yes / We derive two principal components (PCs) of temporal magnetic field variations over the solar cycles 21–24 from full disk magnetograms covering about 39% of data variance, with σ = 0.67. These PCs are attributed to two main magnetic waves travelling from the opposite hemispheres with close frequencies and increasing phase shift. Using symbolic regeression analysis we also derive mathematical formulae for these waves and calculate their summary curve which we show is linked to solar activity index. Extrapolation of the PCs backward for 800 years reveals the two 350-year grand cycles superimposed on 22 year-cycles with the features showing a remarkable resemblance to sunspot activity reported in the past including the Maunder and Dalton minimum. The summary curve calculated for the next millennium predicts further three grand cycles with the closest grand minimum occurring in the forthcoming cycles 26–27 with the two magnetic field waves separating into the opposite hemispheres leading to strongly reduced solar activity. These grand cycle variations are probed by α − Ω dynamo model with meridional circulation. Dynamo waves are found generated with close frequencies whose interaction leads to beating effects responsible for the grand cycles (350–400 years) superimposed on a standard 22 year cycle. This approach opens a new era in investigation and confident prediction of solar activity on a millenium timescale.

L’étude de l’impact des changements climatiques passés sur le domaine continental permet de comprendre les mécanismes, les vitesses et le calendrier des réponses des écosystèmes aux perturbations.La Transition Eocène-Oligocène (TEO) de la limite Eocène-Oligocène (EOb) se prête bien à ce type d’étude car elle enregistre la dernière transition climatique entre le mode greenhouse et le mode icehouse en passant par un intervalle mal compris : le doubthouse. Cette transition climatique a été étudiée sur un enregistrement lacustre riche en Matière Organique. Le modèle d’âge est construit par cyclostratigraphie,les évolutions de la végétation par des biomarqueurs moléculaires, et le climat local (température ethydrologie) par des proxies moléculaires et isotopiques. Les évolutions du climat mettent en évidence un refroidissement et une aridification marqués, en réponse au refroidissement EO. La végétation ne montre pas ce changement brutal, mais des changements rythmiques et marqués, en phase avec l’excentricité,durant un intervalle qui commence 1750 ka avant l’EOb et qui se termine 300 ka après. Cet intervalle qualifié d’Intervalle de Transition Environnementale (ITE), plus chaud et plus humide, coïncide avec le doubthouse. La mise en place de cet ITE correspond à un enregistrement distinct des paramètres orbitaux.Une meilleure expression des cycles solaires dans les sédiments résulte de la mise en place ou du renforcement des couplages océan-atmosphère, en relation avec l’installation de la calotte antarctique. Au total, ce travail résout en partie les incertitudes qui régnaient jusqu’alors sur le doubthouse. / The study of past climate changes on the terrestrial realm provides clues to understand the mechanisms,chronology, and timing of ecosystems response to climate disturbances. The Eocene-Oligocene Transition(EOT) of the Eocene-Oligocene boundary (EOb) is well suited for this type of study because it records the last climatic transition between the greenhouse and icehouse modes via a misunderstood interval: thedoubthouse period. This climatic transition was studied through the analysis of organic-rich lacustrine sediments. After an astro-calibrated age model was set up, we reconstructed the evolution of vegetation by using molecular biomarkers specific of plant groups and of local climate (temperature and hydrological conditions) by using molecular and isotopic proxies. The climate record exhibits a marked cooling and drying at the EOT. The evolution of vegetation did not show any abrupt change but exhibited pronounced and rhythmic changes in phase with excentricity during an interval that started 1750 ka before the EOb and lasted until 300 ka after. This interval named Environmental Transition Interval (ETI) was warmer and wetter, and coincides with the doubthouse period. The start of the ETI is concomitant with changes in the recording of orbital parameters. The good expression of solar cycles in the sediments from that period attests to the setting or strengthening of ocean-atmosphere couplings linked to the establishment of the Antarctic icesheet. This work partly solves the uncertainties that prevailed on the doubthouse period.

