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Aims.  We study the properties of the coronal magnetic field according to the current sheet source surface (CSSS) model in 1976–2017 for all physically reasonable values of the three model parameters (cusp surface radius  R  cs , source surface radius  R  ss , and current parameter  a ), and compare the CSSS field with the potential field source surface (PFSS) model field.   Methods.  We used the synoptic maps of the photospheric magnetic field from the Wilcox Solar Observatory (WSO), National Solar Observatory/Kitt Peak (NSO/KP), and the NSO Synoptic Optical Long-term Investigations of the Sun Vector Spectromagnetograph (SOLIS/VSM) in order to calculate the coronal magnetic field according to the CSSS and PFSS models. We calculated the coronal field strength, its latitudinal variation and neutral line location, as well as its polarity match with the heliospheric magnetic field.   Results.  The CSSS model can correct the erroneous latitudinal variation of the PFSS model if the source surface is sufficiently far out with respect to the cusp surface ( R  ss  ≥ 3 ⋅  R  cs ). The topology of the neutral line only slightly depends on source surface radius or current parameter, but excludes very low values of the cusp surface ( R  cs  ≤ 1.5). A comparison of the polarities gives an optimum cusp surface radius that varies in time between 2 and 5; a stronger current yields a larger optimum  R  cs . Interestingly, the optimum polarity match percentages and optimum radii vary very similarly in the two models over the four solar cycles we studied.   Conclusions.  The CSSS model can produce a stronger total coronal flux than the PFSS model and correct its latitudinal variation. However, the topology of the CSSS model is rather independent of horizontal currents and remains very similar to that of the PFSS model. Therefore, the CSSS model cannot improve the match of field polarities between corona and heliosphere.

Revisiting the coronal current sheet model: Parameter range analysis and comparison with the potential field model