The Groundwater Problem And The Dimension-reduction Modeling Based On POD Study

Soil water connecting surface water and groundwater affects climate by influenc-ing the water and energy exchange between land surface and atmosphere, and it plays a important role in climate and water circulation system. Dynamic variations in the water table over a region directly influence soil moisture at the surface, which leads to effects on latent and sensible heat fluxes and the growth and development of natural vegetation over the region. Water table fluctuations are influenced by surface fluxes such as infil-tration or evapotranspiration through the unsaturated zone, thus there is an important connection between soil water and ground water.It is difficult to represent reasonably the interaction between soil water and ground water in climate and land circulation model with the fully three-dimensional soil wa-ter and groundwater model. There are many computational quantities when the three-dimensional interaction model is applied to large-scale regions. According to the main character of soil water flow and ground water flow in land surface processes, we have developed a quasi three-dimensional groundwater model including the equations of one-dimensional vertical soil water flow and two-dimensional horizonal groundwater flow. The model reduces computation and make it possible that representing reasonably the interaction of soil water and groundwater in climate and land water circulation model.The numerical computation is the most effective method in solving the two-dimensi onal or high-dimensional partial difference equation. however, the discrete equations ob-tained by numerical method tend to be more unknown variables, the computation will be time-consuming. Proper orthogonal decomposition (POD) is an effective method for ap-proximating a large amount of data. Reducing computational dimensions?diminishing computational quantity and saving computation time are the most obvious advantage of POD. Combining the POD and usually numerical computation method and constructing a kind of numeric format with high accuracy and lower free degrees will be the broad application prospects.Research objective of this paper is building a quasi three-dimensional ground-water model suitable for the simulation of the climate and land water circulation system, and developing a kind of dimension-reduction numerical solution based on POD for the two-dimensional soil water model, so as to improve numerical compu- tation efficiency. The main content of this paper includes as follows:(1) Built a quasi two-dimensional numerical model based on soil water-groundwater and stream-aquifer interactions. The estimation of water table depth and soil water content on the soil profile under stream-aquifer interaction was reduced to be the two-dimensional moving boundary problem with soil water-groundwater interaction. The soil water flow was approximately divided into an unsaturated vertical soil water flow and a horizontal groundwater flow for the simulation of the interaction between soil water and groundwater. We developed a quasi two-dimensional numeric model based on vertical soil water equation and horizontal water table equation under stream-aquifer interaction. The sensitivities of the main parameters of the developed model were dis-cussed and its validation at the Yingsu Section of the lower reaches of the Tarim River with stream water conveyance showed the model can simulate water table dynamic vari-ation reasonably.(2) Built a quasi three-dimensional variably saturated groundwater numeri-cal model based on soil water-groundwater interaction. The interaction of soil water and groundwater was reduced to be a three-dimensional saturated-unsaturated soil water flows problem. We developed a quasi three-dimensional, variably saturated groundwater flow model by approximately dividing the three-dimensional soil water and groundwater flow into an unsaturated vertical soil water flow and a horizontal groundwater flow for simulation of the interactions between soil water and groundwater. For each unsaturated soil column, a new soil layer structure was presented and an adaptive grid refinement method was applied to simulate the soil moisture content at the cell nodes. Synthetic ex-periments using the quasi three-dimensional numerical model were conducted to test the sensitivities of the main parameters of the model, including the river elevation, ground surface horizontal hydraulic conductivity, and surface flux. The results showed the ro-bustness of the developed model under different conditions. The estimation scheme of water table depth based the developed quasi three-dimensional model and SCE-UA pa-rameter calibration method was validated by a case of stream water conveyance in the lower reaches of the Tarim River. The simulation results of the water table elevations were in good agreement with the observations in the four monitoring wells. The param-eter test and model application for the prediction of water table elevations at the Yingsu section in the lower reaches of the Tarim River showed that it can be more reasonable to use the developed model with an adaptive refinement grid to substitute the original ten-layer unsaturated soil water structure. A numerical experiment by the model for Tarim River Basin was conducted to test the model on simulation of the effects of lateral groundwater flow for large-scale high-relief topography with stream water conveyance. The results showed that the model had the potential to be used in large-scale groundwa-ter latent flow.(3)Developed dimension-reduce numerical method based on POD for the two-dimensional unsaturated soil water flow equation. For the two-dimensional unsatu-rated soil water equation, an optimizing reduced implicit difference scheme (IDS) and reduced finite element scheme (FES) based on singular value decomposition (SVD) and proper orthogonal decomposition (POD) was presented, respectively. The error esti-mates of the corresponding reduced POD numerical scheme were given and proved. The numerical examples showed the error between the reduced POD solution and usu-ally numerical solution was small enough, and computation time was reduced. Thus, both the feasibility and efficiency of our reduced IDS were validated.