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yes / A comprehensive spectral analysis of both the solar background magnetic field (SBMF) in cycles 21-23 and the sunspot magnetic field in cycle 23 reported in our recent paper showed the presence of two principal components (PCs) of SBMF having opposite polarity, e. g., originating in the northern and southern hemispheres, respectively. Over a duration of one solar cycle, both waves are found to travel with an increasing phase shift toward the northern hemisphere in odd cycles 21 and 23 and to the southern hemisphere in even cycle 22. These waves were linked to solar dynamo waves assumed to form in different layers of the solar interior. In this paper, for the first time, the PCs of SBMF in cycles 21-23 are analyzed with the symbolic regression technique using Hamiltonian principles, allowing us to uncover the underlying mathematical laws governing these complex waves in the SBMF presented by PCs and to extrapolate these PCs to cycles 24-26. The PCs predicted for cycle 24 very closely fit (with an accuracy better than 98%) the PCs derived from the SBMF observations in this cycle. This approach also predicts a strong reduction of the SBMF in cycles 25 and 26 and, thus, a reduction of the resulting solar activity. This decrease is accompanied by an increasing phase shift between the two predicted PCs (magnetic waves) in cycle 25 leading to their full separation into the opposite hemispheres in cycle 26. The variations of the modulus summary of the two PCs in SBMF reveals a remarkable resemblance to the average number of sunspots in cycles 21-24 and to predictions of reduced sunspot numbers compared to cycle 24: 80% in cycle 25 and 40% in cycle 26.

Our Sun is a variable star. The magnetic fields in the Sun play an important role for the existence of a wide variety of phenomena on the Sun. Among those, sunspots are the slowly evolving features of the Sun but solar ares and coronal mass ejections are highly dynamic phenomena. Hence, the solar magnetic fields could affect the Earth directly or indirectly through the Sun's open magnetic flux, solar wind, solar are, coronal mass ejections and total solar irradiance variations. These large scale magnetic fields originate due to Magnetohydrodynamic dynamo process inside the solar convection zone converting the kinetic energy of the plasma motions into the magnetic energy. Currently the most promising model to understand the large scale magnetic fields of the Sun is the Flux Transport Dynamo (FTD) model. FTD models are mostly axisymmetric models, though the non-axisymmetric 3D FTD models are started to develop recently. In these models, we assume the total magnetic fields of the Sun consist of poloidal and toroidal components and solve the magnetic induction equation kinematicaly in the sense that velocity fields are invoked motivated from the observations. Differential rotation stretches the poloidal field to generate the toroidal field. When toroidal eld near the bottom of the convection zone become magnetically buoyant, it rises through the solar convection zone and pierce the surface to create bipolar sunspots. While rising through the solar convection zone, the Coriolis force keeps on acting on the flux tube, which introduces a tilt angle between bipolar sunspots. Since the sunspots are the dense region of magnetic fields, they diffuse away after emergence. The leading polarity sunspots (close to equator) from both the hemisphere cancel each other across the equator and trailing polarity sunspots migrate towards the pole to generate effective poloidal fields. This mechanism for generation of poloidal field from the decay of sunspots is known as Babcock-Leighton process. After the poloidal field is generated, the meridional flow carries this field to the pole and further to the bottom of the convection zone where differential rotation again acts on it to generate toroidal field. Hence the solar dynamo goes on by oscillation between the poloidal field and toroidal field, where they can sustain each other through a cyclic feedback process. Just like other physical models, FTD models have various assumptions and approximations to incorporate these different processes. Some of the assumptions are observationally verified and some of them are not. Considering the availability of observed data, many approximations have been made in these models on the theoretical basis. In this thesis, we present various studies leading to better understanding of the different processes and parameters of FTD models, which include magnetic buoyancy, meridional circulation and Babcock-Leighton process. In the introductory Chapter 1, we first present the observational features of the solar magnetic fields, theoretical background of the FTD models and motivation for