Although the substorm current wedge (SCW) is recognized as a basic 3-D current system of the substorm expansion phase, its existing models still do not extend beyond a cartoon-like sketch, and very little is known of how well they reproduce magnetic variations observed in the magnetosphere during substorms. A lack of a realistic quantitative SCW model hampers testing model predictions against large sets of spacecraft data. This paper (1) presents a computationally efficient and flexible model with a realistic geometry of field-aligned currents, conveniently parameterized by the SCW strength, longitudinal width, and position, all derived from ground-based midlatitude magnetic variations; and (2) tests the model against INTERMAGNET network observations during substorms and compares its predictions with space magnetometer data. The testing demonstrated significant and systematic discrepancies between the observed and predicted magnetic variations, depending on spacecraft location, concurrent magnetotail configuration, and substorm phase. In particular, we found that the net SCW current derived from the midlatitude field variations corresponds to only a relatively small and variable fraction of the distant 3-D substorm current, inferred from spacecraft data in the lobe and at geosynchronous distance. The discrepancy can be partly attributed to additional region 2 polarity field-aligned currents in the same longitudinal sector, associated with azimuthal diversion of the earthward plasma flow when it encounters the region of strong quasi-dipolar field in the inner magnetosphere.