Search NASA⌕ Search

SEARCH · Search NASA

Results for “root development”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Metabolome and RNA-seq Analysis of Responses to Nitrogen Deprivation and Resupply in Tea Plant (Camellia sinensis) Roots

Nitrogen (N) is an important contributor in regulating plant growth and development as well as secondary metabolites synthesis, so as to promote the formation of tea quality and flavor. Theanine, polyphenols, and caffeine are important secondary metabolites in tea plant. In this study, the responses of Camellia sinensis roots to N deprivation and resupply were investigated by metabolome and RNA-seq analysis. N deficiency induced content increase for most amino acids (AAs) and reduction for the remaining AAs, polyphenols, and caffeine. After N recovery, the decreased AAs and polyphenols showed a varying degree of recovery in content, but caffeine did not. Meanwhile, theanine increased in content, but its related synthetic genes were down-regulated, probably due to coordination of the whole N starvation regulatory network. Flavonoids-related pathways were relatively active following N stress according to KEGG enrichment analysis. Gene co-expression analysis revealed TCS2 , AMT1;1 , TAT2 , TS , and GOGAT as key genes, and TFs like MYB, bHLH, and NAC were also actively involved in N stress responses in C. sinensis roots. These findings facilitate the understanding of the molecular mechanism of N regulation in tea roots and provide genetic reference for improving N use efficiency in tea plant.

Xu, Wenluan↗
DOE OSTI2023

Root phenotypes for improved nitrogen capture

Abstract Background Suboptimal nitrogen availability is a primary constraint for crop production in low-input agroecosystems, while nitrogen fertilization is a primary contributor to the energy, economic, and environmental costs of crop production in high-input agroecosystems. In this article we consider avenues to develop crops with improved nitrogen capture and reduced requirement for nitrogen fertilizer. Scope Intraspecific variation for an array of root phenotypes has been associated with improved nitrogen capture in cereal crops, including architectural phenotypes that colocalize root foraging with nitrogen availability in the soil; anatomical phenotypes that reduce the metabolic costs of soil exploration, improve penetration of hard soil, and exploit the rhizosphere; subcellular phenotypes that reduce the nitrogen requirement of plant tissue; molecular phenotypes exhibiting optimized nitrate uptake kinetics; and rhizosphere phenotypes that optimize associations with the rhizosphere microbiome. For each of these topics we provide examples of root phenotypes which merit attention as potential selection targets for crop improvement. Several cross-cutting issues are addressed including the importance of soil hydrology and impedance, phenotypic plasticity, integrated phenotypes, in silico modeling, and breeding strategies using high throughput phenotyping for co-optimization of multiple phenes. Conclusions Substantial phenotypic variation exists in crop germplasm for an array of root phenotypes that improve nitrogen capture. Although this topic merits greater research attention than it currently receives, we have adequate understanding and tools to develop crops with improved nitrogen capture. Root phenotypes are underutilized yet attractive breeding targets for the development of the nitrogen efficient crops urgently needed in global agriculture.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Root-associated bacterial communities and root metabolite composition are linked to nitrogen use efficiency in sorghum

ABSTRACT The development of cereal crops with high nitrogen use efficiency (NUE) is a priority for worldwide agriculture. In addition to conventional plant breeding and genetic engineering, the use of the plant microbiome offers another approach to improving crop NUE. To gain insight into the bacterial communities associated with sorghum lines that differ in NUE, a field experiment was designed comparing 24 diverse Sorghum bicolor lines under sufficient and deficient nitrogen (N). Amplicon sequencing and untargeted gas chromatography–mass spectrometry were used to characterize the bacterial communities and the root metabolome associated with sorghum genotypes varying in sensitivity to low N. We demonstrated that N stress and sorghum type (energy, sweet, and grain sorghum) significantly impacted the root-associated bacterial communities and root metabolite composition of sorghum. We found a positive correlation between sorghum NUE and bacterial richness and diversity in the rhizosphere. The greater alpha diversity in high NUE lines was associated with the decreased abundance of a dominant bacterial taxon, Pseudomonas . Multiple strong correlations were detected between root metabolites and rhizosphere bacterial communities in response to low N stress. This indicates that the shift in the sorghum microbiome due to low N is associated with the root metabolites of the host plant. Taken together, our findings suggest that host genetic regulation of root metabolites plays a role in defining the root-associated microbiome of sorghum genotypes differing in NUE and tolerance to low N stress. IMPORTANCE The development of crops that are more nitrogen use-efficient (NUE) is critical for the future of the enhanced sustainability of agriculture worldwide. This objective has been pursued mainly through plant breeding and plant molecular engineering, but these approaches have had only limited success. Therefore, a different strategy that leverages soil microbes needs to be fully explored because it is known that soil microbes improve plant growth through multiple mechanisms. To design approaches that use the soil microbiome to increase NUE, it will first be essential to understand the relationship among soil microbes, root metabolites, and crop productivity. Using this approach, we demonstrated that certain key metabolites and specific microbes are associated with high and low sorghum NUE in a field study. This important information provides a new path forward for developing crop genotypes that have increased NUE through the positive contribution of soil microbes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Intrinsic and extrinsic effects on the fracture toughness of ductile metallic glasses

