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At least 19 records

Spatiotemporal Variations of Evapotranspiration in Amazonia Using the Wavelet Phase Difference Analysis

The relationships and seasonal-to-annual variations among evapotranspiration (ET), precipitation (P), terrestrial water storage anomalies (TWSA), radiation (downward shortwave radiation, DSR), and phenology (leaf area index, LAI) are complex across the Amazon basin. Here, to analyze how ET is controlled by these influencing factors, we used wavelet phase difference (WPD) to investigate the effects of P, TWSA, DSR, and LAI on ET at different spatiotemporal scales. The Amazon-scale averaged ET has strong correlations with these factors at the annual and multi-year periodicities. The patterns of WPDs have south-north and west-east divides due to the significant variation in climatic conditions. The results demonstrate that ET is mainly affected by water and energy availability while vegetation regulates both processes. The deep soil moisture/groundwater can provide strong subsidies to ET during the meteorological dry season in the water-limited area of Amazon. The WPD can well reflect the responses of ET to the variations of P, TWSA, DSR, and LAI, and the process of vegetation sustaining ET in the dry years in the water-limited area of the Amazon.

54 ENVIRONMENTAL SCIENCES↗

Detection of the significant impact of source clustering on higher order statistics with DES Year 3 weak gravitational lensing data

We measure the impact of source galaxy clustering on higher order summary statistics of weak gravitational lensing data. By comparing simulated data with galaxies that either trace or do not trace the underlying density field, we show that this effect can exceed measurement uncertainties for common higher order statistics for certain analysis choices. We evaluate the impact on different weak lensing observables, finding that third moments and wavelet phase harmonics are more affected than peak count statistics. Using Dark Energy Survey (DES) Year 3 (Y3) data, we construct null tests for the source-clustering-free case, finding a p-value of p = 4 × 10 −3 (2.6σ) using third-order map moments and p = 3 × 10 −11 (6.5σ) using wavelet phase harmonics. The impact of source clustering on cosmological inference can be either included in the model or minimized through ad hoc procedures (e.g. scale cuts). We verify that the procedures adopted in existing DES Y3 cosmological analyses were sufficient to render this effect negligible. Failing to account for source clustering can significantly impact cosmological inference from higher order gravitational lensing statistics, e.g. higher order N-point functions, wavelet-moment observables, and deep learning or field-level summary statistics of weak lensing maps.

79 ASTRONOMY AND ASTROPHYSICS↗

Spectroscopic Study of Solar Transition Region Oscillations in the Quiet-Sun Observed By IRIS Using Si IV Spectral Line

In the present paper, we use Si IV 1393.755 Å spectral line observed by the Interface Region Imaging Spectrograph (IRIS) in the quiet-Sun to determine physical nature of the solar transition region (TR) oscillations. We analyze the properties of these oscillations using wavelet tools (e.g., power, cross-power, coherence, and phase difference) along with the stringent noise model (i.e., power-law + constant). We estimate the period of the intensity and Doppler velocity oscillations at each chosen location in the quiet-Sun (QS) and quantify the distribution of the statistically significant power and associated periods in one bright and two dark regions. In the bright TR region, the mean periods in intensity and velocity are 7 min, and 8 min respectively. In the dark region, the mean periods in intensity and velocity are 7 min, and 5.4 min respectively. We also estimate the phase difference between the intensity and Doppler velocity oscillations at each location. The statistical distribution of phase difference is estimated, which peaks at -119°± 13°, 33°± 10°, 102°± 10° in the bright region, while at -153°± 13°, 6°± 20°, 151°± 10° in the dark region. The statistical distribution reveals that the oscillations are caused by propagating slow magnetoacoustic waves encountered with the TR. Some of these locations may also be associated with the standing slow waves. Even, in the given time domain, several locations exhibit presence of both propagating and standing oscillations at different frequencies.

