In the present study, a Linear Programming (LP) model is developed for the conjunctive use of surface water and ground water to obtain the optimal operating policy for a multipurpose single reservoir. The objective of the present study is to maximize the net benefit from the command area under consideration. The constraints imposed on the objective function are maximum and minimum irrigation demands, reservoir storages and canal capacity. The model takes into account the continuity constraint which includes inflows in to the reservoir, releases for irrigation, releases for hydro-power generation, evaporation losses, feeder canal releases, initial and final storages in the reservoir in each time period. The developed model is applied to the case study of Jayakwadi reservoir stage-I, built across river Godavari, Maharashtra, India. Initially the model is solved for the availability of surface water which results in net benefit of 3373.45 million rupees with irrigation intensity is 57.07%. Next the model solved by considering the availability of surface water and available potential of groundwater in the area, which results in net benefits of 3590.02 million rupees with an intensity of irrigation 58.48%. The present model takes in to account the socio-economic requirement of growing the essential crops to meet the requirement of the society. The model has also generated the canal wise optimal releases for irrigation and power, monthly utilization of groundwater, storages in the reservoir at the end of every month and corresponding head over the turbine.
The optimal operation of a reservoir system for efficient utilization of both surface and groundwater resources conjunctively requires knowledge of reservoir process and infield process. This knowledge facilitates to arrive at decisions on reservoir operation and cropping pattern by use of optimization models. These are characterized by a mathematical statement of objective function to give global optimum solutions.
Many researchers have worked on several aspects of the conjunctive use of surface and ground water such as 1) reservoir/stream and aquifer interaction for assessment of conjunctive use potential; 2) modeling of conjunctive use of surface and groundwater; 3) optimal planning using different techniques.
A comprehensive knowledge of surface-ground water interaction is essential to assess and plan of conjunctive use policies. Gupta and Paundyal [
Varieties of conjunctive use optimization models are available in the literature as applicable to reservoir systems. Yeh [
A mathematical conjunctive use model to maximize the net benefits has been developed by Kashyap and Chandra [
The objective of the study is to maximize net benefits by suggesting an optimum irrigation release policy and a cropping pattern by use of both surface water and groundwater conjunctively. A monthly model has been developed by considering various variables such as irrigation demand, land use restrictions, socio economic constraint, drinking water demand, industrial water demand, live storage restrictions, canal capacity restrictions and availability of groundwater. The uncertainty in the flow is tackled through its dependability.
In this direction an attempt is made to perform optimal reservoir operations using optimization tool. Present work deals with modeling for multi crop irrigation, considering continuity equation and the available groundwater potential.
In the present study, the reservoir operation model is developed for Irrigation Planning with Conjunctive use of surface and groundwater. Model considers the objective of maximizing the net benefits from the available water resource from the command of a reservoir. It is expressed as:
where,
Z = Total net benefit i.e. value of objective function in Rs.
NBzc = It is net benefit estimated from irrigation of cth crop from zth canal zone.
Azc = Area under the cth crop in m2 grown in zth canal zone.
CSWzt = Total cost of providing surface water during tth month in zth zone.
ηs is efficiency of surface water system.
SWAzt = Surface water available at the head of the zth canal at tth time period.
CGWzt = Total cost of providing groundwater during tth month in zth zone. It also includes the capital cost, pumping cost, operation and maintenance cost.
ηg is the efficiency of groundwater.
GWAzt = Available groundwater in zth zone during time period tth without allowing mining.
The objective function of maximization of net benefit is subjected to the following constraints such as:
The total area allocated for different crops in a particular season should be less than or equal to the total culturable command area (TCCA) available during that season.
Season wise area constraints are given below:
1) Kharif Crops Area Constraint
where,
TCCAzc = Total culturable command area during Kharif season in zth canal zone.
c = 1 to nkc Crops in Kharif season,
2) Rabi Crops Area Constraint
TCCAzr = Total culturable command area during rabi season in zth canal zone.
c = 1 to nrc Crops in rabi season
3) Bi-seasonal Crops Area Constraint
TCCAzb = Total culturable command area during bi season in zth canal zone.
c = 1 to nbc crops in bi-season
4) Hot Weather Crops Area Constraint
TCCAzh = Total culturable command area during hot weather season in zth canal zone.
c = 1 to nhc crops in hot weather
5) Perennial Crops Area Constraint
TCCAzp = Total culturable command area during perennial season in zth canal zone.
c = 1 to npc crops in perennial season.
