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Observations the Sun's photospheric magnetic field are often confined to the Sun-Earth line. Surface flux transport (SFT) models, such as the Advective Flux Transport (AFT) model, simulate the evolution of the photospheric magnetic field to produce magnetic maps over the entire surface of the Sun. While these models are able to evolve active regions that transit the near-side of the Sun, new far-side side flux emergence is typically neglected. We demonstrate a new method for creating improved maps of magnetic field over the Sun's entire photosphere using data obtained by the STEREO mission. The STEREO He II 304 \AA intensity images are used to infer the time, location, and total unsigned magnetic flux of far-side active regions. We have developed and automatic detection algorithm for finding and ingesting new far-side active region emergence into the AFT model. We conduct a series of simulations to investigate the impact of including active region emergence in AFT, both with and without data assimilation of magnetograms. We find that while the He II 304 \AA can be used to improve surface flux models, but care must taken to mitigate intensity surges from flaring events. We estimate that during Solar Cycle 24 maximum (2011-2015), 4-6 x 10^22 Mx of flux is missing from SFT models that do not include far-side data. We find that while He II 304 \AA data alone can be used to create synchronic maps of photospheric magnetic field that resemble the observations, it is insufficient to produce a complete picture without direct magnetic observations from magnetographs., Comment: 14 pages, 9 figures, submitted with revisions to ApJ

Sunspot Cycle 25 over 3 years past the cycle minimum of December 2019. At this point, curve-fitting becomes reliable and consistently indicates a maximum sunspot number of 135+/-10 - slightly larger than Cycle 24's maximum of 116.4, but well below the Cycles 1-24 average of 179 (ranging from 81 for Cycle 6 to 285 for Cycle 19). A geomagnetic precursor, the minimum in the aa-index, and the Sun's magnetic precursors, the polar field strength and axial dipole moment at the time of minimum, are often used to predict the amplitude of the cycle at (or before) the onset of the cycle. We examine Cycle 25 predictions produced by these precursors. The geomagnetic precursor indicated a Cycle 25 slightly stronger than Cycle 24, with a maximum of 132+/-8. The Sun's magnetic precursors indicated that Cycle 25 would be similar to Cycle 24, with a maximum sunspot number of 120+/-10 or 114+/-15. Combining the curve-fitting results with the precursor predictions, we conclude that Cycle 25 will have a maximum smoothed sunspot number of 134+/-8 with maximum occurring late in the fall of 2024. Models for predicting the Sun's magnetic field ahead of minimum, were generally successful at predicting the polar precursors years in advance. The fact that Sun's magnetic precursors at cycle minimum were successfully predicted years before minimum and that the precursors are consistent with the size of Cycle 25 suggests that we can now more reliably predict the solar cycle., Comment: 14 pages, 5 figures, manuscript submitted to JGR: Space Physics on 5/9/2023

We measure differential rotation and meridional flow in the Sun's surface shear layer by tracking the motions of the magnetic network seen in magnetograms from SOHO/MDI and SDO/HMI over solar cycles 23, 24, and the start of 25 (1996-2022). We examine the axisymmetric flows derived from 15-24 daily measurements averaged over individual 27-day Carrington rotations. Variations in the differential rotation include the equatorial torsional oscillation - cyclonic flows centered on the active latitudes with slower flows on the poleward sides of the active latitudes and faster flows equatorward. The fast flow band starts at $\sim$45$^\circ$ latitude during the declining phase of the previous cycle and drifts equatorward, terminating at the equator at about the time of cycle minimum. Variations in the differential rotation also include a polar oscillation above 45$^\circ$ with faster rotation at cycle maxima and slower rotation at cycle minima. The equatorial variations were stronger in cycle 24 than in cycle 23 but the polar variations were weaker. Variations in the meridional flow include a slowing of the poleward flow in the active latitudes during cycle rise and maximum and a speeding up of the poleward flow during cycle decline and minimum. The slowing in the active latitudes was less pronounced in cycle 24 than in cycle 23. Polar countercells (equatorward flow) extend from the poles down to $\sim$60$^\circ$ latitude from time to time (1996-2000 and 2016-2022 in the south and 2001-2011 and 2017-2022 in the north). Both axisymmetric flows vary in strength with depth. The rotation rate increases inward while the meridional flow weakens inward.

