Konstantin V. Parchevsky

Three-dimensional numerical simulations of the acoustic wave field in the upper convection zone of the sun

Results of numerical three-dimensional (3D) simulations of propagation of acoustic waves inside the Sun are presented. A linear 3D code which utilizes the realistic OPAL equation of state was developed. A modified convectively stable standard solar model with a smoothly joined chromosphere was used as a background model. A high-order dispersion relation-preserving numerical scheme was used. The top nonreflecting boundary condition established in the chromosphere absorbs waves with frequencies greater than the acoustic cutoff frequency which pass through the chromosphere, simulating a realistic situation. We simulate acousto-gravity wave fields on the Sun, generated by localized randomly distributed sources in a subphotospheric layer. Three applications for solar wave physics are presented: changes in oscillation properties due to the mechanism of wave damping, effects of nonuniform distribution of sources, and effects of nonuniform localized perturbations on wave properties. In particular, we studied two models of wave damping with leakage and with an explicit friction-type damping term in the photospheric layers and chromosphere. In both cases we were able to reproduce observed characteristics of the acoustic spectrum (line widths and amplitude distribution). We found that the suppression of acoustic sources, e.g., in sunspots, may significantly contribute to the observed power deficit. The lower sound speed in sunspot areas may cause an increase of the wave amplitude, but this effect is less important for the acoustic power distribution than the suppression of the acoustic sources.

Intradaily Variability of Water Quality in a Shallow Tidal Lagoon: Mechanisms and Implications

Although surface water quality and its underlying processes vary over time scales ranging from seconds to decades, they have historically been studied at the lower (weekly to interannual) frequencies. The aim of this study was to investigate intradaily variability of three water quality parameters in a small freshwater tidal lagoon (Mildred Island, California). High frequency time series of specific conductivity, water temperature, and chlorophylla at two locations within the habitat were analyzed in conjunction with supporting hydrodynamic, meteorological, biological, and spatial mapping data. All three constituents exhibited large amplitude intradaily (e.g., semidiurnal tidal and diurnal) oscillations, and periodicity varied across constituents, space, and time. Like other tidal embayments, this habitat is influenced by several processes with distinct periodicities including physical controls, such as tides, solar radiation, and wind, and biological controls, such as photosynthesis, growth, and grazing. A scaling approach was developed to estimate individual process contributions to the observed variability. Scaling results were generally consistent with observations and together with detailed examination of time series and time derivatives, revealed specific mechanisms underlying the observed periodicities, including interactions between the tidal variability, heating, wind, and biology. The implications for monitoring were illustrated through subsampling of the data set. This exercise demonstrated how quantities needed by scientists and managers (e.g., mean or extreme concentrations) may be misrepresented by low frequency data and how short-duration high frequency measurements can aid in the design and interpretation of temporally coarser sampling programs. The dispersive export of chlorophylla from the habitat exhibited a fortnightly variability corresponding to the modulation of semidiurnal tidal currents with the diurnal cycle of phytoplankton variability, demonstrating how high frequency interactions can govern long-term trends. Process identification, as through the scaling analysis here, can help us anticipate changes in system behavior and adapt our own interactions with the system.

THEORETICAL MODELING OF PROPAGATION OF MAGNETOACOUSTIC WAVES IN MAGNETIC REGIONS BELOW SUNSPOTS

We use two-dimensional numerical simulations and eikonal approximation to study properties of magnetohydrodynamic (MHD) waves traveling below the solar surface through the magnetic structure of sunspots. We consider a series of magnetostatic models of sunspots of different magnetic field strengths, from 10 Mm below the photosphere to the low chromosphere. The purpose of these studies is to quantify the effect of the magnetic field on local helioseismology measurements by modeling waves excited by subphotospheric sources. Time-distance propagation diagrams and wave travel times are calculated for models of various field strengths and compared to the nonmagnetic case. The results clearly indicate that the observed time-distance helioseismology signals in sunspot regions correspond to fast MHD waves. The slow MHD waves form a distinctly different pattern in the time-distance diagram, which has not been detected in observations. The numerical results are in good agreement with the solution in the short-wavelength (eikonal) approximation, providing its validation. The frequency dependence of the travel times is in good qualitative agreement with observations.

Effect of Suppressed Excitation on the Amplitude Distribution of 5 Minute Oscillations in Sunspots

Five minute oscillations on the Sun (acoustic and surface gravity waves) are excited by subsurface turbulent convection. However, in sunspots the excitation is suppressed because a strong magnetic field inhibits convection. We use three-dimensional simulations to investigate how the suppression of excitation sources affects the distribution of the oscillation power in sunspot regions. The amplitude of random acoustic sources was reduced in circular-shaped regions to simulate the suppression in sunspots. The simulation results show that the amplitude of the oscillations can be approximately 2-4 times lower in the sunspot regions in comparison to the quiet Sun, just because of the suppressed sources. Using SOHO MDI data we measured the amplitude ratio for the same frequency bands outside and inside sunspots and found that this ratio is approximately 3-4. Hence, the absence of excitation sources inside sunspots makes a significant contribution (about 50% or higher) to the observed amplitude ratio and must be taken into account in sunspot seismology.

