A simulation-optimization-based decision support system for water allocation 14. Workshop Modellierung und Simulation von Ökosystemen 27.10-29.10.2010 Divas Karimanzira • Goals • Problem situation • Structure of the decision support system • Selected results • Benefits and applications • Conclusions 2 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 3 Total area [sq. km] Beijing vs Thuringia 16.800 16.172 Inhabitants, 2003 14.560.000 2.373.000 Beijing Province Per capita water consumption [l/d], 2003 248 87 Precipitation, annual mean [mm], 1993-2003 Beijing City 509 626 Average monthly values (1993-2003) Thuringia Erfurt Precipitation [mm]) 180 Beijing Thuringia 160 140 120 100 80 60 40 20 0 jan feb mar apr may jun jul aug sep oct nov dec Month 4 Yongding river downstream of the Sanjiadin-Sluice Miyun Largest drinking water reservoir o Max. storage 4,37 bn m³. o 03.2004, 30m below the highest admissible level, o Corresponds to a storage volume of only 0,8 bn. m³ water. o o Dry since 1998 Water directed to Beijing. 5 Sources Huairou Miyun Baihebao Guanting Transport systems BeijingMiyunChannel Bai river Guishui river Waterworks Customers WW 9 Tianchunsan Households & Industry Changxindian Chengzi Yongding r. Industry Yanhua ... Pipeline groundwater Agriculture WW 8 Aggr. WW Live environment 6 • 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. 7 8 • 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 9 Chaobai River Miyun-Inflow Huai Chaobai River Inflow Huai-Xiangyang Sluice Data source TS_Q_ChaobaiFinalFlowStation ChaobaiFinalFlowStation Wenyu River TS_Q_Miy un_FROM_OtherRiv ers 0 Other rivers Huai River River / Channel / Pipeline TS_Q_Xiahui Qing River Catchment area Miyun TS_Q_Zhangjiaf en Catchment area TS_Q_Chaobai_FROM_Bai Catchment area Bai river Miyun Reservoir Bai River Pipeline Miyun-9th Waterworks Huairou-WW9 TS_Q_Koutou Jing Mi-Tuancheng Huairou Reservoir TS_Q_Xiapu Water Tunnel Catchment area Huairou XXX Sluice Yongding-Yuyuantan Reservoir Guishui River SNWT-Tuancheng TS_Q_Guanting_FROM_Guishui Initial states: Hucheng + Tonghui River Jing Mi Channel Huairou-Tuancheng TS_Q_Qianxinzhuan Baihebao Reservoir WenyuFinalFlowStation Miyun-WW9 Pipeline Huairou-9th Waterworks Split Jing Mi Channel Bai River Jing Mi Channel Miyun-Huairou Catchment area Baihebao TS_Q_Weny uFinalFlowStation Wenyu River Qing-Tonghui South-North Water Transfer Yongding Channel Sluice IS_H_Miyun IS_H_Baihebao IS_H_Guanting IS_H_Huairou Beijing City Demand TS_Q_Sanjiadian_TO_YongdingChannel TS_Q_Sanjiadian_FROM_Yongding TS_Q_Xiangshuibao TS_Q_Sanjiadian_TO_Yongding Yongding River Guanting-Zhaitang TS_Q_Shixiali Defines initial states Catchment area Guanting Guanting Reservoir Yongding River Zhaitang-Sanjiadian Sanjiadian Sluice TS_Q_Yongding_FROM_MiddleWatershed Water from middle watershed Confluence Groundwater 10 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 11 Integration of GW and SW-Models 12 13 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! 14 • Inputs: – Groundwater recharge, – Withdrawal rates, water supply • Output: – Hydraulic heads of representative points 15 • The water resources allocation problem is formulated as a discrete-time optimal control problem: K 1 K k k k k min F x f x , u , z 0 u k , k 1,, K k 0 • subject to x0 xt0 Initial state (reservoir level, groundwater head …) xk 1 f k xk , uk , z k Process equations (balance of reservoir and groundwater storages …) Equality constraints (balance of nonhk xk , uk , z k 0 storage nodes …) g k xk , uk , z k 0 Inequality constraints (min (max) reservoir level …) Optimization horizon K • 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. 16 Example objective function: A maximize supply to customers T n max WS ij i 1 j 1 B minimize demand deficit T min n i 1 j 1 WDi , j WS i , j WDi , j ; WS i , j WDi , j C maximize level at Miyun reservoir at final time max H T , Miyun D maximize groundwater head at final time max H T ,GW 17 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), 18 Reservoir water levels Groundwater hydraulic head Consumed water Result evaluation Desired management policies Groundwater Surface water (hydrology, optimization, decision maker) Simulation inputs Human experts Balance at surface level Definition of the optimal control problem Objective functions, constraints, initial state and prediction of external influences Model transfer Optimization Node-Link Network q Reservoir outflows q Groundwater withdrawal Decision proposal for water allocation (Management plans) 19 Discharge Simulation Land use Climate Flow rates Surface water model Water demand Groundwater model Exploitation Flow rates Hydraulic heads Recharge Discharge Optimization Water levels Land use Objective function Flow rates Climate Model-based optimizer Water demand Water levels Flow rates Hydraulic heads Exploitation Recharge 20 ... Land use economic