Sun: oscillations↗

Spectroscopic Study of Solar Transition Region Oscillations in the Quiet-Sun Observed By IRIS Using the Si IV Spectral Line

In this paper, we use the Si IV 1393.755 Å spectral line observed by the Interface Region Imaging Spectrograph (IRIS) in the quiet-Sun (QS) to determine the physical nature of the solar transition region (TR) oscillations. We analyse the properties of these oscillations using wavelet tools (e.g. power, cross-power, coherence, and phase difference) along with the stringent noise model (i.e. power law + constant). We estimate the period of the intensity and Doppler velocity oscillations at each chosen location in the QS and quantify the distribution of the statistically significant power and associated periods in one bright region and two dark regions. In the bright TR region, the mean periods in intensity and velocity are 7 min and 8 min, respectively. In the dark regions, the mean periods in intensity and velocity are 7 min and 5.4 min, respectively. We also estimate the phase difference between the intensity and Doppler velocity oscillations at each location. The statistical distribution of the phase difference is estimated, which peaks at −119° ± 13°, 33° ± 10°, 102° ± 10° in the bright region and at −153° ± 13°, 6° ± 20°, 151° ± 10° in the dark regions. The statistical distribution reveals that the oscillations are caused by propagating slow magneto-acoustic waves encountered with the TR. Some of these locations may also be associated with standing slow waves. Moreover, in the given time domain, several locations exhibit the presence of both propagating and standing oscillations at different frequencies.

MHD – Sun: oscillations↗

Exploring Causal Relationships and Adjustment Timescales of Aerosol-Cloud Interactions in Geostationary Satellite Observations and CAM6 Using Wavelet Phase Coherence Analysis

We present for the first time within the cloud physics context, the application of wavelet phase coherence analysis to disentangle counteracting physical processes associated with the lead-lag phase difference between cloud-proxy liquid water path (LWP) and aerosol-proxy cloud droplet number concentration ( N d ) in an Eulerian framework using satellite-based observations and climate model outputs. This approach allows us to identify the causality and dominant adjustment timescales governing the correlation between LWP and N d . Satellite observations indicate a more prevalent positive correlation between daytime LWP and N d regardless of whether LWP leads or lags N d . The positive cloud water response, associated with precipitation processes, typically occurs within 1 hr, while the negative response resulting from entrainment drying, usually takes 2–4 hr. CAM6 displays excessively rapid negative responses along with overly strong negative cloud water response and insufficient positive response, leading to a more negative correlation between LWP and N d compared to observations.

54 ENVIRONMENTAL SCIENCES↗

Detection of Extreme Phenomena in the Stable Boundary Layer over the Amazonian Forest

We apply different methods for detection of extreme phenomena (EP) in air-turbulent time series measured in the nocturnal boundary layer above the Amazon forest. The methods used were: (a) a Morlet complex wavelet transform, which is often used in analysis of non-linear application processes. Through the use of the wavelet, it is possible to observe a phase singularity that involves a strong interaction between an extensive range of scales; (b) recurrence plot tests, which were used to identify a sudden change between different stable atmospheric states. (c) statistical analysis of early-warning signals, which verify simultaneous increases in the autocorrelation function and in the variance in the state variable; and (d) analysis of wind speed versus turbulent kinetic energy to identify different turbulent regimes in the stable boundary layer. We found it is adequate to use a threshold to classify the cases of strong turbulence regime, as a result of the occurrence of EP in the tropical atmosphere. All methods used corroborate and indicate synergy between events that culminate in what we classify as EP of the stable boundary layer above the tropical forest.

54 ENVIRONMENTAL SCIENCES↗

Dark Energy Survey Year 3 results: Simulation-based cosmological inference with wavelet harmonics, scattering transforms, and moments of weak lensing mass maps. II. cosmological results

Here, we present a simulation-based cosmological analysis using a combination of Gaussian and non-Gaussian statistics of the weak lensing mass (convergence) maps from the first three years of the Dark Energy Survey. We implement the following: (1) second and third moments; (2) wavelet phase harmonics; (3) the scattering transform. Our analysis is fully based on simulations, spans a space of seven 𝑤 Cold Dark Matter (𝑤⁢ CDM) cosmological parameters, and forward models the most relevant sources of systematics inherent in the data: masks, noise variations, clustering of the sources, intrinsic alignments, and shear and redshift calibration. We implement a neural network compression of the summary statistics, and we estimate the parameter posteriors using a simulation-based inference approach. Including and combining different non-Gaussian statistics is a powerful tool that strongly improves constraints over Gaussian statistics (in our case, the second moments); in particular, the figure of merit (𝑆 8 , Ω m ) is improved by 70% (Λ ⁢CDM) and 90% (𝑤 ⁢CDM). When all the summary statistics are combined, we achieve a 2% constraint on the amplitude of fluctuations parameter 𝑆 8 ≡ 𝜎 8 ⁢(Ω m /0.3) 0.5 , obtaining 𝑆 8 = 0.794 ±0.017 (Λ⁢ CDM) and 𝑆 8 = 0.817 ±0.021 (𝑤 ⁢CDM), and a ∼10% constraint on Ω m , obtaining Ω m =0.259 ±0.025 (Λ ⁢CDM) and Ω m = 0.273 ±0.029 (𝑤⁢ CDM). In the context of the 𝑤⁢ CDM scenario, these statistics also strengthen the constraints on the parameter 𝑤, obtaining 𝑤 <−0.72. The constraints from different statistics are shown to be internally consistent (with a 𝑝-value>0.1 for all combinations of statistics examined). We compare our results to other weak lensing results from the first three years of the Dark Energy Survey data, finding good consistency; we also compare with results from external datasets, such as planck constraints from the cosmic microwave background, finding statistical agreement, with discrepancies no greater than <2.2⁢𝜎.

