Simulation-Optimization Modeling for Efficient Groundwater Management in a Deltaic Aquifer by India Water Week

Simulation-Optimization Modeling for Efficient Groundwater Management in a Deltaic Aquifer of Eastern India (S. Mohanty, M. K. Jha and Ashwani Kumar) Directorate of Water Management, Bhubaneswar Introduction Excessive groundwater exploitation has led to alarming decrease in groundwater levels in several parts of the country such as Tamil Nadu, Gujarat, Rajasthan, Punjab and Haryana (CGWB, 2006). The analysis of GRACE satellite data revealed that the groundwater reserves in the states of Rajasthan, Punjab and Haryana are being depleted at a rate of 17.7 ± 4.5 km3/yr (Rodell et al., 2009). The groundwater simulation models have emerged as the tool of choice among water resources researchers and planners for addressing questions about the impacts of groundwater development.

Objectives (i) To develop a groundwater-flow simulation model for the Kathajodi-Surua Inter-basin using Visual MODFLOW. (ii) To develop a simulation-optimization model for optimal land and water utilization in the basin.

Study Area

Longitude - 85o 54’ 21” to 86o 00’ 41” E Latitude - 20o 21’ 48” to 20o 26’ 00” N Area- 35 km2

(a) Real Aquifer System

(b) Conceptual Model

Conceptual Model of the Study Area

Design of Finite Difference Grid of the Study Area with Boundary Conditions and Location of Pumping Nodes

3-D Cross-section of the modeled study area showing the pumping wells

3-D Cross-section of the modeled study area showing the observation wells

Development and calibration of groundwater-flow simulation model  Model was designed for two layers, the top layer and the bottom confined aquifer. The study area was discretized into 40 rows and 60 columns using the Grid module of the software.  Boundaries of the groundwater basin were modeled as head-dependent flow or Cauchy boundary condition.  Aquifer parameters, groundwater abstractions and groundwater recharge were assigned to the model.  Model calibration was done for the period Feb. 2004 to May 2006.  Groundwater elevations at 19 observation wells were used as calibration target.  Hydraulic conductivity, specific storage and recharge were considered as calibration parameters.  A combination of trial and error method and automated calibration code PEST was used to calibrate the model.  Validation was done for the period June 2006 to May 2007.  The calibration and validation of the model was done satisfactorily with the RMSE values of 0.62 m and 0.632 m and NSE values of 0.915 and 0.914 respectively.

Simulation-optimization model for maximization of pumping Objective Function 69

Max Q = ∑∑ qij d j i =1 j =1

where, Q = maximum permissible pumpage from the existing wells (m3); qij = pumpage of the ith well in the jth month (m3/sec); dj = number of days of pumping in the jth month; i = index for well number; and j = index for time period (j = 1 to 7; 1 for November; 2 for December and so on).

Drawdown constraint

max β q ≤ S ∑∑ ki ( n− j +1) ij k

k = 1, 2, 3,………….69

i =1 j =1

Where, βki(n-j+1) = average drawdown at the kth site due to a unit pulse of pumpage at the ith well during jth month; n = total number of time periods; k = index for site number; Skmax = maximum allowable drawdown at the kth site (m). 69

Water demand constraint

∑q d i =1

≥ Dj

j = 1, 2, ……7

Where, Dj = water demand of the crops in the jth month (m3); dj = number of days of pumping in the jth month

Pumping capacity constraint

0 ≤ qij ≤ qijmax

i = 1, 2, 3.….69; j = 1, 2…7

Optimization model for land and water management Z = net annual return (Rs.), Pj = market price of the jth crop (Rs./kg); Yj = yield of the jth crop (kg/ha); Cj = cost of cultivation per unit area for the jth crop, excluding the cost of irrigation water (Rs./ha); Iij = irrigation cost for the jth crop in the ith type of land (Rs./ha); aij = area under the jth crop in the ith type of land (ha); i = index for land type (1 for high land, 2 for medium land, and 3 for low land); and j = index for crop type (1, 2, 3,…,11).