Crop area constraint is also called as socio economic constraint. This constrain depends on the proposed cropping pattern considering socio-economic needs of the area. The land area constraint discussed in 2.2.1, restricts the maximum value of irrigated area under the crops in a particular season. Sometimes the benefit optimization model does not allow area for certain crops may be because of more water requirement and low benefit coefficient. However, crop area constraint restricts some minimum value for irrigated areas under such crops in a particular season to meet the local requirement of food.
Pc = It is the percentage of Cth crop in Zth canal zone with respect to TCCA.
Net irrigation water requirement by all crops during time period t in each zone is to be satisfied from monthly available surface water and groundwater at the field.
Aztc = Area of cth crop under canal zone z during time period t.
ηs and ηg are efficiencies of surface water and groundwater systems respectively.
Releases from the reservoir in the canal during the time period t should be less than or equal to the canal capacity in each zone during the time period t.
CCzt = Capacity of zth canal during time period t, (i.e. per month in m3).
The live storage in the reservoir in any time period t should be less than or equal to the maximum capacity and should be more than or equal to and the dead storage.
St = reservoir storage at the beginning of the month t (t = 1, 2, …, 12).
The continuity constraint involves releases, overflows, storages, inflows and losses through the reservoir during the period “t” i.e. for period t expressed in unit of volume. The evaporation losses are expressed as function of storage. The storage continuity equation given by Loucks et al. [
where,
at = 0.5Aa*Et.
Et = Average evaporation rate for each period.
Aa =Area corresponding to month wise average storage.
A0 = Surface area corresponding to dead storage.
St =is reservoir storage at the beginning of the month t.
St+1 = reservoir storage at the end of the month t and also at the beginning storage at the month
Rt = Releases other than irrigation.
It = inflow in the reservoir during month t.
Ot = the overflow from the reservoir during month t, it should be greater than zero.
The developed model is applied to the case study of Jayakwadi Reservoir Stage-I on the river Godavari in the State of Maharashatra, (India). The
It is a multipurpose project with gross and live storage capacities 2909 Mm3 and 2170 Mm3 respectively. The system of two canals i.e. Left Bank Canal 208 km in length and the Right Bank Canal 132 km in length serves an irrigable command area of 141,640 ha and 41,700 ha respectively. The reservoir has a pump storage power generation unit with 12 MW reversible pump turbine unit at the foot of the dam. The entire command area of the project lies within the Latitude 18˚46'N to 19˚30'N and Longitude 75˚20'E to 77˚45'E.
The total intensity of irrigation of Jayakwadi reservoir stage I is 102% distributed in 22% for kharif crops (Jowar 12% and Paddy 10%), 45% for rabi crops (Wheat 25%, Jowar 15% and Gram 5%), 28% for two seasonal crops (Cotton 25% and chilly 3%), 3% for hot heather ground nut and 4.5% for perennial crops (Sugarcane 3% and Banana 1.5%).
1) The language for Interactive General Optimization (LINGO) has been used to solve the linear optimization problem.
2) The model considers the 75% dependable inflows in to the reservoir considering crops are grown throughout the year.
3) The inter-relationship between the variables and parameters involved in the model formulation is linear.
4) The soil in the command of the reservoir is considered to be homogeneous in nature.
5) Losses during conveyance in surface and groundwater system are considered as 40% and 20% respectively.
6) It is observed that the utilization of the groundwater is not uniform throughout the year. Farmers use more groundwater during the post monsoon period and before hot weather. It is, therefore, suitably assumed in absence of the data that about 60% of the total available groundwater would be utilized equally during October to March and rest during the remaining part of the year.
7) Releases for power generation in the pump storage power station are restricted between the monthly turbine capacity of 33.96 Mm3 and release for firm power 22.67 Mm3.
8) Month wise heads over the turbine are worked out from the storage-elevation curve of the reservoir.
