Total Variance, an Estimator of Long-Term Frequency Stability
Total variance is a statistical tool developed for improved estimates of frequency stability at averaging times up to half the test duration.
frequency stability total variance↗
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Total Variance: A Progress Report on a New Frequency Stability Characterization
We give results of recent work on a newly developed frequency stability characterization, called Total variance, whose main advantages are improved confidence at and near the longest averaging time of half the data duration, and lower sensitivity to drift removal.
FM noise types frequency response empirical distri↗
Total Variance: A Progress Report on a New Frequency Stability Characterization
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Total variance random variable function of tau All↗
Viscoelastic deformation near active plate boundaries
Model deformations near the active plate boundaries of Western North America using space-based geodetic measurements as constraints are discussed. The first six months of this project were spent gaining familarity with space-based measurements, accessing the Crustal Dynamics Data Information Computer, and building time independent deformation models. The initial goal was to see how well the simplest elastic models can reproduce very long base interferometry (VLBI) baseline data. From the Crustal Dynamics Data Information Service, a total of 18 VLBI baselines are available which have been surveyed on four or more occasions. These data were fed into weighted and unweighted inversions to obtain baseline closure rates. Four of the better quality lines are illustrated. The deformation model assumes that the observed baseline rates result from a combination of rigid plate tectonic motions plus a component resulting from elastic strain build up due to a failure of the plate boundary to slip at the full plate tectonic rate. The elastic deformation resulting from the locked plate boundary is meant to portray interseismic strain accumulation. During and shortly after a large interplate earthquake, these strains are largely released, and points near the fault which were previously retarded suddenly catch up to the positions predicted by rigid plate models. Researchers judge the quality of fit by the sum squares of weighted residuals, termed total variance. The observed baseline closures have a total variance of 99 (cm/y)squared. When the RM2 velocities are assumed to model the data, the total variance increases to 154 (cm/y)squared.
Ward, S. N.↗
The proton temperature and the total hourly variance of the magnetic field components in different solar wind speed regions
A comparison has been made between the predictions of the theory for radial variations of both Alfvenic fluctuations and solar wind proton temperatures proposed by Tu (1987, 1988) and the statistical results of hourly averaged plasma and magnetic field data observed by Helios 1 and 2 from launch through 1980 for different solar wind speed regimes. The comparison shows that for speed ranges between 500-800 km/s, the radial variation of the proton temperature between 0.3 and 1 AU can be explained by heating from the cascade energy which is determined by the radial variation of the total variance of magnetic field vector.
Tu, Chuan-Yi↗
Solar Cycle Variations in Mesospheric Carbon Monoxide
As an extension of Lee et al. (2013), solar cycle variation of carbon monoxide (CO) is analyzed with MLS observation, which covers more than thirteen years (2004-2017) including maximum of solar cycle 24. Being produced primarily by the carbon dioxide (CO2) photolysis in the lower thermosphere, the variations of the mesospheric CO concentration are largely driven by the solar cycle modulated ultraviolet (UV) variation. This solar signal extends down to the lower altitudes by the dynamical descent in the winter polar vortex, showing a time lag that is consistent with the average descent velocity. To characterize a global distribution of the solar impact, MLS CO is correlated with the SORCE measured total solar irradiance (TSI) and UV. As high as 0.8 in most of the polar mesosphere, the linear correlation coefficients between CO and UV/TSI are more robust than those found in the previous work. The photochemical contribution explains most (68%) of the total variance of CO while the dynamical contribution accounts for 21% of the total variance at upper mesosphere. The photochemistry driven CO anomaly signal is extended in the tropics by vertical mixing. The solar cycle signal in CO is further examined with the Whole Atmosphere Community Climate Model (WACCM) 3.5 simulation by implementing two different modeled Spectral Solar Irradiances (SSIs): SRPM 2012 and NRLSSI. The model simulations underestimate the mean CO amount and solar cycle variations of CO, by a factor of 3, compared to those obtained from MLS observation. Different inputs of the solar spectrum have small impacts on CO variation.