investigating different processes. Most of the results of our work are presented in Chapters 2 - 7. In the Chapters 2 - 5, we explain various important issues regarding the treatment of magnetic buoyancy, irregularities of the solar cycle during descending phase, effect of different spatial structure of meridional flow on the dynamo and how dynamo generated fields would a ect the meridional ow using 2D axisymmetric Flux Transport Dynamo model. In the Chapters 6 & 7, the build up of polar fields from the decay of sunspots and a proper treatment of Babcock-Leighton process by invoking realistic convective flows, are presented using 3D Flux Transport Dynamo model. Finally the conclusions and future works are given in the Chapter 8. In 2D axisymmetric Flux Transport Dynamo models, the rise of the toroidal magnetic field through the convection zone due to magnetic buoyancy and then the generation of the poloidal magnetic field from these bipolar sunspots, has been treated mainly in two ways|a non-local method and a local method. In Chapter 2, we have analyzed the advantages and disadvantages of both the methods. We find that none of them are satisfactory to depict the correct picture of magnetic buoyancy because it is an inherently 3D process. Unless we go to the 3D framework of Flux Transport Dynamo models, we have to treat the magnetic buoyancy in such simplistic way. We find that the non-local treatment of magnetic buoyancy is very robust for a large span of parameter space but it does not take into account the depletion of flux from the bottom of the convection zone which has a significant importance in irregularity study of the solar cycle. The local treatment of magnetic buoyancy includes the flux depletion from the bottom of the convection zone and treats the magnetic buoyancy much realistically than the non-local treatment. But this local treatment of magnetic buoyancy is not so robust. We also pointed out that the long-standing issue about appearance of sunspots in the low-latitudes needs to be studied carefully. In Chapter 3, we have studied various irregularities of the solar cycle during its decaying phase. We have reported that the decay rate of the cycle is strongly correlated with amplitude of the same cycle as well as the amplitude of the next cycle from different sunspot proxies like sunspot number, sunspot area and 10.7 cm radio flux data. We explain these correlation from flux transport dynamo models. We nd that the correlations can only be reproduced if we introduce stochastic fluctuations in the meridional circulations. We also reproduced most of the correlation found in ascending and descending phase of the solar cycle from century long sunspot area data (Mandal et al., 2017) from Kodaikanal observatory, India which are in great agreement with the correlations found earlier from Greenwich sunspots data. In most of the FTD models, a single cell meridional circulation is assumed within the solar convection zone, with the equatorward return flow at its bottom. But with recent development in helioseismology, plenty of results have come out about various spatial structure of meridional circulation (Zhao et al., 2013; Schad et al., 2013; Rajaguru & Antia, 2015; Jackiewicz et al., 2015). Some helioseismology group (Zhao et al., 2013) reported that the meridional circulation has a double cell structure in solar convection zone and some groups (Schad et al., 2013; Jackiewicz et al., 2015) have reported a multi-cellular structure of meridional circulation in the convection zone. By probing the supergranular motion Hathaway (2012) estimated that the meridional ow has an equatorward return ow at the upper convection zone 70 Mm below the surface. In view of the above observed results, we have discussed in Chapter 4 what would happen to Flux Transport Dynamo model if we consider other structure of meridional circulation instead of single cell meridional circulation encompassing whole convection zone. We nd that the our dynamo model works perfectly ne as long as there is an equatorward propagation at the bottom of the convection zone. Our model also works with shallow meridional circulation as found by Hathaway (2012), if we consider the latitudinal pumping in our model. The temporal variation of meridional circulation on the surface is also observed from various measurement techniques. Chou & Dai (2001) rst observed a variation of meridional circulation with the solar cycle from their helioseismic measurements. Hathaway & Rightmire (2010) also found a variation up to 5 m s 1 for the solar cycle 23 by measuring the magnetic elements on the surface of the Sun. Recently Komm et al. (2015) have analyzed MDI and HMI Dopplergram data and reported a solar cyclic variation with detail latitudinal dependence. To explain this variation of the meridional