Non-linear regression analysis and analysis of variance of periods defined by irregular observations
Nonlinear regression and variance analyses of periods defined by irregular observations
VARIANCE↗
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Sporadic E Morphology from GPS-CHAMP Radio Occultation
The scintillations of phase and amplitude in terms of signal-to-noise ratio (SNR) of the GPS radio occultation signal are caused by thin ionization layers. These thin irregular electron density layers in the E region ionosphere are often called sporadic E (Es). For a monthly retrieval of Es morphology we use the variances of the phase and SNR fluctuations of worldwide ~6000 GPS/CHAMP occultations in the E region. The Es climatology is studied globally with the SNR and phase variances in terms of monthly zonal means, seasonal maps, and diurnal and long-term variations. The zonal mean variances reveal strong, extended Es activities at summertime midlatitudes but weak, confined activities in wintertime high latitudes, peaking at ~105 km. Global maps at 105-km altitude show clear dependence of Es activities on the geomagnetic dip angle, where the summertime midlatitude Es occurs mostly at dip angles of 30 deg. - 60 deg. and the wintertime high-latitude enhancement occurs mostly at dip angles greater than 80 deg. The midlatitude Es variances exhibit a strong semidiurnal variation with peak hours near 0800 1000 and 2000 local solar time, respectively. The peak hours are delayed slightly with decreasing height, suggesting influences from the semidiurnal tide. To provide more insights on the observed SNR and phase variances, we model radio wave propagation for the CHAMP observing geometry under several perturbed cases in the E region ionosphere. The model simulations indicate that the SNR variance has the maximum response to Es perturbations at vertical wavelengths of 1.2 km, whereas the phase response maximizes at ~2 km (for the 1-s variance analysis). The characteristic scale depends little on the truncation time used in the SNR variance analysis, but it increases with the truncation time for the phase variances. Initial studies show that reasonable global Es morphology can be produced on a monthly and seasonal basis with the CHAMP one-antenna occultations. Better results from other existing and upcoming GPS occultation missions are anticipated in future studies, and they will significantly improve our understanding of this important phenomenon.
signal to noise ration (SNR)↗
A comparison of coronal and interplanetary current sheet inclinations
The HAO white light K-coronameter observations show that the inclination of the heliospheric current sheet at the base of the corona can be both large (nearly vertical with respect to the solar equator) or small during Cararington rotations 1660 - 1666 and even on a single solar rotation. Voyager 1 and 2 magnetic field observations of crossing of the heliospheric current sheet at distances from the Sun of 1.4 and 2.8 AU. Two cases are considered, one in which the corresponding coronameter data indicate a nearly vertical (north-south) current sheet and another in which a nearly horizontal, near equatorial current sheet is indicated. For the crossings of the vertical current sheet, a variance analysis based on hour averages of the magnetic field data gave a minimum variance direction consistent with a steep inclination. The horizontal current sheet was observed by Voyager as a region of mixed polarity and low speeds lasting several days, consistent with multiple crossings of a horizontal but irregular and fluctuating current sheet at 1.4 AU. However, variance analysis of individual current sheet crossings in this interval using 1.92 see averages did not give minimum variance directions consistent with a horizontal current sheet.
Behannon, K. W.↗
A comparison of coronal and interplanetary current sheet inclinations
The HAO white light K-coronameter observations show that the inclination of the heliospheric current sheet at the base of the corona can be both large (nearly vertical with respect to the solar equator) or small during Cararington rotations 1660 - 1666 and even on a single solar rotation. Voyager 1 and 2 magnetic field observations of crossing of the heliospheric current sheet at distances from the sun of 1.4 and 2.8 AU. Two cases are considered, one in which the corresponding coronameter data indicate a nearly vertical (north-south) current sheet and another in which a nearly horizontal, near equatorial current sheet is indicated. For the crossings of the vertical current sheet, a variance analysis based on hour averages of the magnetic field data gave a minimum variance direction consistent with a steep inclination. The horizontal current sheet was observed by Voyager as a region of mixed polarity and low speeds lasting several days, consistent with multiple crossings of a horizontal but irregular and fluctuating current sheet at 1.4 AU. However, variance analysis of individual current sheet crossings in this interval using 1.92 see averages did not give minimum variance directions consistent with a horizontal current sheet. Previously announced in STAR as N83-31566
Behannon, K. W.↗
Stratospheric Assimilation of Chemical Tracer Observations Using a Kalman Filter: Chi-Square Validated Results and Analysis of Variance and Correlation Dynamics - Pt. 2
A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I (Menard et al. 1998) The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board of the Upper Atmosphere Research Satellite are described in this paper. A robust (chi)(sup 2) criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only three days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. We further found that the model error due to numerical discretization as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave-breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, we have conducted an analysis of the variance and correlation dynamics to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.