79 ASTRONOMY AND ASTROPHYSICS↗

Wavelets, period-doubling, and time-frequency localization with application to organization of convection over the tropical western Pacific

In this paper, preliminary results in using orthogonal and continuous wavelet transform (WT) to identify period doubling and time-frequency localization in both synthetic and real data are presented. First, the Haar WT is applied to synthetic time series derived from a simple nonlinear dynamical system- a first-order quadratic difference equation. Second, the complex Morlet WT is used to study the time-frequency localization of tropical convection based on a high-resolution Japanese Geostationary Meteorological Satellite infrared (IR) radiance dataset. The Haar WT of the synthetic time series indicates the presence and distinct separation of multiple frequencies in a period-doubling sequence. The period-doubling process generates a multiplicity of intermediate frequencies, which are manifested in the nonuniformity in time with respect to the phase of oscillations in the lower frequencies. Wavelet transform also enables the detection of extremely weak signals in high-order subharmonics resulting from the period-doubling bifurcations. These signals are either undetected or considered statistically insignificant by traditional Fourier analysis. The Morlet WT of the IR radiance dataset indicates the presence of multiple timescales, which are localized in both frequency and time. There are two regimes in the variation of IR radiance, corresponding to the wet and dry periods. Multiple timescales, ranging from semidiurnal, diurnal, synoptic, to intraseasonal with embedding structures, are active in the wet regime. In particular, synoptic variability is more prominent during the wet phase of an intensive intraseasonal cycle. These are not only consistent with, but also show more details than, previous findings by using other techniques. The phase-locking relationships among the oscillations with different time-scales suggest that both synoptic and intraseasonal variations may be mixed oscillations due to the interaction of self-excited oscillations in the tropical atmosphere and external forcings such as annual and diurnal solar radiation variations. Both examples show that WT is a powerful tool for analysis of phenomena involving multiscale interactions that exhibit localization in both frequency and time. A discussion on the caveats in the use of WT in geophysical data analysis is also presented.

Weng, Hengyi↗

Fine structure of the isovector giant dipole resonance in Nd 142 – 150 and Sm 152

Inelastic proton scattering at energies of a few hundred MeV and very-forward scattering angles including 0° has been established as a tool for the study of electric-dipole strength distributions in nuclei. The present work reports a systematic investigation of the chain of stable even-mass Nd isotopes representing a transition from spherical to quadrupole-deformed nuclei. Extraction of the equivalent photo-absorption cross sections and analysis of their fine structure in the energy region of the isovector giant dipole resonance (IVGDR). Method: Proton inelastic scattering reactions of 200 MeV protons were measured at the iThemba Laboratory for Accelerator Based Sciences in Cape Town, South Africa. The scattering products were momentum-analyzed by the K600 magnetic spectrometer positioned at θ Lab = 0°. Using dispersion-matching techniques, energy resolutions of ΔE ≈ 40–50 keV (full width at half maximum) were obtained. After subtraction of background and contributions from other multipoles, the spectra were converted to photoabsorption cross sections using the equivalent virtual-photon method. Wavelet-analysis techniques are used to extract characteristic energy scales of the fine structure of the IVGDR from the experimental data. Fine structure of the IVGDR is observed even for the most deformed nuclei studied. Comparisons between the extracted experimental energy scales and those energy scales obtained from the quasiparticle-phonon model (QPM) and Skyrme separable random phase approximation (SSRPA) predictions provide insight into the role of different giant-resonance damping mechanisms. It can be seen that the scales in the spherical and most likely also in the deformed nuclei mainly result from the fragmentation of the one-particle-one-hole (1p1h) strength into several dominant transitions serving as doorway states. In cases where calculations beyond the 1p1h level are available, some impact of the spreading due to coupling of the two-particle-two-hole (2p2h) states to the 1p1h doorway states is observed. New virtual-photon absorption data for the chain of stable Nd isotopes and 152 Sm are presented, with a focus on the phenomenon of nonstatistical cross-section fluctuations, referred to as fine structure, in the energy region of the IVGDR. The wavelet-analysis techniques used allowed for the features of the fine structure to be quantified in the form of characteristic scales. Finally, comparisons between experimental results and model predictions indicate that Landau damping seems to be the main source of the fine structure in both the spherical and deformed nuclei, but calculations including 2p2h degrees of freedom would be beneficial to confirm this for the deformed cases.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Dark Energy Survey Year 3 results: Simulation-based cosmological inference with wavelet harmonics, scattering transforms, and moments of weak lensing mass maps. Validation on simulations

