The proposed monitoring design involves sampling resources systematically via a triangular grid that is overlaid on the United States. This grid is applied in different ways to sample different types of resources. For continuous resources, such as extensive waterbodies, the observations may be point measurements of the response variable. The specific problem investigated in the paper is motivated by design considerations for open-water sampling in the estuary component of the Near Coastal resource. Statistical properties of two sampling design alternatives imposed on the triangular grid are explored, and contrasted to a third design that does not use the grid. The three designs were evaluated on the criteria of precision and suitability of variance estimation, by a mixture of analysis and simulation. The surface models used throughout the evaluation to explore properties of the designs were planar, quadratic, and sinusoidal.