The potential application of metallic glasses (MGs) as structural materials demands accurate measurements of their toughness and the understanding of the underlying factors affecting it. Currently, it is challenging to precisely measure the toughness of MGs, especially ductile MGs. Measured toughness values are widely scattered, even for MGs with identical compositions. That is attributed to the combined effect of intrinsic and extrinsic factors including processing, sample geometries, and loading conditions. A fundamental understanding of the influences of these elements is thus of great significance. In the present study, molecular dynamics simulations are performed to investigate the influence of intrinsic and extrinsic effects on the fracture toughness of CuZr MGs. In particular, focused is placed on the effects of cooling rate, notch shape and size, strain rate, and temperature. The results indicate that the fracture toughness of a MG scales with the cooling rate used to prepare it. This is attributed to increased free volume content generated at high cooling rates, which enhances plastic deformation and amplifies the associated energy dissipation during plastic deformation events. Fracture toughness also increases with the strain rate, arguably due to strain rate-induced crack extension delay. Overall, the results demonstrate that the largest fracture toughness are achieved when MG samples are fabricated at high cooling rates and subjected to high strain rate deformation. In addition, results suggest that the fracture toughness decreases with increasing temperature, due to the significant decrease in strength. Here, the correlations revealed between these crucial intrinsic and extrinsic parameters and the calculated MG fracture toughness support the development of a framework to understand the root of the discrepancies in the measurement of the toughness of MGs and provide insights into the design of tough MGs for structural applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Comparisons of biomass, water use efficiency and water use strategies across five genomic groups of Populus and its hybrids

Abstract Genetic improvement and hybridization in the Populus genus have led to the development of genotypes exhibiting fast growth, high rooting ability and disease resistance. However, while large biomass production is important for bioenergy crops, efficient use of resources including water is also important in sites lacking irrigation and for maintaining ecosystem water availability. In addition, comparison of water use strategies across a range of growth rates and genetic variability can elucidate whether certain strategies are shared among the fastest growing and/or most water use efficient genotypes. We estimated tree water use throughout the second growing season via sapflow sensors of 48 genotypes from five Populus taxa; P. deltoides W. Bartram ex Marshall × P. deltoides (D × D), P. deltoides × P. maximowiczii A. Henry (D × M), P. deltoides × P. nigra L. (D × N), P. deltoides × P. trichocarpa Torr. & Gray (D × T) and P. trichocarpa × P. deltoides (T × D) and calculated average canopy stomatal conductance ( G S ). We regressed G S and atmospheric vapor pressure deficit (VPD) wherein the slope of the relationship represents stomatal sensitivity to VPD. At the end of the second growing season, trees were harvested, and their dry woody biomass was used to calculate whole tree water use efficiency (WUE T ). We found that D × D and D × M genotypes exhibited differing water use strategies with D × D genotypes exhibiting high stomatal sensitivity while retaining leaves while D × M genotypes lost leaf area throughout the growing season but exhibited low stomatal sensitivity. Across measured taxa, biomass growth was positively correlated with WUE T , and genotypes representing each measured taxa except D × N and T × D had high 2‐year dry biomass of above 6 kg/tree. Overall, these data can be used to select Populus genotypes that combine high biomass growth with stomatal sensitivity and WUE T to limit the negative impacts of bioenergy plantations on ecosystem water resources.

