There is a new paper on this topic that was recently published in Water Resources Research, Betterle, A., M. Schirmer, and G. Botter (2017), Characterizing the spatial correlation of daily streamflows, Water Resour. Res., 53, 1646–1663, doi:10.1002/2016WR019195. They conclude that the synchroneity in intensity and frequency of rainfall events is a principal driver of spatial autocorrelation of streamflows. I am not sure whether you are contemplating approaches for minimizing autocorrelation so that you can perform statistical analyses of streamflow data, but there are approaches such as pre-whitening that can be applied to data sets so that the assumption of independence is valid.
Autocorrelation function measures the the correlation of a time series with itself after lagging. So it measures the stochastic component in a time series. Refer to any textbook on (time series analysis: forecasting and control) especially by Box-Jenkins. Best regards.