Approximation and Visualization of Interactive Decision Maps

Short course of lectures

Alexander V. Lotov

Dorodnicyn Computing Center of Russian Academy of Sciences and

Lomonosov Moscow State University

Lecture 4. Real-life application of the IDM/FGM technique: water quality

planning

Plan of the lecture1. General features of methodology for decision

screening in environmental problems2. The problem3. The methodology for decision screening4. The Oka River basin5. The model and screening criteria6. The investigation 7. Film

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.

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.

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.

The Problem

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.

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.

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.

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.

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

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.

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.

Pollution transport modelMathematical 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 Qk is given (it is computed by using water flow model in advance).

Let I be the number of pollutants under consideration. Then, the pollution balance equation for i-th pollutant and k-th reach looks as

where Mki is the flow of the i-th pollutant through the k-th monitoring station,

M(k-1)i is the inflow of the i-th pollutant from the reach related to the (k-1)-th monitoring station,

ki is the decay coefficient for the i-th pollutant, which arrived from the (k-1)-th reach,

mrki is the discharge of the i-th pollutant in the k-th reach from the r-th region,

arki is the decay coefficient for the i-th pollutant discharged in the k-th reach from the r-th

region,

Rk is the subset of regions, which discharge pollution in the k-th reach.

All the flows and discharges are related to some unit of time (say, per second).The value M0i equals to zero for all pollutants.

The discharge purification modelThe discharge purification model is 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 mr

ki, 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,

in is the purification coefficient of the i-th pollutant treated by the n-th technology.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.

Concentration of pollutantsConcentration of the i-th pollutant near the k-th monitoring station is given by

where 0ki is 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 imax is 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.

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.

Screening Criteria

Water quality in the r-th region is 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

where an is 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.

The investigation

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.

After the approximation was

completed, visual exploration of

decision maps is started.

To explore dependencies between more than three criteria, user can animate the decision map or use a

matrix of decision maps

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.

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.

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

User can explore the strategy by studying

various diagrams

Pollutant concentrations that result from the project (green) are displayed against the existing concentrations that are given in blue.

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.

The upper diagram provides data on investment in the regions

Six other diagrams show regional pollution levels

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

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.

Icons on the map provide an opportunity to get information on pollution levels and pollution discharges in each of the seven regions.

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.

Demonstration of the film prepared by water quality engineers