Abstraction costs represent the main variable operating cost for the Sofia water company

For operational purposes, water company costs are divided into two components:

variable operating costs and fixed operating costs. The variable operating costs are those costs that are determined by the throughput of treatment plants (potable or wastewater) run by the water company (Sofiyska Voda), so, importantly, from SV’s

a)

b)

perspective, are the only costs that are relevant when considering the benefits of reducing water demand. Variable operating costs can be further disaggregated, and for SV, there are three key components: raw water costs, chemical costs, and power costs.

The water company supplied information on variable operational costs of supplying water (i.e. raw water, power and treatment costs) for the year 2005 and 2006 (these are presented in Appendix J). The data presented in Table A and Table B permitted a comparison of variable operating cost components. The data shows that raw water costs make up approximately 75% of the total variable operating costs. As described in the LAC method, a change in variable operating costs affects the payback period from WDM measures, and as such, the Ministry of Environment and Water’s (MoEW’s) decision regarding abstraction permit and raw water costs is a policy area that needs to be addressed in the context of water efficiency.

Further consultation revealed that two factors result in power costs being remarkably low for operation of the water network in Sofia. Firstly, the water supply network in Sofia is gravity-fed and secondly there is no reliance on aquifers for public water supplies so there is no requirement for pumping groundwater. These factors mean that the variable operational costs and, therefore, the actual avoided costs from WDM are relatively low in Sofia compared to other cities. This information is valuable in the context of developing generic models to facilitate water conservation decisions in other river basins.

Comparing the Bayesian networks of the LAC method in Figure 4.14 (above) with the Influence Diagram in Figure 4.15 (below), which is the sub-model for the decision to introduce WDM programme used in the conceptual model described in Chapter 5, demonstrates the process of analysis that occurs during the development of Bn models for use in policy analysis.

The only remaining chance nodes in the version shown in Figure 4.15 from the diagnostic Bn models in Figure 4.14 are the nodes, ‘WDM programme water savings’, ‘WDM programme payback period’ and ‘Lifetime of the WDM programme’.

These nodes represent uncertain variables that remain in the mode and require consideration at the planning and legislating stage. These variables are subject to different approaches to WDM programme design and are examined in Chapter 6.

Figure 4.15. Lifetime avoided costs components as represented in the conceptual model presented in Chapter 5

As explained above, the only variable operational costs component that is subject to change is the raw water cost (Figure 4.14a) and this is determined by the MoEW’s decision. This cause-effect relationship is represented in Figure 4.15 by a directed link between the decision node labelled abstraction permit and raw water costs (MoEW) and the chance node labelled WDM programme payback period.

Because different WDM components will impact on metered demand differently (e.g.

reducing pressure in the water network will reduce UfW but will have less impact on metered demand), a directed link is included from the node, ‘WDM programme options’, to the node, ‘metered demand’.

4.6 Conclusions

The model development described above supported identification of strengths and weaknesses of Bns relating to the research questions presented in Table 1.4. The findings are summarised below.

Research question 1: How does Bayesian network modelling provide support for analysing uncertainty in water supply and demand forecasts?

Strengths of Bns for water supply and demand forecasting were identified from the model development reported in Chapter 4. In Section 4.2.2, structural learning and parameter sensitivity analysis were applied to hydrological data collected from the

Iskar dam between 1966 and 2000, and the results were used to develop a water balance model and forecasting model of future water availability. In practice, the resulting models (Figure 4.1 & Figure 4.5) supports exploration of scenarios to identify risks of low water availability. The forecasting model also demonstrates how Bns can be used to model over a single time-step. In Chapter 5 the forecasting sub-model (Figure 4.5) is included as part of a larger conceptual sub-model for supporting water management policy decisions in the Upper Iskar.

A further strength of Bns is the wide range of data types (see below) that can be used to populate conditional probability tables (cpts). This addresses some of the issues of data availability often encounters in forecasting and backcasting. Four types of information that can be used to populate cpts in Bns have been identified.

These are:

 Raw data collected by direct measurement (e.g. River flow or reservoir levels, population measured by census, income measured by accounting).

 Information collected from regional reports (e.g. from water companies, environment agencies, research institutions) of water demand and supply.

 Raw data collected through stakeholder elicitation (e.g. stakeholder perceptions of water availability, population and income).

 Output from process-based models calibrated using raw data collected by direct measurement.

With regard to using Bns for hydrological modeling, until recently limitations existed with modeling feedback cycles using Bayesian networks due to the necessary calculus not being developed (Jensen, 2001). Recent developments (e.g. Montani et al, 2008; Neil et al, 2008), however, mean that there is now scope to use Bns in domains where feedback cycles exist.

Because historical hydrological data rarely include all possible scenarios of water demand (i.e. all possible demand management scenarios) it will be desirable to use outputs from other hydrological models (i.e. simulation models). However, this is a universal problem with collecting data for hydrological modelling and the facility to use expert knowledge in Bns in combination with actual data has potential advantages.

Research question 2: How does Bayesian network modelling provide support for economic analysis of impacts of demand management programmes?

The strengths of using Bayesian networks for analysing causes of uncertainty in economic evaluations of demand management options were examined in Chapter 4, Section 4.5.1. The lifetime avoided costs (LAC) method described in Section 4.5.1 is only one of many methods that could potentially be used to support economic evaluations of demand management. In Section 4.5.2.1 the LAC method was used to support structuring of a Bn model and demonstrates how Bayesian networks support quantification of conditional dependencies between variables. When quantified, the model was used to identify the variables that could be affected by interventions to reduce uncertainty about potential programme impacts. This makes it possible to understand how human actions (adaptive policies) will lead to more certainty about implementation effectiveness. Regarding the use of knowledge elicitation to support model development, the use of supply curves, as reported in Turner et al., (2003), will be a helpful approach for structuring future knowledge elicitation activities. An example of a supply curve is given in Appendix K.

In addition to the above strengths and weaknesses addressing research questions 1

& 2, a number of advantages and disadvantages of using discrete ranges (i.e. states) in Bns were identified from the model development in Chapter 4 and these are listed in Table 4.1 below.

Table 4.1. Advantages and disadvantages of using discrete ranges in Bayesian network forecasting models

Advantages Disadvantages

 Discretisation allows identification of model parameters with dispersed probability distributions, allowing research to be focused on areas of greater uncertainty

 Encourages the identification of tipping-points between model variables

 Conditional probabilities for discrete ranges can be used to derive utilities using utility theory

 The use of states can be counter to the objective of reducing uncertainty

 Increasing the number of states reduces statistical significance during structural learning

 Increasing the number of states may make knowledge elicitation impractical

The suitability of Delphi methods for developing CPTs and combining expert knowledge with other data is an area for further research. Methods used would ideally be (i) efficient in terms of resources used in the collection of data, whilst (ii) achieving sufficient accuracy to provide valid models. Four Delphi approaches are described in detail in Appendix H.

The following chapter presents the conceptual model for WDM legislation in the Upper Iskar case which incorporates issues addressed in the models developed above (i.e. water availability forecasting indicators, impacts of water pricing, impacts of WDM on water company revenues and uncertainty about economics of WDM).

Chapter 5

Technical evaluation 1: Bayesian networks to