Weather forecasting is a canonical predictive challenge that relies on extensive data gathering operations. We explore new directions with forecasting weather as a data-intensive challenge that involves large-scale sensing of the required information via planning and control of a swarm of aerial vehicles. First, we will demonstrate how commercial aircraft can be used to sense the current weather conditions at a continental scale and help us create Bayesian deep-hybrid predictive model for weather forecasts. Beyond making predictions, these probabilistic models can provide the guidance of sensing with value-of-information analyses, where we consider uncertainties and needs of sets of routes and maximize information value in light of the costs of acquiring data from a swarm of sensors. The methods can be used to select ideal subsets of locations to sense and also to evaluate the value of trajectories of flights for sensing. Finally, we will discuss how to carry out such large sensing missions using novel algorithms for robot planning under uncertainty.