Combined inversion and statistical workflow for advanced temporal analysis of the Nile River's long term water level records

We present a workflow for the improved interpretation of the Nile River's unique dataset implying quantitative water level data from A.D. 622 to 1921 with some breaks. In the framework of the proposed methodology, innovative algorithms are presented for (1) filling in missing data, (2) extraction of spectral information content of the completed dataset, and (3) applying statistical pattern recognition using the same imputed dataset. In the first step of the workflow an inversion-based Fourier transformation method is developed to replace the missing data with reliable estimated values in case of non-equidistant sampling and modeling fast variations in the time series. The robust inversion algorithm is less affected by data noise than the conventional discrete Fourier transformation algorithms. In the second step, the completed water level records are then explored to find a more detailed series of periodic components and time variations, e.g., the Grand Solar Cycle with 435-year cycle is detected. As a new result the spectrum of the difference of the annual maximum and the annual minimum water levels is also calculated and analyzed. In the third step of the workflow, non-hierarchical cluster analysis is used to find similarities between the time series of water levels and their difference signal, too. We implement the Most Frequent Value (MFV) method to robustify the conventionally used K-means clustering process. The resulting temporal distribution of the clusters is analyzed, which provides a unique and unbiased basis for searching the causes of the water-level variations of the river Nile over 1300 years. The results confirm the quasiperiodical causal features. The proposed methodology may be suitable for predicting future events in other river catchment areas providing a very important tool in water management.