maharastra ground water data analysis - iit bombaymaharastra ground water data analysis by ravi...

Maharastra Ground Water Data Analysis

By Ravi Sagar[10305037]Guided by Prof. Milind Sohoni

October 25, 2011

By Ravi Sagar[10305037] Guided by Prof. Milind Sohoni Maharastra Ground Water Data Analysis

Outline

Variance Analysis of Groundwater Level

Improved Single Well Seasonal Model

Introduction to Spatial Models

Krigging - Spatial Interpolation Technique

Database and Geo Server Demo

Conclusion

Future Work


Variance Analysis of Groundwater Level


Variance And Its Impact on Models

Variance: Measure of how far the values are spread out fromexpected value(or mean)

It gives the variation of water level over the period

Difficult to model the behavior of wells with high variance

Reasons behind Variance

NoiseGeological PropertiesRainfall

Models should be developed considering causes of variance


Low variance and High variance observation wells

Figure: Well with high variance


Low variance and High variance observation wells

Figure: Well with low variance


Variance of Current Model

Mean varies depending on time for our data

Assuming time constant variance:

σ = {∑n

i=1 (yi−µi )2

n } 12

Table: Top 5 Bore wells with high variance

Well name Variance Depth(m)

Mandawa 12.561928 30Tokavde 10.591332 24Safale 4.466477 25.9Kudan 4.302190 30Sakharshet chalatwad 3.640198 22.5


Variance of Current Model

Table: Top 5 Dug wells with high variance

Well name Variance Depth(m)

Washind 1 6.396629 7Talasari 5.252879 7Mangrul 3.221694 7.6Satiwali 3.102799 7.2Dahisar 3.084735 9.5


Time Line Graph

Figure: Behavior of Mandawa Bore Well over the period


Time Line Graph

Figure: Behavioor of Washind1 DugWell over the period


Variance Vs Discrepancy

Is variance affected by discrepancy

Discrepancy is compared with normalized variance

Normalized Variance = Variance / Depth of the well

We are intended to extend the use of variance to R2 model (that isdividing the error value with variance)

Table: Variance Vs Discrepancy for Bore Well

Village Normalized variance Depth(m) Discrepancy countTokavde 0.135601 24.000 1

Mandawa 0.118143 30.000 2Gokhiware 0.090139 18.000 4

Satiwali 0.033998 18.000 23Bhatsai 0.050426 18.000 17


Variance Vs Discrepancy

Table: Variance Vs Discrepancy for Dug Well

Village Normalized variance Depth(m) Discrepancy countWashind 1 0.361308 7.000 7

Talasari 0.286490 8.000 5Satiwali 0.244649 7.200 15Dapode 0.208616 5.250 7Titwala 0.150577 7.000 10

Unable to infer the relationship with above results.


How to know the Causes of variance

Need to classify the years that are below the model and above themodel

Comparing the variance value with Rainfall and Geological data

This will be done after getting the data from GSDA

Field visits to know human interference and some other noise.

Figure: Observation well


Extension to Single Well Seasonal Models


Drawbacks in Periodic Model

Periodic models generaly smoother than what actual behavior seemsto be.

Unusual raise of model before monsoon starts

Discontinuity of groundwater data

- i.e sudden raise of water level in the month of June

Need a new model to solve this problems


Drawbacks in Periodic Model

Figure: Periodic model of Mandawa bore well


Reason behind rapid raise of water level

AGRAR case study of Kolwan valley,Pune,Maharashtra byACWADAMAim is to study

Physical dynamics of rechargeEffect of artificial recharge

Chikhalgaon Water shed with shallow aquifer(20m)

8 Dug wells, 8 Bore wells

Found the interesting results

Dug wells and shallow bore wells (both tap the shallow aquifer) haverapid recharge in the beginning of monsoonBore wells that tap deeper aquifer have consistently slow recharge.


Results of AGRAR Case Study

Figure: Taken from AGRAR report


Need for Polynomial Model

To solve the problems in previous model

Monotonically increasing behavior of groundwater Data

Starts with zero level in monsoonEnds with any value between zero to depth of the well at the end ofmonsoon.

Can be best represented with polynomial functions


Polynomial Model

Generalized function used to fit the datay = akx

k + ak−1xk−1 + · · ·+ a1x + a0 for K=3,4,5.

Figure: Polynomial model of Gokhiware bore well


Variance of Polynomial Model

Computed the variance polynomial model

Table: Variance Vs Discrepancy for Dug Well

Village Site Type Normalized variance Depth(m)

Awale Dug Well 0.760082 7.35Kajali Dug Well 0.724898 14Kogde Dug Well 0.695927 7

Kalamdevi Dug Well 0.690580 5.5Mandawa Bore Well 0.597985 30Tokavde Bore Well 0.372142 24


Regional Models


Need of Regional Models

Scope of single well seasonal model is limited to well

How to know the behavior of ground water level at any arbitrarypoint

How to predict the behavior of entire region

Can be done using the regional models

Regional model divides the space in to sub regions where eachregion has its own behavior model

similar to spatial models


Spatial Model

Divides spatial area in to grids or polygons depending up onparticular property value.