The Sun's axisymmetric flows, differential rotation and meridional flow, govern the dynamics of the solar magnetic cycle and variety of methods are used to measure these flows, each with its own strengths and weaknesses. Flow measurements based on cross-correlating images of the surface magnetic field have been made since the 1970s which require advanced numerical techniques that are capable of detecting movements of less than the pixel size in images of the Sun. We have identified several systematic errors in addition to the center-to-limb effect that influence previous measurements of these flows and propose numerical techniques that can minimize these errors by utilizing measurements of displacements at several time-lags. Our analysis of line-of-sight magnetograms from the {\em Michelson Doppler Imager} (MDI) on the ESA/NASA {\em Solar and Heliospheric Observatory} (SOHO) and {\em Helioseismic and Magnetic Imager} (HMI) on the NASA {\em Solar Dynamics Observatory} (SDO) shows long-term variations in the meridional flow and differential rotation over two sunspot cycles from 1996 to 2020. These improved measurements can serve as vital inputs for solar dynamo and surface flux transport simulations., Comment: 16 pages, 9 figures, 2 tables

The Waldmeier Effect is the observation that the rise time of a sunspot cycle varies inversely with the cycle amplitude: strong cycles rise to their maximum faster than weak cycles. The shape of the cycle and thus the rise time does not depend on the scale factor of the sunspot number and can thus be used to verify the constancy of the scale factor with time as already noted by Wolfer (1902) and Waldmeier (1978). We extend their analysis until the present using the new SILSO sunspot number (version 2) and group number and confirm that the scale factors have not varied significantly the past 250 years. The effect is also found in sunspot areas, in an EUV (and F10.7) proxy (the daily range of a geomagnetic variation), and in Cosmic Ray Modulation. The result is that solar activity reached similar high values in every one of the (17th?) 18th, 19th, and 20th centuries, supporting the finding that there has been no modern Grand Maximum., Comment: 16 pages, 12 figures

Measurements of the large cellular flows on the Sun were made by local correlation tracking of supergranules seen in full-disk Doppler images obtained by the HMI instrument on the NASA SDO satellite. The hourly measurements were averaged over 34 days to produce daily maps of the latitudinal and longitudinal velocities. While flows at all latitudes are largely in the form of vortices with left-handed helicity in the north and right-handed helicity in the south, there are key distinctions between the low latitude and high latitudes cells. The low latitude cells have roughly circular shapes, lifetimes of about one month, rotate nearly rigidly, do not drift in latitude, and do not exhibit any correlation between longitudinal and latitudinal flow. The high latitude cells have long extensions that spiral inward toward the poles. They have lifetimes of several months, rotate differentially with latitude, drift poleward at speeds approaching 2 m s$^{-1}$, and have a strong correlation between prograde and equatorward flows. Spherical harmonic spectral analyses confirm that the flows are dominated by the curl component with RMS velocities of about 12 m s$^{-1}$ at wavenumber $\ell$ = 10. Fourier transforms in time indicate two notable components - an $m = \pm\ell$ feature representing the low latitude component and an $m = \pm1$ feature representing the high latitude component. The dispersion relation for the low latitude component is well represented by that derived for Rossby waves. The high latitude component has a constant temporal frequency for all $\ell$ indicating features advected by differential rotation at rates representative of the base of the convection zone high latitudes. The poleward motions of these features further suggest that the high latitude meridional flow at the base of the convection zone is poleward - not equatorward., Comment: 16 pages, 11 figures

Over the last decade there has been mounting evidence that the strength of the Sun's polar magnetic fields during a solar cycle minimum is the best predictor of the amplitude of the next solar cycle. Surface flux transport models can be used to extend these predictions by evolving the Sun's surface magnetic field to obtain an earlier prediction for the strength of the polar fields, and thus the amplitude of the next cycle. In 2016, our Advective Flux Transport (AFT) model was used to do this, producing an early prediction for Solar Cycle 25. At that time, AFT predicted that Cycle 25 will be similar in strength to the Cycle 24, with an uncertainty of about 15% . AFT also predicted that the polar fields in the southern hemisphere would weaken in late 2016 and into 2017 before recovering. That AFT prediction was based on the magnetic field configuration at the end of January 2016. We now have 2 more years of observations. We examine the accuracy of the 2016 AFT prediction and find that the new observations track well with AFT's predictions for the last two years. We show that the southern relapse did in fact occur, though the timing was off by several months. We propose a possible cause for the southern relapse and discuss the reason for the offset in timing. Finally, we provide an updated AFT prediction for Solar Cycle 25 which includes solar observations through January of 2018., Comment: 8 pages, 3 figures

Evidence strongly indicates that the strength of the Sun's polar fields near the time of a sunspot cycle minimum determines the strength of the following solar activity cycle. We use our Advective Flux Transport (AFT) code, with flows well constrained by observations, to simulate the evolution of the Sun's polar magnetic fields from early 2016 to the end of 2019 --- near the expected time of Cycle 24/25 minimum. We run a series of simulations in which the uncertain conditions (convective motion details, active region tilt, and meridional flow profile) are varied within expected ranges. We find that the average strength of the polar fields near the end of Cycle 24 will be similar to that measured near the end of Cycle 23, indicating that Cycle 25 will be similar in strength to the current cycle. In all cases the polar fields are asymmetric with fields in the south stronger than those in the north. This asymmetry would be more pronounced if not for the predicted weakening of the southern polar fields in late 2016 and through 2017. After just four years of simulation the variability across our ensemble indicates an accumulated uncertainty of about 15\%. This accumulated uncertainty arises from stochastic variations in the convective motion details, the active region tilt, and changes in the meridional flow profile. These variations limit the ultimate predictability of the solar cycle., Comment: 8 pages 7 figures Accepted for publication in Journal of Geophysical Research - Space Physics

