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At least 397 records · Page 22

Revisiting the Causes of the US Midwest Great Flood of 1993

The floods that occurred in the Midwest during the summer of 1993 remain one of the greatest flooding events in US history. While a considerable amount of work has already been done addressing its causes there still remain uncertainties as to the relative roles of forcing from the tropics and the extra-tropics as well as the extended nature of the excessive rainfall that lasted throughout much of the late spring and summer of that year. Here we use a novel “replay” technique in which the GEOS AGCM is constrained to remain close to the MERRA-2 reanalysis over specified regions of the globe to isolate the causes of the excessive rain. We show the main rainfall event in the upper Midwest in July (extending into August) was the result of the development of a large amplitude Rossby wave (and associated pronounced moisture influx from the Gulf of Mexico) apparently forced by anomalous transient eddies in the western North Pacific. Rainfall that fell in the Midwest during the two months prior to that, while not as intense, acted to precondition the soil, with forcing from the tropics contributing to the May precipitation, while the excessive Midwest rain that fell during June was part of a record hemispheric-wide precipitation signal that appears to be linked to an unusually cold north polar stratosphere. The nature of the stratospheric impact and the possible delayed influence of the Pinatubo eruption is currently being assessed.

Midwest↗

High-Temperature MEMS Based Venus Seismometer

Seismology is the method of choice for studying a planet’s interior and assessing current tectonic activity. With a single strategically placed seismometer, or preferably a network of seismometers, a variety of key aspects of a planet can be evaluated. The level and nature of seismicity observed provides a gauge of current geologic, especially tectonic, activity. Where tectonic activity is and is not occurring illuminates what regions and geologic features on the planet are currently active, thus, constraining global geodynamics. Larger distal earthquakes can be used to determine major compositional and structural boundaries within a planet’s interior, providing major constraints on planet formation and interior evolution. Seismometers have been deployed successfully on the Moon and Mars. Only small subsets of the scientific knowledge that can be gained from seismology can be obtained from alternative scientific approaches, such as global gravity solutions or repeat-pass interferometry. By virtue of its similar size to Earth, Venus is likely to be highly seismically active (Fig. 1). Even at Earth-like levels of seismology, returning meaningful data would require observation over a period that is at least 2–3 orders of magnitude longer than the 1–2 h lifetime of previous Soviet landers. Clever insulation could extend the lifetime of standard electronics in a modern lander to perhaps 24 h. While active cooling of electronics for a Venusian lander is plausible, this approach would require considerable technological advancement and will likely come at a high monetary and mass cost. The high density of the Venusian atmosphere at the surface should mean that there is good coupling of seismic energy into the atmosphere, such that seismology using infrasound from a balloon platform is currently being explored, and observations of the upper levels of the atmosphere from orbit has also been proposed [3]. Besides losing all shear wave information with these two methods, calibrating and interpreting seismic information that has been distorted by, and convolved with, atmospheric phenomena will be challenging without existing seismology data collected through surface seismometers (optimally, simultaneous surface seismological observations would be made).

silicon carbide↗

Soil Carbonyl Sulfide (OCS) Fluxes in Terrestrial Ecosystems: An Empirical Model

Measurements of carbonyl sulfide (OCS) enable independent estimates of regional stomatal conductance provided that non-stomatal OCS fluxes are well constrained. OCS is taken up through plant leaves, following the same pathway as CO 2 ; in contrast to CO 2 , OCS is irreversibly destroyed in plant leaves and plants do not typically exhibit OCS emissions. Ecosystem uptake of OCS can indicate changes in stomatal opening. Here we present an empirical model to assess the potential impact of soil OCS exchange, the non-Stomatal OCS exchange Empirical Model (SOCSEM, version 0). We created biome-specific response curves characterizing soil OCS exchange and restricted the model design to require only knowledge of soil moisture and surface temperature because remote sensing observations are available for these two features. Comparing the model to field-based chamber observations reveal deviations that can be attributed to missing complexity of the ground surface (having excluded litter and plants without regulated stomata), shortwave radiation, or the soil environment. For agricultural regions with known net emissions, we use remotely-sensed surface temperature data and demonstrate that data resolution can affect anticipated fluxes. We further investigate the influence of regions with unknown soil OCS responses, for example, Arctic tundra. We compare our model to a process-based and respiration-based soil OCS exchange model that has been implemented in a land surface model. Further field study of tropical and arctic ecosystems in conjunction with studies of non-stomatal surfaces in addition to soil (e.g., bryophytes) will increase confidence in applying OCS as a regional tracer for stomatal conductance.