Beyond-two-point statistics contain additional information on cosmological as well as astrophysical and observational (systematics) parameters. In this methodology paper we provide an end-to-end simulationbased analysis of a set of Gaussian and non-Gaussian weak lensing statistics using detailed mock catalogs of the Dark Energy Survey (DES). Here, we implement: 1) second and third moments; 2) wavelet phase harmonics (WPH); 3) the scattering transform (ST). Our analysis is fully based on simulations, it spans a space of seven $νw$CDM cosmological parameters, and it forward models the most relevant sources of systematics of the data (masks, noise variations, clustering of the sources, intrinsic alignments, and shear and redshift calibration). We implement a neural network compression of the summary statistics, and we estimate the parameter posteriors using a likelihood-free-inference approach. We validate the pipeline extensively, and we find that WPH exhibits the strongest performance when combined with second moments, followed by ST, and then by third moments. The combination of all the different statistics further enhances constraints with respect to second moments, up to 25 percent, 15 percent, and 90 percent for S 8 , Ω m , and the figure-of-merit FoM S8;Ωm , respectively. We further find that non-Gaussian statistics improve constraints on w and on the amplitude of intrinsic alignment with respect to second moments constraints. The methodological advances presented here are suitable for application to Stage IV surveys from Euclid, Rubin-LSST, and Roman with additional validation on mock catalogs for each survey. In a companion paper we present an application to DES Year 3 data.

79 ASTRONOMY AND ASTROPHYSICS↗

Detection and Interpretation of Long-lived X-Ray Quasi-Periodic Pulsations in the X-Class Solar Flare on 2013 May 14

Quasi-periodic pulsations (QPP) seen in the time derivative of the GOES soft X-ray light curves are analyzed for the X3.2 event on 2013 May 14. The pulsations are apparent for a total of at least two hours from the impulsive phase to well into the decay phase, with a total of 163 distinct pulses evident to the naked eye. A wavelet analysis shows that the characteristic timescale of these pulsations increases systematically from approx. 25 s at 01:10 UT, the time of the GOES peak, to approx. 100 s at 02:00 UT. A second ridge in the wavelet power spectrum, most likely associated with flaring emission from a different active region, shows an increase from approx. 40 s at 01:40 UT to approx. 100 s at 03:10 UT. We assume that the QPP that produced the first ridge result from vertical kink-mode oscillations of the newly formed loops following magnetic reconnection in the coronal current sheet. This allows us to estimate the magnetic field strength as a function of altitude given the density, loop length, and QPP timescale as functions of time determined from the GOES light curves and Ramaty High Energy Solar Spectroscopic Imager (RHESSI) images. The calculated magnetic field strength of the newly formed loops ranges from approx. 500 G at an altitude of 24Mm to a low value of approx. 10 G at 60 Mm, in general agreement with the expected values at these altitudes. Fast sausage-mode oscillations are also discussed and cannot be ruled out as an alternate mechanism for producing the QPP.