circulation with the solar cycle, we construct a theoretical model by coupling the equation of the meridional circulation (the component of the vorticity equation within the solar convection zone) with the equations of the flux transport dynamo model in Chapter 5. We consider the back reaction due to the Lorentz force of the dynamo-generated magnetic fields and study the perturbations produced in the meridional circulation due to it. This enables us to model the variations of the meridional circulation without developing a full theory of the meridional circulation itself. We obtain results which reproduce the observational data of solar cycle variations of the meridional circulation reasonably well. We get the best results on assuming the turbulent viscosity acting on the velocity field to be comparable to the magnetic diffusivity (i.e. on assuming the magnetic Prandtl number to be close to unity). We have to assume an appropriate bottom boundary condition to ensure that the Lorentz force cannot drive a flow in the sub-adiabatic layers below the bottom of the tachocline. Our results are sensitive to this bottom boundary condition. We also suggest a hypothesis how the observed inward flow towards the active regions may be produced. In Chapter 6 and Chapter 7, we have studied some of the aspects of solar magnetic eld generation process using 3D dynamo model that were not possible to study earlier using axisymmetric 2D Flux Transport dynamo models. We have used the 3D dynamo model developed by Mark Miesch (Miesch & Dikpati, 2014; Miesch & Teweldebirhan, 2016) and study how polar fields build up from the decay of sunspots more realistically in Chapter 6. We first reproduce the observed butter y diagram and periodic solution considering higher diffusivity value than earlier reported results and use it as a reference model to study the build up polar fields by putting a single sunspot pair in one hemisphere and two sunspot pairs in both the hemispheres. The build up of the polar fields from the decay of sunspots are studied earlier using Surface Flux Transport model (Wang et al., 1989; Baumann et al., 2004; Cameron et al., 2010) which solve only radial component of the induction equation on the surface of the Sun ( | plane). But these 2D SFT models have some inherent limitation for not considering the 3D vectorial nature of the magnetic fields and subsurface processes. We have shown that not considering the vectorial nature and subsurface process has an important effect on the development of the polar fields. We have also studied the effect of a few large sunspot pairs violating Hale's law on the strength of the polar field in this Chapter. We nd that such ant-Hale sunspot pairs do produce some effect on the polar fields, if they appear at higher latitudes during the mid-phase of the solar cycle|but the effect is not dramatic. In Chapter 7, we have incorporated observed surface convective ows directly in our 3D dynamo model. As we know that the observed convective flows on the photosphere (e.g., supergranulation, granulation) play a key role in the Babcock-Leighton (BL) process to generate large scale polar fields from sunspots fields. In most surface flux transport (SFT) and BL dynamo models, the dispersal and migration of surface fields is modeled as an effective turbulent diffusion. Recent SFT models have incorporated explicit, realistic convective flows in order to improve the fidelity of convective transport but, to our knowledge, this has not yet been implemented in previous BL models. Since most Flux-Transport (FT)/BL models are axisymmetric, they do not have the capacity to include such flows. We present the first kinematic 3D FT/BL model to explicitly incorporate realistic convective flows based on solar observations. Though we describe a means to generalize these flows to 3D, we find that the kinematic small-scale dynamo action they produce disrupts the operation of the cyclic dynamo. Cyclic solution is found by limiting the convective flow to surface flux transport. The results obtained are generally in good agreement with the observed surface flux evolution and with non-convective models that have a turbulent diffusivity on the order of 3 1012 cm 2 s 1 (300 km2 s 1). However, we nd that the use of a turbulent diffusivity underestimates the dynamo efficiency, producing weaker mean fields than in the convective models. Also, the convective models exhibit mixed polarity bands in the polar regions that have no counterpart in solar observations. Also, the explicitly computed turbulent electromotive force (emf) bears little resemblance to a diffusive flux. We also find that the poleward migration speed of poloidal flux is determined mainly by the meridional flow and the vertical diffusion.

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