Menard, Richard↗
A test of source-surface model predictions of heliospheric current sheet inclination
The orientation of the heliospheric current sheet predicted from a source surface model is compared with the orientation determined from minimum-variance analysis of International Sun-Earth Explorer (ISEE) 3 magnetic field data at 1 AU near solar maximum. Of the 37 cases analyzed, 28 have minimum variance normals that lie orthogonal to the predicted Parker spiral direction. For these cases, the correlation coefficient between the predicted and measured inclinations is 0.6. However, for the subset of 14 cases for which transient signatures (either interplanetary shocks or bidirectional electrons) are absent, the agreement in inclinations improves dramatically, with a correlation coefficient of 0.96. These results validate not only the use of the source surface model as a predictor but also the previously questioned usefulness of minimum variance analysis across complex sector boundaries. In addition, the results imply that interplanetary dynamics have little effect on current sheet inclination at 1 AU. The dependence of the correlation on transient occurrence suggests that the leading edge of a coronal mass ejection (CME), where transient signatures are detected, disrupts the heliospheric current sheet but that the sheet re-forms between the trailing legs of the CME. In this way the global structure of the heliosphere, reflected both in the source surface maps and in the interplanetary sector structure, can be maintained even when the CME occurrence rate is high.
Burton, M. E.↗
Structure analysis of simulated molecular clouds with the Δ-variance
Here, we employ the Δ-variance analysis and study the turbulent gas dynamics of simulated molecular clouds (MCs). Our models account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of the gas. We investigate simulations using three different initial mean number densities of n 0 = 30, 100 and 300 cm -3 that span the range of values typical for MCs in the solar neighbourhood. Furthermore, we model the CO line emission in a post-processing step using a radiative transfer code. We evaluate Δ-variance spectra for centroid velocity (CV) maps as well as for integrated intensity and column density maps for various chemical components: the total, H 2 and 12 CO number density and the integrated intensity of both the 12 CO and 13 CO (J = 1 → 0) lines. The spectral slopes of the Δ-variance computed on the CV maps for the total and H 2 number density are significantly steeper compared to the different CO tracers. We find slopes for the linewidth–size relation ranging from 0.4 to 0.7 for the total and H 2 density models, while the slopes for the various CO tracers range from 0.2 to 0.4 and underestimate the values for the total and H 2 density by a factor of 1.5–3.0. We demonstrate that optical depth effects can significantly alter the Δ-variance spectra. Furthermore, we report a critical density threshold of 100 cm -3 at which the Δ-variance slopes of the various CO tracers change sign. We thus conclude that carbon monoxide traces the total cloud structure well only if the average cloud density lies above this limit.
79 ASTRONOMY AND ASTROPHYSICS↗
Relation Between Polar Plumes and Fine Structure in the Solar Wind from Ulysses High-Latitude Observations
Ulysses observations showed that pressure balance structures (PBSs) are a common feature in the high-latitude and high-speed solar winds near the solar minimum. On the other hand, coronal plumes are common in polar coronal holes. PBSs are believed to be remnants of coronal plumes and to be related to network activity such as magnetic reconnection in the photosphere from previous studies. This suggests that information on the magnetic structure of PBSs would help to confirm the relation between PBSs and polar plumes We have investigated the magnetic structures of the PBSs by applying a minimum variance analysis to Ulysses/Magnetometer data and by examining the pitch-angle distribution of energetic electrons measured with Ulysses/SWOOPS. We have found that PBSs have relatively more tangential discontinuities rather than rotational from the minimum variance analysis. Further, most PBSs also show bi-directional electron flux or isotropic pitch-angle distribution or the distribution expected in association with current-sheet structures from the analysis of high-energy electron data. In this, we find further evidence that PBSs are generated due by network activity at the base of polar plumes and their magnetic structures are like current sheets or plasmoids.
Yamauchi, Yohei↗
Analysis of Variance Including the Diurnal Cycle
Geophysical data at high time frequency (3-hourly, hourly, etc.) can be resolved into components that include a 24-hour diurnal cycle.
