With localized increases in water stress, countries have become more reliant on sources of freshwater which are often times shared with other riparian countries. Such transboundary rivers are governed by treaties. Most river treaties specify quantities of water allocated between the riparians according to long-term mean flows. However, as the value of water increases due to shortages, it raises the incentive to violate treaty provisions. An additional source of complexity is that countries differ in their ability to resist flow variabilities and thereby face different levels of risk from natural disasters and hence are likely to have different propensities to co-operate with others. With Climate Change the causes of non-compliance are exacerbated and this might hinder the ability of river treaties to manage riparian conflicts. This raises concern whether arguments over use of a limited resource might turn into international tensions and increase the likelihood of conflicts. In view of the above, this dissertation attempts to estimate the risk faced by each riparian from natural disasters caused by extreme surface flows and explores whether this risk inflicts the risk of breaking down of a treaty as one or more parties retract from it. In order to do this a theoretical model is developed estimating the accepted level of risk premium associated with signing an international treaty and deriving the general conditions under which a riparian would choose to retract from an existing treaty. The model is then applied to the Tajo basin, to evaluate the effect of an existing river treaty (the Albufeira Convention) between Spain and Portugal on riparian welfare using satellite data on several water availability indices. Subsequently, it adopts a cooperative game theoretic exposition to assess the sustainability of the above treaty under extreme surface flows (drought conditions).