Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 1 erent scenar- ff , and P. Bauer-Gottwein 1 5932 5931 , D. Rosbjerg 2 , X. Mo 2 . The model can be used to guide decision makers to ensure long- 1 − , S. Liu 1,2,3 ers in the water supply system during droughts (Tsur and Graham-Tomasi, ff This discussion paper is/has beenSciences under (HESS). review Please for refer the to journal the Hydrology corresponding and final Earth paper System in HESS if available. Technical University of Denmark, Department of Environmental Engineering, Chinese Academy of Sciences, Key Laboratory of Water Cycle andSino-Danish Related Center Land for Surface Education and Research, Aarhus C, Denmark ios, and the5.47 billion cost CNY yr of ending groundwater overdraft in the basin is estimated to be Groundwater aquifers are ofact as high bu economic importance1991; Tsur, around 1990). the On worldover the the and North past often China decades has Plain,(Liu caused persistent decline et groundwater of al., overexploitation the 2001). shallowceed The and the deep immediate groundwater costs benefits tables of of pumping, satisfying which the highlights water the demands problem greatly of ex- the present self-regulating term sustainability ofbasin groundwater in and an surface economically optimal water way. resources management in the 1 Introduction Abstract Over-exploitation of groundwater reservesthe is world. a In majortively many environmental and river problem joint around basins, optimizationproach groundwater is strategies and used are to surface required. findtion water strategies cost-optimal A for are sustainable a hydroeconomic surface river used modelling water basin,A given and conjunc- ap- an simplified groundwater arbitrary alloca- management initial groundwater problemgroundwater level in with under the conjunctive aquifer. inflow use anddependent of groundwater recharge pumping scarce costs uncertainty surface the optimization isconvex, water problem and presented. is and a non-linear Because and genetic non- of algorithmthe head- is objective used of to minimizingworld solve the the application sum 1-step-ahead in of sub-problemsthe the with immediate model Ziya and capabilities. Persistent expected River overdraft future from BasinChina the costs. Plain in groundwater A aquifers has northern on real- caused thewastewater. China North declining is The groundwater used tables, model salinization to maps and demonstrate infiltration the of opportunity cost of water in di 1 Kgs. Lyngby, Denmark 2 Processes, Institute of Geographic3 Sciences and Natural Resources Research, Beijing, China Received: 28 April 2015 – Accepted: 20Correspondence May to: 2015 C. – Davidsen Published: ([email protected]),P. 22 S. Bauer-Gottwein Liu June ([email protected]) 2015 ([email protected]), Published by Copernicus Publications on behalf of the European Geosciences Union. The cost of ending groundwateron overdraft the North China Plain C. Davidsen Hydrol. Earth Syst. Sci. Discuss.,www.hydrol-earth-syst-sci-discuss.net/12/5931/2015/ 12, 5931–5966, 2015 doi:10.5194/hessd-12-5931-2015 © Author(s) 2015. CC Attribution 3.0 License. 5 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (Zheng 1 − erent scenar- ff and groundwater ff ects of ending long-term against the long-term in- ff ff . Pumping costs were linked linearly to ering capacity. ff 5934 5933 basin, shown in Fig. 1, is home to approximately 2 curse of dimensionality . Non-linearity arising from the head dependent pumping costs ff This study demonstrates how a hydroeconomic modeling approach can be used to The case study area is the Ziya River Basin, which is located in the Hebei Province Optimal management of conjunctive use of surface water and groundwater has been While a high level of complexity can be accommodated in deterministic simulation recharge and non-linearity arising from headcosts. and The rate dependent cost groundwater minimization pumping problemof is SDP solved (Pereira with and theThe water Pinto, non-linear value 1991; method, discrete Stage a suband and variant linear problems Larsson, programming are method 1961; solved similar Stedingera to with coupled that et a groundwater-surface used al., water by combined management 1984). Cai genetic problem et in al. algorithm an (2001), SDP but framework. applied to 2 Methods 2.1 Study area Northern China andcreasing particularly water the scarcity Northeconomic problems China development over Plain and the (NCP) reducedthe past have water precipitation balance 50 experienced (Liu has years historically in- and dueaquifer, been Xia, causing covered to a by 2004). overexploitation regional population of The lowering the growth, deficit of groundwater the in groundwater table by up to 1 myr groundwater overdraft in California. The linear model was run under di et al., 2010). on the NCP andinto with the the Shanxi upper Province. catchmentmultiple The stretching basin conflicts. through is The the subject 52 Taihang to 300 Mountains km severe water scarcity, which causes addressed widely in the literature. Harouconomic and optimization Lund approach (2008) used to a examine deterministic the hydroe- economic e ios and used tothe estimate benefits the of water conjunctive users’ useistic willingness-to-pay, water facilities. AQUATOOL simulation Andreu scarcity software et costs based al. and deficits on (1996) the in developed Out-of-Kilter demand the Algorithm and determin- toronment. minimum This minimize flows model was in later applied aet in coupled a al. hydroeconomic surface context (2006) water–groundwater by Pulido-Velázquez envi- toa coupled minimize setup the with sumaquifer a model of distributed-parameter scarcity allowed groundwater simulation. variable costsframework The but pumping and lacked integrated costs variable the ability operating inment to environment. costs a An give for alternative forward predictions optimization in moving,et approach an was scenario-based al. uncertain demonstrated (2013), by real-time Riegels who manage- time-constant water maximized prices. welfare subject to ecosystem constraintsmodels, by the adjusting objective functionsremain of computationally stochastic feasible. Philbrick optimization and modelsnamic Kitanidis are Programming (1998) (SDP) kept applied to simpler Stochasticsurface a to Dy- water multi-reservoir and system groundwater to givennamic stochastic optimize programming inflow. method, conjunctive The a use second modification of of ordermitigate the gradient the classical dy- well-known recursive SDP, was used to pumping rates but changes inwere pumping not costs considered. due Head-dependent pumping toby costs long-term were Knapp depletion included of and in the the Olson aquifer SDP (1995), model who analyzed conjunctive use of groundwater with ran- domly generated runo identify the least-cost strategycontext, to “sustainable” achieve means sustainable groundwater that abstraction.the the In long-term long-term this average average abstraction recharge.of does A not surface water exceed water managementIncreased problem and with complexity groundwater conjunctive is similar use caused to by Harou uncertain and surface Lund water (2008) runo is addressed. was overcome with lattice programming techniques in this qualitative model setup. crease in pumping costs and reduced bu management. As the groundwaterof resource the is increased unsustainable overexploited, supply the have immediate to benefits be traded o 5 5 10 15 20 25 10 15 20 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 1 (1) (2) (3) + t hp b t sw, r − t , m
ct x ! ct c  1 + + t l sw, based on the classical Bell- Q ,  SNWTP t 1 x + t k sw, . This allows for more flexible man- 3 Q sw, , V t , SNWTP 1 sw, c + t V , + t t . This is a reasonable assumption because , gw, ff gw V m gw, and a monthly limited volume of groundwater, x  5935 5936 V 1 ff  dm gw + ∗ ∗ t t c = F F + kl m , p t sw  ct, x 1 x L = sw l X + c + m , 1 t  = t M X m k sw, = = Q ,   SNWTP, t t t x sw, k sw, k sw, + V Q Q , m , t , , t t t gw, sw, sw, gw, V V V x  , , are located in the basin. In this study, it is assumed that the full storage capacity t t + 3 IC gw, gw, m , V