With multiple vantage points around the Sun, STEREO and SDO imaging observations provide a unique opportunity to view the solar surface continuously. We use He II 304 A data from these observatories to isolate and track ten active regions and study their long-term evolution. We find that active regions typically follow a standard pattern of emergence over several days followed by a slower decay that is proportional in time to the peak intensity in the region. Since STEREO does not make direct observations of the magnetic field, we employ a flux-luminosity relationship to infer the total unsigned magnetic flux evolution. To investigate this magnetic flux decay over several rotations we use a surface flux transport model, the Advective Flux Transport (AFT) model, that simulates convective flows using a time-varying velocity field and find that the model provides realistic predictions when information about the active region's magnetic field strength and distribution at peak flux is available. Finally, we illustrate how 304 \AA\ images can be used as a proxy for magnetic flux measurements when magnetic field data is not accessible., Comment: ApJ in press

Spectra of the cellular photospheric flows are determined from full-disk Doppler velocity observations acquired by the Helioseismic and Magnetic Imager (HMI) instrument on the Solar Dynamics Observatory (SDO) spacecraft. Three different analysis methods are used to separately determine spectral coefficients representing the poloidal flows, the toroidal flows, and the radial flows. The amplitudes of these spectral coefficients are constrained by simulated data analyzed with the same procedures as the HMI data. We find that the total velocity spectrum rises smoothly to a peak at a wavenumber of about 120 (wavelength of about 35 Mm), which is typical of supergranules. The spectrum levels off out to wavenumbers of about 400, and then rises again to a peak at a wavenumber of about 3500 (wavelength of about 1200 km), which is typical of granules. The velocity spectrum is dominated by the poloidal flow component (horizontal flows with divergence but no curl) at wavenumbers above 30. The toroidal flow component (horizontal flows with curl but no divergence) dominates at wavenumbers less than 30. The radial flow velocity is only about 3\% of the total flow velocity at the lowest wavenumbers, but increases in strength to become about 50\% at wavenumbers near 4000. The spectrum compares well with the spectrum of giant cell flows at the lowest wavenumbers and with the spectrum of granulation from a 3D radiative-hydrodynamic simulation at the highest wavenumbers., Comment: 13 pages, 13 figures, in press in The Astrophysical Journal

The Solar Cycle is reviewed. The 11-year cycle of solar activity is characterized by the rise and fall in the numbers and surface area of sunspots. A number of other solar activity indicators also vary in association with the sunspots including; the 10.7cm radio flux, the total solar irradiance, the magnetic field, flares and coronal mass ejections, geomagnetic activity, galactic cosmic ray fluxes, and radioisotopes in tree rings and ice cores. Individual solar cycles are characterized by their maxima and minima, cycle periods and amplitudes, cycle shape, the equatorward drift of the active latitudes, hemispheric asymmetries, and active longitudes. Cycle-to-cycle variability includes the Maunder Minimum, the Gleissberg Cycle, and the Gnevyshev-Ohl (even-odd) Rule. Short-term variability includes the 154-day periodicity, quasi-biennial variations, and double-peaked maxima. We conclude with an examination of prediction techniques for the solar cycle and a closer look at cycles 23 and 24., Comment: 81 pages, 47 figures, 5 tables, Submitted Oct. 20, 2014 to Living Reviews in Solar Physics

The faster meridional flow that preceded the solar cycle 23/24 minimum is thought to have led to weaker polar field strengths, producing the extended solar minimum and the unusually weak cycle 24. To determine the impact of meridional flow variations on the sunspot cycle, we have simulated the Sun's surface magnetic field evolution with our newly developed surface flux transport model. We investigate three different cases: a constant average meridional flow, the observed time-varying meridional flow, and a time-varying meridional flow in which the observed variations from the average have been doubled. Comparison of these simulations shows that the variations in the meridional flow over cycle 23 have a significant impact (~20%) on the polar fields. However, the variations produced polar fields that were stronger than they would have been otherwise. We propose that the primary cause of the extended cycle 23/24 minimum and weak cycle 24 was the weakness of cycle 23 itself - with fewer sunspots, there was insufficient flux to build a big cycle. We also find that any polar counter-cells in the meridional flow (equatorward flow at high latitudes) produce flux concentrations at mid-to-high latitudes that are not consistent with observations., Comment: 12 Pages, 5 Figures, accepted for publication in ApJ