54 ENVIRONMENTAL SCIENCES↗

The plasma and magnetic field properties of coronal loops observed at high spatial resolution

Two data sets are analyzed in order to improve understanding of the plasma and magnetic field properties of active region coronal loops. Each set consists of coaligned, high spatial resolution soft X-ray, microwave, and magnetogram images that are used to compare observations of coronal loops and their feet in the photosphere and to constrain possible microwave emission mechanisms. The loops are found to have plasma parameters typical of quiescent active region loops. Each loop has a compact microwave source with peak brightness temperature T(b) = 1-2.5 x 10 to the 6th K cospatial with or near the loop apex. No complete loops are imaged in microwaves. The loop emission observed at 4.9 GHz is best described by fourth harmonic gyroresonance emission from a dipole loop model, but with less field variation along the loop than in the models of Holman and Kundu (1985).

Webb, D. F.↗

Biomass burning emission analysis based on MODIS aerosol optical depth and AeroCom multi-model simulations: implications for model constraints and emission inventories

We assessed the biomass burning (BB) smoke aerosol optical depth (AOD) simulations of 11 global models that participated in the AeroCom phase III BB emission experiment. By comparing multi-model simulations and satellite observations in the vicinity of fires over 13 regions globally, we (1) assess model-simulated BB AOD performance as an indication of smoke source–strength, (2) identify regions where the common emission dataset used by the models might underestimate or overestimate smoke sources, and (3) assess model diversity and identify underlying causes as much as possible. Using satellite-derived AOD snapshots to constrain source strength works best where BB smoke from active sources dominates background non-BB aerosol, such as in boreal forest regions and over South America and southern hemispheric Africa. The comparison is inconclusive where the total AOD is low, as in many agricultural burning areas, and where the background is high, such as parts of India and China. Many inter-model BB AOD differences can be traced to differences in values for the mass ratio of organic aerosol to organic carbon, the BB aerosol mass extinction efficiency, and the aerosol loss rate from each model. The results point to a need for increased numbers of available BB cases for study in some regions and especially to a need for more extensive regional-to-global-scale measurements of aerosol loss rates and of detailed particle microphysical and optical properties; this would both better constrain models and help distinguish BB from other aerosol types in satellite retrievals. More generally, there is the need for additional efforts at constraining aerosol source strength and other model attributes with multi-platform observations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The cosmological moduli problem and naturalness

Nowadays, the cosmological moduli problem (CMP) comes in three parts: 1. potential violation of Big-Bang nucleosynthesis (BBN) constraints from late decaying moduli fields, 2. the moduli-induced gravitino problem wherein gravitinos are overproduced and their decays violate BBN or dark matter overproduction bounds and 3. the moduli-induced lightest SUSY particle (LSP) overproduction problem. Also, the CMP may be regarded as either a problem or else a solution to scenarios with dark matter over- or under-production. We examine the cosmological moduli problem and its connection to electroweak naturalness. We calculate the various two-body decay widths of a light modulus field into MSSM particles and gravitinos within general supersymmetric models. We include both phase space and mixing effects. We examine cases without and with helicity suppression of modulus decays to gravitinos (cases 1 & 2) and/or gauginos (cases A & B). For case B1, we evaluate regions of gravitino mass m 3/2 vs. modulus mass mΦ parameter space constrained by BBN, by overproduction of gravitinos and by overproduction of neutralino dark matter, along with connections to naturalness. For this case, essentially all of parameter space is excluded unless mΦ ≳ 2.5 × 10 3 TeV with mΦ< 2m 3/2 For a potentially most propitious case B2 with Φ decay to Higgs and matter turned off, then modulus branching fractions to SUSY and to gravitinos become highly suppressed at large m Φ . But since the modulus number density increases faster than the branching fractions decrease, there is still gross overproduction of neutralino dark matter. We also show that in this scenario the thermally produced gravitino problem is fixed by huge entropy dilution, but non-thermal gravitino production from moduli decay remains a huge problem unless it is kinematically suppressed with m Φ < 2m 3/2 . In a pedagogical appendix, we present detailed calculations of modulus field two-body decay widths.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for long-lived particles decaying into muon pairs in proton-proton collisions at $\sqrt{s}$ = 13 TeV collected with a dedicated high-rate data stream

