Prepared by:
Greg Parry
CEE 6440
GIS in Water Resources
Fall 2008
David Tarboton
David Maidment
Ayse Irmak
1. Introduction
Because recharge is
not a process that can be observed directly, it is deduced through stream flow
measurements, groundwater level measurements coupled with groundwater
withdrawal data. Pattern Recognized by Image Processing and Segmentation
in GIS (PRO-GIS) offers a different approach to identifying recharge and
discharge zones with existing ancillary data that initiates a cross analyses of
various methods and uses pattern recognition plug-ins for ArcMap to estimate
recharge and discharge more efficiently.
Figure 1.
2. Objectives
The purpose of this
project is to explore the feasibility of the application tool PRO-GIS, for
ArcGis 9.3 to better understand the interactions among the complex and
uncertain processes within the hydrological cycle of the
3. Methodology
3.1 Pattern
Recognized by Image Processing and Segmentation in GIS (PRO-GIS)
The Pattern
Recognized by Image Processing and Segmentation in GIS (PRO-GIS) application
uses multiple image processing algorithms to estimate and visualize recharge
and discharge patterns and rate. The organization
of multiple image processing algorithms is visualized into a graphical user
interface (GUI). The visual organization provides a new approach for scientists
to analyze images and compare the images with ancillary information that has
not been quantified (Lin,2008). PRO-GIS
is a general utility that organizes several image processing algorithms into
one user interface to extract spatial patterns according to set
parameters. The image processing provides generic pattern recognition
functions that support Spatial Decision Support System, which is a computer-based
system that is interactive and designed to facilitate a user or group of users
in achieving a higher effectiveness of decision making and simultaneously
solving a semi-structured spatial problem (Sprague, 1982). It is
designed to assist the spatial planner with guidance in making land use
decisions and assist water resource
management. PRO-GIS uses three methods of image processing to create a
deterministic function to define recharge and discharge as it relates to water
features, soil type, and topography:
1. 2D
Moving Average uses ArcGIS Spatial Analyst Extension to inherit functions of
the Neighborhood ArcObjects. This block statistic calculates statistics for a
non-overlapping neighborhood, where a circular, annulus-shaped, or wedge-shaped
neighborhood is specified, depending on the size of the neighborhood, cells
that are not perpendicular to the x- or y-axis may not be considered in the
calculations. However, these cell locations will receive the resulting value
from the calculations of the neighborhood because they fall within the
minimum-bounding rectangle (or the output block) of the three circular
neighborhoods. The width and height of the moving window for averaging
computations can be specified, where a larger window results in a smoother
image, but takes longer to compute.
2. Normalization
is based on existing FORTRAN code for normal score transformation algorithms,
nscore.f, in GSLIB (Deutsch and Journal 1998). This method takes the input data
and transforms to a normal distribution and reduces the degree of asymmetry of
a distribution as it relates to the image histogram.
3. TVL1 Low Pass Filter uses the algorithm, Total Variation Regularized L1 Function Approximation (TV + L1), developed by Chan and Esedoglu (2005). TV + L1 minimizes the total variation of the image, which preserves edge capacity, simplicity with minimum signal distortion and extraction of special details (Lin 2008). TV + L1 minimizes the total variation of the image, which allows for resolution of the pattern edge integrity. With minimal signal distortion the ability to extract varying degrees of special detail is enhanced. The TV frame work uses an image f to model the sum of image pattern u (low pass signal) and texture v (high pass signal), where f, u and v are defined as functions. The pattern u contains background hues and significant boundaries, where texture v is excluded by its nature of small-scale oscillation
patterns and u
becomes minimized by being close to f
with respect to a fidelity (distance) measure (Yin et al. 2005). TV- L1 Low Pass Filter is similar
to Medical Magnetic Resonance Imaging (MRI) scan analysis.
3.2 Data
Collection
PRO-GIS only requires
data for the water table, bedrock elevations and hydraulic conductivities in
order to create a recharge and discharge map. Water level can be found on the
USGS Active Ground-Water Level Network site and bedrock elevations from the
Utah Geological Survey GIS Geologic Maps index as well as for Hydraulic
Conductivity.
