Research on Monitoring Plan for Xiaolangdi Reservoir Based on Nonlinear Programming

Abstract

The water and sediment flux of the Yellow River fluctuates under the influence of various natural and human factors, significantly impacting ecological management and water resources in the Yellow River basin.This study investigates the patterns of sediment-water flux variation in the Yellow River and evaluates the practical effectiveness of the “water diversion and sediment regulation” project. Utilizing multiple linear regression models, seasonal ARIMA models, and grey prediction models, it comprehensively employs Excel, Matlab, and SPSS to analyze the relationship between sediment concentration and time, water level, and flow rate. The research summarizes the patterns of sediment-water flux variation and assesses the actual outcomes of the “water diversion and sediment regulation” initiative to enhance Yellow River basin management and address practical challenges.

Addressing the first issue, Excel was first used to clean the water-sediment monitoring data from a specific hydrological station on the Yellow River between 2016 and 2021 (Appendix 1), removing invalid data lacking sediment concentration values. Subsequently, Matlab was employed to plot scatter diagrams of sediment concentration versus time, water level, and flow rate. These plots indicated a preliminary linear relationship between sediment concentration and water level/flow rate, suggesting the applicability of a multiple linear regression model.SPSS was employed to solve the multiple linear regression model, yielding regression coefficients of 0.568 for water level and 0.002 for flow rate, confirming the linear relationship between independent and dependent variables. A multiple linear regression model was then re-established to estimate sediment concentration in the Yellow River over the past six years. Excel was used to calculate annual total water flow and annual total sediment discharge.

For Problem 2, the water-sediment flux research methodology was first defined, dividing water-sediment flux into water flux and sediment flux. Water flux was measured by flow rate indicators, while sediment flux was measured by sediment discharge indicators. Excel was used to filter and consolidate the required research data.Second, employing a “combination of numbers and shapes,” annual line charts for water and sediment fluxes were plotted, along with 72-month variation patterns (January to December) for each year from 2016 to 2021. This enabled visual analysis of the hydrological station’s water-sediment flux characteristics, including abrupt changes, seasonality, and periodicity.

For Problem 3: First, aggregate the water and sediment flux data from 2016 to 2021 at this hydrological station. Construct a seasonal ARIMA model and solve it using SPSS to verify that the original sequence passes the stationarity test. Analyze the autocorrelation and partial autocorrelation plots to obtain the model results. Use Excel to plot line charts showing the future two-year trends in water and sediment flux at this hydrological station. Second, based on the patterns of water and sediment flux variation, a nonlinear programming model was constructed. Using Matlab to solve the nonlinear programming model, an optimal sampling and monitoring plan for the next two years was formulated. This approach aims to understand the dynamic changes in water and sediment flux while minimizing sampling and monitoring costs and resource utilization.

For Question 4, first use Excel to plot a line chart based on the water and sediment data from May to October 2016–2021 in Appendix 1 and the riverbed elevation data in Appendix 3. This will enable a comparative analysis of the actual effectiveness of the “water and sediment regulation” measures at Xiaolangdi Reservoir.Second, exclude the June data from Appendix 2 to calculate the elevation changes (either rise or fall) of the riverbed over the two-year period. Construct a grey prediction model and solve it using SPSS to forecast the future changes in riverbed elevation over the next decade.