Conditional Operation Rules For Optimal Conjunctive Use of Surface And Groundwater


 The current study presents an efficient method for deriving precise operation rules from all subsystems of a distributed conjunctive use system (CUS), including aquifer, river, and reservoir. Distributed aquifer simulation has been performed using the URM method. Given that the historical flow time series can only represent one of the possible situations in the future and its use to determine the performance of the CUS is certainly not very reliable, in this study, river flow uncertainties are implicitly considered. To develop the operation rules, the time series of river flow were generated using autoregressive model. Then, the operation optimization model of the system was implemented with the objective function of minimizing water shortage for different river flow time series. 70% of the data was used for model training and 30% for model validation. Finally, using the decision tree algorithm (M5Rules), the conditional operation rules were extracted and compared with the single linear regression operation rules. Using five efficiency criteria CC, MAE, RMSE, RAE, and RRSE, the comparison of conditional and single linear regression operating rules has been done. The results showed that the the conditional operation rules reduces relative absolute error by a minimum of 39% and a maximum of 71%. If the system is operated according to the conditional rules, in the worst case, the amount of water shortage imposed will be 16.61 MCM over ten years.


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Given that the optimal use of water resources systems requires operation rules, it is necessary to 41 provide valid methods for their extraction (Nayak et  suffers from a curse of dimensionality as the optimization problem grows (Loucks et al., 1981). 61 For this reason, ISO models are important in the analysis of water resources systems (Draper,62 2001). In the ISO approach, two methods are mainly used. In the first method, the operation rules  Each of these studies, which presents the operation rules of a CUS, has shortcomings and 76 needs to be examined in more depth. Some of these studies did not address uncertainties in the  However, water resources management with the view of integrated management of SW and GW 82 resources needs to provide valid rules for all subsystems in a CUS. 83 Our reviews show that the presentation of operating rules for all subsystems of a distributed 84 river-reservoir-aquifer system with regard to hydrological uncertainties remains intact. Therefore, 85 in this study, the development of a simulation-optimization framework for extracting the operation 86 rules of a complete and distributed CUS has been considered. In this study, we have used decision 87 tree algorithm to derive the conditional operation rules (multi-linear regression operation rules or M5Rules). Using the concepts of ISO, the operation rules of different parts of the CUS are 89 presented as a function of available SW and GW. In this regard, first 50 river flow time series were 90 produced using autoregressive model. Then, by implementing the optimization model with the 91 objective function of minimizing water shortage in the agricultural sector, the decision variables 92 of the optimization problem that indicate the optimal water transmission between various parts of 93 the system were extracted. 70% of the output of the optimization model was used as training data 94 and 30% as validation data. To extract the operation rules, in addition to fitting the multi-regression 95 model, a single-regression model was used to confirm the efficiency of the decision tree algorithm 96 in this field. It should be noted that in this study, distributed aquifer simulation has been performed 97 using the unit response matrix (URM) method. The study region includes the Abhar River basin and Kinevers Dam (SW reservoir), which is 102 located in Iran. The studied system consists of a local aquifer with an area of 80 km 2 . Table 1 103 shows the historical series of the Abhar River in 40 seasonal time steps from 2008 to 2018. SW is 104 conjunctively used with GW for urban water supply and agricultural purposes in the region.

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Seasonal environmental, urban, and agricultural water demands are shown in Table 2 According to studies, the best area for artificial recharge is the pumping wells. The  Table 3. According to Figure 1, the CUS is a complete system including SW reservoir, 121 river, and GW reservoir that meet the region's water demands. The amount of transmission 122 between different parts of the CUS is directly or indirectly determined by the operation rules. For  variables of the optimization problem are R d s (t), Div d riv (t), Div ar riv (t), R d g (t), and R riv s (t). The 141 problem of nonlinear non-convex optimization is solved with Lingo software.

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The objective function of model is to minimize the water shortage (WS) in NT time steps.

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Reservoir Water Mass Balance: In which ∆S (t) = dam storage volume changes in time step t; S (t) = dam storage volume 146 at the beginning of the time step t.

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In which ΔS g (t) = GW volume changes in time step t; S g (t) = GW volume at the 149 beginning of the time step t; q ar (w, t) = volume of recharge to the well w; q p (w, t) = volume of 150 pumping from well w; kqv(t) = conversion factor (discharge to volume) in time step t; AQA = 151 the aquifer surface area; NW, NR = number of total wells and river reaches, respectively; Prc = 152 precipitation depth.

