赵振华, 马曾虎, 袁革新, 王冬青, 肖威. 2018: 基于数字高程模型推定区域地下水流场的方法. 工程地质学报, 26(s1): 457-463. DOI: 10.13544/j.cnki.jeg.2018137
    引用本文: 赵振华, 马曾虎, 袁革新, 王冬青, 肖威. 2018: 基于数字高程模型推定区域地下水流场的方法. 工程地质学报, 26(s1): 457-463. DOI: 10.13544/j.cnki.jeg.2018137
    ZHAO Zhenhua, MA Zenghu, YUAN Gexin, WANG Dongqing, XIAO Wei. 2018: A METHOD OF SIMULATING THE REGIONAL GROUNDWATER LEVEL DISTRIBUTION BASED ON DIGITAL ELEVATION MODEL. JOURNAL OF ENGINEERING GEOLOGY, 26(s1): 457-463. DOI: 10.13544/j.cnki.jeg.2018137
    Citation: ZHAO Zhenhua, MA Zenghu, YUAN Gexin, WANG Dongqing, XIAO Wei. 2018: A METHOD OF SIMULATING THE REGIONAL GROUNDWATER LEVEL DISTRIBUTION BASED ON DIGITAL ELEVATION MODEL. JOURNAL OF ENGINEERING GEOLOGY, 26(s1): 457-463. DOI: 10.13544/j.cnki.jeg.2018137

    基于数字高程模型推定区域地下水流场的方法

    A METHOD OF SIMULATING THE REGIONAL GROUNDWATER LEVEL DISTRIBUTION BASED ON DIGITAL ELEVATION MODEL

    • 摘要: 利用实测数据推定区域地下水流场是水文地质研究中非常重要的一项内容,传统的方法通常是利用已有水位数据进行插值计算,这样获得的地下水流场的准确性受钻孔的数量及分布的合理性影响太大,在某些无资料地区是不适用的。从区域尺度上来说,大多数平原地区的地下水运动受地形影响最大,地形和地下水运移的路径呈一定的相关性,据此,本文提出了一种基于数字高程模型计算区域地下水流场的方法,其中,趋势面方程参量的确定和系数率定是关键点和难点。在利用地表高程数据进行地下水位计算时,当选择低次多项式时,容易造成趋势面方程不能很好地拟合实测数据,而当选择高次多项式时,会造成方程求解的不稳定,因此,本文首先建立高次多项式作为初始趋势面方程,分别对趋势面方程中趋势项的各个参量与实测地下水位标高进行相关性分析,选取与地下水位标高具有明显相关性的参量组成趋势项方程,然后利用实测数据,对地下水面趋势平均水平实现了最优化的估计,求得和实测数据吻合最佳的趋势项方程,最后根据Lanczos奇异值分解理论,求得趋势项方程的解,并对残差部分使用泛克里金插值方法进行了无偏最优的估计。该方法在西北某区进行了应用,计算结果的误差远小于克里金插值法,与实测值吻合得更好,而且还可以进行外推计算,该技术方法在西北无资料地区地下水流场的推定中有较好的应用前景。

       

      Abstract: It is very important to use the measured data to obtain the regional groundwater level distribution in groundwater flow modeling, which can provide the initial flow field or boundary condition for modeling, and can be used as the verification basis for the simulation results. Traditional methods are usually interpolated using existing water level data, and the accuracy of the results is greatly influenced by the number of boreholes and the rationality of distribution, so it is not applicable in ungauged region of northwest China. Actually, the flow of groundwater in most areas is affected by the topography at the regional scale, and the terrain and groundwater flow path are correlated. In this paper, a method based on digital elevation model to simulate the regional groundwater level distribution is presented. The selection of the trend surface equation and parameter calibration are the key points and difficulties, because low order polynomial may lead the trend surface equation cannot fit the measured data well, and high order polynomial maybe lead the instability of the solution to the equation. Therefore, this paper established the high order polynomial as the initial trend surface equation. The correlation between each parameter in the trend surface equation and the elevation of the measured groundwater level was analyzed, and the parameters with obvious correlation with the elevation of groundwater level compose the trend surface equation. And then using the measured data realized the optimal estimation of the average trend level of groundwater, to ensure the best trend surface equation. Finally, according to Lanczos singular value decomposition theory, the trend surface equation solution were obtained, and an unbiased and optimal estimation of the residual using the method of universal kriging interpolation was presented. This method was applied in a certain area of northwest China, and the error of the calculation results was much less than that of the kriging interpolation method, which was more consistent with the measured values and could be used to extrapolate. This method has a good prospect in the simulation of groundwater flow field in ungauged region of northwest China.

       

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