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NASA NTRS2017

Early Estimation of Solar Activity Cycle: Potential Capability and Limits

The variable solar magnetic activity known as the 11-year solar cycle has the longest history of solar observations. These cycles dramatically affect conditions in the heliosphere and the Earth's space environment. Our current understanding of the physical processes that make up global solar dynamics and the dynamo that generates the magnetic fields is sketchy, resulting in unrealistic descriptions in theoretical and numerical models of the solar cycles. The absence of long-term observations of solar interior dynamics and photospheric magnetic fields hinders development of accurate dynamo models and their calibration. In such situations, mathematical data assimilation methods provide an optimal approach for combining the available observational data and their uncertainties with theoretical models in order to estimate the state of the solar dynamo and predict future cycles. In this presentation, we will discuss the implementation and performance of an Ensemble Kalman Filter data assimilation method based on the Parker migratory dynamo model, complemented by the equation of magnetic helicity conservation and longterm sunspot data series. This approach has allowed us to reproduce the general properties of solar cycles and has already demonstrated a good predictive capability for the current cycle, 24. We will discuss further development of this approach, which includes a more sophisticated dynamo model, synoptic magnetogram data, and employs the DART Data Assimilation Research Testbed.

Kitiashvili, Irina N.↗
NASA NTRS2017

Using Data Assimilation Methods of Prediction of Solar Activity

The variable solar magnetic activity known as the 11-year solar cycle has the longest history of solar observations. These cycles dramatically affect conditions in the heliosphere and the Earth's space environment. Our current understanding of the physical processes that make up global solar dynamics and the dynamo that generates the magnetic fields is sketchy, resulting in unrealistic descriptions in theoretical and numerical models of the solar cycles. The absence of long-term observations of solar interior dynamics and photospheric magnetic fields hinders development of accurate dynamo models and their calibration. In such situations, mathematical data assimilation methods provide an optimal approach for combining the available observational data and their uncertainties with theoretical models in order to estimate the state of the solar dynamo and predict future cycles. In this presentation, we will discuss the implementation and performance of an Ensemble Kalman Filter data assimilation method based on the Parker migratory dynamo model, complemented by the equation of magnetic helicity conservation and long-term sunspot data series. This approach has allowed us to reproduce the general properties of solar cycles and has already demonstrated a good predictive capability for the current cycle, 24. We will discuss further development of this approach, which includes a more sophisticated dynamo model, synoptic magnetogram data, and employs the DART Data Assimilation Research Testbed.

Prediction↗
NASA NTRS2017

Using Data Assimilation Methods for Prediction of Solar Activity

The variability of solar magnetic activity known as the 11-­‐year solar cycles has the longest history of observations. These solar cycles dramatically affect conditions in the heliosphere and the Earth’s space environment. Our current understanding of the physical processes that make up global solar dynamics and the dynamo that generates the magnetic fields is sketchy, resulting in unrealistic descriptions in theoretical and numerical models of the solar cycles. The absence of long-­‐term observations of solar interior dynamics and photospheric magnetic fields hinders development of accurate dynamo models and their calibration. In such situations, mathematical data assimilation methods provide an optimal approach for combining the available observational data and their uncertainties with theoretical models in order to estimate the state of the solar dynamo and predict future cycles. In this presentation, we will discuss the implementation and performance of an Ensemble Kalman Filter data assimilation method based on the Parker migratory dynamo model complemented by the equation of magnetic helicity conservation and long-­‐term sunspot data series. This approach has allowed us to reproduce the general properties of the solar cycles and has already demonstrated a good predictive capability for the current cycle, 24. We will discuss further development of this approach, which includes a more sophisticated dynamo model, synoptic magnetogram data, and employs the DART Data Assimilation Research Testbed.

Solar Activity↗
NASA NTRS2019

Global Evolution of Solar Magnetic Fields and Prediction of Solar Activity Cycles

Prediction of solar activity cycles is challenging because the physical processes inside the Sun involve a broad range of multiscale dynamics that no model can reproduce, and the available observations are highly limited and cover mostly surface layers. Helioseismology makes it possible to probe solar dynamics in the convective zone, but variations in the differential rotation and meridional circulation are currently available for only two solar activity cycles. It has been demonstrated that sunspot observations, which cover over 400 years, can be used to calibrate the Parker-Kleeorin-Ruzmaikin model and that the Ensemble Kalman Filter (EnKF) method can be used to link the model magnetic fields to sunspot observations to make reliable predictions of a following cycle. However, for more accurate predictions, it is necessary to use actual observations of the solar magnetic fields, which are available for only four solar cycles. This raises the question of how limitations in observational data and model uncertainties affect predictive capabilities and implies the need for the development of new forecast methodologies and validation criteria. In this presentation, I will discuss the influence of the limited number of available observations on the accuracy of EnKF estimates of solar cycle parameters.