Dennis, Brian R.↗

Wavelet Analysis of Turbulent Spots and Other Coherent Structures in Unsteady Transition

This is a secondary analysis of a portion of the Halstead data. The hot-film traces from an embedded stage of a low pressure turbine have been extensively analyzed by Halstead et al. In this project, wavelet analysis is used to develop the quantitative characterization of individual coherent structures in terms of size, amplitude, phase, convection speed, etc., as well as phase-averaged time scales. The purposes of the study are (1) to extract information about turbulent time scales for comparison with unsteady model results (e.g. k/epsilon). Phase-averaged maps of dominant time scales will be presented; and (2) to evaluate any differences between wake-induced and natural spots that might affect model performance. Preliminary results, subject to verification with data at higher frequency resolution, indicate that spot properties are independent of their phase relative to the wake footprints: therefore requirements for the physical content of models are kept relatively simple. Incidentally, we also observed that spot substructures can be traced over several stations; further study will examine their possible impact.

Lewalle, Jacques↗

Comparison of Mesospheric Winds From a High-Altitude Meteorological Analysis System and Meteor Radar Observations During the Boreal Winters of 2009-2010 and 2012-2013

We present a study of horizontal winds in the mesosphere and lower thermosphere (MLT) during the boreal winters of 2009-2010 and 2012-2013 produced with a new high-altitude numerical weather prediction (NWP) system. This system is based on a modified version of the Navy Global Environmental Model (NAVGEM) with an extended vertical domain up to approximately 116 km altitude coupled with a hybrid four-dimensional variational (4DVAR) data assimilation system that assimilates both standard operational meteorological observations in the troposphere and satellite-based observations of temperature, ozone and water vapor in the stratosphere and mesosphere. NAVGEM-based MLT analyzed winds are validated using independent meteor radar wind observations from nine different sites ranging from 69 deg N-67 deg S latitude. Time-averaged NAVGEM zonal and meridional wind profiles between 75 and 95 km altitude show good qualitative and quantitative agreement with corresponding meteor radar wind profiles. Wavelet analysis finds that the 3-hourly NAVGEM and 1-hourly radar winds both exhibit semi-diurnal, diurnal, and quasi-diurnal variations whose vertical profiles of amplitude and phase are also in good agreement. Wavelet analysis also reveals common time-frequency behavior in both NAVGEM and radar winds throughout the Northern extra tropics around the times of major stratospheric sudden warmings (SSWs) in January 2010 and January 2013, with a reduction in semi-diurnal amplitudes beginning around the time of a mesospheric wind reversal at 60 deg N that precedes the SSW, followed by an amplification of semi-diurnal amplitudes that peaks 10-14 days following the onset of the mesospheric wind reversal. The initial results presented in this study demonstrate that the wind analyses produced by the high altitude NAVGEM system accurately capture key features in the observed MLT winds during these two boreal winter periods.

McCormack, J.↗

Photoacoustic 3-D imaging of polycrystalline microstructure improved with transverse acoustic waves

Non-invasive fast imaging of grain microstructure of polycrystalline ceria with sub-micrometric spatial resolution is performed via time-domain Brillouin scattering. The propagation of a nanoacoustic pulse is monitored down to 8 µm deep in a 30 × 30 µm2 area. Grains boundaries are reconstructed in three-dimensions via a twostep processing method, relying on the wavelet synchro-squeezed transform and the alpha shape algorithm. Imaging contrast is improved by taking advantage of stronger sensitivity to anisotropy of transverse acoustic waves, compared with longitudinal waves. Utilization of transverse waves in the image processing reveals additional boundaries that are not discerned using longitudinal waves, confirmed by an electron backscattering diffraction pattern. A buried inclined interface between differently oriented grains is identified by monitoring changes in amplitude (phase) of the portion of the signal associated with transverse (longitudinal) waves. Estimates of the inclination angle of this interface prove the sensitivity of our laser ultrasonic method to image inclined boundaries.

36 MATERIALS SCIENCE↗

Time-resolved biphase signatures of quadratic nonlinearity observed in coupled Alfvén eigenmodes on the DIII-D tokamak

We report the detection of nonstationary quadratic coupling between toroidicity-induced Alfvén eigenmodes (TAEs) on sub-millisecond time scales. Identification of phase coherency between multiple TAEs and nonlinearly generated modes is facilitated by wavelet-based bicoherence analysis of time-series from inductive coils, taken from a DIII-D discharge heated by neutral beam injection (NBI). Characterization of nonlinear three-wave interaction is inferred by stationary local bispectrum phase (biphase) and confirmed via bandpass filtering. Biphase dynamics associated with prominent bispectral features are well-resolved in time and consistent with transient quadratic coupling. Onset and duration of nonlinearity are correlated with enhanced amplitude of participating TAEs; coincident changes in amplitude are observed for modes at difference frequency |f TAE,1 - f TAE,2 |.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On the Investigation of Phase Fault Classification in Power Grid Signals: A Case Study for Support Vector Machines, Decision Tree and Random Forest

