The Digital Earth (DE) metaphor is very useful for both end users and hydrological modelers. We analyse different categories of models, with the view of making them part of a Digital eARth Twin Hydrology system (called DARTH). We also stress the idea that DARTHs are not models in and of themselves, rather they need to be built on an appropriate information technology infrastructure. It is remarked that DARTHs have to, by construction, support the open-science movement and its ideas.