Dear Mostafa,

Data don't need to have a stochastic nature in order to be used for an extreme value analysis. You can use for instance observed water level or discharge data for such an analysis. Important boundary conditions are the independency and homogeneity of the data set, i.e. the (monthly) water levels should be independent (which is probably not the case) and should originate from a homogeneous population (e.g. not before and after the regulation of the river started). The independency condition can be achieved by e.g. working with annual water levels or a peak over threshold (POT) approach (ensuring independency). The homogeneity of the data set should be tested by using statistical tests such as Mann-Kendall for trends and the Pettitt test for abrupt changes.

Good luck,

Martijn

Dear friend. All process that are represented by an mathematic equation, are deterministics, course, included stochastics process. The theory of extreme value, permits us to make predictions in cases where are involucred natural and/or human extreme phenomenon able to be predictable. The suggest of Mr.Martijn J. Booij it is very idoneous, to give it your study more fundamentation..

Regards

I think you should NOT use extreme-value analysis on inputs that are not stochastic. The methods were developed for random variables. The stream flow regulation may imply that there is an upper limit, a maximum flow rate release, determined by dam discharge capacity.

Additionally, please remember that the sea level itself cannot be used directly, even if the inputs were stochastic.  That's because it is an integral of inputs minus outputs over time, which means that its time series has a very strong memory, or auto-correlation. The value at time t+1 is strongly dependent on the value at time t, as in a strong Markov Chain.  This could perhaps be solved by studying only the inputs, or maybe by using the first derivative of the lake level.

Any method have an error. None can be considered perfect and infallible. Many systems can be described with a model, in your case, extreme value, but you must estimate an error, that can be quantified. In the process where the decisions humans are involucrated, it is important the diffuse logic. You can use a mixture, however. Try, calculate, work with others possibilities. You will obtain interesting results, another's absurds, perhaps; but, if you are acucious and very carefully, you will know what to do.

Regards