V t . The water users located downstream the reservoir (d) have access to reservoir ) and constant curtailment costs of not meeting the demand (see Table 1), as also  3  A conceptual sketch of the management problem is shown in Fig. 2. The water users In Davidsen et al. (2015), the groundwater resource was included as a simple ∗ gw sw, t 2.2 Optimization model formulation An SDP formulation is used toof find the surface expected water value or of storing groundwater,surface an given and incremental the groundwater amount reservoirs month and ofequation the the calculates inflow year, scenarios. the the The availablenations sum backward storage recursive of in of discrete immediate reservoirThe and storage immediate expected levels (states) management future andment, costs costs whereas monthly for the (IC) time expected all steps arise future combi- (stages). costs from (EFC) water are the supply optimal and value function water in curtail- applied by Davidsen et al.tic (2015). and The decoupled water from the demandsthe stochastic are runo assumed rainfall to on be theter determinis- NCP demands normally are occurs concentratedplanned and in in typically the the the summer same dryter every reservoir months, spring. year. (u) while The have The access water irrigation to irrigation usersX the wa- upstream runo schedule the is surface wa- centrally releases, water delivered through theand South-to-North groundwater Water from Transfer Project the (SNWTP) dynamic aquifer. weighed by the corresponding transition probabilities.to In weighted the the present IC setup, wepossible. and decided Because EFC of equally, the but head inclusionwill and of be rate discount dependent described rates groundwater in pumping othercision costs, than detail variables. which The zero later, is objective the is immediategiven to cost by minimize depends the the optimal non-linearly total value costs on function over the the de- planning period, F mestic water users. Each water user(m group is characterized by constant water demands man formulation: min are divided into groups of economic activities; irrigation agriculture, industrial and do- box model with an upper storageagement capacity with of 275 larger km abstractions in drygroundwater years aquifer and can increased thereby recharge be in used wet years. to The bridge longer drought periods. monthly upper allocation constraint,between which the groundwater prevents and analysisIn surface of water the dynamic resources present interactions and model limits setup, the the decision groundwater space. is included as a simple dynamic aquifer 25 million people (dataZiya from River 2007; by Bright Davidsen et etsurface al., al. water 2008). (2015) resources. A focused hydroeconomic Five primarily3.5 study km major on of optimal reservoirs the management with ofcan a be the managed combined flexibly storage withoutor capacity consideration existing of management of storage rules. reserved for flood protection x with IC being the immediate costs: IC subject to: 5 5 20 25 10 15 15 10 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (4) (5) (6) (7) (8) (9) (10) ) for each 1 − ) as initial con- t max,gw V cient of 17.5 % of sw, ffi V ≤ t gw, and V , t gw, V max,sw V and normalized. A Markov chain ≤ ff t sw, V , E 1 1, weighted by the Markov chain transition + Q t + t ≥ 5938 5937 gw, t V 1 E, + = t (IBM, 2013) to solve the linear sub-problems. q , t gw, into reservoirs. The 51 years (1958–2008) of simu- V gw, ff s = − t SNWTP cplexlp t t Q gw, serial correlation between three flow classes defined as dry E, sw, s ≤ r q ff − − + t , t ! t , , d u d d model. The average monthly precipitation (mm month gw, ff sw, sw, model based on the Budyko Framework (Budyko, 1958; Zhang et al., sw, are aggregated to monthly runo x x x x ff SNWTP,Bei 1 t t 1 1 ff 1 = x D = = U D = D (Eq. 7), while the upstream groundwater allocations are constrained to X d u sw, X gw, X d X d + , X ff Q − − = t t gw ≤ ≤ t V t t , gw, , sw, sw,Bei sw, u

u Q Q x class is calculated, and a simple groundwater recharge coe s f , sw, gw, + + ff + = R x x t t t 1 1 The sets of equilibrium shadow prices, referred to as the water value tables, can A rainfall–runo The SDP loop is initiated with EFC set to zero and will propagate backward in time Eqution (3) is the water demand fulfillment constraint, i.e. the sum of water allocation ≤ gw = = U U sw, gw, sw, t u u X X in the rainfall–runo (0–20th percentile), normal (20th–80th percentile),established and and wet validated (80th–100th to percentile),2005). ensure is The second order groundwater stationarity recharge (Loucks is and estimated van from Beek, the precipitation data also used which describes the runo probabilities. The algorithm will continuei.e. backward until in the time shadow until pricescessive equilibrium years (marginal is remain value reached, constant. of The storingInc., SDP water 2013) model for and is future uses developed the use) in fast in MATLAB two (MathWorks suc- subsequently be used to guide optimal water resources management forward in time lated daily runo runo ditions, and reservoir inflowThe is optimization given algorithm by will theimmediate search present management for (water inflow the allocations class and optimalreleases in water and solution, the curtailments, groundwater given Markov including pumping) the chain. reservoir whichfuture costs costs. have As of to the the be SDP algorithm balancedbe is equal against propagating to backward the in the expected time, minimum the total future costs costs from will pumping cost, which dependsas on described the later. combined downstream groundwater allocations 2008) and previously appliednatural by daily Davidsen surface et water al. runo (2015) is used to estimate the near- discrete combination of states, aproblem cost will minimization have sub-problem the will be discrete solved. reservoir A storage sub- levels ( through all the discrete system states as described in the objective function. For each the precipitation (Wang et al., 2008) is used. V r V balance of the combinedof the surface reservoir water releases. reservoir, Afollows while similar in water Eq. Eq. balance (5) (6). forstream is the The runo dynamic the upstream groundwater surface water aquifer water balance allocations are constrainedstraints to on the the decision up- variables are shown. Last, Eq. (10) is the marginal groundwater r and water curtailments equals the water demand of each user. Eq. (4) is the water a fixed sustainable monthly average (Eq. 8). In Eq. (9), the upper and lower hard con- c (see Table 3). 5 5 10 25 20 15 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ). is 2 g (15) (11) (12) (14) (13) ), 3 is used. − 1 is defined − w ) in Northern Q 1 − time series are ff is the transmissivity ), distributed evenly to 1 T (CNYWh − ), el 1 c − erence between groundwater is the distance from origin to ff month is the area of the aquifer (m w 3 erent initial groundwater aquifer r ff A month 3 for silty loam (Qin et al., 2013) which is the density of water (kg m ciency (–). The marginal pumping cost 1 1 ρ − − ffi A ), 1 3 − − y is the head di S 5940 5939 month h 2 ! ∆ 1 m + ), 6 t 2 − − gw, is the pump e depending on power source, province and consumer 10 V 2 ε 1: 1 × + − t + t t . In this study, the available historic runo gw, ff gw, V x and − el  c t 1 w in − r r is the radius of influence (m) and  max,gw hε in V ln ∆ r ) is found from the average electricity price

