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The forecasting method is explained in detail by

Kauristie, K., M. Myllys, N. Partamies, A. Viljanen, P. Peitso, L. Juusola, S. Ahmadzai, V. Singh, R. Keil, U. Martinez, A. Luginin, A. Glover, V. Navarro and T. Raita, 2016: Forecasting auroras from regional and global magnetic field measurements. Geosci. Instrum. Method. Data Syst., 5, 253-262, doi:10.5194/gi-5-253-2016.

Empirical oval model is described by

Sigernes, F., M. Dyrland, P. Brekke, S. Chernouss, D.A.Lorentzen, K. Oksavik and C.S. Deehr, 2011: Two methods to forecast auroral displays. J. Space Weather Space Clim., 1, A03, doi:10.1051/swsc/2011003.

Sunrise and sunset times are calculated according to the formulas presented by the Astronomical Applications Department of the United States Naval Observatory (USNO). Moonrise and moonset times are calculated with the suncalcPy python package by Abe Miessler.
A detailed description of astronomical calculations is given, for example, by
J. Meeus, Astronomical Algorithms, 2nd edition 1998, Willmann-Bell, Inc., Richmond, Virginia, USA.