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Demand Site Water Mass Balance: In which WS(t) = water shortage; Demand(t) and Supply(t) are refer to water demand 160 and supply in time step t, respectively.

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Water Table Fluctuations in Aquifer:

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The amount of fall/rise in wells and river reaches can be calculated using the URM method In which, D(x, n) is the drawdown at node x at the end n th of the time period, 167 β x (x, j, n − t + 1) or unit response coefficient is the change of water table in node x at the end of 168 n th the time period with unit stimuli at the node j at the end of t th time period, P(j, t) is the amount 169 of stimuli at node j, and time period t and NS is the total number of stimuli nodes.

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In which Criv(r) = the hydraulic conductance of the stream-aquifer interconnection which 172 is a function of semi pervious streambed hydraulic conductivity, length, width and thickness of 173 river reach r; h riv s (r, t) = hydraulic head in the river reach r; h riv bot (r) = elevation of semi pervious 174 streambed bottom; h riv g (r, t) = elevation of the aquifer water table below river reach r.

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Sustainable Abstraction:   Table 4).  It should be noted that 30% of the data is used to verify operation rules. Available SW 231 (S(t) + Q s (t)) and available GW (S g (t)) are considered as independent variables in single-  By implementing the three steps mentioned above, the results for the single regression 241 model are presented in Tables 5 and 6. Table 5 shows that Div d riv (t) has no dependence on the 242 volume of water stored in the aquifer. Table 6 shows that the fit of the single linear regression 243 model is not very accurate except for the variable R riv s (t). In addition, the predicting error of 244 variable Div ar riv (t) in the single-regression method is significant. Given that 50-time series, both 245 low water and high water, have been generated to apply uncertainty in the future, it seems that the 246 high-efficiency criterion in the multi-regression method is due to the classification of independent 247 and dependent data.  Then Div ar riv (t) = 0.0005 × (S(t) + Q s (t)) − 0.0005 × S g (t) + 1.3258 (21)

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Given that the M5 decision tree algorithm classifies the environment of decision variables 258 and presents a regression model in each class, it is obvious that the rules obtained from this method 259 will be better than the single-regression method. The results of the decision tree method for 260 decision variables are showed in Table 7. As can be seen in Table 7, the errors of the multi-261 regression method are significantly reduced compared to the single-regression method. For 262 example, in the multi-regression method, the value of the efficiency criteria of CC (for training 263 data) for the variable Div ar riv (t) is improved by about 60%. By comparing Tables 6 and 7, it can be 264 seen that the least improvement is for variable R riv s (t). A comparison of the actual and predicted 265 values of both models for this variable is shown in Figure 3.   a way that the amount of water stored in SW and GW reservoirs at the end of the simulation period 300 is equal to their initial. In fact, these two reservoirs will be operated sustainably. The fact that 301 acting according to the M5rules can reduce the amount of water shortage by 6.763 MCM indicates 302 that at the end of the10-year period, the total water stored in SW and GW reservoirs will be 6.763 303 million MCM less than their initial amount. It is important to know that among the 50 river flow 304 series, the maximum error of the multi-regression model is for river flow No. 2. One of the notable 305 points of Figure 4 is that in 28 cases, the water allocation conditions are the same as river flow No. artificial recharge, water diversion from the river to demand area, GW pumping, water transfer 328 from the reservoir to demand area, and release from the SW reservoir to the river improved by 329 59%, 37%, 54%, 48%, and 9%, respectively. In the single regression method, the CC was obtained 330 desirable only for release from the dam, and for other variables, this coefficient was less than 0.5.

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Conditional operation rules ensure the sustainability of SW and GW water resources and 332 the sustainability of water allocation to the demand site. The maximum cost of conditional 333 operation rules was obtained 16.61 MCM of water shortage. Considering that the average cost of M5rules was estimated to be about 4 MCM during the ten years of the planning horizon, the use 335 of conditional operation rules is highly recommended.

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The present study can be improved by considering other existing uncertainties such as 337 rainfall, aquifer hydraulic characteristics, climate change and water demands.

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There is no conflict of interest.