3 w is the distance from the land surface to the top of the aquifer at full storage is a decision variable and once substituted into Eq. (13), it is clear that the ), − ρg /ε πT is the pumping rate of each well (m + 1 Q 1 ) is found as the mean depth from the land surface to the groundwater table 2 − = + top h is the specific pump energy (J m t w P top t h is the specific yield (–) of the aquifer and h = ∆ el Q h P ∆ ∆ gw, Y c gw, V ρg S x (CNY m ( = month t = ∆ Thiem 2 In Eq. (14) the drawdown is assumed uniform over the entire aquifer. This simplifi- = h h gw gw gw, the point of interesta hydraulic (m), conductivity here of 1.3 the radius of the well. The transmissivity is based on (see Fig. 2) between where as the total allocated groundwater within the stage (m where ∆ (m was tested to be realisticField in interviews a revealed MIKE that SHE the model wellsface, of typically which reach the results no Ziya in deeper River than a Basin 200 specific (Marker, m 2013). yield below of sur- 5 %. The thickness of the aquifer where the gravitational acceleration (m s table and land surface (m) and Hence this cost will vary withelectricity the stored price volume in structure thebetween groundwater in aquifer. 0.4 The China present and is 1 CNYtype kWh quite (Li, 2012; complex, Yu, 2011). with In the this study users a fixed typically electricity paying price of 1 CNY kWh with unknown future runo c China: c P Here used to demonstrate howoperation. the The derived water simulation valuestorage will tables levels be thereby should demonstrating initialized be whichNCP used from pricing back in di policy into real a should time sustainable be state. used to bring2.3 the Dynamic groundwater aquifer The groundwater aquiferrecharge is and represented groundwater pumping asthe determining aquifer a (Eq. the 6). simple change Theenergy in pumping box needed is the to model associated lift stored with the (see volume water a from of pumping Fig. the cost groundwater determined 2) table by to with the the land surface (Eq. 10): where the steady statedrawdown Thiem at drawdown the pumping (Thiem, wells.total Local 1906) required drawdown solution is lift: then is added used to Eq. to (15) to estimate estimate local ∆ (m), cation might be problematiccontribute as significantly the to local the pumping cone cost of and depression thereby around the each optimal well policy. Therefore, could problem becomes non-linear. The immediate costs of supplying groundwater to a singlec user follow: 5 5 20 15 20 15 10 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | is 1 (16) + t gw, V . Assum- 2 population − . If 1 + t and others), the gw, are kept discrete. V 1 1, cient tools to get the + . With two state vari- t + ffi t sw, V and 1 + t function tolerance gw, , V t gw, s curse of dimensionality 5941 5942 stall limit − , t gw, (number of top parents to be guaranteed survival) Q . Each of the candidate solutions contains a set of ciency of the GA for the present optimization problem. w + ffi n 1 + t (how the initial population is generated). The options were fitness limit gw, V − elite count population t gw, V , the = t , d w gw, is the number of wells in the downstream basin. Erlendsson (2014) estimated n x can be calculated from the water balance. The groundwater pumping price is generation function 1 w = D n P w d Q , the stopping criteria ( = is 500 m, overlapping cones of depression from 8 surrounding wells are included in The computation time for one single sub-problem is orders of magnitude larger than This study uses a genetic algorithm implemented in MATLAB to solve the cost min- Non-linear optimization problems can be solved with evolutionary search methods, The SDP framework is subject to the w in adjusted to achieve maximum e the method used bythat Cai cause et non-linearity al. are (2001), identifieddecision was and variables developed chosen (see by are the Fig. chosen, GA.thereby 3). Once solvable the Decision these with remaining variables complicating LP. In objectiveis the function caused present becomes by optimization the linear problemBoth (Eq. head-dependent and the 1) pumping the regional costs non-linearity as loweringcones depend explained of on in the the Eqs. decision groundwater variable (13) for table and the stored and (14). volume the in Thiem local drawdown solving a simplewith LP. increasing As number the of decision optimization variables, problem a hybrid becomes version computationally of GA heavier and LP, similar to and the decision variables (sampled within thetion decision to space), which the will optimization yield problem.size a In feasible MATLAB, solu- a set ofcrossover options fraction specifies: the imization sub problems. Thislutions GA function known will as initially the generate a set of candidate so- with LP. The GA wasfor used the optimal to solution. test The combination combinationswas yielded used of faster to computation the estimate time fixed than all parameters if the the while parameters. GA looking approximate solution to complex non-linear optimization1989; problems (see, Reeves, e.g., 1997). Goldberg, GAstion use and a have random been searchet applied approach al. to inspired (2001), McKinney the by and field natural Lina evolu- (1994) of combined and genetic water Nicklow algorithm resources et and al.non-linear management linear (2010). surface by, programming Cai water e.g., (LP) et management Cai approach al. problem.cision (2001) to By used fixing solve variables, a some the of highly remaining the objective complicating function de- became linear and thereby solvable pre-selected, the regional drawdownrate is given and the resulting groundwater pumping ables and non-linearity, the computation timechoosing is model significant discretization. and With is aerror a low limiting increases, number factor particularly of when discrete if states, the the discretization end storages thereby also given, and the remaining optimization problem becomes linear. Q the number of wells in the catchment: a sub division ofods global is optimizers. genetic A algorithms widely (GA), used group which of have been evolutionary found search to meth- be e the well density in the Ziya River Basin from Google Earth to be 16 wells km where ing that the wells are distributedr evenly on a regular gridthe and that calculation the of radius of the influence principle local of drawdown. superposition This as additional also drawdown applied is by included Erlendsson using2.4 (2014). the Solving non-linear and non-convex sub-problems In the previous studylinear by and Davidsen strictly et convex. The al. individualfore sub-problems (2015), be of the the solved optimization SDP scheme with problemnon-linearity could was a there- from strictly fast the linear head-dependentture programming groundwater cost pumping function algorithm. is costs, In no the this longer expected strictly study fu- convex. however, with 5 5 20 15 10 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 1 1 − + t (17) sw, V ect of the ff and 1 + t gw,
V 1 + t the marginal cost of 1 sw, − V , ect the present manage- 1 ff 1 between the determinis- + t = ected. The water values after gw, ff p V
and thereby less than the lowest cur- EFC 3 + −
1 + t flow class and time of the year. A sample of 5944 5943 sw, ff V , 1 + t gw, V . It requires an electricity price higher than 2.8 CNY kWh IC 3 − min =
data. For low storage capacity and long time scales, the e 1 ff + t being the decisions: sw, 1 V + t , 1 + sw, t V , 1 gw, V + t The backward recursive SDP algorithm was run with a looped annual dataset until The performance of the GA-SDP model is compared to a deterministic Dynamic gw, 1980 are clearly highercaused than by a in reduction the intables period the are before regional uniform, 1980 precipitation. with In duevalue contrast, tables variation increased are the only water included groundwater as with scarcity value Supplement. groundwater storage. The detailed water the resulting equilibrium waterthe value temporal tables variations are of presented water inother values state Fig. as variable 4. a at function This a offull figure fixed one value. storage shows state The respectively. state variable, During keeping variables thetion the are rainy fixed rates at season reduce empty, from half water June fullgroundwater scarcity, to and storage resulting capacity August, in is high lower much precipita- for surface larger, later increased water use, recharge values. and can groundwater Because values easily the are be therefore stored not a lifting groundwater 200 mfound (typical with depth Eqs. of (13) and wells (14) observed to in be 0.8 the CNY m study area) can be 3 Results Without any regulation or considerationexploitation of of the expected the future groundwatermediate costs aquifer, arising profits the from (producers) water over- or userscosts for utility will groundwater, continue (consumers). the maximizing users Becausegroundwater will im- there cost continue exceeds are pumping the groundwater only curtailment until costs. electricity the At marginal 1 CNY kWh tailment cost at 2.3 CNY m values represent the truevary with values reservoir of storage storing levels, a runo unit volume of water for later use and equilibrium water values, i.e. no inter-annualincrease changes, fastest were obtained. during The the water first values creases years, and become after small. approximately Due 100 yearsequilibrium to the is the annual in- large however not storage capacity achieved until of the after groundwater 150–180 years. aquifer, These marginal water before the lowest-value user stops pumping from 200 m below surface. are chosen by theclasses, the GA. objective For of a theV GA given is combination to of minimize the stages, total discrete costs, states TC, with and the flow free states Piecewise linear interpolation oflows the for future free cost end function storagespolation (Pereira but between and requires the strict Pinto, future cost 1991) convexity.our With points al- problem, two will the state yield EFC variables, is a inter- no hyper-plane longer in strictly three convex dimensions. and In therefore both TC ment. with EFC being thechosen