A search for long-lived particles decaying into muon pairs is performed using proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the CMS experiment at the LHC in 2017 and 2018, corresponding to an integrated luminosity of 101 fb -1 . The data sets used in this search were collected with a dedicated dimuon trigger stream with low transverse momentum thresholds, recorded at high rate by retaining a reduced amount of information, in order to explore otherwise inaccessible phase space at low dimuon mass and nonzero displacement from the primary interaction vertex. No significant excess of events beyond the standard model expectation is found. Upper limits on branching fractions at 95% confidence level are set on a wide range of mass and lifetime hypotheses in beyond the standard model frameworks with the Higgs boson decaying into a pair of long-lived dark photons, or with a long-lived scalar resonance arising from a decay of a b hadron. The limits are the most stringent to date for substantial regions of the parameter space. These results can be also used to constrain models of displaced dimuons that are not explicitly considered in this paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Light-flavor particle production in high-multiplicity pp collisions at $\sqrt{\textrm{s}}$ = 13 TeV as a function of transverse spherocity

Results on the transverse spherocity dependence of light-flavor particle production (π, K, p, ϕ, K *0 , K$^{0}_{S}$, Λ, Ξ) at midrapidity in high-multiplicity pp collisions at $\sqrt{\textrm{s}}$ = 13 TeV were obtained with the ALICE apparatus. The transverse spherocity estimator ($S$$^{p_T=1}_{O}$) categorizes events by their azimuthal topology. Utilizing narrow selections on $S$$^{p_T=1}_{O}$, it is possible to contrast particle production in collisions dominated by many soft initial interactions with that observed in collisions dominated by one or more hard scatterings. Results are reported for two multiplicity estimators covering different pseudorapidity regions. The $S$$^{p_T=1}_{O}$ estimator is found to effectively constrain the hardness of the events when the midrapidity (|η| < 0.8) estimator is used.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Comprehensive Northern Hemisphere Particle Microphysics Data Set From the Precipitation Imaging Package

Microphysical observations of precipitating particles are critical data sources for numerical weather prediction models and remote sensing retrieval algorithms. However, obtaining coherent data sets of particle microphysics is challenging as they are often unindexed, distributed across disparate institutions, and have not undergone a uniform quality control process. This work introduces a unified, comprehensive Northern Hemisphere particle microphysical data set from the National Aeronautics and Space Administration precipitation imaging package (PIP), accessible in a standardized data format and stored in a centralized, public repository. Data is collected from 10 measurement sites spanning 34° latitude (37°N–71°N) over 10 years (2014–2023), which comprise a set of 1,070,000 precipitating minutes. The provided data set includes measurements of a suite of microphysical attributes for both rain and snow, including distributions of particle size, vertical velocity, and effective density, along with higher-order products including an approximation of volume-weighted equivalent particle densities, liquid equivalent snowfall, and rainfall rate estimates. The data underwent a rigorous standardization and quality assurance process to filter out erroneous observations to produce a self-describing, scalable, and achievable data set. Case study analyses demonstrate the capabilities of the data set in identifying physical processes like precipitation phase-changes at high temporal resolution. Bulk precipitation characteristics from a multi-site intercomparison also highlight distinct microphysical properties unique to each location. This curated PIP data set is a robust database of high-quality particle microphysical observations for constraining future precipitation retrieval algorithms, and offers new insights toward better understanding regional and seasonal differences in bulk precipitation characteristics.

54 ENVIRONMENTAL SCIENCES↗

Ensemble‐Based Spatially Distributed CLM5 Hydrological Parameter Estimation for the Continental United States

