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Accurate and timely crop mapping is essential for yield estimation, insurance claims, and conservation efforts. Over the years, many successful machine learning models for crop mapping have been developed that use just the multispectral imagery from satellites to predict crop type over the area of interest. However, these traditional methods do not account for the physical processes that govern crop growth. At a high level, crop growth can be envisioned as physical parameters, such as weather and soil type, acting upon the plant, leading to crop growth which can be observed via satellites. In this paper, we propose a weather-based Spatio-Temporal segmentation network with ATTention (WSTATT), a deep learning model that leverages this understanding of crop growth by formulating it as an inverse model that combines weather (Daymet) and satellite imagery (Sentinel-2) to generate accurate crop maps. We show that our approach provides significant improvements over existing algorithms that solely rely on spectral imagery by comparing segmentation maps and F1 classification scores. Furthermore, effective use of attention in WSTATT architecture enables the detection of crop types earlier in the season (up to 5 months in advance), which is very useful for improving food supply projections. We finally discuss the impact of weather by correlating our results with crop phenology to show that WST