dx.doi.org/10.22093/wwj.2017.34336.1991 68 developing a

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dx.doi.org/10.22093/wwj.2017.34336.1991 68 Journal of Water and Wastewater Vol.29, No. 2, 2018 Developing a Water Quantity-Quality Equitable Allocation Model in River-Reservoir Systems: Application of Scenario Optimization Technique S. H. Afzali 1 , N. Taleb Beydokhti 2 , A. Poya 3 , M.R. Nikoo 4 Assist Prof of Civil-Environmental Engineering, Faculty of Engineering, University of Shiraz, Shiraz, Iran (Corresponding Author) (M&$ 2) 3<33#&2 afzaliJshirazuacir 2 Prof of Civil-Environmental Engineering, Faculty of Engineering, University of Shiraz, Shiraz, Iran 3 Former 7raduate Student of Civil-Environmental Engineering, Faculty of Engineering, University of Shiraz, Shiraz, Iran # Assist Prof of Civil-Environmental Engineering, Faculty of Engineering, University of Shiraz, Shiraz, Iran (Received Apr. 11, 2016 Accepted May 21, 2017) To cite this article : Afzali, S.H., Taleb Bidokhti, N., Poya, A., Nikoo, M.R., 2018, “Developing a water quantity-quality equitable allocation model in river-reservoir systems: application of scenario optimization technique” Journal of Water and Wastewater, 29(2), 68-84. Doi: 10.22093/wwj.2017. 34336.1991. (In Persian) Abstract Water quantity-quality equitable allocation model in river-reservoir systems provides the possibility of decision making on the amount of allocated water by considering the hydrological, economical, and environmental effects. Water allocation is done according to three criteria, namely equity, efficiency, and sustainability by considering uncertainties in hydrological parameters. In this method, at first a water quantity-quality allocation model was developed in GAMS optimization model based on the mentioned three criteria. Scenarios were built based on scenario optimization technique by identifying the uncertainties in the model inputs. Water was allocated using the initial model for each sub-scenario. Afterward, water allocation in each scenario was obtained by the tracking model. To assess the applicability of the proposed method, it was applied to Roodbal river basin in south-east of Fars province, south of Iran. After analyzing basic data, upstream inflow and TDS concentration were identified as the uncertain input and the most critical quality parameter respectively. Due to the existing uncertainty, three scenarios of wet, normal and dry year were built. The results of using the proposed model showed that 100 percent of the users’ demands are supplied in wet and normal years and 61 percent in dry years. The volume of reservoir was always more than minimum volume (35 MCM) and TDS concentration was lower than 1000 mg/L (TDS water quality standard). The value of these three criteria were also at their highest possible. Based on the results of the model, the Roodbad River-Reservoir system faces no problem in supplying agricultural water demands in wet and normal years. Therefor, water can be stored in wet and normal years to be used during dry years. In dry years, water is allocated to the users in a way that the mentioned criteria have the maximum values and the reservoir storage doesn’t reach the minimum value except for the last month of the optimization period. Keywords: Water Quality-quantity Allocation, Equity, River-Reservoir Systems, Optimization of Scenarios

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Page 1: dx.doi.org/10.22093/wwj.2017.34336.1991 68 Developing a

dx.doi.org/10.22093/wwj.2017.34336.1991 68

����� � �� �� Journal of Water and Wastewater ����� ���� ����� ����� Vol.29, No. 2, 2018

Developing a Water Quantity-Quality Equitable Allocation Model in River-Reservoir Systems:

Application of Scenario Optimization Technique

S. H. Afzali1, N. Taleb Beydokhti2, A. Poya3, M.R. Nikoo4

1.Assist.Prof.ofCivil-EnvironmentalEngineering,FacultyofEngineering,UniversityofShiraz,Shiraz,Iran

(CorrespondingAuthor) (+9871) [email protected]. Prof.ofCivil-EnvironmentalEngineering,FacultyofEngineering,UniversityofShiraz,Shiraz,

Iran3.FormerGraduateStudentofCivil-EnvironmentalEngineering,FacultyofEngineering,

UniversityofShiraz,Shiraz,Iran4.Assist.Prof.ofCivil-EnvironmentalEngineering,FacultyofEngineering,UniversityofShiraz,

Shiraz,Iran

(Received Apr. 11, 2016 Accepted May 21, 2017)

To cite this article : Afzali, S.H., Taleb Bidokhti, N., Poya, A., Nikoo, M.R., 2018, “Developing a water quantity-quality

equitable allocation model in river-reservoir systems: application of scenario optimization technique” Journal of Water and Wastewater, 29(2), 68-84. Doi: 10.22093/wwj.2017. 34336.1991. (In Persian)