Influence of Nonuniform Distribution of Acoustic Wavefield Strength on Time-Distance Helioseismology Measurements

By analyzing numerically simulated solar oscillation data we study the influence of nonuniform distribution of acoustic wave amplitude, acoustic source strength, and perturbations of the sound speed on the shifts of acoustic travel times measured by the time-distance helioseismology method. It is found that for short distances, the contribution to the mean travel-time shift caused by nonuniform distribution of acoustic sources in sunspots may be comparable to (but smaller than) the contribution from the sound-speed perturbation in sunspots, and that it has the opposite sign to the sound-speed effect. This effect may cause some underestimation of the negative sound-speed perturbations in sunspots just below the surface, which was found in previous time-distance helioseismology inferences. This effect cannot be corrected by artificially increasing the amplitude of oscillations in sunspots. For large time-distance annuli, the nonuniform distribution of wavefields does not have significant effects on the mean travel times, and thus the sound-speed inversion results. The measured travel-time differences, which are used to determine the mass flows beneath sunspots, can also be systematically shifted by this effect, but only by an insignificant magnitude.

Local helioseismology of sunspot regions: Comparison of ring-diagram and time-distance results

Local helioseismology provides unique information about the subsurface structure and dynamics of sunspots and active regions. However, because of complexity of sunspot regions local helioseismology diagnostics require careful analysis of systematic uncertainties and physical interpretation of the inversion results. We present new results of comparison of the ring-diagram analysis and time-distance helioseismology for active region NOAA 9787, for which a previous comparison showed significant differences in the subsurface sound-speed structure, and discuss systematic uncertainties of the measurements and inversions. Our results show that both the ring-diagram and time-distance techniques give qualitatively similar results, revealing a characteristic two-layer seismic sound-speed structure consistent with the results for other active regions. However, a quantitative comparison of the inversion results is not straightforward. It must take into account differences in the sensitivity, spatial resolution and the averaging kernels. In particular, because of the acoustic power suppression, the contribution of the sunspot seismic structure to the ring-diagram signal can be substantially reduced. We show that taking into account this effect reduces the difference in the depth of transition between the negative and positive sound-speed variations inferred by these methods. Further detailed analysis of the sensitivity, resolution and averaging properties of the local helioseismology methods is necessary for consolidation of the inversion results. It seems to be important that both methods indicate that the seismic structure of sunspots is rather deep and extends to at least 20 Mm below the surface, putting constraints on theoretical models of sunspots.

Determination of instantaneous growth rates using a cubic spline approximation

Abstract The well-known equation for the evaluation of relative growth rate (RGR) RGR=ln ( w 2 w 1 )/(t 2 −t 1 ) was shown to be an average relative rate. Only in the case of exponential growth law is this equation valid for both average and instantaneous rates. It depends not only on the time interval of averaging [t1, t2] but also on the error of measurements. Under certain conditions, real growth rate could not be seen among noise resulted from data errors. Other equations often used such as RGR = [w 2 −w 1 ] [w 1 ((t 2 −t 1 )] or its modification RGR = [w 2 −w 1 ] [0.5((w 1 +w 2 )((t 2 −t 1 )] and % increase =( w 2 w 1 )^[ 1 (t 2 −t 1 ) ]t-1100% , do not describe rates and cannot be used for the purpose in mind. Such a situation impelled us to develop a new approach for determining instantaneous rates directly from the experimental data for any process. The idea of this method consists of an approximation of data by a cubic spline regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimisation of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate directly from the experimental data. The instantaneous rate is a highly sensitive characteristic for study of natural and anthropogenic influences on the biological and ecological processes. For illustration, we analysed heat production of microplankton and growth rate of red seaweed Gracilaria verrucosa versus temperature. The program is written in C++.

VERIFICATION OF THE HELIOSEISMOLOGY TRAVEL-TIME MEASUREMENT TECHNIQUE AND THE INVERSION PROCEDURE FOR SOUND SPEED USING ARTIFICIAL DATA

We performed three-dimensional numerical simulations of the solar surface acoustic wave field for the quiet Sun and for three models with different localized sound-speed perturbations in the interior with deep, shallow, and two-layer structures. We used the simulated data generated by two solar acoustics codes that employ the same standard solar model as a background model, but utilize different integration techniques and different models of stochastic wave excitation. Acoustic travel times were measured using a time-distance helioseismology technique, and compared with predictions from ray theory frequently used for helioseismic travel-time inversions. It is found that the measured travel-time shifts agree well with the helioseismic theory for sound-speed perturbations, and for the measurement procedure with and without phase-speed filtering of the oscillation signals. This testing verifies the whole measuring-filtering-inversion procedure for static sound-speed anomalies with small amplitude inside the Sun outside regions of strong magnetic field. It is shown that the phase-speed filtering, frequently used to extract specific wave packets and improve the signal-to-noise ratio, does not introduce significant systematic errors. Results of the sound-speed inversion procedure show good agreement with the perturbation models in all cases. Due to its smoothing nature, the inversion procedure may overestimate sound-speed variations in regions with sharp gradients of the sound-speed profile.

Comparison of numerical simulations and observations of helioseismic MHD waves in sunspots

Numerical 3D simulations of MHD waves in magnetized regions with background flows are very important for the understanding of propagation and transformation of waves in sunspots. Such simulations provide artificial data for testing and calibration of helioseismic techniques used for analysis of data from space missions SOHO/MDI, SDO/HMI, and HINODE. We compare with helioseismic observations results of numerical simulations of MHD waves in different models of sunspots. The simulations of waves excited by a localized source provide a detailed picture of the interaction of the MHD waves with the magnetic field and background flows (deformation of the waveform, wave transformation, amplitude variations and anisotropy). The observed cross-covariance function represents an effective Green’s function of helioseismic waves. As an initial step, we compare it with simulations of waves generated by a localized source. More thorough analysis implies using multiple sources and comparison of the observed and simulated cross-covariance functions. We plan to do such calculations in the nearest future. Both, the simulations and observations show that the wavefront inside the sunspot travels ahead of a reference ”quiet Sun” wavefront, when the wave enters the sunspot. However, when the wave passes the sunspot, the time lag between the wavefronts becomes unnoticeable.