Entropy Applications to Water Monitoring Network Design: A Review <s> Water Quality Networks <s> This paper aims at evaluating and revising the spatial and temporal sampling frequencies of the water quality monitoring system of the Jajrood River in the Northern part of Tehran, Iran. This important river system supplies 23% of domestic water demand of the Tehran metropolitan area with population of more than 10 million people. In the proposed methodology, by developing a model for calculating a discrete version of pair-wise spatial information transfer indices (SITIs) for each pair of potential monitoring stations, the pair-wise SITI matrices for all water quality variables are formed. Also, using a similar model, the discrete temporal information transfer indices (TITIs) using the data of the existing monitoring stations are calculated. Then, the curves of the pair-wise SITI versus distance between monitoring stations and TITI versus time lags for all water quality variables are derived. Then, using a group pair-wise comparison matrix, the relative weights of the water quality variables are calculated. In this paper, a micro-genetic-algorithm-based optimization model with the objective of minimizing a weighted average spatial and temporal ITI is developed and for a pre-defined total number of stations, the best combination of monitoring stations is selected. The results show that the existing monitoring system of the Jajrood River should be partially strengthened and in some cases the sampling frequencies should be increased. Based on the results, the proposed approach can be used as an effective tool for evaluating, revising, or redesigning the existing river water quality monitoring systems. <s> BIB001 </s> Entropy Applications to Water Monitoring Network Design: A Review <s> Water Quality Networks <s> In this paper, a methodology is proposed for evaluating sampling locations in an existing river water quality monitoring network. The dynamic factor analysis is utilized to extract the independent dynamic factors from time series of water quality variables. Then, the entropy theory is applied to the independent dynamic factors to construct transinformation–distance (T–D) curves. The computation time in the case of using dynamic factors is significantly less than when the raw data is used because the number of independent dynamic factors is usually much less than the number of monitored water quality variables. In this paper, it is also shown that by clustering the study area to some homogenous zones and developing T–D curves for each zone, the accuracy of the results is significantly increased. To evaluate the applicability and efficiency of the proposed methodology, it is applied to the Karoon River which is the most important river system in Iran. <s> BIB002 </s> Entropy Applications to Water Monitoring Network Design: A Review <s> Water Quality Networks <s> [1] The total maximum daily load program aims to monitor more than 40,000 standard violations in around 20,000 impaired water bodies across the United States. Given resource limitations, future monitoring efforts have to be hedged against the uncertainties in the monitored system, while taking into account existing knowledge. In that respect, we have developed a hierarchical spatiotemporal Bayesian model that can be used to optimize an existing monitoring network by retaining stations that provide the maximum amount of information, while identifying locations that would benefit from the addition of new stations. The model assumes the water quality parameters are adequately described by a joint matrix normal distribution. The adopted approach allows for a reduction in redundancies, while emphasizing information richness rather than data richness. The developed approach incorporates the concept of entropy to account for the associated uncertainties. Three different entropy-based criteria are adopted: total system entropy, chlorophyll-a standard violation entropy, and dissolved oxygen standard violation entropy. A multiple attribute decision making framework is adopted to integrate the competing design criteria and to generate a single optimal design. The approach is implemented on the water quality monitoring system of the Neuse River Estuary in North Carolina, USA. The model results indicate that the high priority monitoring areas identified by the total system entropy and the dissolved oxygen violation entropy criteria are largely coincident. The monitoring design based on the chlorophyll-a standard violation entropy proved to be less informative, given the low probabilities of violating the water quality standard in the estuary. <s> BIB003 </s> Entropy Applications to Water Monitoring Network Design: A Review <s> Water Quality Networks <s> Abstract A core problem in monitoring water quality of a river basin is identifying an optimal positioning of a limited number of water-sampling sites. Various optimality criteria have been suggested for this selection process in earlier studies. However, the search for sets of sampling sites that satisfy such criteria poses a challenging optimization problem, especially for a large basin. Here, we show that for particular types of objective functions, the optimization procedure can be dramatically simplified via an analogy with the formulation of Shannon entropy. On this basis, we propose an efficient algorithm that can easily determine the optimal location of water quality sampling sites in a river network. The proposed algorithm can be used standalone or in conjunction with a heuristic optimization algorithm such as a genetic algorithm. For the latter, the proposed algorithm filters only competitive candidates and makes a contribution to reducing the problem size significantly. The superior performance of the proposed method is demonstrated via its application to actual river networks examined in earlier studies, in which the proposed method determines more optimal solutions in a shorter computation time. The idea presented in this study can also be applied to other problems in which the objective function can be formulated in a similar functional form. <s> BIB004 </s> Entropy Applications to Water Monitoring Network Design: A Review <s> Water Quality Networks <s> The reliable assessment of water quality through water quality monitoring programs (WQMPs) is crucial in order for decision-makers to understand, interpret and use this information in support of their management activities aiming at protecting the resource. The challenge of water quality monitoring has been widely addressed in the literature since the 1940s. However, there is still no generally accepted, holistic and practical strategy to support all phases of WQMPs. The purpose of this paper is to report on the use cases a watershed manager has to address to plan or optimize a WQMP from the challenge of identifying monitoring objectives; selecting sampling sites and water quality parameters; identifying sampling frequencies; considering logistics and resources to the implementation of actions based on information acquired through the WQMP. An inventory and critique of the information, approaches and tools placed at the disposal of watershed managers was proposed to evaluate how the existing information could be integrated in a holistic, user-friendly and evolvable solution. Given the differences in regulatory requirements, water quality standards, geographical and geological differences, land-use variations, and other site specificities, a one-in-all solution is not possible. However, we advance that an intelligent decision support system (IDSS) based on expert knowledge that integrates existing approaches and past research can guide a watershed manager through the process according to his/her site-specific requirements. It is also necessary to tap into local knowledge and to identify the knowledge needs of all the stakeholders through participative approaches based on geographical information systems and adaptive survey-based questionnaires. We believe that future research should focus on developing such participative approaches and further investigate the benefits of IDSS's that can be updated quickly and make it possible for a watershed manager to obtain a timely, holistic view and support for every aspect of planning and optimizing a WQMP. <s> BIB005 </s> Entropy Applications to Water Monitoring Network Design: A Review <s> Water Quality Networks <s> The paper presents an entropy-based method for designing an optimum bay water salinity monitoring network in San Francisco bay (S.F. bay) considering maximum-monitoring-information and minimum-data-lost criteria. Due to cost concerns, it is necessary to design the optimal salinity monitoring network with a minimal number of sampling stations to provide reliable data. The monthly data recorded from January 1995 to December 2014 were obtained over 37 active stations located in S.F. bay and is applied in the research. Transinformation entropy in discrete mode is used to calculate the stations9 optimum distance. The discrete approach uses the frequency table to calculate transinformation measures. After calculating these measures, a transinformation–distance (T-D) curve is developed. Then, the optimum distance between salinity monitoring stations is elicited from the curve. The study shows that the S.F. bay salinity monitoring stations provide redundant information and the existing stations can be reduced to 21 with an approximate distance of 7.5 km. The coverage of the proposed monitoring network by using the optimum distance is complete and the system does not generate redundant data. The results of this research indicate that transinformation entropy is a promising method for the design of monitoring networks in bays such as those found in San Francisco bay. <s> BIB006
The importance of water quality monitoring networks is their ability to assist in identifying those parameters that exceed water quality standards. Several water quality monitoring strategies, including two methods that utilized entropy measures BIB001 BIB002 , were recently reviewed by Behmel et al. BIB005 . This review found that identifying a single approach to water quality monitoring network design would be virtually impossible. Despite this, various applications of the transinformation-distance curve methods have shown promise in the optimal redesign and reduction of water quality monitoring networks BIB006 BIB001 BIB002 . Lee  found that by maximizing the multivariate transinformation between chosen and unchosen stations, using the storm water management model to simulate the total suspended solids and a GA for optimization, an optimal water quality network could be designed for a sewer system. Banik et al.  compared information theory, detection time and reliability measures for the design of a sewer system monitoring network through both single and multi-objective optimization approaches. It was shown that for a small monitoring network, the methods had similar performances, while the single objective detection time-based method had slightly better performance when the number of monitoring station is larger. Alameddine et al. BIB003 used exceedance probabilities to determine violation entropy of dissolved oxygen and chlorophyll-a in the Neuse River estuary. Along with violation entropy, the total system entropy was used as a measure to identify areas of importance of monitoring. A multi-objective optimization scheme based on expert assigned weights was used to develop a compromise solution from the three entropy measures. Ultimately, the method allowed for the identification of high uncertainty areas, which would benefit from future water quality monitoring. Data availability is an issue when using entropy methods, particularly when attempting to use them in the design of a monitoring network in an ungauged basin. To address this, Lee et al. BIB004 developed a method that uses a measure analogous to marginal entropy. This method uses characteristics of the basin such as the length and number of reaches in the river network as part of the cost function, which is then optimized using a combined GA and filtering algorithm. This was shown to be a computationally-efficient method for use in optimal network design of an ungauged river basin.