In this paper, design of a neural network for a domain-specific problem is described. The problem of concern is forecasting flood events where data is contaminated heavily by noise, training examples have different importance levels and noisy data coincides with the most important ones. To this end, two ideas are explored namely, changing the loss function and integrating a coefficient that reflects on the relative importance of training examples. To this end, backpropagation is re-derived considering implication of having a more general objective function. Independently, inclusion of scores associated with each training examples and its implication of overall loss function and the way weights are optimized is explored. The derived model is implemented in MATLAB and flood data from Talebudgera, Australia is considered for investigations. Compared to the base case being backpropagation, the results suggest that inclusion of scored for training examples corresponds to visible improvement when predicting peaks.