Kitiashvili, Irina N.↗
NASA NTRS1993

Radial and latitudinal variations of the magnetic field strength in the outer heliosphere

The radial, latitudinal, and temporal variations of the magnetic field in the outer heliosphere are analyzed on the basis of observations from Voyagers 1 and 2 and Pioneers 10 and 11. The radial variation of the magnetic field strength measured during 1973-1989 from 1 to 19 AU is compared with that predicted by Parker's (1963) spiral field model. Additional Voyager 2 magnetic field data from 1986 through most of 1989 are discussed. Latitudinal variations in the magnetic field strength are examined on Voyager 1 and 2 observations from 1981 to 1989. It is concluded that both the Voyager and the Pioneer observations are consistent with Parker's model for the variation of the strength of the magnetic field as a function of distance from the sun in the region from 1 to 19 AU. The topology of the spiral interplanetary magnetic field, as well as a program for analyzing more general magnetic fields and velocity fields in the heliosphere are also discussed.

Burlaga, L. F.↗
NASA NTRS1977

The gross energy balance of solar active regions

Parker's (1974) model in which sunspots denote regions of increased heat transport from the convection zone is briefly described. The amount of excess mechanically transported power supposed to be delivered to the atmosphere is estimated for a typical active region, and the total radiative power output of the active-region atmosphere is computed. It is found that only a very small fraction (about 0.001) of the sunspot 'missing flux' can be accounted for by radiative emission from the atmosphere above a spot group in the manner suggested by Parker. The power-loss mechanism associated with mass loss to the solar wind is briefly considered and shown not to be sufficient to account for the sunspot missing flux.

Evans, K. D.↗
NASA NTRS1974

Sweet's mechanism in the solar wind

Sweet (1956, 1958) proposed a mechanism for the rapid, steady-state dissipation of a magnetic field in a resistive plasma. It is shown that Sweet's mechanism operates in the interplanetary medium near 1 AU in structures which Burlaga and Ness (1968) have identified and called D-sheets. The basic equations are considered of a specific mathematical model provided by Parker (1963) for the case of antiparallel fields and incompressible flow. The theoretical conclusions are related to interplanetary observations.

Burlaga, L. F.↗
NASA NTRS1976

The quiet solar wind

Data from nine spacecraft are combined to study the properties of solar wind protons and the interplanetary magnetic field under unusual conditions that proton speed, density, and temperature variations are small over periods comparable to the solar wind expansion time. From the 14 quiet intervals studied it is determined that (1) the square root of T versus velocity relation is less steep than was calculated from long-term-averaged or 3-hour quiet data; (2) the density varies approximately as the inverse square of the velocity; however, the data scatter is large, and an alternative interpretation is that mass flux is constant for velocities over about 400 km/s, in agreement with earlier studies; (3) the magnitude of the interplanetary magnetic field is independent of solar wind speed and density; and (4) the average field direction varies with the solar wind speed as predicted by Parker's spiral model. The intercalibration of solar wind measurements by different spacecraft is discussed in an appendix.

Neugebauer, M.↗
NASA NTRS1983

Digital analysis of narrow-band imagery of the Cygnus Loop

Calibrated surface brightness and spectral line ratio maps which involve emission from six different ionic species are derived from the digital analysis of narrow passband direct imagery of a field in the southeast part of the Cygnus Loop SNR, and the spatial structure is categorized on the basis of the presence or absence of features in images isolating different emission lines. While features present in all emission lines are found to have spectral behavior consistent with steady flow shock model calculations for a range of v(s), the features present only in such 'hot' lines as the O III forbidden line 5007 A are found to account for relative intensities of that line greater than can be matched by steady flow model calculations.

