We analyse in this work the propagation and geoeffectiveness of four successive coronal mass ejections (CMEs) that erupted from the Sun during 21--23 May 2013 and that were detected in interplanetary space by the Wind and/or STEREO-A spacecraft. All these CMEs featured critical aspects for understanding so-called problem space weather storms at Earth. In the first three events a limb CMEs resulted in moderately geoeffective in-situ structures at their target location in terms of the disturbance storm time (Dst) index (either measured or estimated). The fourth CME, which also caused a moderate geomagnetic response, erupted from close to the disc centre as seen from Earth, but it was not visible in coronagraph images from the spacecraft along the Sun--Earth line and appeared narrow and faint from off-angle viewpoints. Making the correct connection between CMEs at the Sun and their in-situ counterparts is often difficult for problem storms. We investigate these four CMEs using multiwavelength and multipoint remote-sensing observations (extreme ultraviolet, white light, and radio), aided by 3D heliospheric modelling, in order to follow their propagation in the corona and in interplanetary space and to assess their impact at 1 AU. Finally, we emphasise the difficulties in forecasting moderate space weather effects provoked by problematic and ambiguous events and the importance of multispacecraft data for observing and modelling problem storms.
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