09 BIOMASS FUELS↗
DOE OSTI2021

Future roots for future soils

Abstract Mechanical impedance constrains root growth in most soils. Crop cultivation changed the impedance characteristics of native soils, through topsoil erosion, loss of organic matter, disruption of soil structure and loss of biopores. Increasing adoption of Conservation Agriculture in high‐input agroecosystems is returning cultivated soils to the soil impedance characteristics of native soils, but in the low‐input agroecosystems characteristic of developing nations, ongoing soil degradation is generating more challenging environments for root growth. We propose that root phenotypes have evolved to adapt to the altered impedance characteristics of cultivated soil during crop domestication. The diverging trajectories of soils under Conservation Agriculture and low‐input agroecosystems have implications for strategies to develop crops to meet global needs under climate change. We present several root ideotypes as breeding targets under the impedance regimes of both high‐input and low‐input agroecosystems, as well as a set of root phenotypes that should be useful in both scenarios. We argue that a ‘whole plant in whole soil’ perspective will be useful in guiding the development of future crops for future soils.

Lynch, Jonathan P.↗
DOE OSTI2021

Anomaly Detection in Accelerator Facilities Using Machine Learning

Synchrotron light sources are user facilities and usually run about 5000 hours per year to support many beamlines operations in parallel. Reliability is a key parameter to evaluate machine performance. Even many facilities have achieved >95% beam reliability, there are still many hours of unscheduled downtime and every hour lost is a waste of operation costs along with a big impact on individual scheduled user experiments. Preventive maintenance on subsystems and quick recovery from machine trips are the basic strategies to achieve high reliability, which heavily depends on experts’ dedication. Recently, SLAC, APS, and NSLS-II collaborated to develop machine-learning-based approaches aiming to solve both situations, hardware failure prediction and machine failure diagnosis to find the root sources. In this paper, we report our facility operation status, development progress, and plans.

Accelerator Physics↗
DOE OSTI2021

A Heterogeneous System for Eagle Detection, Deterrent, and Wildlife Collision Detection for Wind Turbines (Final Technical Report)

This report summarizes the design, implementation, and test of an integrated system for automated detection and deterrence of eagles, with included wind turbine blade strike detection and imaging functionality. A machine learning approach was used in conjunction with a 360° camera system for automated detection and classification of golden eagles. This was developed using footage obtained from trained golden eagles and other raptors, in collaboration with wildlife biologists and professional bird handlers. Oregon State University developed a visual deterrent system, which uses inflatable anthropomorphic sculptures with random, kinetic motion to deter eagles, and conducted limited field testing on live eagles; the deterrent can be triggered by the visual detection of eagles using the vision system. Finally, a multi-sensor module was developed that is mounted at the turbine blade root. This module measures vibration and other motions to detect blade strikes, and an integrated on-blade camera captures an image of any impacting objects. Long-term, this blade strike detection system is intended to support an automatic monitoring and certification system for the eagle detection and deterent system. Independent field testing of each system component is described. Testing of the integrated system on an operational wind turbine was conducted across three separate field tests. This includes multi-day fields tests on a General Electric 1.5MW wind turbine at the National Renewable Energy Laboratory (NREL) National Wind Technology Center (NWTC) in Boulder, CO in October 2018 and July 2019; installation procedures, test procedures, and a summary of collected data are presented. A third multi-day on-turbine field test is also presented, which was performed using a General Electric 1.5MW wind turbine at the North American Wind Research and Training Center (NAWRTC) at Mesalands Community College, Tucumcari, NM in April 2019. Across these field tests, the vision system was demonstrated using unmanned aerial vehicles (UAV), and the eagle classification algorithm was not tested; the visual deterrent system was demonstrated, including automatic, remote deployment following surrogate visual detections; and, multi-sensor on-blade data was recorded across multiple wind turbine operational conditions and through more than 100 surrogate blade strikes using soft projectiles, including the successful demonstration of automatic image capture of striking objects. This data set was also used for offline development and validation of enhanced collision detection algorithms. As summarized in this report, the development and field validation of an integrated detection, deterrent, and blade collision detection system represents a critical proof of concept for future technology development of related detection and deterrent technologies, where both deterrent as well as collision detection recording devices are needed for future siting, monitoring, and operation of wind turbine installations, both onshore and offshore.

