Contents lists available at ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement Retrospective analysis: A validation procedure for the redesign of an environmental monitoring network E. Barca a , D.E. Bruno a , A. Lay-Ekuakille b , S. Maggi a, ⁎ , G. Passarella a a CNR-IRSA, Water Research Institute, 70132 Bari, Italy b Department of Innovation Engineering, University of Salento, 73100 Lecce, Italy ARTICLE INFO Keywords: Groundwater monitoring Monitoring network optimization Kriging Retrospective analysis ABSTRACT Monitoring networks are essential tools for the effective management of vulnerable or limited environmental resources. Cost and logistics constraints often suggest to reduce the number of monitoring sites while minimizing the loss of information determined by these changes. The problem can be rigorously addressed through the optimization of one or more objective functions that represent the managerial goals associated to the network. However, the use of objective functions is based on assumptions that in practical cases can be inaccurate. To overcome this problem, we have developed a retrospective analysis procedure that validates the degree of ac- ceptability of the optimal reduced configuration at a local and global level. The procedure has been applied to a case study in Apulia, Italy, finding that the optimal reduced network was unable to recover the measured values of the monitored parameter of two discarded locations, making it unable to accomplish its monitoring goals. 1. Introduction The optimal design of an environmental monitoring network is a key aspect of the effective and sustainable management of vulnerable or limited natural resources and much research effort has been spent to provide practical solutions to this problem. An environmental monitoring network must be able to assess the state of a natural resource by reliably measuring a set of physical, chemical or biological parameters that characterize the system with the minimum amount of economic resources. In practice, these require- ments correspond to maximizing the information content of the net- work while minimizing the costs and labor involved in the task. For its inherent difficulty and practical usefulness, the problem has attracted the interest of several scientists, who have proposed a wide array of possible technical solutions [1–10]. The search of an optimal solution addresses two possible situations: the design of a new network and the redesign of an already existing network. The latter case is more frequent and also more challenging, since it can be very difficult to adapt an already existing network to new monitoring needs. Network redesign can either aim at increasing (net- work upsizing) or decreasing (network downsizing) the number of net- work monitoring sites over a given study area. A last and less common case consists in the rearrangement of the monitoring sites, while keeping unchanged the number of sites (network relocation), usually to increase the global efficiency of the network. The redesign of a monitoring network can be performed by using one or more objective functions that capture the main features of the monitored parameters and the goals of the network management and assign a score to each of the possible configurations of the redesigned network. The network configuration that minimizes the objective function (or linear combinations of multiple objective functions) is considered the best possible redesigned network with respect to the selected features. Therefore, a great care must be taken in the proper choice of the objective function according to the managerial goals as- sociated to the redesign of the network. The spatial nature of monitoring networks and the successful ap- plication of geostatistics to spatial mathematical modeling problems, has paved the way to the use of objective functions based on geosta- tistical indices. Kriging is a geostatistics interpolation technique that predicts the value of a parameter at locations where no measurement exists in terms of actual measurements at surrounding sites. A specific characteristic of kriging is that it associates to the prediction the kriging estimation variance (KEV), usually interpreted as a measure of the uncertainty of the prediction. For this reason, objective functions based on KEV have been pro- posed for the optimization of monitoring networks [11–13]. The con- figuration that minimizes these objective function thus has the least http://dx.doi.org/10.1016/j.measurement.2017.08.014 Received 10 April 2017; Received in revised form 7 August 2017; Accepted 9 August 2017 ⁎ Corresponding author. E-mail addresses: emanuele.barca@ba.irsa.cnr.it (E. Barca), delia.bruno@ba.irsa.cnr.it (D.E. Bruno), aime.lay.ekuakille@unisalento.it (A. Lay-Ekuakille), sabino.maggi@cnr.it (S. Maggi), giuseppe.passarella@ba.irsa.cnr.it (G. Passarella). Measurement 113 (2018) 211–219 Available online 10 August 2017 0263-2241/ © 2017 Elsevier Ltd. All rights reserved. MARK