We have measured the meridional motions of the magnetic elements in the Sun's surface layers since 1996 and find systematic and substantial variations. In general the meridional flow speed is fast at cycle minima and slow at cycle maxima. We find that these systematic variations are characterized by a weakening of the meridional flow on the poleward sides of the active (sunspot) latitudes. This can be interpreted as a inflow toward the sunspot zones superimposed on a more general poleward meridional flow profile. We also find variations in the meridional flow which vary from cycle-to-cycle. The meridional flow was slower at both the minimum and maximum of cycle 23 compared to similar phases of cycles 21, 22, and 24. Models of the magnetic flux transport by a variable meridional flow suggest that it can significantly modulate the size and timing of the following sunspot cycle through its impact on the Sun's polar magnetic fields. We suggest that the meridional flow variations observed in cycle 23 contributed to the weak polar fields at the end of the cycle which then produced a weak cycle 24 and the extraordinary cycle 23/24 minimum., Comment: 6 Pages, 6 Figures, to be published in J. Geophys. Res. - Space Sci

Heat is transported through the outermost 30% of the Sun's interior by overturning convective motions. These motions are evident at the Sun's surface in the form of two characteristic cellular structures - granules and supergranules (~1000 and ~30,000 km across respectively). The existence of much larger cells has been suggested by both theory and observation for over 45 years. We found evidence for giant cellular flows that persist for months by tracking the motions of supergranules. As expected from the effects of the Sun's rotation, the flows in these cells are clockwise around high pressure in the north, counter-clockwise in the south and transport angular momentum toward the equator, maintaining the Sun's rapid equatorial rotation., Comment: 11 pages, 7 figures

The Sun's polar magnetic fields are directly related to solar cycle variability. The strength of the polar fields at the start (minimum) of a cycle determine the subsequent amplitude of that cycle. In addition, the polar field reversals at cycle maximum alter the propagation of galactic cosmic rays throughout the heliosphere in fundamental ways. We describe a surface magnetic flux transport model that advects the magnetic flux emerging in active regions (sunspots) using detailed observations of the near-surface flows that transport the magnetic elements. These flows include the axisymmetric differential rotation and meridional flow and the non-axisymmetric cellular convective flows (supergranules) all of which vary in time in the model as indicated by direct observations. We use this model with data assimilated from full-disk magnetograms to produce full surface maps of the Sun's magnetic field at 15-minute intervals from 1996 May to 2013 July (all of sunspot cycle 23 and the rise to maximum of cycle 24). We tested the predictability of this model using these maps as initial conditions, but with daily sunspot area data used to give the sources of new magnetic flux. We find that the strength of the polar fields at cycle minimum and the polar field reversals at cycle maximum can be reliably predicted up to three years in advance. We include a prediction for the cycle 24 polar field reversal., Comment: 12 pages, 9 figures, ApJ accepted

Among many other measurable quantities the summer of 2009 saw a considerable low in the radiative output of the Sun that was temporally coincident with the largest cosmic ray flux ever measured at 1AU. A hemispheric asymmetry in magnetic activity is clearly observed and its evolution monitored and the resulting (prolonged) magnetic imbalance must have had a considerable impact on the structure and energetics of the heliosphere. While we cannot uniquely tie the variance and scale of the surface magnetism to the dwindling radiative and particulate output of the star, or the increased cosmic ray flux through the 2009 minimum, the timing of the decline and rapid recovery in early 2010 would appear to inextricably link them. These observations support a picture where the Sun's hemispheres are significantly out of phase with each other. Studying historical sunspot records with this picture in mind shows that the northern hemisphere has been leading since the middle of the last century and that the hemispheric "dominance" has changed twice in the past 130 years. The observations presented give clear cause for concern, especially with respect to our present understanding of the processes that produce the surface magnetism in the (hidden) solar interior - hemispheric asymmetry is the normal state - the strong symmetry shown in 1996 was abnormal. Further, these observations show that the mechanism(s) which create and transport the magnetic flux magnetic flux are slowly changing with time and, it appears, with only loose coupling across the equator such that those asymmetries can persist for a considerable time. As the current asymmetry persists and the basal energetics of the system continue to dwindle we anticipate new radiative and particulate lows coupled with increased cosmic ray fluxes heading into the next solar minimum., Comment: Accepted to appear in the ApJ - 44 pages in referee format

The meridional circulation at high latitudes is crucial to the build-up and reversal of the Sun's polar magnetic fields. Here we characterize the axisymmetric flows by applying a magnetic feature cross-correlation procedure to high resolution magnetograms obtained by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). We focus on Carrington Rotations 2096-2107 (April 2010 to March 2011) - the overlap interval between HMI and the Michelson Doppler Investigation (MDI). HMI magnetograms averaged over 720 seconds are first mapped into heliographic coordinates. Strips from these maps are then cross-correlated to determine the distances in latitude and longitude that the magnetic element pattern has moved, thus providing meridional flow and differential rotation velocities for each rotation of the Sun. Flow velocities were averaged for the overlap interval and compared to results obtained from MDI data. This comparison indicates that these HMI images are rotated counter-clockwise by 0.075 degrees with respect to the Sun's rotation axis. The profiles indicate that HMI data can be used to reliably measure these axisymmetric flow velocities to at least within 5 degrees of the poles. Unlike the noisier MDI measurements, no evidence of a meridional flow counter-cell is seen in either hemisphere with the HMI measurements: poleward flow continues all the way to the poles. Slight North-South asymmetries are observed in the meridional flow. These asymmetries should contribute to the observed asymmetries in the polar fields and the timing of their reversals., Comment: 6 pages, 3 color figures, accepted for publication in The Astrophysical Journal Letter

