Comparison of Variance‐Reduction and Space‐Filling Approaches for the Design of Environmental Monitoring Networks

Abstract

This article focuses on the design of groundwater monitoring networks to detect contamination with nitrates from agricultural origin. This is a problem that has been in the minds of the general public, scientists, governmental agencies, and legislators for some time now. If one looks at European statistics, despite still incomplete data, in 13% of the regions the 50 mg/l European water quality standard for drinking water (Drinking Water Directive, 98/83/EC) is exceeded in more than 25% of the monitoring stations. A compliance groundwater nitrate‐monitoring network is developed for a case study in the south of Portugal (Gabbro of Beja aquifer system), using both variance‐reduction and space‐filling approaches. In the first the variance of the error of estimation obtained by ordinary kriging is used, after building a covariance model, and the objective is to minimize the average kriging variance. In the second approach a criterion for the quality of spatial coverage is used, usually based on a metric. The objective here is also usually to minimize a function of the metric (criterion). The search for a solution is made in an iterative manner, by replacing one station, analyzing the result, and deciding whether to keep the solution or not. Due to the enormous number of possible combinations even for small networks, a structured search method, the simulated annealing method, is used to obtain the final network.

MSANOS: Data-Driven, Multi-Approach Software for Optimal Redesign of Environmental Monitoring Networks

“…The main target user and the requested wide range of application moved to focus on data-driven algorithms while neglecting physically based methods (e.g., data assimilation and Kalman-Filter based methods). Within this class of methods, the choice fell upon SSA, whose efficacy has been largely proved, both theoretically (Metropolis et al 1953;Kirkpatrick et al 1983;Tsitsiklis 1989;Christakos and Killam 1993;Deutsch and Cockerham 1994;Drosou and Pitoura 2009;Richey 2010) and practically (Pardo-Igùzquiza 1998;Van Groenigen and Stein 1998;Van Groenigen et al 1999, 2000Nunes et al 2006;Nunes et al 2007), by a large amount of scientific literature (Henderson et al 2003).…”

Optimal selection of groundwater-level monitoring sites in the Zhangye Basin, Northwest China

“…The second type of optimization sampling design model includes statistical approaches that describe the spatial structure of a monitoring variable via statistical modeling and then use this information to design the network. For example, methods based on geostatistics aim to minimize the average kriging prediction-error variance; they have been widely used to design groundwater monitoring networks (Cameron and Hunter, 2002;Yeh et al, 2006;Nunes et al, 2007;Yang et al, 2008;Dhar and Datta, 2009;Nowak et al, 2010;Junez-Ferreira and Herrera, 2013). Yang et al (2008) used the average kriging standard deviation as a criterion to determine the density of the groundwater-level monitoring network in the Chaiwopu Basin, Xinjiang Uygur Autonomous Region, China.…”

“…Dhar (2013) developed a multi-objective solution based on the optimization model and the kriging model for optimally designing a groundwater head and quality monitoring plan. All of these methods were carefully developed for applications based on various types of geostatistical algorithms (Nunes et al, 2007). Second-order stationarity is assumed for the geostatistical method of groundwater monitoring in a study area, i.e., the mean and variance are independent of the location, and the covariance only depends on the lag separation.…”

Structural Reliability Assessment by Local Approximation of Limit State Functions Using Adaptive Markov Chain Simulation and Support Vector Regression

“…Once the training samples are generated, the support vector classifier is used to predict the failure probability. Other methods, such as the Kriging model and the particle swarm optimization algorithm have also been developed to approximate limit state functions (Elegbede, 2005; Nunes et al, 2007; Echard et al, 2011; Plevris and Papadrakakis, 2011). The recursive algorithm was also used for assessing the reliability of lifeline systems (Dueñas‐Osorio and Rojo, 2010).…”