Zahlen, bitte! Full drought protection only 183 meters above sea level

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On December 10, 1902, the first Aswan Dam, constructed by British engineers, was ceremonially opened in Egypt. The world's largest structure at the time was intended to ensure year-round irrigation of the canal, enabling the cultivation of cotton on a large scale. In order to protect cotton production – and the Suez Canal –, Great Britain occupied Egypt in 1882 and later declared it a protectorate. The first Aswan Dam was unable to compensate for the low water levels during periods of drought as hoped, although it was raised twice.

In 1906, Harold Edwin Hurst came to Egypt and began exploring and documenting the Nile as an employee of the British administration. He remained in the country for 61 years, traveling the Nile and its tributaries on numerous expeditions, first on donkeys, then by bicycle and car, and finally by plane to further improve the data situation.

River data collection as a basis for calculation

He compiled the largest collection of data ever kept on a river. With his retirement in sight, he set about the task of calculating the "Century Strorage": What capacity of water intake must a Nile dam have in order to provide sufficient water over several years in the event of a major drought, which statistically occurs every 100 years? Hurst calculated the "Century Storage" with an evaporation rate of 10 percent at 90 km³. Accordingly, the dam designed by the Egyptian Adrian Daninos in 1947 had to be 183 meters high.

Zahlen, bitte!

In this section, we present amazing, impressive, informative and funny figures ("Zahlen") from the fields of IT, science, art, business, politics and, of course, mathematics every Tuesday. The wordplay "Zahlen, bitte!" for a section about numbers is based on the ambiguity of the German word "Zahlen." On one hand, "Zahlen" can be understood as a noun in the sense of digits and numerical values, which fits the theme of the section. On the other hand, the phrase "Zahlen, bitte!" is reminiscent of a waiter's request in a restaurant or bar when they are asked to bring the bill. Through this association, the section acquires a playful and slightly humorous undertone that catches the readers' attention and makes them curious about the presented numbers and facts.

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The "father of the Nile" (Abu Nil) died in 1978 and did not live to see his calculations confirmed in the catastrophic drought years of 1985 to 1988. While Ethiopia was hit hard, Egypt survived the drought unscathed. Hurst did, however, live to see mathematicians Benoît Mandelbrot and James Willis prove what is now known as the Hurst phenomenon and named the Hurst exponent in the groundbreaking 1968 paper "Noah, Joseph, and Operational Hydrology" (PDF) using Hurst's Law.

In hydrology, it refers to the tendency for particularly wet and dry years to occur in multi-year clusters. Mandelbrot also spoke of the Joseph effect in reference to the Bible: seven years of plenty are followed by seven years of famine, for which provision must be made. Such cluster effects have not only been proven for rivers such as the Nile or the tributary of Lake Maggiore, but can also be found in wind power in Ireland or in certain financial crises and even in medicine (cardiology)

Calculations to combat drought

In his essay on the storage problem of the Nile published in 1951, Hurst explained how he used the long-term data on the discharge of a river to relate the cumulative sum of the water discharged to the statistical mean in order to obtain the maximum and minimum storage volumes that could be used to avert a flood or drought. The 71-year-old retiree determined the Hurst exponent, later known as 0.72. Hurst received the Telford Gold Medal from the Institute of Civil Engineers in 1957 for his time-consuming calculations without the aid of a computer.

The Aswan Dam

Construction time: from 1960–1971
Height of the barrier structure: 111 m
Construction volume: 44.3 million m³
Crown length: 3,830 m
Crown width: 40 m
Base width: 980 m
Power plant output: 2,100 MW
Workers killed during construction: 451

His calculations on the water capacities in the Nile basin (PDF) initially assumed that only Lake Albert and Lake Victoria would be suitable as long-term reservoirs against possible periods of drought, until he saw other possibilities after flying over the Sudd and neighboring areas by plane. The construction of a dam on the Sudd el Aali became possible when Sudan and Egypt signed a water agreement.

Realization as an Egyptian-Soviet project

The dam proposals that emerged in the 1950s also included a German project. Later, as part of Egypt's reorientation under Abdel Nasser, the Soviet Union came on board. Nasser paid for the construction of the Aswan Dam with the revenues from the nationalized Suez Canal. After ten years of construction, the dam was completed, holding back not only the water but also the Nile mud used as fertilizer.

"The next conflict in the Middle East will be over water," predicted UN Secretary-General Boutros Boutros-Ghali in his inaugural speech in 1992, "Water will be a more precious resource than oil." With the 145-metre-high Grand Ethiopian Renaissance Dam (GERD), Ethiopia wants to avert a drought like the one in the 1980s, but above all generate electrical energy – and sell it to neighboring countries as far away as Tanzania.

The hydroelectric part is expected to produce up to 6000 MW, with a current electricity demand of 800 MW in the country. The last of the four turbines in the first construction phase was only put into operation in August of this year, amid sabre-rattling from all sides. The reservoir should be filled by the beginning of 2025.

(olb)