Parker, R. A. R.↗
NASA NTRS2000

Satellite Motion Effects on Current Collection in Low Earth Orbit

Results from the Tethered Satellite System (TSS) missions unambiguously show that the electrodynamic tether system produced 2 to 3 times the predicted current levels in the tether. The pre-mission predictions were based on the well-known Parker-Murphy (PM) model, which describes the collection of current by an electrically biased satellite in the ionospheric plasma. How the TSS satellite was able to collect 2-3 times the PM current has remained an open question. In the present study, self-consistent potential and motional effects are introduced into the Thompson and Dobrowolny sheath models. As a result, the magnetic field aligned sheath-an essential variable in determining current collection by a satellite-is derived and is shown to be explicitly velocity dependent. The orientation of the satellite's orbital motion relative to the geomagnetic field is also considered in the derivation and a velocity dependent expression for the collected current is obtained. The resulting model provides a realistic treatment of current collection by a satellite in low earth orbit. Moreover, the predictions, using the appropriate parameters for TSS, are in good agreement with the tether currents measured during the TSS-1R mission.

Zhang, T. X.↗
NASA NTRS2010

Formation and Reconnection of Three-Dimensional Current Sheets in the Solar Corona

Current-sheet formation and magnetic reconnection are believed to be the basic physical processes responsible for much of the activity observed in astrophysical plasmas, such as the Sun s corona. We investigate these processes for a magnetic configuration consisting of a uniform background field and an embedded line dipole, a topology that is expected to be ubiquitous in the corona. This magnetic system is driven by a uniform horizontal flow applied at the line-tied photosphere. Although both the initial field and the driver are translationally symmetric, the resulting evolution is calculated using a fully three-dimensional magnetohydrodynamic (3D MHD) simulation with adaptive mesh refinement that resolves the current sheet and reconnection dynamics in detail. The advantage of our approach is that it allows us to apply directly the vast body of knowledge gained from the many studies of 2D reconnection to the fully 3D case. We find that a current sheet forms in close analogy to the classic Syrovatskii 2D mechanism, but the resulting evolution is different than expected. The current sheet is globally stable, showing no evidence for a disruption or a secondary instability even for aspect ratios as high as 80:1. The global evolution generally follows the standard Sweet- Parker 2D reconnection model except for an accelerated reconnection rate at a very thin current sheet, due to the tearing instability and the formation of magnetic islands. An interesting conclusion is that despite the formation of fully 3D structures at small scales, the system remains close to 2D at global scales. We discuss the implications of our results for observations of the solar corona. Subject Headings: Sun: corona Sun: magnetic fields Sun: reconnection

Edmondson, J. K.↗
NASA NTRS2017

Data Assimilation and Uncertainties in Early Solar Cycle Predictions

Stochastic nature of solar activity variations together with our limited knowledge of the dynamo mechanism and subsurface dynamics causes uncertainty in predictions of the solar cycle. For improving the physics-­‐based predictions we can take advantage of the mathematical data assimilation approach that allows us to take into account both, observational errors and model uncertainties, and provide estimates of the next solar cycle along with prediction uncertainties. In this study we use the Parker's migratory dynamo model together with the equation of magnetic helicity balance, which reproduces main properties of the sunspot cycles and allow us to minimize discrepancies between the observed global activity variations and the model solution. The test simulation runs show that a reliable prediction can be obtained for two phases of preceding solar cycle: 1) if the polar field reversals shortly after the solar maxima (strong toroidal field and weak poloidal field), and 2) during the solar minima (strongest poloidal and weak toroidal fields). The early estimate of Cycle 25 obtained by this method shows that this cycle will start in 2019 – 2020, reach the maximum in 2023 – 2024, and that the mean sunspot number at the maximum will be about 90 (for the v2.0 sunspot number series).

