Quasi-analytical Solution And Model Inversion For Depth To Water Table Driven By Multi-periodic Evapotranspiration And Precipitation

The dynamic change law of depth to water table(DWT)is an important content of groundwater research,and also restricts the activities of human production and life.In shallow groundwater area,groundwater depth is mainly afected by evapotranspiration and precipitation,and precipitation and evapotranspiration are the main supply and discharge mechanisms.Many researchers have established groundwater dynamic models to study the variation rule of DWT by giving analytical or numerical solutions of DWT,and calibrating the model parameters.However,here almost no literature studied the multi-periodic characteristics of evapotranspiration and precipitation,and there are few models about evapotranspiration and precipitation driving DWT,and no explicit expression has been given to further quantify the driving mechanism.In this paper,a dynamic model about groundwater depth driven by multi-periodic evapotranspiration and precipitation is proposed.By means of mathematical methods and computer software,the quasi-analytical solution of the DWT is given,and the depth to water table is predicted.Besides,the change rule of DWT is studied and the model parameters are further determined with multi-modes truncated Fourier series to approximate evapotranspiration and precipitation.The frst chapter is the introduction,which mainly introduces the research background,research methods and research progress of the dynamic change characteristics of DWT.The research progress of driving mechanism of evapotranspiration and precipitation on DWT and the relevant means of parameter calibration of DWT model parameters are analyzed based on literature.The second chapter introduces the Fourier series expansion,Composite Simpson formula,wavelet analysis and the model assessment and other preliminary knowledge.In the third chapter,the dynamic model of DWT driven by evapotranspiration and precipitation is introduced,and the model is linearized and dimensionless.The fourth chapter is based on the Fourier series expansion with the second order and parameter identifcation method to solve the DWT model and give the quasi-analytic solution expression.Based on the experimental data obtained from diferent experimental sites,the driving mechanism of combined multi-periodic evapotranspiration and precipitation on the DWT in the presence and absence of lateral groundwater fow is discussed respectively.In the ffth chapter,parameter calibration and prediction of DWT model are introduced.Based on the experimental data,the analytical solution of the DWT is derived by Fourier series expansion to diferent truncated orders and Composite Simpson formula,and the model parameters are calibrated to explain the movement law of groundwater.The conclusions obtained in this paper have been rigorously derived by mathematical theory,calculated and verifed by experiments,which provide a new method for studying the shallow groundwater depth driving problem.