expected the future end states, costs.hence the Given solvable immediate initial with cost LP states minimization (see2013) and problem Fig. once is becomes 3). The linear the used IBM and GA tocubic CPLEX interpolation has linear solve of programming the the solver discrete linear (IBM, of neighboring programs. the future matrix. cost The The grid expected GA points approachesThe in future the each total costs global dimension costs optimum are are until stored, acomputation found and fitness time, by the limit the algorithm criteria outer continues is loop to met. through the the next groundwater state. states To reduce isProgram the parallelized. (DP), which findsinflows the and groundwater optimal recharge. solution The DP givenmodel model perfect and uses knowledge the 1-dimensional same state about algorithm transition future as matrices the SDP with end storage volume becomes negligible.looped Similar and to the run SDP until model, the the end DP of model was period condition does not a tic monthly runo 5 5 25 20 15 10 10 15 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (95 % 3 . Time series of the ff erent scenarios can be seen ff 5946 5945 . The allocation pattern to this user is shown in 3 − zero future costs). The resulting groundwater table is continuously de- = The average total costs of the 51 years simulation for di At the equilibrium groundwater storage level, the user’s prices shown in Fig. 6 indi- We simulate management using the equilibrium water value tables as decision rules The surface water reservoir storage level varies over time, and in contrast to the In the simulated management runs, water will be allocated to the users up to a point full). If the storageaverage in pumping the until aquifer the is equilibriumequilibrium, below storage average this is pumping level, reached. will the exceed Ifstorage average average the is recharge, recharge storage reached. and level will over is time exceed above equilibrium findings by Davidsen et al.most (2015) every the year. This storage can capacity bemodel, now explained which becomes by close the allows increased to increased groundwater zerodemonstrate groundwater availability al- the in allocation the business-as-usual in solution, multi-annualperiod the dry with simulation periods. the model To present is waterset run demands to for and infinity a curtailment ( 20 costs year creasing and as with shown a in discount Fig. rate 5. where reductions in immediate costcosts. are The compensated user’s price, by which increasesthe can in marginal be expected value applied of future in the last ansum unit opportunity of of cost water the pricing allocated actual scheme, togiven is the pumping by users. cost The the user’s (electricity equilibrium priceter used) is water and the value and surface tables. the water In additional aresustainable Fig. shown opportunity groundwater 6, for storage cost the level. the When 51 user’s yearequilibrium, the prices simulation groundwater the at for storage user’s level and groundwa- prices is below ofods close the with groundwater to long-term water and scarcity. surface In waterto wet are surface months water equal with allocation during reduced only, water peri- andthe scarcity, the time the groundwater series model user’s switches in price Fig. isgroundwater undefined 6). user’s (gaps If price in the will groundwater be storage higher level causing is an below increase the in equilibrium, water the curtailments and in Table 1. A simplemodel. local Davidsen sensitivity et analysis al.to is estimate used (2015) to the used assess uncertainty Montetional the of state Carlo uncertainty variable the simulations of has model the an based increased outputs. approach on the infeasible. However, Approximately 50 the optimization 4000 time CPU inclusionto samples hours significantly of reach per and an climate equilibrium period made addi- inof are such 12 the needed parallel present processors model,the are equivalent used local to in sensitivity MATLAB two R2013a. relateddirectly weeks, The to in if analysis the the the was water focused objectivelocal maximum on drawdown demands function (Eq. and (Eq. 14). The water 1)the uncertain curtailment sensitivity and input evaluated costs parameters the based were used transmissivity onbe increased the used by seen simulation 10 to % in results. and estimate The Tableincrease 1. resulting the in total A the costs total 10 % can costs,increase increase while in costs. a in The similar the transmissivity increase can curtailment of vary the costs over many demands is orders generates of returned a magnitude as 2.1 because % a 6.0 % Fig. 7: the modelon switches water between availability high and curtailmentbetween storage and satisfying high in 0 allocations, the depending drawdown and reservoirs. cones 80 Groundwater in % the allocations of optimization fluctuate ing model the increases cost the demand. with marginal Inclusion increased groundwaterevenly pump- pumping of over rates. the the Groundwater months, steady allocationsremain which state constant, are results while Thiem distributed 1 in % more less ofsurface water, the local if total drawdown. the water The stationary abstraction is total Thiem shifted drawdown curtailments is from groundwater included. to cate frequent curtailment of wheat agriculturehas in a the downstream willingness Hebei to Province, pay which of 2.3 CNY m increasing storage level aswater shown user’s price in increases Fig. up to 5. a Under point these where the circumstances two the prices meet. surface and force the system with 51 years of simulated historical runo simulated storage levels can be seengroundwater in Fig. aquifer 5 for approaches the an dynamic groundwater equilibrium aquifer. The storage level around 260 km 5 5 15 20 25 10 10 15 20 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ap- ) is high: a 1.3 % change T curse of dimensionality as previously mentioned. The erence highlights the problem of ff . This di 1 − 5948 5947 er to the system, which significantly stabilizes ff curse of dimensionality to 8.47 billion CNY yr 1 ect on total costs and total allocated water, it is clear from Fig. 7 − ff ) from the baseline value results in a 1.5 % change in the cost. T ine, the resulting optimization time of 2 weeks on 12 cores is acceptable. Another addition to the modelling framework was the Thiem stationary drawdown. Computation time was a major limitation in this study, and the transition from the Replacement of the hard upper groundwater pumping constraint used by David- A great advantage of the SDP-based water value method is the capability to obtain ffl defining realistic boundaries to optimizationstraints, problems and here shows fixed that simple groundwaterspace. hard pumping With con- limits, inclusion can ofgroundwater a highly storage dynamic limit capacity groundwater the as aquifer, optimalthe the a model decision user’s bu can price useecosystem of the flow large surface constraints water canwhich as be results satisfied shown in with reductions in less in Fig. the impact respective on 6. shadow the prices. Finally, expensiveThe policies users, long like time minimum stepswell drawdown (monthly) significantly make changed stationarityslightly the increased a simulated computation realistic management time. assumption. Whilehas but addition Inclusion only resulted of a in of the small only Thiemthat e stationary the drawdown additional Thiemthe drawdown water highly users. impacts High groundwaterthus the pumping in allocation rates higher pattern result pumping to in costs. larger some This local of mechanism drawdown leads and to a more uniform groundwater o previous much simpler linearpresented single non-linear state SDP SDP50 model 000 model with times (Davidsen two more etTechnical CPU state al., University of hours. variables 2015) Denmark We proved to to used to the solve the the require SDP, high and around performance as the cluster optimization (HPC) can at besen the run et al.11.39 (2015) billion CNY with yr a dynamic groundwater aquifer, lowered the total costs from ming (SDDP, Pereira and Pinto,for 1991; multi-reservoir Pereira river et basin al., wateronly 1998) samples management has around problems. shown the However, because great optimalcomplete SDDP potential decisions, set this of method shadow will pricesfor not for adaptive be all management. able state to combinations provide and the is therefore less suitable it is a log-normally distributed variable. The sensitivity of log( number of sub-problems to beexponentially solved with in the the number backward movingto of SDP 2–3 state inter-linked scheme variables. storage increases facilities Innot and our higher be case dimensional computationally management we feasible problems today. arevoirs This will therefore and limit limited on groundwater the aquifers numberworld requires of situation strongly surface in simplified water reser- the representationsimulation optimization of phase the model. that real These followsplies requirements the to the can optimization. backward moving While be SDPto the relaxed scheme, the the in forward same moving the extent simulation is asvalues not just determined limited one by single the sub-problemusing is a SDP solved much scheme at more can each spatiallytage stage. resolved of thus model The SDP be with water is used aadaptive that management, high to it provided number provides that simulate of the a management users. systemfeasible complete The can set level. be advan- of An simplified to decision alternative a rules computationally approach that can known be as applied stochastic in dual dynamic program- optimal decision rulesSDP-approach for is, any however, combination the of system states. A first limitation of the of log( 4 Discussion This study presents adecision hydroeconomic rules optimization in approach termsment. that of The provides method water economic was values usedBasin for to should demonstrate joint be how surface priced the water–groundwater over waterbelieve time resources manage- to that in reach the the a Ziya sustainable River presenteddecision situation support modelling at tool minimum framework in cost. real-time has We and water great simplifications management. However, need potential a to number use be of as discussed. limitations a robust 5 5 15 20 25 10 15 25 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 3 ected. ff . The present study 1 − ect of wrong timing, which is ff er to the system and eliminates ff for a comparable setup but with sustain- 1 − 5950 5949 . 