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The need for reliable predictions of the solar activity cycle motivates thedevelopment of dynamo models incorporating a representation of surfaceprocesses sufficiently detailed to allow assimilation of magnetographic data.In this series of papers we present one such dynamo model, and document itsbehavior and properties. This first paper focuses on one of the model's keycomponents, namely surface magnetic flux evolution. Using a genetic algorithm,we obtain best-fit parameters of the transport model by least-squaresminimization of the differences between the associated synthetic synopticmagnetogram and real magnetographic data for activity cycle 21. Our fittingprocedure also returns Monte Carlo-like error estimates. We show that the rangeof acceptable surface meridional flow profiles is in good agreement withDoppler measurements, even though the latter are not used in the fittingprocess. Using a synthetic database of bipolar magnetic region (BMR) emergencesreproducing the statistical properties of observed emergences, we alsoascertain the sensitivity of global cycle properties, such as the strength ofthe dipole moment and timing of polarity reversal, to distinct realizations ofBMR emergence, and on this basis argue that this stochasticity represents aprimary source of uncertainty for predicting solar cycle characteristics.

A coupled 2$\times$2D Babcock-Leighton solar dynamo model. I. Surface magnetic flux evolution