  Recent advances in safety-critical risk-aware control are predicated on
apriori knowledge of the disturbances a system might face. This paper proposes
a method to efficiently learn these disturbances online, in a risk-aware
context. First, we introduce the concept of a Surface-at-Risk, a risk measure
for stochastic processes that extends Value-at-Risk -- a commonly utilized risk
measure in the risk-aware controls community. Second, we model the norm of the
state discrepancy between the model and the true system evolution as a
scalar-valued stochastic process and determine an upper bound to its
Surface-at-Risk via Gaussian Process Regression. Third, we provide theoretical
results on the accuracy of our fitted surface subject to mild assumptions that
are verifiable with respect to the data sets collected during system operation.
Finally, we experimentally verify our procedure by augmenting a drone's
controller and highlight performance increases achieved via our risk-aware
approach after collecting less than a minute of operating data.