1 − erence indicates a very good performance of SDP, ff reflects the expected cost of ending the groundwater overdraft in erences between the total costs with and without perfect foresight. ff 1 − ect of discounting of the future costs on the equilibrium water value ta- ff erence between total costs with SDP and with DP (perfect foresight) is sur- ff A significant impact of including groundwater as a dynamic aquifer is the more stable The derived equilibrium groundwater value tables in Fig. 4 (and the Supplement de- In the previous study by Davidsen et al. (2015), total costs, without restrictions on From any initial groundwater reservoir storage level, the sustainable management The di user’s prices shown in Fig. 6.immediate The groundwater user’s pumping price costs of (electricity groundwater costs) consists and of the two expected parts: future the costs reflected in small di tution of the groundwaternumber values of with states a and thereby simpler thei.e. cost computation the function time. groundwater The could values equilibrium around greatly groundwater the price, possibly reduce long-term be the equilibrium estimated groundwater storage, from can of the the total optimization, renewable but wateraddress further and the work e the is water requiredbles demands and to ahead the test long-term this. steadylarge state Further groundwater groundwater aquifer work table. storage In should capacity the forces also to present the run model backward moving setup, through SDP the 200–250 algorithm modelequilibrium. years, Another great until improvement, the if waterwater data values demands allow, converge would with be to elastic to the demand replace long-term curves the in constant the highly flexible GA-LP setup. tailed water value tables) show thatstorage alone that and the are groundwater independent values of varyage time with in of groundwater the the surface year, water the reservoir. inflow This scenario finding and is the important stor- for future work, as a substi- Inclusion of the large groundwater aquifer reduces the e a user in month 1,step. the Wrong same decisions user are will therefore simplyas not receive observed a punished by bit with less Davidsen curtailmentthe water et of users in expensive with a al. users following curtailment (2015) time study costs but the close will farmers). to The shift the inclusionmodel allocations long-term of self-regulate, a equilibrium in dynamic as water time groundwater price periods aquifer andwith thereby (in with a between makes this too more the unrestrained strict policy.sensitivity policy The analysis. will robustness The is be impact also compensatedis of supported by small, changes by periods in as the the it simple input local is parameters mainly on the the timing total and costs not the amount of curtailment being a the groundwater pumping, were estimated to 3.09 billion CNY yr fore the equilibrium groundwatererrors. storage level is subject to significant discretization the economic consequences of a wrong decision. If too much water is allocated to brings the groundwater tablethe to aquifer an storage equilibrium capacity. storage Onlyserved level small at after variations approximately the in 95 %equilibrium the storage of groundwater aquifer level storage storage reaches level level to are equilibrium.still be ensuring ob- Intuitively, as that one close any incoming as wouldequilibrium groundwater possible recharge expect groundwater to can storage full the be level capacity stored. wouldwhich, while, Finding require given the a the exact very size fine of storage the discretization, groundwater storage, is computationally infeasible. There- pumping strategy, which ismanagement clearly policy. seen in Fig. 7 and results in much more realistic estimates an increase to 8.56able billion CNY groundwater yr pumping and5.47 billion groundwater CNY yr storage atthe equilibrium. basin This once the increase groundwater aquifer of the is aquifer at from equilibrium the storage. present The storage costTable level of 1, below recharging the the equilibrium scenario is significantly withthat higher. initial In the groundwater average storage below cost(one equilibrium of third (LGW) full) sustainable shows is management 13.32 billion from CNY yr an initial storage at 100 km the model setupWith also the simulates SNWTP small inways economic have operation consequences enough (post-2014) of water, the andlarge wrong downstream most the groundwater decisions. remaining expensive aquifer serves users user as have (Beijing) a access bu will to al- groundwater. The prisingly small (1 %). While this di 5 5 20 25 10 15 10 20 25 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | er ff , independent of 3 − ected by the actual ff . The aquifer serves as bu set by a similar reduction in the 1 ff − . After equilibrium is reached, the 1 − 5952 5951 . This long-term equilibrium is not a 3 − S. Liu and X. Mo were supported by the grant of the project of Chinese Na- , J.: China: the South–North Water Transfer Project – is it justified?, Water Policy, 5, ff water-resources planning and operational management, J. Hydrol., 177, 269–291,1–28, 1996. 2003. //www.ornl.gov/landscan/ (last access: 15 June 2015), 2008. ton, 1958. librium water value tablesfor any represent combination the of shadowues time, prices at inflow class equilibrium of and were surface reservoir found and storage. to groundwater The be groundwater almost val- constant at 2.2 CNY m This study presented how arive hydroeconomic a optimization pricing approach policy can tosustainable be bring used state. an to The de- overexploited model groundwaterof aquifer quantifies a back potential to complex savings a riveroptimized of long-term basin in joint in a water China. SDP management Surface framework water based and groundwater on management a was coupled GA-LP setup. The derived equi- opportunity costs. A constant electricityinternalize price the can user’s prices therefore of bewill groundwater used ease shown as the in a Fig. implementation policy 6. ofis tool Stable one e.g. to water of an user’s the opportunity prices available costmanagement. policy options pricing to (OCP) enforce scheme, long-term which sustainability of groundwater 5 Conclusion Berko Bright, E. A., Coleman, P. R., King, A. L.,Budyko, M.: and The Rose, Heat A. Balance N.: of the LandScan Earth’s 2007, Surface, available US at: Departmenthttp: of Commerce, Washing- References Andreu, J., Capilla, J., and Sanchís, E.: AQUATOOL, a generalized decision-support system for average costs are estimated to be 5.47 billion CNY yr and allows for overexploitationwater in prices. dry These years, stable and user’sthe prices this representation are mechanism of suitable the stabilizes for management use the problemmodel, in must user’s the an be OCP kept OCP simple prices scheme. inwhich While can the includes be optimization a used detailed to physical representation drive of a the much system. more detailed simulation model, The Supplement related to thisdoi:10.5194/hessd-12-5931-2015-supplement. article is available online at Acknowledgements. of Sciences (2012ZD003). Thethe authors Ziya thank River the BasinPlatform numerous for for sharing farmers sharing their and hisN. experiences; strong water Marker willingness L. managers to S. and in assist Andersen L.development with of from B. the his the Erlendsson presented expert China-EU optimization insight for framework. Water from their China; extensive and work K. on a related approach early in the tional Natural Science Foundation (31171451)Plan and in of Institute the of Key Geographic Project Sciences for and the Strategic Natural Science Resources Research, Chinese Academy electricity price, as increasing electricity prices will be o the time ofcaused the by year, the the groundwater surfaceand reservoir water was could storage further be and extendedsion accommodated of to the with a include dynamic inflow the groundwater stationary class.compared use aquifer greatly to Thiem Non-convexity of reduced a local a the setup total GA drawdown withwill costs cones. fixed of recharge monthly water Inclu- the scarcity, pumping aquifer limits.storage until The at the sustainable one management equilibrium third storageoverdraft of level are the is estimated aquifer reached. to capacity, From the be an average 13.32 initial billion costs CNY yr of ending groundwater represented by the groundwater valueis for the run last to allocated equilibrium, unitapproximately of the 2.2 water. CNY user’s As m prices the model converge towards the long-term equilibrium at 5 5 15 10 20 15 10 20 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . Web Portal, ff -the-deep-end-beijings-water-demand- ff 5954 5953 the Deep End – Beijing’s W ater Demand Outpaces Sup- ff ciency in arid and semiarid areas of China, Agr. Water Manage., 80, 23–40, ffi Huai and Hai River basins of2004. China, Hydrol. Process., 18, 2197–2210,, 10.1002/hyp.5524 doi: the North China Plain, Water Int., 26, 265–272, 2001. Applications, UNESCO PUBLISHING, Paris, France, 2005. (China) with stochasticmark, dynamic Department programming, of M.Sc. Environmental Engineering, thesis, Kongens Technical Lyngby, Denmark, University 2013. ofMassachusetts, 2013. Den- els, Water Resour. Res., 30, 1897–1906, doi:10.1029/94WR00554, 1994. measurement data shows storage depletion inAfrica, Hai 35, River 663–670, basin, 2010. Northern China, Water South Chinese Statistical Association, availablehtm at: (lasthttp://www.stats.gov.cn/tjsj/ndsj/2011/indexeh. access: 15 June 2015), 2011. Baishengcun, Zizhuyuan, Beijing, China, 100044, 2009. Minsker, B., Ostfeld, A., Singh,and A., beyond in and water Zechman, resources136, E.: planning 412–432, State doi:10.1061/(ASCE)WR.1943-5452.0000053, and of 2010. management, the J. art Water for Resour. genetic Plan. algorithms Manag., Stochastic Models,download/papers/pereira_epsom98.pdf EPSOM’98,(last access: Zurich, 29 October 1–22, 2012), 1998. availableplanning, at: Math. Program.,http://www.psr-inc.com/psr/ 52, 359–375, 1991. sour. Res., 34, 1307–1316, doi:10.1029/98WR00258, 1998. using a combined genetic algorithm24, and 667–676, linear, doi:10.1016/S0309-1708(00)00069-5 programming 2001. approach, Adv. Water Resour., P.: Using Stochasticin Dynamic the Programming,doi:10.1061/(ASCE)WR.1943-5452.0000482 to Ziya 2015. Support River Water Basin, Resources China, Management e J. Water,doi:10.1016/j.agwat.2005.07.021 2006. Resour. Plann. Manage., 141,and surface 04014086, water resourcesTechnical University in of the Denmark, Kongens Ziya Lyngby, Denmark, River 18–19, basin, 2014. China,Wesley Thesis, Publishing B.Sc. Company, Inc., in North engineering, China Plain, China, 1989. Boston, MA, USA, 2013. Hydrogeol. J., 16, 1039–1055,, doi:10.1007/s10040-008-0300-7 2008. available at: http://www.gov.cn/english/2006-05/24/content_290068.htm (last access: 152015), Jue 2006. ply Despitehttp://www.circleofblue.org/waternews/2011/world/o Conservation, Recycling, and Imports, Circ. Blue, available at: outnumbers-supply-despite-conservation-recycling-and-imports/ (last access: 18 July2011. 