Abstract Water quantity-quality equitable allocation model in river-reservoir systems provides the possibility of decision making on the amount of allocated water by considering the hydrological, economical, and environmental effects. Water allocation is done according to three criteria, namely equity, efficiency, and sustainability by considering uncertainties in hydrological parameters. In this method, at first a water quantity-quality allocation model was developed in GAMS optimization model based on the mentioned three criteria. Scenarios were built based on scenario optimization technique by identifying the uncertainties in the model inputs. Water was allocated using the initial model for each sub-scenario. Afterward, water allocation in each scenario was obtained by the tracking model. To assess the applicability of the proposed method, it was applied to Roodbal river basin in south-east of Fars province, south of Iran. After analyzing basic data, upstream inflow and TDS concentration were identified as the uncertain input and the most critical quality parameter respectively. Due to the existing uncertainty, three scenarios of wet, normal and dry year were built. The results of using the proposed model showed that 100 percent of the users’ demands are supplied in wet and normal years and 61 percent in dry years. The volume of reservoir was always more than minimum volume (35 MCM) and TDS concentration was lower than 1000 mg/L (TDS water quality standard). The value of these three criteria were also at their highest possible. Based on the results of the model, the Roodbad River-Reservoir system faces no problem in supplying agricultural water demands in wet and normal years. Therefor, water can be stored in wet and normal years to be used during dry years. In dry years, water is allocated to the users in a way that the mentioned criteria have the maximum values and the reservoir storage doesn’t reach the minimum value except for the last month of the optimization period.

Keywords: Water Quality-quantity Allocation, Equity, River-Reservoir Systems, Optimization of Scenarios

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C:,; 7�� "�C/�&; �!H9��C� "%��

���� R�����+ ������+�$�$ ��#%$��� �����$�� ���$%����^�$�!��") �%��-� }��$�� �������E�� �# ���$ �$ ;�3� ����$�� ��� ������+

X�� "���g���?�$��� L���������E�� �# ��N�~Q.-�Q�����V�����(��)�-4��#�!+��6 �$E���+ ��DJ���5����?��J+ ������+

�/-�$���%�?J+ }L�� �����) �%��e� ��7 �$���� �$ ��$���$ #%�N� ���+��� ��-?% �!�-[E��+ ����a� @�1 ��L9�����

�� �-�]�$� @� �+ �:��� �/%�/��+ �+$�' .(Nikoo et al.

2012; Karimi 2010) 0���$ 4�9# �� 9�D��C��!��) ��' �$��-4E�+ K�T N�1�L�$����+ $��� �*� $�'.K��T N�1 �� �#$��� L

�� �� �$=!�� �-�/ $�Q �-�%.� �$��� ���%� ��-E��+ $��� #� �$ .�'�-�� 4-���� L�"� $�Q- K�.g K�$ �� \F!���9�D� 4� C9D� ������ C%� � �#-MJ� �$ �#%+ ��� E��+ ^�@!J+ ��&��4

9��D� ���01����G C���+ $���'�� �$ .-@*� $���Q���.�) 0���� ����%(� �-K�T L� ' �� ~6 #� N�1�� L�-� � �-����%�$ .$��9�

�-4M#�]6 ��� �/�� � ��!�� �����+ ���' ���� + �$ X���SPI ���%E� #%��� X�� W���� ^@!J+ �>�,���� ���' � ��+���n

�1��T E�� �$ $�]�rypu ����*+ �'�.!� ��� ��/�� �� ~{�����O����' SPI E����/ �r� ���� ���� ��� ©-@��7� ��;��3� �����

������ �� �� K�����# � ����' �!�� E+�� �-��� #� ��� �� ��� f��-�� ��-#�%;�3� ������'-� ,���!+ � N�o�� E�+�� ^

$?�-����� E�+�� �� ;���'-� ,���!+ � N�o���' �!�"Q' ^(Karamouz & Araghinezhad 2010).