Data Assimilation↗
NASA NTRS2019

Solar Activity Modeling: From Subgranular Dynamical Scales to the Solar Cycles

The dynamical effects of solar magnetoconvection span a wide range spatial and temporal scales that extend from the interior to the corona and from fast turbulent motions to global magnetic activity. To study the solar activity on short temporal scales (from minutes to hours), we use 3D radiative MHD simulations that allow us to investigate complex turbulent interactions that drive various phenomena, such as plasma eruptions, spontaneous formation of magnetic structures, funnel-like structures and magnetic loops in the corona, and others. In particular, we focus on multi-scale processes of energy exchange across layers of the solar interior and atmosphere, which contribute to coronal heating and eruptive dynamics. For modeling global-scale activity, we use a data assimilation approach that has demonstrated great potential for building reliable long-term forecasts of solar activity. In particular, it has been shown that the Ensemble Kalman Filter (EnKF) method applied to the Parker-Kleeorin-Ruzmakin dynamo model is capable of predicting solar activity up to one sunspot cycle ahead in time, as well as estimating the properties of the next cycle a few years before it begins. In this presentation, using the available magnetogram data, we discuss development of the methodology and forecast quality criteria (including forecast uncertainties and sources of errors). We demonstrate the influence of observational limitations on prediction accuracy, and we present the EnKF predictions of the upcoming Solar Cycle (25) based on both the sunspot number series and observed magnetic fields and discuss the uncertainties and potential of the data assimilation approach for modeling and forecasting solar activity.

Kitiashvili, I. N.↗
NASA NTRS2019

Solar Activity Modeling: From Subgranular Dynamical Scales to the Solar Cycles

Dynamical effects of solar magnetoconvection span a wide range spatial and temporal scales that extends from the interior to the corona and from fast turbulent motions to the global-Sun magnetic activity. To study the solar activity on short temporal scales (from minutes to hours), we use 3D radiative MHD simulations that allow us to investigate complex turbulent interactions that drive various phenomena, such as plasma eruptions, spontaneous formation of magnetic structures, funnel-like structures and magnetic loops in the corona, and others. In particular, we focus on multi-scale processes of energy exchange across the different layers, which contribute to the corona heating and eruptive dynamics, as well as interlinks between different layers of the solar interior and atmosphere. For modeling the global-scale activity we use the data assimilation approach that has demonstrated great potential for building reliable long-term forecasts of solar activity. In particular, it has been shown that the Ensemble Kalman Filter (EnKF) method applied to the Parker-Kleeorin-Ruzmakin dynamo model is capable of predicting solar activity up to one sunspot cycle ahead in time, as well as estimating the properties of the next cycle a few years before it begins. In this presentation, using the available magnetogram data, we discuss development of the methodology and forecast quality criteria (including forecast uncertainties and sources of errors). We demonstrate the influence of observational limitation on the prediction accuracy. We present the EnKF predictions of the upcoming Solar Cycle 25 based on both the sunspot number series and observed magnetic fields, and discuss the uncertainties and potential of the data assimilation approach for modeling and forecasting the solar activity.

Kitiashvili, I. N.↗
NASA NTRS1981

On the significance of including the thermal motion of ions in determining the ion distribution behind a satellite

A comparative investigation concerning the spatial distribution of ions in the wake of small bodies was conducted using the theoretical wake models of Call (1969) and Parker (1976). Results for bodies with radius/ambient Debye length ratios of 2 and 5, with an electron temperature equal to the ambient electron temperature, and for the ionic Mach numbers S = 2, 4, 6, 8 are presented. Since the main physical difference between the models is in the consideration of the thermal motion of ions (Parker) versus ignoring this component (Call), a comparison between the models yields the quantitative significance of this component in determining the distribution of ions in the wake of artificial satellites. The application of this result to future experiments to be conducted on board the Spacelab and for any other large space platform in the area of space plasma physics is mentioned.

Samir, U.↗
NASA NTRS1974

Termination of the solar wind in the hot, partially ionized interstellar medium

Theoretical foundations for understanding the problem of the termination of the solar wind are reexamined in the light of most recent findings concerning the states of the solar wind and the local interstellar medium. The investigation suggests that a simple extention of Parker's (1961) analytical model provides a useful approximate description of the combined solar wind, interstellar wind plasma flowfield under conditions presently thought to occur. A linear perturbation solution exhibiting both the effects of photoionization and charge exchange is obtained for the supersonic solar wind. A numerical algorithm is described for computing moments of the non-equilibrium hydrogen distribution function and associated source terms for the MHD equations. Computed using the algorithm in conjunction with the extended Parker solution to approximate the plasma flowfield, profiles of hydrogen number density are given in the solar wind along the upstream and downstream axes of flow with respect to the direction of the interstellar wind. Predictions of solar Lyman-alpha backscatter intensities to be observed at 1 a.u. have been computed, in turn, from a set of such hydrogen number density profiles varied over assumed conditions of the interstellar wind.

Lombard, C. K.↗