2013), agement withdoi:10.1006/jeem.1995.1022, stochastic 1995. surface supplies, J.com/html/2012-05/17/content_2046027.htm (last Environ. access: 5 Econ. August 2014), 2012. Manag., 28, 340–356, Goldberg, D. E.: Gentic Algorithms in Search, Optimization, and Machine Learning, Addison- Harou, J. J. and Lund, J. R.:Honge, Ending M.: groundwater N. overdraft China in drought hydrologic-economic triggers systems, water disputes, GOV.cn, Chinese Gov. O IBM: ILOG CPLEX Optimization StudioIvanova, v. 12.4, 2013. N.: O Erlendsson, L. B.: Impacts of local drawdown on the optimal conjunctive use of groundwater Google Inc.: Google Earth, (version 7.1.2.2041), Addison-Wesley Longman Publishing Co., Inc. Knapp, K. C. and Olson,Li, V.: L. Tiered power bill J.: debated, Shenzhen Dly., The 17 May, 1, economics available at: http://szdaily.sznews. of conjunctive groundwater man- Liu, C. and Xia, J.: Water problems and hydrologicalLiu, research C., Yu, in J., the and Yellow Kendy, E.: River Groundwater andLoucks, exploitation the D. and P. its and impact van on Beek, the E.: environmentMarker, Water in K. Resources Systems N.: Planning Optimizing and surface Management water and and groundwater allocationMathWorks in Inc.: the MATLAB Ziya (R2013a), River v. 8.1.0.604, basin including theMcKinney, D. Optimization C. Toolbox, and Natick, Lin, M.-D.: Genetic algorithm solutionMoiwo, of J. P.,Yang, groundwater Y., Li, management H., mod- Han, S., and Hu, Y.: Comparison of GRACE with in situ hydrological National Bureau of Statistics of China: Statistical Yearbook of the Republic of China 2011,NGCC: The Shapefile with provincialNicklow, boundaries J., Reed, in P., China, Savic, D., Natl. Dessalegne, T., Geomatics Harrell, L., Cent. Chan-Hilton, China, A., Karamouz, 1 Pereira, M., M., Campodónico, N., and Kelman, R.:Pereira, M. Long-term V. F. Hydro and Pinto, Scheduling L. based M.Philbrick, V. on G.: C. R. Multi-stage and stochastic Kitanidis, optimization P. K.: applied Optimal to conjunctive-use energy operations and plans, Water Re- Cai, X., McKinney, D. C., and Lasdon, L. S.:Davidsen, Solving nonlinear C., water Pereira-Cardenal, management S., models Liu, S., Mo, X., Rosbjerg,Deng, D., X.-P., Shan, and L., Bauer-Gottwein, Zhang, H., and Turner, N. C.: Improving agricultural water use 5 5 15 30 10 20 25 10 15 20 25 30 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | cient water pricing policies ffi 5956 5955 er value of groundwater with stochastic surface wa- ff Maryland, College Park, Maryland, 2004. cover scheme, United tablambert_euras_as.php (last States access: 18 Geological July 2013), Survey, 2013. available at: Hebei Plain,http://edc2.usgs.gov/glcc/ China underHydrol., 356, varying 209–222, land, doi:10.1016/j.jhydrol.2008.04.011 2008. use practices using tritiumReport and No. 22040-CHA bromide CHINA, available tracers, at: WDSContentServer/WDSP/IB/2005/11/23/000012009_20051123104326/Rendered/PDF/ J. http://www-wds.worldbank.org/external/default/ 220400rev00WHITE0Volume121Main1Report.pdf (last access: 15 June 2015), 2001. business/2011-04/15/content_12335703.htm (last access: 5 August 2014), 2011. time scales based360, on 117–131, the, doi:10.1016/j.jhydrol.2008.07.021 2008. Budyko framework–model development and testing,water J. crisis? Hydrol., –doi:10.1111/j.1745-6584.2010.00695_3.x, 2010. Perspectives from the North China Plain, Groundwater, 48, 350–354, ter supplies, J. Environ.1991. Econ. Manag., 21, 201–224, doi:10.1016/0095-0696(91)90027-G, NumberGrainandFeedAnnual_Beijing_China-PeoplesRepublicof_3-2-2012.pdf CH12022,(lastJune 2015), available Peoples Republic access: of China, 2012. at: 15 http://gain.fas.usda.gov/RecentGAINPublications/ of surface water and454–467, groundwater,10.1061/(ASCE)0733-9496(2006)132:6(454) doi: at 2006. the basin scale, J. Waterand Resour. Zheng, Plan. C.: Integrated Manag., hydrological 132, modelingsustainable of water the management, North Hydrol. China Earth Plain,17-3759-2013 and Syst. 2013. implications Sci., for 17, 3759–3778,10.5194/hess- doi: Comput., 9, 231–250,, doi:10.1287/ijoc.9.3.231 1997. Gottwein, P.: Systems analysisunder approach the to EU,doi:10.1061/(ASCE)WR.1943-5452.0000284 water the 2013. framework design directive, of J. e Water Resour.actions Plan. Am. Inst. Manag., Electr. 139, Eng., 80, 574–582, 361–364, 1961. models for,doi:10.1029/WR020i011p01499 1984. reservoir operation optimization,people, available Water at: http://www.chinadaily.com.cn/china/2012-12/27/content_16062623.htm (last Resour. access: 19 Res., April 2013), 2012. 20, 1499–1505, tain: the implicationsdoi:10.1029/WR026i005p00811, 1990. for groundwater development, Water Resour. Res., 26, 811–818, USGS: Shuttle Radar Topography Mission, 1 Arc Second scenes, Unfilled UnfinishedUSGS: 2.0, Univ. Eurasia land cover characteristics databaseWang, B., version Jin, M., 2.0, Nimmo, J. R., USGS Yang, L., land and Wang, W.: use/land EstimatingWorld groundwater recharge Bank: in Agenda for Water Sector Strategy for North China,Yu, Volume H.: 2, Shanxi to Main raise Report, electricity price, Chinadaily,Zhang, available L., at: Potter, N.,http://www.chinadaily.com.cn/ Hickel, K., Zhang, Y., and Shao, Q.: Water balance modeling over variable Zheng, C., Liu, J., Cao, G., Kendy, E., Wang, H., and Jia, Y.: Can China cope with its USDA Foreign Agricultural Service: Grain and Feed Annual 2012, GAIN Rep. Pulido-Velázquez, M., Andreu, J., and Sahuquillo, A.: Economic optimization of conjunctive use Qin, H., Cao, G., Kristensen, M., Refsgaard, J. C., Rasmussen, M. O., He, X., Liu, J., Shu,Reeves, Y., C. R.: Feature article – geneticRiegels, algorithms N., for Pulido-Velazquez, M., the Doulgeris, operations C., researcher, Sturm, Informs V., Jensen, J. R., Møller, F., and Bauer- Stage, S. and Larsson, Y.: Incremental cost of waterStedinger, power, Power Appar. Syst. J. Part III. R., Trans- Sule, B.The F., People’s Government and of Hebei Loucks, Province: Water diversion D. project will P.: benefitThiem, Stochastic G.: 500 Hydrologische million Methoden, dynamic Gebhardt,Tsur, Leipzig, 56 Y.: programming pp., 1906. The stabilization role of groundwaterTsur, Y. when and Graham-Tomasi, surface T.: The water bu supplies are uncer- 5 5 15 10 20 30 10 15 20 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 3 − minimum = CNY m erent scenario 3 ff − CNY m 1 − DP SP E SP SNWTP Thiem steady state draw- hp h a b c c d e f f g g = CNY y 6 10 marginal hydropower benefits, 1 = − hp b CNY y ) 9 1 , all other scenarios are initiated at equi- − 10 3 shadow price. , 2003; Moiwo et al., SNWTP partly finished (emergency plan), ) ff 1 = 3 − = − SDP TCDP b month hp 3 CNY y ciency (Deng et al., 2006) and 6 m ffi 5958 5957 10 6 Upstream Downstream 1 − (2003). 8.478.56 103.6 104.3 8.46 101.5 0.91 4.9 4.9 8.698.749.08 103.5 103.3 103.1 4.8 4.7 4.5 ff 14.87 103.6 11.69 103.5 3.2 13.32 99.2 1.2 CNY y 9 Total 1331Beijing 10 119 – 5.5 IndustriesDomesticMaizeWheat 539BeijingEcosystems 223 569 543 – – 864 Industries –Domestic 1522 MaizeWheat 6089 100 5.3 1000 3.2 1.8 5.3 – 3.2 2.8 2.1 + + + + + ++ + + ++ + + + + Demands scaled with area, (Berko Based on daily water demand (National Bureau of Statistics Based on plan by The People’s Government of Hebei Estimated deficit in the Baiyangdian Lake (Honge, 2006). Based on the water use e Estimate by Berko Based on the land cover (USGS, 2013) and irrigation Curtailment costs (CNY m Water demands (10 Estimate by World Bank (2001). a 2010; World Bank, 2001). b of China, 2011) scaled withLandscan the (Bright 2007 etc population al., from 2008). practices collected in the field.evenly The distributed wheat in irrigation Mar, demand Apr,in is May July. and Jun. Maized is irrigated Province (2012), (Ivanova,e 2011). f g producers’ prices (USDA Foreignh Agricultural Service, 2012). minimum ecosystem flow constraint (to Baiyangdian Lake), TC Special run TD E 10 = before the SNWTP, 2008–2014 = SNWTP finished (water from Yangtze to Beijing), LGW are results from a run with = Average total costs, hydropower benefits and shadow prices for di Annual water demands and curtailment costs for the users in the Ziya River Basin. dynamic programming (perfect foresight), SP SNWTP scenario Scenario settingspre-2008 TCSDP b 2008–2014 post-2014post-2014 post-2014 post-2014 LGW 8.43 103.5 5.0 post-2014post-2014post-2014 T dm ct = Post 2014 initial groundwater storage below equilibriumlibrium (100 km groundwater storage),higher (dm) curtailment are costs and the (T) with results 10 % with higher transmissivity, higher TD demands, (ct) areDP with 10 % runs. Pre 2008 down included, E total costs over the planning period (51 years tested), Table 2. Table 1. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Gulf 39°N 38°N 37°N Bohai ) Tianjin ! 1 PROVINCE − SHANDONG ) 1 ) − ) 1 1 − − month which is correlated to the 3 117°E month