Raster files for water
tables, hydraulic conductivity, and bedrock elevation data for two-dimensional
steady-state unconfined aquifer systems data were created from the data obtained
from the following online sites:
1. USGS
Active Ground-Water Level Network
http://groundwaterwatch.usgs.gov/countymaps/UT_005.html
http://pubs.er.usgs.gov/usgspubs/ds/ds302
2. USDA
Soil Survey
http://websoilsurvey.nrcs.usda.gov/app/HomePage.htm
3.
http://ugs.utah.gov/maps/gis/index.htm
Further exploration
of data sets can be explored in the appendix of this report.
A 1994 recharge map
of
Figure 2. 1994 Recharge Map of
3.3 Image Processing
It has been
determined in
The water table,
soil type and bedrock elevation will be implemented into the application
PRO-GIS and processed three times using different approaches—the 2D Moving
Average, normalization, and TVL1 Low Pass Filter.
PRO-GIS adheres to
the default raster file developed by ESRI as the standard for storing spatial
information and uses a finite difference mass balance approach for
two-dimensional steady state conditions (Lin,2007). This can be summarized
as follows:
A raster format defines how pixels are stored such as number of rows and
columns, number of bands, actual pixel values, and other raster format-specific
parameters. However, by adding raster data according to a raster type, the
ArcGIS Image Server reads the appropriate metadata and uses it to define any
processing that has to be applied (ESRI,2008).
In order for these
three raster files to work for this application, the raster files must be synchronize to the same:
·
Coordinate Projection
·
Grid Size
·
Grid Number
This is for the
cell-by-cell generation of recharge and discharge rates in the raster file,
which are automatically synchronized with input rater files.
Figure 3. Raster creation for each PRO-GIS
parameter
3.4 Hydraulic
conductivity Raster Input
Figure 4. Soil Hydraulic Conductivity Raster over 1994
3.5 Water table
Raster Input
Figure 5. Water Table Raster over 1994
3.6 Bedrock elevation
Raster Input
Figure 6. Bedrock Elevation Raster over 1994
4.
Results/Discussion
4.1
Image Processing of 2D Moving Average
The 2D Moving
Average was calculated using focal statistics, which uses FocalStatistics
ArcObject. The median statistical calculation was preformed on each of the
three inputs, which calculates the median value of the cells in the
neighborhood. The statistics performed on an input raster over a specific
neighborhood have a default shape of a rectangle around each cell that is used
in the statistical calculation (ESRI, 2008). The following equation was used to
process the x, y position within the neighborhood (upper-left corner):
X = (width of the neighborhood +1) /
2
Y = (height of the neighborhood + 1)
/ 2
If the input number
of cells is even, the x, y coordinates are computed using truncation
(ESRI,2008). The following figure illustrates that in a 5 x 5 cell neighborhood
the x and y values are 3,3. Where as, in a 4 x 4 neighborhood the x and y
values are 2,2.
Figure 7.
Neighborhood Settings for Focal Statistics (ArcGIS 9.3 Desktop Help)
Figure 8. Screen
shots of processing methods and required input
4.2
Image Processing of Normalization
The reduction of
skewness in the Normalization processing method transforms the original z-data
into y-values with a standard normal histogram. This transformation y = φ(z)
identifies the cumulative probability corresponding to the Z and Y p-quanties
(Lin,2008):
y = FY-1 (FZ(z))
with FY-1(.) being the inverse cumulative distribution function (CDF).
If Y is standard normal with CDF FY(y) = G(y), the transform G-1(FZ(.)) is the normal score transform (Lin,2008). Then the normal score transform of z (k) is the k/n quantile of the standard normal CDF, e.g.
Y(k) = G-1 (k/n)
PRO-GIS avoids the problem of a large sample size by resetting the cumulative probability of the data to the average between its cumulative probability and that of the next lowest datum (Lin, 2008).
4.3
Image Processing of TV + L1
TV + L1 Low Pass Filter (TVL1) required two parameters: Lambda and Max Iterations. Lambda (λ) is the Lagrange multiplier, where its outcome is based on the radius of the pattern required. For example a 2D image has the λ = 2/r. The second parameter is iteration and generally, a higher iteration will result in generating a more accurate result.
4.4
PRO-GIS Processed Images for 2D Moving
Average, Normalization and TVL1
Figure 9. Bedrock Elevation Raster Using PRO-GIS various process methods
Figure 10. Water Table Raster Using PRO-GIS various process methods
Figure 11. Soil Hydraulic Conductivity Raster Using PRO-GIS various process methods
4.5
Comparison of Image Processing of 2D
Moving Average with Original Raster Histogram
Figure 12. Original Histogram Figure 13. 2D Moving Average Histogram of Bedrock Elev.