Objective Function 3

Max Z = ∑∑ ( Pj Y j − C j − I ij )aij i =1 j =1

∑a

Land availability constraint

j =1

≤ Ai

i = 1, 2, 3

Where, aij = area under the jth crop in the ith type of land, and Ai = total area of the ith type of land (i =1 for high land, i = 2 for medium land and i = 3 for low land). 3

Water requirement constraint

∑∑ a i =1 j =1

ijk

.wijk ≤ Wk

k = 1, 2,…., 7

Where aijk = area under the jth crop in the ith type of land in the kth month, wijk = water requirement of the jth crop in the ith type of land in the kth month, Wk = available irrigation water (i.e., maximum groundwater withdrawals) in the kth month

Maximum/minimum area constraint

A ≤ ∑ aij ≤ AUj L j

i =1

k = 1, 2,……., 7

Optimal Cropping Pattern, Net Irrigation Requirement and Net Annual Income in the Normal Scenario Crop

Allocated Land (ha)

Net Irrigation Requirement (m3)

Low Land

Medium Land

High Land

Total

177

16.01 × 105

Sugarcane

195

8.71 × 105

Potato

300

7.77 × 105

Onion

0.79 × 105

Groundnut

123

2.95 × 105

Winter Vegetables

231

369

600

12.72 × 105

Summer Vegetables

248

5.40 × 105

Greengram

315

3.96 × 105

Blackgram

193

285

3.85 × 105

Horsegram

202

3.47 × 105

Mustard

0.16 × 105

408

1081

995

2484

65.78 × 105

Paddy

Total

Net Annual Income = Rs. 76.36 × 106



  



The total monthly maximum allowable pumpage from the river basin are estimated at 1.63, 1.68, 1.60, 1.45, 1.60, 1.47 and 1.52 million m3 in the months of November, December, January, February, March, April and May, respectively. The crops such as sugarcane, potato, onion, winter vegetables and summer vegetables are allotted the maximum area possible in all the three scenarios. Paddy crop is limited to 304 ha in the wet scenario and a minimum area of 177 ha in the normal and dry scenarios. All the areas under low land (408 ha), medium land (1081 ha) and high land (956 ha) are covered under crops in the wet scenario, whereas in the normal and dry scenarios, only entire low land and medium land are covered under crops. Total maximum area under high lands at a particular time in wet, normal and dry scenarios are 956 ha, 747 ha and 327 ha respectively. Total net irrigation requirement for optimal cropping pattern in wet, normal and dry scenarios are 61.40 × 105 m3, 65.78 × 105 m3, and 66.30 × 105 m3, respectively. The net incomes from the optimal cropping patterns for the wet, normal and dry scenarios are estimated at Rs. 81.83 million, Rs. 76.36 million and Rs. 71.55 million respectively. With adoption of optimal cropping patterns there will be saving in the irrigation water requirement by 23.66 × 105 m3 (27.82%) in the wet scenario, 35.22 × 105 m3 (34.87%) in the normal scenario, and 44.71 × 105 (40.28%) in the dry scenario. There will be an increase in total net income by Rs. 18.02 million (28.24%), Rs. 14.15 million (22.75%) and Rs. 10.34 million (16.89%) in the wet, normal and dry scenarios, respectively.

Conclusions  A groundwater-flow simulation model was developed for the study area using Visual MODFLOW. The calibration and validation of the model was done satisfactorily with the RMSE values of 0.62 m and 0.632 m and NSE values of 0.915 and 0.914 respectively.  A simulation-optimization model was developed by integrating the response matrix generated from the simulation model with an optimization model.  Based on the simulation-optimization model, the maximum groundwater withdrawals from the river basin are 1.63, 1.68, 1.60, 1.45, 1.60, 1.47 and 1.52 million m 3 in the months of November, December, January, February, March, April and May, respectively.  The optimal cropping patterns will help reduce the net annual irrigation water requirements by about 28 %, 35% and 40% during wet, normal and dry scenarios, respectively.  The net annual income due to optimal cropping patterns will increase by 28%, 23% and 17% for the wet, normal and dry scenarios, respectively.