I think the most effective way to conduct this analysis is to apply the Reconstructing the flow series from the analysis of tree rings , there are some studies in Africa and in the Nile Basin in this field such as:
Reconstructing the flow of the River Nile from Juniperus
procera and Prunus africana tree rings (Ethiopia) – an
explorative study on cross-dating and climate signal
T.H.G. Wils1
& Z. Eshetu2
1
University of Wales Swansea, School of the Environment and Society, Department of Geography, Singleton
You may need to construct the time series stochastically, The nilometer is a good resource but there is some literature i.e. Sivapalan, 2003, which says that nilometer lacks to incorporate the nile basin characteristics in its flow...