3Dembo 4Index Sequential Modeling 5 Standardized Precipitation Index (SPI)

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������� � �� Journal of Water and Wastewater ����� ���� ����� ����� Vol.29, No. 2, 2018

��#NZ)L�No�;3� ��� W���� ��' SPI )Karamouz &

Araghinezhad 2010(Table 1. Drought condition according to SPI

(Karamouz & Araghinezhad 2010) Situation of climatic drought SPI

Too intense drought -3Intense drought -2.5Average drought -2Poor drought -1.5Close to normal -1Normal -0.5 to +0.5Close to normal 1Poor wet year 1.5Average wet year 2Intense wet year 2.5Too intense wet year 3

N�1 E�+���� 0�1 L9"1 �$ ��' �!��%�#-� �� ;-� ���-#��c .�� ��6 � 0G���� .�'-E�+ 4# �-"+�@£+� ����+ ���.����'� �!�� �� �/�� �-"+�@£��� ��1 ����� $� �$�#�!+��6 $�/� 0%

_�N�1�����$ %K�T N�1 �� �+ L�� ��� � �'� �- 41����� $� ���7�"+�%����+.���' � �� �/�� �-9D� Y�o�+ 4��� ��' ��!��) C

e!+���/ ��3�/�$� E��+ \��# 8��� �$ �?�J+ ��� $��� 4�-5�

��� .$�' �$=!��%���� ���' 5�J!�� �����+ E�! �%��-e!+ 4���$ �.� ������ ��%:� �G %+ � ����� ���&��6 �G � $��� 4�-�� 4

� �� �$ $��� 01���G �� �����-#�%��' �$�$ ����1 ^�@!J+.E��+$�-�� �$ 5-.� $�Q�� ���%� ��-��� #� N� ���a + ��� ��!.� 4-4��-.� $�Q�� ��%�$=!�� ^@!J+ :G Y�1� �*� � ��+ $��' .

$� E�+-��� 5%-�!.� 4!�-�� �� 0�G ��� 4�0�G ��� K�9� 4�#%.����� � %� � �#-� �+ �� ��.� ��6 kF�7� �� � $����� �- ��� @G�+ �>��� ���.� ��6 �� �@7� Y�9O+ 01��G �� � ��;� ;� � �-� ��-� �$ .�'� �!'�$ �� #�-4M#�]6$� E�+ �-f��1 �$ 5

� �!��-�' �>��� �

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rr()I

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)Z

ZZ(ZMin

Subject to: )tv(mmmm

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)tz(max*min SSS ≤≤

)tp(normal*1 SS =

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mm,im EFIDDDDAR +++≤∑

)ys(mmi

mm,im AEFIDDDRAAR +++=∑

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L�� � H9# .� 4*Ie!+ �� �Q9� ���3�/�$� E��+ �$ $��� 4�- 5

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����J�� ;�s�� c�6C ��- dx.doi.org/10.22093/wwj.2017.34336.1991 77

����� � �� �� Journal of Water and Wastewater ����� ���� ����� ����� Vol.29, No. 2, 2018

�g�# ���!3 �� 5� � �/���L� )(9D� � �����C)��M�J� ��� 5���6 �� M��� ML9� �+ ��*�-�-� 5� 8� + L-���' f@/ �!�� 4

) L����Mojarrad 2011� �$ ���N��+ $����+ ����� + .(��- 4M#�]��6 E�$�� ���$�� � �� 0+'L�� $?� �$ ���-�Q��!���.' 5���$

�$ ��' �!�� W�� ���1 $��$.E� �$ ��=��!+ #%���;3� �� �/�� � ��������$�� 5�

�� � � ��' C� �'�=�� �� 5� L��� ?�$�)$��� $��� 0�� �� ��� #4� H9# M#� ���$�� $��� M#� -.L��� �!� ����� �� ~�6�

e!+���#�%����=��$�$ �$ ���N��+ $����+ ����� + ��#%��=��� 5� L���9� )��%���� + 5� �+�� ,��� ��' �%�J�3+ W��� �' ����*����-� �!+��6 4��=���� 5� �� �$������ �J�3+ ��+

� � �$���$����!�� �G �� ML��� � ���' ��=�TDS L��� �$ . 0Q'tLa@_ ,��!+ TDS ���! � ����� �� �$�����%�-���$ ;

-;.L�� ��' �>��� ���

Fig. 2. TDS variations in Khordad at three QC points (2005-2007)

_e��)�=�� ��e!+ ����e�TDS E�! � ���� �� �$ $�$�� �+ �$

) L�=������j����(

�� E�$�� �� Y�� ��� �& �-�?�%��!"# ���L��� �py��!+ Y=��� $��$ .E�+�� ���� COG ��� E��$�� pt+�@������!+ f�NQ+ L�� .�$E��/ tDJ3+ � * + h��jCOGjY=��� �?J+ ���

E�$�� �$�/�+ TF�� �� �/�� W���� �3�� %��$�� %# KO�� ��' �$�$���*+ �?�J+ �� �$ � L��� ���' ��>��� ������ ���Q��'

