Approximation and Visualization of Interactive Decision Maps Short course of lectures

1. Approximation and Visualization of Interactive Decision MapsShort course of lectures Alexander V. Lotov Dorodnicyn Computing Center of Russian Academy of Sciences and Lomonosov Moscow State University

2. Lecture 4. Real-life application of the IDM/FGM technique:water quality planning Plan of the lecture • General features of methodology for decision screening in environmental problems • The problem • The methodology for decision screening • The Oka River basin • The model and screening criteria • The investigation • Film

3. Methodology for decision screening Remind that any decision process consists of the two main phases. The first one is the early decision screening, i.e. selecting a small number of decision alternatives from the whole variety of possible alternatives for further exploration. The second stage is related to the final choice among a small number of alternatives on the basis of their detailed exploration.

4. In environmental problems, decision screening requires the integration of models and knowledge of experts in a number of diverse fields. Say, in water quality planning integration of models of wastewater discharge, wastewater treatment, pollutants transport, effect of pollution, and so forth is needed. Integrated models are required, which may be simplified and fairly rough, but it should describe all important features of the decision situation. We apply this idea and use models, expert knowledge, etc. for preparation of data for integrated models.

5. Constructing of an integrated model is based on integration of simplified descriptions of the subsystems of the system. Simplified description can be derived from an original mathematical model of the subsystem, often in the form of one or several influence matrices, i.e. matrices that relate outputs of the model to its inputs. The most universal way to construct influence matrices is parameterization of the original models, i.e. providing an approximation of its input-output dependencies.

6. TheProblem The water quality problem studied here is related to the selection of an efficient strategy of investment into the wastewater treatment facilities that must be constructed in a large river basin to improve the water quality. Several regions are located in the river basin. The problem is how much investment is needed and how to allocate the investment between regions, what kind of wastewater treatment technologies to apply, etc.

7. In order to get a moderate investment, it is necessary to persuade stakeholders that the investment will result in a substantial improvement of environmental situation. Different interests and concerns must be taken into account. It means that the traditional search for strategies of water quality planning based on a single-criterion optimization is not adequate to the task. That is why the IDM/FGM technique was used.

8. The DSS was developed for screening possible alternative investment projects. It calibrated for the Oka River that is one of the largest tributaries of the Volga River. Seven regions are located at the main flow of the river. The river-bed was split into fourteen segments that approximately describe membership of riverbanks to the regions. Six most important pollutants were considered in the DSS, such as suspension, phosphates, nitrates, oil products, and ferrous combinations as well as biological oxygen demand.

9. Oka River Basin • The DSS was calibrated for the Oka River that is one of the largest tributaries of the Volga River. Seven regions are located at the main flow of the river. The river-bed was split into fourteen segments that approximately describe membership of riverbanks to the regions. • Six most important pollutants were considered in the DSS, such as suspension, phosphates, nitrates, oil products, and ferrous combinations as well as biological oxygen demand.

12. The integrated model used in the DSS includes three sub-models: pollution transport sub-model that provides an opportunity to compute the concentration of pollutants in monitoring points for given discharge, a wastewater discharge sub-model that describes the volume and structure of the discharge attributed to a particular region, river segment and industry, a wastewater treatment sub-model that relates the decrement of wastewater discharge to the cost related to constructing and performance of the wastewater treatment installation

13. Constructing of a simplified description of the pollution transport (influence matrices for particular pollutants) was based on the simulation of the system for modeling of rivers and channels MIKE 11. Six influence matrices for particular pollutants describe pollutant transport and are used to relate the decrement of the wastewater discharge to concentration of the pollutants at monitoring stations. The simplified model of the wastewater discharge treatment used in the DSS was based on the concept of wastewater purification technologies elaborated by experts. The wastewater discharge was described on the basis of a collection of parameters partially based on discharge reports received from the industrial enterprises and municipal authorities.

14. Influence matrices, technological matrices, balance equations, and discharge data constituted the integrated model. Decision variables were the investment strategies that described investment into particular purification technologies in particular regions. The integrated model was used for the display of aggregated decision information in the form of decision maps, graphic exploration of which helps user to identify a preferable feasible goal that defines results of decision screening.

