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A ray-tracing program based on the Haselgrove equations and the Appleton-Hartree formula has been developed and used to synthesize sweep-frequency ionograms. We have looked at ionograms taken in summer periods at high-latitude ionosonde stations in the vicinity of the dayside auroral oval. Especially the traces on ionograms from oblique reflections from an electron density enhancement have been studied. The enhanced ionization is simulated either by a two-dimensional Gaussian distribution or by a double exponential function similar to the bottom part of a Chapman function. The enhancements are aligned with the earth's magnetic field direction. Ray paths in the magnetic meridian plane are calculated and discussed in connection with computed ionograms and observed ionograms from Canada and Greenland. The ray-tracing exercise was done in order to estimate characteristics of the electron density enhancement from observed ionograms. By varying the parameters in the models of the ionosphere to obtain agreement between observed and synthesized ionograms we have been able to analyze temporal and spatial progress of an electron density enhancement that could be a feature of the auroral oval like the field-aligned current sheets in the cusp region.