MLS↗
The Principle of Energetic Consistency
A basic result in estimation theory is that the minimum variance estimate of the dynamical state, given the observations, is the conditional mean estimate. This result holds independently of the specifics of any dynamical or observation nonlinearity or stochasticity, requiring only that the probability density function of the state, conditioned on the observations, has two moments. For nonlinear dynamics that conserve a total energy, this general result implies the principle of energetic consistency: if the dynamical variables are taken to be the natural energy variables, then the sum of the total energy of the conditional mean and the trace of the conditional covariance matrix (the total variance) is constant between observations. Ensemble Kalman filtering methods are designed to approximate the evolution of the conditional mean and covariance matrix. For them the principle of energetic consistency holds independently of ensemble size, even with covariance localization. However, full Kalman filter experiments with advection dynamics have shown that a small amount of numerical dissipation can cause a large, state-dependent loss of total variance, to the detriment of filter performance. The principle of energetic consistency offers a simple way to test whether this spurious loss of variance limits ensemble filter performance in full-blown applications. The classical second-moment closure (third-moment discard) equations also satisfy the principle of energetic consistency, independently of the rank of the conditional covariance matrix. Low-rank approximation of these equations offers an energetically consistent, computationally viable alternative to ensemble filtering. Current formulations of long-window, weak-constraint, four-dimensional variational methods are designed to approximate the conditional mode rather than the conditional mean. Thus they neglect the nonlinear bias term in the second-moment closure equation for the conditional mean. The principle of energetic consistency implies that, to precisely the extent that growing modes are important in data assimilation, this term is also important.
Cohn, Stephen E.↗
Ocean-Land Teleconnections and Chaotic Atmospheric Variability in Climate Models, with Implications for Real-World Behavior
This study introduces a unique approach to estimating a fundamental but unmeasurable property of Nature: ρo 2 , the fraction of the variance of a given meteorological variable that is determined by boundary forcing (specifically, SSTs) as opposed to chaotic atmospheric dynamics. Here, we focus on continental monthly-averaged near-surface air temperature, or T2M. Rather than determining the fractions of SST-explained T2M variance found for a specific atmospheric general circulation model (AGCM) and then assuming that these fractions also represent Nature, we perform an analysis that entails: (i) evaluating a specific AGCM’s ability to capture observed variability with an infinite number of ensemble members, (ii) quantifying the degree to which different modeling systems agree on SST-land teleconnections, and (iii) combining these results into our novel estimates of ρo 2 . The derived ρo 2 fields suggest, with caveats, that AGCMs tend to overestimate the fraction of explained T2M variance (the signal-to-total variance ratio) in the Tropics.
Randal D Koster↗
Quantitative Comparison of the Variability in Observed and Simulated Shortwave Reflectance
The Climate Absolute Radiance and Refractivity Observatory (CLARREO) is a climate observation system that has been designed to monitor the Earth's climate with unprecedented absolute radiometric accuracy and SI traceability. Climate Observation System Simulation Experiments (OSSEs) have been generated to simulate CLARREO hyperspectral shortwave imager measurements to help define the measurement characteristics needed for CLARREO to achieve its objectives. To evaluate how well the OSSE-simulated reflectance spectra reproduce the Earth s climate variability at the beginning of the 21st century, we compared the variability of the OSSE reflectance spectra to that of the reflectance spectra measured by the Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY). Principal component analysis (PCA) is a multivariate decomposition technique used to represent and study the variability of hyperspectral radiation measurements. Using PCA, between 99.7%and 99.9%of the total variance the OSSE and SCIAMACHY data sets can be explained by subspaces defined by six principal components (PCs). To quantify how much information is shared between the simulated and observed data sets, we spectrally decomposed the intersection of the two data set subspaces. The results from four cases in 2004 showed that the two data sets share eight (January and October) and seven (April and July) dimensions, which correspond to about 99.9% of the total SCIAMACHY variance for each month. The spectral nature of these shared spaces, understood by examining the transformed eigenvectors calculated from the subspace intersections, exhibit similar physical characteristics to the original PCs calculated from each data set, such as water vapor absorption, vegetation reflectance, and cloud reflectance.
