Point Versus Block Ordinary Kriging in Rain Gauge Network Design Using Artificial Bee Colony Optimization
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RESEARCH PAPER
Point Versus Block Ordinary Kriging in Rain Gauge Network Design Using Artificial Bee Colony Optimization Mahdi Attar1 · Mohammad Javad Abedini2 · Reza Akbari3 Received: 12 September 2019 / Accepted: 1 October 2020 © Shiraz University 2020
Abstract Optimal design of rain gauge stations results in making the point and/or areal estimation of rainfall more accurate. The measure of network accuracy depends on the number and spatial location of rain gauge stations. In this paper, a new areal variance-based estimator using point ordinary kriging is developed to assess the level of accuracy for prioritizing rain gauge stations in a given network with no simplification considered. To the best of authors’ knowledge, this is the first time thereby a new point-based goodness of fit criterion so-called the percentage of area with acceptable accuracy is coupled with artificial bee colony optimization (ABC) to prioritize rain gauge stations and then validate the associated measure via coupling ABC with block ordinary kriging (BOK). This measure is applied to move from point to block and obtain the measure of accuracy. The coupled algorithm is applied to a case study with 34 existing rain gauge stations. The proposed algorithm is equipped with minimum tuning parameters and mimics the spatial pattern of rainfall variability in a distributed fashion. The results of the proposed approach showed that only eight rain gauge stations are required to achieve the same level of accuracy as the original network. In addition, the computed measure of network accuracy reproduces the BOK results for all values of n. In conclusion, the proposed scheme can be considered as a benchmark in rain gauge network design to assess the correctness of other paradigms in network design for all values of C(N, n). Keywords Point versus block ordinary kriging · Rain gauge network design · Artificial bee colony optimization List of Symbols AAreal The percentage of area with acceptable accuracy APoint “Acceptable probability” at an ungauge point 𝐬0 𝐡ij Separation vector between two spatial locations i, j k A multiplier M The number of points inside a typical block * Mohammad Javad Abedini [email protected] Reza Akbari [email protected] 1
Department of Civil Engineering, Islamic Azad University, Shiraz Branch, Shiraz, Iran
2
Civil and Environmental Engineering, School of Engineering, Shiraz University, Shiraz, Iran
3
Computer Engineering (Software Systems), Department of Computer Engineering and Information Technology, Shiraz University of Technology, Shiraz, Iran
N Total number of rain gauge stations N ( 𝐡ij) Number of data pairs whose separation vector is 𝐡ij n Number of holding rain gauge stations ( ) The true value of annual rainfall at 𝐬0 P 𝐬(0 ) PV 𝐬0 The true value of mean annual rainfall over block V index at 𝐬0 ( ) ( ) P 𝐬i , P 𝐬j Observed rainfall at spatial locations 𝐬i , 𝐬j ( ) P̂ 𝐬(0 Estimated value of annual rainfall at 𝐬0 ) P̂ V 𝐬0 Estimated value of mean annual rainfall over block V index at
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