I've been tasked with generating synthetic streamflow scenarios through disaggregation.
First, I will generate 50 years of streamflow data. For that, I will probably use a simple model as AR(1) or an ARMA(1,1) and am adopting some probabilistic parameters based on streamflow data I have. These data come from the historical record a gauge station.
From my yearly flow, I have to generate monthly streamflows. In the end, instead of 50 streamflow realizations, each one representing an annual flow; I'll have 600 streamflow realizations, each representing a monthly stream flow.
Now, to get from annual to monthly stream flow, I will need a correlation matrix.
I could simply estimate the monthly correlation from January to December by calculating the correlation among monthly streamflows from a set of historical streamflow.
One could say that the physical aspects involving the (auto)correlation are implicit in the data itself. However, the data I have for this gauge station - as for any other - is only one realization of the stochastic process from which the observed streamflows were generated.
How, then, could I enrich this monthly (auto)correlation with physical concepts stemming from the river where the gauge station is located? I should add that my question also applies to cross-correlation between two different time-series. How, in that case, could I enrich the cross-correlation matrix employing physical aspects between 2 observed time-series?