  The astounding success of these methods has made it imperative to obtain more
explainable and trustworthy estimates from these models. In hydrology, basin
characteristics can be noisy or missing, impacting streamflow prediction. For
solving inverse problems in such applications, ensuring explainability is
pivotal for tackling issues relating to data bias and large search space. We
propose a probabilistic inverse model framework that can reconstruct robust
hydrology basin characteristics from dynamic input weather driver and
streamflow response data. We address two aspects of building more explainable
inverse models, uncertainty estimation and robustness. This can help improve
the trust of water managers, handling of noisy data and reduce costs. We
propose uncertainty based learning method that offers 6\% improvement in $R^2$
for streamflow prediction (forward modeling) from inverse model inferred basin
characteristic estimates, 17\% reduction in uncertainty (40\% in presence of
noise) and 4\% higher coverage rate for basin characteristics.
