

58 GEOSCIENCES↗

DOE OSTI2021

Bacterial xylan utilization regulons: systems for coupling depolymerization of methylglucuronoxylans with assimilation and metabolism

Abstract Bioconversion of lignocellulosic resources offers an economically promising path to renewable energy. Technological challenges to achieving bioconversion include the development of cost-effective processes that render the cellulose and hemicellulose components of these resources to fermentable hexoses and pentoses. Natural bioprocessing of the hemicellulose fraction of lignocellulosic biomass requires depolymerization of methylglucuronoxylans. This requires secretion of endoxylanases that release xylooligosaccharides and aldouronates. Physiological, biochemical, and genetic studies with selected bacteria support a process in which a cell-anchored multimodular GH10 endoxylanase catalyzes release of the hydrolysis products, aldotetrauronate, xylotriose, and xylobiose, which are directly assimilated and metabolized. Gene clusters encoding intracellular enzymes, including α-glucuronidase, endoxylanase, β-xylosidase, ABC transporter proteins, and transcriptional regulators, are coordinately responsive to substrate induction or repression. The rapid rates of glucuronoxylan utilization and microbial growth, along with the absence of detectable products of depolymerization in the medium, indicate that assimilation and depolymerization are coupled processes. Genomic comparisons provide evidence that such systems occur in xylanolytic species in several genera, including Clostridium, Geobacillus, Paenibacillus, and Thermotoga. These systems offer promise, either in their native configurations or through gene transfer to other organisms, to develop biocatalysts for efficient production of fuels and chemicals from the hemicellulose fractions of lignocellulosic resources.

Biotechnology & Applied Microbiology↗

DOE OSTI2024

The Dynamic Assimilation Technique measures photosynthetic CO 2 response curves with similar fidelity to steady-state approaches in half the time

The net CO 2 assimilation (A) response to intercellular CO 2 concentration (C i ) is a fundamental measurement in photosynthesis and plant physiology research. The conventional A/C i protocols rely on steady-state measurements and take 15–40 min per measurement, limiting data resolution or biological replication. Additionally, there are several CO 2 protocols employed across the literature, without clear consensus as to the optimal protocol or systematic biases in their estimations. We compared the non-steady-state Dynamic Assimilation Technique (DAT) protocol and the three most used CO 2 protocols in steady-state measurements, and tested whether different CO 2 protocols lead to systematic differences in estimations of the biochemical limitations to photosynthesis. The DAT protocol reduced the measurement time by almost half without compromising estimation accuracy or precision. The monotonic protocol was the fastest steady-state method. Estimations of biochemical limitations to photosynthesis were very consistent across all CO 2 protocols, with slight differences in Rubisco carboxylation limitation. The A/C i curves were not affected by the direction of the change of CO 2 concentration but rather the time spent under triose phosphate utilization (TPU)-limited conditions. Our results suggest that the maximum rate of Rubisco carboxylation (V cmax ), linear electron flow for NADPH supply (J), and TPU measured using different protocols within the literature are comparable, or at least not systematically different based on the measurement protocol used.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Expanded Diversity of Microbial Groups Capable of Anaerobic Pyrite Reduction and Assimilation of Dissolution Products

Pyrite, the most abundant iron sulfide mineral in the Earth's crust, has traditionally been considered as a sink for iron and sulfur in the absence of oxygen. Recent research, however, has shown that anaerobic methanogenic archaea can reductively dissolve pyrite and assimilate its products as sources of iron and sulfur. This study explores whether other anaerobic bacteria, including fermentative, nitrate-, iron oxide-, fumarate-, and sulfate-respiring bacteria, can also reduce pyrite and use its dissolution products as sources of iron and sulfur. Results indicate that heterotrophic bacteria respiring fumarate or sulfate, or fermenting organic carbon, can reduce pyrite and assimilate released iron and sulfur. In contrast, nitrate- or iron oxide-respiring cells did not reduce pyrite, suggesting that microbial pyrite reduction is metabolism-specific. All strains capable of reducing pyrite could also use mackinawite as an iron and sulfur source. With the exception of fermentative Bacteroides, strains did not require direct contact with pyrite to reduce the mineral, indicating extracellular electron transfer via electron shuttles. These findings expand the known diversity of microbial groups capable of pyrite reduction and highlight the mineral's lability in various anaerobic environments, with potential implications for the biogeochemical cycles of iron, sulfur, carbon, and oxygen.

