The goal of this PhD-thesis was the development of a fast yet accurate chemistry scheme for an interactive calculation of the extrapolar stratospheric ozone layer. The SWIFT-model is mainly intended for use in Global Climate Models (GCMs). For computing-time reasons GCMs often do not employ full stratospheric chemistry modules, but use prescribed ozone instead. This method does not consider the interaction between atmospheric dynamics and the ozone layer and can neither resolve the inter-annual variability of the ozone layer nor respond to climatological trends. Various studies [Calvo et al., 2015, Gillett and Thompson, 2003, Thompson and Solomon, 2002] have pointed out these insufficiencies. Existing fast ozone schemes, as in Cariolle und Teyssedre [2007] and McLinden et al. [2000], use a Taylor expansion of the first order to expand the rate of change of ozone about reference conditions of ozone mixing ratio, temperature and the locale ozone column and thus can not sufficiently adept to climate change scenarios, differing from the reference conditions. The SWIFT-model, in contrast, considers the full chemical system of a stratospheric chemistry model, including non-linearities and fluctuations of ozone depleting species, to determine the rate of change of ozone. The SWIFT-model consists of two modules, a polar and an extrapolar module. The polar module calculates vortex-averaged ozone loss by solving a set of coupled differential equations for the key species in polar ozone chemistry. Coefficients of the equation system are determined by simulations with a full chemistry model [Wohltmann et al., 2016]. This dissertation presents the extrapolar SWIFT-module, where we use algebraic functions to approximate the rate of change of ozone of the full model. In the full model, 55 initial and boundary conditions (e.g. various chemical species and atmospheric parameters) determine the function of rate of change of ozone, creating a 55-dimensional hypersurface. The numerical output of several simulations with the full model characterize the shape of the hypersurface. Using linear combinations of these variables, we can reduce the parameter space to the following nine dimensions: latitude, pressure, temperature, local ozone co- lumn, mixing ratio of ozone and of the ozone depleting families (Cly , Bry, NOy and HOy ). These nine variables sufficiently describe the shape of the 55-dimensional hypersurface. An automated procedure fits 9-dimensional polynomials of degree four to the reduced function. One global polynomial per month is determined which calculates the rate of change of ozone over 24 h. The full model used to fit the polynomials is the chemistry- and transport-model ATLAS. Two 2.5-years ATLAS-simulations from separate decades constitute the fitting-dataset. A key aspect for the robustness of the SWIFT-model is the incorporation of a wide range of stratospheric variability in the fitting-datasets. The systematic error between ATLAS and SWIFT causes the ozone mixing ratios to drift by less than 0.5% per day in the central regions of the 9-dimensional parameter space. Higher errors are located in the boundary regions, where the sampling density of the fitting-dataset is low, i.e. for rarely occurring atmospheric conditions. Here, the errors can rise to 4% per day. However, steep ozone gradients and non-linearities in the rate of change function are not the sources of significant errors. The extrapolar SWIFT-module has been integrated into the ATLAS-CTM as an optional chemistry scheme. Simulations with SWIFT in ATLAS have proven that the systematic error does not accumulate in the course of a run. In a 10 year simulation SWIFT has continuously produced a stable annual cycle, with inter-annual variations of the ozone layer well comparable to the full ATLAS-CTM. Horizontal gradients in the ozone distribution due to planetary waves, are well resolved by SWIFT. The average deviations between partial ozone columns in ATLAS and SWIFT are less than ±15 DU. Especially in the mid- and high-latitudes the extrapolar SWIFT-module yields better results than existing fast ozone schemes. The application of SWIFT requires the calculation of polynomials with 30 – 100 terms. Nowadays, computers can solve such polynomials at thousands of grid points in seconds. Therefore SWIFT provides the desired numerical efficiency and computes the ozone layer 10000 times faster than the chemistry model in the ATLAS-CTM.