As the number of weather stations declines globally, ensuring that meteorological monitoring networks efficiently and effectively monitor weather variables becomes increasingly important. Multi-variable weather sensors are becoming more widely available and make monitoring weather phenomena more economical. However, when seeking an optimal spatial distribution of these stations, choosing an objective function that weights these variables in a way that is relevant to a majority of the data consumers poses a significant challenge. We propose the use of physically based combinations of parameters, and illustrate this approach with an objective function based on a model of evapotranspiration (ET) that can combine precipitation, temperature, relative humidity, solar radiation, wind speed, barometric pressure, and soil moisture capacity data in a meaningful way. We calculate this objective using a gridded weather data set. We assess the suitability of different network design techniques to be employed with gridded data sets and proposed an optimization method that allows us to minimize the mean squared interpolation error for our objective. Our network design method is able to reduce interpolation error by about 10% when compared to a maximally spaced monitoring network or a network designed based solely on expert recommendations. Our network design is further improved by the inclusion of expert recommended sites in our set of candidate locations.