Application of commensurability method for the long-term forecasting of the highest summer floods on the Danube River at Bratislava

Borys Khrystyik, Liudmyla Gorbachova, Pavla Pekárová, Pavol Miklánek
2019 Meteorology Hydrology and Water Management  
This paper reports the use of the commensurability method for long-term forecasting of the highest summer floods on the Danube River at Bratislava. Bratislava is the capital of the Slovak Republic, as well as its major administrative and industrial centre. In the past, Bratislava has suffered from dangerous floods. The highest floods have occurred most frequently in the summer. Consequently, long-term forecasting of summer floods on the Danube River at Bratislava has important scientific and
more » ... t scientific and practical significance. We used the dates of the highest summer floods for the period 1876-2018, as well as historical information about the highest summer floods that occurred before the beginning of regular hydrometric observations. The commensurability method supports prediction of various natural phenomena, including floods and other dangerous events. It is characterized by the simplicity of the calculations and minimum needs for input information. Four methods of forecasting were used: (1) the calculated value of commensurability; (2) the two-dimensional and three-dimensional graphs of commensurability; (3) the time intervals between floods that have occurred in the past; and (4) the number of commensurability equations with three components. The results indicate that the highest summer floods are likely to occur on the Danube at Bratislava in 2020, 2025, and 2030. Application of the commensurability method for long-term forecasting of the highest summer floods on the Danube River at Bratislava Borys Khrystiuk, Liudmyla Gorbachova, Pavla Pekárová, Pavol Miklánek 71 At Bratislava, regular monitoring of the Danube River runoff began in 1876. During the period 1876-2018, fourteen of the highest summer floods were recorded. The maximum discharges of such floods were more than 8,050 m 3 s -1 (Table 1) . This value corresponds approximately to a discharge of 10% probability (Q 10% = 8,140 m 3 s -1 ). Forecasting results by the calculated value of commensurability Applying equation (3) , we calculated the commensurability values of the highest summer floods that were observed on the Danube River at Bratislava in the period from 1876 to 2018 (Table 2). The value of commensurability (ΔX) is 2.60 years, the value of К varies in the range 0-13, and the forecast error is ±1 year. The value ΔX was determined by successive approximation, which minimized the error. We have applied the criteria Σ|Error| and Σ(Error). The results of these calculations determine the dates of the possible subsequent highest summer floods on the Danube River at Bratislava (Table 3) . Application of the commensurability method for long-term forecasting of the highest summer floods on the Danube River at Bratislava The value of commensurability (∆Х = 2.60 years) can be used not only to predict the dates of the future highest summer floods, but also to determine the dates on which such floods occurred in the past on the Danube at Bratislava. The analysis shows that the dates of the highest summer floods from historical archives (Pekárová et al. 2014), which occurred before regular hydrometric observations, are closely consistent with the dates calculated using the value of commensurability (Table 4) . Forecasting results by the two-dimensional and three-dimensional graph of commensurability Analyzing the date array of the highest summer floods, we found that the time intervals between individual floods were the same values: = 34. This information supplies the two-dimensional graph of commensurability of the highest summer floods on the Danube at Bratislava (Fig. 3). According to this graph, we can predict the following highest summer flood: vertically 2009 + 21 = 2030 and horizontally 1975 + 55 = 2030. We also created the three-dimensional graph, which also shows that the highest summer flood can occur in 2030 (Fig. 4). Forecasting results by the time intervals between floods that have occurred in the past The time intervals between the individual highest summer floods that occurred in the past (1876-2013) were determined. We extrapolated these time intervals for the future to determine the dates of the highest summer floods that may occur in the coming years (2019-2036) (Table 5). We did not use dates of flood events before the regular monitoring because we are not sure that all the dates of high summer floods for the period 1210-1883 were identified in the historical archives. Forecasting results by the number of commensurability equations with the three components For the period 2019-2031, we have created all possible commensurability equations with three components, using the dates of the highest summer floods that have occurred in the past (1876-2018) on the Danube at Bratislava. The largest number of equations (9) with three components was compiled for 2020 (Table 9). Consequently, the next high summer flood on the Danube at Bratislava may occur in 2020. Also, high summer floods are possible in 2025, 2029 and 2030. For these dates, 5 equations were compiled ( Table 9). The application of the commensurability method supported forecasts of the possible dates of high summer floods on the Danube at Bratislava. Although our results are tentative, it can be argued that they can be reliable. This confidence is reinforced by the application of the four commensurability forecasting methods, as well as by the retrospective analysis based on historical data. Strong consistency can be seen between historical flood dates that occurred before the beginning of regular hydrometric observations, and dates that were calculated by the values of commensurability. Thus, commensurability reflects the laws determining the occurrence of high floods as well as other natural disasters. The methodologi-cal approach of Weng Wen-Bo may be applicable to forecasting other dangerous natural phenomena, thus meriting further in-depth research. Long-term forecasting of possible dangerous spring floods can be used to prevent and minimize the negative effects for the population and economy.
doi:10.26491/mhwm/114482 fatcat:7rcn54rkqzgr5mj4mxq3eusfhe