Recent analysis revealed that supergranules (convection cells seen at the Sun's surface) are advected by the zonal flows at depths equal to the widths of the cells themselves. Here we probe the structure of the meridional circulation by cross-correlating maps of the Doppler velocity signal using a series of successively longer time lags between maps. We find that the poleward meridional flow decreases in amplitude with time lag and reverses direction to become an equatorward return flow at time lags > 24 hours. These cross-correlation results are dominated by larger and deeper cells at longer time lags. (The smaller cells have shorter lifetimes and do not contribute to the correlated signal at longer time lags.) We determine the characteristic cell size associated with each time lag by comparing the equatorial zonal flows measured at different time lags with the zonal flows associated with different cell sizes from a Fourier analysis. This association gives a characteristic cell size of ~50 Mm at a 24 hour time lag. This indicates that the poleward meridional flow returns equatorward at depths > 50 Mm -- just below the base of the surface shear layer. A substantial and highly significant equatorward flow (4.6 +/- 0.4 m/s) is found at a time lag of 28 hours corresponding to a depth of ~70 Mm. This represents one of the first positive detections of the Sun's meridional return flow and illustrates the power of using supergranules to probe the Sun's internal dynamics., Comment: 8 pages, 5 color figures, accepted for publication in The Astrophysical Journal

Supergranules are convection cells seen at the Sun's surface as a space filling pattern of horizontal flows. While typical supergranules have diameters of about 35 Mm, they exhibit a broad spectrum of sizes from ~10 Mm to ~100 Mm. Here we show that supergranules of different sizes can be used to probe the rotation rate in the Sun's outer convection zone. We find that the equatorial rotation rate as a function of depth as measured by global helioseismology matches the equatorial rotation as a function of wavelength for the supergranules. This suggests that supergranules are advected by flows at depths equal to their wavelengths and thus can be used to probe flows at those depths. The supergranule rotation profiles show that the surface shear layer, through which the rotation rate increases inward, extends to depths of ~50 Mm and to latitudes of at least 70 degrees. Typical supergranules are well observed at high latitudes and have a range of sizes that extend to greater depths than those typically available for measuring subsurface flows with local helioseismology. These characteristics indicate that probing the solar convection zone dynamics with supergranules can complement the results of helioseismology., Comment: 6 pages, 3 figures, Accepted for publication in The Astrophysical Journal Letters

The Sun's global meridional circulation is evident as a slow poleward flow at its surface. This flow is observed to carry magnetic elements poleward - producing the Sun's polar magnetic fields as a key part of the 11-year sunspot cycle. Current theories for the sunspot cycle assume that this surface flow is part of a circulation which sinks inward at the poles and turns equatorward at depths below 100 Mm. Here we use the advection of the Sun's convection cells by the meridional flow to map the flow velocity in latitude and depth. Our measurements show the largest cells clearly moving equatorward at depths below 35 Mm - the base of the Sun's surface shear layer. This surprisingly shallow return flow indicates the need for substantial revisions to solar/stellar dynamo theory., Comment: 10 pages, 3 color figures, revised

We measure the axisymmetric transport of magnetic flux on the Sun by cross-correlating narrow strips of data from line-of-sight magnetograms obtained at a 96-minute cadence by the MDI instrument on the ESA/NASA SOHO spacecraft and then averaging the flow measurements over each synodic rotation of the Sun. Our measurements indicate that the axisymmetric flows vary systematically over the solar cycle. The differential rotation is weaker at maximum than at minimum. The meridional flow is faster at minimum and slower at maximum. The meridional flow speed on the approach to the Cycle 23/24 minimum was substantially faster than it was at the Cycle 22/23 minimum. The average latitudinal profile is largely a simple sinusoid that extends to the poles and peaks at about $35\degr$ latitude. As the cycle progresses a pattern of in-flows toward the sunspot zones develops and moves equatorward in step with the sunspot zones. These in-flows are accompanied by the torsional oscillations. This association is consistent with the effects of the Coriolis force acting on the in-flows. The equatorward motions associated with these in-flows are identified as the source of the decrease in net poleward flow at cycle maxima. We also find polar counter-cells (equatorward flow at high latitudes) in the south from 1996 to 2000 and in the north from 2002 to 2010. We show that these measurements of the flows are not affected by the non-axisymmetric diffusive motions produced by supergranulation., Comment: 13 pages, 11 figures

