The application of a Grey Markov Model to forecasting annual maximum water levels at hydrological stations |
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| Authors: | Sheng Dong Kun Chi Qiyi Zhang Xiangdong Zhang |
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| Institution: | 1. College of Engineering, Ocean University of China, Qingdao, 266100, P. R. China
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| Abstract: | Compared with traditional real-time forecasting, this paper proposes a Grey Markov Model (GMM) to forecast the maximum water
levels at hydrological stations in the estuary area. The GMM combines the Grey System and Markov theory into a higher precision
model. The GMM takes advantage of the Grey System to predict the trend values and uses the Markov theory to forecast fluctuation
values, and thus gives forecast results involving two aspects of information. The procedure for forecasting annul maximum
water levels with the GMM contains five main steps: 1) establish the GM (1, 1) model based on the data series; 2) estimate
the trend values; 3) establish a Markov Model based on relative error series; 4) modify the relative errors caused in step
2, and then obtain the relative errors of the second order estimation; 5) compare the results with measured data and estimate
the accuracy. The historical water level records (from 1960 to 1992) at Yuqiao Hydrological Station in the estuary area of
the Haihe River near Tianjin, China are utilized to calibrate and verify the proposed model according to the above steps.
Every 25 years’ data are regarded as a hydro-sequence. Eight groups of simulated results show reasonable agreement between
the predicted values and the measured data. The GMM is also applied to the 10 other hydrological stations in the same estuary.
The forecast results for all of the hydrological stations are good or acceptable. The feasibility and effectiveness of this
new forecasting model have been proved in this paper. |
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| Keywords: | Grey Markov Model forecasting estuary disaster prevention maximum water level |
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