Abstract One of the major challenges in large‐domain hydrological modeling efforts lies in the estimation of spatially distributed hydrological parameters while simultaneously accounting for their associated uncertainties. Addressing this challenge is particularly difficult in ungauged locations. With growing societal demands for large‐scale streamflow projections to inform water resource management and long‐term planning, evaluating and constraining hydrological parameter uncertainty is increasingly vital. This study introduces a hybrid regionalization approach to enhance hydrological predictions of the Community Land Model version 5 (CLM5) across the Continental United States (CONUS), with a total of 50,629 1/8° grid cells. This hybrid method combines the strengths of two existing techniques: parameter regionalization and streamflow signature regionalization. It identifies ensemble behavioral parameters for each 1/8° grid cell across the CONUS domain, tailored to three distinct streamflow signatures focused on low flows, high flows, and annual water balance. Evaluating this hybrid method for 464 CAMELS (Catchment Attributes and Meteorology for Large‐sample Studies) basins demonstrates a significant improvement in CLM5 hydrological predictions, even in challenging arid regions. In CONUS applications, the derived spatially distributed parameter sets capture both spatial continuity and variation of parameters, highlighting their heterogeneous nature within specific regions. Overall, this hybrid regionalization approach offers a promising solution to the complex task of improving hydrological modeling over large domains for important hydrological applications.

CLM5↗

Holography of the photon ring

Space-based next-generation interferometers propose to measure the Lyapunov exponents of the nearly bound geodesics that comprise the photon ring surrounding the black hole M87*. We argue that these classical Lyapunov exponents equal the quantum Ruelle resonances describing the late-time approach to thermal equilibrium of the quantum microstate holographically dual to any Kerr black hole such as M87*. Moreover, we identify 'near-ring regions' in the phase space of fields propagating on Kerr that exhibit critical behavior, including emergent conformal symmetries. These are analogues for sub-extremal Kerr of the much-studied 'near-horizon regions' of (near-)extremal black holes. Here, the emergent conformal symmetries greatly constrain the observational predictions for the fine photon ring substructure around M87* and for quasinormal gravitational-wave ringdowns, as well as any proposal for a quantum holographic dual to the Kerr black hole. More generally, we hope that our identification of several universal features of Kerr spectroscopy provides a useful starting point for a bottom-up approach to holography for astrophysical black holes.

79 ASTRONOMY AND ASTROPHYSICS↗

Evolutionary constraints and climate variability jointly shape starch–sugar balance in woody plants

Nonstructural carbohydrates (NSC) buffer plants against carbon imbalances, yet their partitioning between storage and soluble pools remains elusive at global scales. Here, we compiled a dataset of starch to soluble sugar ratio (St : Su) for 308 woody species across 220 sites world-wide and introduce a dimensionless index that integrates storage and demand while minimizing methodological artifacts. St : Su was strongly associated with growth, identifying it as a key axis of carbon allocation. Foliage consistently exhibited lower St : Su than lignified organs, reflecting a division between transient and conservative pools. Conifers accumulated more starch in foliage but less in stems relative to angiosperms, while leaf habits and mycorrhizal associations further modulated organ-specific strategies. Contrary to expectation, foliar and root St : Su varied little among biomes, but stems exhibited higher ratios in tropical rainforests than in boreal or arid regions, reflecting differences in species composition and adaptive storage under disturbance. Phylogeny constrained stem storage, whereas climatic variability, rather than mean conditions, dominated allocation in leaves and roots. These findings establish St : Su as a robust functional trait linking allocation strategies, growth, and resilience, which can be used to improve vegetation model prediction of forest productivity and mortality under climate variability.