We show that the motions of supergranules are consistent with a model in which they are simply advected by the axisymmetric flows in the Sun's surface shear layer. We produce a 10-day series of simulated Doppler images at a 15-minute cadence that reproduces most spatial and temporal characteristics seen in the SOHO/MDI Doppler data. Our simulated data have a spectrum of cellular flows with just two components -- a granule component that peaks at spherical wavenumbers of about 4000 and a supergranule component that peaks at wavenumbers of about 110. We include the advection of these cellular components by the axisymmetric flows -- differential rotation and meridional flow -- whose variations with latitude and depth (wavenumber) are consistent with observations. We mimic the evolution of the cellular pattern by introducing random variations to the phases of the spectral components at rates that reproduce the levels of cross-correlation as functions of time and latitude. Our simulated data do not include any wave-like characteristics for the supergranules yet can reproduce the rotation characteristics previously attributed to wave-like behavior. We find rotation rates which appear faster than the actual rotation rates and attribute this to the projection effects. We find that the measured meridional flow does accurately represent the actual flow and that the observations indicate poleward flow to $65\degr-70\degr$ latitude with equatorward counter cells in the polar regions., Comment: 15 pages, 8 figures

This deep, extended solar minimum and the slow start to Cycle 24 strongly suggest that Cycle 24 will be a small cycle. A wide array of solar cycle prediction techniques have been applied to predicting the amplitude of Cycle 24 with widely different results. Current conditions and new observations indicate that some highly regarded techniques now appear to have doubtful utility. Geomagnetic precursors have been reliable in the past and can be tested with 12 cycles of data. Of the three primary geomagnetic precursors only one (the minimum level of geomagnetic activity) suggests a small cycle. The Sun's polar field strength has also been used to successfully predict the last three cycles. The current weak polar fields are indicative of a small cycle. For the first time, dynamo models have been used to predict the size of a solar cycle but with opposite predictions depending on the model and the data assimilation. However, new measurements of the surface meridional flow indicate that the flow was substantially faster on the approach to Cycle 24 minimum than at Cycle 23 minimum. In both dynamo predictions a faster meridional flow should have given a shorter cycle 23 with stronger polar fields. This suggests that these dynamo models are not yet ready for solar cycle prediction., Comment: SOHO 23 Workshop (SOHO-23: Understanding a Peculiar Solar Minimum, Northeast Harbor, ME, USA, 2009 September 21-25) Invited Paper, 8 pages, 9 figures

We produce a 10-day series of simulated Doppler images at a 15-minute cadence that reproduces the spatial and temporal characteristics seen in the SOHO/MDI Doppler data. Our simulated data contains a spectrum of cellular flows with but two necessary components --- a granule component that peaks at wavenumbers of about 4000 and a supergranule component that peaks at wavenumbers of about 110. We include the advection of these cellular components by a differential rotation profile that depends on latitude and wavenumber (depth). We further mimic the evolution of the cellular pattern by introducing random variations to the amplitudes and phases of the spectral components at rates that reproduce the level of cross-correlation as a function of time and latitude. Our simulated data do not include any wave-like characteristics for the supergranules yet can accurately reproduce the rotation characteristics previously attributed to wave-like characteristics., Comment: GONG 2008/SOHO 21 Meeting (Solar-stellar dynamos as revealed by helio- and asteroseismology, Boulder, CO, USA, August 11-15, 2008), 6 pages, 2 figures

The existence of Giant Cells has been suggested by both theory and observation for over 45 years. We have tracked the motions of supergranules in SDO/HMI Doppler velocity data and find larger (Giant Cell) flows that persist for months. The flows in these cells are clockwise around centers of divergence in the north and counter-clockwise in the south. Equatorward flows are correlated with prograde flows - giving the transport of angular momentum toward the equator that is needed to maintain the Sun's rapid equatorial rotation. The cells are most pronounced at mid- and high-latitudes where they exhibit the rotation rates representative of those latitudes. These are clearly large, long-lived, cellular features, with the dynamical characteristics expected from the effects of the Sun's rotation, but the shapes of the cells are not well represented in numerical models. While the Giant Cell flow velocities are small (<10 m/s), their long lifetimes should nonetheless substantially impact the transport of magnetic flux in the Sun's near surface layers.

The International Sunspot Number is used as a measure of the level of solar activity in many important studies. This includes studies of the effects of solar activity on climate change and on the generation of radioisotopes used to infer levels of solar activity going back thousands of years. Any systematic errors in the historical record of the sunspot number can profoundly alter the conclusions of these studies. There is substantial evidence that the currently accepted International Sunspot Numbers have been subjected to changes in the way the numbers are calculated and to changes in the weights given to observations of various observers. In this talk I will focus on the time period from 1826 to 1980 which covers principal observers Schwabe, Wolf, Wolfer, Brunner, and Waldmeier. Previous investigations have indicated problems associated with Schwabe's observations (1826 to 1867), the first decades of the Greenwich observations (1874 to about 1910), and the introduction of a different counting method by Waldmeier (1946-1980). I will examine the evidence for these problems and the possible solutions that might be used to provide improved estimates of the sunspot numbers and their errors over this time interval.

