Data Assimilation Application To The Saturated-unsaturated Flow

Saturated-unsaturated flow has always been the focus of research in groundwater resources and environmental protection, various numerical algorithms have been developed for saturated-unsaturated flow modeling. These models usually contain a lot of soil hydraulic parameters which are difficult to measure directly. In practical application, modelers have to estimate the parameters by limited drill hole data or just personal experience. Thus, there are always pre-existing uncertainty in the model parameters and resulting deviation in model prediction. As the rapid development of observational techniques, many kinds of observation data (etc., satellite remote sensing data) can be acquired. But the observations from these techniques are usually indirectly related to the model parameters, and it is difficult to integrate the indirect observation information into traditional deterministic models. It is of great significance to introduce new numerical techniques into saturated-unsaturated flow modeling for more effective parameter estimation and model prediction.This work reviews the progress of data assimilation research and the most representative method, Ensemble Kalman Filter (EnKF), in weather forecasting, ocean forecasting, geohydrology, and reservoir inversion. The development of saturated-unsaturated flow modeling and the advantages and disadvantages of various models are analyzed. The main observation type in vadose zone are are summarized. Based on the investigated research results, a modular framework is established to develop efficient data assimilation methods for saturated-unsaturated water flow. The work applies the EnKF and its iterative variants into several popular traditional deterministic models and fully discusses the controlling factors in saturated-unsaturated data assimilation. In the last of the study, a field infiltration study is conducted to test the application of data assimilation methods. The detailed studies are presented as follows.Firstly, the data assimilation method based on EnKF is applied to solve the two-dimensional saturated groundwater flow problem. The uncertainty of precipitation recharge and saturated hydraulic conductivity is considered. The interaction between different types of observations and state variables is studied. The results show that the EnKF method can effectively improve the estimation of groundwater model parameters via long term water head observation, and that the method performs better under higher rainfall supply. Secondly, the data assimilation method based on EnKF and Ensemble Randomized Maximum Likehood (EnRML) is applied to solve the one-dimensional saturated-unsaturated water flow problem. The feasibility of different numerical models (e.g. Picard-h, Picard-mix and Ross methods), state variables (e.g. water content and pressure head), and data assimilation methods (e.g. EnKF and EnRML) in one-dimensional saturated-unsaturated data assimilation are fully discussed. As the Picard-mix and Picard-h based numerical models (such as HYDRUS) is easily to collapse when water content changing rapidly, the Ross model is a more suitable alternative. The probability distribution of water content is closer to Gaussian distribution than pressure head, which make it perform better than pressure head in unsaturated zone. The EnRML method shows barely no advantages than EnKF in one-dimensional saturated-unsaturated data assimilation.Thirdly, the data value of water table level is discussed via the proposed one-dimensional saturated-unsaturated data assimilation model. Based on theoretical analysis and numerical experiments, the water table level data is proved to reflect soil hydraulic parameters properties in study area. And the data assimilation methods can retrieve the parameters by assimilating long-terms of water table level data.Fourthly, the EnKF and three algorithms of iterative EnKFs (Confirming EnKF, Restart EnKF, and modified Restart EnKF) are developed to solve the two-dimensional saturated-unsaturated water flow problem (via SWMS-2D code). The inconsistency problem (i.e., updated model parameters and state variables do not follow the Richards' equation) in vadose zone data assimilation due to model nonlinearity is fully investigated. Numerical experiments are designed to investigate the performance of EnKF, Confirming EnKF, Restart EnKF and modified Restart EnKF with different types and spatial configuration of observations (pressure head and water content) and different values of observation error variance, initial guess of ensemble mean and variance, ensemble size, and damping factor. The numerical study shows that Confirming EnKF produces considerable inconsistency for the nonlinear unsaturated flow problem, which differs from the seemingly consensus opinion that Confirming EnKF can resolve the inconsistency problem. In contrast, Restart EnKF and its modification can resolve the inconsistency problem. Restart EnKF and its modification outperform EnKF and Confirming EnKF in the various cases considered in this study. It is also found that combining different types of observations can achieve better assimilation results, which is useful to monitoring network design.Fifthly, a field infiltration experiment is conducted at the Irrigation and Drainage Experiment Site in Wuhan University to validate the data assimilation model. The soil hydraulic parameters are detailed measured by centrifuge experiments and double-ring infiltrometer tests first. The fitted parameters are closed to the parameters estimated via the data assimilation model, which indicates the effectiveness of the proposed data assimilation model in unsaturated parameter inversion. The study also proves that the surface soil moisture measurement can retrieve the whole soil moisture via the proposed data assimilation model, even under inaccurate initial condition and lower boundary condition.Lastly, the major research work and contributions are summarized, and the issuers that need further investigation are presented. The possible extensions of the study and further research work are also issued.