Li, Weibin [Lanzhou Univ. (China)] (ORCID:00000001↗

Global Methane Budget 2000–2020

Abstract. Understanding and quantifying the global methane (CH4) budget is important for assessing realistic pathways to mitigate climate change. CH4 is the second most important human-influenced greenhouse gas in terms of climate forcing after carbon dioxide (CO2), and both emissions and atmospheric concentrations of CH4 have continued to increase since 2007 after a temporary pause. The relative importance of CH4 emissions compared to those of CO2 for temperature change is related to its shorter atmospheric lifetime, stronger radiative effect, and acceleration in atmospheric growth rate over the past decade, the causes of which are still debated. Two major challenges in quantifying the factors responsible for the observed atmospheric growth rate arise from diverse, geographically overlapping CH4 sources and from the uncertain magnitude and temporal change in the destruction of CH4 by short-lived and highly variable hydroxyl radicals (OH). To address these challenges, we have established a consortium of multidisciplinary scientists under the umbrella of the Global Carbon Project to improve, synthesise, and update the global CH4 budget regularly and to stimulate new research on the methane cycle. Following Saunois et al. (2016, 2020), we present here the third version of the living review paper dedicated to the decadal CH4 budget, integrating results of top-down CH4 emission estimates (based on in situ and Greenhouse Gases Observing SATellite (GOSAT) atmospheric observations and an ensemble of atmospheric inverse-model results) and bottom-up estimates (based on process-based models for estimating land surface emissions and atmospheric chemistry, inventories of anthropogenic emissions, and data-driven extrapolations). We present a budget for the most recent 2010–2019 calendar decade (the latest period for which full data sets are available), for the previous decade of 2000–2009 and for the year 2020. The revision of the bottom-up budget in this 2025 edition benefits from important progress in estimating inland freshwater emissions, with better counting of emissions from lakes and ponds, reservoirs, and streams and rivers. This budget also reduces double counting across freshwater and wetland emissions and, for the first time, includes an estimate of the potential double counting that may exist (average of 23 Tg CH4 yr−1). Bottom-up approaches show that the combined wetland and inland freshwater emissions average 248 [159–369] Tg CH4 yr−1 for the 2010–2019 decade. Natural fluxes are perturbed by human activities through climate, eutrophication, and land use. In this budget, we also estimate, for the first time, this anthropogenic component contributing to wetland and inland freshwater emissions. Newly available gridded products also allowed us to derive an almost complete latitudinal and regional budget based on bottom-up approaches. For the 2010–2019 decade, global CH4 emissions are estimated by atmospheric inversions (top-down) to be 575 Tg CH4 yr−1 (range 553–586, corresponding to the minimum and maximum estimates of the model ensemble). Of this amount, 369 Tg CH4 yr−1 or ∼ 65 % is attributed to direct anthropogenic sources in the fossil, agriculture, and waste and anthropogenic biomass burning (range 350–391 Tg CH4 yr−1 or 63 %–68 %). For the 2000–2009 period, the atmospheric inversions give a slightly lower total emission than for 2010–2019, by 32 Tg CH4 yr−1 (range 9–40). The 2020 emission rate is the highest of the period and reaches 608 Tg CH4 yr−1 (range 581–627), which is 12 % higher than the average emissions in the 2000s. Since 2012, global direct anthropogenic CH4 emission trends have been tracking scenarios that assume no or minimal climate mitigation policies proposed by the Intergovernmental Panel on Climate Change (shared socio-economic pathways SSP5 and SSP3). Bottom-up methods suggest 16 % (94 Tg CH4 yr−1) larger global emissions (669 Tg CH4 yr−1, range 512–849) than top-down inversion methods for the 2010–2019 period. The discrepancy between the bottom-up and the top-down budgets has been greatly reduced compared to the previous differences (167 and 156 Tg CH4 yr−1 in Saunois et al. (2016, 2020) respectively), and for the first time uncertainties in bottom-up and top-down budgets overlap. Although differences have been reduced between inversions and bottom-up, the most important source of uncertainty in the global CH4 budget is still attributable to natural emissions, especially those from wetlands and inland freshwaters. The tropospheric loss of methane, as the main contributor to methane lifetime, has been estimated at 563 [510–663] Tg CH4 yr−1 based on chemistry–climate models. These values are slightly larger than for 2000–2009 due to the impact of the rise in atmospheric methane and remaining large uncertainty (∼ 25 %). The total sink of CH4 is estimated at 633 [507–796] Tg CH4 yr−1 by the bottom-up approaches and at 554 [550–567] Tg CH4 yr−1 by top-down approaches. However, most of the top-down models use the same OH distribution, which introduces less uncertainty to the global budget than is likely justified. For 2010–2019, agriculture and waste contributed an estimated 228 [213–242] Tg CH4 yr−1 in the top-down budget and 211 [195–231] Tg CH4 yr−1 in the bottom-up budget. Fossil fuel emissions contributed 115 [100–124] Tg CH4 yr−1 in the top-down budget and 120 [117–125] Tg CH4 yr−1 in the bottom-up budget. Biomass and biofuel burning contributed 27 [26–27] Tg CH4 yr−1 in the top-down budget and 28 [21–39] Tg CH4 yr−1 in the bottom-up budget. We identify five major priorities for improving the CH4 budget: (i) producing a global, high-resolution map of water-saturated soils and inundated areas emitting CH4 based on a robust classification of different types of emitting ecosystems; (ii) further development of process-based models for inland-water emissions; (iii) intensification of CH4 observations at local (e.g. FLUXNET-CH4 measurements, urban-scale monitoring, satellite imagery with pointing capabilities) to regional scales (surface networks and global remote sensing measurements from satellites) to constrain both bottom-up models and atmospheric inversions; (iv) improvements of transport models and the representation of photochemical sinks in top-down inversions; and (v) integration of 3D variational inversion systems using isotopic and/or co-emitted species such as ethane as well as information in the bottom-up inventories on anthropogenic super-emitters detected by remote sensing (mainly oil and gas sector but also coal, agriculture, and landfills) to improve source partitioning. The data presented here can be downloaded from https://doi.org/10.18160/GKQ9-2RHT (Martinez et al., 2024).

