Fig. 1.
The Nile has two streams flowing from two sources, Lake Victoria and Ethiopian highlands, which converge in Khartoum and continue its journey to the Mediterranean Sea (Gebre and Ludwig, 2015). The Nile river discharge was measured and recorded monthly from 1870 to 2002 in Aswan area, where two major dams, Aswan Low dam and Aswan High dam, were constructed during this time-period (a). The entire time-series is shown in (b), which suggests various time-scales including the major seasonal cycle. The climatological seasonal cycle of the river discharge, constructed by averaging 133 seasonal cycles of the time-series, is shown in (c) along with standard TWO deviation bars representing confidence interval. The seasonal cycle shows a dramatic change from June (3 BCD) to September (23 BCD). This is reflected in the power spectrum (d) showing one dominant peak associated with the annual cycle, and a low frequency (decadal) variability. The 95% confidence limits (dashed lines) are included with the spectrum of the red noise background (red) for comparison.
Fig. 2.
Stochastic model, construction based on the Nile river discharge for the period 1870–2002. Equations (11), (13), (14) are used to construct the three functions a(t), N(t), and (a) The two periodic functions: the stability function a(t) (blue), and the noise amplitude N(t) (red). (b) The long-term forcing spanning from 1870 to 2002 calculated from Eq. (14). (c) Time series of the Nile river discharge data (blue), and a model simulation (red). (d) Monthly standard deviation of the observation data (blue) and the model (red).
Fig. 3.
Stochastic model, constructed based on the Nile river discharge for the period 1870–1899. (a) The two periodic functions: the stability function a(t), and the noise amplitude N(t) (top) along with a stochastic realization (red) to be compared with the original time-series (blue) (bottom). (b) Monthly standard deviations derived from the ensemble members (red) and the original data (blue). (c) Seasonal stability a(t) (blue) along with the standard deviation (red) for ENSO. Positive feedback is associated with positive a(t), yielding exponential increase of variability and corresponds to June-August for the Nile and July-Nov for ENSO. Maximum variability occurs approximately near the transition when a(t) changes sign, i.e. September (Nile) and December (ENSO). The occurrence of extreme phases of the Nile discharge (flooding and drought) and ENSO (El-Nin and La-Nin) takes place at specific time of the year due to the feedback mechanism strongly associated with phase locking, as summarized in (d).
Fig. 4.
30-yr window characteristics of monthly stability and noise of the Nile discharge. (a) Time evolution of the seasonal stability a(t) (top) and various stages of Aswan dam construction/amendment (bottom). Positive feedback is shown by the hot colour (positive a(t)) and occurs between June and August, characterized by its slow time evolution, which is related to the history of dam construction. A decrease of a(t), during summer, started from 1930. From 1946, corresponding to the last stage of raising Aswan low dam, the dominant positive summer feedback starts to weaken as a result. Aswan high dam was constructed during 1960 to 1970. The difference between a(t) before 1902 and after the construction of the two dams suggests an impact of the dams on the Nile river variability. (b) Time evolution of the noise amplitude N(t) (top) and the annual as well as a 30-yr moving average of the PDO index (bottom). The noise amplitude N(t) shows multi-decadal variability, and is correlated with the 30-year PDO average, where positive (negative) PDO is associated with large (small) noise amplitude on multi-decadal time scales.
Fig. 5.
One point correlation map between the annual average of the Nile river discharge and that of SST (a), showing similar spatial pattern with ENSO, and the same map between 10-year moving averaged Nile river discharge and SST (b) showing a PDO pattern. The correlation of the annual mean of the Nile river discharge with SLP is also shown in (c). The normalized annual mean Nile river discharge (thick black) is compared with the normalized PDO index (dashed blue) and the normalized Nino4 index (red dots) (d). The normalized Nile maximum height recorded by the Nilometer for the last millennium is compared with the normalized PDO index deduced from tree rings (e). The Nile river discharge (or height) as given by the Nilometer is negatively correlated with the PDO on inter-annual time-scales, but positively correlated with the PDO on multi-decadal time-scales.