Figure 14. Original Histogram Figure 15. 2D Moving Average Histogram of Water Table
Figure 16. Original
Histogram Figure 17. 2D Moving
Average Histogram of Conductivity
4.6
Comparison of Image Processing of
Normalization with Original Raster Histogram
Figure 18. Original Histogram Figure 19. Normalization of Bedrock Elev.
Figure 20. Original Histogram Figure 21. Normalization of Water Table
Figure 22. Original Histogram Figure 23. Normalization of Conductivity
4.7
Comparison of Image Processing of TV + L1
Figure 24. Original Histogram Figure 25. TVL1
Figure 26. Original Histogram Figure 27. TVL1
Figure 28. Original Histogram Figure 29. TVL1
4.8
Discussion
The approaches
demonstrated by using PRO-GIS highlight that not all image processing methods
will work in all cases. When given a variety of methods to assess water issues,
the analysis will reflect an outcome that is 1) more informative and 2) easier
to revisit when new information comes forward. Visualizing is an approach that
helps with all decisions and can be helpful in communicating a final result.
PRO-GIS helps in generating multiple patterns from data that would ordinarily
illustrate a single outcome.
4.9
Recharge and Discharge Area Maps
Groundwater recharge
and discharge area maps show the presence or absence of protective fine-grained
layers (sediments or rocks). Primary recharge areas do not have protective
fine-grained layers and vertical ground-water movement is downward; these areas
are the most vulnerable to land-surface activities. Discharge areas have
protective fine-grained layers and vertical ground-water movement is upward.
These maps can be used by land-use planners to help properly site facilities.
Figure 30. 1994 Recharge Map of
Figure 31. Soil
Hydraulic Conductivity with Lowest Conductivity Site Highlighted in Red
Figure 32. Water
Table Levels
Figure 33. Bedrock Elevation with Lowest Elevation Highlighted in Red
5. Conclusion
PRO-GIS is a
powerful utility in that it uses pattern recognition to address a solution to a
common problem in analyzing spatial data, noise reduction. By creating
alternative maps with current data that can be compared to other information in
GIS, PRO-GIS can help visualize a credible option. The ranking of subjective ancillary
data with the conceptual model of alternative recharge and discharge maps has
the potential to be used for water resource management and the integration of
development as it relates to agriculture and land use.
References
Chan, T.F. and
Esedoglu, S. 2005 Aspects of total variation regularized L1 function
approximation. Journal of Applied
Mathematics, 65: 1817-1837
Deutsch, C.V. and
Journal, A.G. 1998 GSLIB Geostatistical Software Library and User’s Guide
(Second Edition).
Lin, Yu-Feng, Wang,
Jihua, and Valocchi, Albert J. 2008 A New GIS Approach for Estimating Shallow
Groundwater Recharge and Discharge. Transactions in GIS, 12 (4); 459-474
Sanderson, I.D. and
Lowe, Mike. 2002 Ground-Water Sensitivity and Vulnerability to Pesticides,
Sprague, R. H., and E. D. Carlson (1982) Building effective
Decision Support Systems.
Stoertz, M.W. and
Bradbury K.R. 1989 Mapping recharge areas using a groundwater flow model: A
case study. Ground Water, 27; 220-228
Yin, W., Chen T., Zhou X.S., and Chakraborty, A. 2005 Background correction for cDNA microarray images using the TV- L1 model. Bioinformatics 21:2410-2416
Buto, Susan G. and Jorgensen, Brent, E. 2007 Geospatial
Database of Ground-Water Altitude and Depth-to-Ground-Water Data for
ESRI. 2008 ArcGIS 9.3 Desktop Help
Appendix
1
Pattern Recognition Organizer for GIS (PRO-GIS)
Guide
Appendix
2
Saturated
Hydraulic Conductivity (Ksat), Standard Classes-Cache Valley Area
Appendix
3
Ground-Water Sensitivity and
Vulnerability to Pesticides, Cache Valley, Cache County, Utah
Appendix
4
Geospatial
Database of Ground-Water Altitude and Depth-to-Ground-Water Data for Utah,
1971-2000