The polar fields on the Sun are directly related to solar cycle variability. Recently there has been interest in studying an important characteristic of the polar fields: the timing of the polar field reversals. However this characteristic has been poorly defined, mostly due to the limitations of early observations. In the past, the reversals have been calculated by averaging the flux above some latitude (i.e. 55deg or 75deg). Alternatively, the reversal could be defined by the time in which the previous polarity is completely canceled and replaced by the new polarity at 90de, precisely at the pole. We will use a surface flux transport model to illustrate the differences in the timing of the polar field reversal based on each of these definitions and propose standardization in the definition of the polar field reversal. The ability to predict the timing of the polar field reversal using a surface flux transport model will also be discussed.

We have measured the meridional motions of magnetic elements observed in the photosphere over sunspot cycles 23 and 24 using magnetograms from SOHO/MDI and SDO/HMI. Our measurements confirm the finding of Komm, Howard, and Harvey (1993) that the poleward meridional flow weakens at cycle maxima. Our high spatial and temporal resolution analyses show that this variation is in the form of a superimposed inflow toward the active latitudes. This inflow is weaker in cycle 24 when compared to the inflow in 23, the stronger cycle. This systematic modulation of the meridional flow should also modulate the amplitude of the following sunspot cycle through its influence on the Sun's polar fields. The observational evidence and the theoretical consequences (similar to those of Cameron and Schussler (2012)) will be described.

The cause of the low and extended minimum in solar activity between Sunspot Cycles 23 and 24 was the small size of Sunspot Cycle 24 itself - small cycles start late and leave behind low minima. Cycle 24 is small because the polar fields produced during Cycle 23 were substantially weaker than those produced during the previous cycles and those (weak) polar fields are the seeds for the activity of the following cycle. The polar fields are produced by the latitudinal transport of magnetic flux that emerged in low-latitude active regions. The polar fields thus depend upon the details of both the flux emergence and the flux transport. We have measured the flux transport flows (differential rotation, meridional flow, and supergranules) since 1996 and find systematic and substantial variation in the meridional flow alone. Here we present experiments using a Surface Flux Transport Model in which magnetic field data from SOHO/MDI and SDO/HMI are assimilated into the model only at latitudes between 45-degrees north and south of the equator (this assures that the details of the active region flux emergence are well represented). This flux is then transported in both longitude and latitude by the observed flows. In one experiment the meridional flow is given by the time averaged (and north-south symmetric) meridional flow profile. In the second experiment the time-varying and north-south asymmetric meridional flow is used. Differences between the observed polar fields and those produced in these two experiments allow us to ascertain the effects of these meridional flow variations on the Sun s polar fields.

We simulate the transport of magnetic flux in the Sun s photosphere by an evolving pattern of cellular horizontal flows (supergranules). Characteristics of the simulated flow pattern match observed characteristics including the velocity power spectrum, cell lifetimes, and cell pattern motion in longitude and latitude. Simulations using an average, and north-south symmetric, meridional motion of the cellular pattern produce polar magnetic fields that are too weak in the North and too strong in the South. Simulations using cellular patterns with meridional motions that evolve with the observed changes in strength and north-south asymmetry will be analyzed to see if they reproduce the polar field evolution observed during the rise of Cycle 24.

Aspects of the structure and dynamics of the flows in the Sun's surface shear layer remain uncertain and yet are critically important for understanding the observed magnetic behavior. In our previous studies of the axisymmetric transport of magnetic elements we found systematic changes in both the differential rotation and the meridional flow over the course of Solar Cycle 23. Here we examine how those flows depend upon the strength (and presumably anchoring depth) of the magnetic elements. Line of sight magnetograms obtained by the HMI instrument aboard SDO over the course of Carrington Rotation 2097 were mapped to heliographic coordinates and averaged over 12 minutes to remove the 5-min oscillations. Data masks were constructed based on the field strength of each mapped pixel to isolate magnetic elements of differing field strength. We used Local Correlation Tracking of the unmasked data (separated in time by 1- to 8-hours) to determine the longitudinal and latitudinal motions of the magnetic elements. We then calculated average flow velocities as functions of latitude and longitude from the central meridian for approx 600 image pairs over the 27-day rotation. Variations with longitude indicate and characterize systematic errors in the flow measurements associated with changes in the signal from disk center to limb. Removing these systematic errors reveals changes in the axisymmetric flow properties that reflect changes in flow properties with depth in the surface shear layer.

Several indices are used to characterize the solar activity cycle. Key among these are: the International Sunspot Number, the Group Sunspot Number, Sunspot Area, and 10.7 cm Radio Flux. A valuable aspect of these indices is the length of the record -- many decades and many (different) 11-year cycles. However, this valuable length-of-record attribute has an inherent problem in that it requires many different observers and observing systems. This can lead to non-uniformity in the datasets and subsequent erroneous conclusions about solar cycle behavior. The sunspot numbers are obtained by counting sunspot groups and individual sunspots on a daily basis. This suggests that the day-to-day and month-to-month variations in these numbers should follow Poisson Statistics and be proportional to the square-root of the sunspot numbers themselves. Examining the historical records of these indices indicates that this is indeed the case - even with Sunspot Area and 10.7 cm Radio Flux. The ratios of the RMS variations to the square-root of the indices themselves are relatively constant with little variation over the phase of each solar cycle or from small to large solar cycles. There are, however, important step-like changes in these ratios associated with changes in observer and/or observer system. Here we show how these variations can be used to construct more uniform datasets.

