Entropy Applications to Water Monitoring Network Design: A Review <s> Introduction <s> This conference is the latest involving conferences whose research includes work in what is called the design of data networks. The broader scope of this conference reflects, in my view, movement toward greater sophistication in research and in subject matter, and it is good that these kinds of critical inquiry are going on. The rough estimates mentioned at the conference show data collection to be big business, even though data storage and retrieval tend to attract most public attention. The design of data systems, that is, the efficiency and effectiveness, must also be concerned with the manner of collection, the places and numbers of observations, their costs, and their utility. These matters constitute the fundamentals. Yet in the face of the wide range of present and prospective uses, the complex range of objectives, and the diversity of variables the products of research and critical inquiry appear to find few applications. That subject as well as the needs and opportunities were examined at this conference. <s> BIB001 </s> Entropy Applications to Water Monitoring Network Design: A Review <s> Introduction <s> Data are of value in the design and operation of water resource projects because they provide information about uncertain states of nature. This information can in turn be used to reduce the risks inherent in the project. In this paper, risk calculations from the preposterior analysis of statistical decision theory are extended to cover nonoptimal decisions. Risk is measured in terms of the project objectives by embedding the data network into an information-response (IR) system. The value of addition or improvement to the data base is measured by the change in the risk. Measures of the performance of the IR system are developed. From these measures, the efficiency of the information subsystem, the response subsystem, and the overall IR system are defined. These concepts are illustrated by a simple example in which the additional data sample for estimating the 6¼-year flow is shown to have different values (negative in one case), depending on the estimation method or decision rule used. Five anomalies and paradoxes in the literature concerning the worth of data are explained. <s> BIB002 </s> Entropy Applications to Water Monitoring Network Design: A Review <s> Introduction <s> [1] Hydrometric network design for surface water monitoring is employed to address a wide range of environmental and water resources problems. Historical overview of hydrometric network design is provided along with a discussion on new developments and challenges in the design of optimal hydrometric networks. This review starts with precise examples of decline in hydrometric network density, then highlights the increasing requirement of optimal network design in a context of climate and land use changes. An extensive survey of methodological development in hydrometric network design is provided along with discussion on the issue of uncertainty in hydrometric network design and the evolution in data collection techniques and technology. Finally, some conclusions are drawn on the future of hydrometric network design. <s> BIB003 </s> Entropy Applications to Water Monitoring Network Design: A Review <s> Introduction <s> Sensors and sensor networks play an important role in decision-making related to water quality, operational streamflow forecasting, flood early warning systems, and other areas. In this paper we review a number of existing applications and analyse a variety of evaluation and design procedures for sensor networks with respect to various criteria. Most of the existing approaches focus on maximising the observability and information content of a variable of interest. From the context of hydrological modelling only a few studies use the performance of the hydrological simulation in terms of output discharge as a design criterion. In addition to the review, we propose a framework for classifying the existing design methods, and a generalised procedure for an optimal network design in the context of rainfall-runoff hydrological modelling. <s> BIB004 </s> Entropy Applications to Water Monitoring Network Design: A Review <s> Introduction <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
Water monitoring networks account for all aspects of the water-related measurement system including precipitation, streamflow, water quality, groundwater, soil moisture, etc. BIB001  [3] . Adequate water monitoring networks and quality data from them comprise one of the first and primary steps towards efficient water resource management. The basic principles of water monitoring network design have simply been a number of monitoring stations, locations of the stations and data period or sampling frequency   . Recent technological advances have allowed gradual transitions from manual sampling to the automated observations, while some water quality parameters still require field and/or lab analyses of water or other environmental samples. One may expect that the more data we collect, the more water resource problems are solved efficiently. However, this is not always true because irrelevant, inadequate or inefficient data in the wrong location or at the wrong time can inhibit the quality of a dataset BIB001  BIB002 . More seriously, the decline of water monitoring networks has been a general trend due to financial limitations and changes of monitoring priority   BIB003 . Therefore, determining the adequate number of monitoring stations and their locations has become critical to network design. However, a standardized methodology for a proper water monitoring network design process has not been drawn yet due to the practical and socioeconomic complexity in diverse design cases BIB001 BIB004 . The existing reviews have investigated the broad range of the water monitoring network design methodologies, such as statistical analysis, spatial interpolation, application of information theory, optimization techniques, physiographic analysis, user survey or expert recommendations and combinations of multiple methods   BIB003 BIB004    BIB005 . A prior comprehensive review by Mishra and Coulibaly BIB003 reviewed evidence of declining hydrometric network density, highlighted the importance of quality data from well-designed networks and considered a range of approaches by which networks were designed. They also compared statistical, spatial interpolation, physiographic, sampling-driven and entropy-based approaches to hydrometric network design. Mishra and Coulibaly BIB003 were able to draw several conclusions about the importance of high quality hydrometric data for water resource management that remain valid. They also concluded that one of the most promising approaches for network design was the application of entropy methods highlighting early studies using the principle of maximum entropy and information transfer. Therefore, this review focuses on the recent studies that have applied information theory. Information theory was initially developed by Shannon in 1948  to measure the information content in a dataset and has been applied to solve water resource problems. Recently, its applications extended to water monitoring network design by adopting the concept that the entropy would be able to explain the inherent information content in a monitoring station or a monitoring network. The basic objective has naturally been to have the maximum amount of information. In other entropy approaches, stations in a monitoring network would have the least sharable or common information, which is called transinformation. To achieve this, the stations should be as independent from each other as possible. The scope of this paper includes water monitoring network design and evaluation studies that (1) applied entropy theory in the design process and (2) were published after the existing comprehensive review by Mishra and Coulibaly in 2009 BIB003 . To the best of our knowledge, no review exists that has focused on entropy applications to water monitoring network design previous to the 2009 study by Mishra and Coulibaly BIB003 . However, there has been considerable progress in the application of entropy theory to monitoring network design following the previous review, including new entropy-based measures, optimization techniques and approaches to estimating information content at ungauged stations. Therefore, a need was identified to consolidate knowledge and recent advances on the subject. For publications prior to 2010, the reader is referred to Mishra and Coulibaly BIB003 . This review firstly describes entropy concepts and various terms that are typically used in network design. The previous studies are then summarized by categorizing the type of networks; i.e., precipitation, streamflow and water level, soil moisture and groundwater and water quality monitoring networks. The integrated design method for multiple types of networks is also reviewed. We define some terminology hereafter to ensure a common understanding for the readers. The term network evaluation is used when the network quality is assessed without changing any station, while network design is a general term that suggests some changes in stations. Specifically, network design includes network reduction, network expansion and network redesign. Network reduction is applied where some monitoring stations should be removed from the network. On the other hand, if financial flexibility meets the monitoring needs, further stations can be added to the existing network, called network expansion. Network redesign refers to rearranging stations without changing the number of stations. The term optimal network is to be used only if the network consists of optimal locations of stations that are identified by the actual use of an optimization technique.