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Water Balance Study to Develop a Technique to Improve the Groundwater System in

Vavuniya

Dr.S.S.Sivakumar

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Objective

An economic policy in operating the minor & medium irrigation schemes

A new technique of peripheral cut off by clay or by geotextile

To improve the groundwater system in Vavuniya using modeling technique

To find

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Modeling Technique

Conceptually the modeling technique used for system representation can be very simply explained as below.

Select or formulate a suitable model Assume the parameters approximately Adopt some error function to quantify the

difference between measured and predicted responses

Minimize the error function Determine the parameters accurately Predict system response

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Modeling TechniqueActual System

ResponseModel predictedSystem Response

MathematicalModel

Modeled InputNon - Modeled

Input

Real PhysicalSystem

Solution Strategy(Optimization)

Schematic representation of the process of system modeling and optimization.

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Modeling Technique

Finite difference method

• rectangular grid system

Integrated Finite difference method

• polygonal net work

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Study area

• Vavuniya District• 71.5 sq.miles(185 sq.km.)• 41 observation points(wells)• 5 medium Irrigation scheme• 42 Minor irrigation schemes

This study area is divided into 41 Thissin polygons based on the 41 observation wells for study.

* Maximum polygonal area - 8440 M2 (node 26) * Minimum polygonal area - 1294 M2 (node 35)

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Aquifer Characteristic

Unconfined

10 to 15 m. thick

Gravelly or decomposed material

Bottom layer of this aquifer is a rarely fractured crystalline rock having vertical Transmissibility less than one sq. meter per day.

Darcy's law (Linear resistance to laminar flow) and Dupuit's assumption (vertical flow can be neglected) are applicable

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Assumptions within polygons* Same ground elevation* Same water table elevation * Unique recharge coefficients* Unique storage coefficient* All the recharge & withdrawal occurs in the centroids of the polygon* Separate transmissibility for each nodal connectivity

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Data collection Field Data

Seasonal water levels collected from September 1997 Monthly water levels collected from April 2005

Data from yearly publications.Irrigation scheme capacity.Irrigable area.Population.Cultivation data

.Paddy

.OFC.Rainfall

*Source1. Statical hand book, Vavuniya2. District Integrated Agriculture Development and Extension program, Vavuniya 3. Central/Provincial Irrigation department rainfall ,water level and water issue reports4. Department of Agrarian Development minor tanks hand book

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Data Processing

.Connecting water levels to MSL

.Converting data obtained from publications in to polygonal seasonal data such as

* Capacity of water stored in irrigation schemes (M3)* Water issued for cultivation in irrigation schemes (M3)* Rainfall volume (M3)* Pumping from domestic wells (M3)* Pumping from agro wells (M3)* Pumping from production wells (M3)

Note : Discharging period 1st June to 31st Sept 122 days Recharging period 1st Oct to 31st May 224 days

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Model Formulation

Observation well

Typical polygon for node B

hi - peizometric head of node i hB - peizometric head at node B YiB = (JiB/LiB) - conductance factor TiB - transmissibility at mid point between node B and i JiB - length of perpendicular bisector associated with node B and i. LiB - distance between nodes i and B AB - polygonal area of node B SB - storage coefficient of node B QB - volumetric flow rate per unit area at node B. M - No of observation wells surrounding node B

∆t - time step between j and j+1

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Model Formulation

1111

1

)()( ++∆

++

=

−−=−∑ jBBB

jB

jBt

SiBiB

jB

ji

M

i

QAAhhTYhh B

iBiBjB

ji

M

i

jB TYhhQQflowSubsurface )( 11

1

1 ++

=

+ −== ∑

)(. 11 jB

jB

BBj hht

SABSTORorageChangeinst −

∆== ++

11111 +++++ −++== jdB

jirB

jifB

jisB

jBB QdQcQbQaQAowVerticalfl BBBB

Subsurface flow = Change in storage - Vertical flow

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Model Calibration

1111

1

1 )()( ++∆

++

=

+ +−−−=∑ jBBB

jB

jBt

SiBiB

jB

ji

M

i

jB QAAhhTYhhRES B

)(. 11 jB

jB

BBj hht

SABSTORorageChangeinst −

∆== ++

iBiBjB

ji

M

i

jB TYhhQQflowSubsurface )( 11

1

1 ++

=

+ −== ∑

11111 +++++ −++== jdB

jirB

jifB

jisB

jBB QdQcQbQaQAowVerticalfl BBBB

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While doing the 2nd node minimisation, if it is connected to the 1st node the corresponding TiB found from previous minimisation was used and that particular constrain was removed from the 2nd optimisation model

Where, M - No of observation well surrounding node B N - No of Seasons Calibration is done

Subject to 0.001 < SB <0.01 15 < TiB <25 0.075 <a <0.15 0.05 <b <0.1 0.05 <c <0.1 0.9 <d <1.1

Model Calibration

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Optimisation

164 variables for polygonal Recharge coefficients 41 variables for Specific yield 100 variables for Transmissibility

For the entire study area

were found by error minimisation using “MATCAD 2000”.

