This paper gives a grounded cognition account of model-based learning of complex scientific knowledge related to socio-scientific issues, such as climate change. It draws on the results from a study of high school students learning about the carbon cycle through computational agent-based models and investigates two questions: First, how do students ground their understanding about the phenomenon when they learn and solve problems with computer models? Second, what are common sources of mistakes in students' reasoning with computer models? Results show that students ground their understanding in computer models in five ways: direct observation, straight abstraction, generalisation, conceptualisation, and extension. Students also incorporate into their reasoning their knowledge and experiences that extend beyond phenomena represented in the models, such as attitudes about unsustainable carbon emission rates, human agency, external events, and the nature of computational models. The most common difficulties of the students relate to "seeing" the modelled scientific phenomenon and connecting results from the observations with other experiences and understandings about the phenomenon in the outside world. An important contribution of this study is the constructed coding scheme for establishing different ways of grounding, which helps to understand some challenges that students encounter when they learn about complex phenomena with agent-based computer models.