A simulation-optimization-based decision support system for water allocation

1. A simulation-optimization-based decision support system for water allocation 14. Workshop Modellierung und Simulation von Ökosystemen 27.10-29.10.2010 Divas Karimanzira

2. Goals Problem situation Structure of the decision support system Selected results Benefits and applications Conclusions Outline

3. Goals • Provide Descision Support (DSS) for comprehensive Water Management: Surface Water (SW) Resources and Groundwater (GW) Resources • Support Water Management through comprehensive Water Models for SIMULATION and Model Based OPTIMIZATION • Support Water Management through SCENARIOS Outline

4. Beijing vs Thuringia Total area [sq. km] 16.800 16.172 Inhabitants, 2003 14.560.000 2.373.000 Per capita water consumption [l/d], 2003 248 87 Precipitation, annual mean [mm], 1993-2003 509 626 Average monthly values (1993-2003) 180 Beijing 160 Thuringia 140 120 Precipitation [mm]) 100 80 60 40 20 0 jan feb mar apr may jun jul aug sep oct nov dec Month Problem situation

5. Miyun Largest drinking water reservoir Yongding river downstream of the Sanjiadin-Sluice • Max. storage 4,37 bn m³. • 03.2004, 30m below the highest admissible level, • Corresponds to a storage volume of only 0,8 bn. m³ water. • Dry since 1998 • Water directed to Beijing. Problem situation

6. Water Supply System

7. Groundwater is the most important source of water for the Beijing region covering 50-70% • Almost all available groundwater resources are already developed.  • Beijing has suffered from over exploitation of this source. • Surface water supply in the Beijing region depend mainly on upstream inflows (Chaobai, North Grand Canal, Yongding) Problems: • excessive withdrawal • lack of regional coordination leads to issues such as • uncoordinated withdrawals • and upstream water contamination. Water Supply system Problems

8. Structure of the DSS

9. Data to identify and describe the physical, social, legal, economic, and institutional factors that affect water resources management. Climatic factors such as temperature, wind, solar radiation, and rainfall Water quantity and quality demands over time and space Land-use and geomorphic information (e.g., slopes, drainage density, geology, Soils, land covers, channel cross-sections, and groundwater depths); Hydrologic data that include flows, water levels, depths, and velocities; Pollutant loads from point sources (e.g., cities, industries, and wastewater Treatment plants that discharge their wastes into surface waters and Pollutant loads from nonpoint sources that enter surface waters along an entire stretch of the river, channel or reservoir. Datatypes: static and dynamic data, numbers, time series, text, and images that characterize the quantity, quality, and spatial and temporal distributions Data required for planning and management – Database

10. Data source River / Channel / Pipeline Catchment area Reservoir Sluice Demand Defines initial states Confluence Simulation models

11. Summary: • Consists of important surface water elements: • 5 catchment areas (sub-catchments neglected) • 4 reservoirs • 2 lakes • 11 rivers and channels • 7 waterworks • 1 reduced groundwater model or interface to FEFLOW simulation • Fast simulation (≈ 0.5 minute per year simulation time) allows simulation horizons of 10 years or more • Possibility to control different outflows manually Simulation models

12. Integration of GW and SW-Models Simulation models

13. Optimization problem formulation

14. Finite Element models are computationally expensive! • But: For optimization GW model has to be started > 1000 times! • 3D-Model: ~100.000 nodes, simulation of 5 years: ~15 Minutes Optimization time: 250 hours ~ 10 days !  Reduction of complexity of Groundwater Model necessary! Optimization problem formulation (Model reduction)

15. Optimization problem formulation (Model reduction) • Inputs: • Groundwater recharge, • Withdrawal rates, water supply • Output: • Hydraulicheadsofrepresentativepoints

16. Initial state (reservoir level, groundwater head …) Process equations (balance of reservoir and groundwater storages …) Equality constraints (balance of non-storage nodes …) Inequality constraints (min (max) reservoir level …) Optimization horizon The water resources allocation problem is formulated as a discrete-time optimal control problem: subject to The equality and inequality constraints of the full discrete-time optimal control problem are composed of the constraints of the individual elements of the network definition. The overall objective function is the sum of all objectives of the network elements. Optimization problem formulation

17. Example objective function: A maximize supply to customers B minimize demand deficit C maximize level at Miyun reservoir at final time D maximize groundwater head at final time Optimization problem formulation

18. Numerical Solver HQP • Efficient and fast solution of time discrete optimal control problems, • Special interface to support the formulation of optimal control problems, • Sequential Quadratic Programming (SQP), • Interior-Point method for the quadratic subproblems within the SQP method, • Gradient calculation by means of Automatic differentiation (software package Adol-C), Optimization problem formulation