17 WIND ENERGY↗
DOE OSTI2025

Root genetics in the field to understand drought adaptation and carbon sequestration (Final Scientific/Technical Report)

For all crop plants, roots play a critical role in growth. Roots anchor the plants, and are the primary site of nutrient and water uptake. Roots are also the main source of C to soil in the form of root tissues and exudates, and thus greatly influence SOM stocks. To perform these functions, primary roots extend into soil, producing a network of branching roots of characteristic form, known as its root system architecture (RSA). RSA varies among species, and among varieties within a species that are adapted to different environments. Root traits are major targets for the second green revolution because of their potential to improve crop productivity, increase drought tolerance and nutrient acquisition, and increase C capture of soil. Improving the quality of roots in maize will be particularly valuable, since this crop is planted on over 92 million acres annually in the US. The future sustainability of agricultural systems relies on their ability to enhance soil organic matter (SOM) storage and reduce GHG emissions, while maintaining or enhancing productivity. This program had two components, Sensors and Models. For the first component, we designed and built a high-throughput phenotyping platform for root pulling of maize plants. This eliminated the physical labor of manually pulling up plants and reduced the number of personnel required down to one. The standardized pulling mechanism allowed recording force curves during the pulling process, providing additional information. We validated that the maximum force for pulling the root system was well-correlated with the root system mass and provided root crowns for further RSA analysis. These root crowns identified significant correlations with 2D root area and root depth, along with 3D root volume, total root length and number of root tips. We then used this system for field-based studies in maize on the genetics of root system architecture and its relation to nitrogen-use efficiency (NUE), including using lines relevant to the Corteva breeding program. Varieties were also evaluated at Corteva sites in the cornbelt and Danforth farm in Missouri, to establish responses across sites. From these studies we have identified genetic loci associated with root traits and created mutant lines for these loci and correlations of root traits with NUE. For the Models component, we worked to incorporate root and soil characteristics into the MEMS 2.0 soil and ecosystem biogeochemical model. Existing soil C models, such as Century, are unable to represent specific root trait interactions with the soil environment and therefore to accurately forecast the potential C sequestration benefits of root breeding under different climatic and soil type conditions. We have developed the MEMS 2.0 ecosystem biogeochemical model to improve quantification of farm-scale soil carbon and greenhouse gas emissions. The new knowledge and large datasets produced by this project will be used to develop and drive an innovative model capable of forecasting the impacts on soil C stocks and nutrient dynamics. An innovation was to use the empirical data from the field studies (in 1, above) to model genetic variation in nitrogen use efficiencies and soil C input. Our work demonstrated that maize root-derived C rapidly replaces existing soil C and after 3 years of continuous maize, up to 20% of soil organic C in the topsoil (0-15cm) and 3% in the subsoil (15-30cm) was contributed by maize. However, this contribution did not entirely represent a net increase. Root C contribution to soil was affected by maize genetics. We have analyzed soils derived from the CSU field trials for C and N stocks, in the different soil physical fractions represented by the MEMS model, using both physical fractionation with elemental analyses, and Fourier transformed infrared spectroscopy. Data will be used to link crop nitrogen use efficiencies with soil C sequestration and provide data to bridge the field trials with the model development, for verification of model predictions. The project had a number of successful outcomes: we have used the new phenotyping platform to identify new genetic loci that can enhance root phenotypes; we have partnered with multiple maize seed companies phenotype varieties in their breeding programs; we have developed the MEMS model that can help inform industry on the potential for carbon sequestration in the agricultural sector, and which is now available at the CSU Soil Carbon Solutions Center for use.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Dynamic Rhizodeposition in the Woody Perennial Populus trichocarpa

