  The coded-mask spectrometer-telescope SPI on board the INTEGRAL observatory
records photons in the energy range between 20 and 8000 keV. A robust and
versatile method to model the dominating instrumental background (BG) radiation
is difficult to establish for such a telescope in the rapidly changing space
environment. From long-term monitoring of SPI's Germanium detectors, we built
up a spectral parameter data base, which characterises the instrument response
as well as the BG behaviour. We aim to build a self-consistent and broadly
applicable BG model for typical science cases of INTEGRAL/SPI, based on this
data base. The general analysis method for SPI relies on distinguishing between
illumination patterns on the 19-element Germanium detector array from BG and
sky in a maximum likelihood framework. We illustrate how the complete set of
measurements, even including the exposures of the sources of interest, can be
used to define a BG model. We apply our method to different science cases,
including point-like, diffuse, continuum, and line emission, and evaluate the
adequacy in each case. From likelihood values and the number of fitted
parameters, we determine how strong the impact of the unknown BG variability
is. We find that the number of fitted parameters, i.e. how often the BG has to
be re-normalised, depends on the emission type (diffuse with many observations
over a large sky region, or point-like with concentrated exposure around one
source), and the spectral energy range and bandwidth. A unique time scale,
valid for all analysis issues, is not applicable for INTEGRAL/SPI, but must and
can be inferred from the chosen data set. We conclude that our BG modelling
method is usable in a large variety of INTEGRAL/SPI science cases, and provides
nearly systematics-free and robust results.
