Twitter accounts have already been used in many scientometric studies, but the meaningfulness of the data for societal impact measurements in research evaluation has been questioned. Earlier research focused on social media counts and neglected the interactive nature of the data. We explore a new network approach based on Twitter data in which we compare author keywords to hashtags as indicators of topics. We analyze the topics of tweeted publications and compare them with the topics of all publications (tweeted and not tweeted). Our exploratory study is based on a comprehensive publication set of climate change research. We are interested in whether Twitter data are able to reveal topics of public discussions which can be separated from research-focused topics. We find that the most tweeted topics regarding climate change research focus on the consequences of climate change for humans. Twitter users are interested in climate change publications which forecast effects of a changing climate on the environment and to adaptation, mitigation and management issues rather than in the methodology of climate-change research and causes of climate change. Our results indicate that publications using scientific jargon are less likely to be tweeted than publications using more general keywords. Twitter networks seem to be able to visualize public discussions about specific topics.