Roberts, Yolanda, L.↗
Analyses of mean and turbulent motion in the tropics with the use of unequally spaced data
Wind velocities from 25 km to 60 km over Ascension Island, Fort Sherman and Kwajalein for the period January 1970 to December 1971 are analyzed in order to achieve a better understanding of the mean flow, the eddy kinetic energy and the Eulerian time spectra of the eddy kinetic energy. Since the data are unequally spaced in time, techniques of one-dimensional covariance theory were utilized and an unequally spaced time series analysis was accomplished. The theoretical equations for two-dimensional analysis or wavenumber frequency analysis of unequally spaced data were developed. Analysis of the turbulent winds and the average seasonal variance and eddy kinetic energy of the turbulent winds indicated that maximum total variance and energy is associated with the east-west velocity component. This is particularly true for long period seasonal waves which dominate the total energy spectrum. Additionally, there is an energy shift for the east-west component into the longer period waves with altitude increasing from 30 km to 50 km.
Kao, S. K.↗
FM oscillator has improved deviation linearity
Device can be obtained by driving basic circuit through nonlinear FET input stage. Frequency of VCO is linearized with FET and total variance is varactor controlled. Experimental device exhibited linearity of better than plus or minus one percent for total frequency of plus or minus 10 millihertz.
Honnell, M. A.↗
Structuring Nutrient Yields throughout Mississippi/Atchafalaya River Basin Using Machine Learning Approaches
To minimize the eutrophication pressure along the Gulf of Mexico or reduce the size of the hypoxic zone in the Gulf of Mexico, it is important to understand the underlying temporal and spatial variations and correlations in excess nutrient loads, which are strongly associated with the formation of hypoxia. This study’s objective was to reveal and visualize structures in high-dimensional datasets of nutrient yield distributions throughout the Mississippi/Atchafalaya River Basin (MARB). For this purpose, the annual mean nutrient concentrations were collected from thirty-three US Geological Survey (USGS) water stations scattered in the upper and lower MARB from 1996 to 2020. Eight surface water quality indicators were selected to make comparisons among water stations along the MARB over the past two decades. Principal component analysis (PCA) was used to comprehensively evaluate the nutrient yields across thirty-three USGS monitoring stations and identify the major contributing nutrient loads. The results showed that all samples could be analyzed using two main components, which accounted for 81.6% of the total variance. The PCA results showed that yields of orthophosphate (OP), silica (SI), nitrate–nitrites (NO 3 -NO 2 ), and total suspended sediment (TSS) are major contributors to nutrient yields. It also showed that land-planted crops, density of population, domestic and industrial discharges, and precipitation are fundamental causes of excess nutrient loads in MARB. These factors are of great significance for the excess nutrient load management and pollution control of the Mississippi River. It was found that the average nutrient yields were stable within the sub-MARB area, but the large nitrogen yields in the upper MARB and the large phosphorus yields in the lower MARB were of great concern. t-distributed stochastic neighbor embedding (t-SNE) revealed interesting nonlinear and local structures in nutrient yield distributions. Clustering analysis (CA) showed the detailed development of similarities in the nutrient yield distribution. Moreover, PCA, t-SNE, and CA showed consistent clustering results. This study demonstrated that the integration of dimension reduction techniques, PCA, and t-SNE with CA techniques in machine learning are effective tools for the visualization of the structures of the correlations in high-dimensional datasets of nutrient yields and provide a comprehensive understanding of the correlations in the distributions of nutrient loads across the MARB.