58 GEOSCIENCES↗

DOE OSTI2021

Inside out: Measuring the effect of wood anatomy on the efflux and assimilation of xylem–transported CO 2

Carbon dioxide concentrations (including aqueous CO 2 , carbonic acid, bicarbonate, and carbonate) in woody tissues can be up to 750 times higher than atmospheric CO 2 concentrations, ranging from <1% to >26% vs atmospheric ~0.04% (Fig. 1) (Teskey et al. 2008). CO 2 formed through respiration is generally assumed to diffuse to the atmosphere from tissues adjacent to where it is produced. Here, this CO 2 buildups in the stem due to the diffusional barriers in woody and bark tissues. CO 2 in the stem has three fates: 1) it can be refixed for photosynthesis, 2) it can be used for anaplerotic reactions, or 3) it can exit the plant either adjacent to where it was produced (radial diffusion) or in an area remote from its point of origin (xylem-transported CO 2 ). Not accounting for assimilation of xylem-transported CO 2 may result in underestimating total plant photosynthesis. Alternatively, overlooking the transport of CO 2 away from its point of origin complicates the estimation of respiration in stems, branches, or even leaves. For example, CO 2 efflux from the stem may not solely represent stem respiration, but it may represent CO 2 generated through respiration in areas remote from the point of efflux (Stutz et al., 2017). Additionally, wood anatomy and branching architecture likely influence how much and how far xylem-transported CO 2 travels (Fig. 2). Few studies have combined measurements of both the efflux of xylem-transported CO 2 from trees together and the assimilation of xylem-transported CO 2 . Excitingly in this issue of Plant, Cell & Environment, Salomón et al. (pp. ) demonstrate the importance of xylem-transported CO 2 in plants with different wood anatomies by comparing the amount of xylem-transported CO 2 used for photosynthesis to the amount effluxed.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Data Assimilation for Robust UQ Within Agent-Based Simulation on HPC Systems

Agent-based simulation provides a powerful tool for in silico system modeling. However, these simulations do not provide built-in methods for uncertainty quantification (UQ). Within these types of models a typical approach to UQ is to run multiple realizations of the model then compute aggregate statistics. This approach is limited due to the compute time required for a solution. When faced with an emerging biothreat, public health decisions need to be made quickly and solutions for integrating near real-time data with analytic tools are needed. We propose an integrated Bayesian UQ framework for agent-based models based on sequential Monte Carlo sampling. Given streaming or static data about the evolution of an emerging pathogen this Bayesian framework provides a distribution over the parameters governing the spread of a disease through a population. These estimates of the spread of a disease may be provided to public health agencies seeking to abate the spread. By coupling agent-based simulations with Bayesian modeling in a data assimilation, our proposed framework provides a powerful tool for modeling dynamical systems in silico. We propose a method which reduces model error and provides a range of realistic possible outcomes. Moreover, our method addresses two primary limitations of ABMs: the lack of UQ and an inability to assimilate data. Our proposed framework combines the flexibility of an agent-based model with UQ provided by the Bayesian paradigm in a workflow which scales well to HPC systems. We provide algorithmic details and results on a simulated outbreak with both static and streaming data.

Spannaus, Adam [ORNL] (ORCID:0000000225213657)↗

DOE OSTI2019

Bayesian Assimilation of Multiscale Precipitation Data and Sparse Ground Gauge Observations in Mountainous Areas

Estimating the spatial distribution of precipitation is important for understanding ecohydrological processes at catchment scales. However, this estimation is difficult in mountainous areas because ground-based observation stations are often sparsely located and do not represent the spatial variability of precipitation. In this study, we develop a Bayesian assimilation method based on data collected on the Tibetan Plateau from 1980 to 2014 to estimate monthly and daily precipitation. To accomplish this, point-scale ground meteorological observations are combined with large-scale precipitation data such as satellite observations or reanalysis data. First, we remove the terrain effects from ground observations by fitting the precipitation data as functions of elevation, and then we spatially interpolate the residuals to 5-km-resolution grids to obtain monthly and daily precipitation. Additionally, we use Tropical Rainfall Measuring Mission (TRMM) satellite observations and ERA-Interim reanalysis data. Cross-validation methods are used to evaluate our method; the results show that our method not only captures the change in precipitation with terrain but also significantly reduces the associated uncertainty. The improvements are more evident in the main river source areas on the edge of the Tibetan Plateau, where elevation changes dramatically, and in high-altitude areas, where the ground gauges are sparse compared with those in low-altitude areas. Our assimilation method is applicable to other regions and is particularly useful for mountainous watersheds where ground meteorological stations are sparse and precipitation is considerably influenced by terrain.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Wave-by-Wave Forecasting via Assimilation of Marine Radar Data