.

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Prediction Process

M - No of observation wells surrounding node B h i - peizometric head of node i h B - peizometric head at node B Y i B = (J i B/L i B) - conductance factor T i B - transmissibil ity at mid point between node B and i J i B - length of perpendicular bisector associated with node B and i. L i B - distance between nodes i and B A B - polygonal area of node B S B - storage coefficient of node B Q B - volumetric f low rate per unit area at node B. j -t ime

For prediction the water balance equation is re arranged to have hB

j+1 in LHS with RHS as function of hBj+1 .

By Gauss-Seidal iteration method hBj+1 is found.

[ ] BBiBiBjB

ji

M

i

jBB

jB

jB AStTYhhQAhh /.)(. 11

1

11 ∆−++= ++

=

++ ∑

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Model Validation

Comparing the predicted results with the

actual Water level an error of –0.8% to

+2.1% is observed. For a groundwater

simulation model in integrated finite

difference method an error of this

magnitude is allowable depending on the

scope of the project .

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Behavior of Aquifer with Various Operational Policies of Irrigation Schemes

Changing the operational policy of minor / medium irrigation schemes by forgoing cultivation by 25% to 35% is giving water table gain in almost all nodes except nodes 37 and 38 by 1.75 ft to 3.0 ft during discharging season (June – Sept).

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The peripheral treatment area boundary

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Behavior of Aquifer with Decrease in Transmissibility

Peripheral boundary treatment up to the reduction of permeability by 35% to 45% is giving water table raise of nodes closer to treated boundary by 1.5 ft. to 2.75 ft. during recharging season (Oct – May).

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Behavior of Aquifer with Various Operational Policies of Irrigation Schemes

with Boundary Treatment

Combining peripheral reduction in permeability by 35% to 45% and forgoing cultivation of minor / medium irrigation scheme by 45% to 55% result an average gain of water table during discharging season (June – Sept) by 3.0 to 4.75 ft excluding node37 and 38.

Summary of benefit/cost ratio greater than unity option and steps

Option Steps for each season Benefit cost ratio

Operational policy

change

Discharging season Recharging season

2 14.52 1.59

3 14.63 1.46

4 12.43 1.33

5 10.27 1.13

Boundary treatment

Year of implementation 20 25

Interest rate 7.5% 10% 7.5% 10%

3 0.73 0.97 1.15 1.66

4 0.88 1.17 1.39 2.01

5 0.83 1.10 1.30 1.88

Combination of policy

change and creation of

artificial boundary

Year of implementation 20 25 20 25

Interest rate 7.5% 10% 7.5% 10% 7.5% 10% 7.5% 10%

3 0.97 1.13 1.28 1.78 0.82 1.09 1.17 1.75

4 1.09 1.19 1.49 2.23 1.01 1.13 1.44 2.18

5 1.04 1.13 1.42 2.22 0.97 1.15 1.37 2.02

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Summery of the Research Finding

Summarizing all the three alternatives based on the operational research and economic analysis, the first alternative out of the three alternatives mentioned previously would be the most economically feasible one for immediate implementation in Vavuniya catchment without any capital investment.

“The change in operational policy of minor / medium irrigation schemes by forgoing one third of the cultivation under minor / medium irrigation schemes or keeping one fourth of the storage of minor / medium irrigation schemes at any time will recover on an average of 45% to 65% of the loss of water table in any consecutive seasons in almost 80% to 90% of the area under consideration”

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Implementation of Finding

This finding is not time bound or area specific and does not require any additional financial resource to implement, but proper knowledge based awareness is required to implement this policy in field among the stake holders. Even now the practice of alternate track cultivation in different years depending on availability of water in the irrigation shames exists. Hence this policy implementation is very easy with proper knowledge based awareness among the stake holders

Conclusion

Construction of new or reconstruction of abundant minor /medium irrigation scheme with 25% of storage exclusively for recharging groundwater and changing the operational policy to keep 25% of the present storage of existing minor /medium irrigation scheme to recharging groundwater will reduce considerably the average cost of irrigation water due to less energy cost and this in turn will increase the extent of cultivation per unit of irrigation water and led to increase productivity in Vavuniya. 26

Thank

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