54 ENVIRONMENTAL SCIENCES↗

The inversion of stratospheric aerosol and ozone vertical profiles from spacecraft solar extinction measurements

The inversions of multi-channel solar extinction measurements have been analyzed for the 0.35-1.0 micron wavelength region to retrieve stratospheric aerosol and ozone vertical profiles using both the constrained linear inversion scheme and the iterative scheme. The inversions of the multi-wavelength solar extinction data obtained from spacecraft have been analyzed based on the inversion of computer simulated data using various atmospheric models with differing amounts of aerosol and ozone in the stratosphere. The sensitivities of the inversion schemes to different experimental errors are discussed in terms of accuracy and resolution of the retrieved profiles.

Chu, W. P.↗

Pulsations in solar hard X-ray bursts

The hard X-ray emission from 28 large solar events has been analyzed in order to search for pulsations in intensity profiles. Periodicity occurred in 26 events, usually soon after the onset, with periods in the range 10-100 s. Pulsations occurring at common frequencies in different energy bands are observed to be closely in phase. Periodic behavior in hard X-ray emission is related to that at microwave and decametric wavelengths. The observations are briefly discussed in terms of two models: that of McClean et al. (1971), applied to X-ray emission, and that of Brown and Hoyng (1975). As periodicity is normal in extended hard X-ray bursts and occurs through a broad energy band, it is probably directly related to a principal flare-acceleration mechanism. These observations constrain possible mechanisms of flare acceleration and physical properties of the acceleration region.

Lipa, B.↗

The lunar interior - A summary report

The complete seismic data set collected by the Apollo network contains about 40 events which provide significant structural information on the lunar interior. The seismograms from these events yield a set of direct wave arrival times that constitutes the most reliable information on the seismic structure of the moon. Secondary data include possible reflected arrivals from crustal and mantle interfaces, an apparent shear wave shadow zone for surface events beginning at about 90 deg distance, and the shear wave amplitude decay with distance. Analysis of these data give well-constrained and stable average velocity values for the upper and lower mantle regions independent of most assumptions. The upper-lower mantle transition can begin no shallower than 400 km depth and may represent a compositional change although the effects of increased temperature cannot be ruled out.

Goins, N. R.↗

Computational vision

The range of fundamental computational principles underlying human vision that equally apply to artificial and natural systems is surveyed. There emerges from research a view of the structuring of vision systems as a sequence of levels of representation, with the initial levels being primarily iconic (edges, regions, gradients) and the highest symbolic (surfaces, objects, scenes). Intermediate levels are constrained by information made available by preceding levels and information required by subsequent levels. In particular, it appears that physical and three-dimensional surface characteristics provide a critical transition from iconic to symbolic representations. A plausible vision system design incorporating these principles is outlined, and its key computational processes are elaborated.

Barrow, H. G.↗

A dynamic measure of controllability and observability for the placement of actuators and sensors on large space structures

The degree of controllability of a large space structure is found by a four step procedure: (1) finding the minimum control energy for driving the system from a given initial state to the origin in the prescribed time; (2) finding the region of initial state which can be driven to the origin with constrained control energy and time using optimal control strategy; (3) scaling the axes so that a unit displacement in every direction is equally important to control; and (4) finding the linear measurement of the weighted "volume" of the ellipsoid in the equicontrol space. For observability, the error covariance must be reduced toward zero using measurements optimally, and the criterion must be standardized by the magnitude of tolerable errors. The results obtained using these methods are applied to the vibration modes of a free-free beam.

Vandervelde, W. E.↗