Voronoi Diagrams: Decomposes the given space in to voronoiregions depending on distance to voronoi sites.


Spatial Interpolation Techniques

Process of estimating the values at unsampled sites with in areacovered by sampled points.

Need spatial interpolation techniques in regional modeling

To estimate the groundwater value at intermediate locationsTo decide the region of a particular point.

Some spatial interpolation techniques

ProximalB-splinesKrigging


Krigging - Spatial Interpolation


Krigging Interpolation


Stationary model.

E [Z(xi )] = µ i = 1, 2, ..nR(‖x − x p‖) = R(h) = E [(Z(x)− µ)(Z(x p)− µ)], where ‖x − x p‖ isthe distance between x , x p

Given n measurements of Z , at different locations x1, x2, ...xn,Estimated value of Z at x0 is

Z0 =∑n

i=1 λiZ (xi )

Estimation error

Z0 − Z (x0) = (∑n

i=1 λiZ (xi ))− Z (x0)



Requirements for good estimator.

Unbiasedness:

E [Z0 − Z (x0)] =∑n

i=1 λiµ− µ = (∑n

i=1 λi − 1)µ = 0∑ni=1 λi = 1

Minimum Variance:

E [(Z0 − Z (x0))2] = −∑n

i

∑nj λiλjγ(‖xi − xj‖) + 2

∑ni λiγ(‖xi − x0‖)

γ(‖x − x p‖) = 12E [(Z (x)− Z (x p))2]



Lagrange multiplier system: Ax = b

−∑n

j=1 λjγ(‖xi − xj‖) + v = −γ(‖xi − x0‖)i = 1, 2, ..n∑nj=1 λj = 1

A =

0 −γ(‖x1 − x2‖) · · · −γ(‖x1 − xn‖) 1

−γ(‖x2 − x1‖) 0 · · · −γ(‖x2 − xn‖) 1...

......

...−γ(‖xn − x1‖) −γ(‖xn − x2‖) · · · 0 1

1 1 · · · 1 0

x =

λ1λ2...λn1

b =

−γ(‖x1 − x0‖)−γ(‖x2 − x0‖)

...−γ(‖xn − x0‖)

1


Issues in Krigging Interpolation

consider 1-D function with γ(h) = 1 + h for h >0.x1 = 0, x2 = 1, x3 = 3 and x0 =?

0 −2 −4 1−2 0 −3 1−4 −3 0 11 1 1 0

λ1λ2λ3v

=

−3−2−21

λ1 = 0.1304, λ2 = 0.3913λ3 = 0.4783 and v = −0.304

Key assumption: correlation is function of distancewhich is not true in the case of groundwater

We can use the soil property to apply krigging interpolation


Example of Krigging Interpolation

Altitude contour map generated using krigging interpolation.


Spatial Correlation Between Rainfall Data

22.5 5 5 3 4 5 5 4 521.5 5 2 3 4 4 4 5 520.5 5 0 3 3 3 4 4 419.5 4 1 3 3 3 3 3 318.5 4 0 0 0 2 2 3 217.5 0 0 1 0 0 1 1 416.5 0 0 1 1 0 1 1 115.5 R 0 0 0 1 1 1 1

LatitudeLongitude 73.5 74.5 75.5 76.5 77.5 78.5 79.5 80.5



22.5 2 1 1 1 1 0 0 521.5 2 1 1 1 0 0 0 020.5 1 1 1 0 0 0 0 019.5 1 1 0 0 R 0 0 -118.5 1 0 0 0 0 0 0 -117.5 0 0 1 0 0 0 -1 -116.5 0 1 0 -1 -1 -1 -1 -115.5 -3 -2 -2 -2 -2 -4 -1 -1




22.5 2 1 1 1 1 0 0 R21.5 2 1 1 1 0 0 0 020.5 2 -5 -5 0 0 0 0 019.5 -4 -5 -5 -5 -5 0 -1 -118.5 -5 -5 -5 -5 -5 -5 -1 -117.5 -4 -5 -5 -5 -5 -5 -5 -516.5 -5 -5 -5 -5 -5 -5 -5 -315.5 -5 0 -3 -5 -5 5 -3 -3



Database and Geo server demo

Back end databases

PostgresPost Gis

Geo Server to show and manipulate the spatial maps

Will update the MRSAC data sooner


Conclusion

Basic data cleaning

Discrepancy analysis

Single well seasonal models With groundwater level as main input

Variance analysis

Initial study on regional models


Future Work

Survey of national and international experience

Understanding data analysis models of different states

Dry well modeling and its validation

Extensive modeling using geological and physical parameters (morethan numeric parameters)

Integrating the spatial models with GIS

Groundwater data analysis for a different district

District level water budget

Developing a regime for groundwater monitoring


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