Abstract This work describes a phase-resolving wave-forecasting algorithm that is based on the assimilation of marine radar image time series. The algorithm is tested against synthetic data and field observations. The algorithm couples X-band marine radar observations with a phase-resolving wave model that uses the linear mild slope equations for reconstruction of water surface elevations over a large domain of O (km) and a prescribed time window of O (min). The reconstruction also enables wave-by-wave forecasting through forward propagation in space and time. Marine radar image time series provide the input wave observations through a previously given relationship between backscatter intensity and the radial component of the sea surface slope. The algorithm assimilates the wave slope information into the model via a best-fit wave source function at the boundary that minimizes the slope reconstruction error over an annular region at the outer ranges of the radar images. The wave model is then able to propagate the waves across a polar domain to a location of interest at nearer ranges. The constraints on the method for achieving real-time forecasting are identified, and the algorithm is verified against synthetic data and tested using field observations.

Engineering↗

DOE OSTI2022

Adjoint sensitivity analysis and data assimilation for verification of dry storage cask contents

Dry cask storage is a method for interim storage of spent fuel assemblies which contain fissile isotopes of uranium and plutonium. These can present a proliferation concern and consequently there is a need for non-destructive testing methods to verify a dry cask's contents for proliferation protection. We present an application of adjoint sensitivity analysis and data assimilation to a multigroup diffusion model of dry cask storage. Adjoint sensitivity analysis allows the efficient calculation of sensitivities for use in data assimilation to calibrate imprecisely known parameter values and data consistency tests to detect diversion scenarios. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

Data Synthesis and Data Assimilation at Global Change Experiments and Fluxnet Toward Improving Land Process Models

The project was conducted during the period from 7/1/2012 to 6/30/2017 with three major tasks: (1) data synthesis and development of data assimilation (DA) techniques to constrain modeled ecosystem feedback to climate change; (2) applications of DA techniques to improve process models at different scales from ecosystem to regions and the globe; and 3) improvements of modeling soil carbon (C) dynamics by land surface models. During this period, we have synthesized published data from soil incubation experiments (e.g., Chen et al., 2016; Xu et al., 2016; Feng et al., 2016), global change experiments (e.g., Li et al., 2013; Shi et al., 2015, 2016; Liang et al., 2016) and fluxnet (e.g., Niu et al., 2012., Xia et al., 2015; Li et al., 2016). These data have been organized into multiple data products and have been used to identify general mechanisms and estimate parameters for model improvement. We used the data sets that we collected and the DA techniques to improve model performance of both ecosystem models and global land models. The objectives are: 1) to improve model simulations of litter and soil carbon storage (e.g., Schädel et al., 2013; Hararuk and Luo, 2014; Hararuk et al., 2014; Liang et al., 2015); 2) to explore the effects of CO 2 , warming and precipitation on ecosystem processes (e.g., van Groenigen et al., 2014; Shi et al., 2015, 2016; Feng et al., 2017); and 3) to estimate parameters variability in different ecosystems (e.g., Li et al., 2016). We developed a traceability framework, which was based on matrix approaches and decomposed the modeled steady-state terrestrial ecosystem carbon storage capacity into four can trace the difference in ecosystem carbon storage capacity among different biomes to four traceable components: net primary productivity (NPP), baseline C residence times, environmental scalars and climate forcing (Xia et al., 2013). With this framework, we can diagnose the differences in modeled carbon storage across ecosystems, biomes, and models. This framework has been successfully implemented by several global land models, such as CABLE (Xia et al., 2013), LPJ-GUESS (Ahlström et al., 2015), CLM (Hararuk et al., 2014; Huang et al., 2017, submitted; Shi et al., 2017, submitted), and ORCHIDEE (Huang et al., 2017, unpublished). Moreover, we have identified the theoretical foundation of the determinants of transient C storage dynamics by adding another term, C storage potential, to the steady-state traceability framework (Luo et al., 2017). The theoretical foundation of transient C storage dynamics has been applied to develop a transient traceability framework to explore the traceable components of transient C storage dynamics responded to the rising CO 2 and climate change in the two contrasting ecosystem types Duke needleleaved forest and Harvard deciduous broadleaved forest (Jiang et al., 2017, in revision). Overall, with the data synthesis, data assimilation techniques, and the steady-state and transient traceability frameworks, we have greatly improved land process models for predicting responses and feedback of terrestrial C dynamics to global change. The matrix approaches has the potential to be applied in theoretical research on nitrogen and phosphorus cycle, and therefore, the coupling of carbon-nitrogen-phosphorus.

58 GEOSCIENCES↗