9) Other uses of water considered in continuity equation are [
a) Releases for water supply 31.63 Mm3 per month.
b) Feeder canal releases for downstream storages during October to February as 50 Mm3, 80 Mm3, 70 Mm3, 90 Mm3, and 60 Mm3 respectively.
10) 10% of the releases for the power generation in pump storage power station are considered as losses.
11) Evaporation losses which are worked out by considering the month wise variation of the surface area given by Loucks et al. [
1) Net benefit i.e. the value of the objective function in Rs is calculated by considering the yield of the crop (t/ha), market price of the crop (Rs/t) and the cost of cultivation.
2) The cost of cultivation of crop is considered excluding the cost of water and including cost of labor, cultivation, planting, growing and harvesting. This is obtained from the Department of Statistics and Economics, Agricultural Department, Govt. of Maharashtra, India.
3) Available groundwater from recharge in the command without allowing mining is estimated using lumped empirical approach and guidelines of GEC-97 which is well established and practiced in India. The aquifer has been considered as a single reservoir of capacity equal to the specific yield. Groundwater utilization is restricted to the recharge to maintain the stable stream aquifer response. Recharge is mainly considered from the rainwater and return flow from the surface water irrigation from the reservoir.
4) Groundwater utilization is restricted to the recharge to avoid overdraft. Based on the joint work of the Central Ground Water Board, Government of India and Ground Water Survey and Development Agency (GSDA) of Government of Maharashtra [
5) The cost of providing surface water is based on the local government norms and the cost of the groundwater is calculated by considering the capital cost, pumping cost, operation and maintenance cost.
6) Land area available for growing the crops is restricted to the cultivable command area under the respective canals. Socio economic constraint is imposed for minimum production of a particular crop by taking into consideration the need of the people.
7) Net irrigation water requirement by all crops during the monthly time period t in each zone is considered to be satisfied during all the seasons from available surface and groundwater. Irrigation water requirement is considered at the canal outlets and that of groundwater at source i.e. well by considering conveyance efficiencies as 60% and 80% respectively.
8) Net Water Requirement of crop during the time period t is estimated by modified Penman Method.
The model developed in the present study is applied to the case study of Jayakwadi reservoir stage-I by considering all considerations and the evaluated parameters as stated in earlier sections 4 and 5, to obtain the optimal cropping pattern and optimal release policies which maximize net benefits.
The model is solved by considering two cases as given below:
1) Case-I―by considering surface water only.
2) Case-II―by considering the conjunctive use of surface water and groundwater.
Being a multipurpose reservoir, after giving first priorities to the water supply for drinking and industrial use the optimal releases for the power generation and for irrigation are obtained from the model which are presented and discussed here.
The optimal cropping patterns for the case I and II obtained from the global optimal solution of the LP model are shown in the
It is required to put socio economic constraints to the crops Rabi Wheat, Rabi Jowar, Rabi Gram and Hot Weather Ground Nuts in case-I and to Rabi Wheat, Rabi Jowar and Hot Weather Ground Nuts in case-II to take care of the requirement of the local population. The benefit optimization model has not allocated area to these crops during its first run. This is because of low benefit coefficients and more water requirement of these crops as compared to other crops. Putting socio economic constraint i.e. crop area constraint reduces the net benefits and increases the intensity of irrigation. However, it assures the production of certain essential crops to meet the need of the population in the command.
An intensity of irrigation of 57.07% and 58.48% is obtained for the Case-I and for Case-II. The intensity of irrigation as per the project report is 102.5%. The conjunctive use of surface and groundwater in the case-II has resulted in rise in the net benefits by 6.42%.
The model has allotted area to the crops kharif Jowar, bi-seasonal cotton, bi-seasonal chilly and perennial banana to the maximum extent for both the cases I and II as compared to the project cropping pattern given in Section 3. Even for sugarcane in case II, the allotted area is almost to its maximum extent due to conjunctive use of surface and groundwater.
