Author(s): Roberto Abraham Vazquez Martinez; Ramon Dominguez Mora; Maritza Arganis; Eliseo Carrizosa Elizondo; Olaf Santana

Linked Author(s):

Keywords: IDW spatial interpolation; Influence parameter p; GRG nonlinear programming

Abstract: The real-time pluviographic measurement systems provide crucial information for the coordination and efficient operation of the control structures in a hydrological system, especially under extreme storm conditions. Unfortunately, the stations sometimes present measurement errors or, in certain cases, do not record the event, which makes it more difficult to accurately determine both the height and intensity of the storm. Therefore, it is crucial to have a reliable tool to estimate rainfall at stations affected by measurement problems. In hydrology, spatial interpolation techniques are used to estimate the value of a variable at an unmeasured point from a weighted average of the recorded values. They are based on the premise that the points closer to the location of interest have a larger influence than those farther away. Therefore, the proximity of the measured points directly affects the calculation of the variable at the site of interest. One of the most common techniques for interpolating precipitation data at unmeasured points is the Inverse Distance Weighted (IDW). This technique assumes that measured points have an influence inversely proportional to their distance from the point of interest, and that such influence is constant and accurate (Echavarria, 2013). It is characterized by the use of an influence parameter p, which adjusts the degree of influence of the measured points on the point of interest. The first part of this paper proposes a methodology for calculating a general parameter pg, of the entire pluviometric network, from the average of the annual maximum records and the spatial distribution of the stations. This calculation is formulated as a nonlinear programming problem, the objective is to minimize the difference between the values estimated by the IDW technique and the recorded averages throughout Nonlinear method. The second part consists of the development of an algorithm designed to improve the IDW interpolation technique by continuously adjusting of a particular parameter pp, based on the available measured information, which makes it possible to deal with specific measurement problems at each station. This process was implemented using a program developed in Python, which allows executing the most appropriate minimization technique to estimate the specific value of parameter pp at any unmeasured point. Although the proposed methodology has been developed for the case study of the Valley of Mexico Basin (VMB), its application can be extended to any rainfall measurement network, which makes it a versatile tool for the accurate estimation of precipitation at unmeasured sites.

DOI: https://doi.org/10.64697/978-90-835589-7-4_41WC-P2141-cd

Year: 2025