54 ENVIRONMENTAL SCIENCES↗
Application of non-linear regression analysis and of analysis of variance to the determina- tion of periods of events defined by irregularly spaced observations
Accurate periods of periodic events observed at irregular intervals of time
TIME FACTOR↗
Program documentation: As-built design specification for Generalized Linear Model Analysis Of Variance program (GLMAOV)
There are no author-identified significant results in this report.
Gor, J. S.↗
Microstructure of the IMF turbulences at 2.5 AU
A detailed analysis of small period (15-900 sec) magnetohydrodynamic (MHD) turbulences of the interplanetary magnetic field (IMF) has been made using Pioneer-11 high time resolution data (0.75 sec) inside a Corotating Interaction Region (CIR) at a heliocentric distance of 2.5 AU in 1973. The methods used are the hodogram analysis, the minimum variance matrix analysis and the cohenrence analysis. The minimum variance analysis gives evidence of linear polarized wave modes. Coherence analysis has shown that the field fluctuations are dominated by the magnetosonic fast modes with periods 15 sec to 15 min. However, it is also shown that some small amplitude Alfven waves are present in the trailing edge of this region with characteristic periods (15-200 sec). The observed wave modes are locally generated and possibly attributed to the scattering of Alfven waves energy into random magnetosonic waves.
Mavromichalaki, H.↗
A general reconstruction of the recent expansion history of the universe
Distance measurements are currently the most powerful tool to study the expansion history of the universe without specifying its matter content nor any theory of gravitation. Assuming only an isotropic, homogeneous and flat universe, in this work we introduce a model-independent method to reconstruct directly the deceleration function via a piecewise function. Including a penalty factor, we are able to vary continuously the complexity of the deceleration function from a linear case to an arbitrary (n+1)-knots spline interpolation. We carry out a Monte Carlo (MC) analysis to determine the best penalty factor, evaluating the bias-variance trade-off, given the uncertainties of the SDSS-II and SNLS supernova combined sample (JLA), compilations of baryon acoustic oscillation (BAO) and H(z) data. The bias-variance analysis is done for three fiducial models with different features in the deceleration curve. We perform the MC analysis generating mock catalogs and computing their best-fit. For each fiducial model, we test different reconstructions using, in each case, more than 10{sup 4} catalogs in a total of about 5× 10{sup 5}. This investigation proved to be essential in determining the best reconstruction to study these data. We show that, evaluating a single fiducial model, the conclusions about the bias-variance ratio are misleading. We determine the reconstruction method in which the bias represents at most 10% of the total uncertainty. In all statistical analyses, we fit the coefficients of the deceleration function along with four nuisance parameters of the supernova astrophysical model. For the full sample, we also fit H{sub 0} and the sound horizon r{sub s}(z{sub d}) at the drag redshift. The bias-variance trade-off analysis shows that, apart from the deceleration function, all other estimators are unbiased. Finally, we apply the Ensemble Sampler Markov Chain Monte Carlo (ESMCMC) method to explore the posterior of the deceleration function up to redshift 1.3 (using only JLA) and 2.3 (JLA+BAO+H(z)). We obtain that the standard cosmological model agrees within 3σ level with the reconstructed results in the whole studied redshift intervals. Since our method is calibrated to minimize the bias, the error bars of the reconstructed functions are a good approximation for the total uncertainty.
79 ASTRONOMY AND ASTROPHYSICS↗
SMAR Sessions
This slide presentation is a series of educational presentations that are on the statistical function of analysis of variance (ANOVA). Analysis of Variance (ANOVA) examines variability between groups, relative to within groups, to determine whether there's evidence that the groups are not from the same population. One other presentation reviews hypothesis testing.