Crop Notation | Crop Name | Case-I―with only surface water Area under the crop in ha | Case-II―Conjunctive use Area under the crop in ha | ||||||
---|---|---|---|---|---|---|---|---|---|
Canal-I | Canal-II | Total | % over available total irrigable command area | Canal-I | Canal-II | Total | % over available total irrigable command area | ||
A1 | Kharif Jawar | 16996.8 | 5004.00 | 22000.8 | 12 | 16996.80 | 5004.00 | 22000.8 | 12 |
A2 | Kharif Paddy | 00.00 | 00.00 | 00.00 | 00 | 1655.79 | 518.54 | 2174.34 | 1.18 |
A3 | Rabi Wheat | 10623.00 | 3127.5 | 13750.05 | 7.5 | 10623.0 | 3127.5 | 13750..05 | 7.5 |
A4 | Rabi Jowar | 6373.8 | 1876.5 | 8250.30 | 5.0 | 6373.80 | 1876.5 | 8250.30 | 5.0 |
A5 | Rabi Gram | 2124.8 | 625.5 | 2750.10 | 1.5 | 00.00 | 00.00 | 00.00 | 00 |
A6 | Bi-Seasonal Cotton | 35410.00 | 10425.00 | 45835.00 | 25 | 35410.0 | 10425.00 | 45835.00 | 25 |
A7 | Bi-seasonal Chilly | 4249.2 | 1251.00 | 5500.20 | 3.0 | 4249.2 | 1251.00 | 5500.20 | 3.0 |
A8 | Hot Weather Groundnut | 1274.76 | 375.30 | 1650.06 | 0.9 | 1274.76 | 375.3 | 1650.00 | 0.9 |
A9 | Perennial Sugarcane | 897.6428 | 1251.00 | 2148.64 | 1.17 | 4067.72 | 1251.00 | 5318.72 | 2.9 |
A10 | Perennial Banana | 2124.6 | 625.50 | 2750.10 | 1.5 | 2124.6 | 625.50 | 2750.10 | 1.5 |
Total | 80074.40 | 24561.30 | 104635.70 | 82775.68 | 24454.35 | 107230.00 | |||
Intensity of irrigation | 56.53% | 58.9% | 57.07% | 57.07% | 58.44% | 58.64% | 58.48% | 58.48% | |
Net benefits in Million Rs | 3373.45 | 3590.02 |
The canal wise optimal monthly releases and the gross storage at the end of every month for both cases I and II obtained from the model are shown in
The amount of surface water utilized for the optimal cropping pattern in case I is 1060.41 Mm3 and for Case-II the corresponding value is 1053 Mm3. However, in case II while using both the surface and groundwater conjunctively, the amount of groundwater utilized is 129.94 Mm3 out of available 132.30 Mm3.
The live storage values at the end of May in case-I and case-II are just 121.19 Mm3 and 144.61 Mm3 respectively. Its values are zero at the end of June in case-I and case-II respectively. The maximum gross storage of 2044.4 Mm3 and 2054.43 Mm3 is observed in the month of October in the both cases which is less than the maximum storage capacity of 2909 Mm3 of the reservoir. Thus, there is no spill over the dam in any of the months.
There are maximum releases of 278.56 Mm3 and 266.51 Mm3 in the month of October in case-I and case-II respectively. No surface water releases are there in the months July and August in the case-II and minimum releases of 3.70 Mm3 in the month of August in the case-I. It shows minimum use of surface water during the months July and August due to low irrigation demand due to precipitation.