Plants undergo physiological and metabolic changes that release specific molecules into the surrounding soil, a process collectively known as rhizodeposition. These compounds play crucial roles in plant‐microbe‐soil interactions, such as supporting plant development and resilience in changing environments. Under nutrient‐limited conditions, these plant‐derived compounds modify the rhizosphere environment, mobilizing otherwise inaccessible nutrients and recruiting stress‐adaptive microbial communities that support stress resilience. Currently, the chemical diversity of rhizodeposition has yet to be fully realized but is expected to be a complex mixture that includes soluble organic compounds excreted from root cells, along with products of root cell turnover, sloughed‐off root cap and border cells, and mucilage. Here, we developed a methodological and conceptual framework for an in‐depth measurement of rhizodeposition through critical advancements in untargeted metabolomics. Further, this approach provided foundational insights into the dynamic changes in rhizodeposition for the woody perennial Populus trichocarpa and rhizodeposit profiles varying by genotype, time, location, and environment. More broadly, this study provides a framework that will help formulate the next steps to effectively study rhizodeposition.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Selecting durable building envelope systems with machine learning assisted hygrothermal simulations database

Hygrothermal simulations provide insight into the energy performance and moisture durability of building envelope components under dynamic conditions. The inputs required for hygrothermal simulations are extensive, and carrying out simulations and analyses requires expert knowledge. An expert system, the Building Science Advisor (BSA), has been developed to predict the performance and select the energy-efficient and durable building envelope systems for different climates. The BSA consists of decision rules based on expert opinions and thousands of parametric simulation results for selected wall systems. The number of potential wall systems results in millions, too many to simulate all of them. We present how machine learning can help predict durability data, such as mold growth, while minimizing the number of simulations needed to run. The simulation results are used for training and validation of machine learning tools for predicting wall durability. We tested Artificial Neural Network (ANN) and Gradient Boosted Decision Trees (GBDT) for their applicability and model accuracy. Models developed with both methods showed adequate prediction performance (root mean square error of 0.195 and 0.209, respectively). Finally, we introduce how the information supports guidance for envelope design via an easy-to-use web-based tool that does not require the end-user to run hygrothermal simulations.

Salonvaara, Mikael↗
DOE OSTI2022

A seed-like proteome in oil-rich tubers

There are numerous examples of plant organs or developmental stages that are desiccation-tolerant and can withstand extended periods of severe water loss. One prime example are seeds and pollen of many spermatophytes. However, in some plants, also vegetative organs can be desiccation-tolerant. One example are the tubers of yellow nutsedge ( Cyperus esculentus ), which also store large amounts of lipids similar to seeds. Interestingly, the closest known relative, purple nutsedge ( Cyperus rotundus ), generates tubers that do not accumulate oil and are not desiccation-tolerant. We generated nanoLC-MS/MS-based proteomes of yellow nutsedge in five replicates of four stages of tuber development and compared them to the proteomes of roots and leaves, yielding 2257 distinct protein groups. Our data reveal a striking upregulation of hallmark proteins of seeds in the tubers. A deeper comparison to the tuber proteome of the close relative purple nutsedge ( C. rotundus ) and a previously published proteome of Arabidopsis seeds and seedlings indicates that indeed a seed-like proteome was found in yellow but not purple nutsedge. This was further supported by an analysis of the proteome of a lipid droplet-enriched fraction of yellow nutsedge, which also displayed seed-like characteristics. One reason for the differences between the two nutsedge species might be the expression of certain transcription factors homologous to ABSCISIC ACID INSENSITIVE3, WRINKLED1, and LEAFY COTYLEDON1 that drive gene expression in Arabidopsis seed embryos.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

IOMiner v0.3

Modern HPC systems are collecting large amounts of I/O performance data. The massive volume and heterogeneity of this data, however, have made timely performance of in-depth integrated analysis difficult. To overcome this difficulty and to allow users to identify the root causes of poor application I/O performance, we developed IOMiner, an I/O log analytics framework.

