Maharastra Ground Water Data Analysis

Transcription

1 By Ravi Sagar[ ] Guided by Prof. Milind Sohoni October 25, 2011

2 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

3 Variance Analysis of Groundwater Level

4 Variance And Its Impact on Models Variance: Measure of how far the values are spread out from expected 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 Noise Geological Properties Rainfall Models should be developed considering causes of variance

5 Low variance and High variance observation wells Figure: Well with high variance

6 Low variance and High variance observation wells Figure: Well with low variance

7 Variance of Current Model Mean varies depending on time for our data Assuming time constant variance: n i=1 σ = { (y i µ i ) 2 n } 1 2 Table: Top 5 Bore wells with high variance Well name Variance Depth(m) Mandawa Tokavde Safale Kudan Sakharshet chalatwad

8 Variance of Current Model Table: Top 5 Dug wells with high variance Well name Variance Depth(m) Washind Talasari Mangrul Satiwali Dahisar

9 Time Line Graph Figure: Behavior of Mandawa Bore Well over the period

10 Time Line Graph Figure: Behavioor of Washind1 DugWell over the period

11 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 R 2 model (that is dividing the error value with variance) Table: Variance Vs Discrepancy for Bore Well Village Normalized variance Depth(m) Discrepancy count Tokavde Mandawa Gokhiware Satiwali Bhatsai

12 Variance Vs Discrepancy Table: Variance Vs Discrepancy for Dug Well Village Normalized variance Depth(m) Discrepancy count Washind Talasari Satiwali Dapode Titwala Unable to infer the relationship with above results.

13 How to know the Causes of variance Need to classify the years that are below the model and above the model 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

14 Extension to Single Well Seasonal Models

15 Drawbacks in Periodic Model Periodic models generaly smoother than what actual behavior seems to 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

16 Drawbacks in Periodic Model Figure: Periodic model of Mandawa bore well

17 Reason behind rapid raise of water level AGRAR case study of Kolwan valley,pune,maharashtra by ACWADAM Aim is to study Physical dynamics of recharge Effect 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) have rapid recharge in the beginning of monsoon Bore wells that tap deeper aquifer have consistently slow recharge.

18 Results of AGRAR Case Study Figure: Taken from AGRAR report

19 Results of AGRAR Case Study Figure: Taken from AGRAR report

20 Need for Polynomial Model To solve the problems in previous model Monotonically increasing behavior of groundwater Data Starts with zero level in monsoon Ends with any value between zero to depth of the well at the end of monsoon. Can be best represented with polynomial functions

21 Polynomial Model Generalized function used to fit the data y = a k x k + a k 1 x k a 1 x + a 0 for K=3,4,5. Figure: Polynomial model of Gokhiware bore well

22 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 Kajali Dug Well Kogde Dug Well Kalamdevi Dug Well Mandawa Bore Well Tokavde Bore Well

23 Regional Models

24 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 arbitrary point 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 each region has its own behavior model similar to spatial models

25 Spatial Model Divides spatial area in to grids or polygons depending up on particular property value. Voronoi Diagrams: Decomposes the given space in to voronoi regions depending on distance to voronoi sites.

26 Spatial Interpolation Techniques Process of estimating the values at unsampled sites with in area covered by sampled points. Need spatial interpolation techniques in regional modeling To estimate the groundwater value at intermediate locations To decide the region of a particular point. Some spatial interpolation techniques Proximal B-splines Krigging

27 Krigging - Spatial Interpolation

28 Krigging Interpolation Krigging Interpolation Stationary model. E[Z(x i )] = µ i = 1, 2,..n R( x x ) = R(h) = E[(Z(x) µ)(z(x ) µ)], where x x is the distance between x, x Given n measurements of Z, at different locations x 1, x 2,...x n, Estimated value of Z at x 0 is Estimation error Ẑ 0 = n i=1 λ iz(x i ) Ẑ 0 Z(x 0 ) = ( n i=1 λ iz(x i )) Z(x 0 )

29 Krigging Interpolation Requirements for good estimator. Unbiasedness: E[Ẑ 0 Z(x 0 )] = n i=1 λ iµ µ = ( n i=1 λ i 1)µ = 0 n i=1 λ i = 1 Minimum Variance: E[(Ẑ 0 Z(x 0 )) 2 ] = n n i j λ i λ j γ( x i x j ) + 2 n i λ i γ( x i x 0 ) γ( x x ) = 1 2 E[(Ẑ(x) Z(x )) 2 ]

30 Krigging Interpolation Lagrange multiplier system: Ax = b n j=1 λ jγ( x i x j ) + v = γ( x i x 0 )i = 1, 2,..n n j=1 λ j = 1 0 γ( x 1 x 2 ) γ( x 1 x n ) 1 γ( x 2 x 1 ) 0 γ( x 2 x n ) 1 A =.... γ( x n x 1 ) γ( x n x 2 ) λ 1 γ( x 1 x 0 ) λ 2 γ( x 2 x 0 ) x =.. b =. λ n γ( x n x 0 ) 1 1

31 Issues in Krigging Interpolation consider 1-D function with γ(h) = 1 + h for h >0. x 1 = 0, x 2 = 1, x 3 = 3 and x 0 =? λ λ λ 3 = v 1 λ 1 = , λ 2 = λ 3 = and v = Key assumption: correlation is function of distance which is not true in the case of groundwater We can use the soil property to apply krigging interpolation

32 Example of Krigging Interpolation Altitude contour map generated using krigging interpolation.

33 Spatial Correlation Between Rainfall Data R Latitude Longitude

34 Spatial Correlation Between Rainfall Data R Latitude Longitude

35 Spatial Correlation Between Rainfall Data R Latitude Longitude

36 Database and Geo server demo Back end databases Postgres Post Gis Geo Server to show and manipulate the spatial maps Will update the MRSAC data sooner

37 Conclusion Basic data cleaning Discrepancy analysis Single well seasonal models With groundwater level as main input Variance analysis Initial study on regional models

38 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 (more than 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