畦田灌溉模拟中田面微地形空间分布插值方法改进

田面微地形是影响灌溉过程及灌溉性能的重要因素之一。针对灌溉模型中田面微地形的插值问题,该文在比较Kriging插值、三次样条插值和反距离加权插值的插值精度和程序运行时间的基础上,进一步分析了不同规格畦田下Kriging插值程序运行时间随插值网格数的变化趋势,提出了利用Kriging插值和三次样条插值及反距离加权插值进行组合插值的方法,并将不同中间插值网格数经组合插值所得田面高程数据用于灌溉模拟。结果表明,Kriging插值所得田面高程的精度最高,程序所需运行时间最长;而三次样条插值和反距离加权插值所需运行时间非常短,但精度较低。为了同时满足田面高程的插值精度和模型计算效率的要求,选用Kriging插值和三次样条插值组合的方式进行灌溉模型中田面高程的插值计算最为适宜。中间插值网格数为1/4及1/8灌溉模型剖分网格数经组合插值的田面高程及Kriging插值数据用于灌溉模型所得水流推进过程与实测水流推进过程基本一致。因此,在实际应用中,中间插值网格数的确定,可根据对插值精度和运行时间的不同要求在灌溉模型剖分网格数的1/4或1/8之间选取。该研究可为灌溉模型的应用提供依据。

Improvement of interpolation methods for surface micro-topography spatial distribution in border irrigation simulation

Abstract: Surface micro-topography is one of the most important factors affecting irrigation process and performances. In view of the interpolation problem of surface micro-topography in irrigation model, using observed data on surface relative elevation of 4 different size ridge field, this study firstly compared the interpolation accuracy and program running time of Kriging interpolation, cubic spline interpolation and inverse distance weighted interpolation (IDW), and then analyzed the trend of Kriging interpolation program running time with the change of interpolation grid numbers under different sizes of ridged field. Furthermore, the combination interpolation methods of Kriging interpolation and cubic spline interpolation, and Kriging interpolation and inverse distance weighted interpolation were proposed, and the surface flow advance processes simulated based on data on surface relative elevation interpolated by the combination method and kriging interpolation were compared with observed surface flow advance process. The results showed that compared to the cubic spline interpolation and IDW, the interpolation accuracy of Kriging interpolation was the highest and Kriging interpolation could truthfully reflect the spatial distribution of micro-topography but the program running time was the longest, which had a great impact on the computational efficiency of irrigation model, while the program running time of cubic spline interpolation and IDW was relatively short, but their accuracies were low, which affected greatly the simulation accuracy of irrigation model. The running time of Kriging interpolating program increased with the size of ridge field and the number of interpolation grid. The reason of that might be there was an increase trend of equations and equations number in Kriging interpolation with the increase of ridge field size and interpolation gird numbers. The program running time of the combination interpolation method of Kriging interpolation and cubic spline interpolation and that of combination interpolation method Kriging interpolation and inverse distance weighted interpolation was the same, but the interpolation accuracy of the former was higher. In order to both meet the requirements of interpolation accuracy and computational efficiency of irrigation model, it was feasible to use the combination method of Kriging interpolation and cubic spline interpolation for surface elevation interpolation in irrigation model. For those ridge fields with their area less than 2700 m2, the combination interpolation could satisfy the requirements of mean absolute error less than 0.5 mm and program running time less than 10 s. For those ridge fields with their area more than 2700 m2, the combination interpolation could satisfy the requirements of mean absolute error less than 0.5mm and program running time less than 20s when the intermediate interpolation grid number was 1/4 of irrigation model grid number and meet the requirements of mean absolute error less than 1 mm and program running time less than 10s when the intermediate interpolation grid number was 1/8 of irrigation model grid number. The surface flow advance processes simulated based on the surface elevation data interpolated by the combination method with the 1/4 and 1/8 irrigation model grid numbers and Kriging interpolation were similar with the observed data. Therefore, the intermediate interpolation grid number could be selected between 1/4 and 1/8 of irrigation model grid number depending on the requirements of interpolation accuracy and running time.