����%G �$ ���� ��� + �$ E�$�� �� P��G� 4-� L��� ���' $�O���� �����3� MJ�%! ����1 �� ���-��� C����G ���7 �� ���

� $��+ 5� ���$���+�� �� $�� ��+ 4����' ��!��) �a� �$ ��$�9�L��.(Ab-Niroo consulting Engineers 2000)

Q' �$�0y���3� MJ� ������%� �$ ��-4M#�]6 �a� �$�� ���' �!��)����7 �9'�9� ;-���' �$�$ M���� ���c ��� K�: .� �$ �� L��-4M#�]6� ���� ��M�J� �#%�� LN �7 � 5��'

]���!�� �� �/��-+�� �$�� ;�� 4-� 4�C� ����+ � #� ��� L�"� �������3� MJ� �%+��� 0�+� ��7 �� �� �$ .L��� ���' 4�-4

�� L3)�� � L'�$�� 0*+ 0Q' �# 5�-� ������ �� ;��J�3+ ?.L���� ����' ����' ���� ���/�� ��� E��G-9#� � ����� + ,��� Y���o�+ L

DJ��.� ��� �$ 5� 8� + ��' E�! � � � ��?�J+ C!�"j����$��9� �+?9# �*� � E�$���� L��=��+� 5� L%����o%.L���

� ��TF����$ �!��3$����+ ���N��+ $����+ ����� + 0���1 8��/��+ �$L�� ���!�$ )Pouya 2013.(

��#N[)^@!J+ %#���� �$ E�$�� �� �?J+ COG � h�� �-$�+

�� �?J+ �$ 5� Table 2. Area and volume of Roodbal dam reservoir at

different water levels Volume (MCM)Area (km2)Level (m)

0013110.4640.0313202.8550.40913308.7760.797134019.2281.315135035.2111.899136057.3932.533137086.5373.2911380

b)cF; � d9�'0 � �$-!� MJ� 4-�� [)����%6 E�+�$. 3%DJ� �$���9� ���

��=�*�� 5� 8� +�.L��� ���' �>��� E�$�� ���$�� �o�G �$ ��' ����+SPI ��� ��� + �$ X�� ����+ W���� ��� +%���N� E��� [ ��6 ����� 4����' E����/ �$ .L����y����+ ������'SPI

�#+ �$���$ �>��� '.L�� �� ��'SPI �+ ��3� ��� +����$ ��#$ �#%;�3� �����$

L�� �+ ���� ��� +� �� }-���$ W�� 4#%���� ��� ��%#��� �-� � �� ;-�� .�' 5J!�� #� �+%��'SPI � �� ��� +�©

� �-� 0Q' �� �-�a��$ �:�' �!��) j���� ;��3� :;��3� ©�����N��o�;��3� ^ ����� ,����!+

;3� ����'-�

0

500

1000

1500

2000

2500

3000

1 2 3

TD

S(m

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)

Year

TDS concentration at first control pointTDS concentration at second control point

TDS concentration at third control pointStandard of TDS concentration

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������� � �� Journal of Water and Wastewater ����� ���� ����� ����� Vol.29, No. 2, 2018

Fig. 3. Schematic of agricultural water users in the studied area _e�^)��� + %���3� ������ ;��9'

j��$?� E+�� :E+�� ©-E+�� �� ;j������ :�� ©����� ,��!+��'-���� ��"���' �-�

�� �� �/�� � E� �$ �� #%@Q�3+ d:�9N+ E+�� � ���+��� �$�4��� $����� $�/� #���DJ� L����� �$ �- E�� 4��� �# � �+%

�c������%5�%���� E�� �#%;�3� L��� ��� . ����%�$ ���E� #%+��� ;�3��� 4��#�%� � ������� �� � �*+�,�!�"-� �$����-LL����� . #%�DJ� E�+ \�# 8�� �$ $�/�+���9� ���

��=������ �J3+ �� ����9#L�� 9#� ��� � �� ���' L�$ �#��L� #%9D��C)��%����a + DJ��N� 0��1 5� 8�� + ���� 4

L��� �$ .-� O �X��?�) ��� ��/�� �� ?%�# )�$ $��/�+ ���%�#%$�N!+%DJ� �� ���� 5� ��:$T ���!�'�$ $�/� ��� + ������ 4L��.��9#��$ 4�N� 0���� �� �' ����) ��� # �%��� ����' c�J��

� \���# 8���� �$ L�����T ����'��!��3-�!��'�$ �� C.��� 4�$ .���'�� �-#�%��� ;3� ©�?%��� �?��-6 M�-���%��01���G C!�"

+���� 4��*+�,�!"-� � ��7�$ LD' � ����� ���*+ ��,�!�"-� .L�� ��' �$�$ ���1 � 4!���) �a� �$ � �-1 4��.� E��+ � �� �$ ���' �

GAMS�O!"/ %��� �� $��%.� 5��/�� �%�DJ� �� �$ ������*+ ��,�!"-� �����+ � �����vs��7�$ � �� �� � �-� ��� �� �!�3

�'� + KO���� � �$ L�� ��c �� K�: .�#$-��� ��/�� � ;3� �1��N� $�-��' ^ 9#����� LDJ� �$ #�$�.3+ �L"�� �$ �+� .

