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Principle component analysis (PCA) of the solar background magnetic field\ud(SBMF) measured from Wilcox Solar Observatory (WSO) magnetograms revealed the\udfollowing principal components (PCs) in latitudes: two main symmetric\udcomponents, which are the same for all cycles 21–23, and three pairs of\udasymmetric components, which are unique for each cycle. These SBMF variations\udare assumed to be those of poloidal magnetic field travelling slightly\udoff-phase from pole to pole while crossing the equator. They are assumed to\udbe caused by a joint action of dipole and quadruple magnetic sources in the\udSun.\ud \udIn the current paper, we make the first attempt to interpret these latitudinal\udvariations in the surface magnetic field with Parker's two-layer dynamo\udmodel. The latitudinal distributions of such waves are simulated for cycles\ud21–23 by the modified Parker's dynamo model taking into account both\udα and ω effects operating simultaneously in the two (upper and\udlower) layers of the solar convective zone (SCZ) and having opposite\uddirections of meridional circulation. The simulations are carried out for\udboth dipole and quadruple magnetic sources with the dynamo parameters\udspecifically selected to provide the curves fitting closely the PCs derived\udfrom SBMF variations in cycles 21–23. The simulations are optimised for\udmatching the positions of maximums in latitude, the number of equator\udcrossings and the phase difference between the two dynamo waves operating in\udthe two layers. The dominant pair of PCs present in each cycle is found to be\udfully asymmetric with respect to the magnetic poles and produced by a\udmagnetic dipole. This pair is found to account for the two main dynamo waves\udoperating between the two magnetic poles. There are also three further pairs\udof waves unique to each cycle and associated with multiple magnetic sources\udin the Sun. For the odd cycle 21 the simulated poloidal field fits the\udobserved PCs, only if they are produced by magnetic sources with a quadruple\udsymmetry in both layers, while for the even cycle 22 the fit to the observed\udPCs is achieved only in the case of quadruple magnetic sources in the upper\udlayer and dipole sources in the inner layer. For the other odd cycle 23 the\udfit to observation is obtained for the quadruple magnetic sources in the\udinner layer and the dipole sources in the upper layer. The magnitudes of\uddynamo numbers D defining the conditions (depth and latitude) of a magnetic\udflux formation and the numbers N of zeros (equator crossings by the waves)\udare found to increase and the meridional circulation speed to decrease with a\udcycle number increase (D = −700, N = 3 for cycle 21 and\udD = −104, N = 9 for cycle 23). The phase delays between the\udwaves in each unique pairs are also found to increase with the cycle number\udfrom ~9° in cycle 21 to ~13° in cycle 23

Probing latitudinal variations of the solar magnetic field in cycles 21–23 by Parker's Two-Layer Dynamo Model with meridional circulation