Broken line smoothing for data series interpolation by incorporating an explanatory variable with denser observations: Application to soil-water and rainfall data

Broken line smoothing is a simple technique for smoothing a broken line fit to observational data and provides flexible means for interpolation. Here an extension of this technique is proposed, which can be utilized to perform various interpolation tasks, by incorporating, in an objective manner, an explanatory variable available at a considerably denser dataset than the initial main variable. The technique incorporates smoothing terms with adjustable weights, defined by means of the angles formed by the consecutive segments of two broken lines. The mathematical framework and details of the method as well as practical aspects of its application are presented and discussed. Also, examples using both synthesized and real world (soil water dynamics and hydrological) data are presented to explore and illustrate the methodology.