The filamentous algae Cladophora is one of the most prevalent algae worldwide. It interferes with water supplies, and negatively affects dissolved oxygen and pH in lakes and rivers. Yet, the complexity of its response to temperature, nutrients availability and hydrodynamics challenges our modeling capabilities. We developed a fully coupled computational model able to capture the temporally varying spatial distribution of Cladophora in the Clark Fork river. The model predictions match with remote sensing measurements of the spatial coverage of Cladophora.