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NASA NTRS2006

The Art and Science of Long-Range Space Weather Forecasting

Long-range space weather forecasts are akin to seasonal forecasts of terrestrial weather. We don t expect to forecast individual events but we do hope to forecast the underlying level of activity important for satellite operations and mission pl&g. Forecasting space weather conditions years or decades into the future has traditionally been based on empirical models of the solar cycle. Models for the shape of the cycle as a function of its amplitude become reliable once the amplitude is well determined - usually two to three years after minimum. Forecasting the amplitude of a cycle well before that time has been more of an art than a science - usually based on cycle statistics and trends. Recent developments in dynamo theory -the theory explaining the generation of the Sun s magnetic field and the solar activity cycle - have now produced models with predictive capabilities. Testing these models with historical sunspot cycle data indicates that these predictions may be highly reliable one, or even two, cycles into the future.

Hathaway, David H.↗

NASA NTRS1997

Solar Cycle Predictions Near Sunspot Minimum

Observations of solar magnetic activity and the dynamics of the solar convection zone have produced severe constraints on models of the Sun's magnetic dynamo. These constraints are so severe that, at present, we do not have numerical models that can accept the current conditions and then march forward in time to predict future activity. Given this state of solar dynamo theory we are forced to examine previous behavior to discover patterns and trends that afford us some measure of predictability. Here we examine the behavior of several indicators of solar activity near solar minimum that are well correlated with the amplitude of the following solar maximum to predict the level of solar activity over cycle 23. Sunspot numbers, areas, and positions are useful for characterizing solar cycle behavior due to the extent of the data (12 cycles or more). These data exhibit several patterns that relate future activity to past behavior. With the Odd-Even effect the odd numbered cycles have been larger than their even numbered predecessors for each of the last six cycle pairs. With the Amplitude-Period effect short period cycles have been followed by large amplitude cycles and long period cycles have been followed by small amplitude cycles for 10 of the last 13 cycles. With the Maximum-Minimum effect the sunspot number at minimum is directly correlated with the sunspot number at maximum for a given cycle. The geomagnetic indices aa and Ap are also related to solar activity by the connections between disturbances in the solar wind and variations in the Earth's magnetic field. Like the Maximum-Minimum effect for sunspots, the size of the aa and Ap indices at minimum are directly related to the amplitude of the following maximum. The number of geomagnetically disturbed days (days with Ap >= 25) over the course of a cycle is another indicator for the size of the next cycle. The aa and Ap indices can each be separated into a component in phase with the current sunspot cycle and an "extended cycle" component that is directly related to the following cycle. Individually each of these indicators provides some measure of predictive ability for the amplitudes of previous cycles. Taken in combination we find that the predictions are much more accurate. Our multi-variate analysis indicates that a maximum sunspot number of 160 +/- 20 should occur near the end of 1999 for cycle 23.

Hathaway, David H.↗

NASA NTRS1988

Bimodality and the Hale cycle

Evidence is provided of a modulation of between 20 and 24 yr for the Hale cycle, and comparison of consecutive pairs of cycles strongly suggests that even-numbered cycles are preferentially paired with odd-numbered following cycles. The results indicate that cycles 22 and 23 form a new cyle pair. The sum of monthly mean sunspot numbers over consecutively paired sunspot cycles for Hale cycle 12 is found to be about 19,100 + or - 3000.

Wilson, Robert M.↗

NASA NTRS1994

The solar cycle variation of coronal temperature and density during cycle 21-22

In this paper we characterize the temperature and the density structure of the corona utilizing co-spatial spectrophotometric observations during the descending phase of cycle 21 through the ascending phase of cycle 22. The data include ground-based intensity observations of the green (5303A Fe XIV) and red (6374A Fe X) coronal forbidden lines from Sacramento Peak and synoptic maps of white-light K-coronal polarized brightness, pB from the High Altitude Observatory, and photospheric magnetographs from the National Solar Observatory, Sacramento Peak. A determination of plasma temperature T can be derived unambiguously from the intensity ratio Fe X/Fe XIV, since both emission lines come from ionized states of Fe, and the ratios are only weakly dependent on density. The latitudinal variation of the temperature and the density within the descending and the ascending phases of solar cycle 21 and 22 are presented. There is a large-scale organization of the inferred coronal temperature distribution; these structures tend to persist through most of the magnetic activity cycle. This distribution differs in spatial and temporal characterization from the traditional picture of sunspot and active region evolution over the range of sunspot cycle.