gw (m 3 month month River Yellow c 3 t ! 3 ) Beijing 3 sw, ) ) 1 Q ) 1 − ) 3 − 1 − ) ) 1 1 − − month month 3 3 month ! 116°E ) 3 (m 1 ) − month month 3 Lake 3 3 ) ) 3 1 max,sw Baiyangdian − month > V 3 t ) 5960 5959 month gw, 3 3 x ) − t 1 − − 115°E t Shijiazhuang 1 ! sw, (2005 Chinese Yuan, CNY) ! + , decision variable (m t t Q l month R + HEBEI 3 to t k (m PROVINCE gw, ). The costs are all constants, except from V 3 m − 114°E ! water users inflow classes in stage downstream users upstream users inflow classes in M K L U D upstream reservoirs, stochastic variable (m SHANXI ff PROVINCE ! 113°E indexes the marginal hydropower benefits (CNY m indexes the transition probability from optimal value function in stage reservoir releases exceeding indexes the indexes the spills from aquifer when stored volume in the groundwater aquifer, decision variable (m upper surface water reservoir turbine capacity (m water demand for user maximum monthly groundwater pumping in theunused upstream surface basin water available (m to ecosystems, decision variable (m maximum capacity of the SNWTP canal (m stored volume in the surface water reservoir, decision variable (m marginal costs (CNY m minimum in-stream ecosystem flow constraint (m indicates the allocated volume, decision variable (m upper storage capacity, surface water reservoir (m groundwater recharge, assumed to be perfectly correlated with specific pump energy (see Eqs.reservoir 11–16) releases through hydropower turbines, decision variable (m upper storage capacity, groundwater aquifer (m river runo Xinzhou Province border SNWTP Basin boundary Rivers/canals Calibration basin Major city Lakes/reservoirs The Ziya River Basin. Watershed and rivers automatically delineated from a digital t ± t t Legend t m t Nomenclature. sw, SNWTP E gw, ∗ gw kl hp E, t sw gw gw, sw, max,sw max,gw t k b l p F V s dm u d s q R X BeiQ Beijing user V c Q V m gwswct groundwater x surface water water curtailments Q r V Q elevation map (USGS, 2004)Inc., and manually 2013). verified The andverified SNWTP corrected with routes with field Google observations. (Central Provincial Earth and boundaries (Google from Eastern) (NGCC, were 2009). sketched in Google Earth and Figure 1. Table 3. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