54 ENVIRONMENTAL SCIENCES↗
Degree of interdependence among atmospheric optical thicknesses in spectral bands between 0.36-2.4 micron
The degree of dependence among the atmospheric optical thicknesses that are measured in nonselective absorption bands is studied. The observations were made previously in many spectral bands within the range 0.36-2.4 micron from near sea level in two continents where urban and industrial pollutions were weak. The sample covariance matrices and corresponding eigenvalues and eigenvectors are computed. The two highest eigenvalues account for 90% of the total variance in 10 spectral bands within the range 0.4-1.6 micron. The linear regression of the optical thickness on the total precipitable water vapor is computed to determine the attenuation coefficient that is associated with water vapor. This coefficient shows a rapid power-law decrease with wavelength in the visible spectrum and indicates that numerous water particles of radius 0.03-0.06 micron cause the attenuation.
Fraser, R. S.↗
A variance deconvolution estimator for efficient uncertainty quantification in Monte Carlo radiation transport applications
Monte Carlo simulations are at the heart of many high-fidelity simulations and analyses for radiation transport systems. As is the case with any complex computational model, it is important to propagate sources of input uncertainty and characterize how they affect model output. Unfortunately, uncertainty quantification (UQ) is made difficult by the stochastic variability that Monte Carlo transport solvers introduce. The standard method to avoid corrupting the UQ statistics with the transport solver noise is to increase the number of particle histories, resulting in very high computational costs. In this contribution, we propose and analyze a sampling estimator based on the law of total variance to compute UQ variance even in the presence of residual noise from Monte Carlo transport calculations. Here, we rigorously derive the statistical properties of the new variance estimator, compare its performance to that of the standard method, and demonstrate its use on neutral particle transport model problems involving both attenuation and scattering physics. We illustrate, both analytically and numerically, the estimator’s statistical performance as a function of available computational budget and the distribution of that budget between UQ samples and particle histories. We show analytically and corroborate numerically that the new estimator is unbiased, unlike the standard approach, and is more accurate and precise than the standard estimator for the same computational budget.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Data driven discovery and quantification of hyperspectral leaf reflectance phenotypes across a maize diversity panel
Abstract Estimates of plant traits derived from hyperspectral reflectance data have the potential to efficiently substitute for traits, which are time or labor intensive to manually score. Typical workflows for estimating plant traits from hyperspectral reflectance data employ supervised classification models that can require substantial ground truth datasets for training. We explore the potential of an unsupervised approach, autoencoders, to extract meaningful traits from plant hyperspectral reflectance data using measurements of the reflectance of 2151 individual wavelengths of light from the leaves of maize ( Zea mays ) plants harvested from 1658 field plots in a replicated field trial. A subset of autoencoder‐derived variables exhibited significant repeatability, indicating that a substantial proportion of the total variance in these variables was explained by difference between maize genotypes, while other autoencoder variables appear to capture variation resulting from changes in leaf reflectance between different batches of data collection. Several of the repeatable latent variables were significantly correlated with other traits scored from the same maize field experiment, including one autoencoder‐derived latent variable (LV8) that predicted plant chlorophyll content modestly better than a supervised model trained on the same data. In at least one case, genome‐wide association study hits for variation in autoencoder‐derived variables were proximal to genes with known or plausible links to leaf phenotypes expected to alter hyperspectral reflectance. In aggregate, these results suggest that an unsupervised, autoencoder‐based approach can identify meaningful and genetically controlled variation in high‐dimensional, high‐throughput phenotyping data and link identified variables back to known plant traits of interest.