� �-e� � E+�� ������� ��+ �#�e� ����� ��� �� E��+ $��Q@9T �$ �E��/ �$ .$�9� ��#3+|���9� �%� ��-e� 4���� �$ �� �- � �� �-�

$?�-�>��� E+�� �� ;��' � �$ .L��-�$ �' ��'� �� ��� �9# O .��-��� L#��� �) ����� �%J!����5��'� ��' ��T ����6 L���

9#������L������-� �����!��� .�����'� \�����# 8������ �$ �����9�� 4����- �

) \�# 8�� �$ K�� �9�� L'�$ �/��max

m3 S

S.w(0G X�� �� �

d��7 ��' 5J!��\�# � + E�! ����� ��?-�?J+ COG � ?}L��� �� 9#��$ 4�"� ��� 0�Qg�� ���$�$ <D!�� �� ���'� ��V��%

User 3

User 2

Irrigation network (user 1)

User 4

Roodbal river

Roodbal dam

Quality control point

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��#N^)��' ����+SPI ) �N��+ $��+ ��� + �$ryq| jrypp(Tabel 3. SPI in study area (1975-2009)

Year SPI Situation of climatic drought

1 -2.31 Intense drought2 -0.38 Normal3 0.39 Normal4 1.53 Average drought5 0.15 Normal6 -0.27 Normal7 0.1 Normal8 0.9 Close to normal9 -0.34 Normal

10 0.71 Close to normal11 0.33 Normal12 -0.69 Close to normal13 -1.14 Poor drough14 -0.57 Close to normal15 0.71 Close to normal16 -0.16 Normal17 -0.76 Close to normal18 -0.72 Close to normal19 0.29 Normal20 0.29 Normal21 2.56 Too intense wet year22 -0.4 Normal23 0.37 Normal24 2.26 Average wet year25 0.03 Normal26 0.3 Normal27 0.26 Normal28 -2.31 Average drought29 -1.12 Poor drough30 -0.38 Normal31 0.41 Normal32 0.1 Normal33 0.78 Close to normal34 -1.31 Poor drough35 0.37 Normal

DJ� ���� ���. � � $��(&� �-���! � 0�+T ;�L���$ 0�G �$ �@£"+ .�'�0Q' �$ #%|ja�|jbE��$�� ��� �?J+ $�Q@9T

.� L�G �$ �$�� ��%��� ��'%� �-�%�����;�3� �����.L�� ��' �>���

���� ��+ #��$�9���$ ����-L��?�� �-����+ �?J+ �� $��� M+�� �7�$ � ��' #� 5��� 4��?�� �-+ M�-.��

E� �$ #%�� E+�� � �� � W���� ��' E9T� L���� C!"���) �%+ 09T��$ .����� $��� ������G C�OG �� �?J+ COG � � �E� #%� ;3��+��� �����+ ����$�� $��� M#�� �� ?�� 4��� �

�?��J+ C��OG���� M#��� ?-��O�� �� ���!��� .L���� ���!��-���+��� ������ ���$ � g ��7 �%�+ 0�9T�.� �����+ �� ����� �� ���' �#� ��

���) �%+ 5J!���E�� �$ ��� �� � �#%��N�%���� ?���g$ C!�"

�!9�-# .$�' 0Q3+ 4��&H %���+���� 4�#� �� �?J+ COG ����+9� 01��G��+ �$ �&+ ��� #%6-��0Q' �$ .k�� l�� �#%qja

�qjd��+�� ����+ ?�� 4������� �-��>��� ��.g �� ;�'.L��� ��0Q' � #��) ?-%�-+ � � !"# �+� 4�$ ����-� ��� ��+��� C!�"�4

�����3� MJ� ������ �%���� � ��-���� L-�� �Q��') ;���% (��� �� �$ � �� �.g�+ KO�� f�.�#$