Sr. No. | Month | Case-I | Case-II | ||||||
---|---|---|---|---|---|---|---|---|---|
Releases in Mm3 | Gross Storage in Mm3 | Releases in Mm3 | Gross Storage in Mm3 | ||||||
Canal-I | Canal-II | Total | Canal-I | Canal-II | Total | ||||
01 | June | 9.74 | 7.01 | 16.75 | 738.00 | 14.02 | 4.26 | 18.28 | 738.00 |
02 | July | 4.41 | 1.69 | 6.10 | 776.44 | 00.00 | 00.00 | 00.00 | 774.92 |
03 | August | 2.77 | 0.93 | 3.70 | 1092.62 | 00.00 | 00.00 | 00.00 | 1097.17 |
04 | September | 49.08 | 15.40 | 64.48 | 1609.51 | 48.14 | 14.23 | 62.37 | 1617.63 |
05 | October | 212.48 | 66.07 | 278.56 | 2044.40 | 205.76 | 60.75 | 266.51 | 2054.43 |
06 | November | 164.19 | 52.75 | 216.94 | 1911.48 | 154.61 | 45.63 | 200.24 | 1933.26 |
07 | December | 85.18 | 28.89 | 114.08 | 1729.08 | 77.55 | 22.91 | 100.46 | 1767.07 |
08 | January | 93.93 | 31.85 | 125.79 | 1601.44 | 93.90 | 27.74 | 121.64 | 1652.49 |
09 | February | 39.98 | 17.39 | 57.37 | 1346.92 | 44.52 | 13.28 | 57.80 | 1401.27 |
10 | March | 36.62 | 17.91 | 54.53 | 1178.00 | 46.02 | 13.81 | 59.83 | 1231.07 |
11 | April | 45.06 | 23.49 | 68.55 | 1030.43 | 68.91 | 20.75 | 89.66 | 1076.50 |
12 | May | 32.97 | 20.51 | 53.48 | 859.19 | 58.65 | 17.77 | 76.42 | 882.61 |
Total | 776.46 | 283.95 | 1060.41 | -- | 812.12 | 241.18 | 1053.3 | -- |
The release of surface water from the reservoir for power generation is at its minimum requirement of 22.67 Mm3 for firm power. The month wise varying values of the head over the turbine and the corresponding magnitude of power generated in MW during every month are shown in
Depending upon the availability of the surface water and the head over the turbine the average power generated in the pump storage power generation unit is 1.66 MW per month.
The variation of the head over the turbine during the year is shown in the
It is observed that an average head of 27 m is available over the turbines in both the cases.
The optimal operation model of multipurpose reservoir for irrigation planning with conjunctive use of surface and groundwater is developed and applied to case study of Jayakwadi reservoir stage-I, Maharashatra State, India. Following conclusions are drawn from the study.
Sr. No. | Month | Release for Power in Mm3 | Case-I | Release for Power in Mm3 | Case-II | ||
---|---|---|---|---|---|---|---|
Head over the turbine in m | Power generated in MW | Head over the turbine in m | Power generated in MW | ||||
01 | June | 22.67 | 24.919 | 1.54 | 22.67 | 24.916 | 1.53 |
02 | July | 22.67 | 25.522 | 1.57 | 22.67 | 25.527 | 1.57 |
03 | August | 22.67 | 26.938 | 1.66 | 22.67 | 26.960 | 1.66 |
04 | September | 22.67 | 28.556 | 1.76 | 22.67 | 28.587 | 1.76 |
05 | October | 22.67 | 29.070 | 1.79 | 22.67 | 29.124 | 1.80 |
06 | November | 22.67 | 28.533 | 1.76 | 22.67 | 28.635 | 1.77 |
07 | December | 22.67 | 28.006 | 1.73 | 22.67 | 28.158 | 1.74 |
08 | January | 22.67 | 27.357 | 1.69 | 22.67 | 27.536 | 1.70 |
09 | February | 22.67 | 26.637 | 1.64 | 22.67 | 26.819 | 1.65 |
10 | March | 22.67 | 26.099 | 1.61 | 22.67 | 26.267 | 1.62 |
11 | April | 22.67 | 25.557 | 1.57 | 22.67 | 25.675 | 1.58 |
12 | May | 22.67 | 25.060 | 1.55 | 22.67 | 25.100 | 1.55 |
1) There is an increase of 2.47% in the intensity of irrigation in case-II as compared to the case-I. This may be due to conjunctive use planning. The benefits in case II is increased to 6.42% giving rise of 6.42% in the net benefits.
2) The socio-economic constraints have been considered to the crops of Rabi Wheat, Rabi Jowar, Rabi Gram and Hot Weather Ground Nuts in case-I and to Rabi Wheat, Rabi Jowar and Hot Weather Ground Nuts in case- II to take care of the minimum requirement of the local population. This also ensures crop rotation.
3) The storages available in hot weather have been allowed for growing perennial and the hot weather crops particularly the sugarcane which assured the running of sugar mills in the area by preventing the migration of labor to certain extent.
4) Being a multipurpose reservoir, after giving first priority to water supply the cropping patterns and the power generation are obtained as presented in the results.
The authors are thankful to the Command Area Development Authority, Aurangabad, Maharashatra State, India for providing necessary data for analysis.