The scrape-off layer and divertor plasma conditions have been carefully analysed in dedicated ASDEX Upgrade experiments consisting of low-density L-mode discharges, with both forward and reversed toroidal magnetic fields and plasma currents. In the forward field, the outer divertor plasma is in a low-recycling regime with peak target temperature above 25 eV. In the reversed field with similar main plasma parameters, the target temperature is below 15 eV and the density is 5 times as high as in the forward field, indicating a higher recycling regime in the outer divertor. The SOLPS5.0 code package is used to model these divertor plasmas. Specifically, it is tested whether a combination of input assumptions exists that enables matching the code solution to all outer divertor diagnostic measurements, and whether these assumptions are compatible with constraints imposed by measurements outside the outer divertor. In the forward field, a good level of agreement with multiple outer target measurements is found with assumptions that simultaneously match the measured density and temperature profiles at the outer midplane, where the uncertainty in the radial position of the separatrix is ±0.5 cm. Similar approaches made previously for higher recycling regimes have not led to such a good consistency between all modelled and measured outer divertor parameters. In the reversed field with higher recycling in the outer divertor, a solution consistent with the outer target Langmuir probe measurements cannot be obtained, at least not without significantly compromising the match to the upstream profile measurements. Significant mismatches are observed also between the modelled and measured upstream Mach number in the forward field. These discrepancies question the global validity of the plasma solutions, and their origin is not yet clear. In part II (Aho-Mantila L. et al 2012 Nucl. Fusion 52 103007), the analysis of outer divertor conditions is complemented by local impurity migration studies, using the divertor plasma solutions presented in this paper.