We report the results of an experiment eliciting individuals' attitudes toward risk and model uncertainty. Using a joint elicitation procedure, we then precisely quantify the strength of individuals' attitude toward ambiguity in the context of the smooth model and characterize its main properties. Our results provide empirical evidence of decreasing absolute ambiguity aversion (DAAA) and constant relative ambiguity aversion (CRAA). These results shed new light on the way ambiguity attitudes may affect important decisions, such as the choice of health insurance policies or the optimal investment strategy in the face of climate change.