climate Model parameters(e.g Volume characteristics) Environment data(e.g.evaporation,land use ) Water demand (e.g. consumption policies ) Control strategies for reservoirs(e.g. timeseries) Simulation control data(e.g. horizont, resolution ) Scenarios Database management system (TIMESERIES GENERATOR) Population Fi x, y, z, t Model Parameters Model Structures Surface water model Prognosis Water demand Modell Prognosis Groundwater model Prognosis Optimization relevant data OPTIMIZATION Objectives, constraints Reporting tools: Plots, Spreadsheet Presentation of relevant Information HUMAN MACHINE INTERFACE (HMI) DSS-WIZARD Semi-automatic model update Information system 21 Scenario - Wizard Report SW-Model (Matlab) Network Editor (Java) GW-Model (FeFlow) Report Water Demand Model (Matlab) Reduced GW Model Report (Matlab) Optimizer (C++) SIM OPT Both Report SW-Model Report (Matlab) GW-Model (FeFlow) Report 22 Attributes Initial stage: Scenario of year 2006 Assumed impact: Precipitation drop from 600mm in year 2006 to 400mm in year 2007 Possible reactions: Increased exploitation of groundwater, Increased waste water reuse, Increased water use from water transfers, Increased prices for household water use, Decreased agricultural irrigation, etc. Procedure: For each possibility, a scenario has to be formulated to derive the input for simulations and running simulations for the possibilities of the reaction Decision support: Comparison of the simulation results and finding an optimum between the possibilities for a given goal function Goal function: e.g., No limitations in water supply of the households and minimal costs. 23 Catchment area outflow [m3/h] Cost Value 90 10 perfect Modell simulation 80 8 measured Simulation Nash-Sutcliffe: 0.73135 Bias: 1.6612 6 70 4 60 2 50 Bias 0 40 -2 30 -4 20 -6 10 -8 -10 -0.4 0 1982/01/01 1984/01/01 1986/01/01 1988/01/01 1990/01/01 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Nash-Sutcliffe Date Catchment area outflow [m3/h] 45 Nash-Sutcliffe: 0.67845 • Results of modeling a selected catchment area as an example. simulation 40 measured 35 30 • Figures show good training and validation Nash-Sutcliffe values of 0.73135 and 0.67845, respectively. 25 20 15 10 5 0 2007/01/01 2011/01/01 2013/01/01 2015/01/01 Date 24 Inflow Guanting Reservior [m3/s] 250 • Figures show the simulated/meas’d water inflow into the Guanting reservoir and 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] 479 478.5 • the corresponding water level for a period of a year. h_Guanting 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 25 FEM vs. Reduced model (Output Nr. 5 - Scenario1) 37 Red. model 36 FEM model 35 h [m] 34 33 32 31 30 29 28 0 1 2 3 4 • 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. Time [yr] 1.8 Measured Model (1) Model (2) Model (3) 1.6 Water demand (100 mil m 3) 1.4 1.2 • Yearly domestic water demand: Different model types: – Model(1) – Kalman predictor- based model – Model(2)-multiple regression model – Model(3)- neural network –based model 1 0.8 0.6 0.4 0.2 0 • 1997 1998 1999 2000 Year 2001 2002 2003 26 • 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. 27 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] Beijing Water System - global demand and supply [m3/s] 350 • 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. global demand • By increasing in Scenario 2 the demand yearly, then we can see that the demand won’t be fulfilled anymore global supply 300 250 200 150 100 50 Scenario 2 0 0 1 2 3 4 5 6 7 8 9 10 28 Average head of global groundwater storage 30 • Within 1.5 years Miyun has already reached its minimum and 28 26 Scenario 1 24 22 20 18 16 Scenario 2 14 12 10 0 2 3 4 5 6 7 8 9 10 6 7 8 9 10 • at the end of the 10 years, the systems groundwater level has sunk rapidly. 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 29 Use Case Short-term Horizon Time Horizon < 1 year Scenario / Main Objectives Result Satisfy water supply of households, industry, agriculture - optimal withdrawal strategies for reservoirs and waterworks Consideration of trends in precipitation and consumption; Reduce groundwater overexploitation Consideration of climatic changes, new resources, consumption; Stop groundwater overexploitation - optimal withdrawal strategies - optimal resources allocation - simulation scenarios Medium-term Horizon 1 ... 5 years Long-term Horizon 5 ... 20 years Extraordinary Events < 1 year Decision support e.g. for - optimal withdrawal environmental catastrophes; strategies objective function depends on the event - simulation scenarios Structural Changes 1 ... 20 years Prediction of impact of new elements of the water system (e.g. new channels or reservoires) - simulation scenarios 30 • • • • 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 31 • 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 32 Thank you for your attention ! Questions? 33