19. The management model

20. Coupling simulation and optimization

21. Organizing module

22. Organizing module

23. Example scenario definition

24. Catchment area outflow [m3/h] Catchment area outflow [m3/h] Cost Value 90 45 10 perfect Modell simulation Nash-Sutcliffe: 0.67845 simulation 8 40 80 Simulation measured measured Nash-Sutcliffe: 0.73135 Bias: 1.6612 6 70 35 4 30 60 2 25 50 Bias 0 20 40 -2 30 15 -4 10 20 -6 10 5 -8 -10 0 0 2007/01/01 -0.4 1982/01/01 -0.2 1984/01/01 0 0.2 1986/01/01 2011/01/01 0.4 1988/01/01 0.6 2013/01/01 0.8 1990/01/01 1 2015/01/01 1.2 Nash-Sutcliffe Date Date Results of modeling a selected catchment area as an example. Figures show good training and validation Nash-Sutcliffe values of 0.73135 and 0.67845, respectively. Catchement area modelling - Selected results

25. Inflow Guanting Reservior [m3/s] 250 Q_In_Guanting Overall inflow (computed) 200 150 100 50 0 1995/01/01 1995/04/01 1995/07/01 1995/10/01 1996/01/01 Date Guanting water level [m] 479 h_Guanting 478.5 Water_level (computed) 478 477.5 477 476.5 476 475.5 475 474.5 474 1995/01/01 1995/04/01 1995/07/01 1995/10/01 1996/01/01 Date Figures show the simulated/meas’d water inflow into the Guanting reservoir and the corresponding water level for a period of a year. Reservoir modelling – Selected results

26. FEM vs. Reduced model (Output Nr. 5 - Scenario1) 37 Red. model 36 FEM model 35 34 h [m] 33 32 31 30 29 28 0 1 2 3 4 Time [yr] • Yearly domestic water demand: • Different model types: • Model(1) – Kalman predictor- based model • Model(2)-multiple regression model • Model(3)- neuralnetwork –based model Groundwater model reduction / Domestic water demand The performance of the drastically red. 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.

27. The proposed concept for optimal water management is evaluated for several sets of experiments. • The first set of experiments compares two scenarios. • Scenario 1: • minimize demand deficit and keep demand constant for the next 10 years and • Scenario 2 • minimize demand deficit and increase demand 5% yearly for the next 10 years. The results of the two scenarios are illustrated in the Figures 4 to 5. Water resources management-Selected results

28. Beijing Water System - global demand and supply [m3/s] 350 global demand global supply 300 250 200 150 100 50 Scenario 2 0 0 1 2 3 4 5 6 7 8 9 10 Beijing Water System - global demand and supply [m3/s] 300 global demand global supply 250 200 150 100 50 Scenario 1 0 0 1 2 3 4 5 6 7 8 9 10 Time [y] Scenario 1 shows that the demand can be fulfilled for the ten years, but without considering sustainability, the Miyun reservoir and the Groundwater are overexploited. By increasing in Scenario 2 the demand yearly, then we can see that the demand won’t be fulfilled anymore Water resources management-Selected results

29. Average head of global groundwater storage 30 28 26 Scenario 1 24 22 20 18 Scenario 2 16 14 12 10 0 2 3 4 5 6 7 8 9 10 Water level of Miyun reservoir 160 max 155 150 145 Scenario 1 140 135 Scenario 2 130 min 125 0 1 2 3 4 5 6 7 8 9 10 Within 1.5 years Miyun has already reached its minimum and at the end of the 10 years, the systems groundwater level has sunk rapidly. Water resources management-Selected results

30. Functionality of the DSS

31. Management of water supply based on optimization • optimized management of water resources • optimized supply in periods of increased demand • priority management in water scarcity periods • Emergency management and water resources protection in case of • natural disasters, terroristic attacks, accidents, • water resources pollution • Optimized adaptation of the water supply system to trends and changes • evaluation and implementation of political decisions • adaptation to changes in economy, population and agriculture • handling climate changes and water quality degradation • evaluation of increased waste water reuse • strategies for sustainability of water use • 4. Support for planning tasks • simulation and optimization of future technical structures • simulation and evaluation of resource recharge strategies • simulation and evaluation of strategies of demand reduction Applications of the DSS

32. Developed to meet the growing demands and pressures on water resources managers. Approach is state of the art and generic Based on a node-link network representation of the water resource system being simulated Include scenario planning in combination with state-of-the-art large-scale network flow optimization algorithm Places demand-side issues and water allocation schemes on an equal footing with supply-side topics Integrated approach to simulating both natural and man-made components of water systems Planner access to a more comprehensive view of the broad range of factors for sustainable water management GUI that facilitate user interaction and stresses out user sovereignty Conclusions

33. Thank you for your attention ! Questions?