Tross, Michael C.↗
Assessing the sensitivity of land-atmosphere coupling strength to boundary and surface layer parameters in the WRF model over Amazon
Modeling tools can be used to diagnose regional land-atmosphere (L-A) coupling strength in the absence of sufficient observations, but subject to uncertainties associated with parameters in model physical parameterizations. Different sensitivity analysis (SA) approaches may lead to different conclusions about the underlying sensitivities. In this study, we quantify simulation uncertainties related to parameter perturbations, and use different approaches to conduct parameter SA on the WRF model pertaining to L-A coupling strength for simulations over the Amazon region. A total of twenty parameters from the Yonsei University (YSU) planetary boundary layer (PBL) and the revised MM5 surface layer (SL) schemes were selected in this analysis. Three different SA methods, the Morris One-at-A-Time (MOAT) method, the Multivariate Adaptive Regression Splines (MARS) method, and the Sobol’ method, were employed to analyze seven WRF-simulated variables and five L-A coupling metrics. Results show that 1) parameter perturbations cause large simulation uncertainties which are comparable to those in the observations; 2) three different SA methods give consistent L-A coupling strength outcomes; 3) six out of the twenty parameters contribute 80%–95% of the total variance in the metrics analyzed, and first-order effects dominate over interaction effects; 4) the twelve variables/metrics of interest show similar sensitivity patterns to the selected parameters, which is consistent across all the methods used. Physical mechanisms for how the sensitive parameters act in determining the L-A coupling strength and associated variables also are illustrated. Our results will help quantifying L-A coupling strength and establishing a basis for parameter calibration over the Amazon region.
Wang, Chen↗
Exploring Afro-Asian water fluxes in CMIP5 and CMIP6 models: Present-day evaluation and future projections
Accurate representation and projection of water fluxes are vital, particularly in monsoon regions where seasonal variability and changes significantly impact water resources, agriculture, hydroelectric power generation, and the economy. This study uses both CMIP5 and CMIP6 models to investigate the present-day representation of key water flux components (including precipitation, evaporation, water vapor, and moisture advection) over the Afro-Asian region during the summer monsoon (JJAS). We also examine future changes under two emission scenarios and assess the underlying physical mechanisms driving these changes while identifying sources of projection uncertainty. Our results show that both models reasonably capture the present-day characteristics of water flux components, although with noticeable biases. Across most regions, we find that CMIP6 models demonstrate slight improvements over CMIP5 in the representation of these components. In a warmer future, a robust intensification of JJAS precipitation (exceeding 0.25 mm/day) is projected across the Afro-Asian region. This increase is largely driven by the vertical thermodynamic term associated with increasing temperature. We find that model uncertainty is the primary source of uncertainty in water flux projections, accounting for over 50 % of the total variance.
Climate change↗
Machine-learning from Pseudomonas putida KT2440 transcriptomes reveals its transcriptional regulatory network
Bacterial gene expression is orchestrated by numerous transcription factors (TFs). Elucidating how gene expression is regulated is fundamental to understanding bacterial physiology and engineering it for practical use. In this study, a machine-learning approach was applied to uncover the genome-scale transcriptional regulatory network (TRN) in Pseudomonas putida KT2440, an important organism for bioproduction. We performed independent component analysis of a compendium of 321 high-quality gene expression profiles, which were previously published or newly generated in this study. We identified 84 groups of independently modulated genes (iModulons) that explain 75.7% of the total variance in the compendium. With these iModulons, we (i) expand our understanding of the regulatory functions of 39 iModulon associated TFs (e.g., HexR, Zur) by systematic comparison with 1993 previously reported TF-gene interactions; (ii) outline transcriptional changes after the transition from the exponential growth to stationary phases; (iii) capture group of genes required for utilizing diverse carbon sources and increased stationary response with slower growth rates; (iv) unveil multiple evolutionary strategies of transcriptome reallocation to achieve fast growth rates; and (v) define an osmotic stimulon, which includes the Type VI secretion system, as coordination of multiple iModulon activity changes. Taken together, this study provides the first quantitative genome-scale TRN for P. putida KT2440 and a basis for a comprehensive understanding of its complex transcriptome changes in a variety of physiological states.
09 BIOMASS FUELS↗