**5. First results of the optimal water management approach**

The proposed concept for optimal water management is applied to the Beijing region. The region has precipitation, which varies geographically, seasonally and yearly. Eighty-five percent of rainfall falls between July and September. Groundwater is the most important source of water for the Beijing region, covers about 50-70%. Beijing has suffered from over exploitation of this source over the years. Surface water supply in the Beijing region de‐ pends mainly on upstream inflows of the major river systems Chaobai, North Grand Canal and Yongding. Aside from problems such as excessive withdrawal and water quality deteri‐ oration of surface waters, the lack of regional coordination leads to issues such as uncoordi‐ nated withdrawals. Besides these problems, the water supply system is subject to other common problems, such as rapid population growth and urbanization, decentralized reser‐ voir/groundwater management, changing attitude towards sustainability and attribution to greater attention of environmental issues.

the final water level from 142 m above sea level to 137 m. In the third scenario a part of this release is replaced by water from outside of the considered region, which reduces the water level decrease at about 2 m. The second reservoir is situated at a channel from the Miyun-reservoir to the city of Beijing and serves only as intermediate storage. The admissible range for water management is completely utilized by the optimal control ap‐ proach. The shift in the management target causes a different operating strategy because water from the connected channel is taken to replace groundwater abstractions in the nearby regions. The change of the management target for scenario 2 and scenario 3 in‐ duce also an increase of the overall demand deficit from 0.1 % to up to 3.5 % (scenario

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Fig. 10 shows the time plot of the mean groundwater level of the optimization scenarios. It is obvious that in scenarios 2 and 3 the aimed increase of the target value for the final groundwater hydraulic head at 5 m is nearly achieved. In Fig. 11 the impact of the dif‐ ferent strategies to the exemplary input 1 (exploitation in a certain region) and exempla‐ ry output 5 (groundwater level at a defined observation point) can be studied. The exploitation is clearly decreased in scenarios 2 and 3 which correspond to an increase of the groundwater level at the observation point. Finally, from Fig. 12 it can be seen that the performance of the drastically reduced groundwater model is good, reflecting the fact that the original FEM model with more than 100,000 nodes has been reduced to a state

**Figure 9.** Water level of the largest reservoir in the water distribution system (Miyun-reservoir) as well as of a reservoir

2), which is nearly 6.8x108 m³ over the full horizon.

space model with 36 states.

with seasonal storage capacity (Huairou-reservoir).

The optimal water management system is evaluated for three scenarios based on the same set of input data, which are a combination of historical rainfall measurements and customer demands reflecting the predicted development of population size and economic growth. The objective function contains four quadratic terms in order to penalize deviations from the desired final water level of largest reservoir in the system (Miyun reservoir), from the de‐ sired final average hydraulic head of the groundwater storage as well as the deficit of the customer demand separated into two groups for household/industry and agriculture. The deficit of the delivered water must be less than 5 % for domestic/industrial clients and less than 25 % for agricultural clients. For the third scenario it is assumed that water can be transferred to the considered region up to an annual amount of 300 Mio. m³ starting from the third year within the optimization horizon.

The overall water demand exceeds noticeable the natural sources. The reduced groundwater model has been derived under the assumption that this over-consumption was covered by the groundwater storage. This leads to a strong reduction of the average hydraulic head of the groundwater storage of about 9 meters during 5 years (scenario 1, see Fig. 10). Using the initial state of the Miyun reservoir and the final value of the reference trajectory for the aver‐ age groundwater head as target in the objective function, for the base scenario (scenario 1) there are only small deviations from these values in combination with a minor demand defi‐ cit observable. In the second scenario the increase of the target value for the final groundwa‐ ter hydraulic head at 5 m and a corresponding shift of penalty coefficients in order to keep this value lead to a better spreading of the overdraft over the different storages as well as to the customers.

Fig. 9 shows the course of the water level for two reservoirs. Because of its capacity of 4.4x109 m³ the Miyun reservoir plays an important role for the long term management of the overall system. As can be seen, the years with above-average precipitation produce only a medium rise of the water level. The second scenario, which attempts to reduce the decline of the average hydraulic head of the groundwater storage, results in an increased release of this reservoir compared to the base scenario, which corresponds to a change of the final water level from 142 m above sea level to 137 m. In the third scenario a part of this release is replaced by water from outside of the considered region, which reduces the water level decrease at about 2 m. The second reservoir is situated at a channel from the Miyun-reservoir to the city of Beijing and serves only as intermediate storage. The admissible range for water management is completely utilized by the optimal control ap‐ proach. The shift in the management target causes a different operating strategy because water from the connected channel is taken to replace groundwater abstractions in the nearby regions. The change of the management target for scenario 2 and scenario 3 in‐ duce also an increase of the overall demand deficit from 0.1 % to up to 3.5 % (scenario 2), which is nearly 6.8x108 m³ over the full horizon.

**5. First results of the optimal water management approach**

greater attention of environmental issues.