Observations of the transport of magnetic flux in the Sun's photosphere show that active region magnetic flux is carried far from its origin by a combination of flows. These flows have previously been identified and modeled as separate axisymmetric processes: differential rotation, meridional flow, and supergranule diffusion. Experiments with a surface convective flow model reveal that the true nature of this transport is advection by the non-axisymmetric cellular flows themselves - supergranules. Magnetic elements are transported to the boundaries of the cells and then follow the evolving boundaries. The convective flows in supergranules have peak velocities near 500 m/s. These flows completely overpower the superimposed 20 m/s meridional flow and 100 m/s differential rotation. The magnetic elements remain pinned at the supergranule boundaries. Experiments with and without the superimposed axisymmetric photospheric flows show that the axisymmetric transport of magnetic flux is controlled by the advection of the cellular pattern by underlying flows representative of deeper layers. The magnetic elements follow the differential rotation and meridional flow associated with the convection cells themselves -- supergranules rule!

The latitudinal location of the sunspot zones in each hemisphere is determined by calculating the centroid position of sunspot areas for each solar rotation from May 1874 to June 2012. When these centroid positions are plotted and analyzed as functions of time from each sunspot cycle maximum there appears to be systematic differences in the positions and equatorward drift rates as a function of sunspot cycle amplitude. If, instead, these centroid positions are plotted and analyzed as functions of time from each sunspot cycle minimum then most of the differences in the positions and equatorward drift rates disappear. The differences that remain disappear entirely if curve fitting is used to determine the starting times (which vary by as much as 8 months from the times of minima). The sunspot zone latitudes and equatorward drift measured relative to this starting time follow a standard path for all cycles with no dependence upon cycle strength or hemispheric dominance. Although Cycle 23 was peculiar in its length and the strength of the polar fields it produced, it too shows no significant variation from this standard. This standard law, and the lack of variation with sunspot cycle characteristics, is consistent with Dynamo Wave mechanisms but not consistent with current Flux Transport Dynamo models for the equatorward drift of the sunspot zones.

The Sun s global magnetic field is produced and evolved through the emergence of magnetic flux in active regions and its transport across the solar surface by the axisymmetric differential rotation and meridional flow and the non-axisymmetric convective flows of granulation, supergranulation, and giant cell convection. Maps of the global magnetic field serve as the inner boundary condition for space weather. The photospheric magnetic field and its evolution determine the coronal and solar wind structures through which CMEs must propagate and in which solar energetic particles are accelerated and propagate. Producing magnetic maps which best represent the actual field configuration at any instant requires knowing the magnetic field over the observed hemisphere as well as knowing the flows that transport flux. From our Earth-based vantage point we only observe the front-side hemisphere and each pole is observable for only six months of the year at best. Models for the surface magnetic flux transport can be used to provide updates to the magnetic field configuration in those unseen regions. In this presentation I will describe successes and failures of surface flux transport and present new observations on the structure, the solar cycle variability, and the evolution of the flows involved in magnetic flux transport. I find that supergranules play the dominant role due to their strong flow velocities and long lifetimes. Flux is transported by differential rotation and meridional flow only to the extent that the supergranules participate in those two flows.

This deep, extended solar minimum and the slow start to Cycle 24 strongly suggest that Cycle 24 will be a small cycle. A wide array of solar cycle prediction techniques have been applied to predicting the amplitude of Cycle 24 with widely different results. Current conditions and new observations indicate that some highly regarded techniques now appear to have doubtful utility. Geomagnetic precursors have been reliable in the past and can be tested with 12 cycles of data. Of the three primary geomagnetic precursors only one (the minimum level of geomagnetic activity) suggests a small cycle. The Sun's polar field strength has also been used to successfully predict the last three cycles. The current weak polar fields are indicative of a small cycle. For the first time, dynamo models have been used to predict the size of a solar cycle but with opposite predictions depending on the model and the data assimilation. However, new measurements of the surface meridional flow indicate that the flow was substantially faster on the approach to Cycle 24 minimum than at Cycle 23 minimum. In both dynamo predictions a faster meridional flow should have given a shorter cycle 23 with stronger polar fields. This suggests that these dynamo models are not yet ready for solar cycle prediction.

A method of stabilizing a video image displayed in multiple video fields of a video sequence includes the steps of: subdividing a selected area of a first video field into nested pixel blocks; determining horizontal and vertical translation of each of the pixel blocks in each of the pixel block subdivision levels from the first video field to a second video field; and determining translation of the image from the first video field to the second video field by determining a change in magnification of the image from the first video field to the second video field in each of horizontal and vertical directions, and determining shear of the image from the first video field to the second video field in each of the horizontal and vertical directions.