The model uncertainty issue is long existing in all applied fields but especially critical in insurance due to data scarcity. As a promising solution, distributionally robust optimization (DRO) has fast developed in operations research during the recent two decades. However, this approach often yields bounds that appear to be over-conservative. We argue that, in most practical situations, the distribution in the local region may be subject to only a mild extent of uncertainty so that it is safe to assume no uncertainty at all, and henceforth we need to apply DRO only to the tail region where the uncertainty presents. To solve this DRO problem, we need to carefully disentangle the twofold uncertainty existing in both a tail indicator and a restricted version of the risk to the tail region. We employ the Wasserstein metric to construct an uncertainty ball for the twofold uncertainty. Our main result is a closed-form estimation for the moment of a risk under partial uncertainty. We implement intensive numerical studies to illustrate the robustness of our result and the benefit of our consideration of partial uncertainty.