gw E Q q max,gw gw

the local Thiem V V 3 + 3 d 3 gw,d ) sw,d x x w 2 2 2 d sw,t+1 Q V gw,d sw,d x x , 1 1 New generation Mutation Crossover sw,d gw,d no gw,t+1 x x 4 V d 1 d d sn 4 x top x h Thiem ∆ sn h q sw ∆ 5962 5961 s sw r the regional groundwater lowering h ∆ + yes max,sw gw V 2 2 X 2 u sw,u gw,u Upper and lower bounds for GA Generate initial population ( Calculate fitness Calculate immediate costs (LP) Interpolate future costs Calculate total costs Stopping critera met? Store total costs x x 1 next for all groundwater states 1 for all surface water states gw,u 1 x sw,u u for all runoff flow classes for all runoff x

Load data for all stages

Conceptual sketch of the Ziya River Basin management problem with water users sw SDP optimization algorithm design. Q ) is composed of the top layer h ∆ Figure 3. located upstream (u) and downstreamables (d) are the indicated surface for water surfaceA reservoir. water conceptual Allocation (blue), decision sketch SNWTP vari- water oflift (green) the ( and downstream groundwater dynamic (orange). aquifer is included and show how the total Figure 2. steady state groundwater drawdown. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | with ff

Normal Wet Dry 3 Dec CNY/m Surface water 3 SDP DP 0 FC = = 100%= (a) sw Jan 2 ). The perfect foresight DP 3 Equilibrium storage = 50%= V sw 1 Groundwater values over time at Jan Dec 0) are also shown. ) for the climate period before 1980. b) Groundwater values b) Groundwater (b) 1990 2000 3 Dec = − 0 = 0%= V sw Jan 5964 5963

1980

flow class and time of the year. 3 ff = 100%= V

gw

= 0 km 0 = 0

Jan Dec

V 3

= 80% = V

= 100 km 100 = 0

gw V V

Jan Dec 3

a) Surface water values a) Surface water = 200 km 200 =

= 0% = 0

1960 1970 V gw V 0 Jan Dec 50 max

250 200 150 100

V Simulated groundwater aquifer storage levels for 51 years of historical runo

E F E F E F

Temporal changes of the water values (CNY m km storage, Groundwater Reservoir storage Reservoir 3 erent initial groundwater storage(0, 100, 200, 258 and 275 km ff di and management without consideration of the future (FC fixed [0, 50, 100 %] surface reservoir. The reservoir storage is shown from E (empty) to F (full). Figure 5. The marginal water valuevaries is with the true reservoir value storagevalues of at levels, storing fixed runo [0, a 50, unit 100 %] volume groundwater of aquifer storage. water for later use, and Figure 4. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | re- =

, M1 , M2 , M1 , M2 , M1 , M2 , M1 , M2 SW GW SW GW SW GW SW GW P P P P P P P P Curtailment Surface water Groundwater user’s price, M1 = ) 3 ) 3 50 0 100 150 1986 1988 1990 1992 1986 1988 1990 1992 ). The results are shown for a simple drawdown 5966 5965 3 Time, monthswith water demand 0 > Time, Initial groundwater storage at equilibrium (258 km at equilibrium storage Initial groundwater Initial groundwater storage below equilibrium (100 km Initial groundwater storage below for two initial groundwater storages. P 1968 1970 1968 1970 ff results from the presented model framework with a combined surface Uniform drawdownThiem drawdown Uniform + stationary = 50 0 0 0 100 150 1964 1966 1964 1966

0

Composition of allocations and curtailments to wheat agriculture in the Hebei

1.5 1.0 0.5 3.0 2.5 2.0 1.5 1.0 0.5 3.0 2.5 2.0

80 60 40 20

User’s price, CNY/m price, User’s User’s price, CNY/m price, User’s Water allocations, % of demand of % allocations, Water 3 3 User’s price for groundwater and surface water through for a 51 year simulation based 100 water reservoir and athe dynamic immediate groundwater pumping aquifer. costs The added user’s the price opportunity for costs groundwater from in the M2 water is value tables. Figure 7. model with uniform regional loweringmodel of which includes the the groundwater stationary table, and Thiem local a drawdown more cones. realistic drawdown Province for the months March,groundwater April, May storage and at June equilibrium through 51 (258 years km simulation from an initial Figure 6. on simulated historical runo sults from Davidsen et al.groundwater costs, (2014) M2 with a single combined surface water reservoir and constant