Guhathakurta, M.↗

NASA NTRS2009

Meridional Flow Variations Over Three Solar Cycles - What Happened in Cycle 23?

The meridional flow speed determines the strength of the Sun s polar fields in both surface flux transport models and in flux transport dynamos. The polar fields produced during cycle 23 were half as strong as those produced in the previous two cycles. Helioseismic measurements of the meridional flow over the rising phase of cycle 23 indicated a decrease in flow velocity. This observation was used in flux transport dynamo models to predict a delayed start for cycle 24 and was consistent with weak polar fields and a slower equatorward drift of the active latitudes during cycle 23. On the other hand, the surface flux transport models require a faster meridional flow to produce the weak polar fields. We have begun measurements of the surface meridional flow by tracking the motions of weak (outside active regions) magnetic field elements in magnetograms from SOHO/MDI over cycle 23 and from NSO/Kitt Peak over cycles 21 to 23. We confirm the slowdown of the meridional flow over the rising phase of cycle 23 but find that the flow speed returned to its previous level during the declining phase of cycle 23. Furthermore, this appears to be a normal feature of the meridional flow during sunspot cycles. The flow is fast at minima and slow at maxima. The lack of a significantly different meridional flow during cycle 23 is very problematic for both surface flux transport models and flux transport dynamos.

Hathaway, David H.↗

NASA NTRS1998

Volcanism, Cold Temperature, and Paucity of Sunspot Observing Days (1818-1858): A Connection?

During the interval of 1818-1858, several curious decreases in the number of sunspot observing days per year are noted in the observing record of Samuel Heinrich Schwabe, the discoverer of the sunspot cycle, and in the reconstructed record of Rudolf Wolf, the founder of the now familiar relative sunspot number. These decreases appear to be nonrandom in nature and often extended for 13 yr (or more). Comparison of these decreases with equivalent annual mean temperature (both annual means and 4-yr moving averages). as recorded at Armagh Observatory (Northern Ireland), indicates that the temperature during the years of decreased number of observing days trended downward near the start of' each decrease and upward (suggesting some sort of recovery) just before the end of each decrease. The drop in equivalent annual mean temperature associated with each decrease, as determined from the moving averages, measured about 0.1-0.7 C. The decreases in number of observing days are found to be closely related to the occurrences of large, cataclysmic volcanic eruptions in the tropics or northern hemisphere. In particular, the interval of increasing number of observing days at the beginning of the record (i.e., 1818-1819) may be related to the improving atmospheric conditions in Europe following the 1815 eruption of Tambora (Indonesia; 8 deg. S), which previously, has been linked to "the year without a summer" (in 1816) and which is the strongest eruption in recent history, while the decreases associated with the years of 1824, 1837, and 1847 may, be linked, respectively, to the large, catacivsmic volcanic eruptions of Galunggung (Indonesia; 7 deg. S) in 1822, Cosiguina (Nicaragua) in 1835, and, perhaps, Hekla (Iceland; 64 deg. N) in 1845. Surprisingly, the number of observing days per year, as recorded specifically b), SchAabe (from Dessau, Germany), is found to be linearly correlated against the yearly mean temperature at Armagh Observatory (r = 0.5 at the 2 percent level of significance); thus. years of fewer sunspot observing days in the historical record seem to indicate years of probable cooler clime, while years (if many sunspot observing days seem to indicate years of probable warmer clime (and Vice versa). Presuming this relationship to be real, one infers that the observed decrease in the number of observing days near 1830 (i.e., during "the lost record years" of 1825 to 1833) provides a strong indication that temperatures at Armagh (and, perhaps, most of Europe, as well) were correspondingly cooler. If true, then, the inferred cooling may have resulted from the eruption of Kliuchevsoi(Russia; 56 deg. N) in 1829.

Wilson, Robert M.↗

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 NTRS1991

Out-of-ecliptic tests of the inverse correlation between solar wind speed and coronal expansion factor

The paper addresses the question of whether out-of-ecliptic measurements satisfy the inverse correlation between wind speed at 1 AU and flux-tube divergence in the corona, already found from measurements in the ecliptic. Using the in-ecliptic calibration, out-of-ecliptic speeds are derived from coronal expansion factors determined from global observations of photospheric field and their current-free coronal extension. These derived speeds are compared with speeds inferred from interplanetary scintillation measurements during 1972-1988 and with in situ speeds measured by the Pioneer 11 spacecraft at 16 deg N latitude during 1984-1988. These three sets of wind speed show the same overall variation with latitude and time during the sunspot cycle, with higher latitudes having more years of fast wind than lower latitudes and all latitudes having slow wind at sunspot maximum. Although some detailed discrepancies are also present, the overall agreement is comparable to that achieved in the ecliptic plane.

