In this work, we will identify the existence of 'rough dependence on initial conditions' in atmospheric phenomena, a concept which is a problem for weather analysis and forecasting. Typically, two initially similar atmospheric states will diverge slowly over time such that forecasting the weather using the Navier-Stokes equations is useless after some characteristic time-scale. With rough dependence, two initial states diverge quickly implying forecasting is impossible. Using previous research in atmospheric science, rough dependence is characterized by using quantities that can be calculated from atmospheric data. Rough dependence will be identified in atmospheric phenomena on different time scales. The nature of rough dependence will be studied using a research model. Data was provided for this project by archives outside MU, and using our MU RADAR at the South Farm experiment station.