0Q'v����+TDS ���! � ����� �� �$�� �� �$-�� ;�3� ��+ �3� �#$�9# . �+ ��a!�� �� ���)������+ L���TDS E��! �

�O+ ����+ �� �!9� � ��' L��� �@*+ �$ K��� ����� .���!��) ����1�� K9� �� L�� !3)�� 5��+ ���$�� $������ ��� �/�� � � $�'

����+ ��TDS )$���� ��� L�a@_ ��� �!"��� 5� �$ $�/�+�$��� ��' L�� �-�"G �� ���� 4���:� L%L�a@_ � L��� ��$�����

TDS � �$-� �� L�"� ���� 4-�� �$ .L��� ��:� R�� �-R��� ��+ �$ �#�-$����� �� �+-4�����+ ���TDS �� �$ !�3)�� 5���

� L�$:��� C!"�L�� �!3 ����+TDS �*����.L�� �� ��a + ������N�1 K��T ������ �$ E��+ $��Q@9T �� ��a� �$ L

��' �!��) \�# 8�� ����+ZN�1 E�+ �$�$� E��+ ��-$���+ 5�������� .L��) ���1%� E�+-� � �$ ����+ 4-�� ~�6 ;�3� �DJ���� ����$� E�+ �@-�� ����� 5tpr/yyL��� �O�� �� .�-

N�1 K�T �������$�� $��� �� ,����+ ���' �!��) �a� �$ LL��� �H� g�$�$ $��� %#+ K���+ X�� ��&��4)��%kF�7� $��' �

N�1 E�+ ���%��� DJ��$�' �$=!�� � �� ������ \�# 8�� ����+pzv/yv��+ L�$��-�.)� ���6 �� �/�� ���$�$ #%$��� ����+

�� _ E�+ �$ ��+� L�$�N�1����� �� L�� �� �&�-$��Q@9T E�+ 4�!.�%%��� � M'�6��$�$ �$�!") ^#$��$ �+ E��+ ����V� ������

N�1 K�T��$�$ �$ L&� �a� �$ �!.� �� #�.$� !� �+�$� �$-�� R���+ [DJ�����+��DJ� E�+ �$ #��9� ��

� ��=��� .L�� ��' �>��� DJ� ����+ ���9� ��� T���� ���' �$�$ ��#-;� � �$ ������ ��-� ;3� ��E���/ �$ K�� � E�� E�q$�+ �-6 ��' �-���%��.� ���%��� L���T �%�$ E�� E��

E��/v!� .L�� ��' �>���-6 E��+ $���� �� 07G [�$. �3%�$��� �o�G-E�$�� ���$�� ? + �3��6 E��+ �#$�$. �3%49�o

?����� � 5����@�+ ����G �$ 5� L����=�� ����=G 4!�����) ����a� �$K�T L�N�1 C!"�� �$ $�/�+ C.+ %# ������-�DJ����+?9# ��9n� �� �=�� � �����$�� C!"j�?J+.$��$ ��

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������� � �� Journal of Water and Wastewater ����� ���� ����� ����� Vol.29, No. 2, 2018

��#Ns)��' ���e� ����+ ��.� � %���-6 L���T %# E�� E� �$ \�# 8���� ��� ���e� �� �'� %�� Table 4. Changes in equity, efficiency and sustainability due to different weights of objective

functions in first year

Year Month

(Persian Calendar)

If, W1=0.5, W2=0.32, W3=0.05 and W4=0.13Equityindex

(User 3, FP) Efficiency index (EP) Sustainability index (SP)

1Farvardin 0.302 1

0.397 Ordibehsht 0.339 1Khordad 0.283 1

Year Month If W1=0.7, W2=0.12, W3 = 0.05 and W4=0.13

Equityindex (User 3, FP) Efficiency index (EP) Sustainability index

(SP)

2Farvardin 0.302 1

0.356 Ordibehsht 0.283 1Khordad 0.283 1

Year Month *If W1=0.3, W2=0.52, W3 = 0.05 and W4=0.13

Equityindex (User 3, FP) Efficiency index (EP) Sustainability index

(SP)

3Farvardin 0.377 0.7

0.417 Ordibehsht 0.377 1Khordad 0.377 0.9

* The coefficients are considered in intial quantity- quality allocation model

Month (Persian Calendar) A: Wet scenario

Month (Persian Calendar) B: Dry scenario

Fig.4. Performance of reservoir a) Wet scenario and b) Dry scenario _e�b)�-� � �$ �$ �?J+ $�Q@9Ta� ����� (b;3� ( ���

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A: User 1 B: User 2

D: User 4 C: User 3 Fig.5. Ratio of allocated water to water demand for each user (users 1 to 4)