Sheeley, N. R., Jr.↗

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 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 NTRS2001

Investigation of the Relative Value of Solar Proxies for Irradiance Variation

Recent space observations of irradiance change during the current solar cycle 23 suggest that of the three proxies currently used (PSI index, total solar magnetic field, and the Mg II c/w index) only the latter yields a consistent result when compared to the two previous cycles for which space observations are available. Possible reasons for this are presented, and a case is made that using actual sunspot areas might work almost as well as the PSI index for estimating irradiance changes, making earlier observations lacking photometric calibration of value in assessing probable irradiance changes over earlier sunspot cycles.

Jordan, Stuart↗

NASA NTRS1983

Solar cycle variations in the interplanetary magnetic field

ISEE 3 interplanetary magnetic field measurements have been used to extend the NSSDC hourly averaged IMF composite data set through mid-1982. Most of sunspot cycle 20 (start:1964) and the first half of cycle 21 (start:1976) are now covered. The average magnitude of the field was relatively constant over cycle 20 with approx. 5-10% decreases in 1969 and 1971, when the Sun's polar regions changed polarity, and a 20% decrease in 1975-6 around solar minimum. Since the start of the new cycle, the total field strength has risen with the mean for the first third of 1982 being about 40% greater than the cycle 20 average. As during the previous cycle, an approx. 10% drop in IMF magnitude accompanied the 1980 reversal of the solar magnetic field. While the interplanetary magnetic field is clearly stronger during the present solar cycle, another 5-7 years of observations will be needed to determine if cycle 21 exhibits the same modest variations as the last cycle. Accordingly, it appears at this time that intercycle changes in IMF magnitude may be much larger than the intracycle variations.

Slavin, J. A.↗

NASA NTRS1990

Using the Boundary Conditions of Sunspots as a Technique for Monitoring Solar Luminosity Variations

Recent satellite observations of the solar total irradiance confirm that it is varying at least on the 11 year time scale. Both blocking by sunspots and re-emission by faculae are components in this variation, but changes in the temperature of the solar photosphere may also be a contributing component. The satellite observations are as yet of insufficient length to answer the question of whether the sun is varying in luminosity on time scales longer than the 11 year sunspot cycle. Examined here are proxy methods of re-constructing these longer term luminosity variations, with an examination of secular changes in sunspot structure as one tool. Solar rotation changes and solar diameter changes are other parameters which may reveal information about solar luminosity variations. All three variables give remarkably similar conclusions. Over the last century the Earth's surface temperatures and the structure of sunspots have varied in a parallel manner. It is hypothesized that sunspots have varied in a convective medium which itself is varying over long time periods. These variations in convective strength alter the boundary conditions on sunspots and hence cause their structure to vary. Simultaneous with the variations in convective strength, the solar luminosity will vary as well. This, in turn, leads to changes in the climate of the Earth. Variations in solar diameter and solar rotation support the hypothesis that solar luminosity has varied over the last century and reached a peak around 1925 to 1935. This evidence is reviewed along with a possible model of why sunspot structure may provide a good proxy measure of solar luminosity changes.

Hoyt, Douglas V.↗

NASA NTRS2003

Validation of Spacecraft Active Cavity Radiometer Total Solar Irradiance (TSI) Long Term Measurement Trends Using Proxy TSI Least Squares Analyses

