the neural network can used in any science

which can used to classified the data and estimated the influence of malty input variables and doing parametric study and a lot of thinks

can see i wrote more than three paper as application of Neural network in concrete

and you can doing the same in your field

On the second question... about hydrology. The neural network is a model. We can modelling hydrological series like the predict of rainfall data (in a certain time in the future) based on historical data of rainfall... or observation data. As I did, the result was very good. It's better than ARIMA.

Generally, an ANN model will outperform other types of models in calibration. This is because of the number of parameters in an ANN. The problem is in using an ANN for prediction. Basically, it comes down to the uncertainty in the modelled output, and how this compares with the uncertainty in the observed output, and in the input data used. Generally, a model assumes the input data used, and the output data the model is calibrated against is exact. This is particularly true when using an objective function based on the sum of squared residuals (e.g. Nash Sutcliffe, RMSE). Check

https://www.researchgate.net/publication/228371805_Representing_uncertainty_in_objective_functions_extension_to_include_the_influence_of_serial_correlation?ev=prf_pub

Using a least squares approach (i.e. ignoring the known structure in the uncertainties), you will generally find that a more complicated model will perform better than a simple model, at least in calibration. Under simulation, the more complicated model can often give worse results due to changes in the distribution of the uncertainties (which may not be stationary). More complicated models not only fit to the behaviour of the system (as seen through the data), but also to patterns in the noise in the data.

Concerning the original question, I'm not sure what you mean by:

What should I do if I want to do acting snowmelt runoff using neural networks or management of water resources

I assume this means that you want to model a catchment that has a significant snowmelt signature for the purpose of WRM. This can be done using a process-based model, or an empirical model (e.g. an ANN). For the snowmelt part, you will need data to calibrate this part of the model. You might be able to rely on just the recorded streamflow providing the snowmelt signature is sufficiently clear. However, you might need to add data on the snow cover to improve the model behaviour, particularly in a predictive sense.

Conference Paper Representing uncertainty in objective functions: extension t...

ANN model is a black-box model that allows you to establish a complex relationship between a set of input and output data. ANN works by training the model using set of known input and output. But as others mentioned, there is uncertainty associated with it, like over-simulation. As I understand, for your case, you want to create a relationship between snow-melt and runoff and then do some prediction scenario analysis for management application. Of course it is possible using ANN, where your input will be snow melt data and output - runoff, you can add other parameters like precipitation, temperature as input during training which improves your simulation and decreases uncertainty. The advantage of ANN is that they require less parameters/data compared to process-based models. However you need enough time series data for training and validation purposes.