42 Water Supply System Analysis - Selected Topics

the third year within the optimization horizon.

the customers.

The proposed concept for optimal water management is applied to the Beijing region. The region has precipitation, which varies geographically, seasonally and yearly. Eighty-five percent of rainfall falls between July and September. Groundwater is the most important source of water for the Beijing region, covers about 50-70%. Beijing has suffered from over exploitation of this source over the years. Surface water supply in the Beijing region de‐ pends mainly on upstream inflows of the major river systems Chaobai, North Grand Canal and Yongding. Aside from problems such as excessive withdrawal and water quality deteri‐ oration of surface waters, the lack of regional coordination leads to issues such as uncoordi‐ nated withdrawals. Besides these problems, the water supply system is subject to other common problems, such as rapid population growth and urbanization, decentralized reser‐ voir/groundwater management, changing attitude towards sustainability and attribution to

The optimal water management system is evaluated for three scenarios based on the same set of input data, which are a combination of historical rainfall measurements and customer demands reflecting the predicted development of population size and economic growth. The objective function contains four quadratic terms in order to penalize deviations from the desired final water level of largest reservoir in the system (Miyun reservoir), from the de‐ sired final average hydraulic head of the groundwater storage as well as the deficit of the customer demand separated into two groups for household/industry and agriculture. The deficit of the delivered water must be less than 5 % for domestic/industrial clients and less than 25 % for agricultural clients. For the third scenario it is assumed that water can be transferred to the considered region up to an annual amount of 300 Mio. m³ starting from

The overall water demand exceeds noticeable the natural sources. The reduced groundwater model has been derived under the assumption that this over-consumption was covered by the groundwater storage. This leads to a strong reduction of the average hydraulic head of the groundwater storage of about 9 meters during 5 years (scenario 1, see Fig. 10). Using the initial state of the Miyun reservoir and the final value of the reference trajectory for the aver‐ age groundwater head as target in the objective function, for the base scenario (scenario 1) there are only small deviations from these values in combination with a minor demand defi‐ cit observable. In the second scenario the increase of the target value for the final groundwa‐ ter hydraulic head at 5 m and a corresponding shift of penalty coefficients in order to keep this value lead to a better spreading of the overdraft over the different storages as well as to

Fig. 9 shows the course of the water level for two reservoirs. Because of its capacity of 4.4x109 m³ the Miyun reservoir plays an important role for the long term management of the overall system. As can be seen, the years with above-average precipitation produce only a medium rise of the water level. The second scenario, which attempts to reduce the decline of the average hydraulic head of the groundwater storage, results in an increased release of this reservoir compared to the base scenario, which corresponds to a change of Fig. 10 shows the time plot of the mean groundwater level of the optimization scenarios. It is obvious that in scenarios 2 and 3 the aimed increase of the target value for the final groundwater hydraulic head at 5 m is nearly achieved. In Fig. 11 the impact of the dif‐ ferent strategies to the exemplary input 1 (exploitation in a certain region) and exempla‐ ry output 5 (groundwater level at a defined observation point) can be studied. The exploitation is clearly decreased in scenarios 2 and 3 which correspond to an increase of the groundwater level at the observation point. Finally, from Fig. 12 it can be seen that the performance of the drastically reduced groundwater model is good, reflecting the fact that the original FEM model with more than 100,000 nodes has been reduced to a state space model with 36 states.

**Figure 9.** Water level of the largest reservoir in the water distribution system (Miyun-reservoir) as well as of a reservoir with seasonal storage capacity (Huairou-reservoir).

**Figure 10.** Time plot of the mean groundwater level in the optimization scenarios 1 – 3.

**Figure 12.** Time plot of output 5 of the full FEM model compared with the reduced model (optimization scenario 1).

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In this paper an optimal control approach as a component of a decision support system (DSS) for the management of the total water resources (surface water, groundwater, external water resources) in a fast developing region under a critical water shortage has been pre‐ sented. It has been proven that in spite of the large area which has to be managed and the corresponding complex surface and groundwater models the optimization problem could be solved in an appropriate computation time (~ minutes). This could be achieved by a dras‐ tic reduction of the complex groundwater model to a state space model of relatively low di‐ mension (n < 50). The user (i.e. water allocation decision maker) is enabled to select from a number of predefined performance criteria as well as to assign constraints to the elements of the water allocation system in order to specify the management targets according to his/her needs. The performance of the proposed concept is demonstrated by close to reality optimi‐ zation scenarios, whereby the benefit of a new strategic channel has been investigated with a planning horizon of 5 years. Actually the developed DSS component is used in a first ver‐ sion by the decision makers. Future work will focus on the application and adaptation of the developed concept and software for the water resources management of further regions

**6. Conclusions**

with critical water shortage.

**Figure 11.** Time plot of input 1 (exploitation in a certain region) and output 5 (groundwater level at a defined point) in the optimization scenarios 1 – 3.

**Figure 12.** Time plot of output 5 of the full FEM model compared with the reduced model (optimization scenario 1).
