  Magnetic clouds (MCs) are flux-rope magnetic structures forming a subset of
solar coronal mass ejections which have significant space weather impacts. The
geoeffectiveness of MCs depends on their properties which evolve during their
interplanetary passage. Based on an analysis of observations spanning two solar
cycles we establish that MCs interacting with the ambient solar wind magnetic
field (i.e., heliospheric open flux) lose a substantial amount of their initial
magnetic flux via magnetic reconnection, which in some cases, reduce their
geoeffectiveness. We find a linear correlation between the eroded flux of MCs
and solar open flux which is consistent with the scenario that MC erosion is
mediated via the local heliospheric magnetic field draping around an MC during
its interplanetary propagation. The solar open flux is governed by the sunspot
cycle. This work therefore uncovers a hitherto unknown pathway for solar cycle
modulation of the properties of MCs.
