In this paper, we explore the crucial role and challenges of computational reproducibility in geosciences, drawing insights from the Climate Informatics Reproducibility Challenge (CICR) in 2023. The competition aimed at (1) identifying common hurdles to reproduce computational climate science; and (2) creating interactive reproducible publications for selected papers of the Environmental Data Science journal. Based on lessons learned from the challenge, we emphasize the significance of open research practices, mentorship, transparency guidelines, as well as the use of technologies such as executable research objects for the reproduction of geoscientific published research. We propose a supportive framework of tools and infrastructure for evaluating reproducibility in geoscientific publications, with a case study for the climate informatics community. While the recommendations focus on future CIRCs, we expect they would be beneficial for wider umbrella of reproducibility initiatives in geosciences.