Long-term, incoming total solar irradiance (TSI) measurement trends were validated using proxy TSI values, derived from indices of solar magnetic activity. Spacecraft active cavity radiometers (ACR) are being used to measure longterm TSI variability, which may trigger global climate changes. The TSI, typically referred to as the solar constant, was normalized to the mean earth-sun distance. Studies of spacecraft TSI data sets confirmed the existence of a 0.1 %, long-term TSI variability component within a 10-year period. The 0.1% TSI variability component is clearly present in the spacecraft data sets from the 1984-2004 time frame. Typically, three overlapping spacecraft data sets were used to validate long-term TSI variability trends. However, during the years of 1978-1984, 1989-1991, and 1993-1996, three overlapping spacecraft data sets were not available in order to validate TSI trends. The TSI was found to vary with indices of solar magnetic activity associated with recent 10-year sunspot cycles. Proxy TSI values were derived from least squares analyses of the measured TSI variability with the solar indices of 10.7-cm solar fluxes, and with limb-darked sunspot fluxes. The resulting proxy TSI values were compared to the spacecraft ACR measurements of TSI variability to detect ACR instrument degradation, which may be interpreted as TSI variability. Analyses of ACR measurements and TSI proxies are presented primarily for the 1984-2004, Earth Radiation Budget Experiment (ERBE) ACR solar monitor data set. Differences in proxy and spacecraft measurement data sets suggest the existence of another TSI variability component with an amplitude greater than or equal to 0.5 Wm-2 (0.04%), and with a cycle of 20 years or more.

Lee, Robert Benjamin, III↗

NASA NTRS1978

Deep space telecommunications and the solar cycle: A reappraisal

Observations of density enhancement in the near corona at solar cycle (sunspot) maximum have rather uncritically been interpreted to apply equally well to the extended corona, thus generating concern about the quality of outer planet navigational data at solar cycle maximum. Spacecraft have been deployed almost continuously during the recently completed solar cycle 20, providing two powerful new coronal investigatory data sources: (1) in-situ spacecraft plasma measurements at approximately 1 AU, and (2) plasma effects on monochromatic spacecraft signals at all signal closest approach points. A comprehensive review of these (solar cycle 20) data lead to the somewhat surprising conclusions that for the region of interest of navigational data, the highest levels of charged particle corruption of navigational data can be expected to occur at solar cycle minimum, rather than solar cycle maximum, as previously believed.

Berman, A. L.↗

NASA NTRS1977

A preliminary analysis of Viking S-X Doppler data and comparison to results of Mariner 6, 7, and 9 DRVID measurements of the solar wind turbulence

S-X Doppler data obtained during more than 135 Viking passes from Aug. 3 to Dec. 15, 1976 were analyzed and compared with data from previous investigations using Mariner differenced range versus integrated Doppler to determine changes in the turbulence over the sunspot cycle. A comparison of the data indicates that: (1) electron density fluctuations decline with heliocentric distance; (2) the level of turbulence may be a factor of two lower near sunspot minimum than at maximum; and (3) the spectrum of the fluctuations may be steeper near sunspot minimum. The expected range error for various time scales and geometries is derived from the results.

Callahan, P. S.↗

NASA NTRS1990

A Review and Reflections on the Sun-Climate Connection

The field of sun-climate is beset with an extraordinary number of numerical correlations attempting to relate various periodicities of solar activity with changes in the Earth's weather and climate. Signatures representing climatological variability have been sought for cycles as short as the solar 28-day rotational period up to Milankovich periods of thousands of years, although a majority of correlations have concentrated on the 11-year sunspot and 22-year Hale double sunspot cycles. For the shorter term, parameters including temperature, pressure, winds storm tracks, rainfall, and water levels in rivers and lakes, etc. have been correlated with solar variability. For longer periods, it has been necessary to seek more indirect evidence in ice cores, tree rings, and geologic deep sea cores. Other atmospheric parameters relating to atmospheric electricity and the global electric circuit have also been correlated in similar fashion. Unfortunately, few, if any, of this wide spectrum of numerical correlations have been associated with any viable physical explanation, making most studies in the field an exercise in numerical statistics. More recently, a few suggestions for plausible coupling processes have begun to appear. These, coupled with new and stronger correlations involving selective binning of climatological data sets have injected new life and hope to this field. An overview is given of the historical past and current perspectives, to evaluate possible avenues for defining physical linking processes in the future.

Goldberg, Richard A.↗

NASA NTRS1988

Earth Radiation Budget Satellite extraterrestrial solar constant measurements - 1986-1987 increasing trend

From June 1986 through Nov 1987, the Earth Radiation Budget Satellite (ERBS) pyrheliometric measurements indicated that the solar constant was increasing approximately +0.02 percent per year. Earlier ERBS measurements indicated that the solar constant was declining approximately -0.03 percent per year during the 1984 through mid-1986 period. Since mid-1986 represents the beginning of solar cycle 22, it is believed that the reversal in the long-term solar constant trend may be linked to increased solar activity associated with the beginning of the 11-year sunspot cycle. The typical value of the solar constant was found to be 1365 Wm-2.

Lee, Robert B., III↗