Coping with Urban & Agriculture Water Demand Uncertainty in Water Management Plan Design: the Interest of Participatory Scenario Analysis

Abstract

Managing water scarcity is a major challenge for regions all over the world. In the European Union, robust methodologies are needed to establish effective programmes of measures aimed at achieving the “good status” of water bodies according to the Water Framework Directive (WFD). These programmes often target the current gap between the actual status of water bodies and the “good” status without accounting for uncertainty in water demand. We develop a new methodological framework that enable to account for uncertainty in future water demand and design programmes in order to increase their likelihood of attaining the good quantitative status. The foresight approach enables to construct and quantify future water demand scenarios hand-in-hand with stakeholders during workshops. They consist in identifying drivers, debating pre-constructed scenarios, reconstructing scenarios and estimating water demand. The impact of the co-constructed scenarios is simulated with a resource-demand balance model for all water resources and a cost-effectiveness analysis makes it possible to construct programmes that target the estimated future water deficits at least cost. The methodology is illustrated with an application to Reunion Island (Indian Ocean, France) considering agriculture (Ag) and urban water (Uw) demand. Three combinations of sector scenarios (Uw, Ag) were produced and coherence was eventually ensured by fitting the land use parameter. This solution can accommodate case studies faced with a binding land constraint for housing and agriculture. As each scenario implies significantly different programmes of measure in terms of intensity and spatial distribution, results demonstrate the importance of taking uncertainty on water demand into account.

Appendixes

1.1 Appendix 1. The Resource-Demand Balance Model (RDM)

All resources are characterized by a yearly and low flow month potential available volume (PAV). This can be done from existing references or estimations. Existing numerical simulation results (Frissant et al. 2006) were weighted by surface area and precipitation amounts on different hydrogeological units where the resource was not quantified. Existing data was used for surface water characterization. Four different PAV are considered: the total annual PAV and the dry month PAV, which represents a situation in which resources are scarcer in the so-called low flow season. These are characterized for an average year and a five year return dry year.

Demands must also be characterized at the resource levels to enable calculation. The water use for the reference situation is taken from observed data (see Graveline et al. 2010a). The model calculates the difference between water use and PAV. Ecological flows are considered when characterizing the PAV for surface water. The RDB model can be formalized as follows:

For each resource, j:

$$ {B}_j= PA{V}_j-{\displaystyle \sum_{i,k}{P}_{i,j,k}} $$

(1)

With

B _j :

resource-demand balance on resource j in volume

PAV _j :

potential available volume on resource j

P _i,j,k :

the amount of water produced (withdrawn) from the production unit i on resource j , for demand unit k.

Four period specific balances are calculated: (i) for an average year, (ii) a five-year return dry year, (iii) for a low-flow month of a mean year and (iv) for a low-flow month in a five year return dry year.

We then introduce the two dimensional matrix S with elements S _{j , k} that represents the water supply scheme such that:

$$ {S}_{j,k}={\displaystyle \sum_i{P}_{i,j,k}} $$

(2)

These supply schemes S _{j , k} are recovered from existing observed data. For the future scenarios, new water supply schemes have to be determined according to some rules discussed with stakeholders. Here, the main rules are: (i) a production unit cannot produce more than the administrative authorization delivers, (2) heavily polluted resources / production units and (3) very small sources are excluded from the supply scheme, because they are too vulnerable and the protection cost would be prohibitive. Extra production points are added according to engaged plans only.

D _k represents the water use for each k demand unit (irrigation or urban water).

$$ {D}_k={\displaystyle \sum_j{S}_{j,k}={\displaystyle \sum_{i,j}{P}_{i,j,k}}} $$

(3)

The urban water demand of municipality y is taken as:

$$ {D}_{dw,y}=\frac{1}{\eta_y}\cdot \left[ Do{m}_y+{M}_y+ Ac{t}_y\right] $$

(4)

$$ Do{m}_y={\displaystyle \sum_t\left({H}_{t,y}*{r}_{t,y}\right)} $$

(5)

Dom _y :

the domestic water demand of y

M _y :

the municipal water demand of y

Act _y :

the economic activities water demand connected to public network y

η _y :

the performance of the distribution network of unit y expressed in percent (%)