15. Pollution transport model Mathematical description of the pollution transportation model follows. The number of regions considered in the model is R. The river is split into K reaches separated by water quality monitoring stations. Water flow near the k-th monitoring station denoted by Qkis given (it is computed by using water flow model in advance). LetIbe the number of pollutants under consideration. Then, the pollution balance equation fori-thpollutant and k-th reach looks as whereMkiis the flow of the i-thpollutant through thek-thmonitoring station, M(k-1)iis the inflow of the i-thpollutant from the reach related to the(k-1)-thmonitoring station, kiis the decay coefficient for the i-thpollutant, which arrived from the (k-1)-th reach, mrki is the discharge of the i-thpollutantinthe k-threach from the r-thregion, arki is the decay coefficient for the i-thpollutant discharged inthe k-threach from the r-thregion, Rkis the subset of regions, which discharge pollution in the k-threach. All the flows and discharges are related to some unit of time (say, per second). The value M0i equals to zero for all pollutants.

16. The discharge purification model The discharge purification modelis based on the concept of production technology. The variety of N possible technologies was considered. A technology was given by cost of purification of the cubic meter of discharge (including cost of constructing) and by the purification coefficients. The resulting discharge denoted by mrki, where r=1,2,..., R,k=1,2,..., K, i=1,2,..., I,is given by the equation where m0rki is the discharge before constructing the purification installations, trkn is the part of the discharge from the r-th region in the k-th reach treated by the n-th technology, inis the purification coefficient of thei-thpollutant treated by the n-thtechnology. Surely, It is clear that the variables trkn are non-negative. The variables trkn are the decision variables. The problem is to decide what kind installations must be constructed and used.

17. Concentration of pollutants Concentration of the i-th pollutant near the k-th monitoring station is given by where 0kiis concentration of the pollution provided by other sources. The relative concentration of the i-th pollutant near the k-th monitoring station is defined as where imaxis the maximum value of the i-th pollutant permitted by the environmental authorities. The indicator of pollution by the i-th pollutant in the r-th region is given by where Kr is the set of reaches that belong (at least partially) to the r-th region.

18. Screening Criteria Since various users are supposed use the DSS for screening the investment strategies, a large list of performance indicators is provided to users. They can specify screening criteria directly in the list. The list includes two kinds of performance indicators (potential criteria): • environmental (water quality) indicators that describe resulting pollutant concentrations in a region or in the river; • economic indicators that include the total cost of the project and investments in particular regions. It is clear that is reasonable to diminish the indicator (criterion) values.

19. Water quality in the r-th regionis given by the vector where Kr is the set of reaches which are in the r-th region. The maximal values of pollution among the regions can be used as indicators, too: The water treatment investment in the r-th region is given by whereanis the cost of the treatment of one cubic meter of by using the n-th technology, qrk is the discharge from the r-th region in the k-th reach. The total cost can be used as one of the criteria, too. The cost function does not take into account the constant cost. However, it can be used since because the aggregated discharge of the region is considered in the model, but not the particular sources of pollution.

20. The investigation

21. DSS allows user to specify two to seven performance indicators from the list to be the screening criteria. Constraints on the indicator values can be imposed. Here the total cost of the project, the investment in the fourth region and the investment in the seventh region have been already specified to be screening criteria.

22. After the approximation was completed, visual exploration of decision maps is started.

23. To explore dependencies between more than three criteria, user can animate the decision map or use a matrix of decision maps

24. Several (5 by 5) decision maps are displayed that are related to certain constraints imposed on investments in M-region (F4) and NN-region (F7). A constraint imposed on F7 that defines a row is given to the right of it. The constraint imposed on F4 that defines a column is given above it. Coordinates of any point of a desired decision map can be found by a mouse click at the point.

26. By clicking at one of the decision maps, user can identify the values of the row and column criteria. The related decision map is displayed. User can identify a feasible goal directly on the decision map by a mouse click. A potential goal is given by the cross.

28. Once a feasible goal is specified, a strategy related to it is computed and displayed in the central column of the table.

29. User can explore the strategy by studying various diagrams

30. The upper diagram provides flow data during dry summer season (cubic meters per second). Six other diagrams display pollution at the ends of river sections stations. In the left column we have BOD, phosphorus and oil products. In the right column suspension, nitrates and ferrous combinations are given. Pollutant concentrations that result from the project (green) are displayed against the existing concentrations that are given in blue.

31. The upper diagram provides data on investment in the regions Six other diagrams show regional pollution levels

32. A strategy may be displayed in the map of the river basin generated by a GIS.

33. Icons on the map provide an opportunity to get information on pollution levels and pollution discharges in each of the seven regions. Any of 14 river sections is associated to a button on the map. To get information on pollutant concentrations in a particular river section, one has to click the related button.

35. Comment Opportunity of evolutionary study of the problem is provided: if decision maker is not satisfied with the strategy or loosely wants to search for additional strategies by playing with the system, he/she can return to the initial criteria specification table and specify a new set of criteria and/or impose new constraints on performance indicators.

36. Demonstration of the film prepared by water quality engineers