In monitoring the power grid, an ability to differentiate between fault types is essential to ensuring electrical safety. Accordingly, this study introduces a fault detection and classification method by considering different machine learning (ML) and feature extraction (FE) methods combinations. Specifically, the proposed method is established in two classification layers; the first layer determines the fault, and the second layer distinguishes the type of fault. Based on the proposed system model, this study seeks to determine the influential data attributes in a power grid signal using FE methods, including fast Fourier transform, power spectral density (PSD), auto-correlation, and wavelet transform (WT). A cross-comparison of the effectiveness of the Support Vector Machine (SVM), Decision Tree (DT), and Random Forest (RF) is also performed to accomplish the classification layers of the proposed method. The designed algorithm is analyzed under the various combinations of FE and ML methods, and outcomes are presented by considering the trade-off between computational complexity and prediction accuracy. The results reveal that the RF-based ML algorithm shows the most accurate classification performance with PSD, and the most time-saving of the models is the DT WT. Also, SVM emerges superior on a subsequent test of the simulated models on real-world signals.

Galbraith, Kelli↗

Data Challenges for Structural Health Monitoring of Electrical Machines [Slides]

Induction motors (ID) consist of a stator and a rotor. Induction motor slip decreases with decreasing load. Induction motor slip decreases with decreasing load. This talk will focus on removing closely coupled power grid frequencies in an effort to observe the true dynamic response signature of induction motors. Using the time difference between the zeros, we found the frequency as it changes over time for each of the 3 phases. The frequencies of the 3 phases were averaged to reduce the effects of sidebands on the instantaneous frequency. The frequencies of the 3 phases were averaged to reduce the effects of sidebands on the instantaneous frequency. The Kalman filter rapidly synchronizes with the expected output. The sidebands were recreated using spectral subtraction. The frequency domain shows the reduction in magnitude of the power grid frequency the Kalman output was subtracted out. Kalman filtering also reveals important data about the sidebands in healthy motors. The Continuous Wavelet Transform is an alternative to a Bandpass IIR filter used in the analysis of the acceleration data. Analysis of the acceleration data reveals 4 sidebands around the slip frequency.

42 ENGINEERING↗

Variation in Coronal Activity from Solar Cycle 24 Minimum to Maximum Using Three-Dimensional Reconstructions of the Coronal Electron Density from STEREO/COR1

Three-dimensional electron density distributions in the solar corona are reconstructed for 100 Carrington rotations (CR 2054 - 2153) during 2007/03 - 2014/08 using the spherically symmetric method from polarized white-light observations with the inner coronagraph (COR1) onboard the twin Solar Terrestrial Relations Observatory (STEREO). These three-dimensional electron density distributions are validated by comparison with similar density models derived using other methods such as tomography and a magnetohydrodynamics (MHD) model as well as using data from the Solar and Heliospheric Observatory (SOHO)/Large Angle and Spectrometric Coronagraph (LASCO)-C2. Uncertainties in the estimated total mass of the global corona are analyzed based on differences between the density distributions for COR1-A and -B. Long-term variations of coronal activity in terms of the global and hemispheric average electron densities (equivalent to the total coronal mass) reveal a hemispheric asymmetry during the rising phase of Solar Cycle 24, with the northern hemisphere leading the southern hemisphere by a phase shift of 7 - 9 months. Using 14 CR (approx. equal to 13-month) running averages, the amplitudes of the variation in average electron density between Cycle 24 maximum and Cycle 23/24 minimum (called the modulation factors) are found to be in the range of 1.6 - 4.3. These modulation factors are latitudinally dependent, being largest in polar regions and smallest in the equatorial region. These modulation factors also show a hemispheric asymmetry: they are somewhat larger in the southern hemisphere. The wavelet analysis shows that the short-term quasi-periodic oscillations during the rising and maximum phases of Cycle 24 have a dominant period of 7 - 8 months. In addition, it is found that the radial distribution of the mean electron density for streamers at Cycle 24 maximum is only slightly larger (by approx. equal to 30%) than at cycle minimum.

Wang, Tongjiang↗