_e�j)K�.g � E�� ������ �$ ��� ��� �� ��' �$�$ ��DJ� 5� ����+ L�"�

Fig. 6. TDS variations at different QC points in dry scenario _e�l)����e�TDS ;3� �-� � �$ ^@!J+ �=�� E�! � R�� �$ ���

0

0.2

0.4

0.6

0.8

1

Rat

ioof

allo

cate

dw

ater

tom

onth

lyw

ater

dem

and

ofus

er2

Month (Persian Calendar)

Normal Scenario Dry Scenario

Wet Scenario

0

0.2

0.4

0.6

0.8

1

Rat

ioof

allo

cate

dw

ater

tom

onth

lyw

ater

dem

and

ofus

er1

Month (Persian Calendar)

Normal Scenario Dry ScenarioWet Scenario

0

0.2

0.4

0.6

0.8

1R

atio

ofal

loca

ted

wat

erto

mon

thly

wat

erde

man

dof

user

4

Month (Persian Calendar)

Normal Scenario Dry Scenario

Wet Scenario

0

0.2

0.4

0.6

0.8

1

Rat

ioof

allo

cate

dw

ater

tom

onth

lyw

ater

dem

and

ofus

er3

Month (Persian Calendar)

Normal Scenario Dry Scenario

Wet Scenario

300

400

500

600

700

800

900

1000

TDS

(mg/

L)

Month (Persian Calendar)

TDS concentration at first control pointTDS concentration atsecond control pointTDS concentration at third control point

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������� � �� Journal of Water and Wastewater ����� ���� ����� ����� Vol.29, No. 2, 2018

��#Nj)������ �� ��' �$�$ ��DJ� 5� ����+r�|) ;3� �-� � �$ 5� ��:$T ��DJ� % �+��MCM(Tabel 5. Water allocated to each user based on equity allocation in dry scenario (MCM)

Year Month

(Persian Calendar)

User 1 User 2 User 3 User 4 Year User 1 User 2 User 3 User 4

1

Mehr 0.313 0.161 0.238 0.867

3

0.311 0.161 0.237 0.836Aban 0.234 0.119 0.047 0.548 0.232 0.119 0.047 0.54Azar 0 0 0 0 0 0 0 0Dey 0 0 0 0 0 0 0 0Bahman 0.74 0.857 0.542 0.798 0.721 0.825 0.534 0.774Esfand 0.868 0.142 0.595 0.851 0.834 0.142 0.585 0.819Farvardin 0.661 0.472 0.941 0.606 0.586 0.466 0.882 0.606Ordibehsht 0.944 0.485 0.923 0.739 0.869 0.478 0.871 0.582Khordad 0.507 0.273 0.229 0.566 0.499 0.271 0.228 0.556Tir 0.501 0.27 0.371 0.805 0.492 0.268 0.367 0.773Mordad 0.466 0.249 0.538 0.935 0.459 0.247 0.528 0.845Shahrivar 0.4 0.211 0.485 0.93 0.395 0.209 0.476 0.844

��#Nl)��' ����+ ��.� � %���-6 L���T %# (;3� �-� �) E�� E� �$ %�� Tabel 6. Equity, efficiency and sustainability indices in the first year (dry scenario)

YearMonth

(Persian Calendar)

Equity index (User 1, FP)

Equity index (User 2, FP)

Equity index (User 3, FP)

Equity index (User 4, FP)

Efficiency index (EP) Sustainability

index (SP)

1

Mehr 0.4 0.26 0.35 0.47 0.6

0.19

Aban 0.41 0.26 0.37 0.6 0.6 Azar 0 0 0 0 1Dey 0 0 0 0 1

Bahman 0.32 0.18 0.31 0.51 0.6 Esfand 0.28 0.26 0.3 0.48 0.6

Farvardin 0.1 0.23 0.2 0.14 0.6 Ordibehsht 0.21 0.23 0.22 0.19 0.6 Khordad 0.37 0.25 0.35 0.59 0.6

Tir 0.37 0.25 0.34 0.5 0.6 Mordad 0.37 0.25 0.31 0.36 0.6

Shahrivar 0.38 0.26 0.32 0.38 0.6

j)�:'0 "&:V � �$-4M#�]69#� �� �/�� � �DJ� Y�o�+ L�8�� + ���:$T �

� �$ 5��C!" #%���$��j���' �$ �?J+-K��T ,N�1 �� L �- ;.� E�+�� ��%DJ��_ ��N�1���9� �+?9#�� ��=�5� 8�� +

� �$�C!" #%���$��j �+�� �?J+%.� X���� ��%� �-#�.� E�+ �� �$=!�� � ��� ��%GAMS ���-� .�' 4-�Q+� E�+ 4

9D��C)��%�$$��+ ����+ DJ���5����o�!+������ ��*� �����V� ����7�D� �����+� @��#�����`�����-Q� $����D!1�%�

*+�,�!"-�N+ �� f�1 �$ ���.� L���T � ��%6 �-���% �$ ��K�T 4!��) �a� N�1��!+��6 �$ L#�`�����-Q��/�-$��� �%���

