Representing a River Network with Graph Theory

1
Representing a River Network with Graph Theory

• Class Project
• CS 8715-Spatial Databases
• Instructor-Shashi Shekhar
• Group - G6
• David Moretz Chandana Gangodagamage

2
Problem Statement 1 of 2

• Input Geospatial data for the South Fork Eel
  River in northern California, including X,Y
  coordinates for nodes and edges that represent
  river
• Output Directed spatial network stored in
  PostGres and PostGIS and visualized via MapServer
  
• Objective Implement a graph theoretic model for
  the river network and then develop SQL queries
  that would process the following information
• Calculate total length of river at each node
• Determine maximum path of river
• Find elevation along flow direction of maximum
  path
• Find total contributing area for maximum path

3
Problem Statement 2 of 2

• Constraints
• River network analysis conducted by using PostGIS
  as spatial database instead of using a more
  powerful GIS package
• Queries and analysis conducted through SQL
  instead of creating complex calculations by using
  a more powerful programming language such as
  Python or PHP
• Data file was a simplified version of the actual
  river network
• Mapserver was used for visualization of results

4
Related Work

• Various approaches have been proposed before, but
  those approaches have been based around the use
  of the ArcGIS/ArcInfo environment
• Davis, Kimberley, et al. 2000. Definition of the
  Arc Hydrology Data Model.University of Texas at
  Austin ed. Vol. 1. Austin, Texas GIS in Water
  Resources Converence.

5
Motivation

• Develop a directed spatial network using PostGIS
  to implement graph theory directly into PostGIS
  by using SQL
• Visualize the results via Mapserver so that the
  data can be widely accessed and distributed over
  the Internet

6
Major Contributions

• Describe how river network data created in ArcGIS
  can be converted from a shapefile and then
  inserted into a PostGIS database
• Apply a graph theoretic framework to the river
  network so that it is possible to perform various
  SQL queries to calculate river network
  connectivity and network attributes
• Implement Mapserver to visualize the results

7
Key Concepts

• Model a river network in a PostGIS environment
• Create a spatial database and load data into
  Postgres Database
• Develop algorithm for river network analysis
• Develop algorithm to create paths from nodes

8
Model River Network

• Input data was shape file created from 1M LIDAR
  Digital Elevation Model
• Simplified river network using the Douglas Pecker
  polyline simplification algorithm
• Generated multiple attributes for each link
• Elevation
• Cumulative contributing area
• Original river length
• Slope of river reach
• Source node
• Destination node
• Path

9
Create Database / Load Data

• Create database within PostGIS system
• Convert shapefile to SQL using shape2sql
• Load SQL file into database

Figure1 Visualization of GIS database for
PostGIS system created from 1M LIDAR DEM.
10
River network analysis algorithm

• Algorithm for nodes

Identify all source points and make a 1D array S,
where S(1) source point 1 Define an array for
path 1 as, P1 Start with source points 1 FOR
i1L where L is the number of source point in
the network S1S(i) P1(i)S1 then select
A,1 find A,1S(i) return index j that tells
the location of S(i) in column 1 then select
Aj,2 P2(i1)AJ,2 END
11
River network analysis algorithm

• Results of the algorithm

12
Validation Methodology

• Combination of theory, experiment, prototype, and
  case study
• Validation criteria
• Theoretical and Empirical equations developed by
  Leopold and Maddock

13
Alternative Solutions

• Expand functionality of traditional GIS software
  package such as ArcGIS or EMS-Is River Tools by
  using VBA scripts
• Implement graph theory in another Spatial DBMS
  such as Oracle Spatial or ArcSDE
• Use programming languages such as Python or PHP
  to develop more complex calculations

14
Conclusions and Future Work

• It is possible to represent a simplified directed
  river network in PostGIS by using graph theory
• Work with more complex network data
• Develop more complex algorithm to conduct more
  complicated analysis
• Utilize MapServer to actually conduct analysis
  instead of just display