Byna, Suren↗
DOE OSTI2022

Design-Space Exploration for Inverse-Design of Wind Turbine Blades Using Data-Driven Methods

The state-of-the-practice aerodynamic design methods for wind turbine blades is typically based on Blade-Element Momentum (BEM) theory using a pre-designed frozen family of airfoils. The airfoils are themselves typically designed using panel methods. The design of the next-generation of large flexible rotors will need to capture the non-linear aerodynamics and three-dimensional flow to reduce the levelized cost of wind energy. Data-driven methods for aerodynamic design using data generated by computational fluid dynamics offer an attractive alternative to BEM-based methods that captures the non-linear aerodynamics of the component airfoils as well as the root and tip sections. In this work, we develop and demonstrate a framework to "smartly" explore the relevant design space in combination with an appropriate automated CFD pipeline to evaluate the aerodynamics of each design. The design-space exploration framework uses appropriate perturbations to the airfoil shape and induction profile from a baseline shape in combination with the inverse-design using BEM. The resulting designs are evaluated using an automated CFD pipeline using the in-house CFD solver framework "Mercury". We perform verification and validation to establish the capability of the Mercury framework to predict the aerodynamic performance of wind turbines. The CFD simulation of the perturbed blade shapes are optimized to restart from the converged baseline simulation to reduce the computational time. Finally, we demonstrate the design-space exploration technique for the design of the outboard section and the full rotor using perturbations to the shape and operating conditions of the NREL 5-MW turbine.

aerodynamic design methods↗
DOE OSTI2021

Surrogate Model of Flexible Research Platform EnergyPlus Models to Enable Sensitivity Analysis

This letter report describes the surrogate models developed from the EnergyPlus model of Oak Ridge National Laboratory’s Flexible Research Platform. Two data-driven black-box models were developed, and the outputs of the surrogate models were compared with the EnergyPlus model. The two models developed are a multilayer perceptron deep learning model, and a long short-term memory (LSTM) neural network model. The three factors for selecting the black-box models are scalability, computation time, and accuracy. A total of 107 input variables were the dominant variables in determining the outputs of building energy consumptions and thermal comfort. A total of 54 output variables were identified as the prediction targets, including the system- and zone-level outputs. The large set of the simulation cases were generated by integrating sensor errors into an emulator based on EnergyPlus and Python EMS, which includes advanced control sequences from ASHRAE Guideline 36-2018: High-Performance Sequences of Operation. The surrogate models were developed based on a set of large-scale simulation runs (i.e., 4,000 runs) on a cloud platform. The comparison analysis shows that the two black-box models had good accuracy for predicting new outputs for sensitivity analysis using the root mean square error metric. As a next step, the developed surrogate models will be used to perform sensitivity analysis for different sensor impacts (e.g., sensor types, sensor locations).

42 ENGINEERING↗
DOE OSTI2022

Transcription Factors Controlling the Rhizobium–Legume Symbiosis: Integrating Infection, Organogenesis and the Abiotic Environment

Abstract Legume roots engage in a symbiotic relationship with rhizobia, leading to the development of nitrogen-fixing nodules. Nodule development is a sophisticated process and is under the tight regulation of the plant. The symbiosis initiates with a signal exchange between the two partners, followed by the development of a new organ colonized by rhizobia. Over two decades of study have shed light on the transcriptional regulation of rhizobium–legume symbiosis. A large number of transcription factors (TFs) have been implicated in one or more stages of this symbiosis. Legumes must monitor nodule development amidst a dynamic physical environment. Some environmental factors are conducive to nodulation, whereas others are stressful. The modulation of rhizobium–legume symbiosis by the abiotic environment adds another layer of complexity and is also transcriptionally regulated. Several symbiotic TFs act as integrators between symbiosis and the response to the abiotic environment. In this review, we trace the role of various TFs involved in rhizobium–legume symbiosis along its developmental route and highlight the ones that also act as communicators between this symbiosis and the response to the abiotic environment. Finally, we discuss contemporary approaches to study TF-target interactions in plants and probe their potential utility in the field of rhizobium–legume symbiosis.

Cell Biology↗
DOE OSTI2023

Non-asymptotic analysis of ensemble Kalman updates: effective dimension and localization

Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in applications where generating each particle is costly. This paper develops a non-asymptotic analysis of ensemble Kalman updates, which rigorously explains why a small ensemble size suffices if the prior covariance has moderate effective dimension due to fast spectrum decay or approximate sparsity. Here, we present our theory in a unified framework, comparing everal implementations of ensemble Kalman updates that use perturbed observations, square root filtering and localization. As part of our analysis, we develop new dimension-free covariance estimation bounds for approximately sparse matrices that may be of independent interest.

Mathematics↗