�� �?J+ �����%L�$ �������� MJ� ��� 5�%�����$�� C!"jE�$�� �?J+ C#��� !� .L�� �$���-DJ� E�+ [��9� ��� ���=�

6 ��:$T�$. 3%+ �3��� �� �#$����$�� C!"j E��$�� �?J++�� �$�� 4�����3� M�J� ������� �%E�� �$ �#%E�+�� � ���@Q3+�+ �(� � $������ �$ ����-E� 4#��� �� 5� �$=!��� ���a +

E� �$ #%�c ;3������%!� l��+ .$�9�-� �$ �@�7G [�-4M#�]6E� �$ #%� �� ;3�� L��� ��/��+ 5� $���9� � C!"

DJ��� 5� ���� ������ 4���.� � L����T ���' W�� ��%��� ���) �%+�� �� L�� �!��) ��7�� 4������� �%��o ���-$��� f

��L�"� �!3 �� ��-���� �$ $��$ ������� ��-&� ����1 L���� ��!��� .$�O���-�� �+��� �� .� ��7�� ��%���$ �� g �%�+ 0�9T� �� �

.� ����+ E�+�����) ��� �� E��$�� ��� �?�J+ �� ��' #� 5� � �%+ 5J!���E� �$ �� � � #%�N�%��� ?���g$ ��Q+� �G � C!"

�!9�- H9# .$�' 0Q3+ 4�4!�-���� [�6 E�+ $�Q@9T�$. �3%

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�-4M#�]6# ���(+ E�+ �� $�$ �3� ��&H %���� +����� 4� �#� ���+ �$ ?��/ �� E���$�� ���� �?��J+ C��OG ��#%6��-��k���� l����

�+��� �-?%9� 01��G ����+ �� �!� .����-� �� 07G [-��N��+ 4�� �� $�$ �3�-6 $�Q�$. 3%� �$-4M#�]6 ��� + $�Q@9T��$

��DJ��9� ���+?9# ���*� ��� 5� ����:$T ����� � L�=��� �$ 5� L��C!" #%���$��jK�T �*� � � �?J+ N�1�L.$��$ #

�� � N��+ ��a +�6 �!3�$. 3 ��+ $��' ����$���) ��*� ��)�$ ^@!J+�� ��N��+ $���+ ���� + �$ ��L�� �#%�DJ���� �

��-��#$�Q%����g ���*� ��������� ���� 4��Q9+ ���G ��� \F!���� 8�4N� ^@!J+ ����$��) ��� 4$��' � H9# .�6 E��+ 4�$. �3%��*� ��

e!+�#�%��=������ �!3%L�G #%DJ����� ��' � g � �)$����.���' �$�$ �N���

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Alcomo, J. & Gollopim, G., 2009, Building and generation of world water scenarios : Water in changing world,The United Nations World Water Development Report 3, United Nations World Water Assessment Programme (WWAP).

Dong, C., Schoups, G. & Giesen, N., 2013, "Scenario development for water resource planning and management : A review", Technological Forecasting and Social Change, 80 (4), 749-761.

Dembo, R. S., 1991, "Scenario optimization", Annals of Operations Research, 30(1), 63-80. Fu, Y. H., Guo, P., Fang, S. & Li, M., 2014, "Optional water resources planning based on interval-parameter two

stage stochastic", Transactions of the Chinese Society Agricultural Engineering, 30 (5), 73-81. Gallopin, G. C. & Rijsberman, F., 2000, "Three global water scenarios", International Journal of Water, 1(1),

16-40. Karamouz, M. & Araghinezhad, Sh., 2010, Advanced hydrology, University of Amir Kabir Technology, Tehran.

(In Persian) Karimi, A., 2010, "Optimum water allocation modeling at basin scale by integration of waterbasin hydrologic

and socio-economic properties and their uncertainties", PhD Thesis, Sharif University of Technology, Tehran, Iran. (In Persian)

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Pouya, A., 2013, "Developing a water quantity- quality allocation model in river basins: Application of Game Theory", MSc. Thesis, University of Shiraz, Iran. (In Persian)

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