Space/time design of water design of water quality monitoring networks by the entropy method

In recent years, the adequacy of collected water quality data and the performance of existing monitoring networks have been seriously evaluated for two basic reasons. First an efficient information system is required to satisfy the needs of water quality management plans. Second, this system has to be realized under the constraints of limited financial sources, sampling and analysis facilities, and manpower. At this point, the major problem is the selection of an appropriate method for network evaluation purposes since the majority of existing water quality monitoring networks reflect significant shortcomings in specific technical design features related to what variables to measure, where, when and how long. Furthermore, benefits of monitoring cannot be defined in quantitative terms for reliable benefit/cost analyses. In essence, there are no definite criteria yet established to decide upon the optimum solutions for these problems. The objective of the presented study is to investigate the above-mentioned two problems. That is, it is intended here: (a) to solve the network design problem in combined space/time dimensions as a network produces information with respect to both the spatial and the temporal dimensions; (b) develop a methodology to define benefits of monitoring in quantitative terms for combined design programs. To this end, the presented study uses the entropy principle, as defined in information theory, to develop a methodology for assessment of combined space/time frequencies and description of benefits accruing from alternative designs. To analyze spatial and temporal frequencies on a joint basis, the best combination of monitoring stations has to be selected first. Next, starting with the first priority station, the number of stations is successively increased by adding to the combination the next station on the priority list. For each number of stations, the temporal frequencies are decreased toin identify how much information provided by those stations at different sampling intervals. Finally, changes in information are plotted on the same graph with respect to both the increases in the number of stations and the decreases in temporal frequencies of sampling. The particular information measure used in this analysis is transinformation which represents redundant information in space and time dimensions. The objective is the selection of a space/time combination that produces the least amount of transinformation. Increases in either the space or the time frequencies implies increases in accruing costs so that one has to compare loss of information due to decreased space/time frequencies versus decreased costs, or vice versa. The analysis of combined space/time frequencies by the entropy principle has to be carried out on available data provided by an existing network. Furthermore, these data series must be adequately long and more or less uniform with respect to the time dimension to properly assess the information produced by the network. The methodology is first developed and tested on available water quality data observed in the Mississippi river basin in the USA, as available data in Turkish basins are quite messy with short sampling durations and significant gaps in data series. Next, the method is applied in the Porsuk river basin in Turkey to demonstrate its applicability to short data series with significant numbers of missing values. Both sample basins used have monthly observed water quality data so that an investigation of temporal frequencies higher than a month is not possible. Accordingly, the methodology is further applied to daily streamflow data in the Upper Ceyhan basin to assess daily, weekly, biweekly frequencies. To extend these short sampling intervals beyond monthly frequencies, synthetic data had to be generated since the Ceyhan streamflow data covered only a period of 8 years. Combined space/time design reflects the basic feature of a network, i.e., redundant information in the network increases with an increase in sampling locations and sampling frequencies. The problem has been approached in two ways. The first approach has considered the same temporal frequency at all stations. The resulting relationships between redundant information, station numbers and sampling intervals have basically delineated the spatial variability of a water quality variable rather than temporal variability. Thus, a second approach has been used whereby the first priority station in the basin is selected as the base station with frequent sampling. Sampling intervals are increased at all other stations, andIV redundant information between the base station and other sites is investigated. The resulting relationships have been found to effectively reflect both the spatial and the temporal variability of water quality in the basin. By means of the above analyses, the presented study has fulfilled its objectives, i.e., a methodology is developed as an information-based strategy for assessment of monitoring networks and the combined space/time design problem is solved to arrive at optimum design alternatives. To finalize the optimum design procedure, costs of monitoring should also be incorporated into the methodology. Essentially, costs of monitoring are easy to assess provided that data exist on unit prices of sampling procedures. As the presented study did not have access to such data, analysis of sampling costs is reserved for future studies on the subject.