Ploutz-Snyder, Robert↗
SMALL-SCALE PRESSURE-BALANCED STRUCTURES DRIVEN BY MIRROR-MODE WAVES IN THE SOLAR WIND
Recently, small-scale pressure-balanced structures (PBSs) have been studied with regard to their dependence on the direction of the local mean magnetic field B{sub 0} . The present work continues these studies by investigating the compressive wave mode forming small PBSs, here for B{sub 0} quasi-perpendicular to the x-axis of Geocentric Solar Ecliptic coordinates (GSE-x). All the data used were measured by WIND in the quiet solar wind. From the distribution of PBSs on the plane determined by the temporal scale and angle θ{sub xB} between the GSE-x and B{sub 0} , we notice that at θ{sub xB} = 115° the PBSs appear at temporal scales ranging from 700 s to 60 s. In the corresponding temporal segment, the correlations between the plasma thermal pressure P{sub th} and the magnetic pressure P{sub B}, as well as that between the proton density N{sub p} and the magnetic field strength B, are investigated. In addition, we use the proton velocity distribution functions to calculate the proton temperatures T and T{sub ∥}. Minimum Variance Analysis is applied to find the magnetic field minimum variance vector B{sub N} . We also study the time variation of the cross-helicity σ{sub c} and the compressibility C{sub p} and compare these with values from numerical predictions for the mirror mode. In this way, we finally identify a short segment that has T > T{sub ∥}, proton β ≅ 1, both pairs of P{sub th}-P{sub B} and N{sub p}-B showing anti-correlation, and σ{sub c} ≈ 0 with C{sub p} > 0. Although the examination of σ{sub c} and C{sub p} is not conclusive, it provides helpful additional information for the wave mode identification. Additionally, B{sub N} is found to be highly oblique to B{sub 0} . Thus, this work suggests that a candidate mechanism for forming small-scale PBSs in the quiet solar wind is due to mirror-mode waves.
79 ASTRONOMY AND ASTROPHYSICS↗
Application of Variance-Based Sensitivity Analysis to a Large System Dynamics Model
Variance-based sensitivity methods can provide insights into large computational models. We present a novel application of sensitivity analysis to the Biomass Scenario Model (BSM) a large and complex system dynamics model of the developing biofuels industry in the United States. We apply a two-stage sensitivity approach consisting of an initial sensitivity screening, followed by a variance decomposition approach. Identifying key system levers and quantifying their strength is not straightforward in complex system dynamics models that have numerous feedbacks and nonlinear results. Variance-based sensitivity analysis (VBSA) offers a systematic, global approach to assessing system dynamics models because it addresses nonlinear responses and interactive effects. Especially when a large model's size makes manual exploration of the input space difficult and time-consuming, the approach can help to provide a comprehensive understanding of interactions that drive model behaviors.
97 MATHEMATICS AND COMPUTING↗
Coronal electron stream and Langmuir wave detection inside a propagation channel at 4.3 AU
Observations of an energetic interplanetary electron event associated with the production of Langmuir waves, both of which are identified at 4.3 AU by instruments on the Ulysses spacecraft, are presented in this paper. This electron event propagates inside a well-defined magnetic structure. The existence of this structure is firmly established by joint particle and plasma observations made by Ulysses instruments. Its local estimated radial width is of the order of 2.3 x 10(exp 7) km (0.15 AU). The electron beam is associated with a type III burst observed from Earth at high frequencies and at low frequencies from Ulysses in association with Langmuir waves detected inside the structure. The consistency of local (Ulysses) and remote (Earth) observations in terms of temporal and geometrical considerations establishes that the structure is anchored in the solar corona near the solar active region responisble for the observed type III emission and gives an accurate determination of the injection time for the observed electron beam. Propagation analysis of the electron event is presented. In order to quantify the magnetic field properties, a variance analysis has been performed and is presented in this paper. The analysis establishes that inside the structure the amount of magnetic energy involved in the fluctuations is less than 4% of the total magnetic energy; the minimal variance direction is well defined and in coincidence with the direction of the mean magnetic field. This configuration may produce conditions favorable for scatter free streaming of energetic electrons and/or Langmuir wave production. The results presented show that the magnetic field might play a role in stabilizing the coronal-origin plasma structures and then preserving them to large, approximately 4 AU, distances in the heliosphere.
Buttighoffer, A.↗
Relation Between Pressure Balance Structures and Polar Plumes from Ulysses High Latitude Observations
Ulysses observations have shown that pressure balance structures (PBSs) are a common feature in high-latitude, fast solar wind near solar minimum. Previous studies of Ulysses/SWOOPS plasma data suggest these PBSs may be remnants of coronal polar plumes. Here we find support for this suggestion in an analysis of PBS magnetic structure. We used Ulysses magnetometer data and applied a minimum variance analysis to discontinuities. We found that PBSs preferentially contain tangential discontinuities, as opposed to rotational discontinuities and to non-PBS regions in the solar wind. This suggests that PBSs contain structures like current sheets or plasmoids that may be associated with network activity at the base of plumes.
Yamauchi, Y.↗