Posavec Kristijan, Giacopetti Marco, Materazzi Marco, Birk Steffen
Department of Geology and Geological Engineering, Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia.
Geology Division, School of Science and Technology, University of Camerino, Gentile III da Varano, 62032, Camerino (MC), Italy.
Ground Water. 2017 Nov;55(6):891-898. doi: 10.1111/gwat.12549. Epub 2017 Jun 26.
A new method was developed and implemented into an Excel Visual Basic for Applications (VBAs) algorithm utilizing trigonometry laws in an innovative way to overlap recession segments of time series and create master recession curves (MRCs). Based on a trigonometry approach, the algorithm horizontally translates succeeding recession segments of time series, placing their vertex, that is, the highest recorded value of each recession segment, directly onto the appropriate connection line defined by measurement points of a preceding recession segment. The new method and algorithm continues the development of methods and algorithms for the generation of MRC, where the first published method was based on a multiple linear/nonlinear regression model approach (Posavec et al. 2006). The newly developed trigonometry-based method was tested on real case study examples and compared with the previously published multiple linear/nonlinear regression model-based method. The results show that in some cases, that is, for some time series, the trigonometry-based method creates narrower overlaps of the recession segments, resulting in higher coefficients of determination R , while in other cases the multiple linear/nonlinear regression model-based method remains superior. The Excel VBA algorithm for modeling MRC using the trigonometry approach is implemented into a spreadsheet tool (MRCTools v3.0 written by and available from Kristijan Posavec, Zagreb, Croatia) containing the previously published VBA algorithms for MRC generation and separation. All algorithms within the MRCTools v3.0 are open access and available free of charge, supporting the idea of running science on available, open, and free of charge software.
一种新方法被开发出来，并以创新的方式应用于Excel应用程序可视化Basic（VBA）算法中，该算法利用三角学定律来重叠时间序列的衰退段并创建主衰退曲线（MRC）。基于三角学方法，该算法对时间序列的后续衰退段进行水平平移，将其顶点（即每个衰退段的最高记录值）直接置于由前一个衰退段的测量点定义的适当连接线上。新方法和算法延续了MRC生成方法和算法的发展，其中首次发表的方法基于多元线性/非线性回归模型方法（波萨韦茨等人，2006年）。新开发的基于三角学的方法在实际案例研究示例上进行了测试，并与先前发表的基于多元线性/非线性回归模型的方法进行了比较。结果表明，在某些情况下，即对于某些时间序列，基于三角学的方法会使衰退段的重叠更窄，从而得到更高的决定系数R，而在其他情况下，基于多元线性/非线性回归模型的方法仍然更具优势。使用三角学方法对MRC进行建模的Excel VBA算法被应用到一个电子表格工具（由克罗地亚萨格勒布的克里斯蒂扬·波萨韦茨编写并可从其处获得的MRCTools v3.0）中，该工具包含先前发表的用于MRC生成和分离的VBA算法。MRCTools v3.0中的所有算法都是开放获取且免费的，支持在可用、开放且免费的软件上运行科学的理念。