H _t,y :

the number of houses of t type (single family with or without pool, multifamily housing)

r _t,y :

the unit demand for t type houses in municipality y

The irrigation water demand at the irrigated perimeter level is taken as:

$$ {D}_{Irr,p}=\frac{1}{\eta_p}\cdot \left[{\displaystyle \sum_z{X}_{z,p}*{r}_{z,p}}\right] $$

(6)

With:

X _z,p :

the area of crop z on perimeter p

r _z,p :

the water application per hectare of crop z in p . We consider a different mean application rate for upper “Hauts” and lower “Bas” parts for each perimeter.

η _p :

the performance of the distribution network of perimeter p

The first step consists in recovering r _t,y , r _z,p from Eqs. (5) and (6) with H _{t ,, y} , Dom _y , X _{z , p} , D _{Irr , p,} η _p observed data. In a second step, these equations can be used to calculate water demands for alternative scenarios, as will be seen later.

Note that even if the focus is the quantitative balance, qualitative aspects can be integrated in the methodology by considering constraints on quality: for instance, a resource can be considered inadequate to supply urban water if it is submitted to industrial pollution. Nevertheless, to ease notation, this qualitative element is not formalized in our models.

1.2 Appendix 2. The Cost-Effectiveness Ratio and the Construction of Programmes of Measures

First, a selection of realistic measures was realized with the implication of stakeholders for identification and pre-selection. Next, the effectiveness of each measure is thoroughly estimated and expressed in cubic metres per unit of implemented measure (for instance, per house). A maximum realistic potential of implementation was then characterized for each measure (for instance, 30 % of all individual housing can adopt the measure). These choices were validated with the stakeholders. The costs of each measure were calculated from a variety of sources (grey literature, experts). The investments, maintenance and recurrent costs were gathered with an actualization rate of 4 % to obtain a mean annual cost. The unit annual cost is divided by the effectiveness of the measure, i.e. the volume of water saved per unit measure implemented to calculate the cost-effectiveness ratio in €/m³. These ratios enable to rank the measures from the least to the most costly per unit of water saved.

An optimization tool has been developed in order to design least cost programmes that target the different deficits calculated with the RDB model. The programme of measure can be formalized as a matrix P of M _m,y volume of water saved by measure m on demand unit y. The optimization programme can be written as follows, by defining J the set of units y that are withdrawing water from resource j.

For each resource j when balance B _j  < 0 (i.e. j with a deficit), we minimize the total costs of measures:

$$ \begin{array}{lll} Min{\displaystyle \sum_{m,y\in J}{M}_{m,y}\cdot {C}_m}\hfill & s.t.\hfill & {\displaystyle {\sum}_{m,y\in J}{M}_{m,y}\ge -{B}_j}\hfill \\ {}\hfill & \hfill & { Pot}_{m,y}\ge {M}_{m,y}\hfill \end{array} $$

(7)

C _m :

Unit cost of measure m that enables 1 m³ to be saved (calculated)

Pot _m,y :

The maximum water saving potential of measure m in demand unit y . This is calculated with assumptions related to each measure. For instance, a maximum of 30 % of households within individual houses can implement measures and the measure enables 20 m³ per house to be saved when the measure is adopted. This is applied to the total numbers of individual houses in municipality y.

1.3 Appendix 3. Situation Map and Land Use of Reunion Island

1.4 Appendix 4. Assumptions and Resulting Water Demand Estimation in Future Scenarios

The two following tables give the calculation assumptions for each scenario and the consequent water demand estimation.

Table 3 Acreage and water use for irrigated crops, reference situation and future scenarios

Table 4 Total drinking water demand for households, small industries and municipality needs

Table 5 Total agricultural water demand per area and efficiency of distribution network (η stands for efficiency of the network i.e. the ratio between the volume produced and the volume used; “Mm3” stands for millions of m3)

1.5 Appendix 5. Classification of Measures According to the Annual Average Cost-Efficiency Ratio and Maximum Volume Saved

Table 6 Classification of measures according to the annual average cost-efficiency ratio and maximum volume saved